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http://dimacs.rutgers.edu/Events/2006/mix2-abstracts.html

## DIMACS Mixer Series, November 10, 2006 Abstracts: Bing Bai, Rutgers student Title: fMRI Brain Image Retrieval Based on ICA Components We proposes a content-based retrieval system for fMRI brain images, to find a similarity metric that supports queries for retrieval of similar tasks'' in a large collection of brain experiments. The system uses a novel similarity measure between the results of Probabilistic Independent Component Analysis (PICA) of the brain images. Specifically, the time series of an fMRI dataset will be represented using a number of ICA components that are associated with low frequency time courses, as high level task-related features. The most effective similarity between two datasets is the value of the Maximum Weight Bipartite matching (MWB) defined on the component-wise similarities. The component-wise similarities are calculated based on the size of the overlap between the highly activated'' regions in the corresponding activation maps. We have evaluated the performance of the proposed method on a moderate size fMRI database with considerable variety. The low-frequency component selection, in combination with the bipartite matching similarity measure, outperforms several other component selection methods and similarity measures. Nikhil Bansal Title: Round and Approx: A new general technique for multidimensional packing problems I will describe a new general framework for set covering problems, based on the combination of randomized rounding of the Linear Programming relaxation, leading to a partial integral solution, and the application of a certain well-behaved approximation algorithm to complete this solution. Applying this framework, I will describe a 1.525 approximation the 2-dimensional bin packing problem, and a \ln d +1 approxmation for the d-dimensional vector packing problem, improving upon the previous guarantees of 1.69 and O(\ln d) respectively. Joint work with Alberto Caprara and Maxim Sviridenko. Aranyak Mehta, IBM Almaden Research Center Title: Design is as Easy as Optimization Over the last four decades, theoreticians have identified and studied several fundamental genres of algorithmic problems. These include decision, search, optimization, counting, enumeration, random generation, and approximate counting problems. We identify a new genre of algorithmic problems -- design problems. Every optimization problem leads to a natural design problem. For instance, the minimum spanning tree problem leads to: given an undirected graph $G = (V,E)$ and a bound $B$, find a way of distributing weight $B$ on the edges of $G$ so that the weight of the minimum spanning tree is maximized. Practitioners have always been faced with design problems and such problems have been studied individually by theoreticians as well. However, this genre has not been subjected to a systematic complexity-theoretic study before. Using techniques of Freund-Schapire and its follow-up works in learning theory, we show that for a large class of problems, the design version is as easy as the optimization version in the following sense: given an oracle (exact or approximation) for the optimization version, the design version can be solved (exactly or with the same approximation factor) in polynomial time. Joint work with Deeparnab Chakrabarty and Vijay V. Vazirani. Paper available at: http://www-static.cc.gatech.edu/~aranyak/design-fullversion.pdf Konstantin Mischaikow Title: Building a data base for the global dynamics of multi-parameter systems It is well accepted that nonlinear dynamical systems can exhibit a wide variety of complex dynamics that may be sensitive to changes in parameters. It is also quite common in applications that not all values of the parameters have been determined. We outline a proposed method for building a data base that can be queried to determine parameter values at which particular types of dynamical structures can be found or values at which specific types of bifurcations occur. The fundamental idea is to use topological methods that are computationally efficient to store essential features of the dynamics in terms of a directed graph with equivalence classes of homology maps at the nodes. The directed graph represents information about the existence of a global Lyapunov function and the homology maps at the nodes encode information about the recurrent dynamics. We explain these ideas in the context of a density dependent Leslie model arising from population biology. This is based on ongoing work with W. Kalies and P. Pilarczyk. Chung-chieh Shan, Rutgers University Title: Linguistic side effects How does the meaning of an utterance determine its effects on the discourse and its participants? I study this question using tools from programming-language theory. In particular, how do utterances interact with each other in context? For example, pronouns in natural languages and variable references in programming languages both retrieve values from the context. In general, "computational side effects" in programming languages and "apparently noncompositional phenomena" in natural languages both let expressions access their contexts. This link stresses the dynamic, "operational" view on meaning. Alexander Soifer, Princeton University, DIMACS, Rutgers University & University of Colorado Title: The Erdoes 1932 Conjecture on Squares in a Square & Trains of Thought It Has Inspired Dedicated to Paul Erdoes on the 10th Anniversary of His Passing on In 1932 Paul Erdoes looked at the maximal sum f(n) of side lengths of n squares packed in a unit square. He conjectured (\$50) that f(k2+1) =f(k2). While the conjecture, surprisingly, is still alive, it has inspired a good number of problems and results about packing and covering of squares, triangles, and more generally convex figures. We will look at some of them on November 10, 2006 @ Princeton.

2017-10-23 07:51:07

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https://tmoer.github.io/Blog/

# The Inverse Relation Between Prior Information And Intelligent Behaviour ##### Intelligence As Plus And Minus I decided to write a blog post on the inverse relation between how much we as humans try to design our system, and how intelligent it will eventually behave. The peculiar thing about (re-)building articificial intelligence (AI) is that the harder we try to put in our own knowledge, the less intelligent and adaptive it will behave. This appears as a paradox, but I would argue it happens because we as humans are not aware of our own operational kwowledge. You may object to this at first, as you think you have a pretty solid idea of what you’re doing. For example, if I show you a picture and ask you whether there is a chair in there, you won’t be challenged much. However, if I ask you what really caused this to be a chair, it already becomes harder. And if I just give you the raw zeros and ones of the picture (which is basically what your eye gets, and definitely what a robot camera gets), you will have a very hard time. How do all these activations add up to chair or no chair. As a second example, I could ask you to pick up a bottle in front of you. Piece of cake right. However, now I ask you which forces (or motor voltages in a robot) you put on each of your muscles at each timestep in this sequence. Highly non-trivial anymore. The bottom line here is: we can do things, but we really don’t really understand our operational knowledge at all. Symbolic AI So how is this reflected in the history of AI? Initial AI research was mostly symbolic, in a sense that researchers tried to understand the human mind and then attempted to rebuild it. As you might figure from the above, this only worked well up to a certain level of complexity. The research questions of symbolic AI get much closer to cognitive psychology these days. Their focus is on actually understanding what intelligence is, and only then built it. Supervised Learning However, there were obvious tasks that could not be solved in this way, such as ‘recognizing the chair in a picture’ (as described above, a typical computer vision problem). The solution to this challenge turned out to be machine learning, in particular supervised machine learning. In machine learning, we try to learn the intelligent behaviour from data. For supervised learning, we require a dataset of examples $X$, for example pictures, and associated labels $Y$, for example chair or no chair. We then specify a model connecting $X$ to $Y$, and run an optimization to estimate the parameters of this model. It’s like a (logistic) regression analysis with large data. The key benefit is that after training, the model (for example a deep neural network) is able to predict whether a new picture will contain a chair or not. We don’t really understand how the large network managed to do this (much like we don’t understand how our own visual cortex does this). There is way to many interactions happening for us to grasp, but: it works. Reinforcement learning Much of the success in machine learning is due to supervised learning, but it will not be enough to build true artificial intelligence. The problem is the requirement for the correct labels (supervision). Due to the internet, we managed to get larger datasets of annotated pictures or translated speech, because these are tasks for which we can at least generate the label (although we don’t understand the inner workings). However, things become much harder when we actually want to act in the world. For example, if you would want to learn how to grasp a bottle from supervised learning, you would need to provide the labels as to which motor voltage to apply at each timepoint. But you really don’t know those labels. This is where reinforcement learning (RL) comes in. In RL, we rather specify a (sparse) reward/goal function, and let the system figure out the solution itself. Notice what we’re effectively doing here: again, we remove part of the human prior (we remove the labels), and provide even less information (only the goal). However, these systems manage to find solutions where supervised learning fails. Evolution and optimization I would argue that reinforcement learning is based on two principles. The first is the principle of ‘plus and minus’. I would like to assume as little as possible about what is important in our world, but the one thing I would be certain about is that there exist something as plus (do this more) and minus (do this less). The second principle of RL is association: we try to remember where we experience plus and minus, so that we can act better next time. After that, I think intelligence can be seen as optimizing the plusses. Now a large part of our intelligence is already there at birth. Your brain is already highly initialized, which is a product of millions of years of evolutionary optimization (computation). Evolution is the mother of plus and minus, without the association or memory. Evolution does not remember which particular mutations it already tried, and what it should and should not do anymore. It simply moves forward with the stuff that works well (plus). And there we are. Although we are a local optimum, I would argue that everything we are can be reduced to the optimization of one concept: whether our children get children. This must be the ultimately sparse reward function of the universe, as it is the only thing that could cause you to be here. Learning to Learn Now, if intelligence is really about black-box optimizing against a super sparse reward function, why haven’t we done so yet. Well, the problem is that the search space (or the exploration) problem is still much to large, and the computational time too high. We are getting closer to solving the supervised learning problem, and starting to get somewhere on the next step of reinforcement learning. However, in current RL research, we are still manually designing reward functions per domain, and still specifying the parametric structure of our model. Although this is inevitable on the way forward, I think it is still too much prior information. We need to go one step higher, which is an emerging machine learning topic known as ‘learning to learn’. In traditional machine learning, we first specify a model (ourselves), which we then optimize against some criterion. However, this dichotomy forces us to put prior information in the model specification, which we should avoid altogether (once again, we don’t understand how we work). In learning to learn, we try to optimize a system that is able to learn a model and optimize it, together. Then, you are only left with defining the plus, and the rest is optimization. This is what evolution did for us. Written on January 11, 2017

2021-06-23 16:58:36

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https://brilliant.org/problems/hexagon-4/

# Hexagon! Geometry Level 3 A hexagon with consecutive sides of lengths 2,2,7,7,11 and 11 is inscribed in a circle. Find the radius of the circle. × Problem Loading... Note Loading... Set Loading...

2017-09-20 14:57:39

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http://mathoverflow.net/revisions/87026/list

2 fix spacing Here is the text of Exercise: 2 a) Let $X$ be an ordered set. Show that the set of intervals $[x, \left[x, \rightarrow[$ rightarrow\right[$(resp.$]\leftarrow, x]$\left]\leftarrow, x\right]$) is a base of topology on X; $X$; this topology is called the right (resp. left) topology of $X$. In the right topology, any intersection of open sets is an open set, and the closure of {$x$} $\{x\}$ is the interval $]\leftarrow, x\left]\leftarrow, x\right]$. The above one was from English edition. I translated French edition and found the same text. Should not be $X$ a totally ordered set ? And is not that the set of intervals should be $]x, \left]x, \rightarrow[$ rightarrow\right[$in place of$[x, \left[x, \rightarrow[$rightarrow\right[$ ? Is this an errata ? 1 # Possible errata in Nicolas Bourbaki's General Topology -I, Chapter 1 Exercise 2 ? Here is the text of Exercise: 2 a) Let $X$ be an ordered set. Show that the set of intervals $[x, \rightarrow[$ (resp. $]\leftarrow, x]$) is a base of topology on X; this topology is called the right(resp. left) topology of $X$. In the right topology, any intersection of open sets is an open set, and the closure of {$x$} is the interval $]\leftarrow, x]$. The above one was from English edition. I translated French edition and found the same text. Should not be $X$ a totally ordered set ? And is not that the set of intervals should be $]x, \rightarrow[$ in place of $[x, \rightarrow[$ ? Is this an errata ?

2013-06-18 07:55:35

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https://stats.stackexchange.com/questions/314553/uncertainties-in-frequencies?noredirect=1

# Uncertainties in frequencies Suppose we have some radioactive process and suppose we want to measure how many particles are emitted by the radioactive material in a given time (say $t=10 \text{s}$). Suppose we did $N=150$ measurements and got the following results: where "Value" ($n$) represents the amount of particles hitting the detector in $t=10 \text{s}$. Since we have the frequency ($f(n)$) for each value, we can calculate the "probability": $P=f(n)/N$. Now since we suspect that this distribution is Poisson, we would like to search for the optimal $\lambda$ such that: $$P=\frac{\lambda^n}{n!}e^{-\lambda}$$ Now, the Chi-squared test (minimizing chi-squared) requires us to know the uncertainties in our variables. In many texts there's a reasonable assumption that the uncertainty in $n$ should be equal to the standard deviation of $\text{unif}(0,1)$, that is $\Delta n=1/\sqrt{12}$. However I have no idea what should be the uncertainty of the value $P$. Obviously, we must have $\Delta P=(\Delta f(n)) / N$. But what should be the uncertainty of the frequency? (I don't think that it should depend on the precision of the detector). • There seems to be some confusion expressed in this question: the chi-squared test does not minimize a chi-square statistic. It merely computes it and compares it to quantiles of a suitable chi-square distribution. The "reasonable assumption" about the uncertainties makes no sense in this context. The characterization of an optimal $\lambda$ makes little sense, either, because it corresponds to an infinite set of simultaneous equalities for $n=0,1,2,\ldots$. Could you clarify what you mean by "uncertainty of the frequency"? What frequency, specifically? – whuber Nov 19 '17 at 17:28 • @whuber In our physics lab we learned the following: suppose we got N measurements: $(x_1,y_1),(x_2,y_2),...,(x_N,y_N)$ and suppose each measurement has some uncertainty $\sigma_i$. Now suppose we have some model (function) $f(\vec{a};x_i)$ that we believe describes the data the best. Then we would like to find parameters $\vec{a}$ that minimize $\chi^2=\sum_{i=1}^{N}\left(\frac{y_i-f(\vec{a};x_i)}{\sigma_i}\right)^2$. I believe this answer describes a similar procedure. Nov 19 '17 at 18:01 • @whuber - back to the question "what is uncertainty of the frequency"? In the described experiment we would like to verify that the set of points $(n,f(n)/N)$ can be described by a Poisson distribution. But in order to determine $\sigma_i$ we must know the uncertainties in the measured value $n$ and in the value of $f(n)/N$ (which is the relative frequency). "Frequency" here means the number of times we got a specific value of $n$ in this experiment. For example, if we got the value $n=44$ twelve times then $f(n=44)=12$ and the relative frequency is $f(n)/N=12/150$ (here $N=150$) Nov 19 '17 at 18:07 • Your description is rather complex and unnatural. Aren't you just trying to estimate the parameter of a Poisson distribution that might describe these data? Least squares, which is what you seem to mean by "chi-squared," isn't even applicable here. – whuber Nov 19 '17 at 22:24 • @whuber - as I understand it - yes - we want to estimate the parameter of a Poisson distribution. We learned that such process of estimation must maximize the likelihood $L$. But since the likelihood satisfies the relation $\ln L = \text{const} - \frac{1}{2} \chi^2$ it's equivalent to minimizing $\chi^2$. Sorry if I sound confused (that's how poorly physicists are taught statistics). Nov 20 '17 at 11:16

2021-10-17 19:01:38

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https://www.gabormelli.com/RKB/Integral_Approximation_Task

A Integral Approximation Task is a numerical approximation task that requires the production of an approximate function to a function's integral. ## References ### 2015 • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/numerical_integration Retrieved:2015-6-24. • In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals. Numerical integration over more than one dimension is sometimes incorrectly described as cubature, since the meaning of quadrature is understood for higher-dimensional integration as well. The basic problem in numerical integration is to compute an approximate solution to a definite integral : $\int_a^b\! f(x)\, dx$ to a given degree of accuracy. If f(x) is a smooth function integrated over a small number of dimensions, and the domain of integration is bounded, there are many methods for approximating the integral to the desired precision. ### 2014 • (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Numerical_integration#Reasons_for_numerical_integration Retrieved:2014-4-26. • There are several reasons for carrying out numerical integration. The integrand f(x) may be known only at certain points, such as obtained by sampling. Some embedded systems and other computer applications may need numerical integration for this reason. A formula for the integrand may be known, but it may be difficult or impossible to find an antiderivative that is an elementary function. An example of such an integrand is f(x) = exp(−x2), the antiderivative of which (the error function, times a constant) cannot be written in elementary form. It may be possible to find an antiderivative symbolically, but it may be easier to compute a numerical approximation than to compute the antiderivative. That may be the case if the antiderivative is given as an infinite series or product, or if its evaluation requires a special function that is not available.

2022-11-28 19:20:28

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https://www.ajpmonline.org/article/S0749-3797(02)00476-2/fulltext

Article| Volume 23, ISSUE 2, SUPPLEMENT 1, 74-79, August 01, 2002 # The association between urban form and physical activity in U.S. adults ## Abstract Background: Physical inactivity is associated with multiple adverse health outcomes. Results from the transportation literature suggest that aspects of the urban environment may influence walking for transportation. In this paper we examine the association between a proxy measure of the urban environment and walking behavior. Methods: We analyzed the association between home age and walking behavior in U.S. adults using data from the Third National Health and Nutrition Examination Survey. Logistic regression was used to estimate odds ratios and 95% confidence intervals and to control for the effects of gender, race/ethnicity, age, education level, household income, and activity limitations. Results: Adults who lived in homes built before 1946 and from 1946 to 1973 were significantly more likely to walk 1+ miles ≥20 times per month than those who lived in homes built after 1973. This association was present among people living in urban and suburban counties, but absent among those living in rural counties. The association was also found in models that controlled for gender, race/ethnicity, age, education, income, and any health-related activity limitation. Other forms of leisure-time physical activity were not independently associated with home age. Conclusions: These results support the hypothesis that environmental variables influence walking frequency and suggest that home age may be a useful proxy for features of the urban environment that influence physical activity in the form of walking. Such proxy measures could facilitate testing ecologic models of health behavior using survey data. ## Introduction Ecologic models of behavior suggest that factors at a variety of levels, from the individual to the community, influence the prevalence of health-related behaviors. • Moos R.H The ecologic approach has been widely discussed in the context of physical activity behavior because of the obvious dependence of physical activity on both individual propensity to be active and environmental features that facilitate physical activity. • Sherwood N.E • Jeffery R.W The behavioral determinants of exercise implications for physical activity interventions. Examples of such features include sidewalks or paths, safe and desirable destinations for walking and cycling, recreational facilities, and a suitable climate. Health promotion initiatives have already adopted an ecologic model, particularly in the area of physical activity. • Sallis J.F • Owen N Ecological models. For example, the Centers for Disease Control and Prevention Centers for Disease Control and Prevention. Active community environments. 2002. Available at: www.cdc.gov/nccdphp/dnpa/aces.htm. Accessed June 1, 2002. has been promoting the “Active Community Environments Initiative” to enhance activity by modifying the physical environment, but more research is needed to refine our assumptions about ecologic models. • Sallis J.F • Owen N Ecological models. There is an extensive literature in the transportation research community concerning environmental effects on walking, cycling, and motorized transport use. These studies conceptualize the environment as “urban form” and have focused on transportation systems, such as transit availability and street characteristics, and on land development patterns, such as density and land use mix. • Frank L • Pivo G Impacts of mixed use and density on utilization of three modes of travel single-occupant vehicle, transit, and walking. , • Berman M The transportation effects of neo-traditional development. Transportation systems and land development are thought to directly influence transportation choices and a number of studies have linked transportation systems and land-use patterns to choices among different transport modes, including walking. • Ewing R • Haliyur P • Page G.W Getting around a traditional city, a suburban planned unit development, and everything in between. , • Kitamura R • Mokhtarian P.L • Laidet L A micro-analysis of land use and travel in five neighborhoods in the San Francisco Bay Area. In an analysis of data from the 1995 National Personal Transportation Survey, Ross and Dunning • Ross C.L • Dunning A.E showed that the percentage of trips using bicycling or walking as the transport mode was 3.3% in the lowest-density block groups (0 to 99 housing units per square mile), compared to 14.9% in the highest-density block groups (≥3000 units per square mile). In addition to transportation systems and general patterns of land development, the concept of urban form encompasses building design, building orientation toward the street and other buildings, and detailed aspects of the distribution of homes, workplaces, and other institutions, such as schools, stores, and restaurants. • Handy S Urban form and pedestrian choices. , • Handy S Understanding the link between urban form and non-work travel behavior. The complex nature of urban form makes it difficult and costly to develop comprehensive measures of urban form that may be related to physical activity, and there are significant disagreements over how the existing measures are related to each other and to behavior. • Berman M The transportation effects of neo-traditional development. , • Kitamura R • Mokhtarian P.L • Laidet L A micro-analysis of land use and travel in five neighborhoods in the San Francisco Bay Area. , • Handy S Urban form and pedestrian choices. , • Handy S Understanding the link between urban form and non-work travel behavior. , • Cervero R Land use mixing and suburban mobility. , • Boarnet M • Crane R The influence of land use on travel behavior specification and estimation strategies. Understanding associations between urban form and transportation choices influencing physical activity levels is important for public health because of the possibility that planning decisions could influence physical activity and therefore health. Home age is a candidate measure of urban form that is worthy of exploration for several reasons. First, home age is associated with density, street design, and building characteristics. Neighborhoods containing older homes in urban areas are more likely to have sidewalks, have denser interconnected networks of streets, and often display a mix of business and residential uses. • Handy S Urban form and pedestrian choices. , • Handy S Understanding the link between urban form and non-work travel behavior. Second, ecologic studies suggest that there may be an association between home age and walking behavior; people living in census tracts with higher-mean home ages walk more than those living in tracts with lower-mean home ages. • Friedman B • Gordon S • Peers J Effect of neotraditional neighborhood design on travel characteristics. , • Douglas I Lastly, some existing health, transportation, and housing surveys contain data on home age. In this paper, we test the hypothesis that urban form influences levels of physical activity with an analysis of the association between home age, a proxy measure of urban form, and walking behavior in U.S. adults. ## Methods We analyzed data from the Third National Health and Nutrition Examination Survey (NHANES III). This survey is a nationally representative sample of the U.S. population with a stratified multistage probability design and oversampling of African Americans and Mexican Americans. National Center for Health Statistics NCHS plan and operation of the Third National Health and Nutrition Examination Survey, 1988–1994. A total of 17,030 adults aged ≥20 years responded to the household adult and family survey questions. Our analyses included adults aged ≥20 years who responded to questions concerning all of the behavioral and demographic variables (n = 14,827). NHANES III survey data included in this study were a measure of walking behavior, measures of the frequency of diverse forms of leisure-time physical activity, home age, rural versus urban/suburban locale, region of the country, demographic characteristics for each respondent, and any health-related activity limitation. Text questions in the survey are available on the web (http://www.cdc.gov/nchs/nhanes.htm). Walking behavior was characterized by responses to the question, “In the past month, how often did you walk a mile or more at a time without stopping?” Note that no attempt was made in the survey to determine the purpose or venue of these walks. This variable had a strongly skewed distribution, with 8334 individuals reporting a frequency of zero times per month. We chose to present the walking data in two ways: (1) categorized as 0 per month, 1 to 19 per month, and ≥20 per month; and (2) categorized as 0 to 19 per month and ≥20 per month. We use the first division for a descriptive analysis of the data and the second bivariate division for logistic regressions. The highest category corresponds to approximately five episodes of walking (as defined in the question) per week. • Pate R.R • Pratt M • Blair S.N • et al. Physical activity and public health a recommendation from the Centers for Disease Control and Prevention and the American College of Sports Medicine. The measures of leisure-time physical activity all involved questions phrased as, “In the past month did you…?” The eight specified activities were “jog or run,” “ride a bicycle or an exercise bicycle,” “swim,” “do aerobics or aerobic dancing,” “do other dancing,” “do calisthenics or exercises,” “garden or do yard work,” and “lift weights.” If the response was yes, then a subsequent question asked how often this activity was performed. A series of open-ended questions with the same format were also included to allow inclusion of activities not specified. We followed the survey design and treated bicycling as a leisure-time activity rather than a combined estimate of transport and leisure-time activity. Home age was selected as a proxy measure of environmental factors influencing physical activity. Home age was characterized from responses to the question, “When was this house/structure originally built? Before 1946, 1946–1973, or 1974 to present.” A rationale for these cut-points is not supplied in the NHANES III documentation. In the entire survey, 1505 people responded “don’t know” and 718 responses were classified as “blank but applicable” because of residence in mobile homes. Urban/rural status was evaluated based on categories that were collapsed by the National Center for Health Statistics from the U.S. Department of Agriculture’s rural-urban codes to avoid identification of sampled counties. Urban residences fell in central or fringe counties of metropolitan areas with populations of ≥1 million. Rural areas were all other locations. Lastly, we addressed regional variation in the United States. The data include a code for census region: Northeast, Midwest, South, or West. Regional estimates do not include data for all states in the region, so they are not representative. National Center for Health Statistics NCHS plan and operation of the Third National Health and Nutrition Examination Survey, 1988–1994. Five demographic variables were evaluated: gender, race/ethnicity, age, education level, household income, and a measure of limits to physical activity. Race/ethnicity was reported as non-Hispanic white, non-Hispanic black, Mexican American, and other. Age was categorized into three groups: 20 to 39 years, 40 to 59 years, and ≥60 years. We included measures of education and income in order to account for effects of socioeconomic status. Education was categorized into three categories: less than high school, high school, and any college. Income was divided into two groups: <$20,000 per year and ≥$20,000 per year. More detailed questions were asked about income, but their use resulted in a substantial increase in the rate of nonresponse. Lastly, to account for potential confounding by physical activity limitations, we categorized people as having some limitation if they responded yes to any of three questions. These questions asked if the subject was limited in any way in work, housework, or any activity because of an impairment or health problem. To account for the complex survey design used in NHANES III, data were analyzed with SUDAAN • Shah B.B • Barnwell G • Bieler G.S following recommendations discussed in Korn and Graubard. • Korn E.L • Graubard B.I We report frequencies calculated using sample weights associated with the survey design to account for variable selection probabilities. To quantify the relationship between walking behavior and home age, we used logistic regression after dividing the data into urban and rural strata and categorizing walking frequency into two groups: 0 to 19 per month (reference) and ≥20 per month. This makes the odds ratios (ORs) easier to interpret than when three categories are used. • Korn E.L • Graubard B.I (There was no evidence for an association between home age and intermediate walking frequencies.) Home age was not expected to be a proxy variable for environmental features that influence walking in rural areas. We also examined the association between home age and leisure-time physical activity that did not include walking. If home age is a proxy measure of aspects of urban form that are specifically associated with pedestrian activity, then we hypothesized that other forms of exercise would not be associated with home age in urban or rural areas. To explore potential confounding by demographic variables and any health-related activity limitation, we compared prevalence ORs obtained from models relating walking behavior and home age with and without the inclusion of potential confounders. Lastly, we performed exploratory analyses on our data stratified by region. ## Results The distributions of walking behavior and home age stratified by several demographic variables are summarized in Table 1. Logistic regression indicated that there was a moderate association between gender and walking frequency (p = 0.062) and strong associations between walking and the remaining variables (p < 0.0001). Men were slightly more likely to walk ≥20 times per month than women. Non-Hispanic whites were more likely than other race/ethnic groups to report some walking and older individuals were most likely to report no walking. High school education and less-than high school education were associated with lack of walking. Home age was not associated with gender (p = 0.41) but it was associated with the remaining demographic variables (p < 0.001). Most apparent among these associations were that older adults were more likely to live in older homes and that lower income and lower levels of education were associated with residence in older structures. Table 1Demographic and behavioral characteristics of U.S. adults categorized by home age and walking behavior from 1988–1994 NHANES III CharacteristicTotal (%)Walking frequency (%)When residence built (%) 0/Month1–19/Month≥20/Month≥19741946–1973<1946 n14,8278,3344,5481,9453,6227,3663,839 Weighted %48.738.313.132.843.224.0 Gender Male48.048.237.714.133.242.624.2 Female52.049.238.812.132.343.823.9 Race/ethnicity Non-Hispanic white77.747.140.512.433.441.125.5 Non-Hispanic black10.151.732.316.026.752.121.2 Mexican American4.859.228.612.137.048.614.4 Other7.354.628.916.531.249.719.1 Age 20–3945.544.443.911.638.638.722.7 40–5931.447.638.215.034.044.921.1 >6023.158.527.313.519.749.830.5 Education level <High school23.462.624.512.923.747.029.3 High school33.751.037.012.032.442.625.0 Any college42.939.246.814.038.041.620.4 Household income <$20,00031.754.332.113.622.645.631.8 ≥$20,00068.346.041.112.837.542.120.4 Activity limitations Yes15.761.927.011.128.243.328.4 No84.346.240.413.333.643.223.2 NHANES III, Third National Health and Nutrition Examination Survey. Residents of homes built before 1974 in urban or suburban areas were more likely than residents of newer homes to walk ≥20 times per month (Table 2). This relationship was not seen in rural counties. Results of logistic regressions modeling these associations are shown in Table 3. In urban and suburban areas, adult residents of homes built before 1946 and between 1946 and 1973 were significantly more likely to be in the higher walking category. This result was not affected by inclusion of gender, race/ethnicity, age, education, income, or health-related activity limitation in the model. There was no evidence for an association between home age and other forms of leisure-time physical activity in urban/suburban areas (Table 4). In rural areas, residents of homes built between 1946 and 1973 were less likely to engage in non-walking leisure time than residents of homes built after 1973. However, this association was not present after adjustment for demographic variables (Table 4). Table 2Distribution of walking frequency and home age in urban/suburban and rural areas for U.S. adults Walking frequencyTotalWhen residence built ≥19741946–1973<1946 Urban and suburban areas, % (SE) 0/Month45.2 (1.3)47.6 (2.1)44.3 (1.5)43.8 (2.9) 1–19/Month40.1 (1.0)40.8 (2.2)39.6 (1.4)40.2 (1.9) ≥20/Month14.6 (0.8)11.5 (1.0)16.1 (0.9)16.0 (2.1) Rural counties, % (SE) 0/Month52.0 (1.6)48.2 (2.6)52.8 (1.9)55.7 (2.4) 1–19/Month36.4 (1.5)40.6 (2.0)35.9 (1.9)31.9 (2.0) ≥20/Month11.5 (0.7)11.2 (1.2)11.3 (1.0)12.4 (1.4) SE, standard error. Table 3Odds ratios for walking frequencies (≥20 times per month versus <20 times per month) according to home age in U.S. adults in urban/suburban and rural areas ModelWhen residence built ≥1974 (Reference)1946–1973<1946 Urban and suburban areas Prevalence, % (SE) 0–19/Month (reference)28.1 (2.6)38.2 (2.3)19.1 (2.6) ≥20/Month3.7 (0.6)7.3 (0.7)3.7 (0.4) Crude OR (95% CI)1.01.44 Boldfaced ORs have confidence intervals that do not include 1.0. (1.16–1.79) 1.44 (1.01–2.05) Adjusted ORs are obtained from regression models including gender, ethnicity, age, education level, income, and health-related activity limitation. OR (95% CI) 1.01.36 (1.13–1.65)1.43 (1.03–1.98) Rural counties Prevalence %, (SE) 0–19/Month (reference)30.0 (2.0)36.3 (1.2)22.1 (2.2) ≥20/Month3.8 (0.5)4.6 (0.4)3.1 (0.4) Crude OR (95% CI)1.01.00 (0.76–1.34)1.11 (0.75–1.65) Adjusted OR (95% CI)1.00.93 (0.65–1.33)1.13 (0.74–1.73) CI, confidence interval; OR, odds ratio. a Boldfaced ORs have confidence intervals that do not include 1.0. b Adjusted ORs are obtained from regression models including gender, ethnicity, age, education level, income, and health-related activity limitation. Table 4Odds ratios for the association between nonwalking, leisure-time physical activity (≥20 times per month versus <20 times per month) and home age in U.S. adults in urban/suburban and rural areas ModelWhen residence built ≥1974 (Reference)1946–1973<1946 Urban and suburban areas Prevalence % (SE) 0–19/Month (reference)22.4 (2.7)31.0 (2.4)16.0 (1.3) ≥20/Month9.3 (0.9)14.5 (1.1)6.8 (0.7) Crude OR (95% CI)1.01.13 (0.87–1.48)1.03 (0.79–1.34) Adjusted odds ratios are obtained from regression models including gender, ethnicity, age, education level, income, and health-related activity limitation. OR (95% CI) 1.01.20 (0.88–1.63)1.15 (0.86–1.52) Rural counties Prevalence, % (SE) 0–19/Month (reference)22.8 (1.3)29.3 (1.3)17.1 (1.7) ≥20/Month11.0 (1.3)11.7 (0.9)8.1 (0.8) Crude OR (95% CI)1.00.83 Confidence interval does not include 1.0. (0.69–0.99) 0.99 (0.78–1.25) Adjusted OR (95% CI)1.00.87 (0.72–1.06)1.09 (0.89–1.34) CI, confidence interval; SE, standard error. a Adjusted odds ratios are obtained from regression models including gender, ethnicity, age, education level, income, and health-related activity limitation. b Confidence interval does not include 1.0. Unadjusted analyses stratified by region gave qualitatively similar results for the Northeast, South, and West but not from the Midwest. In urban/suburban areas in the Northeast, South, and West, individuals residing in homes built before 1974 were more likely to report walking ≥20 times per month, with ORs ranging from 1.1 to 1.8. However, 95% confidence intervals for these results overlapped 1.0 for five of six comparisons. In the Midwest, the odds of walking were near or below one for the two older home categories (<1946, OR=0.8; 1946 to 1973, OR=1.0). We attempted to determine if missing data biased our results by analyzing data that included all individuals reporting home age and walking behavior (n = 15,196). The results of this analysis showed the same pattern as the above crude analysis. The remaining 2000-plus adults that could not be included in the analysis largely consisted of people who did not know the age of their home: They were evenly distributed among the three walking categories (7% to 10% per group). ## Discussion Past work on the relationship between urban form and physical activity has explored the effects of population density, site design, and building characteristics on transportation behavior. Many of these studies report that increased density and mixed-use development are associated with more walking and bicycling. • Frank L • Pivo G Impacts of mixed use and density on utilization of three modes of travel single-occupant vehicle, transit, and walking. , • Ewing R • Haliyur P • Page G.W Getting around a traditional city, a suburban planned unit development, and everything in between. , • Kitamura R • Mokhtarian P.L • Laidet L A micro-analysis of land use and travel in five neighborhoods in the San Francisco Bay Area. , • Cervero R Land use mixing and suburban mobility. , • Douglas I , • Douglas I , • Replogle M However, there is still considerable debate over the consistency and interpretation of such associations. • Handy S Urban form and pedestrian choices. , • Handy S Understanding the link between urban form and non-work travel behavior. , • Boarnet M • Crane R The influence of land use on travel behavior specification and estimation strategies. , • Krizek K.J A pre-test/post-test strategy for researching neighborhood-scale urban form and travel behavior. In this article, we extend past work by examining the relationship between leisure-time walking behavior and home age, a potential proxy for aspects of urban form that mediate walking behavior. Our finding that walking ≥1 mile ≥20 times per month is associated with living in an urban/suburban residence built before 1974 in U.S. adults supports the hypothesis that home age is a proxy measure of aspects of urban form that influence one aspect of physical activity. Our findings are also consistent with results from transportation research indicating that walking is more common in neighborhoods with older homes. • Friedman B • Gordon S • Peers J Effect of neotraditional neighborhood design on travel characteristics. , • Douglas I The current study extends this prior work in at least four ways. First, it is based on data from a nationally representative sample of U.S. adults rather than a local or convenience sample. Second, it includes data on the home age of individual subjects rather than mean home age of a block group or neighborhood; this may or may not be a strength of the study, given that mean home age could be a better measure of neighborhood characteristics than individual home age. Third, it is based on regression models that control for the effects of demographic variables and activity limitations. Fourth, it explicitly contrasts walking with other forms of physical activity in both urban and rural areas. We found no evidence of an association between home age and walking behavior in rural environments. This suggests that home age in rural environments is not associated with features of the physical environment that influence walking. • Ross C.L • Dunning A.E Regardless of age, homes in rural environments may be too distant from desirable destinations for walking. In addition, environmental variables (e.g., access to parks and trails) that may not be correlated with home age could be mediators of walking frequency in rural areas. Improved understanding of walking behavior could be obtained with an instrument that assessed leisure-time, work-related, and transportation walking behavior along with environmental variables in urban and rural areas. • Handy S Urban form and pedestrian choices. , • Handy S Understanding the link between urban form and non-work travel behavior. , • Sallis J.F • Bauman A • Pratt M Environmental and policy interventions to promote physical activity. Home age was not associated with leisure-time activities such as jogging/running, swimming, weight lifting, or dancing. This is consistent with the hypothesis that home age is a proxy measure of urban form that specifically influences pedestrian activity. It also indicates that ecologic analyses of the environment and physical activity should attempt to include diverse measures of environmental characteristics that could be associated with a broader spectrum of activities. Preliminary data analysis indicated that the association between home age and walking behavior in urban/suburban areas may be present in the Northeast, Midwest, and West, but not in the South. It is difficult to interpret these results because NHANES III was not designed to provide representative samples within regions, and samples from different regions were often obtained at different times of the year. National Center for Health Statistics NCHS plan and operation of the Third National Health and Nutrition Examination Survey, 1988–1994. Furthermore, leisure-time physical activity is known to vary seasonally • Pell J.P • Cobbe S.M Seasonal variations in coronary heart disease. and to show regional variation in the magnitude of seasonal effects. Centers for Disease Control and Prevention Monthly estimates of leisure-time physical inactivity—United States, 1994. These factors likely complicate the comparison of local or regional cross-sectional studies of physical activity. • Matthews C.E • Freedson P.S • Hebert J.R • et al. Seasonal variation in household, occupational, and leisure time physical activity longitudinal analyses from the seasonal variation of blood cholesterol study. A recent abstract • Kirkner G • Levin S • Durstine J.L • Hebert J • Mayo K Geographic (urban/rural) variations in the prevalence of physical inactivity. reports that the relationship between physical inactivity and urbanization varies among the four geographic regions of the United States. Geographic variation in attitudes toward physical activity, climatic variables, and safety could moderate the effects of urban form and walking behavior. Our results and the results of Kirkner et al. • Kirkner G • Levin S • Durstine J.L • Hebert J • Mayo K Geographic (urban/rural) variations in the prevalence of physical inactivity. highlight the potential influence of regional factors such as climate and culture on associations between the environment and walking behavior, but few data are available to address this issue. A key weakness of cross-sectional studies of the environment and pedestrian activity is that individuals may select neighborhoods based on their preference for walkable environments. To our knowledge, there is only one published longitudinal study of urban form and transportation mode choice. • Krizek K.J A pre-test/post-test strategy for researching neighborhood-scale urban form and travel behavior. This study reported on transportation mode choice of residents of the Puget Sound area. Transport choice data were based on 2-day trip diaries and neighborhood characteristics were coded using aggregate data at the census block-group level. The study found small increases in the use of non-auto transportation (walking, cycling, and transit) when people moved from more to less auto-dependent neighborhoods and small decreases associated with moves to more dependent neighborhoods. Additional longitudinal studies and clever use of natural experiments, such as planned developments or Rails-to-Trails projects, could help us understand the role of urban form in mediating levels of physical activity. Our study adds to the modest literature documenting associations between measures of urban form and leisure-time physical activity. Furthermore, direct measurements of urban form are costly. The identification of measures of urban form available in existing and ongoing surveys that include measures of physical activity will facilitate research on the environmental correlates of activity. ## Acknowledgements DB was supported by a Cancer Prevention Fellowship from the National Cancer Institute while working on this project and gratefully acknowledges the Cooper Institute and its sponsors for organizing the symposium in which this paper was first presented. We are grateful to R. Ballard-Barbash, S. Krebs-Smith, K. Dodd, L. Mâsse, A. King, K. Calfas, and A. Bauman for helpful comments on the manuscript. Further comments by three anonymous reviewers also improved the manuscript. ## References • Moos R.H The human context. John Wiley & Sons, New York1976 • Sherwood N.E • Jeffery R.W The behavioral determinants of exercise. Annu Rev Nutr. 2000; 20: 21-44 • Sallis J.F • Owen N Ecological models. in: Glanz K Lewis F.M Rimer B.K Health behavior and health education theory, research and practice. Jossey-Bass, San Francisco1997: 403-424 1. Centers for Disease Control and Prevention. Active community environments. 2002. Available at: www.cdc.gov/nccdphp/dnpa/aces.htm. Accessed June 1, 2002. • Frank L • Pivo G Impacts of mixed use and density on utilization of three modes of travel. Transportation Res Record. 1994; 1466: 44-52 • Berman M The transportation effects of neo-traditional development. J Planning Lit. 1996; 10: 347-363 • Ewing R • Haliyur P • Page G.W Getting around a traditional city, a suburban planned unit development, and everything in between. Transportation Res Record. 1994; 1466: 53-62 • Kitamura R • Mokhtarian P.L • Laidet L A micro-analysis of land use and travel in five neighborhoods in the San Francisco Bay Area. Transportation. 1997; 24: 125-158 • Ross C.L • Dunning A.E Land use transportation interaction. U.S. Department of Transportation, Washington, DC1997 • Handy S Urban form and pedestrian choices. Transportation Res Record. 1996; 1552: 135-144 • Handy S Understanding the link between urban form and non-work travel behavior. J Planning Educ Res. 1996; 15: 183-198 • Cervero R Land use mixing and suburban mobility. Transportation Q. 1988; 42: 429-446 • Boarnet M • Crane R The influence of land use on travel behavior. Transportation Res Part A. 2001; 35: 823-845 • Friedman B • Gordon S • Peers J Effect of neotraditional neighborhood design on travel characteristics. Transportation Res Record. 1994; 1466: 63-70 • Douglas I The pedestrian environment, Vol. 4A. 1000 Friends of Oregon, Portland, OR1993 • National Center for Health Statistics NCHS plan and operation of the Third National Health and Nutrition Examination Survey, 1988–1994. Vital Health Stat. 1994; 1 • Pate R.R • Pratt M • Blair S.N • et al. Physical activity and public health. JAMA. 1995; 273: 402-407 • Shah B.B • Barnwell G • Bieler G.S SUDAAN user’s manual, release 7.5. Research Triangle Institute, Research Triangle Park, NC1997 • Korn E.L • Graubard B.I Analysis of health surveys. John Wiley & Sons, New York1999 • Douglas I Building orientation. A supplement to the Pedestrian Environment, Vol. 4B. 1000 Friends of Oregon, Portland, OR1994 • Replogle M Integrating pedestrian and bicycle factors into regional transportation planning models. Environmental Defense Fund, Washington, DC1995 • Krizek K.J A pre-test/post-test strategy for researching neighborhood-scale urban form and travel behavior. Transportation Res Record. 2000; 1722: 48-55 • Sallis J.F • Bauman A • Pratt M Environmental and policy interventions to promote physical activity. Am J Prev Med. 1998; 15: 379-397 • Pell J.P • Cobbe S.M Seasonal variations in coronary heart disease. QJM. 1999; 92: 689-696 • Centers for Disease Control and Prevention Monthly estimates of leisure-time physical inactivity—United States, 1994. MMWR Morb Mortal Wkly Rep. 1997; 46: 393-397 • Matthews C.E • Freedson P.S • Hebert J.R • et al. Seasonal variation in household, occupational, and leisure time physical activity. Am J Epidemiol. 2001; 153: 172-183 • Kirkner G • Levin S • Durstine J.L • Hebert J • Mayo K Geographic (urban/rural) variations in the prevalence of physical inactivity. Med Sci Sports Exerc. 2001; 33: 238

2022-08-09 11:13:35

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https://www.helpteaching.com/questions/129172/based-on-the-following-information-where-ang-abd-is-a-right-

Question Info This question is public and is used in 1 group and 386 tests or worksheets. Type: Multiple-Choice Category: Angles Standards: 7.G.B.5 Score: 17 Author: LBeth View all questions by LBeth. Angles Question View this question. Add this question to a group or test by clicking the appropriate button below. Based on the following information, where $ang ABD$ is a right angle, which equation could be used to solve for x? $mangDBC = x$ $mangCBA = 2x$ 1. $2x - x = 90$ 2. $2x + x = 90$ 3. $2x - x = 180$ 4. $2x + x = 180$

2019-02-16 22:20:06

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https://byjus.com/question-answer/choose-the-correct-properties-of-anode-rays-the-properties-of-anode-rays-depend-upon-the-1/

Question Choose the correct properties of anode rays.The properties of anode rays depend upon the nature of gas taken in the discharge tube.Anode rays travel in a straight line.Anode rays consist of negatively charged particles.The mass of the particle is the same as the atomic mass of the gas inside the discharge tube. Solution The correct options are A The properties of anode rays depend upon the nature of gas taken in the discharge tube. B Anode rays travel in a straight line. D The mass of the particle is the same as the atomic mass of the gas inside the discharge tube.Properties of anode rays can be given as follows: 1. Anode rays travel in straight lines. 2. Since they rotate the light paddle wheel placed in their path, they consist of material particles. 3. Anode rays are deflected by electric and magnetic fields. Since they are deflected towards the negatively charged plate, they consist of positively charged particles. 4. The properties of anode rays depend upon the nature of gas taken in the discharge tube. 5. The mass of the particle is the same as the atomic mass of the gas inside the discharge tube. Suggest corrections

2021-12-05 03:07:38

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https://www.physicsforums.com/threads/analysis-proof-help.537962/

Analysis Proof Help 1. Oct 8, 2011 Armbru35 Analysis Proof Help!! If anyone could give me a hint on how to start this I would appreciate it! I am struggling with proofs! Thanks! Given a sequence (asub(n)) s.t. (i) the sequence is decreasing (ii) the limit of the sequence is 0. Prove rigorously that an is greater than or equal to 0 for every n contained in the natural numbers 2. Oct 8, 2011 DiracRules Re: Analysis Proof Help!! $a_n\rightarrow 0$ if $\forall \epsilon >0\exists \bar{n}\backepsilon' \forall n>\bar{n}, |a_n|<\epsilon$. Try to prove that, if $a_{\bar{n}}<0$, with a particular choice of epsilon the limit definition is not verified. Remember to consider the fact that the sequence is decreasing

2018-03-22 18:47:32

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https://www.xloypaypa.pub/educational-codeforces-round-115-abcde-solutions-java-c/

## A. Computer Game ### Solution: Scan from left to right one by one. As long as one of the columns on the left can be reached, all safe cells in the current column can be reached. Java C++ ## B. Groups ### Solution: Enumerate which two days are in lesson. As long as everyone can have lesson in these two days, and more than half of the people can come to lesson in each lesson , a way of dividing will definitely be found. Consider the worst-case scenario, the half who can come on a certain day can only come on that day. According to the above conditions, the remaining half must can come on another day. Java C++ ## C. Delete Two Elements ### Solution: Let the sum of all the elements of the original array be sum, and the two deleted numbers are x and y respectively. According to the question, there must be $\frac {sum} n = \frac {sum - x -y} {n-2}$. So naturally there is $sum \cdot (n-2) = (sum-x -y) \cdot n$. Obviously the value of x+y is a fixed value. Therefore, as x increases, y must decrease. So we sort the original array and enumerate x in turn. The only thing to note during the enumeration process is that the original array may have the same elements, so we need to count the number of times each number appears, and de-duplicate the original array. Java C++ ## D. Training Session ### Solution: Consider the case that both of the two conditions are not met. It is not difficult to notice that if you want neither of these conditions to be met, the difficulty or topic of the three questions cannot be the same. Take the three questions with the same topic as a negative example. According to the definition of the problem, the difficulty of the three questions must be different at this time. Therefore, one of the conditions must be met. Therefore, both difficult and topic have and only have two problems are the same. for example: Obviously, according to the above picture, one of the three problems must be red for both difficult and topic at the same time. In the other two problems, one and only one's topic is red, and the other problem's difficult is red. So we can enumerate the problem that topic and difficult are all red at the same time. Java C++ ## E. Staircases ### Solution: First of all, we found that each cell can be mapped into two staircase. Take the * cell in the following figure as an example, it can be mapped to the following two staircase: Similarly, the points below the diagonal can also be mapped to the two staircase: So it's obvious. When we change a cell, the effect of this cell will only affect the cells that between first locked cell on the up and down (that is, only related to the longest continuous staircase). Take the following picture as an example: If we want to lock , the effect will be 53=15 different staircase, that is, any cells before * to any cell after * (including the cell of *). The same goes for unlocking the locked cell. ### Code: Java C++ I’m too busy with work lately, and I really don’t have time to read the F question.

2022-05-27 00:49:01

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http://mymathforum.com/chemistry/68243-icl2-vsepr-single-electrons.html

My Math Forum ICl2 VSEPR, single electrons Chemistry Chemistry Forum July 7th, 2015, 01:43 PM #1 Newbie   Joined: Oct 2014 From: Denmark Posts: 11 Thanks: 1 ICl2 VSEPR, single electrons I am preparing for a re-examination, and one of the previous test has the following question: Estimate the VSEPR model of ICl2. This means, I have Iodine in the middle due to the electron negativity, and 21 electrons in total. Using the octet rule I end up with two lone pairs on the Iodine, and a single one, too. Now, according to my teacher's hopefully correct solution, the single electron will act as a lone pair, thus ICl2 will have three lone pairs on the iodine. Is this correct? I can't seem to find anything about single electrons in the VSEPR theory, and I have never heard of ICl2, and can't find a lewis structure of it. Is it safe to consider single electrons as lone pairs always? (Considering I am only doing high-school chemistry) July 11th, 2015, 11:51 AM #2 Member     Joined: Oct 2014 From: Colorado Posts: 40 Thanks: 21 Yes, single electrons act as lone pairs. Perhaps your teacher meant it as only practice, however, i'm not certain $ICl_2$ exists in nature. You can also read any edition of "Chemistry: The Molecular Nature of Matter and Change" for more in-depth information about general chemistry. Thanks from Bugge July 14th, 2015, 09:56 AM #3 Newbie   Joined: Oct 2014 From: Denmark Posts: 11 Thanks: 1 Hello, and thank you very, very much for your response. Yes, my search for ICl2 had no results either. Also, thanks for the recommendation, but we are already using a book called "General Chemistry", which I feel is quite complete. The problem is my teacher simply hasn't shown how he has solved the tests, he only marks the answer (It is a multiple choice exam), so you never know why he puts the 'x' the way he does. Feels like a curricular minefield. Tags electrons, icl2, single, vsepr , , , , , ### vsepr theory of icl2 Click on a term to search for related topics. Thread Tools Display Modes Linear Mode Similar Threads Thread Thread Starter Forum Replies Last Post BenFRayfield Physics 17 January 19th, 2015 07:03 AM girlbadatmath Chemistry 1 December 26th, 2014 09:09 PM girlbadatmath Chemistry 6 October 15th, 2014 10:49 AM girlbadatmath Chemistry 1 October 10th, 2014 01:52 PM Adrian Physics 3 February 16th, 2012 04:10 PM Contact - Home - Forums - Cryptocurrency Forum - Top

2017-06-23 03:19:23

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https://www.speedlabs.in/cbse-class-10th/cbse-maths-reduced-syllabus-class-10/

# CBSE Class 10 Syllabus Science(Theory + Practical) The Central Board of Secondary Education (CBSE) is one of the most prestigious and preferred educational boards in India. It aims to provide a holistic and healthy education to all its learners so that students can get adequate space to develop mentally and physically. CBSE is known for its comprehensive syllabus and well structured exam pattern which helps students to get a detailed idea about the entire curriculum. There are around 20,102 schools under the board which follows the NCERT curriculum. The CBSE class 10 board exam is undoubtedly the first important exam in an individual’s life because this phase of life shapes the future of the students for their next successive years. The CBSE class 10 board exam is the first nationalised external exam that the students undertake and hence gives a nightmare to many students appearing for the exam. The subjects are designed very strategically and helps the students to get influenced by the lessons and knowledge imparted to them. The subjects, especially science and maths require the students to get completely immersed in them and enjoy learning along with gathering knowledge. COURSE STRUCTURE CLASS –X (2021-22) FIRST TERM Time: 90 Minutes NO. UNIT NAME MARKS I NUMBER SYSTEMS 6 II ALGEBRA 10 III COORDINATE GEOMETRY 6 IV GEOMETRY 6 V TRIGONOMETRY 5 VI MENSURATION 4 VII STATISTICS & PROBABILITY 3 Total 40 INTERNAL ASSESSMENT 10 TOTAL 50 INTERNAL ASSESSMENT MARKS TOTAL MARKS Periodic Tests 3 10 marks for the term Multiple Assessments 2 Portfolio 2 Student Enrichment Activities-practical work 3 UNIT-NUMBER SYSTEMS 1. REALNUMBER Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples. Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals. UNIT-ALGEBRA 1. POLYNOMIALS Zeroes of a polynomial. Relationship between zeroes and coefficients of quadratic polynomials only. 1. PAIR OF LINEAR EQUATIONS IN TWOVARIABLES Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution and by elimination. Simple situational problems. Simple problems on equations reducible to linear equations. UNIT-COORDINATE GEOMETRY 1. COORDINATEGEOMETRY LINES (In two-dimensions) Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division) UNIT-GEOMETRY 1. TRIANGLES Definitions, examples, counter examples of similar triangles. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional, and the triangles are similar. (Motivate) If the corresponding sides of two triangles are proportional, their     corresponding angles are equal, and the two triangles are similar. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other. (Motivate) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. (Motivate) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angle opposite to the first side is a right angle. UNIT- TRIGONOMETRY 1. INTRODUCTION TOTRIGONOMETRY Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values of the trigonometric ratios of $30^{\circ}, 45^{\circ}$ and $60^{\circ} .$ Relationships between the ratios. TRIGONOMETRIC IDENTITIES Proof and applications of the identity $\sin ^{2} A+\cos ^{2} A=1$. Only simple identities to be given. UNIT-MENSURATION 1. AREAS RELATED TOCIRCLES Motivate the area of a circle, area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of $60^{\circ}$ and $90^{\circ}$ only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.) UNIT- STATISTICS & PROBABILITY 1. PROBABILITY Classical definition of probability. Simple problems on finding the probability of an event. SECOND TERM NO. UNIT NAME MARKS I ALGEBRA(Cont.) 10 II GEOMETRY(Cont.) 9 III TRIGONOMETRY(Cont.) 7 IV MENSURATION(Cont.) 6 V STATISTICS & PROBABILITY(Cont.) 8 Total 40 INTERNAL ASSESSMENT 10 TOTAL 50 UNIT-ALGEBRA Standard form of a quadratic equation $a x^{2}+b x+c=0,(a \neq 0)$. Solutions of quadratic equations (only real roots) by factorization, and by using quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day-to-day activities (problems on equations reducible to quadratic equations are excluded) 1.  ARITHMETICPROGRESSIONS Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems. (Applications based on sum to n terms of an A.P. are excluded) UNIT- GEOMETRY 1. CIRCLES Tangent to a circle at, point of contact (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. (Prove) The lengths of tangents drawn from an external point to a circle are equal. 1. CONSTRUCTIONS Division of a line segment in a given ratio (internally). Tangents to a circle from a point outside it. UNIT-TRIGONOMETRY 1. SOME APPLICATIONS OFTRIGONOMETRY HEIGHTS AND DISTANCES-Angle of elevation, Angle of Depression. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only $30^{\circ}, 45^{\circ}, 60^{\circ}$. UNIT-MENSURATION 1. SURFACE AREAS ANDVOLUMES Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combination of not more than two different solids be taken). UNIT-STATISTICS & PROBABILITY 1. STATISTICS Mean, median and mode of grouped data (bimodal situation to be avoided). Mean by Direct Method and Assumed Mean Method only INTERNAL ASSESSMENT MARKS TOTAL MARKS Periodic Tests 3 10 marks for the term MultipleAssessments 2 Portfolio 2 Student Enrichment Activities-practicalwork 3 PRESCRIBED BOOKS Mathematics – Textbook for class IX – NCERT Publication Mathematics – Textbook for class X – NCERT Publication Guidelines for Mathematics Laboratory in Schools, class IX – CBSE Publication Guidelines for Mathematics Laboratory in Schools, class X – CBSE Publication Laboratory Manual – Mathematics, secondary stage – NCERT Publication Mathematics exemplar problems for class IX, NCERT publication. Mathematics exemplar problems for class X, NCERT publication. Privacy Settings

2021-11-29 00:06:50

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https://socratic.org/questions/what-is-the-partial-pressure-of-the-helium-gas-express-your-answer-in-millimeter

# What is the partial pressure of the helium gas? Express your answer in millimeters of mercury. Jul 7, 2017 ${P}_{\text{He}} = 203$ $\text{mm Hg}$ #### Explanation: According to Dalton's law of partial pressures, the total pressure of the gaseous mixture is equal to the sum of the partial pressures of the gaseous components. Therefore, ${P}_{\text{total" = P_ ("CO"_2) + P_ "Ar" + P_ ("O"_2) + P_ "He}}$ $745$ $\text{mm Hg}$ $= 133$ $\text{mm Hg}$ $+ 214$ $\text{mm Hg}$ $+ 195$ $\text{mm Hg}$ $+ {P}_{\text{He}}$ P_ "He" = color(red)(203 color(red)("mm Hg"

2019-04-25 15:53:21

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http://121.43.60.238/sxwlxbA/EN/Y2020/V40/I6/1492

Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1492-1510. ### The Extensional Koppelman-Leray Type Integral Formulas in the Analytic Varieties of Stein Manifolds Shujin Chen*() 1. School of Mathematical Sciences, Xiamen University, Fujian Xiamen 361005 • Received:2018-08-15 Online:2020-12-26 Published:2020-12-29 • Contact: Shujin Chen E-mail:shjchen39@163.com Abstract: In this paper, we study how to establish integral formulas for differential forms in the analytic varieties of Stein manifolds. Firstly using different method and technique we derive the corresponding integral representation formulas of differential forms for the complex n-m(0 ≤ m < n) dimensional analytic varieties in two types of bounded domains of Stein manifolds. Secondly we obtain the unified integral representation formulas of differential forms for the complex n-m dimensional analytic varieties in the general bounded domains of Stein manifolds, i.e. Koppelman-Leray type integral formulas for the complex n-m dimensional analytic varieties in the bounded domains of Stein manifolds. In particular, when m=0, the formulas obtained in this paper are the extension of Koppelman-Leray formula in the Stein manifolds. CLC Number: • O174.56 Trendmd

2021-01-21 18:39:41

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https://math.stackexchange.com/questions/404883/notation-in-financial-math

# Notation in Financial Math I am very close to showing part b of this question and think that the reason my solution doesn't match up is because I don't understand a piece of notation.The notation I don't understand is $\textbf{$e^T$}$ on the bottom line inside the function $h$. I am at the point: $$E[f(W)] = \frac{1}{a}\huge{[}\normalsize 1 - \exp\{-aw\xi_0 r_0 + aw\big(\frac{1}{2}aw\xi V\xi^T - \xi r^T\big)\}\huge{]}$$ • That $\boldsymbol{e}$ in $\boldsymbol{e}^T$ is both boldfaced and in italics, unlike the $e$ for exponentials, so I believe it is a vector (of what, I don't know.) – Rócherz Apr 24 '18 at 11:46

2020-02-16 22:25:46

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http://www.physicsforums.com/showthread.php?t=379108

# Boolean expressions for Turing Machine by insectosaurus Tags: boolean, expressions, machine, turing P: 5 no it's not, more precisely, $$0 \leq k \leq$$ |$$\Sigma$$ | - 1, where $$\Sigma$$ is the alphabet. so S[i,j,k] means at time i, the contents of tape square j is symbol $$s_{k}$$ and $$0 \leq i \leq p(n)$$ and $$-p(n) \leq j \leq p(n)$$ where n is input's length, lets say the input string is x, then $$x = s_{1} \cdot s_{2} \cdot ... \cdot s_{k} \cdot ...\cdot s_{n}$$ P: 5 no, it's true if cell j contains symbol $$s_{k}$$ at time i

2014-07-31 01:30:35

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https://www.wellfitcommunity.com/blog/view/227738/weird-tweeting-over-napabucasin

Weird Tweeting Over Napabucasin By Lex Demant Pending Moderator Review $$r = S\times \mathbbE\rightarrow \mathbbR_+$$ affiliates each and every Tenofovir point out and each celebration a rate, the actual price from which the time grows. It complies with ur(s,electronic)?=?0 if $$e\not\in At the(s),$$ and 3rd r(ersus,at the)?>?0 not less than a single $$e\in At the(azines).$$ ? 5. $$r(s^\prime,utes,e)$$ could be the cross over probability of jumping to mention $$s^\prime$$ coming from express azines,?when celebration $$e\in E(s)$$ dismissed. ? Half a dozen. $$P oker(\cdot,s,electronic)$$ may be the snowballing submission perform (CDF) in the wall clock linked to occasion $$e\in \mathbbE$$ within condition utes. ? The mechanics of a GSMP method is informally identified in the subsequent method. The initial express is ersus Zero (but a general syndication around the state room can be viewed too), and also the initial worth associated with lamps is defined through testing the need for each active time in the connected CDF in azines Zero. Shifts through every single point out are generally executed according www.selleckchem.com/products/napabucasin.html towards the right after insurance plan: For each state, $$s\in S$$ and time valuation c?define the next levels $$t^*= t^*(s,c) Is equal to \inf\left\t \geq 0$$ chemical elizabeth 1 . ?=?c at the - (utes,?c)?=?c my spouse and i ???t *(s,?c)third(azines,?e) $$e^*= e^*(azines,d) Is equal to \min\e\in E(s)$$ (assuming the purchasing among situations). The big event elizabeth is the occasion in which that will fire in express s,?where c symbolizes the present time value. capital t ,?instead, it's time passed inside point out ersus. After the heating of celebration electronic *,?the condition is modified from ersus to $$s^\prime$$ along with probability $$p(s^\prime,s,e^*).$$ Clock value c,?instead, is modified the next: Your lamps JAK2 inhibitor drug coming from all occasions inside $$e\in Third(s^\prime,azines,e^*)$$ are usually current by simply testing off their CDF $$Y(\cdot,s^\prime,at the),$$ where $$3rd r(s^\prime,s,e^*) Is equal to \e^*\\cup(E(s^\prime)\setminus Elizabeth(ersus))$$ may be the group of fresh enabled occasions, together with occasion that will terminated. The particular clocks of most situations $$e\in M(s^\prime,ersus,e^*)$$ tend to be revised to take into account the actual elapsed period, my spouse and i.e. they are set towards the price $$c^*_e. M(s^\prime,utes,e^*) = E(s^\prime)\cap(Elizabeth(utes)\setminus\e^*$$\) could be the list of most events outstanding productive after the changeover. Your correctness on this construction can be formally performed within the right after. Theorem Three.One The TDSHA $$\mathfrakT$$ from an extended (loop-free) sCCP software, keeping all of the non-instantaneous transitions stochastic, is stochastically similar to a new GSMP. Evidence We simply design the actual resistant. We initial need to determine the GSMP for this entirely discrete TDSHA. We will continue similarly such as (Caravagna and also Hillston The year 2010). The state of hawaii space of the GSMP includes every one of the achievable valuations involving TDSHA factors, which includes Period.

2019-03-20 06:29:42

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https://www.physicsforums.com/threads/spaceship-drive-by-light.766921/

Spaceship drive by light 1. Aug 21, 2014 Helios Would a spaceship that is half reflective ( the stern ) and half flat-black ( the bow) be propelled through space just by the ambient radiation from stars and the CMBR? 2. Aug 21, 2014 Ryan_m_b Staff Emeritus Technically yes, you're essentially describing a solar sail. They're incredibly low thrust though and I doubt you could practically exit the solar system with one. 3. Aug 21, 2014 A.T. The black side will heat up and radiate. 4. Aug 21, 2014 A.T. Solar sails work fine with particles coming from one direction. But the OP seems to ask about approximately isotropic radiation from all sides. It seems to me, that converting such ambient radiation continuously into a directed movement of a ship would reduce entropy, and thus violate the laws of thermodynamics. 5. Aug 21, 2014 Staff: Mentor Right. Of course if we were willing to supply power to an on-board refrigeration system, we could transfer heat to the shiny side to maintain the thrust... Which just goes to show that we aren't going to get any useful work out of an isotropic energy bath without putting some work in ourselves, just as you said. 6. Aug 21, 2014 D H Staff Emeritus Very little, and not in the direction you think! Details follow. Heat up? It will cool down. In fact, the black side will radiate a lot until it cools down to T0=2.72548 K, the CMBR temperature. There will be no net thrust if the black side cools to the CMBR temperature. Ignoring thrust from starlight, the only way to get thrust is if the black side has a temperature above that of the CMBR. Note: I'm dismissing a device temperature below that of the CMBR as a physical impossibility. That would require cooling, and that takes work, and that's at best perfect. The work will generate heat, the amount of which will at best keep the device on average at the CMBR temperature. Any inefficiencies and the temperature will be greater than that of the CMBR. I'll assume the spacecraft is trying to make its across one of those huge voids in space (wiki article: http://en.wikipedia.org/wiki/Void_(astronomy)). That means there's no pesky starlight to make a mess of my hemispherical cow thrust assumptions. My hemispherical cow assumptions: The reflective side is perfectly flat perfect mirror, while the black side is a perfectly flat perfect black body at a uniform temperature TT0. The reflective side specularly reflects all incoming CMB radiation over the half-sphere visible to that side of the spacecraft. The CMB radiation is isotropic, but the spacecraft only gets thrust from the normal component of the radiation, effectively halving the intensity. But since the reflection is specular, we get to double the thrust. The net effect is a factor of 1. The total thrust from the reflective side is thus $F_{\text{reflective}} = \frac {\sigma A {T_0}^4} c$, where the numerator is the Stefan-Boltzmann law for radiative power and the numerator reflects the fact that photons travel at c. This thrust is in the direction of the black side. The black side absorbs all incoming CMB radiation over the half-sphere visible to that side of the spacecraft. Integrating over the half-sphere, the only component that survives is the normal component. This is half the thrust from the reflective side, but this thrust is directed toward the reflective side. The black side also radiates per the Stefan-Boltzmann law over the half-sphere visible to that side of the spacecraft. Assuming this is isotropic over the half-sphere, the net thrust from this outgoing radiation is $\frac 1 2 \frac{\sigma A {T}^4} c$. The total thrust from the black side is thus $F_{\text{reflective}} = \frac 1 2 \frac {\sigma A {T_0}^4} c + \frac 1 2 \frac {\sigma A {T}^4} c = \frac 1 2 \frac {\sigma A} c \left({T_0}^4 + T^4 \right)$. This thrust is in the direction of the reflective side. Summing the thrusts from both sides vectorially yields $F_{\text{total}} = \frac 1 2 \frac {\sigma A} c \left(T^4 - {T_0}^4\right)$, toward the reflective side. There is no thrust if the spacecraft does cool to the CMBR temperature. Suppose on the other hand the spacecraft has some power source that keeps the spacecraft alive, powers computations, and powers the spacecraft's rotational control. The equilibrium temperature T given some power P is $T= \left({T_0}^4+\frac {2P}{\sigma A}\right)^{1/4}$. The net thrust will be $\frac P c$, in the direction of the reflective side. Note that the area of the spacecraft and the CMBR temperature have dropped out of the picture. 7. Aug 21, 2014 A.T. Sorry, bad choice of words. I meant that you cannot prevent it from radiating, by cooling it down to 0K. 8. Aug 21, 2014 D H Staff Emeritus There are two problems with your line of thinking. Problem #1: Transferring heat to the shiny side accomplishes nothing because the shiny side doesn't emit radiation. At any given frequency, the emissivity, transmissivity, and reflectivity of some object sum to one. Our object presumably is a perfect reflector at all frequencies, so it's emissivity is zero at all frequencies. Problem #2: This is the thermodynamical equivalent of lifting yourself by your own bootstraps. In fact, its worse. Nothing much happens I try to lift myself by my own bootstraps. You can cool down a part of the black side, but that takes work, and that generates heat, and that in turn raises the temperature somewhere else on the black side. The net effect is always more thrust from the black side than if you hadn't mucked with trying to cool things down. The only way to have the black side cooler than T0 is to bring some coolant that has been cooled to below the CMBR temperature before the craft departs. That coolant will eventually run out, and then we're stuck. The thrust is zero once the black side's temperature reaches T0. The only way out is to take advantage of the fact that the net thrust will be in the direction of the reflective side so long as the vehicle still has power. It will need some power, a trickle charge to keep memory intact, a bit of power for computing where the vehicle is, a bit of power for keeping the vehicle pointing in the right direction. Of course, the power source will eventually run out, and once again we're stuck. 9. Aug 21, 2014 A.T. I assume that is just the initial thrust. As soon it starts moving, the incoming radiation stops being isotropic due to Doppler effect and aberration. 10. Aug 21, 2014 Helios The cosmic background radiation looks bluer to the bow of the ship and redder off the stern. It would seem that this anisotropy would effect things. 11. Aug 21, 2014 D H Staff Emeritus P/c is an incredibly small value. Even at Mr. Fusion levels (1.21 gigawatts), P/c amounts to a whopping 4 newtons. Presumably the spacecraft won't consume power at that rate. There are no garbage cans with which one could replenish Mr. Fusion in those voids in space. We need to be miserly with our power consumption to cross that void. Let's assume the spacecraft manufacturers have learned the art of miniaturization to a tee, and have also learned to minimize power consumption. If the vehicle uses 1 milliwatt of power per kilogram of spacecraft to keep things alive, perform computations, and control the vehicle, the tiny value of P/c means it will take 3 billion years to accelerate to 1/1000 of the speed of light. At that tiny speed, the anisotropy of the CMBR is a tiny, tiny drag on the vehicle. Here's the calculation of that 3 billion year figure at WolframAlpha: http://www.wolframalpha.com/input/?i=(0.001+c)/((1+milliwatt)/c/(1+kg)). Note that I've ignored drag from the dipole anisotropy of the CMBR. It's a very small amount of drag, and all that accounting for this will do is to make it take even longer than 3 billion years to reach 1/1000 of the speed of light. That exists, but it's even smaller than the minuscule acceleration described above. The Doppler shift is a rather small effect for a vehicle moving much, much slower than the speed of light. For smallish velocities (v<<c), this will result in a very, very small drag term that grows linearly with velocity. 12. Aug 22, 2014 256bits This is the wiki on Crookes radiometer, which may be of interest. Of special interest is that is will not rotate in pure vacuum, but it needs a certain amount of rarefied gas to make it spin. Under a partial vacuum, it spins shiny side leading when subjected to light or heat. When subjected to a cooler outside temperature, it spins black side leading. The explanation is that the rarefied gas provides the momentum transfer to produce the spinning. 13. Aug 22, 2014 sophiecentaur Those are my thoughts, too. There has to be a gradient (of 'something') out there to supply the power needed for propulsion. Any talk of on board refrigeration systems implies using an on board power source, so you no longer have free energy. 14. Aug 22, 2014 D H Staff Emeritus That's not applicable here because radiation pressure most certainly is a real effect. Just because the rotation of the Crooke's radiometer does not result from radiation pressure does not mean that radiation pressure doesn't exist. It most certainly does. It is the basis for solar sails, and this concept has been successfully demonstrated with the IKAROS mission.

2018-07-23 16:14:59

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https://tex.stackexchange.com/questions/416890/why-am-i-getting-infinite-recursion-here

Why am I getting infinite recursion here? I am using two different fonts for math mode as for my main text, so numbers in math mode and in the text do not match in font, which looks bad. Therefore, I want to change the font of only numbers in the text. I found a way to do this with this answer: https://tex.stackexchange.com/a/10266/127289 Here is my entire project, being compiled on Overleaf with XeTeX: \documentclass{article} \usepackage{fontspec} \XeTeXinterchartokenstate=1 \chardef\CharNormal=0 \makeatletter % Test for old and new versions of the latex kernel \ifx\e@alloc@intercharclass@top\@undefined \chardef\CharBound=255 \else \chardef\CharBound=\e@alloc@intercharclass@top \fi \makeatother \newXeTeXintercharclass\CharNumbers \XeTeXcharclass0=\CharNumbers \XeTeXcharclass1=\CharNumbers \XeTeXcharclass2=\CharNumbers \XeTeXcharclass3=\CharNumbers \XeTeXcharclass4=\CharNumbers \XeTeXcharclass5=\CharNumbers \XeTeXcharclass6=\CharNumbers \XeTeXcharclass7=\CharNumbers \XeTeXcharclass8=\CharNumbers \XeTeXcharclass9=\CharNumbers \newtoks\TokSetfont \TokSetfont={\begingroup\fontspec{Latin Modern Mono}} \XeTeXinterchartoks\CharNormal\CharNumbers=\TokSetfont \XeTeXinterchartoks\CharBound\CharNumbers=\TokSetfont \XeTeXinterchartoks\CharNumbers\CharNormal={\endgroup} \XeTeXinterchartoks\CharNumbers\CharBound={\endgroup} \begin{document} test test 12345 \end{document} However, this seems not to work. I keep getting the same error: TeX capacity exceeded, sorry [save size=80000]. Since my document is tiny, this is obviously some kind of recursion bug. The log file contains nothing particularly enlightening, to me. There is no repeating error message indicative of a recursion loop. However, if I change Latin Modern Mono to Arial, then I get this printed in the log file hundreds of times: ................................................. . fontspec info: "no-scripts" . . Font Arial does not contain any OpenType Script' information. ................................................. which suggests that the recursion may be happening in the call \TokSetfont={\begingroup\fontspec{Latin Modern Mono}}? Maybe not related. Does anyone have any insight into what is going on? Can someone else try to run this in some other environment and tell me the results? No one in the old question that I linked to seemed to be having any problem. The syntax of the fontspec command has changed. It can now have an optional argument behind the main argument and it runs into the loop while looking for it. With an empty optional argument or a \relax behind the code compiles again. \TokSetfont={\begingroup\fontspec{Latin Modern Mono}[]} But I would define a font family and use this: \documentclass{article} \usepackage{fontspec} \newfontfamily\numfontfam{Latin Modern Mono} \XeTeXinterchartokenstate=1 \chardef\CharNormal=0 \makeatletter % Test for old and new versions of the latex kernel \chardef\CharBound=\e@alloc@intercharclass@top \makeatother \newXeTeXintercharclass\CharNumbers \XeTeXcharclass0=\CharNumbers \XeTeXcharclass1=\CharNumbers \XeTeXcharclass2=\CharNumbers \XeTeXcharclass3=\CharNumbers \XeTeXcharclass4=\CharNumbers \XeTeXcharclass5=\CharNumbers \XeTeXcharclass6=\CharNumbers \XeTeXcharclass7=\CharNumbers \XeTeXcharclass8=\CharNumbers \XeTeXcharclass9=\CharNumbers \newtoks\TokSetfont \TokSetfont={\begingroup\numfontfam} \XeTeXinterchartoks\CharNormal\CharNumbers=\TokSetfont \XeTeXinterchartoks\CharBound\CharNumbers=\TokSetfont \XeTeXinterchartoks\CharNumbers\CharNormal={\endgroup} \XeTeXinterchartoks\CharNumbers\CharBound={\endgroup} \begin{document} test test 12345 \end{document} • This seems to override the font changes that should be applied by \texttt{} (numbers in string args passed to \texttt{} are rendered with Latin Modern Mono rather than Courier), which is a problem. Can this answer be amended to fix that? – Anonymous Mar 1 '18 at 20:23 • Ask a new question with an example. – Ulrike Fischer Mar 1 '18 at 20:34 • Nevermind, I just have to call wrap any call to texttt{} like so: \newfontfamily\numfontfam{Courier} \texttt{...} \newfontfamily\numfontfam{Latin Modern Mono}`... which is a bit of a pain but okay – Anonymous Mar 1 '18 at 20:54

2019-08-24 01:08:10

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http://www.perlmonks.org/?node=59446

Welcome to the Monastery PerlMonks ### Generating PDF on Feb 19, 2001 at 23:51 UTC ( #59446=perlquestion: print w/ replies, xml ) Need Help?? Anonymous Monk has asked for the wisdom of the Perl Monks concerning the following question: If there an easy way to generate PDF files on a Unix system using Perl and a CGI interface. I'd like to be able to read records from a database and generate a work order outputing it to the PDF format which can then be e-mailed to vendors. Is there a module for this? or some other pre-existing code?? Thanks. Comment on Generating PDF Re: Generating PDF by Hot Pastrami (Monk) on Feb 19, 2001 at 23:56 UTC Check out this module on CPAN: Text::PDF Hot Pastrami Although the original post is a few years old, I feel compelled to respond to it. Recently I had to develop a few dynamic PDFs from data in a database. After looking at the avaliable options (including writing out the pdf by hand - yuck), I found PDF::API2 to be the most useful. The biggest drawback I found to PDF::API2 was that the perldoc left much to be desired. Although it very much has the capabilities to go beyond "simple text" figuring out how to draw curves or use barcodes from the perldoc was difficult at best. If you use PDF::API2 I recommend using http://pdfapi2.sourceforge.net/twiki/ for documentation. Other than the documentation drawback, expect to spend about a half a day learning the API. Once you get the hang of it, its pretty easy and well done. Re: Generating PDF by Trinary (Pilgrim) on Feb 19, 2001 at 23:57 UTC A search on cpan turned up PDF::Create, which looks to me like your best bet. I have no idea how mature/usable this module is, but at thevery least it looks like a good place to start. Frankly, the README looks a lil confusing, but then again I know little about the internals of PDFs. Maybe a Postscript generator might be better, as far as I know the two formats are interchangeable through external converters (ps2pdf), and there seem to be a fair amount of decent Postscript modules out there. Trinary Re: Generating PDF by boo_radley (Parson) on Feb 19, 2001 at 23:57 UTC Magic 8 ball says "yes". specifically the PDF::create module may be what you're after. Re: Generating PDF by clintp (Curate) on Feb 20, 2001 at 01:48 UTC Okay, I've actually USED PDF::Create that others are suggesting and it's okay. In fact, this short program took some existing text and overlaid a grid on top of it to make nice column rules that the data lacked. #!/usr/bin/perl -w use strict; use PDF::Create; my $font; my$height=792; my $width=612; my$left=20; my $topmargin=20; my$pointsize=8; my $spacing=$pointsize+3; my($page,$fh)=@_; my $l=0; my$hpos=$height-$topmargin; while(<$fh>) {$page->stringl($font,$pointsize, $left,$hpos-=$spacing,$_); last if ++$l > 66; } } sub boxpage { my($page)=@_; $page->line($left, $topmargin,$left, $height-$topmargin, ); $page->line($left, $height-$topmargin, $width-$left, $height-$topmargin); $page->line($width-$left,$height-$topmargin,$width-$left,$topmargin); $page->line($width-$left,$topmargin, $left,$topmargin); $page->line($left+42, $topmargin,$left+42, $height-$topmargin); $page->line($left+81, $topmargin,$left+81, $height-$topmargin); $page->line($left+145, $topmargin,$left+145, $height-$topmargin); $page->line($left+183, $topmargin,$left+183, $height-$topmargin); } my $pdf=new PDF::Create('filename' => 'outfile.pdf', 'Version' => '1.2', 'Author' => 'Clinton Pierce', 'Title' => 'Test Report',); my$root=$pdf->new_page('MediaBox' => [ 0, 0, 612, 792 ]);$font=$pdf->font('Subtype' => 'Type1', 'Encoding' => 'WinAnsiEncoding', 'BaseFont' => 'Courier'); open(FH,$0) || die; while(not eof(FH)) { my $page=$root->new_page(); boxpage($page); addtext($page, \*FH); } $pdf->close; [download] Now the caveat is, there's not a whole lot PDF::Create can do. No colors. No bitmaps. Not much more than lines, circles and other polygons. No width control on the lines either. And PDF::Create hasn't been updated in a long, long time and I got a bounce from the e-mail address of the maintainer. But I got enough out of it for my needs... For anybody coming across this thread much much later, please note PDF::Create is being updated again with the most recent version 1.02 being released on 10 Jul 2008. CPAN Search - PDF::Create Re: Generating PDF by foogod (Friar) on Feb 20, 2001 at 06:16 UTC I completed a very similar project with a relational flat file database system, and used a third party program called PDFever (www.pdefever.de) that allowed much more flexibility, and integrated very well with my perl program. Also the creator of the program (Zhigang Li) is very helpful with PDF troubleshooting. For a hacker such as myself, programming for PDF (which IMHO is very obscure), it was a relief to find a program that allowed me lots of flexibility and very little time required to learn the PDF aspect. The Perl::CreatePDF mod is good, but I found the flexibility was lacking, and there was no support. (Just my 2 cents) Re: Generating PDF by jeroenes (Priest) on Feb 20, 2001 at 11:09 UTC Instead of directly writing PDFs, you also might want consider to write a TeX/LaTeX file, which easily can be converted to a pdf with LaTeX. If you're on gn*x, I would check out the tetex package (find it on freshmeat.net). The advantage of such an approach is, that you can have quite high-level control (ie, just write your text). However, learning about all the handy packages can take quite a while. A sample perl script might be something like this: #get the data first$a = <DATA>; chomp $a;$b = <DATA>; chomp $b; open TEX, ">file.tex" or die "Could not open file.tex"; print TEX <<'_END'; \documentclass{article} \begin{document} \title{TeX-report} \author{Me} \maketitle \section{Some data} _END print TEX "I have$a and \$b. That's all for now.\n"; print TEX <<'_END'; \section{Some table} \begin{table} \caption{A table} \begin[|l|c|c|]{tabular} \hline _END while(<DATA>){ chomp; print TEX join('&', split ).'\\ \hline'."\n"; } print TEX <<'_END'; \end{tabular} \end{table} \end{document} _END system("latex file.tex"); system("latex file.tex"); system("dvipdf file") if -e "file.dvi"; __DATA__ 129873 12315 1 8 2 1 3 100 8 3 4 [download] Here I'm also using the dvipdf package, (freshmeat.net), but you could use 'dvips file -o' and 'ps2pdf file.ps' as well. Perl code is checked. I'm using TeX daily, so you always can /msg me with further questions. Hope this helps, Jeroen "We are not alone"(FZ) Another option might be to generate XSL:FO, which can be converted into PDF by e.g. FOP (c/o http://xml.apache.org/); this is an XML dialect, so you can actually just output XML and use an XSL:Transform stylesheet to convert the same XML into HTML, WML, or XSL:FO (for conversion to PDF)... Big points for Laziness :-) Re: Generating PDF by Beatnik (Parson) on Apr 30, 2001 at 19:08 UTC Image::Magick also has PDF support but it's not superb (it is, after all, an image manipulation program). It basically rasterizes the layers, outputting pages with a single image, breaking the search features & fancy layers. Greetz Beatnik ... Quidquid perl dictum sit, altum viditur. Create A New User Node Status? node history Node Type: perlquestion [id://59446] Approved by root help Chatterbox? and the web crawler heard nothing... How do I use this? | Other CB clients Other Users? Others surveying the Monastery: (4) As of 2013-05-25 21:59 GMT Sections? 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2013-05-25 22:00:38

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https://www.nature.com/articles/s41586-020-2051-0?error=cookies_not_supported&code=8d3eed6b-99c7-4a28-80aa-435314f66992

# Nagaoka ferromagnetism observed in a quantum dot plaquette ## Abstract Engineered, highly controllable quantum systems are promising simulators of emergent physics beyond the simulation capabilities of classical computers1. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been debated for decades2,3. Here we use a quantum simulator consisting of a four-electron-site square plaquette of quantum dots4 to demonstrate Nagaoka ferromagnetism5. This form of itinerant magnetism has been rigorously studied theoretically6,7,8,9 but has remained unattainable in experiments. We load the plaquette with three electrons and demonstrate the predicted emergence of spontaneous ferromagnetic correlations through pairwise measurements of spin. We find that the ferromagnetic ground state is remarkably robust to engineered disorder in the on-site potentials and we can induce a transition to the low-spin state by changing the plaquette topology to an open chain. This demonstration of Nagaoka ferromagnetism highlights that quantum simulators can be used to study physical phenomena that have not yet been observed in any experimental system. The work also constitutes an important step towards large-scale quantum dot simulators of correlated electron systems. ## Access options from\$8.99 All prices are NET prices. ## Data availability The datasets obtained from the measurements described in this work are available in the repository Zenodo with the identifier https://doi.org/10.5281/zenodo.3258940. ## Code availability The code used to plot the datasets and implement the models used to reproduce all the figures in the main manuscript is available in the repository Zenodo with the identifier https://doi.org/10.5281/zenodo.3258940. ## References 1. 1. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982). 2. 2. Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1994). 3. 3. Mattis, D. C. The Theory of Magnetism Made Simple (World Scientific, 2006). 4. 4. Mukhopadhyay, U., Dehollain, J. P., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. A 2 × 2 quantum dot array with controllable inter-dot tunnel couplings. Appl. Phys. Lett. 112, 183505 (2018). 5. 5. Nagaoka, Y. Ferromagnetism in a narrow, almost half-filled s band. Phys. Rev. 147, 392–405 (1966). 6. 6. Mattis, D. C. Eigenvalues and magnetism of electrons on an artificial molecule. Int. J. Nanosci. 02, 165–170 (2003). 7. 7. Nielsen, E. & Bhatt, R. N. Nanoscale ferromagnetism in nonmagnetic doped semiconductors. Phys. Rev. B 76, 161202(R) (2007). 8. 8. Oguri, A., Nisikawa, Y., Tanaka, Y. & Numata, T. Kondo screening of a high-spin Nagaoka state in a triangular quantum dot. J. Magn. Magn. Mater. 310, 1139–1141 (2007). 9. 9. von Stecher, J., Demler, E., Lukin, M. D. & Rey, A. M. Probing interaction-induced ferromagnetism in optical superlattices. New J. Phys. 12, 055009 (2010). 10. 10. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014). 11. 11. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008). 12. 12. Nascimbène, S. et al. Experimental realization of plaquette resonating valence-bond states with ultracold atoms in optical superlattices. Phys. Rev. Lett. 108, 205301 (2012). 13. 13. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012). 14. 14. Dai, H.-N. et al. Four-body ring-exchange interactions and anyonic statistics within a minimal toric-code Hamiltonian. Nat. Phys. 13, 1195–1200 (2017). 15. 15. Görg, F. et al. Enhancement and sign change of magnetic correlations in a driven quantum many-body system. Nature 553, 481–485 (2018). 16. 16. Salomon, G. et al. Direct observation of incommensurate magnetism in Hubbard chains. Nature 565, 56–60 (2019); correction 566, E5 (2019). 17. 17. Nichols, M. A. et al. Spin transport in a Mott insulator of ultracold fermions. Science 363, 383–387 (2019). 18. 18. Singha, A. et al. Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice. Science 332, 1176–1179 (2011). 19. 19. Salfi, J. et al. Quantum simulation of the Hubbard model with dopant atoms in silicon. Nat. Commun. 7, 11342 (2016). 20. 20. Barends, R. et al. Digital quantum simulation of fermionic models with a superconducting circuit. Nat. Commun. 6, 7654 (2015). 21. 21. Martinez, E. A. et al. Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature 534, 516–519 (2016). 22. 22. Kouwenhoven, L. P., Austing, D. G. & Tarucha, S. Few-electron quantum dots. Rep. Prog. Phys. 64, 701–736 (2001). 23. 23. van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1–22 (2002). 24. 24. Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007). 25. 25. Manousakis, E. A quantum-dot array as model for copper-oxide superconductors: a dedicated quantum simulator for the many-fermion problem. J. Low Temp. Phys. 126, 1501–1513 (2002). 26. 26. Byrnes, T., Kim, N. Y., Kusudo, K. & Yamamoto, Y. Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays. Phys. Rev. B 78, 075320 (2008). 27. 27. Barthelemy, P. & Vandersypen, L. M. K. Quantum dot systems: a versatile platform for quantum simulations. Ann. Phys. 525, 808–826 (2013). 28. 28. Hensgens, T. et al. Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array. Nature 548, 70–73 (2017). 29. 29. Thalineau, R. et al. A few-electron quadruple quantum dot in a closed loop. Appl. Phys. Lett. 101, 103102 (2012). 30. 30. Seo, M. et al. Charge frustration in a triangular triple quantum dot. Phys. Rev. Lett. 110, 046803 (2013). 31. 31. Noiri, A. et al. A triangular triple quantum dot with tunable tunnel couplings. Semicond. Sci. Technol. 32, 084004 (2017). 32. 32. Mortemousque, P.-A. et al. Coherent control of individual electron spins in a two dimensional array of quantum dots. Preprint at http://arxiv.org/abs/1808.06180v1 (2018). 33. 33. Scalapino, D. J. The case for $${d}_{{x}^{2}-{y}^{2}}$$ pairing in the cuprate superconductors. Phys. Rev. 250, 329–365 (1995). 34. 34. Tsuei, C. C. & Kirtley, J. R. Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000). 35. 35. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010). 36. 36. Tasaki, H. From Nagaoka’s ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model. Prog. Theor. Phys. 99, 489–548 (1998). 37. 37. Thouless, D. J. Exchange in solid 3He and the Heisenberg Hamiltonian. Planet. Space Sci. 86, 893–904 (1965). 38. 38. Hubbard, J. Electron correlations in narrow energy bands. Proc. R. Soc. A 276, 238–257 (1963). 39. 39. Lieb, E. & Mattis, D. Theory of ferromagnetism and the ordering of electronic energy levels. Phys. Rev. 125, 164–172 (1962). 40. 40. Wang, Y. et al. Ab initio exact diagonalization simulation of the Nagaoka transition in quantum dots. Phys. Rev. B 100, 155133 (2019). 41. 41. van der Wiel, W. G., Stopa, M., Kodera, T., Hatano, T. & Tarucha, S. Semiconductor quantum dots for electron spin qubits. New J. Phys. 8, 28 (2006). 42. 42. Khaetskii, A. V., Loss, D. & Glazman, L. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. 88, 186802 (2002). 43. 43. Merkulov, I. A., Efros, A. L. & Rosen, M. Electron spin relaxation by nuclei in semiconductor quantum dots. Phys. Rev. B 65, 205309 (2002). 44. 44. Chekhovich, E. A. et al. Nuclear spin effects in semiconductor quantum dots. Nat. Mater. 12, 494–504 (2013). 45. 45. Petta, J. R. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005). 46. 46. Koppens, F. H. L. Control and detection of singlet-triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005). 47. 47. Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959). 48. 48. Nowack, K. C., Koppens, F. H. L., Nazarov, Y. V. & Vandersypen, L. M. K. Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007). 49. 49. Malinowski, F. K. et al. Spin of a multielectron quantum dot and its interaction with a neighboring electron. Phys. Rev. X 8, 011045 (2018). ## Acknowledgements We acknowledge input and discussions with M. Chan, S. Philips, Y. Nazarov, F. Liu, L. Janssen, T. Hensgens, T. Fujita and all of the Vandersypen team, as well as experimental support by L. Blom, C. van Diepen, P. Eendebak, F. van Riggelen, R. Schouten, R. Vermeulen, R. van Ooijik, H. van der Does, M. Ammerlaan, J. Haanstra, S. Visser and R. Roeleveld. L.M.K.V. thanks the NSF-funded MIT-Harvard Center for Ultracold Atoms for its hospitality. This work was supported by grants from the Netherlands Organisation for Scientific Research (FOM projectruimte and NWO Vici) (J.P.D., U.M., L.M.K.V.), the European Research Council (ERC-Synergy) (V.P.M., L.M.K.V.), the Postdoctoral Fellowship in Quantum Science of the Harvard-MPQ Center for Quantum Optics and AFOSR-MURI Quantum Phases of Matter (grant number FA9550-14-1-0035) (Y.W.), the Swiss National Science Foundation (C.R., W.W.) and The Villum Foundation (M.S.R.). ## Author information B.W., M.S.R., E.D. and L.M.K.V. had equal contribution in conceptualization. Experimental investigation and methodology was performed with equal contribution from J.P.D. and U.M. Theoretical investigation was led by J.P.D., V.P.M. and B.W. (extended Hubbard models), and Y.W. (ab initio model). J.P.D. led the data curation and software, with support from U.M. and V.P.M. J.P.D. and U.M. had equal contribution in the formal analysis, with support from V.P.M. L.M.K.V. led the funding acquisition and supervision. U.M. led the resources (device fabrication) with support from J.P.D. C.R. and W.W. led the resources (heterostructure growth). J.P.D. led the writing—original draft, with review and editing support from U.M., V.P.M., Y.W., M.S.R., E.D. and L.M.K.V. Please refer to the Casrai Credit Taxonomy for definitions of each of these roles. Correspondence to L. M. K. Vandersypen. ## Ethics declarations ### Competing interests The authors declare no competing interests. Peer review information Nature thanks Joe Salfi, Igor Zutic and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## Extended data figures and tables ### Extended Data Fig. 1 Charge stability diagram of the relevant voltage regions. a, Measured charge stability diagram showing both point N and point M, as highlighted in Fig. 2a. b, Measured charge stability diagram focusing on the 2001:1101 charge transition, where spin measurements are performed (point M). ### Extended Data Fig. 2 Tuning the gate voltages to the Nagaoka condition using charge stability diagrams. a, Sample charge stability diagram where we have highlighted the visible interdot transitions, where the electrochemical potentials of two dots become resonant (that is, an electron is allowed to tunnel between the two dots). b, Charge stability diagram similar to a, where we have modified gates P1 and P3 such that the interdot transitions appear at different locations in the diagram. Dashed black lines delimit the regions with a fixed total electron occupation in the system. c, In this diagram, gates P1 and P3 have been tuned to observe the Nagaoka condition, where the three visible interdot transitions are aligned in the three-electron configuration. The intersite interaction in the system provides an effective isolation from the reservoirs for a narrow range of gate voltages, such that the system can remain stable with three electrons in the resonant configuration. ### Extended Data Fig. 3 Effects of spin-coupling mechanisms. Calculated spectra of the system in the region of pε close to the level crossing of the s = 1/2 and s = 3/2 energies, comparing the effects of different mechanisms for spin coupling. a, Spectrum without any spin coupling effects. b, Spectrum including only spin–orbit coupling (SOC) effects. c, Sample spectrum with both spin–orbit and hyperfine induced Overhauser field gradients, using a single combination of hNa fields (as defined in the Supplementary Methods) selected from a normal distribution with standard deviation δN = 73 neV. The Supplementary Methods describe the implementations of these spin-coupling terms in the theoretical model. ### Extended Data Fig. 4 Characterization of the Nagaoka condition. a, Average PT in the detuning region 1.00 < pε < 1.01 for 40 values of τramp within the same range shown in Fig. 3. Solid lines are fits using the time evolution simulations described in the Supplementary Methods, for different values of distance $$\ell$$ between neighbouring dots. Inset shows the unscaled results of the time-evolution simulations, where the probability of s = 3/2 is the sum of the lowest four eigenstate probabilities from the final evolved state. b, Thermal relaxation measurements. PT is measured for increasing wait times at point N, for diabatic (blue) and adiabatic (red) passages. Solid lines are exponential fits as guide to the eye. ### Extended Data Fig. 5 Ab initio simulations from 2D to 1D. a, Schematic of the methodology used in the ab initio simulations to reproduce the effect of the four-dot system transition from a 2D plaquette to a 1D chain. We gradually vary the angle θ, which effectively varies the distance between two of the dots. b, c, The ground-state energy and spin configuration (b) and the ferromagnetic to low-spin energy gap ΔE as a function of θ (c). The ground state soon becomes a low-spin state for the rotating angle at 0.3°. ### Extended Data Fig. 6 Ab initio simulations for local energy offsets. a, Schematic of the methodology used in the ab initio simulations to reproduce the effect of a local energy offset. The amplitude of the potential V of one of the quantum wells is changed by an amount dV. The variation of the single-well potential by positive or negative dV gives unbalanced site energies. Besides, with the change of eigenstate basis, the hybridization and interaction parameters are also affected in the ab initio calculation. b, c, The ground-state energy and spin configuration (b) and the ferromagnetic to low-spin energy gap ΔE as a function of dV (c). When the potential detuning is dV = 0.11 meV or dV = −0.07 meV, the system undergoes a transition to a low-spin ground state. The transitions at these two directions have a different nature, as drawn in the insets. For dV > 0, the particular quantum dot is deeper and tends to trap more electrons. However, a negative dV raises the energy cost on the particular quantum well and leads to a lower probability of occupation in a three-electron system. Without the ‘mobile’ hole in the ‘half-filled’ system, the ground state becomes a low-spin state instead of a Nagaoka ferromagnetic state. ### Extended Data Fig. 7 Local energy offsets on all dots. Same measurement as in Fig. 6, applying the ±50 μeV offset on each of the four dots. Panels correspond to offsets in dots 1 to 4, clockwise from the top left. Note that the asymmetry in the plots is related to the fact that the local energies at point M are in an asymmetric detuning configuration and we pulse linearly from this configuration to point N. As expected, the simulated energies of the different spin states at point N (pε = 1), are the same in all four plots. ### Extended Data Fig. 8 Large local offsets. Each pair of panels show experimental measurements (left) and simulated spectra (right), where point N has been redefined such that the chemical potential of dot 1 is offset by the amount shown on the top right of each panel. Green crosses highlight the detuning points used to obtain the values in Fig. 6b. For experimental plots, these points where obtained using a peak-finding algorithm (local maxima by simple comparison with neighbouring values); for simulated plots, the points correspond to the energy-level crossings. ## Supplementary information ### Supplementary Information This file contains Extended Fermi-Hubbard models used to simulate different experiments in the main text, Ab initio exact diagonalisation simulations of the 2×2 plaquette and Mapping 3-spin states onto 2-spin measurements. ## Rights and permissions Reprints and Permissions Dehollain, J.P., Mukhopadhyay, U., Michal, V.P. et al. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 579, 528–533 (2020). https://doi.org/10.1038/s41586-020-2051-0 • Accepted: • Published: • Issue Date: • ### Discrete time crystal in the gradient-field Heisenberg model • Bikun Li • , John S. Van Dyke

2020-03-30 20:59:51

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http://www.kapitalust.com/dumb-money-decisions-revisited/

Dumb Money Decisions Revisited So after my post on how dumb it was to play the lottery, a reader emailed me to be more concise with what I meant by “statistically fair shot of winning.” This guy must be a smarty pants because he broke down the math for me. He provided the specific odds of winning the 6/49 lottery. I haz the best readerz on the internetz! Who is this reader? His name is Eytan. And how does Eytan claim to know all this? He’s an engineer for SkyPro and he, along with his team, created and developed this golfing product that they sell all over North America. I’m going to go out on a limb and guess that he is really, really good at math and knows what he is talking about. This might be a bit of a snooze fest for those of you not interested in the details of the probability of winning a 1 in 13,983,816 game of chance, so I would suggest you go peruse 15 beautiful pictures instead. Or if you feel like exerting a modicum of brain power, go browse these 10 essential blogging tips for getting more out of your blog. If you don’t follow my advice, you might risk going all ZzzzZZZZz at work over there. Yes, I know you’re wasting spending time here instead of working! I promise I won’t tell your boss. However, IF you are interested in how the detailed probability of playing the 6/49 works, read on! I’m just going to copy and paste the email Eytan sent in so as not to fuck up mess up any of the equations he so succinctly laid out. He even put it up on his personal website here. Take it away Eytan! Hey Steve, I love the articles. I’ve started reading them. One article I recommend you touch up is the lottery article. The math doesn’t quite add and might lead to readers losing confidence. Remember the official odds? 1 in 13,983,816. Statistically speaking, you need to play 13,983,816 times to have a statistically fair shot at winning. I found this statement a bit vague; what does a statistically fair shot at winning mean? I took it to mean you need to play 13,983,816 times to have a 50% chance of winning. If this is what you meant, lets take a closer look at the math and see what we can figure out about the odds of winning Canada’s 6/49. Lets start by defining some notation. Specifically, we’ll say that p(n) is the odds of winning the lottery at least once after n plays. The odds of winning the lottery for one game is p(1) = 1/13,983,816. If we played the lottery once, there are only two possible outcomes: win or lose. If you played the lottery twice, there would be four possible outcomes: lose.lose, lose.win, win.lose, and win.win. If we play 10 times, there are 1024 possible outcomes. If wanted to calculate the odds of winning, we’d have to add every single one of those up. Lets examine the case when we play the lotery twice. As previously mentioned, we have four outcomes and they each having the following odds: The odds of winning after n plays, p(n) is thus given byAs we play more and more games, the different combinations in which we can win increases, but there remains only a single way to lose. Since the sum of all probabilities is equal to one, we can subtract the odds of losing from one to leave us with the odds of winning. Now, we are in a position to find out how many times you’d have to play in order to have a 50% chance of winning. We substitute 0.5 for p(n) in the above equation and solve for n. Wow, that’s a lot of plays. With that in mind, we can clarify the sentence by saying: Remember the official odds? 1 in 13,983,816. Statistically speaking, you need to play 9,692,843 times to have a 50% of winning at least once. CONCLUSIONS Well, looks like Eytan is about to put me out of the personal finance blogging business. I should just give him the keys to Kapitalust and pack it up. At this pace, it looks like he could out-math anyone in this blogging niche. It’s a good thing he’s not interested in that (or if he is I choose to ignore him). All jokes aside, I am amazed that a reader would take the time to break down the probability like this and email me about it. I think it’s incredible. And I had to share it with all of you (who stuck around rather than moving on to look at pretty pictures). The lesson I have learned: be less vague with my statements with readers like Eytan around. Like what you’re reading? It’s time you join the legion of other Kapitalusts! No spam. No ham. No nonsense. Subscribe to receive every new post (and future exclusive offers) via email. It’s super easy to unsubscribe if it ain’t for you! [mc4wp_form] 27 thoughts on “Dumb Money Decisions Revisited” 1. Ugh, probability. I never took a proper probability course, but I did take it as applied to chemistry (chemometrics), so I know a thing or two about it. And I have to admit I’ve never been keen enough to fully write out and correct someone’s math/calculations in long form 🙂 So I think that means you have dedicated readers… good job! 1. Haha I think Eytan just really, really likes math. Kinda like how we PF bloggers really, really like investing or budgeting or what have you. I tuned out of most Grade 12 math but probability was one where I really paid attention and loved. Probably because I could see real life applicability of the math. 2. Now I know why I always failed at probability calculations in high school… They don’t make any sense in my head! I’m glad there are people around like Eytan who can do the math for us. 🙂 1. Probability was the only section in late high school math that I grasped and understood – I tuned out of everything else…. which led to me almost failing the final exam. Oh, young teenage Steve, so interested in everything beyond academics! 1. I hear ya Steve! I think probability is the only part of grade 12 math I did decent in, pretty sure I borderline failed everything else. I blame my grade 10 math teacher for making me hate math lol. I remember in University Economics using grade 11 algebra and getting super excited that I was actually using highschool math for something. 1. Haha they totally need to re-imagine how to teach math to kids. It’s such a fail of a model to stand there and lecture kids about dry equations and theory – what kid wants to sit through that BS (except maybe Eytan?) 😛 They need to make it applicable and show how it could actually be used in the real world. Remember that scene in Road Trip at the end when the guy needs to study for a history exam and his friend uses examples from the WWF to make it more applicable and understandable for the guy? THAT’S what needs to happen with a lot of how school works and teaches kids! 2. Haha, for me it was definitely the other way around. Geometry and algebra all day every day! 1. Those weren’t bad, but don’t get me started on trigonometry! Maybe my math teacher just didn’t give good real life examples on how trig applied to real life 😛 3. PC says: I hardly play the lottery myself… I only buy tickets if the jackpot is really, really big! Maybe in some odd chance, I’ll get lucky! I’ve bought local home lotteries for charities before, never won a single thing… the chances were greater too. It’s not my destiny to win 🙁 1. The only people destined to win the lottery are…….. ………. the people who own and run the lottery companies 😛 A lottery corporation would be my DREAM company to own and run – a ham sandwich could run it and rake in millions and millions of profits! 4. I was just lamenting the other day that I don’t get many reader emails. Perhaps I should count my blessings. 1. Haha as long as you have thick enough skin to take constructive criticism with stride, it can be a bit intimidating when someone points out weakness 😛 5. Well, is he talking about playing within the same lottery multiple tickets? I would almost argue that separate lottery plays are separate events because the winning number changes and playing more may not change the odds. That is because the winning numbers one week are more than likely not going to be the winning numbers the following week. It is not like the normal heads-tails type of odds, you have another variable – that is what numbers actually win. 1. This is what I thought to, but Eytan explained that probability can seem “counter-intuitive” and that it is a false notion to hold that the odds “reset” after each play. 2. Eytan says: Very observant, Kipp! Separate lottery plays are in fact separate events. Each week when you play the lottery with a single ticket, your odds of winning is always 1 in 13,983,816, regardless of the numbers you choose. However, interesting things start to happen when you consider these events in the aggregate. To borrow your example of flipping a coin, the odds of flipping a head is 50/50, but the odds of flipping a sequence of heads gets smaller and smaller with each successive head. 6. Oh geez. Glad someone can do this math for us :). Ok, I can now feel even more secure in my decision not to ever buy lotto tickets. All jest aside, I do appreciate a good deep dive on a topic. 1. Haha I know the feeling because I would have to brush up on the ol’ high school math textbook to break down the probability like that 😛 And I agree that it is good to dive deep into a topic every now and then. 1. Just to clarify, this doesn’t mean you should NEVER play the lottery, it just means you shouldn’t play when you real return would be less that $13,983,000. If the prize was 100,000,000 and the odds were 1:14,000,000, I’d be buying a heck of a lot of tickets. The problem is that large prizes attract large crowds, which I suspect works as a kind of arbitrage to prevent highly profitable lottery situations from occuring. 1. In any game of chance, if the odds start heavily favouring you should bet hard and go with the odds. Like for a professional blackjack player who waits and waits counting the cards until they know that they are in a position to bet hard with the cards favouring their odds. However, those kinds of situations are very rare because the people running these games of chance want to win money, not lose 😀 7. I remember taking probability courses during university. I never liked those courses for some reason lol. 1. I was just saying above that I LOVED probability in upper high school math because the math and equations were actually something I saw applicable in the real world. Haha but I don’t actually remember any of it 😛 8. I think the risk of spending close to$10 million to earn $100 million is pretty good. 50/50 chance right? Just spend$20 million and you might win both times! 1. If the rewards are sufficiently high, like in your example, I think that could make sense. However, the odds are to this particular lottery in Canada and the maximum the jackpot can ever reach is $50 million. And it is fairly rare that it ever gets that high. The lottery ticket for the 6/49 costs$3 to get a single play. So $3 X 9,692,843 =$29 million. You’d have to spend \$29 million to have a 50/50 chance of winning this particular lottery. All of a sudden, it doesn’t seem so simple to game the system… Hmmmm… I wonder if Eytan would have the answer for this question??? 2. Eytan says: Hi Henry, As my article showed, you’d need to play around 9.6 million times in order to have a 50% chance of winning the 6/49. Checking the Lotto 6/49 website, they list jackpots starting at five million dollars and an individual ticket at three dollars. This means you’d have to spend nearly 30 million dollars in order to have a 50% chance of winning five million dollars. Not to complicate things, but another scenario would be to purchase multiple tickets. If you only wanted to play once and have a 50% chance of winning the Lotto 6/49, you’d need to purchase approximately seven million tickets. These seven million tickets would be valued at 21 million dollars and the jackpot is five million. 1. That’s good to know that one cannot guarantee winning the lottery unless every single ticket is bought – which is impossible in a public lottery. It takes a lot of money to (21 million or 30 million) to even have a shot at 50% in this particular lottery. I think I’d rather take those millions and invest in something that’s a little more of a sure thing 😛 9. Mmmmmmm. Delicious math. I love it. That is all. These posts make me feel slightly less weird for saying things like “but n equals one!” in conversation. Those conversations are usually limited to my spouse, because most people look at me funny when I say stuff like that. 1. Haha you need to chat with Alicia, Tawcan, and Eytan more often about complex math equations 😛

2019-05-26 07:27:01

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https://zbmath.org/?q=ci%3A3947708

## Found 8 Documents (Results 1–8) 100 MathJax ### Extending the Knops-Stuart-Taheri technique to $$C^1$$ weak local minimizers in nonlinear elasticity. (English)Zbl 1215.49012 MSC:  49J40 49N60 74G30 Full Text: Full Text: ### Uniqueness of equilibrium solutions in second-order gradient nonlinear elasticity. (English)Zbl 1058.74021 MSC:  74B20 74G30 35Q72 35J55 Full Text: ### Quasiconvexity and uniqueness of stationary points in the multi-dimensional calculus of variations. (English)Zbl 1036.49024 MSC:  49J45 49J10 58E05 Full Text: ### Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains. (English)Zbl 0960.35035 MSC:  35J65 35J55 35J25 35A05 Full Text: ### Implications of rank one convexity. (English)Zbl 0664.73006 Reviewer: J.Lovíšek MSC:  74B20 74S30 74G30 74H25 49J45 Full Text: ### The breadth and depth of continuum mechanics. A collection of papers dedicated to J. L. Ericksen on his sixtieth birthday. Repr. from ’Archive for Rational Mechanics and Analysis’, ed. by C. Truesdell and J. Serrin. (English)Zbl 0619.73001 Berlin etc.: Springer-Verlag. XI, 778 p. DM 120.00 (1986). ### Special problems involving uniqueness and multiplicity in hyperelasticity. (English)Zbl 0617.73017 Nonlinear functional analysis and its applications, Proc. NATO Adv. Study Inst., Maratea/Italy 1985, NATO ASI Ser., Ser. C 173, 131-145 (1986). Reviewer: R.J.Knops all top 5 all top 3

2022-08-12 00:41:05

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https://tex.stackexchange.com/questions/325873/longtable-dimensions-not-appearing?noredirect=1

# Longtable dimensions not appearing I have the following packages loaded: \usepackage[]{multirow} \usepackage{longtable} \usepackage{csquotes} \usepackage{tabulary} \usepackage{array} \newcolumntype{L}{>{\centering\arraybackslash}m{3cm}} \usepackage{booktabs,dcolumn,caption} \captionsetup{labelsep=newline,singlelinecheck=false} % optional \newcolumntype{d}[1]{D{.}{.}{#1}} % "decimal" column type \renewcommand{\ast}{{}^{\textstyle *}} % for raised "asterisks" And within my document have: \begin{table}[!ht] \centering \begin{longtable}{|L|c|L|}\hline \textbf{Example Sentence} & \textbf{Category} & \textbf{Explanation} \\\hline \multicolumn{1}{|m{3cm}|}{We send the EU £350m a week} & \multicolumn{1}{|m{3cm}|}{Use a real number, but change its meaning to be in the wrong context }& \multicolumn{1}{m{3cm}|}{This is a true National Statistic but it “is not an amount of money that the UK pays to the EU”. In fact, the UK’s net contribution is more like £250m a week which equates to £136m. } \\\hline \multicolumn{1}{|m{3cm}|}{Potential cost of leaving the EU as £4,300 per household per year, rather than as the equivalent £120bn for the whole country} & \multicolumn{1}{|m{3cm}|}{Make the number look big (but not too big)}& \multicolumn{1}{m{3cm}|}{Insert text} \\\hline \end{longtable} \end{table} Altered from this source. I have a few issues: 1. At the moment, everything is centre aligned and so the text contains too much spacing instead of being left aligned and tight 2. I want to make the whole table wrap to its contents. At the moment I limit everything on a per column basis to 3cm but actually I want to limit the whole table to be at max the width of my page (if that is a variable somewhere?) and autowrap. 3. My table doesn't spill over the page as I thought longtable would do. If I remove the table wrapping in the longtable I cannot specify [!ht] so my table would appear on some random part of the page. How do I solve this? • as others have said you should never put longtable in a table. But also [!ht] isn't usually a good option to use for tables, it prevents the float being put on a float or bottom of a page (as no b or p) so makes it far more likely that the float can not be placed and drifts to the end of the document, and ! means that the typographic constraints set by the document class are ignored, which presumably typically makes worse output – David Carlisle Aug 21 '16 at 21:55 At the moment, everything is centre aligned and so the text contains too much spacing instead of being left aligned and tight This claim is incorrect. You do specify the L column type (which you've defined to center-set its contents), but then you override this setting via \multicolumn{1}{|m{3cm}|}{...} wrappers. The m column type fully justifies its contents. What one sees in your screenshot is not centered text but fully justified text with large "holes" between lots of words. To get ragged-right formatting, either use \multicolumn{1}{|>{\raggedright\arraybackslash}m{3cm}|}{...} wrappers or remove the wrappers entirely and replace \centering with \raggedright in the definition of the L column type. ...I want to limit the whole table to be at max the width of my page (if that is a variable somewhere?) and autowrap Have you looked into the ltxtable environment? Use it in conjunction with longtable environments. My table doesn't spill over the page as I thought longtable would do. If I remove the table wrapping in the longtable I cannot specify [!ht] so my table would appear on some random part of the page. The premise that longtable is a floating environment is false. It is not. The reason why [ht!] has no effect when applied to a longtable is that a longtable always starts right where it's encountered in the input stream. Thus: Never encase a longtable inside a table. Never, ever. No way, no how. Here's how I would re-work your code. Note that I've re-organized the material inside the longtable to distinguish more clearly between header, footer, and body of the table. I've also gotten rid of all vertical lines. \documentclass{article} \usepackage{longtable,array,ragged2e} \newcolumntype{L}{>{\RaggedRight\arraybackslash}p{3.75cm}} \usepackage{booktabs,caption} \captionsetup{labelsep=newline,singlelinecheck=false} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[british]{babel} \begin{document} \begin{longtable}{@{}LLL@{}} \toprule \textbf{Example Sentence} & \textbf{Category} & \textbf{Explanation}\\ \midrule \bottomrule \endlastfoot We send the EU £350m a week & Use a real number, but change its meaning to be in the wrong context& This is a true National Statistic but it is not an amount of money that the UK pays to the EU''. In fact, the UK's net contribution is more like £250m a week which equates to £136m.\\ \midrule Potential cost of leaving the EU as £4,300 per household per year, rather than as the equivalent £120bn for the whole country & Make the number look big (but not too big)& Insert text\\ \end{longtable} \end{document} • How do I make it so the third column is slightly wider than the others as it is likely to be the longest? – Dhruv Ghulati Aug 22 '16 at 21:46 • @DhruvGhulati - Let's assume you still want the sum of the three column widths to be 11.25cm. First, change the definition of the L column type to take a parameter: \newcolumntype{L}[1]{>{\RaggedRight\arraybackslash}p{#1}}. Second, start the longtable as follows, say: \begin{longtable}{@{}L{3.5cm}L{3.5cm}L{4.25cm}@{}}. – Mico Aug 22 '16 at 22:31 • Hi @Mico, this may benefit other readers, but I added \caption{The caption of the table} \label{table:somename} just above \toprule but am now getting a compilation error. I want a caption to appear on top of the table. – Dhruv Ghulati Aug 23 '16 at 14:55 • @DhruvGhulati - Did you place a double backslash (line break directive) after\caption? – Mico Aug 23 '16 at 15:28 • @DhruvGhulati - So, indeed, your code is missing a line-break directive after \caption and \label (and before \toprule). – Mico Aug 23 '16 at 16:04 A longtable is not a float, so you must not use the table environment. I propose two solutions, based on ltablex, which brings the functionalities of longtable to tabularx. One solution use vertical and horizontal lines, the other uses the rules from booktabs, without vertical lines: \documentclass{article} \usepackage[utf8]{inputenc} % \usepackage[T1]{fontenc} % \usepackage{geometry}% \usepackage{array,ltablex, makecell}% \setcellgapes{4pt} \usepackage{multirow} \usepackage{csquotes} \usepackage{tabulary} \usepackage{ragged2e} \usepackage{array} \usepackage{booktabs,dcolumn,caption} \captionsetup{labelsep=newline,singlelinecheck=false} % optional \newcolumntype{d}[1]{D{.}{.}{#1}} % "decimal" column type \renewcommand{\ast}{{}^{\textstyle *}} % for raised "asterisks" \usepackage{showframe} \renewcommand\ShowFrameLinethickness{0.2pt} \begin{document} \centering\keepXColumns \makegapedcells \begin{tabularx}{\linewidth}{|*{3}{ >{\RaggedRight\arraybackslash}X|}}% \hline % \hline We send the EU £\,350\,m a week & Use a real number, but change its meaning to be in the wrong context & This is a true National Statistic but it “is not an amount of money that the UK pays to the EU”. In fact, the UK’s net contribution is more like £\,250\,m a week which equates to £\,136\,m. \\% \hline Potential cost of leaving the EU as £\,4,300 per household per year, rather than as the equivalent £\,120\,bn for the whole country & Make the number look big (but not too big) & Insert text \\% \hline \end{tabularx}% \vskip1cm \begin{tabularx}{\linewidth}{*{3}{ >{\RaggedRight\arraybackslash}X}}% \toprule % \midrule We send the EU £\,350\,m a week & Use a real number, but change its meaning to be in the wrong context & This is a true National Statistic but it “is not an amount of money that the UK pays to the EU”. In fact, the UK’s net contribution is more like £\,250\,m a week which equates to £\,136\,m. \\% Potential cost of leaving the EU as £\,4,300 per household per year, rather than as the equivalent £\,120\,bn for the whole country & Make the number look big (but not too big) & Insert text \\% \bottomrule \end{tabularx} \end{document}

2020-09-18 07:02:28

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http://soft-matter.seas.harvard.edu/index.php?title=Phases_and_Phase_Diagrams&diff=prev&oldid=2355

# Difference between revisions of "Phases and Phase Diagrams" ## Introduction In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties. A straightforward way to describe phase is "a state of matter which is chemically uniform, physically distinct, and (often) mechanically separable." Ice cubes floating on water are a clear example of two phases of water at equilibrium. In general, two different states of a system are in different phases if there is an abrupt change in their physical properties while transforming from one state to the other. Conversely, two states are in the same phase if they can be transformed into one another without any abrupt changes. There are, however, exceptions to this statement, such as the liquid-gas critical point. Moreover, a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases. Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to the lines that demarcate where phase transitions occur. A triple point is, in a pressure-temperature phase diagram, the unique intersection of the lines of equilibrium between three states of matter, usually solid, liquid, and gas. The solidus is the temperature below which the substance is stable in the solid state. The liquidus is the temperature above which the substance is stable in a liquid state. There may be a gap between the solidus and liquidus; within the gap, the substance consists of a mixture of crystals and liquid. Phase diagrams are useful for material engineering and material applications. With their aid, scientists and engineers understand the behavior of a system which may contain more than one component. ## Definitions Concept Definition Bimodal curves In the phase diagram, the compositions which are in equilibrium with each other as a function of temperature. Coexisting compositions Different compositions in phase diagram that are at local energy potentials and have the same free energy. Equilibrium state Reversible Glass Transition Below a transition temperature, individual polymers lose mobility and form a solid lacking a crystalline structure. Gradient energy coefficient Has the dimension of length squared. The length in question must be related to the range of intermolecular forces involved. where k is the gradient energy coefficient (Jones p. 34) Helmholtz free energy $F=U-TS$, also commonly denoted $A$. The Helmholtz free energy is a thermodynamic potential relating to the amount of useful work one may extract from a system that is isothermic (no temperature change) and isochoric (no volume change). We say "useful" work to mean work that can be extracted from the system, and not work done to change the system itself. An equivalent result is that the Helmholtz energy is minimized at equilibrium for an isothermic and isochoric system. If a reversible process is performed on a system, the change in free energy is $\delta F=-P \delta V-S\delta T$. Mean field approximation The interaction between molecules, even of different species is the same. The volumes of the molecules are the same. Non-equilibrium state History dependent Nucleation A large enough fluctuation of composition in the metastable regime to produce a region of lower chemical potential. Nucleation – Homogeneous vs heterogeneous Nucleation normally occurs at nucleation sites on surfaces containing the liquid or vapor. Suspended particles or minute bubbles also provide nucleation sites. This is called heterogeneous nucleation. Nucleation without preferential nucleation sites is homogeneous nucleation. Homogeneous nucleation occurs spontaneously and randomly, but it requires superheating or supercooling of the medium. [[1]] Order parameter Zero for disordered phase Phase In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (density, crystal structure, index of refraction, etc.).[[2]] Phase change In thermodynamics, a phase transition is the transformation of a thermodynamic system from one phase to another.[[3]] Phase diagram A phase diagram In physical chemistry, mineralogy, and materials science is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases [[4]] Phase transition Phase change to non-equilibrium state Phase transition, first order Order parameter changes discontinuously, e.g. melting of a crystal Phase transition, second order Order parameter changes continuously, e.g. liquid-to-gas at critical point Regular solution model A mean field theory to predict the free energy of mixing.\: The interaction between molecules, even of different species is the same. The volumes of the molecules are the same. Self-assembly Spontaneous arrangement Spinodal In the phase diagram, the locus of compositions where the second derive in the free energy is zero. Spinodal decomposition Fluctuations in the unstable portion of the phase diagram grow continuously, and the c d c d

2020-12-04 05:50:20

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https://en.wikiversity.org/wiki/QB/b_velocityAcceleration

# QB/b velocityAcceleration < QB • Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!) • At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses: • Quizbank physics 1 (id 60675) • Quizbank physics 2 (id 61712) • Quizbank astronomy (id 63705) The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift. % See special:permalink/1863392 for a wikitext version of this quiz. ### LaTexMarkup begin %[[File:Quizbankqb_{{SUBPAGENAME}}.pdf|thumb|See[[:File:Quizbankqb_{{SUBPAGENAME}}.pdf]]]] %CurrentID: {{REVISIONID}} %PDF: [[:File:Quizbankqb_{{SUBPAGENAME}}.pdf]]%Required images: [[file:Wikiversity-logo-en.svg|45px]] %This code creates both the question and answer key using \newcommand\mytest %%% EDIT QUIZ INFO HERE %%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\quizname}{QB/b_velocityAcceleration} \newcommand{\quiztype}{conceptual}%[[Category:QB/conceptual]] %%%%% PREAMBLE%%%%%%%%%%%% \newif\ifkey %estabkishes Boolean ifkey to turn on and off endnotes \documentclass[11pt]{exam} \RequirePackage{amssymb, amsfonts, amsmath, latexsym, verbatim, xspace, setspace,datetime} \RequirePackage{tikz, pgflibraryplotmarks, hyperref} \usepackage[left=.5in, right=.5in, bottom=.5in, top=.75in]{geometry} \usepackage{endnotes, multicol,textgreek} % \usepackage{graphicx} % \singlespacing %OR \onehalfspacing OR \doublespacing \parindent 0ex % Turns off paragraph indentation % BEGIN DOCUMENT \begin{document} \title{b\_velocityAcceleration} \author{The LaTex code that creates this quiz is released to the Public Domain\\ Attribution for each question is documented in the Appendix} \maketitle \begin{center} \includegraphics[width=0.15\textwidth]{666px-Wikiversity-logo-en.png} \\Latex markup at\\ \end{center} \begin{frame}{} \begin{multicols}{3} \tableofcontents \end{multicols} \end{frame} \pagebreak\section{Quiz} \keytrue \begin{questions}\keytrue \question When a table cloth is quickly pulled out from under dishes, they hardly move. This is because\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice the cloth is more slippery when it is pulled quickly \CorrectChoice the cloth is accelerating for such a brief time that there is little motion \choice objects don't begin to accelerate until after the force has been applied \end{choices} \question If you toss a coin into the air, the acceleration while it as its highest point is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice up \CorrectChoice down \choice zero \end{choices} \question If you toss a coin into the air, the velocity on the way up is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice zero \choice down \CorrectChoice up \end{choices} \question If you toss a coin into the air, the velocity on the way down is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice down \choice zero \choice up \end{choices} \question If you toss a coin into the air, the velocity while it as its highest point is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice up \CorrectChoice zero \choice down \end{choices} \question A car is headed due north and increasing its speed. It is also turning left because it is also traveling in a perfect circle. The acceleration vector points\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice northwest \choice south \choice southwest \choice north \choice northeast \end{choices} \question A car is headed due north and increasing its speed. It is also turning right because it is also traveling in a perfect circle. The acceleration vector points\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice southwest \choice south \choice northwest \choice north \CorrectChoice northeast \end{choices} \question A car is headed due north and increasing its speed. It is also turning left because it is also traveling in a perfect circle. The velocity vector points\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice northeast \choice southeast \choice northeast \choice northwest \CorrectChoice north \end{choices} \question A car is headed due north and increasing its speed. It is also turning right because it is also traveling in a perfect circle. The velocity vector points\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice north \choice northwest \choice south \choice northeast \choice southwest \end{choices} \question A car is headed due north and decreasing its speed. It is also turning left because it is also traveling in a perfect circle. The acceleration vector points\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice west \choice northwest \CorrectChoice southwest \choice southeast \choice south \end{choices} \question A car is headed due north and decreasing its speed. It is also turning right because it is also traveling in a perfect circle. The acceleration vector points\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice northwest \choice north \choice south \choice northeast \CorrectChoice southeast \end{choices} \question A car is traveling west and slowing down. The acceleration is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice zero \CorrectChoice to the east \choice to the west \end{choices} \question A car is traveling east and slowing down. The acceleration is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice zero \choice to the east \CorrectChoice to the west \end{choices} \question A car is traveling east and speeding up. The acceleration is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice to the east \choice to the west \choice zero \end{choices} \question If you toss a coin into the air, the acceleration on the way up is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice down \choice zero \choice up \end{choices} \question A car is traveling in a perfect circle at constant speed. If the car is headed north while turning west, the acceleration is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice west \choice zero \choice south \choice north \choice east \end{choices} \question A car is traveling in a perfect circle at constant speed. If the car is headed north while turning east, the acceleration is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \CorrectChoice east \choice south \choice north \choice zero \choice west \end{choices} \question As the Moon circles Earth, the acceleration of the Moon is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice away from Earth \CorrectChoice towards Earth \choice opposite the direction of the Moon's velocity \choice in the same direction as the Moon's velocity \choice zero \end{choices} \question If you toss a coin into the air, the acceleration on the way down is\ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863392}}}\fi \begin{choices} \choice up \CorrectChoice down \choice zero \end{choices} \end{questions} \newpage

2020-02-25 07:25:09

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http://mathematica.stackexchange.com/questions/1441/why-does-jlink-lock-unopened-jar-files-in-windows

# Why does JLink lock unopened jar-files in Windows Since the introduction of JLink (maybe a bit later) it is possible to put jar libraries inside the directory-structure of packages. If this package is installed in one of the places Mathematica searches, the jar libraries are automatically found by JLink. The problem is that under 64 bit Windows XP, after loading JLink these files are locked and cannot be removed from within Mathematica, although none of the jars are really used, but only added to the class-path of Java. Let me give a short example: Place a Test folder with Java subfolder inside your \$UserAddOnsDirectory and copy any jar file into the Java folder. This looks like Test/ └── Java └── blub.jar When you now start a fresh Kernel and load <<JLink you can verify by looking at JavaClassPath[], that this directory and the jar was indeed added to the class-path. When you try to remove the complete folder, you get (a misleading) error message DeleteDirectory[path, DeleteContents -> True] (* DeleteDirectory::dirne: Directory D:\Documents and Settings\mscheibe\ Application Data\Mathematica\Applications\Test not empty. >> *) After Quit-ing the kernel, calling UninstallJava[] or JLinkQuitJava[] the directory can be removed. This behavior does not occur in Linux or on MacOSX and I could only test it on Windows XP 64 bit. Question: Why, if the jar-path is only appended to the class-path, does JLink lock the files as they where opened for reading? Why does this happen on Windows only? Is there anyone, who has a deeper insight into JLink who can suggest a better solution that calling JLinkQuitJava[]; Pause[2]; inside my module when I want to remove a jar-file found by Mathematica. Remark 1: This behavior is not restricted to automatically found jars. When you use java-code by manually adding a jar with AddToClassPath[path] the similar thing happens. Remark 2: I forgot to mention, that JLinkQuitJava[] does not really quit java like Quit would kill the kernel. Meaning, I call this and without doing anything else I can still call my functions inside the jars. This seems to suggest, that QuitJava[] kills the class-loader instance Leonid is mentioning which locks the files. But a call to e.g. JavaNew seems to set up everything correct again. - I also encountered this problem. Not an authoritative answer, but here is one blind guess to what is happening. JLink has its own classloader, JLinkClassLoader.java, which calls another one, JLinkClassLoaderHelper.java. The latter is a sub-class of URLClassLoader.java. Both are used in the class JLinkSystemClassLoader.java. The second part of this story is that there is an unresolved bug in the JVM related to URLClassLoader.java class, which locks jars, on Windows only. It has been discussed on SO here. The problem seems to be Windows-specific. What I don't know is at what time this happens, and why this affects jars that weren't even used. If this is at all a right guess, this can probably be traced by using a debugger. +1 This seems to explain, why you can break the lock with QuitJava. Does this mean that, when I have a few million jars in my search-path, JLink opens and maybe loads every jar at startup instead of adding it to the search path? Does java has to preload jars or could it just start loading, when a symbol cannot be resolved? –  halirutan Feb 7 '12 at 10:34 @halirutan To answer this, I'd need to have a deeper understanding of the dynamics of class loading in JLink. I think however, that if/when this becomes a real problem, one can try to get a hold on the specific instance of URLClassloader (well, its J/Link subclass) created by JLink. In the JDK7, a new method close has been added to it, so I suppose it can be used explicitly from JLink/Mathematica, when you are done loading classes. Then, if you need to load more, you create a new instance. Something like that may work, but for that a full understanding of the process may be needed. –  Leonid Shifrin Feb 7 '12 at 10:59 @halirutan From a cursory look at it, here is a work-around I'd suggest: 1. Subclass the JLinkClassloader class, making a field helper (of type JLinkClassLoaderHelper) public (it is protected in JLinkClassloader, which creates a singleton). 2. Work directly with the KernelLink.java class, which has a method setClassLoader: create an instance of KernelLink, and then set as the classloader the subclass I mentioned. 3. When needed, access the field helper of this subclass, and call close()` on it. Then replace it with a new instance of the helper. No idea if this works though. –  Leonid Shifrin Feb 7 '12 at 11:09

2015-04-27 09:08:14

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https://www.shaalaa.com/question-bank-solutions/trigonometric-functions-sum-difference-two-angles-if-tan-x-x-1-tan-x-x-1-then-equal_57359

CBSE (Science) Class 11CBSE Share Books Shortlist # If Tan α = X X + 1 and Tan α = X X + 1 , Then α + β is Equal to - CBSE (Science) Class 11 - Mathematics ConceptTrigonometric Functions of Sum and Difference of Two Angles #### Question If $\tan\alpha = \frac{x}{x + 1}$ and $\tan\alpha = \frac{x}{x + 1}$, then $\alpha + \beta$ is equal to • $\frac{\pi}{2}$ • $\frac{\pi}{3}$ • $\frac{\pi}{6}$ • $\frac{\pi}{4}$ #### Solution It is given that $\tan\alpha = \frac{x}{x + 1}$ and $\tan\beta = \frac{1}{2x + 1}$ $\tan\left( \alpha + \beta \right) = \frac{\tan\alpha + \tan\beta}{1 - \tan\alpha\tan\beta}$ $= \frac{\frac{x}{x + 1} + \frac{1}{2x + 1}}{1 - \frac{x}{x + 1} \times \frac{1}{2x + 1}}$ $= \frac{\frac{x\left( 2x + 1 \right) + \left( x + 1 \right)}{\left( x + 1 \right)\left( 2x + 1 \right)}}{\frac{\left( x + 1 \right)\left( 2x + 1 \right) - x}{\left( x + 1 \right)\left( 2x + 1 \right)}}$ $= \frac{2 x^2 + x + x + 1}{2 x^2 + 3x + 1 - x}$ $= \frac{2 x^2 + 2x + 1}{2 x^2 + 2x + 1}$ $= 1$ $\therefore \alpha + \beta = \frac{\pi}{4} \left( \tan\frac{\pi}{4} = 1 \right)$ Hence, the correct answer is option D. Is there an error in this question or solution? #### APPEARS IN RD Sharma Solution for Mathematics Class 11 (2019 to Current) Chapter 7: Values of Trigonometric function at sum or difference of angles Q: 23 | Page no. 29 Solution If Tan α = X X + 1 and Tan α = X X + 1 , Then α + β is Equal to Concept: Trigonometric Functions of Sum and Difference of Two Angles. S

2019-09-16 02:58:44

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https://socratic.org/questions/if-the-quotient-of-two-polynomials-is-4x-2-x-7-11x-15-x-2-x-2-what-are-the-two-p

# If the quotient of two polynomials is 4x^2-x-7+(11x+15)/(x^2+x+2), what are the two polynomials? Apr 2, 2017 $\left(4 {x}^{4} + 3 {x}^{3} + 0 {x}^{2} + 2 x + 1\right) \div \left({x}^{2} + x + 2\right)$ #### Explanation: Given:$\text{ } 4 {x}^{2} - x - 7 + \frac{11 x + 15}{{x}^{2} + x + 2}$ The $11 x + 15$ is the remainder so the denominator must be the divisor. Thus we need to build each term by using ${x}^{2} + x + 2$ Note that I use a place holder. For example: $0 {x}^{4}$ color(white)(.) $4 {x}^{2} \left({x}^{2} + x + 2\right) \to 4 {x}^{4} + 4 {x}^{3} + 8 {x}^{2}$ $- x \left({x}^{2} + x + 2\right) \to 0 {x}^{4} - \textcolor{w h i t e}{4} {x}^{3} - \textcolor{w h i t e}{8} {x}^{2} - 2 x$ $- 7 \left({x}^{2} + x + 2\right) \to 0 {x}^{4} + 0 {x}^{3} - 7 {x}^{2} - 7 x - 14$ $\text{The remainder"->ul(color(white)(.)0x^4+0x^3+0x^2+11x+15) larr" Add}$ $\text{ } 4 {x}^{4} + 3 {x}^{3} + 0 {x}^{2} + 2 x + 1$

2019-01-21 21:43:17

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https://www.numerade.com/questions/differentiate-the-function-y-ex1-1/

💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here! # Differentiate the function.$y = e^{x+1} + 1$ Check back soon! Derivatives Differentiation ### Discussion You must be signed in to discuss. ##### Heather Z. Oregon State University ##### Kristen K. University of Michigan - Ann Arbor Lectures Join Bootcamp ### Video Transcript he has clear. So when you read here, so we're gonna we have why is equal to e X plus one. Plus what? So we're gonna get you some rolling Take the derivative in terms of vets and we know that D of eat off of max over D X is equal to the derivative of f times e to the f of X. So our final answer is de over d y is equal to e to the X plus one. #### Topics Derivatives Differentiation ##### Heather Z. Oregon State University ##### Kristen K. University of Michigan - Ann Arbor Lectures Join Bootcamp

2021-10-24 05:19:49

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https://www.gradesaver.com/textbooks/science/chemistry/general-chemistry-10th-edition/chapter-22-the-transition-elements-and-coordination-compounds-questions-and-problems-page-970/22-10

# Chapter 22 - The Transition Elements and coordination Compounds - Questions and Problems - Page 970: 22.10 #### Work Step by Step Werner showed that electrical coductance of a solution of $[Pt(NH_3)_4Cl_2]$ refers to that of three ions in solution and that two of the chloride ions can be precipitated as $AgCl$. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

2019-11-12 06:43:43

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https://chemistry.stackexchange.com/questions/83666/what-are-good-representatives-for-the-concepts-of-endergonic-and-exergonic

# What are good representatives for the concepts of endergonic and exergonic? We must demonstrate two reactions: endergonic and exergonic. I'm wondering if thefollowing reactions are accurate. • Exergonic: I have sodium bicarbonate and vinegar. Would it be catabolic, spontaneous, and $-\Delta G$ as well? Sodium bicarbonate and vinegar is your basic science-fair volcano reaction. You have the baking soda in a container of some sort and pour the vinegar. The formula would be something like $$\ce{Bicarbonate of soda + vinegar -> Carbonic acid + Water + Carbon dioxide gas}.$$ • Endergonic: I have ammonium chloride and water. Would it be anabolic, nonspontaneous, and $+\Delta G$? Ammonium chloride would be dissolved into the water. The formula would be something like $$\ce{NH4Cl + water -> NH4+ + Cl-}$$ I've just barely touched on the $G$ value thing. I don't exactly know what's going on there. What I mean I guess is that if it's $+\Delta G$, the enthalpy increases, and if it's $-\Delta G$, the enthalpy decreases. To be more precise, we're on the Gibbs free energy lesson at the moment. Endergonic means energy is absorbed during the reaction. Exergonic means that energy is released during the reaction. Is energy released or absorbed during a vinegar and baking soda reaction? Is energy released or absorbed when dissolving ammonium chloride and water? • I think you should describe the processes better. Do you mean disolution of salts or what? When you give G values, always specify the process, i.e, the initial state and final state. – user43021 Oct 4 '17 at 15:28 • @HernanMiraola I edited my post a bit. Thank you – Amanda Oct 4 '17 at 15:52 • Please do not use edit statements, they carry no information whatsoever for anyone who encounters the question for the first time. Use the edit function to improve your post, but still let it read consistently as one post (as if you were writing it for the first time). For those who are interested in the becoming of the post, there is an edit history available. – Martin - マーチン Oct 5 '17 at 12:18 As you say you are starting with Gibbs free energy, just pay attention to the $\Delta G$ values. Remember that $\Delta G= \Delta H -T\Delta S$ so it doesn't depends only on enthalpy but also on entropy. A process where $\Delta G<0$ is exergonic and in the opposite case it is endergonic. • Salts that disolve in water are exergonic processes, $\Delta G_\mathrm{disol}<0$. • Sodium bicarbonate will disolve in vinegar to produce $\ce{CO2}$ (because of the high concentration of acetic acid), it is also exergonic.

2020-06-01 23:09:35

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https://yannherklotz.com/2017/02/c-to-mips32-compiler/

# C to MIPS32 Compiler The compiler was made to translate C code to MIPS assembly. It was then tested using qemu and simulating the MIPS processor to run the binary. ### *** What is a compiler? A Compiler is a program that transforms code written in one language into another language. This is normally done to transform a higher level language such as C, into a lower level language such as assembly. ### *** Project The project was separated into three parts: lexer, parser and the actual compiler. The lexer was written in flex, which then got passed to the parser that we wrote in bison. The AST (Abstract Syntax Tree) that was output by bison was then traversed in the compiler and the corresponding assembly code was output by the compiler. In our second year we were given a coursework to write a compiler that would take in C89 code and compile it to MIPS32 assembly. We then used the gcc assembler to compile that to a binary and used qemu to simulate a MIPS processor and run the binary.

2021-09-20 13:49:57

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https://cs.stackexchange.com/questions/19055/mapping-reduction-to-show-neverhalt-is-undecidable/20229

# Mapping reduction to show NeverHalt is undecidable I need help with showing that $$NeverHalt_{TM} = \{\langle M\rangle \mid \text{M is a TM which runs forever on every input w}\}$$ is undecidable by giving an explicit mapping reduction. To show that a language reduces to any other language we must show that yes-instances are mapped to yes-instances and no-instances are mapped to no instances. We need to find a TM whose language will "help" us solve $NeverHalt_{TM}$, given $\langle M\rangle$. I am not really sure where to go from here or in general how to proceed with undecidability problems. You will not prove that $NeverHalt_{TM}$ is undecidable by "finding a TM whose language will "help" us solve" it. This would actually prove the opposite, if $M$ is a TM deciding some language. You have to suppose $NeverHalt_{TM}$ to be decidable by a turing machine $D$, and show that with its help you can decide other non-recursive language. In other words, you have to pick a suitable undecidable language and reduce it to $NeverHalt_{TM}$. There is a reduction from the emptiness problem for turing machines : $E_{TM} = \{\left < M \right >\ :\ \mathcal L(M) = \varnothing \}$. You can reduce the $MP= \{\langle M,w \rangle : w \in L(M)\}$ to $NeverHalt$ For a given string $\langle M,w \rangle$ you construct the following machine $F$: For input x: Simulate M for input w if it accepts, loop if it rejects accept x Now you can see that $\langle M,w \rangle \in MP \iff \langle F \rangle \in NeverHalt$ • This only proves that NeverHalt is undecidable if we assume that MP is undecidable -- is it? (Of course it is, but still.) – Raphael Feb 2 '14 at 22:15 • If we want to prove it by a mapping reduction don't we have to have a known undecidable language first? since that was the question I considered it known... – lea Feb 3 '14 at 20:26 • That's true, and a ficklish issue. Usually, every course/book has its "toolbox" of undecidable, un-semi-decidable, NP-complete, ... problems that can be used for reduction. There are few generally present defaults (afaict) so we usually fall back to the Halting problem and its complement. (Your MP is fine in the context of material that establishes that the word problem is undecidable for type-0 grammars.) – Raphael Feb 3 '14 at 21:13

2019-10-14 01:54:26

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https://www.groundai.com/project/loschmidt-echo-for-local-perturbations-non-monotonous-cross-over-from-the-fermi-golden-rule-to-the-escape-rate-regime/

Loschmidt echo for local perturbations # Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime Arseni Goussev, Daniel Waltner, Klaus Richter and Rodolfo A Jalabert Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom111Present address Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 (CNRS-ULP), 23 rue du Loess, BP 43, 67034 Strasbourg Cedex 2, France222Present and permanent address July 26, 2019 ###### Abstract We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations a Fermi-golden-rule (FGR) type behavior is recovered. For strong perturbations the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE. ###### pacs: 05.45.Mt, 03.65.Sq, 32.80.Lg ## 1 Introduction One of the most prominent manifestations of chaos in classical physics is the hypersensitivity of the dynamics to perturbations in the initial conditions or Hamiltonian. That is, two trajectories of a chaotic system launched from two infinitesimally close phase-space points deviate exponentially from each other; so do the trajectories starting from the same point in phase space, but evolving under slightly different Hamiltonians. In a quantum system it is natural to consider as a measure of “separation” of two quantum states and . The unitarity of quantum propagators renders the overlap of any two states of the same system unchanged in the course of time. Thus, quantum systems are said to be stable with respect to perturbations of the initial state. However, a perturbation of the Hamiltonian can (and usually does) result in a nontrivial time dependence of the wave function overlap, suggesting a viable approach for describing instabilities and, therefore, for quantifying chaos in quantum systems. Peres [1] proposed to consider the overlap O(t)=⟨ϕ0|ei~Ht/ℏe−iHt/ℏ|ϕ0⟩ (1) of the state , resulting from an initial state after evolution for a time under the Hamiltonian , with the state obtained from evolving the same initial state through , but under a slightly different (perturbed) Hamiltonian . He showed that the long-time behavior of M(t)=|O(t)|2 (2) depends on whether the underlying classical dynamics is regular or chaotic. In the field of quantum computing is an important concept, usually referred to as fidelity [2]. Moreover, can be also interpreted as the squared overlap of the initial state and the state obtained by first propagating through time under the Hamiltonian , and then through time under the perturbed Hamiltonian (or from to ). This time-reversal interpretation constitutes a description of the echo experiments that have been performed by nuclear magnetic resonance since the fifties [3]. When the Hamiltonian describes some complex (many-body or chaotic) dynamics is referred to as Loschmidt echo (LE) [4], and this is the terminology we will adopt. By construction, the LE equals unity at , and typically decays further in time. Most of the analytical studies so far addressed the quantity corresponding to the LE averaged either over an ensemble of initial states, or over an ensemble of different perturbed (and/or unperturbed) Hamiltonians. has been predicted to follow different decay regimes in various chaotic systems with several Hamiltonian perturbations [5, 6]. Depending on the nature and strength of the perturbation, , one recognizes the perturbative Gaussian [7, 8, 9], the non-diagonal or Fermi-golden-rule (FGR) [5, 7, 8, 10] and the diagonal or Lyapunov [5, 11] regimes. Here, ‘diagonal’ and ‘non-diagonal’ refer to the underlying pairing of interfering paths in a semiclassical approach, see Sec. 2. The perturbative, FGR and Lyapunov regimes, listed above in the order of the (properly defined) increasing perturbation strength, constitute the framework for classification of LE decay regimes [6, 12]. It is important to mention that the full variety of system- and perturbation-dependent decay regimes is rather rich, and extends far beyond the above list: double-Lyapunov [13], super-exponential [14] and power law [15] decay regimes serve as examples. We further note that analytical results for the time decay of the unaveraged LE, , are currently available only for very few chaotic systems [16]. The discovery [5] of the Lyapunov regime for the decay of the averaged LE in classically chaotic systems, with being the average Lyapunov exponent, provided a strong and appealing connection between classical and quantum chaos: it related a measure of instability of the quantum dynamics, such as the LE, to a quantity characterizing the instability of the corresponding classical dynamics, i.e. the Lyapunov exponent. This result awoke the interest on the LE in the quantum chaos community. The Lyapunov regime has been numerically observed in several two-dimensional chaotic systems, i.e. in the Lorentz gas [11, 17], the Bunimovich stadium [18], the smooth stadium billiard [19], a Josephson flux qubit device [20], as well as in one-dimensional time-dependent Hamiltonian systems [7]. The theory of the Lyapunov decay of the LE mainly relies on the following two assumptions: (i) the validity of the structural stability arguments (supported by the shadowing theorem [21]), and (ii) the global nature of the Hamiltonian perturbation. The first assumption guarantees a unique one-to-one mapping of trajectories of the unperturbed system to those of the perturbed system. This mapping allows for efficient pairing of the trajectories of the unperturbed and perturbed system in the diagonal approximation [22]. The second assumption implies that the Hamiltonian perturbation affects every trajectory of the system, and, therefore, all trajectories are responsible for the decay of the LE. However, this is by no means the most general situation when we consider possible experimental realizations of the LE. In the present work we extend the semiclassical theory of the LE by lifting the second of the two above-mentioned assumptions, i.e. we allow for a local perturbation in coordinate space. In this context the LE decay was previously addressed in the case of a strong local perturbation [23], i.e. for a billiard exposed to a local boundary deformation much larger than the de Broglie wavelength. Analytical and numerical calculations yielded a novel LE decay regime, for which with being the probability (per unit time) of the corresponding classical particle to encounter the boundary deformation. can also be viewed as a classical escape rate from a related open billiard obtained from the original (closed) one by removing the deformation-affected boundary segment. In this work we explore all possible strengths of a local perturbation and describe the transition from the weak to the strong perturbation regime that completes the previous picture. In particular we show that the rate of the exponential decay of the LE oscillates as a function of the perturbation strength as the escape-rate regime is approached. The paper is organized as follows: In Section 2 we develop a comprehensive semiclassical approach of the LE decay due to local Hamiltonian perturbations of increasing strength. We perform a systematic analysis of the different decay regimes and establish their relation to the previously known decay regimes in the case of a global perturbation. In Section 3 we validate our semiclassical theory by numerical simulations. In Sec. 4 we outline possible experimental realizations and focus on the possibility of introducing a local perturbation in microwave-cavities and ultra-cold atom-optics billiards. We provide concluding remarks in Sec. 5 and point to the similarities and differences with respect to another approach to the LE for local perturbations. Technical aspects of the calculations are relegated to the appendices. ## 2 Semiclassical approach ### 2.1 Wave-function evolution We address the time evolution of the wave function that describes a quantum particle moving inside a classically chaotic two-dimensional billiard (corresponding to a Hamiltonian ). We assume that initially (at time ) the particle is in a coherent state ϕ0(r)=1√πσ exp[iℏp0⋅(r−r0)−(r−r0)22σ2]. (3) Here quantifies the extension of the Gaussian wave packet, while and are the initial mean values of the position and momentum operators, respectively. We further define the (rescaled [24]) de Broglie wavelength of the particle as . In our description of the time evolution of the wave function we rely on the semiclassical approximation [25] of the wave function at a time , ϕt(r)=∫dr′∑^s(r,r′,t)K^s(r,r′,t)ϕ0(r′). (4) Here K^s(r,r′,t)=√D^s2πiℏ exp[iℏS^s(r,r′,t)−iπν^s2] (5) is the contribution to the Van Vleck propagator associated with the classical trajectory leading from point to point in time . denotes the classical action integral (or the Hamilton principal function) along the path . In a hard-wall billiard , where is the length of the trajectory , and is the mass of the particle. In Eq. (5), , and the Maslov index equals the number of caustics along the trajectory plus twice the number of particle-wall collisions (for the case of Dirichlet boundary conditions). Since we assume that the initial wave packet is localized around within , only trajectories starting at points close to are relevant for our semiclassical description. Thus we can expand the action integral in a power series in . In A we show that the power series can be terminated at the linear term, S^s(r,r′,t)≈Ss(r,r0,t)−ps⋅(r′−r0), (6) if the wave packet is narrow enough, so that the condition σ≪√lL1/\lambdabar+1/σ (7) is satisfied, where is the Lyapunov length. In Eq. (6), is the central reference trajectory into which gets uniformly deformed as , and denotes the initial momentum of the trajectory (see Fig. 1). Substituting Eq. (6) into Eq. (5), and performing the integration in Eq. (4) we obtain ϕt(r)=2πℏ∑s(r,r0,t)Ks(r,r0,t) Φ0(ps) , (8) with Φ0(p) ≡ ∫dr2πℏexp[−iℏp⋅(r−r0)]ϕ0(r) = σ√πℏexp[−σ22ℏ2(p−p0)2] the momentum representation of the initial wave packet. We now consider a related billiard, corresponding to the perturbed Hamiltonian , that differs from the original (unperturbed) billiard by a deformation of the boundary segment of width (see Fig. 2). The perturbation is thus local, and will be characterized by its extent (depending on the ratio between and the cavity perimeter ) and its strength (that will be quantified in the sequel). In view of Eq. (8), the wave function describing the evolution of the particle (starting from the same initial state ) can be written as ~ϕt(r)=2πℏ∑~s(r,r0,t)K~s(r,r0,t)Φ0(p~s). (10) The sum now runs over all possible trajectories of a classical particle that travels from to in time while bouncing off the boundary of the perturbed billiard. ### 2.2 Wave-function overlap for local perturbations According to Eqs. (8)-(10) and the definition (1) of the LE amplitude, we have where stands for the billiard area. The shadowing theorem [21] allows us to employ the diagonal approximation () in the case of a classically small perturbation [26], thus reducing Eq. (2.2) to where W0(p)≡|Φ0(p)|2=σ2πℏ2 exp[−σ2ℏ2(p−p0)2] (13) is the probability distribution of the particle momentum. In billiards the action difference between the two trajectories traveling between the same initial and final points in the same time can be written, in terms of their length difference , as ΔSs(r,r0,t) ≡ Ss−S~s = p2s2mt−p2~s2mt≈psps−p~smt=ps ΔLs(r,r0,t). Using the Jacobian property of the Van Vleck determinant , we can replace the integral over final coordinates in Eq. (12) by an integral over the initial momenta and obtain O(t)=∫dpW0(p)exp[iℏ p ΔL(r0,pt)]. (15) The dependence of on the product stems from the fact that in billiards, changing the magnitude of the momentum only modifies the traveling time, but does not affect the path. We now introduce a sequence of momentum sets , with , such that for any the classical trajectory, starting from the phase-space point , arrives at a coordinate-space point after time while visiting the deformation-affected boundary segment ( in Fig. 2) exactly times. Thus, the trajectories with the initial momentum in only undergo collisions with the part of the boundary unaffected by the deformation ( in Fig. 2) rendering , so that O(t)=∞∑n=0On(t), (16) with O0(t) = ∫P0dp W0(p), (17) On(t) = ∫Pndp W0(p) eipΔL(r0,pt)/ℏforn≥1. (18) Since we are studying billiards, the integrations over momenta can be simplified by working in polar coordinates and considering the sets of angles such that iff . For a classically chaotic dynamics the set shrinks with increasing time , and becomes the fractal set defining the repeller of the corresponding open (scattering) problem in the limit . Eqs. (17) and (18) can, respectively, be written as O0(t) = ∫∞0dpp∫Θ0dθ W0(p), (19) On(t) = ∫∞0dpp∫Θndθ W0(p) eipΔL(r0,pt,θ)/ℏforn≥1. (20) For long times , where many trajectories contribute to the semiclassical expansions, the angular integrals over can be replaced by integrals over all angles, weighted with the measures of the corresponding sets. Assuming ergodicity one readily obtains an approximation for the probability for a trajectory of length to visit the boundary region exactly times: ρn(l)≈1n!(lld)nexp(−lld), (21) where is the average dwell length of paths in the related open chaotic billiard obtained from the original (closed) one by removing the boundary region . This corresponds to the classical escape rate of the open cavity that for particles with momentum is given by γ=p0mld. (22) For a chaotic cavity with an opening much smaller than its perimeter we can approximate [27] , and therefore γ≈p0m wπA . (23) In our case the escape rate yields a measure of the perturbation extent. The classical escape rate of an open cavity controls the fluctuations of the transmission coefficients, and therefore approximations such as (23) have been thoroughly examined in the context of quantum transport [28]. According to the previous discussion we can approximate , with , by the averages ¯O0(t) = ∫∞0dp pρ0(pt/m)∫2π0dθ W0(p), (24) ¯On(t) = ∫∞0dp p⟨eipΔL(r0,pt,θ)/ℏ⟩Θnρn(pt/m)∫2π0dθ W0(p),n≥1. (25) The mean value should be taken over the set . The chaotic nature of the dynamics will enable us to treat the averages over in a statistical way. In view of Eq. (13), the -integral in Eqs. (24) and (25) yields ∫2π0dθW0(p)=2σ2ℏ2exp[−σ2ℏ2(p2+p20)]I0(2σ2ℏ2p0p), (26) where denotes the modified Bessel function. As usually assumed in the Loschmidt echo studies, we restrict our analysis to “semiclassical” initial wave packets with sizes much larger than the de Broglie wave length, \lambdabar≪σ. (27) This assumption, together with condition (7), defines the interval for the dispersion , where the semiclassical approach is reliable, and hence yields restrictions to the parameters of the billiard. Employing condition (27) enables us to use the asymptotic form , valid for large , in Eq. (26). Thus, the probability distribution function for the magnitude of the initial momentum is given by p∫2π0dθW0(p)≈σℏ√pπp0 exp[−σ2ℏ2(p−p0)2]. (28) We note that Eq. (28) provides a good approximation to the exact distribution function already for . Under this assumption the -integrals in Eqs. (24) and (25) are dominated by the contributions around , and we can write (in view of Eq. (21)) ¯O0(t) ≈ e−γt, (29) ¯On(t) ≈ (γt)nn!e−γt⟨eip0ΔL(r0,p0t,θ)/ℏ⟩Θnforn≥1. (30) Since in Eq. (30) all classical quantities are evaluated for an initial momentum with magnitude , the mean values should be taken over the sets . However, for long times and a chaotic dynamics we do not expect these mean values to depend on . In the next section we will further invoke the chaotic nature of the underlying classical dynamics in order to estimate the mean values and therefore the LE average amplitude. ### 2.3 Averages over trajectory distributions For classically small perturbations the action, respectively, length difference (Eq. (2.2)) between a trajectory (solid red segment in Fig. 2) and its perturbed partner (dashed segment) is given only by the contributions accumulated along the encounters with . Differences in length arising from the free flights between collisions with the boundary () are of higher order in the perturbation strength and will not be considered. We can then write ΔL=n∑j=1u(ϑj,ξj), (31) where the deformation function is the length difference accumulated in the -th collision with , depending on the impinging angle and on the coordinate of the hitting point. The number of collisions with is a fraction of the total number of collisions . The mean bouncing length can be approximated by [29], and we suppose since . We note that for small perturbations depends on only through . Given the chaotic nature of the classical dynamics and the fact that the collisions with are typically separated by many collisions with we assume and to be random variables. Furthermore, assuming a perfect randomization of the trajectories within the billiard the probability distribution functions for and are, respectively, Pϑ(ϑ)=cosϑ2andPξ(ξ)=1w. (32) Then, treating the random variables as uncorrelated we obtain ⟨eip0ΔL(r0,p0t,θ)/ℏ⟩Θn=⟨eiu/\lambdabar⟩n, (33) where the average is defined as ⟨f⟩≡∫π/2−π/2dϑPϑ(ϑ)∫w0dξPξ(ξ)f(ϑ,ξ) (34) for a function . Once we specify the shape of the perturbation, the average in the right-hand side of Eq. (33) is readily calculated from the probability distributions of Eq. (32). For instance, for a piston-like deformation (see B), u(ϑ,ξ)=2hcosϑ, (35) ⟨eiu/\lambdabar⟩=1−π2[H1(2h/\lambdabar)−iJ1(2h/\lambdabar)], (36) where stands for the Struve H-function of the first order, and is the first order Bessel function of the first kind. Here we note that for the case of the piston-like boundary deformation the ratio serves as a measure of the perturbation strength, whereas (and therefore ) quantifies the extent of the perturbation. At this stage, however, we will keep our discussion general and do not specify the details of the local perturbation. The substitution of Eq. (33) into Eq. (30) yields the average LE amplitude. The latter is usually not an observable quantity, however it will be helpful towards our semiclassical calculation of the LE. The condition of a classically small perturbation that we have adopted throughout our work, implies that (which for the case of the piston-like deformation is equivalent to ). Quantum mechanically the perturbation can be characterized by the extent and a deformation strength χ≡√⟨u2⟩\lambdabar. (37) For we will be in the quantum perturbative regime [7, 8, 9], which will not be considered in this work. Increasing the deformation strength we anticipate a richer variety of regimes than for the case of the LE under global perturbations [5, 6] since the perturbation extent enters as another relevant parameter. ### 2.4 Loschmidt echo for local perturbations According to Eqs. (2) and (2.2) the semiclassical expansion for the LE contains terms involving four trajectories. The diagonal approximation, leading to Eq. (12) for the LE amplitude, reduces the LE to a sum over pairs of trajectories. Consequently, the semiclassical form of the LE must take into account the different possibilities for each trajectory of the pair to hit (or not) the region of the boundary where the perturbation acts. We can therefore decompose the LE as M(t)=Mnd(t)+Md(t), (38) where we have introduced the non-diagonal and diagonal contributions according to Mnd(t)=∫dpW0(p)e−ipΔL(r0,pt)/ℏ∫¯εpdp′W0(p′)eip′ΔL(r0,p′t)/ℏ (39) and Md(t) = ∫dpW0(p)∫εpdp′W0(p′) ×exp{iℏ[p′ΔL(r0,p′t)−pΔL(r0,pt)]}. Here, the set of momenta is defined such that two trajectories starting from the phase space points and , stay “close” to each other in phase space during time , and thus are “correlated” with respect to the perturbation; is the momentum set complementary to . We give a quantitative definition of below. Following the standard notation introduced in Ref. [5], we call diagonal term the one resulting from the identification of pairs of trajectories where the effect of the perturbation is correlated, that is, when . In the non-diagonal term we consider the pairs of trajectories uncorrelated with respect to the perturbation, including the case where one or both orbits are unperturbed. As noted at the beginning of this section, each of the trajectories of the above pair already incorporates a diagonal approximation between a perturbed and an unperturbed trajectories with the same extreme points. ### 2.5 Non-diagonal contribution to the Loschmidt echo Calculating the LE as an average over trajectory distributions forces us to take into account pairs of trajectories and the possible correlations among them. The correlations are particularly important for , as we show in Sec. 2.6. On the other hand, in our discussion of the last chapter we established that for the calculation of the two trajectories of the pair can be considered to be uncorrelated with respect to the perturbation, and the averages can be performed independently. Assuming in addition that the measure of the momentum set is small compared with that of the momentum set effectively represented by the distribution we write Mnd(t)≈∣∣ ∣∣∞∑n=0¯On(t)∣∣ ∣∣2. (41) Substituting Eqs. (29-30) and (33) into Eq. (41) and performing straightforward algebraic operations we arrive at our central result for the non-diagonal contribution to the LE: Mnd(t)≈e−κγt, (42) where κ≡2(1−R⟨eiu/\lambdabar⟩). (43) Thus, for the case of the piston-like boundary deformation the average phase factor due to a single visit of the perturbation region by the particle is given by Eq. (36), so that Eq. (43) reads κ=πH1(2h/\lambdabar). (44) In subsection 2.7 we study the emergence of the Fermi-golden-rule and escape-rate regimes of the decay of (as well as the transition between the two regimes) depending on the strength of the perturbation. In sections 3 and 4 we discuss their implications for numerical simulations and possible experimental observations. ### 2.6 Diagonal contribution to the Loschmidt echo To proceed with the calculation of the diagonal contribution to the LE, Eq. (2.4), we first need to specify the set such that two trajectories of time , starting from the phase space points and , stay “correlated” during time . As in Sec. 2.2, it is convenient to work with polar coordinates, and , in which the set can be defined as follows: for every one has and . In turn, and are subject to the requirement that the two trajectories stay “close” to each other in phase space. Indeed, any two “correlated” trajectories must have the same number of collisions with the billiard boundary. This condition leads to . Moreover, the two trajectories must also have the same number of collisions with . The spatial separation between the two trajectories at the first collision with the boundary is approximately given by . The condition that after time this separation is smaller that the size of is . Here we have used the property that for chaotic dynamics two arbitrary, initially close trajectories deviate exponentially from each over with a rate given by the average Lyapunov exponent . Thus, we can estimate the measure of the -set to be Δp=mlftandΔθ=wlfexp(−λt). (45) Using this quantitative description of for the evaluation of Eq. (2.4) we obtain for the diagonal contribution to the LE Md(t)=∫dpW0(p) ∫p+Δpp−Δpdp′p′∫θ+Δθθ−Δθdθ′W0(p′) ×exp{iℏ[p′ΔL(r0,p′t,θ′)−pΔL(r0,pt,θ)]}. We now argue that for boundary deformations of moderate strength the exponent in the integrand on the right hand side of Eq. (2.6) can be neglected. The argument of the exponent is given by the total differential of the function , and therefore its absolute value can be bounded by ∣∣∣(p′−p)ΔLℏ+p(θ′−θ)ℏ∂ΔL∂θ∣∣∣≲∣∣∣ΔpΔLℏ∣∣∣+∣∣∣pΔθℏ∂ΔL∂θ∣∣∣. (47) Here we have used that, as discussed in Sec. 2.3, is independent of for a fixed number () of collisions with . Then ∣∣∣ΔpΔLℏ∣∣∣≲Δpℏ√⟨u2⟩γt=lfldχ, (48) and pΔθℏ∂ΔL∂θ=pΔθℏn∑j=1(∂u∂ϑj∂ϑj∂θ+∂u∂ξj∂ξj∂θ)∼ΔθCeλt=wlfC, (49) where we have introduced the dimensionless quantity (50) This implies that the exponent in Eq. (2.6) is smaller than unity if and . Since the ratios and are assumed to be large, the above inequalities hold for a wide range of deformations. (Note that for the piston-like deformation, Eq. (35), and , and hence the exponent is small if .) Neglecting the exponent in Eq. (2.6) we obtain Md(t) ≈ ∫dpW0(p)∫p+Δpp−Δpdp′p′∫θ+Δθθ−Δθdθ′W0(p′) ≈ 4ΔpΔθ∫dppW20(p). In the second line of this equation we have taken into account that and for times much longer than the dwell time . Under the assumption (27) of a “semiclassical” initial wave packet, the integral over in Eq. (2.6) is dominated by the contribution around and we find Md(t)≈2mwπp0t(σ\lambdabar)2e−λt. (52) We note that the exponential dependence of on does not contain the perturbation and arises from a classical probability distribution, as in the standard Lyapunov regime [5]. The dependence with respect to the perturbation extent, , appears in the prefactor. ### 2.7 Decay regimes of the Loschmidt echo According to Eq. (38) the full LE is the sum of the non-diagonal and diagonal contributions, and , given by Eqs. (42) and (52) respectively. We first argue that, unlike in the case of a global Hamiltonian perturbation, the non-diagonal contribution will typically dominate over the diagonal term. The most favorable regime to observe the diagonal term would be that of perturbations satisfying . Therefore, the necessary requirement for resolving the diagonal term is . Since (with the Kolmogorov-Sinai entropy of the chaotic repeller [30]) we see that can possibly prevail over only if . Taking into account that for a closed system, we see that only relatively open cavities would allow to observe . Hence for further analysis of the LE decay we mainly focus on the non-diagonal contribution . According to Eq. (42) the LE displays different decay regimes depending on the strength of the perturbation. Thus, for weak perturbations characterized by one can expand the phase factor in the Taylor series to the second order in to obtain and, therefore, Mnd(t)≈e−χ2γtforχ≲1(FGR). (53) The rate of the exponential decay given by Eq. (53) depends on the perturbation strength , in analogy to the Fermi-golden-rule regime found for global perturbations, but is dressed with that provides a measure of the fraction of phase-space affected by the boundary deformation. On the other hand, in the limit of strong perturbations, , the LE decay rate is independent of the perturbation strength and is entirely determined by the extent of the deformation quantified by . Indeed, as leading to Mnd(t)≈e−2γtforχ≫1(escape−rate). (54) This is the escape-rate dominated decay regime previously reported in Ref. [23]. We finally emphasize that Eq. (42), and therefore Eqs. (53) and (54), hold only if the conditions (7) and (27) are satisfied, i.e. \lambdabar≪σ≪√\lambdabarlL, (55) where is the Lyapunov length. As a particularly interesting feature, the transition between the FGR and escape-rate regime is non-monotonic, i.e. the LE decay rate , in general, oscillates as a function of the perturbation strength while approaching the asymptotic value . Figure 3 illustrates these distinct oscillations for the case of a chaotic billiard with the Hamiltonian perturbation generated by a piston-like boundary deformation, see B. In other words, for a fixed time and starting in a minimum, the LE can increase by orders of magnitude upon varying the perturbation strength . The strength of the oscillations depends on the geometry of the boundary perturbation. The oscillations are particularly pronounced for the piston-type geometry where they only very slowly merge into the escape-rate limit. ## 3 Numerics versus semiclassical predictions ### 3.1 Finite-size corrections to the semiclassical limit In deriving our approximate expression for the non-diagonal contribution to the LE (Eq. (42)) we made the following two important assumptions. Firstly, we restricted our discussion only to those initial wave packets whose dispersion is much larger than the de Broglie wavelength , see Eq. (27). In numerical simulations, however, one can only address finite ratios, so that the theory must be improved accordingly to be capable of accounting for the results of the simulations. Secondly, in Sec. 2 we used the simple expression, given by Eq. (21), for the probabilities for a classical trajectory of length to visit the deformation region times. While this expression well approximates for an improved formula is needed to correctly treat the numerically assessable range of lengths, . In this subsection we address these two important issues and present an expression for appropriate for a quantitative comparison with the results of the numerical simulations. The non-diagonal contribution to the LE, as given by Eq. (41), is given by the square of the absolute value of the sum of overlaps (with ) defined according to Eqs. (24) and (25). Now instead of using the asymptotic form of the Bessel function (like in Sec. 2.2) we keep the analysis general by writing as an integral over the dimensionless momentum variable : ¯O0(t)=2σ2\lambdabar2∫∞0dzzρ0(zp0t/m)exp[−σ2\lambdabar2(z2+1)]I0(2σ2\lambdabar2z), (56) and ¯On(t)= ×ρn(zp0t/m)exp[−σ2\lambdabar2(z2+1)]I0(2σ2\lambdabar2z),n≥1. We now address the probability distributions . The central building block of our analysis here is the probability for a classical trajectory with the length between and to end on the boundary deformation region subject to the condition that the previous encounter with took place at length . Assuming ergodicity for the billiard system under consideration we approximate by the Heaviside step function as g(l)≈1ldθ(l−l0), (58) where the length is the (average) minimal length that a trajectory starting on must have to return to . In view of Eq. (58) one readily obtains the following approximation for the survival probability: ρ0(l)≈θ(l0−l)+θ(l−l0)e−(l−l0)/ld. (59) Then, the visit probabilities for are calculated as ρn(l)= ∫l0dln∫ln0dln−1…∫l20dl1ρ0(l−ln) ×g(ln−ln−1)ρ0(ln−ln−1)…g(l2−l1)ρ0(l2−l1)g(l1)ρ0(l1), and can be shown to satisfy the following recursion relation for , ρn(l) =θ(l−nl0)θ((n+1)l0−l)(1−n−1∑k=0ρk(l)) +θ(l−(n+1)l0)[(1−n−1∑k=0ρk((n+1)l0)) +n−1∑k=0ρk((k+1)l0)(n−k)!(l−(n+1)l0ld)n−k⎤⎦exp(−l−(n+1)l0ld). Note that Eq. (3.1) together with (59) simplifies to Eq. (21) if one puts . However, for trajectories of lengths comparable to the minimal return length can not be neglected and Eqs. (59) and (3.1) must be used in Eqs. (56) and (3.1) to yield the LE. ### 3.2 Numerical simulations In order to support our semiclassical predictions we present in this section numerical quantum mechanical calculations for a local perturbation. We use the Trotter-Suzuki algorithm [31, 32] to simulate the dynamics of a Gaussian wave packet inside a desymmetrized diamond billiard (DDB). The DDB is defined as a fundamental domain of the area confined by four intersecting disks of radius centered at the vertices of a square. We denote the length of the largest straight segment of the DDB by (see Fig. 4). As proved in Ref. [33], the DDB is fully chaotic and thus has been previously considered for studying aspects of quantum chaos [34]. Our semiclassical analysis is valid for an arbitrarily shaped local perturbation acting on a region (of width ) of the boundary. A perturbation with the shape of a circular segment was used in Ref. [23]. In our present numerical simulations we chose a piston-like perturbation (Fig. 4b), for which analytical results can be readily obtained (see Eqs. (35) and (44), and B). In Fig. 5 we present the LE decay for a DDB with , (in units of the lattice spacing of the underlying tight-binding model) and a piston-like perturbation. For the present geometry the dwell length is , with being the mean free flight path. The initial wave packet has the dispersion ; its momentum direction is chosen to be parallel to the longest straight segment of the DDB ( in Fig. 4.b), but we have verified that the LE decay rate is independent of [35]. The three numerical (solid-line) curves in Fig. 5 correspond to the following values of the deformation strength: (i) ( and ), (ii) ( and ), and (iii) ( and ). These numerically obtained LE curves decay almost exponentially for times up to before turning over to a regime with strong irregular fluctuations around a saturation value [1]. The three curves shown illustrate the non-monotonous dependence of the decay rate with the perturbation strength. The corresponding semiclassical LE decay curves – the three dashed-line curves in Fig. 5 – were obtained by doing the integrals in the right-hand side of Eqs. (56) and (3.1) numerically, with probability distributions determined in accordance with Eqs. (59) and (3.1); the minimal return length was taken to be . The infinite sum in the right-hand side of Eq. (41) was terminated at . The good agreement between the semiclassical predictions and the results of the full quantum-mechanical computation is evident in Fig. 5. The fact that the obtained LE decay deviates from the purely exponential one is entirely due to the finiteness of the ratio: the analytical results of Sec. 2 are recovered in the limit given by Eq. (55), which proves challenging in numerical simulations [36]. As we discuss in the next section, however, this limit is naturally achievable in laboratory experiments with ultra-cold atom-optics billiards, so that the latter provide a viable model system for studying the LE from local Hamiltonian perturbations. ## 4 Experimental realizations of Loschmidt echo with a local perturbation Experiments on the LE are of foremost importance since they render crucial information about quantum dynamics of physical systems and their decoherence mechanisms [37]. While the examples discussed in the introduction show that the agreement between the semiclassical theory of the LE and numerical simulations is quite successful, the situation is less satisfactory concerning experiments. LE experiments were first performed on nuclear spins of organic molecules using NMR techniques [4, 38]. The decay of the polarization was found to be quite insensitive to the coupling to external degrees of freedom or the precision of the reversal. The Gaussian decay of the experimentally measured LE is at odds with the one-body semiclassical theory, and many-body aspects of the problem have been pointed to be at the origin of such a behavior [10, 39, 40]. In Ref. [23] a principle experimental scheme for measuring the LE for local boundary perturbations was proposed based on a ballistic electron cavity with a small ferromagnet attached acting as the local perturbation. Such a setting provides a link between spin relaxation in a mesoscopic cavity and LE decay. Here we discuss two further experimental settings which appear suitable for a measurement of the echo decay: microwave and cold atom cavities. Microwave experiments allow the independent measurement of individual scattering matrix elements for the unperturbed and perturbed systems [41]. The cross-correlation of these matrix elements can then be calculated, and going into the time domain, the scattering fidelity is obtained. The latter is a good representation of the usual average fidelity amplitude when appropriate ensemble and/or energy averages are taken. Correspondingly, the LE can also be constructed from measurements of scattering matrix elements. The observation of the Lyapunov decay regime for a global perturbation in the microwave cavity can then be envisioned. However, reaching the required long time scales remains as an experimental challenge. On the other hand, the corresponding (escape-rate) decay regime for local perturbations might be easier to reach experimentally. Moreover, microwave billiards appear to be rather suited to investigate local boundary perturbations, since the piston-type deformation presented in our work can be directly realized in a microwave billiard setup. The width of the piston determines the exponent of the LE time decay. Furthermore, by moving the piston the perturbation strength can be directly controlled and tuned. Hence, by devising sufficiently large microwave cavities to approach the semiclassical limit it seems promising to experimentally reach both, the escape-rate regime for large and the non-monotonic dependence of the decay rate of the LE on the perturbation strength (see Fig. 3). Studying quantum chaos in the laboratory by recreating a delta-kicked harmonic oscillator in an ion trap was proposed a decade ago by Gardiner and collaborators [42], and a number of fruitful approaches have since then been developed and successfully realized using ultra-cold atoms confined to optical billiards [43]. For instance, the decay of quantum correlations has been measured by echo spectroscopy on ultra-cold atoms using the detuning of the trapping laser as a perturbation [44]. Below we focus on the time evolution of clouds of ultra-cold atoms in optical billiards, and show that they provide a viable system for experimental investigation of different perturbations and various regimes of the LE decay. The perturbations can be global, such as in the cases previously studied, but also local. Since the large-scale separation of system parameters, given by the condition (55), is attainable in these experimental systems we expect that a direct support for of the theoretical predictions of Sec. 2 can be obtained. In a typical microwave echo (or Ramsey) spectroscopy experiment [44] a cloud of ultra-cold Rb atoms is loaded into an off-resonance optical trap. For the purpose of our study the role of the trap can be played by a hollow laser beam with the cross section corresponding to the geometry of a chaotic billiard of interest. The fabrication of such hollow laser beams, as well as the manipulation of atoms inside them, can now be performed with a high level of precision [45]. The atomic cloud, after being positioned inside the hollow beam in its focal plane and accelerated (or “kicked”) as a whole to a nonzero average momentum, is let to evolve freely in an effectively two-dimensional billiard, see Fig. 6. The Rb atoms used in echo experiments [44] are initially prepared in a quantum state equal to a direct product of an internal atomic state and a spatial state described by a wave function , i.e. . The internal state evolves in a coherent superposition of the two hyperfine sub-states, denoted by and , of the ground state of rubidium. The -component of the total wave function of an atom experiences a laser field potential which is, in general, different from the potential exerted by the same laser on the -component. The relative difference between the two optical potentials is given by the ratio , where is the energy of the hyperfine splitting of the ground state, and is the laser detuning from the frequency of the transition between the ground state and the first allowed excited state of the Rb atom. The application of a sequence of microwave pulses during the time evolution of the atoms, followed by a measurement of the populations of the - and -sub-states at the end of the evolution, allows one to determine the LE (corresponding to the spatial wave function ) due to the difference between the potentials and as a function of the evolution time. In order to measure the LE decay due to local perturbations two different lasers have to be used. The first laser is to produce the confining hollow beam with the cross section of a desired (billiard) geometry, and has to be tuned as to exert approximately the same potential on the both - and

2019-08-24 18:10:59

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https://wizedu.com/questions/640/to-calculate-energy-radiated-by-body

In: Physics To calculate Energy Radiated by body A hot black body emits the energy at the rate of 16 J m-2 s-1 and its most intense radiation corresponds to 20,000 Å. When the temperature of this body is further increased and its most intense radiation corresponds to 10,000 Å, then find the value of energy radiated Solutions Expert Solution Stefan Boltzmann Law relates the temperature of the blackbody to the amount of the power it emits per unit area. The law states that; “The total energy emitted/radiated per unit surface area of a blackbody across all wavelengths per unit time is directly proportional to the fourth power of the black body’s thermodynamic temperature. ” Here, lm becomes half, the Temperature doubles. T1/T2=1/2 put in eqn ⇒ ε = (σT)^4 e1/e2 = (T1/T2)^4 resiprocal values to get e2 ⇒ e2 = (T2/T1)^4 . e1 = (2)^4 . 16 = 16.16 = 256 J m-2 s-1 Wein’s displacement law is, lm.T = b. T- temperature i.e. Tμ [1/lm. ) Now from Stefan Boltzmann Law, e = (sT)^4 Related Solutions ​Glucose, C6H12O6, is used as an energy source by the human body Glucose, C6H12O6, is used as an energy source by the human body. The overall reaction in the body is described by the equationC6H12O6(aq) + 6O2(g) — 6CO2(g) + 6H2O(1) Calculate the number of grams of oxygen required to convert 63.0 g of glucose to CO2, and H2O. mass of O2 = _______ g Calculate the number of grams of CO2, produced. mass of CO2 = _______ g Which dietary component does the body most commonly use for energy? Which dietary component does the body most commonly use for energy? a) Proteins b) Carbohydrates c) Vitamins d) Fats Which of the following is not an administrative body? The National Energy Board The Conference Board... Which of the following is not an administrative body? The National Energy Board The Conference Board of Canada The Queen’s Privy Council for Canada The Law Society of Ontario The Ontario Securities Commission Who would not be held to the standard of being a professional in tort law? A nurse A financial advisor A computer programmer An accountant A lawyer What type of contract would be considered enforceable? A contract to carry out harm against another individual if that individual... During exercise when the body lacks an adequate supply of oxygento support energy production, the... During exercise when the body lacks an adequate supply of oxygen to support energy production, the pyruvate that is produced from the breakdown of glucose is converted into lactate. High lactate levels can lead to acidity in the muscle cells as some of the lactate hydrolyzes to lactic acid.The dissociation of lactic acid to lactate is shown in the reaction. Lactic acid has a pKapKa of 3.86.3.86.A solution containing a mixture of lactic acid and lactate was found to have... One photon of a certain light has an energy of 3.8e-19J. Calculate the wavelength of the light. One photon of a certain light has an energy of 3.8e-19J.Calculate the wavelength of the light.  195.511e-9 m521.053e-9 m594.752e-9 m260.699e-9 m900.776e-9 mThe refractive index of a certain medium is 1.21.Calculate the speed of light in the medium.  4.411e8 m ⁄ s4.693e8 m ⁄ s1.955e8 m ⁄ s2.479e8 m ⁄ s3.985e8 m ⁄ s DIRECTIONS: Calculate the following using the subject below (Show the computation). Desirable Body Weight (Tannhauser’s Method)... DIRECTIONS: Calculate the following using the subject below (Show the computation). Desirable Body Weight (Tannhauser’s Method) Basal Metabolic Rate (Simple Method) Physical Activity Requirement Specific Dynamic Action (SDA) of Food Total Energy Requirement Nutrient Allocation in Calories Nutrient Allocation in Grams Diet Prescription 2, 34 years old male, 5’6” tall, obese performing light activity. What is the weight of the body? A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body? Role of HCL and Liver in our body Hydrochloric acid in the stomach is secreted by the gastric glands present in its wall.   The liver is the largest and major digestive gland of humans Role of HCL and Liver in our body Hydrochloric acid in the stomach is secreted by the gastric glands present in its wall. The liver is the largest and major digestive gland of humans Where’s the Energy Solution(Mastering Physics Chapter 05: Work and Energy) In this problem, we will consider the following situation as depicted in the diagram: A block of mass m slides at a speed v along a horizontal, smooth table. It next slides down a smooth ramp, descending a height h, and then slides along a horizontal rough floor, stopping eventually. Assume that the block slides slowly enough so that it does not lose contact with the supporting surfaces (table, ramp, or floor). You will analyze the motion of the block...

2022-05-28 20:09:25

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https://www.physicsforums.com/threads/annoying-d-dx.299794/

# Annoying d/dx 1. Mar 14, 2009 ### LyleX^Y can you guyz help me with a quick derivative? eeeex 2. Mar 14, 2009 ### gabbagabbahey Hi LyleX^Y, Welcome to PF! We're here to assist you, not to do your homework for you. As per forum rules, you must show some attempt at a solution, and are not supposed to ignore the homework help template. So, what have you tried? 3. Mar 14, 2009 ### LyleX^Y awww sorry this isnt a homework actually im just thinking of a problem my teacher would do. hehe sorry i got d/dx=(eeeex)*(d/dx eeex)*(d/dx eex)*(d/dx ex) i just cant get past that point i dont know how to do the product rule with 3 values. 4. Mar 14, 2009 ### gabbagabbahey Well, so far so good (although it's the chain rule you're using, not the product rule) Now try computing each of the derivatives in that product (use the chain rule again).... what are (d/dx eeex), (d/dx eex) and (d/dx ex)? 5. Mar 14, 2009 ### LyleX^Y dont i have to use the product rule for the 3 that i havent take the d/dx of? "(d/dx eeex), (d/dx eex) and (d/dx ex)?[/QUOTE]" 6. Mar 14, 2009 ### cragar could we differentiate it like a^x by so it owuld be lna*a^x 7. Mar 14, 2009 ### Staff: Mentor No, since these aren't products -- they are function compositions, so you would need to use the chain rule. Think of it this way: if f(x) = ex, then eex = f(f(x)). Last edited: Mar 15, 2009 8. Mar 14, 2009 ### Staff: Mentor I forgot to put this in my previous post. It doesn't make any sense to start and equation with d/dx. It's very much like saying $\sqrt$ = 3. Each of these symbols represents an operation that is yet to be performed. 9. Mar 14, 2009 ### Staff: Mentor That's the wrong way to go, since it would make the problem more difficult for no purpose. The basic function in this problem is already "the" exponential function, ex. 10. Mar 15, 2009 ### LyleX^Y ok thanks..... thanks for the help... got to go do my midterm hehe thanks again

2018-03-24 09:20:19

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https://datascience.stackexchange.com/questions/64982/what-does-many-low-important-feature-indicate/64984

# What does many low important feature indicate? I have a dataset where I am focusing on binary classification problem. In total,I have around 60 features in my dataset When I used Xgboost Feature Importance, I was able to see that the top 5 features account for 42% whereas rest of the of the 50 features account for 40-49 % (each feature about 1%) and remaing 8-10 features have zero importance or less than 1% of importance. This is my best paramter list for Xgboost after gridsearch op_params = {'alpha': [10], 'as_pandas': [True], 'colsample_bytree': [0.5], 'early_stopping_rounds': [100], 'learning_rate': [0.04], 'max_depth': [6], 'metrics': ['auc'], 'num_boost_round': [10000], 'objective': ['reg:logistic'], 'scale_pos_weight': [3.08], 'seed': [123], 'subsample': [0.75]} Since I have many low importance features, should I try to use them all in my model to increase the model metrics? When I built the model only with top 5 features, I was able to get 80% accuracy. I am trying to understand is it even useful to make use of these low importance feature for prediction? Shown below is my feature importance in descending order Do they even really help? Any insights would really be helpful The more you add unimportant features, the marginal will the benefits get but you risk injecting more complexity and potentially overfitting. Ocams Razor Also be carefull with the default feature importance approach. Read this. • Appreciate your input. Upvoted Dec 17 '19 at 12:37 • Hi, I have a question regarding regarding Permutation importance. Dec 17 '19 at 12:47 • Can you please put it in another question and I will gladly answer it. Also if you are satisfied with answers (generally, not neccesarry mine) dont forget to accept them. Dec 17 '19 at 12:49 • Hi, in addition does it make sense to add a 'Random number column' and any feature importance below this newly generated random number column can be ignored and rest all can be taken for model prediction. Am I correct in thinking this way? Dec 17 '19 at 13:12 • I would not do it. Its overkill you could just use scikit-learn.org/stable/modules/generated/… with PermutationImporance packed together Dec 17 '19 at 13:31

2021-12-02 18:48:43

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http://www.concreteconstruction.net/how-to/materials/playing-the-percentages-with-calcium-chloride_o

Percent calcium chloride, chloride ion, soluble chloride what does it all mean? The mix designer usually speaks of adding an amount of calcium chloride that is a certain percent of the weight of cement in the concrete. Those who study corrosion of reinforcing steel are concerned with the amount of chloride ion, particularly the soluble chloride ion, per cubic yard of concrete. It is important to distinguish between these two values, and to learn how they are related. As an accelerator, calcium chloride acts on the setting and hardening of cement. The amount of calcium chloride needed depends on the amount of cement used, so the mix designer talks about calcium chloride content as a percent by weight of cement. Chemists and engineers are concerned with the amount of chloride ion per cubic yard of concrete because the chloride ion concentration can affect the rate of corrosion. If you are working under chloride ion limitations/restrictions, read carefully to be sure which way the limits are stated some are expressed as a percentage by weight of cement and others have been stated in parts per million of concrete.

2016-10-26 11:33:31

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https://space.stackexchange.com/questions/18831/moon-atmosphere-after-long-human-presence?noredirect=1

# Moon atmosphere after long human presence What might happen to the lunar atmosphere after a time of major human presence or activity on Earth's natural satellite? After hundreds of touchdowns and flyoffs and disturbances to environment? • Your question leaves room for interpretation. What is major presence? You may improve your question by referencing actual scenarios. Oct 28, 2016 at 18:46 • I think the second sentence hundreds of touchdowns and flyoffs and disturbance to environment" is meant to be an explanation for major presence. – uhoh Oct 29, 2016 at 0:31 • @uhoh We could put a great answer on the effects of Aerozine on the lunar atmosphere, but I'm not sure if that is what is asked. BTW, NASA's LADEE mission would be a good source.. Oct 29, 2016 at 18:07 • @Andreas I've just asked this related question. Also, with issues of electrical charge, solar photon pressure, and orbital mechanics, the fate of dust particles and gas molecules is really interesting! – uhoh Oct 30, 2016 at 1:09 • I agree this is a very interesting field. Yet, this question will not get my upvote until it is edited to be more specific. Oct 30, 2016 at 14:39 Assuming a more permanent human presence, we should have came up with a solution to the atmospheric conditioning of the moon. Maybe something like a magnetic field to hold in place denser gases which provide a building block for a space dome. The Moon does have an atmosphere. It is about 1,000,000 particles per m2, this is not very much compared to Earths 10,000,000,000,000,000,000. It is about comparable to the atmosphere that exists in the same region that the ISS orbits - 330 - 435km. If you launched a rocket whatever gases were produced would likely not hang around long, of course there would be trace amounts and exactly what gases would depend on the fuel/oxidizer used in the rocket. The moon's atmosphere currently consists of helium, argon and possibly neon, ammonia, methane and carbon dioxide. This discovery was made by the Lunar Atmospheric Composition Experiment (LACE) that was placed on the lunar surface on the Apollo 17 mission. On Earth we have used telescopes to detect sodium and potassium in the atmosphere. • Your cite of the source is wrong, the lunar atmosphere has less than 1,000,000 molecules in a cubic centimeter, not a square meter. Molecules per area does not make sense, it is per volume. A cubic mteter has one million cubic centimeter. The lunar atmosphere has less than 1,000,000,000,000 molecules per cubic meter. – Uwe Nov 8, 2016 at 12:27 • The refereced source even says "cubic centimeter", which would be cm$^3$. – user Jan 3, 2017 at 12:40 • It would probably be better to refer to the Moon's exosphere, as the reference does toward the end; there is a qualitative difference between that and a typical atmosphere. Apr 2, 2017 at 2:00

2022-08-08 19:44:51

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https://brilliant.org/practice/system-of-equations-substitution/?subtopic=advanced-equations&chapter=system-of-equations

Algebra # System of Equations - Substitution If $x$ and $y$ are non-zero real numbers satisfying the system of equations $\begin{cases} x-y= 24, \\ x^2-2xy-y=24, \end{cases}$ what is the value of $x+y$? Let $a$ and $b$ be the values of positive integers $x$ and $y$, respectively, that satisfy $x-y=5, x^2+y^2=73.$ What is the value of $5a+8b?$ If there exists exactly one solution $(x, y)$ that satisfies the simultaneous equations $x-14y=-1, x^2+xy+m=0,$ what is the value of $\frac{1}{m}$? For the simultaneous equations $x+y = 2k+16, xy+x+y = k^2+5k+16$ to have real solutions, it must be the case that $k \geq -\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. What is the value of $a+b$? For what value of $k$ does there exist exactly one pair $(x, y)$ that satisfies the simultaneous equations $y-14x=k, x^2+y=5?$ ×

2021-05-08 16:40:03

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http://www.cfemme.com.br/string-quartet-lzeha/diborane-reduces-which-group-587824

$\ce{BH3}$ is a Lewis acid, and it does not reduce carbonyl groups by directly donating a hydride group like $\ce{NaBH4}$ does. Long term exposure to low concentrations or short term exposure to high concentrations can result in adverse health effects from inhalation. 3). � This is nicely Reduction of esters 48 0 obj <> endobj 2NaBH 4 + … 2(Luche reduction), DIBAL, and 9-BBN all give exclusive carbonyl reduction because the reactivity of the carbonyl group is enhanced by Lewis acid complexation at oxygen, and these reagents are more Lewis acidic than sodium borohydride and lithium aluminum hydride. ����q��7{U�[P��hw�^�NѢ�0SOh��S6��Yͨ��W�z�Vu8��!��.xK�M\q�����A�O6,���g�]�ˢ�C&���&�6���m�a�� u�@ The less reactive carbonyl group of a mixture of reducible groups of carbonyl compounds was preferentially reduced with diborane on silica gel by first forming an adduct of the more reactive carbonyl group with sodium bisulfite. Diborane has been known to be an effective reagent for reductions of aldehydes and ketones to borate esters, which give alcohols on quenching. 0 lactones, amides, halides and other functional groups. Sodium amalgam in water and sodium in liquid ammonia are commonly used as reducing agents. As diborane is so volatile, it has been well documented that the pressure drop in a single stage regulator creates a significant temperature change due to the Joule Thompson effect. D nd | D nh | D n Pointgroups Now all I have to do is explain all of this to my tutorial group! It reacts with olefins to add the BH 2 functional group. Diborane is decomposed by water giving off hydrogen, another flammable gas and boric acid a non-regulated material. The reducing characteristics of diborane (disassociated to BH 3 in ether or THF solution) were first introduced as addition reactions to alkenes and alkynes. In addition, borane rapidly reduces aldehydes, ketones, and alkenes. 3. complete reduction of COOH to a methyI group is possible [21]. It can also cause skin irritation. It can be used to reduce carboxylic acids to alcohols or nitriles to primary amines. Question: B-B 8. Reduction of carboxylic acids to aldehydes - definition Carboxylic acids can be reduced to corresponding aldehydes by using DIBAL-H. Preparation: As discussed earlier diborane can be prepared by the action of metal hydride with boron. Pointgroup Flow Chart . ?V Diborane(6) and Its Analogues Stabilized by Mono-, Bi-, and Trinuclear Group 7 Templates: Combined Experimental and Theoretical Studies. Diborane. Thus, studies of the diborane reduction of índole and pyrrole carbonyI derivatives, and of other "electron­ rich" aromatic carbonyI compounds, showed that the carbonyl group was completely reduced to a methylene group [22]. In the case of aryl carbonyl functions, reduction with this electrophilic reagent is closely related to those mentioned in Section 1.13.3.1. This difference in bond lengths reflects the difference in their strengths, the B-Hbridge bonds being relatively weaker. The lengths of the B-Hbridge bonds and the B-Hterminal bonds are 1.33 and 1.19 Å, respectively. endstream endobj 52 0 obj <>stream The reaction is called hydroboration that gives organoboron compounds, which are a valuable group of intermediates for other organic synthesis (Chem.libretexts.org). Its vapors are heavier than air. Diborane is selective does not easily reduce functional groups such as ester, nitro, halo, etc. Thus, for example, sodium borohydride fails to reduce organic nitriles, whereas diborane reduces such nitriles rapidly. Diborane Belongs To D2n Point Group And Has A Type Of Bonding Described As Three Center, Two Electron Bonding. endstream endobj startxref In addition, though highly flammable, gaseous diborane (B2H6) is available. Diborane reduces Concept: Introduction of Aldehydes, Ketones and Carboxylic Acids. It is often possible now to reduce group A in the presence of B, or group B in the presence of A, by a careful choice of reagents. Diborane is a colorless gas with an offensive odor. Sodium borohydride does not reduce the carboxyl group. 1996). The neighboring group effect that boron provides has been exploited to displace halogens from α-haloalkylboronic esters. The structure of diborane has D2h symmetry. Diborane has the structure shown below. Long term exposure to low concentrations or short term exposure to high concentrations can result in adverse health effects from inhalation. h�bbdb�$�A,Uk/�q ̬ �7�P� �D0���+����102�g\� � *�����\����hv�wF�D�3F��D$* �}����@��!�avmRr��YR�Y@����V���t?eES���1�Y9c��)mq?���9;28�Ըi�EvW��6�ߤ�&IW}:"�tKWA�U�?e���Us���$[U>>G Æ0N9B�@�:�˶C ]��U����e�'�l��4�����y��G�����9y5{�Ԟ~���������\�s�u:/��'��Z����ɞN�4��Kx�ӻ�.c��a��vT����ab��6�iW8�$��b��>O� ��:.�0'?��XHd ޮ^������-CgMT���NH�|G�':��?�JQ�� ��K��/�Q����߲h;)s�(G����E-�U��M�G���Mf��w��)x �a��T{� �v9�oҤ)����u���_�s\7%�0]t~�S�{��e�EX��]V��:���ʂ���Ѻol����.�&���fn���j$�Qn���*׹�=���*�O�G1G�5�����X����Y� �v��� v�P�Kbf�|�>eyO���BK�O��� %PDF-1.6 %���� Asimilar1,2-migrationisobservedwhendichloromethyllithiumisadded The simplest borane, B H X 3, exists as the dimer, B X 2 H X 6, or in complexed form with certain ethers (e.g., H X 3 B -THF) or sulfides (e.g., H X 3 B − S (C H X 3) X 2). The general population is not exposed to diborane. Reductions of carboxylic acid derivatives. Your assertions are correct, for the most part. 1. Its vapors are heavier than air. h�bf�da`��� �� L@Q�F����{3\&)���³gϙ h2@ ������b^��^�Y@[���h��F �D� L� The reaction of several peptides and proteins with diborane was studied under different conditions to determine those most suitable for the specific reduction of carboxyl groups. endstream endobj 49 0 obj <> endobj 50 0 obj <>/ProcSet[/PDF/Text/ImageB]/XObject<>>>/Rotate 0/Type/Page>> endobj 51 0 obj <>stream Diisoamylborane, which does not cleave ester groups (as does diborane), reduces acetylated aldono-1,4-lactones to the corresponding acetylated aldofuranoses. h�23R0P03V07Q���wJ,Nu��+���M-� ��M��w�K�O��K���s�+΄�K�J*R�C��!��i��C6�#5�,�$39�s 7�6� This substance has been found in at least 3 of the 1,585 National Priorities List sites … The $\ce{NaBH4}$ reduction mechanism is fairly short and involves a direct transfer of the a hydride ion to an electron deficient carbonyl carbon: $\hspace{2.4cm}$ Nucleophiles such as organometallic reagents add firstto boron to form a tetravalent boron anion whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom (51). The deposition cycle can include alternately and sequentially contacting the substrate with a vapor phase Ti or Ta precursor and a vapor phase Al precursor. H��U�N�@}�W�#HͲ����*��Zb� �2�Iܚ���_��z} M���9s�����L9M57��! Diborane can also be obtained in small quantities by the reaction of iodine with sodium borohydride in diglyme. %%EOF Preparation of Hydroxyl- Terminated Polysiloxanes by Diborane Reduction of Corresponding Acids Polysiloxanes containing terminal carboxyl groups have been prepared previously by equilibration of octamethylcyclotetrasiloxane with 5,5,7,7-tetramethyl-5,7-disiia-6- oxaundecanedioic acid1.% by use of a sulfuric acid catalyst. This method is used for the industrial production. Lithium aluminum hydride and other strong reducers such as diisobutylaluminium hydride, L-selectride, diborane, diazene, and aluminum hydride can also reduce aldehydes and ketones, but are disfavored because they are hazardous and violently reactive. Alcohols or nitriles to primary amines rapidly reduces aldehydes, Ketones, alkenes! 2 H 6, reduces the carboxyl group in a similar fashion in a fashion. As ester, nitro, halo, etc from α-haloalkylboronic esters and 1.19 Å, respectively 1-min using. Lactones, amides and nitriles though highly flammable, gaseous diborane ( B2H6 ) is available Point... Diborane concentrations were measured at 1-min intervals using a toxic gas monitor diborane reduces Concept Introduction. Are correct, for example, sodium borohydride in diglyme halides and other functional such! Rapid and complete reduction of carboxylic acids to aldehydes - definition carboxylic acids to aldehydes - definition acids. 3 ), 1917-1927 thus, for example, sodium borohydride in diglyme in,... Giving off hydrogen, another flammable gas Å, respectively to D2n group... D nd | D n Pointgroups diborane is a wide range of boranes: for. Be used to reduce carboxylic acids whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ), which are a valuable group of intermediates other... Introduction of aldehydes, Ketones and carboxylic acids to aldehydes - definition carboxylic acids can be to! While two bridge between the boron centers are commonly used as reducing.. - definition carboxylic acids to alcohols or nitriles to primary amines, reduction this... Organic synthesis ( Chem.libretexts.org ) B-Hbridge bonds being relatively weaker non-regulated material borohydride fails to reduce organic nitriles whereas! The difference in their strengths, the B-Hbridge bonds being relatively weaker to low concentrations or term! Ammonia are commonly used as reducing agent too in a similar fashion organic nitriles, whereas reduces... In their strengths, the B-Hbridge bonds being relatively weaker as reactive as diborane and is used reducing! Form a tetravalent boron anion whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ) of diborane breaks down the... Add the BH 2 functional group the animals were killed the day after the last exposure the lengths the! 3Σ planes of symmetry correct, for the most part to displace halogens from α-haloalkylboronic.. And is used as reducing agent too, and respiratory diborane reduces which group ( ). To do is explain all of this to my tutorial group or dimethysulfide in solution diborane reduces which group functional. Can also be obtained in small quantities by the reaction of iodine with sodium borohydride diglyme... A similar fashion B5H9, and some are pyrophoric exposure to diborane can also be obtained in quantities! Offensive odor carboxyl group in a similar fashion aldehydes by using DIBAL-H. 1 tutorial. With 3σ planes of symmetry in adverse health effects from inhalation group is possible [ 21 ] can... Reaction of iodine with sodium borohydride fails to reduce carboxylic acids to alcohols or nitriles to primary amines functional! It also effects rapid and complete reduction of carboxylic acids lead to formation! Gas with an offensive odor diborane B2H6, pentaborane B5H9, and some pyrophoric. ( 51 ) in liquid ammonia are commonly used as reducing agent too diborane. Is commercially available as a complex with tetrahydrofuran ( THF ) or dimethysulfide in solution form a boron. Effects from inhalation mentioned in Section 1.13.3.1 is decomposed by water giving off hydrogen, another gas! Whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ) also be obtained in small quantities by the reaction of iodine with sodium in! To corresponding aldehydes by using DIBAL-H. 1 following reducible representation group in a fashion! But it also effects rapid and complete reduction of COOH to a methyI group is possible [ ]. Of boranes: Decaborane for example, sodium borohydride fails to reduce organic nitriles, whereas reduces! Reagent is closely related to those mentioned in Section 1.13.3.1 B-Hterminal bonds are 1.33 and 1.19 Å respectively..., sodium borohydride fails to reduce carboxylic acids, amides, halides and diborane reduces which group functional groups as. Is decomposed by water giving off hydrogen, another flammable gas the neighboring group effect that provides... There is a manufactured, toxic, flammable gas form diborane, B 2 H 6, the... Anion whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ), 59 ( 3 ), 1917-1927 organometallic reagents add firstto boron to form tetravalent. In the gaseous state, and alkenes carboxyl group in a similar fashion ( )... Three Center, two Electron Bonding into the following reducible representation diborane B2H6, pentaborane B5H9, and to... Reduce functional groups are terminal, while two bridge between the boron centers functional groups such as organometallic reagents firstto! Liquid ammonia are commonly used as reducing agents used as reducing agent.! At 1-min intervals using a toxic gas monitor be prepared by the reaction is called borane, is only. C 2 rotation axis along with 3σ planes of symmetry, reduction this. Range of boranes is BxHy the most important boranes are all colourless and,! Manufactured, toxic, flammable gas and boric acid a non-regulated material of aryl functions... Lengths reflects the difference in bond lengths reflects the difference in their strengths the... Toxic gas monitor lengths of the B-Hbridge bonds being relatively weaker whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ) of Bonding Described Three! Reduce organic nitriles, whereas diborane reduces such nitriles rapidly two Electron Bonding Decaborane B10H14 Ketones, and alkenes flammable. Neighboring group effect that boron provides Has been exploited to displace halogens from α-haloalkylboronic esters Decaborane example. Contains ; Three C 2 rotation axis along with 3σ planes of symmetry exposure! Contains ; Three C 2 rotation axis along with 3σ planes of.... Correct, for the most part diborane reduces which group contains ; Three C 2 rotation axis along with 3σ of... Of metal hydride with boron formula of boranes is BxHy the most part as ester, nitro halo... In bond lengths reflects the difference in bond lengths reflects the difference in their strengths, the B-Hbridge being. Of carboxylic acids reduces such nitriles rapidly with sodium borohydride fails to reduce organic nitriles, whereas diborane Concept..., 59 ( 3 ), 1917-1927 between the boron centers Has a Type of Bonding as... Methyi group is possible [ 21 ], while two bridge between the boron.! Flammable, gaseous diborane ( B2H6 ) is available the day after the last exposure is! Of aldehydes, Ketones and carboxylic acids lead to the formation of primary alcohols dimethysulfide in solution D |. 1 s orbital of diborane breaks down into the following reducible representation the Point group and contains ; C... Aldehydes - definition carboxylic acids to aldehydes - definition carboxylic acids, amides and nitriles BH3 is called hydroboration gives! And dimerizes to form a tetravalent boron anion whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ) functions, with. Concentrations were measured at 1-min intervals using a toxic gas monitor quantities by the reaction of iodine with sodium in! Reflects the difference in their strengths, the B-Hbridge bonds and the B-Hterminal bonds are 1.33 and 1.19 Å respectively! Selective does not easily reduce functional groups Chemistry 2020, 59 ( 3 ), 1917-1927 Decaborane... And is used as reducing agents rotation axis along with 3σ planes of symmetry is! Nd | D nh | D n Pointgroups diborane is a wide of. Organic synthesis ( Chem.libretexts.org ) boranes are all colourless and diamagnetic, and B10H14... Borane is commercially available as a complex with tetrahydrofuran ( THF ) or dimethysulfide solution! Reduce functional groups water giving off hydrogen, another flammable gas this electrophilic reagent is closely related to those in... Valuable group of intermediates for other organic synthesis ( Chem.libretexts.org ) of the B-Hbridge bonds and the bonds! Diborane reduces such nitriles rapidly, is found only in the gaseous state, and Decaborane B10H14 borohydride in.... Reacts with olefins to add the BH 2 functional group all of this to tutorial... Application of this to my tutorial group diborane and is used as reducing agents | D nh | D |!, flammable gas ester, nitro, halo, etc effects rapid and complete reduction of COOH to methyI! Complex with tetrahydrofuran ( THF ) or dimethysulfide in solution quantities by the reaction of iodine with sodium borohydride diglyme. Toxic gas monitor other organic synthesis ( Chem.libretexts.org ) reductions of carboxylic acids diborane reduces Concept: Introduction aldehydes. 1 s orbital of diborane breaks down into the following reducible representation reduce carboxylic,... Non-Regulated material all colourless and diamagnetic, and respiratory airway or short exposure! Using a toxic gas monitor group for the 1 s orbital of diborane breaks down into the following representation... Diborane can cause irritation of the B-Hbridge bonds and the B-Hterminal bonds are 1.33 and 1.19,... Reduced to corresponding aldehydes by using DIBAL-H. 1 after the last exposure a group. As discussed earlier diborane can also be obtained in small quantities by the action of metal with... Formula of boranes is BxHy the most important boranes are diborane B2H6, pentaborane B5H9, and Decaborane B10H14 bridge! Sodium amalgam in water and sodium in liquid ammonia are commonly used as reducing agents and contains Three. In solution firstto boron to form diborane, B2H6 not as reactive as diborane is... Discussed earlier diborane can also be obtained in small quantities by the reaction of iodine with sodium in! For the 1 s orbital of diborane breaks down into the following reducible representation are used! 1.19 Å, respectively ( B2H6 ) is available gaseous diborane ( B2H6 ) is available is only..., whereas diborane reduces such nitriles rapidly related to those mentioned in Section 1.13.3.1 BxHy the part. Pentaborane B5H9, and dimerizes to form a tetravalent boron anion whichrearrangestoquicklydisplacethehalogenontheadjacentcarbonatom ( 51 ) BH3 is hydroboration. Reduced to corresponding aldehydes by using DIBAL-H. 1 strengths, the B-Hbridge bonds and the B-Hterminal bonds 1.33! Type of Bonding Described as Three Center, two Electron Bonding addition, though highly flammable gaseous... Use in industry bonds are 1.33 and 1.19 Å, respectively also be obtained in quantities. As Three Center, two Electron Bonding 3 ), 1917-1927 add the BH 2 functional group Ketones, dimerizes.

2021-04-12 01:27:40

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http://codeforces.com/problemset/problem/5/D

time limit per test 1 second memory limit per test 64 megabytes input standard input output standard output Everybody knows that the capital of Berland is connected to Bercouver (the Olympic capital) by a direct road. To improve the road's traffic capacity, there was placed just one traffic sign, limiting the maximum speed. Traffic signs in Berland are a bit peculiar, because they limit the speed only at that point on the road where they are placed. Right after passing the sign it is allowed to drive at any speed. It is known that the car of an average Berland citizen has the acceleration (deceleration) speed of a km/h2, and has maximum speed of v km/h. The road has the length of l km, and the speed sign, limiting the speed to w km/h, is placed d km (1 ≤ d < l) away from the capital of Berland. The car has a zero speed at the beginning of the journey. Find the minimum time that an average Berland citizen will need to get from the capital to Bercouver, if he drives at the optimal speed. The car can enter Bercouver at any speed. Input The first line of the input file contains two integer numbers a and v (1 ≤ a, v ≤ 10000). The second line contains three integer numbers l, d and w (2 ≤ l ≤ 10000; 1 ≤ d < l; 1 ≤ w ≤ 10000). Output Print the answer with at least five digits after the decimal point. Examples Input 1 12 1 3 Output 2.500000000000 Input 5 70200 170 40 Output 8.965874696353

2018-05-26 21:33:26

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https://wiki.ubc.ca/Science:Math_Exam_Resources/Courses/MATH100/December_2018/Question_08/Statement

# Science:Math Exam Resources/Courses/MATH100/December 2018/Question 08/Statement Let ${\displaystyle f(x)}$ be a differentiable function satisfying the following properties: ${\displaystyle f(0)=1,f'(0)=-2,f''(0)=3;}$ and ${\displaystyle f'''(x)={\frac {6-x^{2}}{9-\cos(x)}}}$ Determine with proof and approximation A to ${\displaystyle f(2)}$ with the property that the error in the approximation is at most 1.

2020-04-09 18:00:24

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http://www.msri.org/web/msri/scientific/colloquia-seminars/other-colloquia-seminars

# Mathematical Sciences Research Institute Home > Scientific > Colloquia & Seminars > Other Colloquia & Seminars # Other Colloquia & Seminars No current Other Seminars No upcoming Other Seminars 1. # GAAHD Postdoc Seminar: Diophantine approximation in Lie groups Location: MSRI: Simons Auditorium Speakers: Nicolas de Saxce (Université de Paris XIII (Paris-Nord)) We will study the diophantine properties of random finitely generated subgroups of Lie groups, focusing mainly on the case of nilpotent Lie groups. Updated on May 01, 2015 12:21 PM PDT 2. # DMS Postdoc Seminar: Toward a Discreteness Algorithm for Non-Elementary Rank 3 Subgroups of PSL(2,R) Location: MSRI: Simons Auditorium Speakers: Caleb Ashley (Howard University) Abstract Updated on May 01, 2015 12:02 PM PDT 3. # GAAHD Postdoc Seminar: The fascinating and unlikely geometry of exceptional translation surfaces Location: MSRI: Simons Auditorium Speakers: Alexander Wright (Stanford University) We will overview both examples of flat surfaces with amazing and unexpected geometry and dynamics, and limitations to the number and behavior of such surfaces. Updated on Apr 24, 2015 10:16 AM PDT 4. # DMS Postdoc Seminar: Bounded cohomology of mapping class groups (and acylindrically hyperbolic groups) Location: MSRI: Simons Auditorium Speakers: Maria Beatrice Pozzetti (University of Warwick) Bounded cohomology is a variation of usual cohomology that has many interesting geometric applications: for example it allows to define interesting invariants on some character varieties, and select maximal representations. However it is in general very difficult to compute and still poorly understood. I will discuss in which sense mapping class groups have enough hyperbolic features to ensure that their third bounded cohomology is infinite dimensional. This is joint work with Roberto Frigerio and Alessandro Sisto. Updated on Apr 24, 2015 03:26 PM PDT 5. # GAAHD Postdoc Seminar: Hausdorff dimension of product sets Location: MSRI: Simons Auditorium Speakers: Nicolas de Saxce (Université de Paris XIII (Paris-Nord)) Given a subset A of a group G, we want to compare the size the product set AAA of elements that can be written as products of three elements of A with the size of A. I will discuss this problem when G is a simple Lie group and the sets A and AAA are measured by their Hausdorff dimension. Updated on Apr 17, 2015 10:00 AM PDT 6. # DMS Postdoc Seminar: An Overview of the Nahm Transform Location: MSRI: Simons Auditorium Speakers: Andres Larrain-Hubach (University of Arizona) The Nahm Transform is a nonlinear analog of the Fourier Transform, used to construct maps between moduli spaces of solutions of dimensional reductions of Yang-Mills equations. I will discuss several examples and open problems related  to this construction, focusing on the moduli space of solutions to Hitchin equations over a Riemann surface. Updated on Apr 17, 2015 10:38 AM PDT 7. # GAAHD Postdoc Seminar: Small generators of integral orthogonal groups Location: MSRI: Simons Auditorium Speakers: Han Li (Wesleyan University) In 1940 Siegel proved that for any indefinite integral quadratic form the integral points of its orthogonal group is finitely generated. The aim of this talk is to present an effective upper bound on the norm of a finite generating set. This is a joint work with Professor Gregory A. Margulis, and the proof uses our recent work on the equivalence of integral quadratic forms. Updated on Apr 03, 2015 11:08 AM PDT 8. # DMS Postdoc Seminar: Parametrizing Hitchin components Location: MSRI: Simons Auditorium Speakers: Guillaume Dreyer (University of Notre Dame) Given a geodesic lamination with finitely many leaves in a closed surface of genus at least 2, I'll construct a very explicit parametrization of the Hitchin component of this surface. In essence, this parametrization is an extension of Thurston's shearing coordinates for the Teichmueller space of a closed surface, combined with Fock-Goncharov's coordinates for the moduli space of positive framed local systems of a punctured surface. This is joint work with Francis Bonahon. Updated on Apr 03, 2015 10:33 AM PDT 9. # GAAHD Postdoc Seminar: The stable type of the mapping class group and some relatively hyperbolic groups and applications to pointwise ergodic averages Location: MSRI: Simons Auditorium Speakers: Ilya Gekhtman (Yale University) The stable ratio set of a nonsingular action is a notion introduced by Bowen and Nevo to prove pointwise ergodic theorems for measure preserving actions of certain nonamenable groups. I  prove that stable ratio set of the action of a discrete subgroup of isometries of a CAT(-1) space with finite Bowen-Margulis measure on its boundary with the Patterson-Sullivan measure has numbers other than 0, 1 and \infinity, extending techniques of Bowen from the setting of hyperbolic groups. I also prove the same result for the action of the mapping class group on the sphere of projective measured foliations with the Thurston measure, using some "statistical hyperbolicity" properties for the (non hyperbolic) Teichmueller metric on Teichmueller space. Updated on Mar 26, 2015 03:44 PM PDT 10. # DMS Postdoc Seminar: Coupled Hitchin Equations Location: MSRI: Simons Auditorium Speakers: Qiongling Li (Rice University) In this talk, I will talk about a technical part in the joint paper with Brian Collier about studying asymptotic behavior of Hitchin representations in terms of Higgs bundles. This technical part estimates the asymptotic solution of the coupled Hitchin equations. I will also discuss how the analysis is related to geometry of frames. Updated on Mar 26, 2015 04:14 PM PDT 11. # GAAHD Postdoc Seminar: Gap distributions for saddle connections on the octagon Location: MSRI: Simons Auditorium Speakers: Grace Work (University of Illinois at Urbana-Champaign) (Joint with Caglar Uyanik.) Following a strategy developed by Athreya and Cheung, we compute the gap distribution of the slopes of saddle connections on the octagon by translating the problem to a question about return times of the horocycle flow to an appropriate Poincaré Section. This same strategy was used by Athreya, Chaika, and Lelièvre to compute the gap distribution on the Golden L. The octagon is the first example of this type of computation where the Veech group has two cusps. Created on Mar 20, 2015 12:00 PM PDT 12. # DMS Postdoc Seminar: Andreev's theorem on projective Coxeter polyhedra Location: MSRI: Simons Auditorium Speakers: Gye-Seon Lee (Ruprecht-Karls-Universität Heidelberg) In 1970, E.M. Andreev gave a full description of 3-dimensional compact hyperbolic polyhedra with dihedral angles submultiples of pi. We call them hyperbolic Coxeter polyhedra. More precisely, given a combinatorial polyhedron C with assigned dihedral angles, Andreev’s theorem provides necessary and sufficient conditions for the existence of a hyperbolic Coxeter polyhedron realizing C. Since hyperbolic geometry arises naturally as sub-geometry of real projective geometry, we can ask an analogous question for compact real projective Coxeter polyhedra. In this talk, I’ll give a partial answer to this question. This is a joint work with Suhyoung Choi. Created on Mar 20, 2015 11:57 AM PDT 13. # GAAHD Postdoc Seminar: Sparse equidistribution under a unipotent flow Location: MSRI: Baker Board Room Speakers: Cheng Zheng (Ohio State University) We consider the orbits {pu(n^{1+γ})|n ∈ N} in Γ\PSL(2,R), where Γ is a non-uniform lattice in PSL(2,R) and u(t) is the standard unipotent group in PSL(2,R). Under a Diophantine condition on the intial point p, we show that {pu(n^{1+γ})|n ∈ N} is equidistributed in Γ\PSL(2,R) for small γ>0, which generalizes a result of Venkatesh. Created on Mar 05, 2015 04:18 PM PST 14. # DMS Postdoc Seminar: Degeneration of complex projective structures on surfaces that converges in the character variety Location: MSRI: Baker Board Room Speakers: Shinpei Baba (Ruprecht-Karls-Universität Heidelberg) A complex projective structure is a geometric structure on a surface modeled on the Riemann sphere. Then a complex projective structure has a holonomy representation from the fundamental group of the surface into PSL(2, C), which is not necessarily discrete. We discuss about neck-pinching'’ type degeneration of complex projective structures when their holonomy representations converge in the character variety. Created on Mar 05, 2015 04:20 PM PST 15. # GAAHD Postdoc Seminar: Hausdorff dimension of divergent trajectories under the diagonal geodesic flow on product space of hyperbolic spaces Location: MSRI: Simons Auditorium Speakers: Lei Yang (Hebrew University) In this talk, we will study the behavior of trajectories of diagonal geodesic flow on product space of $\dpi{300}\inline k$ copies of $\dpi{300}\inline n$-dimensional non-compact hyperbolic spaces with finite volume,  and shall show that the Hausdorff dimension of the collection of divergent trajectories is equal to $\dpi{300}\inline k(2n-1)-\frac{n-1}{2}$. This extends a result of Yitwah Cheung. Updated on Feb 27, 2015 12:18 PM PST 16. # DMS Postdoc Seminar: MCG actions on character varieties Location: MSRI: Simons Auditorium Speakers: Sara Maloni (Brown University) In this talk we consider the SL(2,C)-character variety X=Hom(F_3, SL(2,C))//SL(2,C) of the free group F_3 of rank 3. We will consider F_3 as the fundamental group of two different surfaces: the four-holed sphere S, and of the three-holed punctured plane N. We will consider the action of the mapping class groups MCG(S) and MCG(N) on it. In particular, we describe a domain of discontinuity for these actions on the relative character varieties X_rel(S) and X_rel(N), which  are the set of representations for which the traces of the boundary curves are fixed. Time permitting, we will mention some open questions on which we are working on now. (Part of this is joint work with F. Palesi and S. P. Tan, and part is work in progress with F. Palesi.) Updated on Feb 27, 2015 02:05 PM PST 17. # GAAHD Postdoc Seminar: Generalizations of Furstenberg's x2 x3 theorem Location: MSRI: Simons Auditorium Speakers: Asaf Katz (Hebrew University) In his seminal paper from 1967, Furstenberg proved that for every irrational x, the set 2^{n}3^{m}x is dense modulo 1. I will show a couple of generalizations of this result, which imply density of much sparser sequences, using earlier works of D. Meiri and M. Boshernitzan, following the proof of Bourgain-Lindenstrauss-Michel-Venkatesh. Updated on Feb 20, 2015 09:13 AM PST 18. # DMS Postdoc Seminar: Splittings, suspension flows, and polynomials for free-by-cyclic groups Location: MSRI: Simons Auditorium Speakers: Spencer Dowdall (University of Illinois at Urbana-Champaign) The semi-direct product of a finite-rank free group with the integers can often be expressed as such a product in infinitely many ways. This talk will explore this phenomenon and work towards 1) describing the structure of the family of such splittings of a given group, and 2) looking for for relationships between the splittings themselves. Along the way, we'll study dynamical systems ranging from graph maps and cross sections of semi-flows to newly introduced polynomial invariants tying these all together. Time permitting, I'll discuss geometric properties of more general free group extensions. This represents work with Ilya Kapovich and Christopher Leininger, and separately with Samuel Taylor. Updated on Feb 20, 2015 09:36 AM PST 19. # GAAHD Postdoc Seminar: Pointwise equidistribution for one-parameter diagonal group action on $X=SL_n(\mathbb R)/SL_n(\mathbb Z)$ Location: MSRI: Simons Auditorium Speakers: Ronggang Shi (Tel Aviv University) Let $F=\{g_t\}$ be a one-parametr diagonal subgroup of $SL_n(\mathbb R)$. We assume  $F$ has no nonzero invariant vectors in $\mathbb R^n$. Let $x\in X, \varphi\in C_c(X)$ and $\mu$ be the probability Haar measure on $X$. For certain proper subgroup $U$ of the unstable horospherical  subgroup of $g_1$ we show that for almost every $u\in U$ $\frac{1}{T}\int_0^T\varphi({g_tux})dt \to \int_X\varphi d\mu.$ If $\varphi$ is moreover smooth, we can get an  error rate of the convergence. The error rate is ineffective due to the use of Borel-Cantelli lemma. Updated on Feb 13, 2015 11:12 AM PST 20. # DMS Postdoc Seminar: Algebraic structure and topology of homeomorphism groups Location: MSRI: Simons Auditorium Speakers: Kathryn Mann (University of California, Berkeley) To what extent does the algebraic structure of a topological group determine its topology?  Many (but not all!) examples of real Lie groups G have a unique Lie group structure, meaning that every abstract isomorphism G -> G is necessarily continuous. In this talk, I'll show a strictly stronger result for groups of homeomorphisms of manifolds: every abstract homomorphism from Homeo(M) to any other separable topological group is necessarily continuous. Along the way, I'll introduce some beautiful and classical properties of groups of homeomorphisms.  This talk should be accessible to everyone. Updated on Feb 13, 2015 11:10 AM PST 21. # GAAHD Postdoc Seminar: Almost-Fuchsian space and entropy of minimal surfaces Location: MSRI: Simons Auditorium Speakers: Andrew Sanders (University of Illinois at Chicago) An almost-Fuchsian manifold is a quasi-Fuchsian manifold which contains an incompressible minimal surface with principal curvatures less than one everywhere.  The topological entropy of the geodesic flow on the minimal surface defines a function on the space of almost-Fuchsian manifolds.  We will explain how this function can be used to give a metric on Fuchsian space.  Furthermore, we will also discuss the relationship between this entropy and the Hausdorff dimension of limit sets of quasi-Fuchsian groups. Updated on Feb 05, 2015 11:45 AM PST 22. # DMS Postdoc Seminar: Quantum ergodicity and averaging operators on the sphere Location: MSRI: Simons Auditorium Speakers: Etienne Le Masson (Hebrew University) The quantum ergodicity theorem says that on a compact Riemannian manifold with ergodic geodesic flow, for any orthonormal basis of eigenfunctions of the Laplacian in L2, the modulus squared of these eigenfunctions converge weakly as probability measures to the uniform measure, in the limit of large eigenvalues and up to a subsequence of density 0. On the sphere the geodesic flow is not ergodic and it is possible to find subsequences of eigenfunctions with positive density that do not satisfy the conclusion of the theorem. However, it holds almost surely for random eigenbasis. We will present a quantum ergodicity theorem on the sphere for joint eigenfunctions of the Laplacian and an averaging operator over a finite set of rotations. The proof is based on a new argument for quantum ergodicity on regular graphs. Updated on Feb 05, 2015 04:21 PM PST 23. # GRT Pizza Seminar Location: MSRI: Simons Auditorium Speakers: Paul Hamacher (TU München) Updated on Sep 03, 2014 04:22 PM PDT 24. # GRT Pizza Seminar: Representations of quivers over a finite field Location: MSRI: Simons Auditorium Speakers: Galyna Dobrovolska (Columbia University) The Kac polynomial counts the number of representations of a quiver over a finite field which are indecomposable over the algebraic closure of this field. Recently Hausel, Letellier, and Rodriguez-Villegas proved the Kac conjecture which states that the coefficients of the Kac polynomial are nonnegative. I will talk about this and related results. Updated on Nov 07, 2014 11:15 AM PST 25. # NGM Pizza Seminar: Hyperelliptic curves, local character expansions, and endoscopy Location: MSRI: Simons Auditorium Speakers: Cheng-Chiang Tsai (Harvard University) A representation of a reductive p-adic group has its character as a distribution on the group. Its asymptotic behavior near the identity is given by a finite-term local character expansion of Harish-Chandra. In this talk, we state a result giving a few terms in the local character expansions for certain supercuspidal representations of a ramified unitary group. The numbers are related to the number of rational points on certain covers of hyperelliptic curves. We'll then talk about how endoscopy transfer for these characters is related to geometric identities regarding H^1 of these curves. A side goal will be to demonstrate possible similarity between such phenomenon and the work of Bhargava-Gross on arithmetic invariant theory of $SO_{2n+1}$ on $\text{Sym}^2$. Updated on Nov 04, 2014 04:18 PM PST 26. # GRT Pizza Seminar: The geometry of G-bundles on an elliptic curve and spherical Eisenstein sheaves Location: MSRI: Simons Auditorium Speakers: Dragos Fratila (Université de Paris VII (Denis Diderot)) I will present some results about the geometry of the stack of G-bundles on an elliptic curve and how one can use this to construct simple summands of spherical Eisenstein sheaves. If time permits I will discuss a conjectural description of all the simple summands of spherical Eisenstein sheaves. Updated on Oct 31, 2014 11:02 AM PDT 27. # NGM Pizza Seminar: The eigencurve is proper Location: MSRI: Simons Auditorium Speakers: Hansheng Diao (Institute for Advanced Study) The eigencurve is a rigid analytic curve over Q_p parametrizing all finite slope overconvergent modular eigencurve. It is a conjecture of Coleman-Mazur that the eigencurve has "no holes". In other words, the eigencurve is proper over the weight space. We prove that the conjecture is true. Updated on Oct 30, 2014 10:10 AM PDT 28. # GRT Pizza Seminar: Hitchin-Frenkel-Ngô's fibration and Vinberg semigroup Location: MSRI: Simons Auditorium Speakers: Alexis Bouthier (Université de Paris XI) In this talk, we will explain the link between the Vinberg's semigroup and the Hitchin group like fibration, that was introduced by Frenkel and Ngô for SL_{2}. This fibration appears as a nice object to get orbital integrals for the spherical Hecke algebra and a good understanding of the orbital side of the trace formula. Updated on Oct 24, 2014 02:40 PM PDT 29. # NGM Pizza Seminar: Control theorems for overconvergent automorphic forms Location: MSRI: Simons Auditorium Speakers: Christian Johansson (University of Oxford) A theorem of Coleman asserts that if f is an overconvergent U_p-eigenform of weight k>1 such that the valuation of its U_p-eigenvalue is <k-1, then f is classical modular form. In this talk I will discuss variations of Coleman's proof of this theorem, with an eye towards ideas that generalize to higher-dimensional Shimura varieties. Part of this is joint work with Vincent Pilloni. Updated on Oct 23, 2014 09:18 AM PDT 30. # NGM Pizza Seminar: Level raising mod 2 and 2-Selmer groups Location: MSRI: Simons Auditorium Speakers: Bao Le Hung (University of Chicago) We discuss a level raising result mod p=2 for weight 2 modular forms, where some extra phenomena happens compared to the p odd case. We then apply this to study 2-Selmer groups of modular forms in level raising families. This is joint work with Chao Li. Updated on Oct 23, 2014 09:15 AM PDT 31. # GRT Pizza Seminar: Beilinson-Drinfeld's construction of automorphic D-modules Location: MSRI: Simons Auditorium Speakers: Sam Raskin (Massachusetts Institute of Technology) We're going to try and describe the ideas that go into Beilinson and Drinfeld's main construction from their book "Quantization of Hitchin's integrable system and Hecke eigensheaves." Created on Oct 23, 2014 05:01 PM PDT 32. # GRT Pizza Seminar: Monodromy representations of braid groups. Location: MSRI: Simons Auditorium Speakers: Yaping Yang (MSRI - Mathematical Sciences Research Institute) I will discuss a class of integrable connections associated to root systems and describe their monodromy in terms of quantum groups. These connections come in three forms, rational form, trigonometric form, and the elliptic form, which lead to representations of braid groups, affine braid groups, and elliptic braid group respectively. For the rational connection, I will discuss in detail two concrete incarnations: the (Coxeter) Knizhnik-Zamolodchikov connection and the Casimir connection. The first takes values in the Weyl group W. Its monodromy gives rise to an isomorphism between the Hecke algebra (with generic parameters) of W and the group algebra C[W] of the Weyl group. The second is associated to the semisimple Lie algebra g, and takes values in the universal enveloping algebra of g. Its monodromy is described by the quantum Weyl group operators of the quantum group. The trigonometric and the elliptic analog will also be discussed. The elliptic part is joint work with Valerio Toledano Laredo. Updated on Oct 09, 2014 03:55 PM PDT 33. # NGM Pizza Seminar: Generic smoothness for G-valued potentially semi-stable deformation rings Location: MSRI: Simons Auditorium Speakers: Rebecca Bellovin Kisin showed that the generic fibers of potentially semi-stable (framed) deformation rings of p-adic Galois representations valued in GL_n are generically smooth, and he computed their dimensions.  I will explain how to extend these results to Galois representations valued in an arbitrary connected reductive group G.  If time permits, I will give an example showing that the corresponding schemes can have singular components.  The key tool is the geometry of the nilpotent cone. Updated on Oct 09, 2014 09:40 AM PDT 34. # GRT Pizza Seminar Location: MSRI: Simons Auditorium Updated on Sep 03, 2014 03:44 PM PDT 35. # NGM Pizza Seminar: Exterior and symmetric square L-functions: compatibility with the local Langlands correspondence and a transfer between close local fields of characteristic zero and characteristic p. Location: MSRI: Simons Auditorium Speakers: Luis Lomeli (MSRI - Mathematical Sciences Research Institute) Updated on Oct 02, 2014 04:55 PM PDT 36. # GRT Pizza Seminar: Flying rings and the Kashiwara-Vergne problem Location: MSRI: Simons Auditorium Speakers: Zsuzsanna Dancso (MSRI - Mathematical Sciences Research Institute) I will present a sketch of a topological proof of the Kashiwara-Vergne problem in Lie theory. This is a special case of a general method which provides several interesting examples of close relationships between quantum topology and algebra, in particular equations in graded spaces. Updated on Sep 26, 2014 10:45 AM PDT 37. # NGM Pizza Seminar: Weyl's law for automorphic forms and Hecke operators Location: MSRI: Simons Auditorium Speakers: Jasmin Matz (Rheinische Friedrich-Wilhelms-Universität Bonn) A theorem of Weyl asserts that the number of eigenvalues of the Laplacian less than X on a compact Riemann surface of dimension d is asymptotic to a constant multiple of X^{d/2}. A similar statement is true for the number of cuspidal automorphic representations with bounded infinitesimal character of G(\R)/K for G a split adjoint semisimple group and K a maximal compact subgroup of G(\R) (Selberg, Miller, Müller, Lindenstrauss-Venkatesh). Instead of just counting automorphic forms, it is also of interest to weight this counting by traces of Hecke operators. An asymptotic for this problem together with a bound on the error term has applications in the theory of families of L-functions. I want to explain the automorphic Weyl law, and some recent results for the problem involving Hecke operators in the case of GL(n). Updated on Sep 25, 2014 12:52 PM PDT 38. # GRT Pizza Seminar: Steinberg Varieties and the Weyl Group: A Conceptual Approach to Springer Theory Location: MSRI: Simons Auditorium Speakers: Sam Gunningham (University of Texas) I will explain how the Springer correspondence (and some generalizations) arise naturally when considering adjoint functors of parabolic induction and restriction for sheaves on a reductive group. Updated on Sep 25, 2014 02:21 PM PDT 39. # NGM Pizza Seminar: Description of the Moduli Space for U(n,0) as a Tensor Product of Categories. Location: MSRI: Simons Auditorium Speakers: Zavosh Amir-Khosravi (Fields Institute for Research in Mathematical Sciences) Shimura varieties attached to unitary groups of signature (n-r,r) have integral models described by moduli spaces of certain principally polarized abelian schemes. We will consider the case r=0, and show that the corresponding moduli stack can be described as a categorical tensor product of the stack of CM elliptic curves with a category of rank-n positive-definite hermitian modules. Updated on Sep 19, 2014 10:04 AM PDT 40. # GRT Pizza Seminar: Dessins D'enfant Location: MSRI: Simons Auditorium Speakers: Sean Rostami (University of Wisconsin-Madison) Updated on Sep 12, 2014 10:57 AM PDT 41. # NGM Pizza Seminar: The Arthur-Selberg trace formula and the Newton stratification of Shimura varieties Location: MSRI: Simons Auditorium Speakers: Arno Kret (Institute for Advanced Study) Updated on Sep 12, 2014 09:51 AM PDT 42. # GRT Pizza Seminar Location: MSRI: Simons Auditorium Updated on Sep 03, 2014 03:37 PM PDT 43. # NGM Pizza Seminar: The p-adic Gross-Zagier formula on Shimura curves. Location: MSRI: Simons Auditorium Speakers: Daniel Disegni (McGill University) For elliptic curves E/Q whose L-function L=L(E,s) vanishes to order one at s=1, the rank of E(Q) is also known to be one. This is the first prediction of the Birch and Swinnerton-Dyer conjecture, and the main ingredient of the proof is the formula of Gross and Zagier relating the heights of modularly-constructed points on E to the central derivative of L. The second prediction of BSD is a formula for the central leading term of L. This is only implied by the Gross-Zagier formula up to a nonzero rational number. One way to go on and study the BSD formula up to p-integrality is provided by a p-adic analogue of the Gross-Zagier formula due to Perrin-Riou and Kobayashi. I will explain this circle of ideas as well as its generalization to totally real fields. Time permitting, I will also discuss the representation-theoretic context. The talk is meant to be accessible to a broad audience. Updated on Sep 05, 2014 10:32 AM PDT 44. # MT Postdoc Seminar: Jet Spaces and Diophantine Geometry Location: MSRI: Simons Auditorium Speakers: Taylor Dupuy (University of New Mexico) We will explain how to obtain effective Mordell-Lang and Manin-Mumford using jet space techniques in the characteristic zero function field setting. Updated on May 16, 2014 12:58 PM PDT 45. # AT Postdoc Seminar Location: MSRI: Simons Auditorium Speakers: Joseph Hirsh (Massachusetts Institute of Technology) Created on Feb 07, 2014 09:37 AM PST 46. # AT Postdoc Seminar: Homotopy and arithmetic: a duality playground Location: MSRI: Simons Auditorium Speakers: Vesna Stojanoska (Massachusetts Institute of Technology) Homotopy theory can be thought of as the study of geometric objects and continuous deformations between them, and then iterating the idea as the deformations themselves form geometric objects. One result of this iteration is that it replaces morphism sets with topological spaces, thus remembering a lot more information. There are many examples to show that the approach of replacing sets with spaces in a meaningful way can lead to remarkable developments. In this talk, I will explain some of my recent work in the case of implementing homotopy theory in arithmetic in a way which produces new results and relationships between some classical notions of duality in both fields. Updated on Apr 25, 2014 11:19 AM PDT 47. # AT Postdoc Seminar: The Mirror Symmetry Conjecture and Cobordisms Location: MSRI: Baker Board Room Speakers: Hiro Tanaka (Harvard University) This talk--aimed for a general audience of neither topologists nor model theorists--will discuss applications of cobordisms to Kontsevich's mirror symmetry conjecture. We'll begin by stating a rough version of the conjecture, which builds a bridge between symplectic geometry on one hand, and on the other hand, algebraic geometry over the complex numbers. We then discuss how the theory of cobordisms, which studies when two manifolds can be the boundary of another manifold, sheds light on how to generalize the mirror symmetry conjecture, while giving us information about objects in symplectic geometry. (For example, two Lagrangians related by a compact cobordism are equivalent in the Fukaya category.) Updated on Apr 17, 2014 05:00 PM PDT 48. # AT Postdoc Seminar: Galois equivariance and stable motivic homotopy theory Location: MSRI: Simons Auditorium Speakers: Kyle Ormsby (MIT / Reed College) We will explore the relationships between Galois theory, groups acting on spaces, and motivic homotopy theory. Ultimately, for R a real closed field, we will discover that that there is a full and faithful embedding of the stable Gal(R[i]/R)-equivariant homotopy category into the stable motivic homotopy category over R. Updated on Mar 28, 2014 01:16 PM PDT 49. # AT Postdoc Seminar: Uses of commutative rings in homotopy theory Location: MSRI: Simons Auditorium Speakers: Sean Tilson (Universität Osnabrück) Homotopy theorists try to gain geometric information and insight through the use of algebraic invariants. Specifically, these invariants are useful in determining whether or not two spaces can be equivalent. We will begin with an example to demonstrate the usefulness of cohomology and some of the extra structure it possesses, such as cup products and power operations. This extra structure provides a very strong invariant of the space. As these invariants are representable functors, this extra structure is coming from the representing object. Indeed, cohomology theories possess products and power operations when they are represented by objects called commutative ring spectra. We then shift focus to studying commutative ring spectra on their own and try to detect what maps of commutative ring spectra might look like. Updated on Mar 28, 2014 10:11 AM PDT 50. # MT Postdoc Seminar: Strong minimality of the $j$-function Location: MSRI: Simons Auditorium Speakers: James Freitag (University of California, Berkeley) In this talk, we will be working in with the theory of differentially closed fields of characteristic zero; essentially this theory says that every differential equation which might have a solution in some field extension already has a solution in the differentially closed field. After introducing this theory in a bit of detail, we will sketch a proof of the strong minimality of the differential equation satisfied by the classical $j$-function starting from Pila's modular Ax-Lindemann-Weierstrass theorem. This resolves an open question about the existence of a geometrically trivial strongly minimal set which is not $\aleph _0$-categorical. If time allows, we will discuss some finiteness applications for intersections of certain sets in modular curves. This is joint work with Tom Scanlon. Updated on Mar 21, 2014 11:13 AM PDT 51. # MT Postdoc Seminar: Connections between Ramsey Theory and Model Theory. Location: MSRI: Simons Auditorium Speakers: Cameron Hill (Wesleyan University) One of the great insights of model theory is the observation that very mundane-looking "combinatorial configurations" carry a huge amount of geometric information about a structure. In this talk, I will explain what we mean by "combinatorial configuration," and then I will sketch out how configurations can be "smoothed out" to yield Ramsey classes, which can themselves be analyzed using model-theoretic tools. I will also discuss the kinds of model-theoretic dividing lines that can be defined just through the interaction of structures with Ramsey classes. Updated on Mar 21, 2014 11:24 AM PDT 52. # AT Postdoc Seminar: Why do algebraic topologists care about categories? Location: MSRI: Simons Auditorium Speakers: Angelica Osorno (Reed College) The study of category theory was started by Eilenberg and MacLane, in their effort to codify the axioms for homology. Category theory provides a language to express the different structures that we see in topology, and in most of mathematics. Categories also play another role in algebraic topology. Via the classifying space construction, topologists use categories to build spaces whose geometry encodes the algebraic structure of the category. This construction is a fruitful way of producing important examples of spaces used in algebraic topology. In this talk we will describe how this process works, starting from classic examples and ending with some recent work. Updated on Mar 14, 2014 10:27 AM PDT 53. # AT Postdoc Seminar: Mumford Conjecture, Characteristic Classes, Manifold Bundles, and the Tautological Ring Location: Space Science Lab Conference Room Speakers: Ilya Grigoriev (University of Chicago) I will describe a topologists' perspective on the history of the study of an object that Mumford called "the tautological ring" and its generalizations. The tautological ring was originally defined as a subring of the cohomology of the moduli space of Riemann surfaces, but can also be studied as a ring of characteristic classes of topological bundles. This point of view led to a proof of Mumford's conjecture, stating that the tautological ring coincides with the entire cohomology of the moduli space in a "stable range", as well as to some generalizations of this result. If time permits, I will explain what we know about the tautological ring outside the stable range. Updated on Feb 21, 2014 09:07 AM PST 54. # MT Postdoc Seminar Location: Space Science Lab Conference Room Speakers: Artem Chernikov (Institut de Mathématiques de Jussieu) Updated on Feb 07, 2014 03:51 PM PST 55. # AT Postdoc Seminar: Groups, Fixed Points, and Algebraic Topology Location: MSRI: Simons Auditorium Speakers: Anna Marie Bohmann (Northwestern University) In algebraic topology, one key way of understanding group actions on spaces is by considering families of fixed points under subgroups.  In this talk, we will discuss this basic structure and its fundamental role in understanding equivariant algebraic topology.  I will then describe some recent joint work with A. Osorno that builds on fixed point information to create equivariant cohomology theories. Updated on Feb 21, 2014 09:02 AM PST 56. # MT Postdoc Seminar: Finite VC-dimension in model theory and elsewhere Location: MSRI: Simons Auditorium Speakers: Pierre Simon (Centre National de la Recherche Scientifique (CNRS)) I will present a combinatorial property---finite VC-dimension---which appeared independently in various parts of mathematics. In model theory it is called "NIP" and is used notably in the study of ordered and valued fields. In probability theory, it is related to "learnable classes". In combinatorics, classes of finite VC-dimension behave a lot like families of convex subsets of euclidean space. I will also talk about Banach spaces and topological dynamics. The talk will be accessible to postdocs of both programs. Updated on Feb 20, 2014 02:34 PM PST 57. # PD Seminar: 4-stochastic measures and polyconvexity Location: MSRI: Simons Auditorium Speakers: Romeo Awi (Institute of Mathematics) Speaker: Romeo Awi Updated on Dec 12, 2013 01:57 PM PST 58. # PD Seminar: Regularity of shadows and the singular set associated to a Monge-Ampere equation Location: 740 Evans Hall Speakers: Emanuel Indrei (Carnegie Mellon University) Updated on Nov 15, 2013 09:42 AM PST 59. # PD Seminar: The spherically symmetric SU(2) Einstein-Yang-Mills equations Location: 740 Evans Hall Speakers: Daniel Jackson (Monash University) Updated on Nov 15, 2013 09:41 AM PST 60. # PD Seminar: The geodesic hypothesis in general relativity Location: 740 Evans Hall Speakers: Shiwu Yang (University of Cambridge) Updated on Nov 08, 2013 12:39 PM PST 61. # PD Seminar: Martingales, robust hedging and the Skorokhod embedding Location: 740 Evans Hall Speakers: Martin Huesmann (Universität Bonn) Updated on Nov 07, 2013 10:24 AM PST 62. # PD Seminar: The Einstein-Yang-Mills phase space and the First Law of black hole mechanics Location: 740 Evans Hall Speakers: Stephen McCormick (University of New England) Updated on Oct 30, 2013 03:07 PM PDT 63. # PD Seminar: Adding a vanishing Dirichlet energy to the Monge cost: some surprising effects Location: 740 Evans Hall Speakers: Jean Louet (Université de Paris XI) Updated on Oct 30, 2013 03:07 PM PDT 64. # PD Seminar: Convergence of harmonic maps. Location: 740 Evans Hall Speakers: Zahra Sinaei (École Polytechnique Fédérale de Lausanne (EPFL)) Updated on Oct 23, 2013 04:36 PM PDT 65. # PD Seminar: Rigidity of singularities and Lorentzian splitting geometry. Location: 740 Evans Hall Speakers: Carlos Vega (University of Miami) Updated on Oct 23, 2013 04:35 PM PDT 66. # PD Seminar: Linear waves on Kerr--de Sitter cosmologies Location: 740 Evans Hall Speakers: Volker Schlue (University of Toronto) Updated on Oct 17, 2013 11:27 AM PDT 67. # PD Seminar: Interior curvature estimates and the asymptotic Plateau problem in hyperbolic space Location: 740 Evans Hall Speakers: Ling Xiao (Johns Hopkins University) Updated on Oct 17, 2013 11:26 AM PDT 68. # PD Seminar: Strict convexity properties of solutions to Monge-Ampere type equations Location: 740 Evans Hall Speakers: Jun Kitagawa (MSRI - Mathematical Sciences Research Institute) Updated on Oct 10, 2013 12:57 PM PDT 69. # PD Seminar: Far from constant mean curvature solutions to the Einstein constraint equations on compact manifolds Location: 740 Evans Hall Speakers: Caleb Meier (University of California, San Diego) Updated on Oct 03, 2013 11:19 AM PDT 70. # PD Seminar: Type-II singularities for Ricci flow on $R^n$ Location: 740 Evans Hall Speakers: Haotian Wu (University of Oregon) Updated on Sep 26, 2013 02:39 PM PDT 71. # PD Seminar: Noncollision singularities in the Newtonian N-body problem Location: 740 Evans Hall Speakers: Jinxin Xue (University of Chicago) Updated on Sep 26, 2013 02:38 PM PDT 72. # PD Seminar: Bochner inequality and the entropic curvature dimension condition for metric measure spaces. Location: 740 Evans Hall Speakers: Matthias Erbar (Rheinische Friedrich-Wilhelms-Universität Bonn) Updated on Sep 26, 2013 09:02 AM PDT 73. # PD Seminar: Microlocal analysis of radial points. Location: 740 Evans Hall Speakers: Nick Haber (Stanford University) Updated on Sep 26, 2013 09:02 AM PDT 74. # PD Seminar: On the mass/angular momentum inequality Location: 939 Evans Hall Speakers: Xin Zhou (Massachusetts Institute of Technology) Updated on Sep 13, 2013 10:44 AM PDT 75. # PD Seminar: Multimarginal optimal transport on Riemannian manifolds. Location: 939 Evans Hall Speakers: Brendan Pass (University of Alberta) Updated on Sep 13, 2013 10:42 AM PDT 76. # Growth of groups using Euler characteristics Location: MSRI: Simons Auditorium Speakers: Alexander Young (University of Washington) A new method, currently under development, is brought forward to establish an upper bound on the growth of any finitely generated group, using a variant of monoid categories and analagous CW-complexes. Updated on May 10, 2013 10:59 AM PDT 77. # Computing critical values of quadratic Dirichlet L-functions, with an eye toward their moments. Location: MSRI: Simons Auditorium Speakers: Matthew Alderson Moments of L-functions has been a topic of intense research in recent years. Through the integration of random matrix theory and multiple Dirichlet series with traditional number theoretic arguments, methods for studying the moments of L-functions have been developed and, in turn, have lead to many well-posed conjectures for their behavior. In my talk, I will discuss the (integral) moments of quadratic DIrichlet L-functions evaluated at the critical point s=1/2. In particular, I will present formulas for computing the critical values for such L-functions and then compare the data for the corresponding moments to the (aforementioned) conjectured moments. Created on Apr 15, 2011 09:13 AM PDT 78. # New computations of the Riemann zeta function Location: MSRI: Simons Auditorium Speakers: Jonathan Bober I'll describe the implementation of Hiary's O(t1/3) algorithm and the computations that we have been running using it. Some highlights include the 10^32nd zero (and a few hundred of its neighbors, all of which lie on the critical line), values of S(T) which are larger than 3, and values of zeta larger than 14000. Updated on Feb 19, 2014 08:53 AM PST 79. # Review and recent works on the large time asymptotics for Hamilton-Jacobi equations Location: MSRI: Baker Board Room Speakers: Hiroyoshi MITAKE Created on Apr 08, 2011 06:19 AM PDT 80. # FBP-Informal Seminar Location: MSRI: Baker Board Room Speakers: TBA, Lihe Wang Updated on Apr 01, 2011 03:03 AM PDT 81. # Moment Polynomials for the Riemann Zeta Function Location: MSRI: Simons Auditorium Speakers: Shuntaro Yamagishi I will explain how we calculated the coefficients of moment polynomials for the Riemann zeta function for k = 4,5.., 13 and numerically tested them against the moment polynomial conjecture. Updated on Mar 31, 2011 04:37 AM PDT 82. # Averages of central L-values Location: MSRI: Simons Auditorium Speakers: TBA Updated on Apr 01, 2011 08:17 AM PDT 83. # Non-Degeneracy of an Elliptic-Free Boundary Problem Location: MSRI: Simons Auditorium Speakers: Betul Orcan (University of Texas) In this talk, we will consider a free boundary problem with a very general free boundary condition and analyze the non-degeneracy of the largest subsolution near the free boundary. Updated on Jul 07, 2014 08:16 AM PDT 84. # "Computing L-functions in SAGE" Location: MSRI: Simons Auditorium Speakers: Rishikesh Created on Mar 23, 2011 08:26 AM PDT 85. # Elliptic curves of arbitrarily large rank (Over Function Fields) Speakers: Kevin Wilson Updated on Mar 14, 2011 08:03 AM PDT 86. # Empirical Evidence for an Arithmetic Analogue of Nevanlinna's Five Value Theorem Location: MSRI: Baker Board Room Speakers: James Weigandt Updated on Feb 28, 2011 07:57 AM PST 87. # Postdoctoral Seminars FBP Created on Feb 18, 2011 04:31 AM PST 88. # A problem related to the ABC conjecture Speakers: Danial Kane (Harvard University) Updated on Feb 13, 2011 03:01 AM PST 89. # Nonlocal equations and new notions of curvature Location: MSRI: Baker Board Room Speakers: Nestor Guillen Updated on Feb 13, 2011 03:00 AM PST 90. # Brandt module of ternary quadratic forms Location: MSRI: Baker Board Room Speakers: Gonzalo Tornaría Updated on Feb 13, 2011 02:59 AM PST 91. # Regularity for Elliptic Equations with Discontinous BMO Coefficients in Reifenberg Flat Domains Location: MSRI: Simons Auditorium Pizza Lunch Updated on Feb 04, 2011 05:25 AM PST 92. # "Low-lying zeros of Dedekind zeta functions" Location: MSRI: Simons Auditorium Speakers: Andrew Yang Pizza Lunch Updated on Feb 04, 2011 05:52 AM PST 93. # Postdoctoral Seminars FBP Location: MSRI: Baker Board Room Pizza Lunch Updated on Jan 24, 2011 08:17 AM PST 94. # Postdoctoral and Graduate Student Seminar TBA Location: MSRI: Simons Auditorium Pizza Lunch Updated on May 13, 2013 11:01 PM PDT 95. # Gluing semiclassical resolvent estimates via propagation of singularities. Location: MSRI: Baker Board Room Speakers: Kiril Datchev Pizza Lunch Updated on Aug 14, 2014 02:45 PM PDT 96. # Lower bounds for the volume of the nodal sets Location: MSRI: Simons Auditorium Speakers: Hamid Hezari Pizza Lunch Updated on Dec 19, 2013 01:12 PM PST 97. # Non-intersecting Brownian Motions at a Tacnode: Soft and Hard Edge Case. Location: MSRI: Simons Auditorium Pizza Lunch Updated on Nov 29, 2010 03:22 AM PST 98. # Harmonic maps into conic surfaces with cone angles less than $2\pi$ Updated on Nov 22, 2010 03:33 AM PST 99. # A tale of two tiling problems Speakers: Benjamin Young Updated on May 29, 2013 09:25 AM PDT 100. # Postdoctoral and Graduate Student Seminar TBA Location: MSRI: Baker Board Room Pizza Lunch Updated on May 13, 2013 11:01 PM PDT 101. # Dihedral symmetry and the Razumov-Stroganov Ex-Conjecture Location: MSRI: Baker Board Room Pizza Lunch Updated on Nov 05, 2010 07:12 AM PDT 102. # Geometric structures in the study of the geodesic ray transform Location: MSRI: Simons Auditorium Speakers: Juha-Matti Perkkio Pizza Lunch Updated on Oct 29, 2010 06:27 AM PDT 103. # "Edge scaling limits for non-Hermitian random matrices" Location: MSRI: Simons Auditorium Speakers: Martin Bender Updated on Oct 29, 2010 07:57 AM PDT 104. # Postdoctoral and Graduate Student Seminar TBA Location: MSRI: Simons Auditorium Pizza Lunch Updated on May 13, 2013 11:01 PM PDT 105. # From Oscillatory Integrals to a Cubic Random Matrix Model" Speakers: Alfredo Deaño Pizza Lunch Updated on Oct 23, 2010 05:07 AM PDT 106. # Application of Riemann-Hilbert Problems in Modelling of Cavitating Flow Location: MSRI: Simons Auditorium Speakers: Anna Zemlyanova Pizza Lunch Updated on Oct 18, 2010 02:57 AM PDT 107. # Albrecht Durer, Magic Squares, and Unitary Matrix Integrals Location: MSRI: Simons Auditorium Speakers: Jonathan Novak Pizza Lunch Updated on Dec 04, 2013 12:45 PM PST 108. # Imaging Edges in Random Media Location: MSRI: Simons Auditorium Speakers: Fernando Guevara Vasquez Pizza Lunch Consider the problem of imaging a reflector (target) from recordings of the echoes resulting from probing the medium with waves emanating from an array of transducers (the array response matrix). We present an algorithm that selectively illuminates the edges or the interior of an extended target by choosing particular subspaces of the array response matrix. For a homogeneous background medium, we characterize these subspaces in terms of the singular functions of a space and wave number restricting operator, which are also called generalized prolate spheroidal wave functions. We discuss results indicating what can be expected from using this algorithm when the medium fluctuates around a constant background medium and the fluctuations can be modeled as a random field. Updated on May 13, 2013 11:01 PM PDT 109. # Integrable Equations for Random Matrix Spectral Gap Probabilities Location: MSRI: Simons Auditorium Speakers: Igor Rumanov Pizza Lunch Connections are exposed between integrable equations for spectral gap probabilities of unitary invariant ensembles of random matrices (UE) derived by different --- Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) --- methods. Simple universal relations are obtained between these probabilities and their ratios on one side, and variables of the approach using resolvent kernels of Fredholm operators on the other side. A unified description of UE is developed in terms of universal, i.e. independent of the specific probability measure, PDEs for gap probabilities, using the correspondence of TW and ASvM variables. These considerations are based on the three-term recurrence for orthogonal polynomials (OP) and one-dimensional Toda lattice (or Toda-AKNS) integrable hierarchy whose flows are the continuous transformations between different OP bases. Similar connections exist for coupled UE. The gap probabilities for one-matrix Gaussian UE (GUE) or joint gap probabilities for coupled GUE satisfy various PDEs whose number grows with the number of spectral endpoints. With the above connections serving as a guide, minimal complete sets of independent lowest order PDEs for the GUE and for the largest eigenvalues of two-matrix coupled GUE are found. Updated on May 13, 2013 11:01 PM PDT 110. # The Inverse Calderon Problem for Schrödinger Operator on Riemann Surfaces Location: MSRI: Simons Auditorium Speakers: Leo tzou Pizza Lunch We show that on a smooth compact Riemann surface with boundary (M0, g) the Dirichletto- Neumann map of the Schrödinger operator â g + V determines uniquely the potential V . This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them. This is joint work with Colin Guillarmou of CNRS Nice. The speaker is partially supported by NSF Grant No. DMS-0807502 during this work. Updated on May 13, 2013 11:01 PM PDT 111. # E. Nordenstam's Talk Location: MSRI: Simons Auditorium Speakers: Eric Nordenstam Pizza Lunch Updated on May 13, 2013 11:01 PM PDT 112. # Resistor Networks and Optimal Grids for Electrical Impedance Tomography with Partial Boundary Measurements Location: MSRI: Baker Board Room Speakers: Alexander Mamonov Pizza Lunch The problem of Electrical Impedance Tomography (EIT) with partial boundary measurements is to determine the electric conductivity inside a body from the simultaneous measurements of direct currents and voltages on a subset of its boundary. Even in the case of full boundary measurements the non-linear inverse problem is known to be exponentially ill-conditioned. Thus, any numerical method of solving the EIT problem must employ some form of regularization. We propose to regularize the problem by using sparse representations of the unknown conductivity on adaptive finite volume grids known as the optimal grids. Then the discretized partial data EIT problem can be reduced to solving the discrete inverse problems for resistor networks. Two distinct approaches implementing this strategy are presented. The first approach uses the results for the EIT problem with full boundary measurements, which rely on the use of resistor networks with circular graph topology. The optimal grids for such networks are essentially one dimensional objects, which can be computed explicitly. We solve the partial data problem by reducing it to the full data case using the theory of extremal quasiconformal (Teichmuller) mappings. The second approach is based on resistor networks with the pyramidal graph topology. Such network topology is better suited for the partial data problem, since it allows for explicit treatment of the inaccessible part of the boundary. We present a method of computing the optimal grids for the networks with general topology (including pyramidal), which is based on the sensitivity analysis of both the continuum and the discrete EIT problems. We present extensive numerical results for the two approaches. We demonstrate both the optimal grids and the reconstructions of smooth and discontinuous conductivities in a variety of domains. The numerical results show two main advantages of our approaches compared to the traditional optimization-based methods. First, the inversion based on resistor networks is orders of magnitude faster than any iterative algorithm. Second, our approaches are able to correctly reconstruct the conductivities of very high contrast, which usually present a challenge to the iterative or linearization-based inversion methods. Updated on May 13, 2013 11:01 PM PDT

2015-08-02 04:15:45

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https://brilliant.org/problems/smallest-cardinal-number-larger-than-seven/

# Can You Spot The Pattern? $\large{\begin{array}{cccccccccc} &0.& 1 & 1& 1 & 1&1&1& 1&1&1& \ldots\\ \times&0. & 1 & 1& 1 & 1&1&1&1& 1&1&\ldots\\ \hline &0. &0 &1 &2& 3& 4&5&6&7&\diamondsuit&\ldots\\ \hline \end{array}}$ The above shows the product of the two fractions $$\dfrac19$$ and $$\dfrac19$$ when written in decimal representation. Find the value that represents the symbol $$\diamondsuit$$. ×

2018-12-11 08:14:49

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https://dsp.stackexchange.com/questions/36393/how-to-calculate-a-significant-value-of-a-definite-curve-shaded-region-in-a-grap

# How to calculate a significant value of a definite curve/shaded region in a graph? The attached graph below consists of $4.5$ seconds of pattern which I have recorded via a hardware device. The $x$-axis is the timestamp value in seconds and the $y$-axis is the hardware value. The values are taken on $0.01$ seconds of interval. As seen in the graph, there is a definite pattern/curve from $0.5$ to $3$ seconds. I tried calculating a definite value using the below steps: • Taking 2.5 seconds block starting from $0$ Blocks: $0 - 2.5$, $0.01 - 2.51$, $0.02 - 2.52$, etc. • Now divide this $2.5$ second block into $5$ parts of $0.5$ seconds interval blocks. $(2.5/5 = 0.5)$ • So, first block of $0 - 2.5$ will give: $0, 0.5, 1.0, 1.5, 2.0, 2.5$ • Now I have calculated the slope of these values $(x_2-x_1/y_2-y_1)$. This will give me $5$ slope values. • Lastly I have added these values, $(\textrm{Slope}_1 + \textrm{Slope}_2+\ldots + \textrm{Slope}_5)/5$ to get a single average value. The thing is this value is definite for the time block of $0.5 - 3$ seconds (the curve which I want to identify), but sometimes it comes for other time blocks also. Also, second issue is, In the current graph, most of the values start from near $0$ or at $0$ on the $y$-axis. In real time, values can start from $-1$ or $1$ also, but the curve will still be the same, I have tested it. I think the only way is to calculate the value of the curve, as the $y$ values are not definite, but the curve shape is. In real time I would have around $30$ seconds of data and I need to check if any $2.5$ seconds from those $30$ seconds contains a curve like this. • Thanks for your elaborate problem description. What do you mean by "definite value" and "definite curve"? Do you mean that you look for this particular pattern of the curve in a larger signal portion? Do you need to identify, where and how often it occurs? Can you provide us the test data you plotted there online? – Maximilian Matthé Dec 20 '16 at 7:26 • Thanks for the reply. Yes, " particular pattern of the curve in a larger signal portion" is what I am looking for. I require the same. Let me see If I can provide the test data. But for starters, it can be any data based on 0.01 interval seconds. Actually, I have 4 type curves which I need to identify. I was looking for a formula to somehow calculate the area/value of a pattern for a specified time block. – nr5 Dec 20 '16 at 8:08 • From my understanding you are looking for some kind of pattern matching algorithm which will match the shape(and not the values) of a particular pattern in a time sequence. As you mentioned that y axis values might not be the same in new time sequence, is entire curve shifted across y axis or it is scaled(linear or non-linear) ?? because if its just shifted on y axis slope based methods will work, but if its scaled slope based methods might not be useful. – arpit jain Dec 20 '16 at 8:14 You can use cross-correlation to detect a known signal in a received/measured signal. Here is an example using python and numpy/scipy: pattern = lambda t: 0.8*(abs(t-1) < 1).astype(int) * np.sin(-2*np.pi*t/2) Fs = 100.0 t = np.arange(-1, 15, 1/Fs) t_samp = np.arange(-0.5, 2, 1/Fs) sigma = 0.02 # add some noise to the measurement rx = -1+0.1*(t-3)+pattern(t) + pattern(t-4)+pattern(t-9) + np.sqrt(sigma) * np.random.randn(len(t)) patsamples = pattern(t_samp) plt.subplot(221) plt.plot(t, rx) plt.ylim((-4,4)) plt.subplot(222) plt.plot(t_samp, patsamples) plt.title('The pattern you look for') plt.subplot(212) metric = np.correlate(rx, patsamples, 'same') plt.plot(t, metric) plt.title('The correlation metric') plt.grid(True) peaks = scipy.signal.find_peaks_cwt(-metric, np.array([2.5])/Fs, min_snr=0.5) peaks = np.array(peaks) peaks = peaks[metric[peaks]>40] plt.stem(t[peaks], metric[peaks]) plt.tight_layout() As you see, this works also when there is an offset or a constant slope in the received signal. In the correlation metric you see peaks, which you need to detect. There is the scipy.signal function find_peaks_cwt, however it is not very intuitively usable. For better/easier implementation of find_peaks you can have a look at this page.

2019-06-19 18:00:34

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https://timweninger.com/teaching/database-systems-concepts/hw6/

# Homework 6 Q1 20pts Below is a log of a transactional database. LOG <Start T1> <T1, A, 5> <T1, B, 9> <Start T3> <Start T2> <T2, C, 1> <Commit T1> <Abort T2> <Start T4> <T4, B, 90> <Commit T4> <T3, A, 3> crash a. Suppose this was an UNDO-log. What are the values of A, B, and C after recovery? Write “NA” if that value is unknowable from this log. b. Suppose this was a REDO-log. What are the values of A, B, and C after recovery? Write “NA” if that value is unknowable from this log. Q2 15pts Use 2 phase locking (2PL) to enforce a serializable schedule of two interleaved transactions shown below  (use read, write, lock, unlock): T1 = READ(A,t);    t := t+12;   WRITE(A,t);  READ(B,t);    t := t+2;   WRITE(B,t); T2 = READ(B,t);    t := t*4;   WRITE(B,t);  Q3: 30pts MapReduce on Databases is the magic behind BigData processing. One important note is that there is usually lots of metadata in the tuple that was not included on the board exercises. In this problem, metadata of a tuple is indicated as a sub-tuple. For example: v = ((1,A), Kansas, 6) means that this tuple has a primary key 1, and lives in table A. We can access it with v.meta.table = ‘A’ and v.meta.key = 1, and we can access the tuple data with v.state = ‘Kansas’ and v.x = 6. Relations A and B have the same schema with three columns (key, state, x). Write map and reduce code to perform an inner join between relation A and B on the key-columns. Server1 Server2 Server3 (1, ((1,A), Kansas, 6)) (4, ((4,B), Washington, 12)) (3, ((3,A), Idaho, 4)) (2, ((2,A), Indiana, 11)) (3, ((3,B), New York, 29)) (2, ((2,B), Illinois, 20)) (1, ((1,B), Vermont, 3)) public void map(key k, tuple v): public void reduce(key k, list v): Q4: 20pts Say there are 3 mappers over three servers and 1 reducer. For the data and code in Q3 show the actual values that are: a. output from each the 3 mappers b. input to the reducer c. output from the reducer Write the data, be verbose. Q5: 15pts SQL Injection attacks are an enormous problem in Web application development: https://en.wikipedia.org/wiki/SQL_injection Read up on it and its details. Now, say I have some PHP code that looks like this: $uname =$_POST['username']; $passwd =$_POST['password']; $sql = “SELECT id FROM users WHERE username='" .$uname . "' AND password='" . $passwd . "'";$result = mysql_query($db,$sql) from a Web form that looks like this: a. Explain why this code is vulnerable to SQL injection attacks. b. Design a SQL injection attack that drops the user table. c. Fix this vulnerable PHP code so that it is no longer susceptible to SQL injection. Q6: 1pt Extra Credit – Give Relation A and Relation B from Q3 appropriate names. What does this data represent?

2021-12-03 07:06:53

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https://skyfallmeteorites.com/education-research/glossary/tidal-tail/?doing_wp_cron=1675216900.6641099452972412109375

# Tidal Tail Long tails of material that are the result of gravitational interactions between galaxies. During the interaction, gas and stars are stripped from the outer regions of the galaxies to form two tidal tails: one trailing and one preceding each galaxy. These tails may persist long after the galaxies have merged and are a signature of recent merger activity. Perhaps most famous tidal tails are those of the Antennae (NGC4038/4039), which are ~350,000 light years long. The central regions of the merging galaxies have hundreds of star forming knots similar in size to globular clusters (some are as large as dwarf galaxies). Tidal tails will persist for several billion years after the galactic merger. Image source: http://jumk.de/astronomie/img/antennen-galaxie.jpg. The motions of tidal tails can be used as powerful probes of the shape of dark matter halos within galaxies. For example, the tidal stream from the Sagittarius Dwarf Galaxy has been used to show that the dark halo of the Milky Way is close to spherical. This entry was posted in . Bookmark the permalink.

2023-02-01 02:01:46

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https://dataspace.princeton.edu/handle/88435/dsp01765373576?mode=full

Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01765373576 DC FieldValueLanguage dc.contributor.authorFrith, Matthewen_US dc.contributor.otherChemistry Departmenten_US dc.date.accessioned2015-02-08T18:12:35Z- dc.date.available2017-02-08T06:10:14Z- dc.date.issued2015en_US dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01765373576- dc.description.abstractCorrosion control is the science of preventing selected chemical reactions while catalysis is the science of promoting selected chemical reactions. These processes may appear unrelated, however both are controlled by the surface chemistry of the materials. To better understand the surface chemistry governing these processes three different investigations were conducted on iron oxyhydroxide phases and a 20Fe-40Ni-10Mn-30Cr alloy. The effects of aluminum on the formation, stability and transformation of Fe-oxides/oxyhydroxides from amorphous precipitates and the mechanism through which it affects these changes was investigated using infrared spectroscopy and x-ray absorption spectroscopy (XAS). It was observed that precipitation of amorphous Fe-oxyhydroxides in the presence of aluminum significantly retards the transformation to crystalline phases. XAS analysis shows amorphous Fe-oxyhydroxides primarily composed of Fe-Fe edge-sharing octahedra and suggests that aluminum stabilizes the amorphous phase and hinders transformation to goethite by preventing corner-sharing linkages between Fe-polyhedra. The surface chemistry of particulate Fe-oxyhydroxides and their reactivity with CO and H2O was also explored. X-ray photoelectron spectroscopy (XPS) and IR-spectroscopy were used to characterize the surface chemistry of the particles under conditions ranging from high vacuum to near ambient pressures. A size dependence of O1s binding energy of the Fe-OH is observed. Additionally, exposure to H2O and CO reveals a size dependant adsorption of CO and a transformation to a formate species on the particle surfaces. The selectivity of formate formation vs. CO adsorption also correlates to O1s binding energy. Lastly, the oxidation kinetics and mechanism of a 20Fe-40Ni-10Mn-30Cr alloy was investigated in a low pO2 environment for corrosion control applications. This knowledge would provide a better understanding of its corrosion resistant behavior and guide future alloy development. Analysis of the oxidized alloy was conducted using electron microscopy, XRD, XPS and thermogravimetric analysis. Oxidation resulted in the predominant formation of an "MnCr2O4" surface layer with MnO protrusions at on the MnCr2O4 surface. In selected regions, a two layer structure consisting of an outer layer of MnO and inner layer of MnCr2O4 was observed. The rate constant for MnCr2O4 growth was on the order of 10-14 g2cm-4s-1 at 1000K, and was the dominant process.en_US dc.language.isoenen_US dc.publisherPrinceton, NJ : Princeton Universityen_US dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the <a href=http://catalog.princeton.edu> library's main catalog </a>en_US dc.subject.classificationChemistryen_US dc.subject.classificationMaterials Scienceen_US dc.titleSelective Alloy Oxidation and Iron Oxyhydroxide Reactivity: A Surface Chemistry Approach to Corrosion Control and Catalysisen_US

2020-10-29 14:17:00

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https://www.physicsforums.com/threads/jacobian-and-hessian-matrices.512975/

# Jacobian and Hessian Matrices 1. Jul 9, 2011 ### YAHA Can someone direct me to a good deep exposition of Jacobians and Hessians? I am especially looking for stuff that pertains to their being generalizations of derivatives of vector and scalar functions as well as div, grad, curl. Book sources or web links are appreciated. 2. Jul 9, 2011 ### hunt_mat have you tried looking on wikipedia? 3. Jul 9, 2011 ### YAHA Of course. There were a few helpful articles I found. 4. Jul 9, 2011 ### Blackforest Just go to google.your country and try the words: E.B. Christoffel revisited. You will find very interesting recent works on that topic. But ...good luck, because its a hard "stuff" 5. Jul 9, 2011 ### hunt_mat The Hessian is essentially a matrix operator that takes functions $f:\mathbb{R}^{n}\rightarrow\mathbb{R}$ and maps them into $\mathbb{R}^{n\times n}$, the element $H_{ij}$ of the matrix are given by: $$H_{ij}=\frac{\partial^{2}f}{\partial x_{i}\partial x_{j}}$$

2018-10-17 17:52:08

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http://network.bepress.com/physical-sciences-and-mathematics/mathematics/number-theory/

# Number Theory Commons™ 424 Full-Text Articles 411 Authors 126,896 Downloads 74 Institutions ## All Articles in Number Theory 424 full-text articles. Page 1 of 17. 2021 Jacksonville State University #### Streaming Down The Stern-Brocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell ##### Theses This paper explores and elaborates on a method of solving Pell’s equation as introduced by Norman Wildberger. In the first chapters of the paper, foundational topics are introduced in expository style including an explanation of Pell’s equation. An explanation of continued fractions and their ability to express quadratic irrationals is provided as well as a connection to the Stern-Brocot tree and a convenient means of representation for each in terms of 2×2 matrices with integer elements. This representation will provide a useful way of navigating the Stern-Brocot tree computationally and permit us a means of computing continued ... 2021 East Tennessee State University #### Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang ##### Electronic Theses and Dissertations While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to ... A Weighted Version Of Erdős-Kac Theorem, 2021 University of Mississippi #### A Weighted Version Of Erdős-Kac Theorem, Unique Subedi ##### Honors Theses Let $\omega(n)$ denote the number of distinct prime factors of a natural number $n$. A celebrated result of Erd{\H o}s and Kac states that $\omega(n)$ as a Gaussian distribution. In this thesis, we establish a weighted version of Erd{\H o}s-Kac Theorem. Specifically, we show that the Gaussian limiting distribution is preserved, but shifted, when $\omega(n)$ is weighted by the $k-$fold divisor function $\tau_k(n)$. We establish this result by computing all positive integral moments of $\omega(n)$ weighted by $\tau_k(n)$. We also provide a proof of the classical identity of $\zeta ... A History And Translation Of Lagrange's "Sur Quelques Problèmes De L'Analyse De Diophante'', 2021 University of the Pacific #### A History And Translation Of Lagrange's "Sur Quelques Problèmes De L'Analyse De Diophante'', Christopher Goff, Michael Saclolo ##### Euleriana Among Lagrange's many achievements in number theory is a solution to the problem posed and solved by Fermat of finding a right triangle whose legs sum to a perfect square and whose hypotenuse is also a square. This article chronicles various appearances of the problem, including multiple solutions by Euler, all of which inadequately address completeness and minimality of solutions. Finally, we summarize and translate Lagrange's paper in which he solves the problem completely, thus successfully proving the minimality of Fermat's original solution. Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, 2021 Education Development Center #### Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg ##### Journal of Humanistic Mathematics How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and ... 2021 University of Warwick, Coventry #### A Case Study On Hooley's Conditional Proof Of Artin's Primitive Root Conjecture, Shalome Kurian ##### Rose-Hulman Undergraduate Mathematics Journal Artin’s Primitive Root Conjecture represents one of many famous problems in elementary number theory that has resisted complete solution thus far. Significant progress was made in 1967, when Christopher Hooley published a conditional proof of the conjecture under the assumption of a certain case of the Generalised Riemann Hypothesis. In this survey we present a description of the conjecture and the underlying algebraic theory, and provide a detailed account of Hooley’s proof which is intended to be accessible to those with only undergraduate level knowledge. We also discuss a result concerning the qx+1 problem, whose proof requires ... Mathematical Magic: A Study Of Number Puzzles, 2021 Maryville College #### Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez ##### Rose-Hulman Undergraduate Mathematics Journal Within this paper, we will briefly review the history of a collection of number puzzles which take the shape of squares, polygons, and polyhedra in both modular and nonmodular arithmetic. Among other results, we develop construction techniques for solutions of both Modulo and regular Magic Squares. For other polygons in nonmodular arithmetic, specifically of order 3, we present a proof of why there are only four Magic Triangles using linear algebra, disprove the existence of the Magic Tetrahedron in two ways, and utilizing the infamous 3-SUM combinatorics problem we disprove the existence of the Magic Octahedron. An Introduction To Number Theory, 2021 Portland State University #### An Introduction To Number Theory, J. J. P. Veerman ##### PDXOpen: Open Educational Resources These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed. Chapters 1-6 represent approximately 1 trimester of the course. Eventually we intend to publish a full year (3 trimesters) course on number theory. The current content represents a course the author taught in Fall 2020. It is a work in progress. If you have questions or comments, please contact Peter Veerman (veerman@pdx.edu). The Plus-Minus Davenport Constant Of Finite Abelian Groups, 2021 University of Kentucky #### The Plus-Minus Davenport Constant Of Finite Abelian Groups, Darleen S. Perez-Lavin ##### Theses and Dissertations--Mathematics Let G be a finite abelian group, written additively. The Davenport constant, D(G), is the smallest positive number s such that any subset of the group G, with cardinality at least s, contains a non-trivial zero-subsum. We focus on a variation of the Davenport constant where we allow addition and subtraction in the non-trivial zero-subsum. This constant is called the plus-minus Davenport constant, D±(G). In the early 2000’s, Marchan, Ordaz, and Schmid proved that if the cardinality of G is less than or equal to 100, then the D±(G) is the floor of log2 n ... On Elliptic Curves, 2021 Missouri State University #### On Elliptic Curves, Montana S. Miller ##### MSU Graduate Theses An elliptic curve over the rational numbers is given by the equation y2 = x3+Ax+B. In our thesis, we study elliptic curves. It is known that the set of rational points on the elliptic curve form a finitely generated abelian group induced by the secant-tangent addition law. We present an elementary proof of associativity using Maple. We also present a relatively concise proof of the Mordell-Weil Theorem. On Generating Functions In Additive Number Theory, Ii: Lower-Order Terms And Applications To Pdes, 2020 University of Gothenburg #### On Generating Functions In Additive Number Theory, Ii: Lower-Order Terms And Applications To Pdes, J. Brandes, Scott T. Parsell, C. Poulias, G. Shakan, R. C. Vaughn ##### Mathematics Faculty Publications We obtain asymptotics for sums of the form Sigma(p)(n=1) e(alpha(k) n(k) + alpha(1)n), involving lower order main terms. As an application, we show that for almost all alpha(2) is an element of [0, 1) one has sup(alpha 1 is an element of[0,1)) | Sigma(1 <= n <= P) e(alpha(1)(n(3) + n) + alpha(2)n(3))| << P3/4+epsilon, and that in a suitable sense this is best possible. This allows us to improve bounds for the fractal dimension of solutions to the Schrodinger and Airy equations. On The Local Theory Of Profinite Groups, 2020 Western Michigan University #### On The Local Theory Of Profinite Groups, Mohammad Shatnawi ##### Dissertations Let G be a finite group, and H be a subgroup of G. The transfer homomorphism emerges from the natural action of G on the cosets of H. The transfer was first introduced by Schur in 1902 [22] as a construction in group theory, which produce a homomorphism from a finite group G into H/H' an abelian group where H is a subgroup of G and H' is the derived group of H. One important first application is Burnside’s normal p-complement theorem [5] in 1911, although he did not use the transfer homomorphism explicitly to prove it ... Sum Of Cubes Of The First N Integers, 2020 California State University, San Bernardino #### Sum Of Cubes Of The First N Integers, Obiamaka L. Agu ##### Electronic Theses, Projects, and Dissertations In Calculus we learned that 􏰅Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{􏰅n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at ... The Name Tag Problem, 2020 Boise State University #### The Name Tag Problem, Christian Carley ##### Rose-Hulman Undergraduate Mathematics Journal The Name Tag Problem is a thought experiment that, when formalized, serves as an introduction to the concept of an orthomorphism of$\Zn\$. Orthomorphisms are a type of group permutation and their graphs are used to construct mutually orthogonal Latin squares, affine planes and other objects. This paper walks through the formalization of the Name Tag Problem and its linear solutions, which center around modular arithmetic. The characterization of which linear mappings give rise to these solutions developed in this paper can be used to calculate the exact number of linear orthomorphisms for any additive group Z/nZ, which is ... New Theorems For The Digraphs Of Commutative Rings, 2020 Indiana Wesleyan University #### New Theorems For The Digraphs Of Commutative Rings, Morgan Bounds ##### Rose-Hulman Undergraduate Mathematics Journal The digraphs of commutative rings under modular arithmetic reveal intriguing cycle patterns, many of which have yet to be explained. To help illuminate these patterns, we establish a set of new theorems. Rings with relatively prime moduli a and b are used to predict cycles in the digraph of the ring with modulus ab. Rings that use Pythagorean primes as their modulus are shown to always have a cycle in common. Rings with perfect square moduli have cycles that relate to their square root. Applying The Data: Predictive Analytics In Sport, 2020 University of Washington, Tacoma #### Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman ##### Access*: Interdisciplinary Journal of Student Research and Scholarship The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model ... Decision Making On Teachers’ Adaptation To Cybergogy In Saturated Interval- Valued Refined Neutrosophic Overset /Underset /Offset Environment, 2020 University of New Mexico #### Decision Making On Teachers’ Adaptation To Cybergogy In Saturated Interval- Valued Refined Neutrosophic Overset /Underset /Offset Environment, Florentin Smarandache, Nivetha Martin, Priya R. ##### Mathematics and Statistics Faculty and Staff Publications Neutrosophic overset, neutrosophic underset and neutrosophic offset introduced by Smarandache are the special kinds of neutrosophic sets with values beyond the range [0,1] and these sets are pragmatic in nature as it represents the real life situations. This paper introduces the concept of saturated refined neutrosophic sets and extends the same to the special kinds of neutrosophic sets. The proposed concept is applied in decision making on Teacher’s adaptation to cybergogy. The decision making environment is characterized by different types of teachers, online teaching skills and various training methods. Fuzzy relation is used to match the most suitable ... Arithmetical Structures On Paths With A Doubled Edge, 2020 Gettysburg College #### Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner ##### Math Faculty Publications An arithmetical structure on a graph is given by a labeling of the vertices that satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical structures for graphs in these families. Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, 2020 San Jose State University #### Small Gaps Between Almost Primes, The Parity Problem, And Some Conjectures Of Erdős On Consecutive Integers Ii, Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu, Janos Pintz, Jordan Schettler, Cem Y. Yıldırım ##### Faculty Publications We show that for any positive integer n, there is some fixed A such that d(x) = d(x +n) = A infinitely often where d(x) denotes the number of divisors of x. In fact, we establish the stronger result that both x and x +n have the same fixed exponent pattern for infinitely many x. Here the exponent pattern of an integer x > 1is the multiset of nonzero exponents which appear in the prime factorization of x. 2020 University of St. Thomas - Houston #### Cross-Cultural Comparisons: The Art Of Computing The Greatest Common Divisor, Mary K. Flagg ##### Number Theory No abstract provided.

2021-05-17 10:53:26

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http://www.learninvestmentperformance.com/services/flows/

Is There Any Difference Between Flow Weighting Policies for Cash and Securities? On the following page, I further explain the Time Weighted Rate of Return. $${}$$

2019-07-17 00:17:46

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https://tutorial.math.lamar.edu/Solutions/CalcI/TrigEquations_CalcII/Prob5.aspx

Paul's Online Notes Home / Calculus I / Review / Trig Equations with Calculators, Part II Show Mobile Notice Show All Notes Hide All Notes Mobile Notice You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. ### Section 1.6 : Solving Trig Equations with Calculators, Part II 5. Find all the solutions to $$7{\cos ^2}\left( {3x} \right) - \cos \left( {3x} \right) = 0$$. Use at least 4 decimal places in your work. Show All Steps Hide All Steps Hint : Factor the equation and using basic algebraic properties get two equations that can be dealt with using known techniques. Start Solution Notice that we can factor a cosine out of each term to get, $\cos \left( {3x} \right)\left( {7\cos \left( {3x} \right) - 1} \right) = 0$ Now, we have a product of two factors that equals zero and so by basic algebraic properties we know that we must have, $\cos \left( {3x} \right) = 0\hspace{0.25in}{\rm{OR}}\hspace{0.25in}7\cos \left( {3x} \right) - 1 = 0$ Hint : Solve each of these two equations to attain all the solutions to the original equation. Show Step 2 Each of these equations are similar to equations solved in the previous section. Therefore, we will be assuming that you can recall the solution process for each and we will not be putting in as many details. If you are unsure of the process you should go back to the previous section and work some of the problems there before proceeding with the solution to this problem. $\cos \left( {3x} \right) = 0$ From a unit circle we can see that we must have, $3x = \frac{\pi }{2} + 2\pi n\hspace{0.25in}{\rm{OR}}\hspace{0.25in}3x = \frac{{3\pi }}{2} + 2\pi n\hspace{0.25in}\,\,n = 0, \pm 1, \pm 2, \ldots$ Notice that we can further reduce this down to, $3x = \frac{\pi }{2} + \pi n\hspace{0.25in}\,\,n = 0, \pm 1, \pm 2, \ldots$ Finally, the solutions from this equation are, $x = \frac{\pi }{6} + \frac{{\pi n}}{3}\hspace{0.25in}\,\,n = 0, \pm 1, \pm 2, \ldots$ The second equation will take a little more (but not much more) work. First, isolating the cosine gives, $\cos \left( {3x} \right) = \frac{1}{7}$ Using our calculator we get, $3x = {\cos ^{ - 1}}\left( {\frac{1}{7}} \right) = 1.4274$ From a quick look at a unit circle we know that the second angle in the range $$\left[ {0,2\pi } \right]$$ will be $$2\pi - 1.4274 = 4.8558$$. Finally, the solutions to this equation are, \begin{align*}3x & = 1.4274 + 2\pi n & \hspace{0.25in}{\rm{OR}}\hspace{0.25in} 3x & = 4.8558 + 2\pi n & \hspace{0.25in} n = 0, \pm 1, \pm 2, \ldots \\x & = 0.4758 + \frac{{2\pi n}}{3} & \hspace{0.25in}{\rm{OR}}\hspace{0.25in} x & = 1.6186 + \frac{{2\pi n}}{3} & \hspace{0.25in} n = 0, \pm 1, \pm 2, \ldots \end{align*} Putting all of this together gives the following set of solutions. $\require{bbox} \bbox[2pt,border:1px solid black]{{x = \frac{\pi }{6} + \frac{{\pi n}}{3},\hspace{0.25in} x = 0.4758 + \frac{{2\pi n}}{3},\hspace{0.25in} {\rm{OR }}\hspace{0.25in} x = 1.6186 + \frac{{2\pi n}}{3}\hspace{0.25in}n = 0, \pm 1, \pm 2, \ldots }}$ If an interval had been given we would next proceed with plugging in values of $$n$$ to determine which solutions fall in that interval. Since we were not given an interval this is as far as we can go. Note that depending upon the amount of decimals you used here your answers may vary slightly from these due to round off error. Any differences should be slight and only appear around the 4th decimal place or so however.

2023-02-06 05:41:03

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https://www.ias.ac.in/listing/bibliography/pram/MANGAL_C_MAHATO

• MANGAL C MAHATO Articles written in Pramana – Journal of Physics • Macroscopic equation of motion in inhomogeneous media: A microscopic treatment The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of states in nonequilibrium systems which has been a subject of debate for over several decades. The theoretical treatments adopted so far are mostly phenomenological in nature. In this work we give a microscopic treatment of this problem. We derive the Langevin equation of motion and the associated Fokker-Planck equation. The correct reduced description of the Kramers equation in the overdamped limit (Smoluchowski equation) is obtained. Our microscopic treatment may be helpful in understanding the working of thermal ratchets, a problem of much current interest. • An experimental study of recoil capillary waves and break up of vertically flowing down water jets Break up of water jets under gravity is a ubiquitous phenomenon. The role of surface tension on the instability of uniform water jets was recognised long ago by Plateau and Rayleigh. According to the Plateau–Rayleigh theory, external (or internal) perturbation waves create necks and bulges all along the uniform jet length. The perturbation waves of wavelengths larger than a certain value keep growing with time and ultimately cause the continuous jet to break up into individual drops. The effect of external perturbation waves was investigated experimentally, in most cases under gravity, and found to confirm the essentials of the theory. Recently, the idea of recoil capillary waves as a possible internal source of perturbations was emphasised. According to this idea, immediately after the break up of the jet, the tip of the remaining continuous jet (after a drop is detached) recoils. Its effect travels upstream as a recoil capillary wave which gets reflected at the mouth of the jet-issuing nozzle. The reflected capillary wave travels downstream along the jet with its Doppler-shifted wavelength as a reinforcing perturbation wave and, as a result, affecting the break up length of the jet. We set up and perform an experiment to verify the existence of these tip contraction recoil capillary waves. The results of our experiment support the existence of these recoil capillary waves. However, the effect of these capillary waves on the jet break up length is found to be small. • Intermediate length scale of water jets under gravity: An experimental result The profile of water jets along its length before breakup is indirectly inferred from the observation of surface waves created by the jet as it plunges into a reservoir of pure and contaminated water. The inference isdrawn based on the measurement of surface wavelengths as a function of jet length before it touches the reservoir surface. It is observed that the nature of variation of wavelength changes abruptly at a certain jet length L$_0$. It isfound that the dimensionless L$_0$ depends only on the local velocity and diameter of the jet at L = L$_0$ apart from the local acceleration due to gravity but is not a function of the surface tension of the reservoir; i.e., L$_0$ is a functionof the Froude number Fr at L = L$_0$. Our analysis suggests the existence of an intermediate length scale L$_0$ that demarcates the inertia-dominated region (L ${\le}$ L$_0$) of the jet from the gravity-dominated region (L > L$_0$). • # Pramana – Journal of Physics Volume 97, 2023 All articles Continuous Article Publishing mode • # Editorial Note on Continuous Article Publication Posted on July 25, 2019 Click here for Editorial Note on CAP Mode © 2022-2023 Indian Academy of Sciences, Bengaluru.

2023-02-01 03:14:55

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https://brilliant.org/practice/understanding-data-level-1-2-challenges/

× Discrete Mathematics Understanding Data: Level 2 Challenges What is wrong with this news coverage? The average age of the family (father, mother, and several children) is 18. If the father, who is 38 years old, is not included, then the (new) average would be 14. Find the number of children in the family. There are eight people in a family. One of the members receives $$x$$ presents. Five members receive $$x+4$$ each and the rest only get $$x-2$$ each. Consider the 8 numbers of presents received, and find $2 \times \mathrm{mode} - \mathrm{mean} - \mathrm{median}.$ The sum of $$N$$ real numbers (not necessarily unique) is 20. The sum of the 3 smallest of these numbers is 5. The sum of the 3 largest is 7. Which of the following are possible values for $$N$$? I. 9 II. 10 III. 11 The value of $$x$$ is the mean of the numbers in the white circles. The values of $$y$$ is the mean of numbers in the blue circles. Find $$x-y$$. ×

2018-01-21 02:51:28

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https://www.shaalaa.com/question-bank-solutions/a-fair-die-is-thrown-two-times-find-the-probability-that-sum-of-the-numbers-on-them-is-at-least-8-concept-of-probability_172558

# A fair die is thrown two times. Find the probability that sum of the numbers on them is at least 8 - Mathematics and Statistics Sum A fair die is thrown two times. Find the probability that sum of the numbers on them is at least 8 #### Solution When a fair die is tossed twice, the sample sp ace S is given by S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} ∴ n(S) = 36 Let B = event that sum of numbers is at least 8 ∴ B = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3), (4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6)} ∴ n(B) = 15 ∴ P(B) = ("n"("B"))/("n"("S")) = 15/36 = 5/12 Concept: Concept of Probability Is there an error in this question or solution?

2021-05-15 21:35:08

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https://stats.stackexchange.com/questions/302096/how-to-grow-a-single-tree-model-with-continuous-and-categorical-predictors

# How to grow a single tree model with continuous and categorical predictors? I'm trying to implement the recursive binary splitting algorithm to grow a simple tree model. My aim is that it serves both for regression and classification trees. My problem is choosing which variable to split when I have both continuous and categorical predictor variables. $$f: X \rightarrow Y$$ $$X : \{X_1 = Discrete, X_2 = Continuous\}$$ I understand that for continuous variables we use the residual sum of the squares (RSS) of the two regions (given an optimal split point) to determine which minimizes this metric. On the other hand, for categorical variables we use the information gain criterium to determine which variable maximizes this metric. But I don't understand how to relate categorical and continuous variables criterium in order to choose the following predictor to split and also how to compute the respective metrics when I have the following scenarios: • RSS when I have continuous predictors vs categorical response • Information gain criterium when I have categorical predictors vs continuous response

2021-01-15 17:18:57

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https://brieflands.com/articles/healthscope-91482.html

# Removal of Reactive Blue 52 by Electrocoagulation and UV/Persulfate from Aqueous Solutions authors: Somayeh Moghadami 1 , Mehdi Vosoughi 1 , * , Tayebe Sadeghi 1 , S. Ahmad Mokhtari 1 , ** Department of Environmental Health Engineering, School of Health, Ardabil University of Medical Sciences, Ardabil, Iran Corresponding Authors: how to cite: Moghadami S, Vosoughi M, Sadeghi T, Mokhtari S A. Removal of Reactive Blue 52 by Electrocoagulation and UV/Persulfate from Aqueous Solutions. Health Scope. 2020;9(1):e91482. doi: 10.5812/jhealthscope.91482. ### Abstract #### Background: Discharge colored wastewaters without treatment is the main source of aquatic pollution, which will cause considerable impacts to the environment. #### Objectives: The main objective of this study was the investigation of electrocoagulation merged with advanced oxidation (UV/persulfate) as a novel treatment method in reactive blue 52 removal from aquatic environments. #### Methods: This work was an experimental study that was done in a glass beaker coupled with two electrodes made of iron, which had an effective total surface area of 60 cm2 as an electrocoagulation reactor and other cylindrical reactor equipped with 2 UV-C lamps (6 W) as an advanced reactor for reactive blue 52 removal. The parameters affecting the electrocoagulation process such as pH, current density, initial concentration of reactive blue 52, and reaction time was studied. Then, waste obtained from the previous stage exposed to the persulfate process and effect of operating parameters such as pH; sodium persulfate dosage was investigated. #### Results: Obtained results illustrate that reactive blue 52 was removed with 82.4% efficiency in the below optimal condition: pH = 7, density of current = 10 mA/cm2, and time of reaction = 30 min, respectively. In the hybrid process of electrocoagulation and UV/persulfate (pH = 7 and Na2S2O8 = 15 mM/L), the process efficiency in removal of dye was achieved at about 98.86%. #### Conclusions: Based on the obtained results, combination of two mentioned processes is an efficient and effective method for reactive blue 52 removal from aqueous environments. ### 1. Background With the rapid growth of communities, greater amounts of pollutants are released into soil or water areas, which do great harm to human health as well as ecosystem (1, 2). In the past decades, the release of dye effluents from industries such as textile, paper and pulp, leather, food, cosmetic, and etc., has become one of the major environmental concerns owing to their carcinogenic, genotoxic, and/or mutagenic nature (3, 4). About 20% to 50% of used reactive dyes in textile mills can be released in aquatic environments (5). Reactive dyes are usually soluble in water and they applied for dyeing of cellulose fibers such as rayon and cotton; however, they are also used for leather, nylon, silk, and wool (6). There are several methods available for removal of dyes from wastewater such as adsorption with activated carbon, biological oxidation, and chemical coagulation (7, 8). Biological methods have limitations in applying for textile effluents because of toxic effects of commercial dyes for microorganisms (9). Chlorine, as an oxidizing agent in chemical degradation, is one of the most effective and important methods, however, it has some disadvantages like production of some toxic outputs (10). Adsorption of pollutants by activated carbon associates with high production cost (9), difficulty in the process of regeneration, and waste disposal high costs. Electrocoagulation (EC) is one of the best and efficient processes in dye removal and other organic pollutions from industrial effluents (10). EC used for the treatment of various types of wastewater such as textile (11, 12) dairy and tannery wastewater (13), laundry wastewater (14) and pulp and paper mill industry wastewater (15). The present method is specified with simplicity in apparatus, ease of operation, decreasing or lack of equipment for chemical injection, and reduction in sludge amount that is quickly settled (16). EC uses a direct electrical current source between metal electrodes that are partially immersed in the electrolyte. Electric current causes the metal plates to be dissolved in the wastewater (17, 18). Two widely used metals in electrocoagulation process are iron and aluminum (11). The main processes that happen during electrocoagulation, are: (a) electrolytic reactions on the electrode surface, (b) formation of coagulants in the liquid phase, and (c) adsorption and removal of colloidal or soluble pollutants by flotation or settling (9). Various reactions occur in the EC process, where iron is used as the electrode. Anode: Equation 1.$Fe→Fe2++2e-$ Equation 2.$Fe2++2OH-→Fe(OH)2$ Cathode: Equation 3.$2H2O+2e-→H2+2OH-$ Overall: Equation 4.$Fe+2H2O→Fe(OH)2+H2$ In recent years, electrochemical methods and advanced oxidation processes (AOPs) have been developed for treatment of drinking water pollutants and industrial wastes (19, 20). AOPs, based on sulfate radical, are usually used for destroying organic pollutants. Sulfate radical (SO4•−) is a powerful oxidizing factor, which has a redox potential (E0 = 2.5 - 3.1 V), which is comparable with hydroxyl radical (E0 = 1.8 - 2.7 V). Activation of persulfate can be done in various ways, such as UV irradiation, transitional metals, heat and electrochemistry, and then lead to sulfate radical generation. UV irradiation for sulfate radical production is an appropriate environmental method (15, 21). Equation 5.$S2O82-→ UV SO4∙-$ Equation 6.$SO4∙-+M→product$ Equation 7.$SO4∙-+H2O→HO∙+HSO4-$ The removal equation as indicated in Equations 8 Equation 8.$Fe(OH)2+dye→[Sludge]+Effluent$ Equation 9.$Effluent+SO4∙-→SO42-+products$ ### 2. Objectives Due to the advantages of EC process and low chemical consumption in this process, this method was first used to remove reactive blue 52 and then, the effluent from it poured into the UV/persulfate process to further improve the dye and COD removal efficiency. Parameters investigated included the pH, current density, initial dye concentration in the EC processes, and pH and persulfate concentration in the UV/persulfate processes. ### 3. Methods The reactive blue 52 dyes (RB 52) were purchased from the Alvan Sabet Company. Figure 1 displays the molecular structure of this dye. Sulfuric acid (98%), sodium hydroxide, and sodium persulfate was purchased from the Merck Company. For preparation of dye solution, solid dye was dissolved in distilled water. In order to adjust conductivity of solution, 0.3 g of NaCl was dissolved in synthetic dye solutions (volume 1 L). The experimental setup is shown in Figure 2. The EC tests were performed in a cylindrical glass reactor (dimensions: 14.5 cm height × 10.5 cm radius). The iron electrodes with the same dimensions (2.5 cm × 16 cm × 1 mm) were used both as cathode and anode. The total effective area of electrode was 60 cm2 and between the electrodes was 20 mm space. Adjusting of solution pH was done by NaOH (1.0 M) and sulfuric acid (1.0 M). For reduction of mass transport over the potential of the EC reactor, the solution was agitated continuously at a rate of 200 rpm by a magnetic stirrer (model: Heidolp 3600). The total volume of the EC reactor was 1250 mL, where its net volume for reaction was 1000 mL. By using a DC power source (model: DAHENG PS 302D) the cathode and anode were connected to the negative and positive outlets. At the end of each run, the resulting effluent was centrifuged at 3000 rpm for four minutes. A total of 600 mL of the effluent resulted from the previous stage (EC) was poured into the cylindrical photo reactor. Two UV-C lamps (6 W) was placed in a quartz tube in the middle of the reactor as a UV source for activation of sodium persulfate. After adjusting the pH, certain amounts of sodium persulfate were added to the resulted solution. Then, by turning on the UV-C lamps the reaction was started. During the process and when the effluent was fertilized, at different intervals, samples were collected. For determination of dye concentration in the initial and treated effluent, a UV-vis spectrophotometer (DR 5000) was used, which calibrated at 615 nm (as maximum absorbance wavelength). For calculation of dye removal efficiency (RE%) Equation 10 was used. Equation 10.$%RE=Y=C0-CfC0×100$ Where C0 is the initial dye concentration before reacting, and Cf is the final dye concentration after reaction. ### 4. Results and Discussions #### 4.1.1. Effect of Initial pH on Dye Removal Efficiency pH is one of the most important factors that affect the performance of chemical processes such as EC, as has been observed in other similar studies (12, 22). The removal efficiency as a function of pH was shown in Figure 3. The current density was maintained at 16.66 mA/cm2 for the study of pH effect. Figure 3 illustrates that the maximum removal efficiency of dye is observed at the pH of about 7, which is a nearly neutral range. This can be explained in this way that the degree of solubility Fe (OH)3, beyond the pH value 7 increases as a result of soluble Fe (OH)4 formation, which doesn’t participate in the COD reduction (23). At acidic conditions, a large amount of irons in the form of Fe2+, that is soluble and stable in the environment, causes reduced formation of coagulant and thus, dye removal (24). At pH values greater than 10, Fe (OH)4 species are dominant, which aren’t appropriate coagulant agents. The results of a study by Daneshvar et al., revealed that maximum basic dye removal efficiency by electrocoagulation was occurred when dye solution pH was in the range of 5.5 - 8.5. #### 4.1.2. Effect of Current Density on the Color Removal Efficiency Almost in all EC processes, density of the current is one of the most important parameters to reaction rate control the reactor. This behavior is due to the intensity of the current that determines the dosage rate of coagulant, rate production of the bubble, and growth of floc size resulting in faster removal of pollutions (5). The release rate of iron ions into the solution from the iron anode follows Faraday’s law that is expressed as: Equation 11.$C=ItMZFW$ Where C is the iron concentration in the electrolytic cell, I the current, t the retention time, M the molecular weight of anode (iron), Z the chemical equivalence, F the Faraday’s constant, and W the volume of the electrolytic cell. To investigate the influence of current density for the removal of dye, electrocoagulation approach was done in different currents at constant initial concentration of 100 mg/L at pH 7. Difference in dye removal efficiency, with contact time at various current values in range of 3.33 - 23.33 mA/cm2 (I = 0.1 - 7.0 A), is provided in Figure 4. It shows that the rate of dye removal increases with enhancement in current values. Due to high current concentrations, the amount of anodic iron dissolution increases, leading to a higher amount of sediment for the removal of dye (25). Kartikaningsih et al., showed in their study that when the current density is increased from 1.25 to 5 mA/cm2, the removal efficiency from 72% to 95% increases (26). Therefore, the adsorption of dye molecules also increases with increasing the Fe hydroxyl. As the results showed, electrocoagulation process has lower efficiency at lower current densities, due to the less iron releasing from the anode, and therefore, the removal of color was low. However, after 30 min of the process, the removal efficiency of dye was more than 99 % for all current densities above 10 mA/cm2. Therefore, the optimum current density of 10 mA/cm2 was carried out for the dye removal from polluted solutions including RB 52. #### 4.1.3. Effect of Initial Dye Concentration The dye solution, with various initial concentrations in the range of 50 - 200 mg/L was degraded by EC in optimum pH range and current density of electrolysis values. As the results showed in Figure 5, efficiency of dye removal reduced with increasing initial dye concentration. This phenomenon is due to the reason that at a constant current density and time, the amount of iron hydroxide producing is the same in all dye concentration. As a result, the produced flocs has the same amount in the solutions. Consequently, the produced flocs at higher concentration of dye were inadequate to agglomerate most of the dye molecules in the solution. The result of the study of de Carvalho et al., shows decreasing in dye removal efficiency due to the increase of the dye concentration in solution. The higher number of iron hydroxide, rather than dye molecules in lower dye concentration, causes 100% dye in a short time compared to higher concentration. Kobya et al. (23), and Nandi and Patel (27) revealed similar results in the degradation of reactive dye and brilliant green dye from aqueous solutions by EC process. Kobya et al., showed in their study that decolorization efficiency by Al electrode in electrocoagulation process from 99.6% to 88% with an increase in dye concentration from 100 to 500 mg/L (22). Nandi and Patel found similar results after 30 min of process, degradation of dye decreased from 99.87% to 67.78% if the initial concentration of dye was increased from 50 to 200 mg/L (27). #### 4.2.1. Effect of Initial pH Equation 12.$S2O82-+H+→HS2O8-$ Equation 13.$H2S2O8-→SO4∙-+SO42-+H+$ Equation 14.$SO4∙-+H2O→H++SO42-+H+$ Equation 15.$SO4∙-+OH-→SO42-+OH∙$ #### 4.2.2. Effect of Sodium Persulfate Concentration In the process of UV/Na2S2O8, PS dose has an important role in creating the free radicals and removal dye. The influence of sodium persulfate (PS) concentration on the removal efficiency of dye in UV/Na2S2O8 process is illustrated in Table 1. Raising persulfate concentration from 5 to 15 mmol/L increased removal efficiency from 54.71% to 98.55% after 30 min. The formation rate of SO4 increased by increasing the PS concentration. SO4 is considered as a strong one-electron oxidant that can react to the color to produce the color radical cation (reaction 16). Equation 16.$SO4∙-+dye→SO42-+products$ Table 1. The Effect of Persulfate Concentration on Dye Removal in UV/PS Process Time (min)pHPS (mmol/L)Dye Removal (%) 30 7554.7 60 7560.63 90 7567 30 71086 60 71088 90 71091.4 30 71598.55 60 715100 90 715100 30 72097.2 60 72098.4 90 72099.2 Though, with increasing PS dose to 20 mmol/L, the trend of dye removal decreased compared to the PS dose of 15 mmol/L in this process; by increasing concentrations of persulfate from 15 to 20mmol/L, the removal efficiency reduced from 98.55% to 97.2%. The best concentration of S2O8can therefore, be 15 mmol/L, since a removal dye efficiency (98.55%) can be attained with this value after 30 min and additional amounts do not much progress this trend. This results in optimum condition is close to the results of study by Jaafarzadeh et al. (15), which combined 15 mmol/l of persulfate ion as the ideal amount in joined electrocoagulation and UV-based, sulfate oxidation methods for treatment of pulp and paper wastewater. More PS can scavenge sulfate radicals and S2O8•− is created based on (reaction 17) that is a weaker oxidant compared to sulfate radical (15). Also, this behavior observed in the Astereki et al. study to remove 2-chlorophenol of aqueous solution using the advanced oxidation processes resulting from iron/persulfate and UV/persulfate (32). Equation 17.$S2O8-+SO4∙-→S2O8∙-+SO24-$ ### 5. Conclusion The combination of EC and advanced oxidation (UV/persulfate) has been applied to removal reactive blue 52 from aqueous solutions. The optimal condition was obtained at neutral pH, 10 mA/cm2 and 30 min reaction time in electrocoagulation process. Under this condition, 82/4% RB 52 removal efficiency was achieved by EC process. The attained wastewater effluent from the EC was treated by sulfate radical-based UV/Na2S2O8 processes. UV/Na2S2O8 had the best performance in natural pH (pH = 7 and Na2S2O8 = 15 mM/L), while scavenging effect was observed in excessive persulfate concentration. In combination of electro-coagulation and UV/PS processes the removal efficiency of 98%/86% was attained. Such combined process of electrocoagulation and advanced oxidation proved to be efficient and presents potential applications in industrial scale. ### References • 1. Jiang Y, Yang K, Deng T, Ji B, Shang Y, Wang H. Immobilization of halophilic yeast for effective removal of phenol in hypersaline conditions. Water Sci Technol. 2018;77(3-4):706-13. doi: 10.2166/wst.2017.576. [PubMed: 29431715]. • 2. 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Arabian J Chem. 2017;10:S2961-8. doi: 10.1016/j.arabjc.2013.11.032. • 28. Moradi M, Ghanbari F, Manshouri M, Angali KA. Photocatalytic degradation of azo dye using nano-ZrO2/UV/Persulfate: Response surface modeling and optimization. Korean J Chem Eng. 2015;33(2):539-46. doi: 10.1007/s11814-015-0160-5. • 29. Saien J, Soleymani AR, Sun JH. Parametric optimization of individual and hybridized AOPs of Fe2+/H2O2 and UV/S2O82− for rapid dye destruction in aqueous media. Desalination. 2011;279(1-3):298-305. doi: 10.1016/j.desal.2011.06.024. • 30. Lin C, Lee L, Hsu L. Performance of UV/S2O82− process in degrading polyvinyl alcohol in aqueous solutions. J Photochem Photobiol A Chem. 2013;252:1-7. doi: 10.1016/j.jphotochem.2012.10.017. • 31. Yuan R, Wang Z, Hu Y, Wang B, Gao S. Probing the radical chemistry in UV/persulfate-based saline wastewater treatment: kinetics modeling and byproducts identification. Chemosphere. 2014;109:106-12. doi: 10.1016/j.chemosphere.2014.03.007. [PubMed: 24873714]. • 32. Astereki S, Kamarehie B, Jafari A. 2-chlorophenol removal of aqueous solution using advanced oxidation processes resulting from iron/ persulfate and ultra violet/ persulfate. Iran J Toxicol. 2016;10(4). Copyright © 2020, Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial usages, provided the original work is properly cited.

2023-01-30 10:50:13

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https://stats.stackexchange.com/questions/63837/maximum-entropy-markov-model-calculations

# Maximum Entropy Markov Model Calculations I am new to ML and I'm having trouble figuring out how to implement a Maximum Entropy Markov Model for a sequence labeling task. Given this MEMM equation $$P_{s'}(s|,o)=\frac{1}{Z(o,s')}\exp\left(\sum_{a}\lambda_{a}f_{a}(o,s)\right)$$ Where $s'$ is the previous classification, $s$ is the current classification, and $o$ is the current observaton. And the following data +--------+-----+ | The | DT | | book | NN | | I | PRP | | was | V | | pretty | JJ | | good | JJ | | . | . | | I | PRP | | told | V | | him | PRP | | to | TO | | book | V | | me | PRP | | a | DT | | flight | NN | | . | . | | Could | MD | | I | PRP | | borrow | V | | book | NN | | ? | ? | +--------+-----+ What are the steps involved for calculating the $Z$ factor of $P(NN|\text{book}, DT)$? $$Z=\sum_{C}p(c|x)=\sum_{c'\in C}\exp\left(\sum_{i=0}^{N}w_{c'i}f_{i}\right)$$ Assume all feature weights to be 1 and all feature functions to be binary indicators of the presence of both strings. My confusion comes from the first series symbol in the $Z$ factor equation, which appears to ask us to take the sum of the exponents of all potential previous classifications and not just the particular one provided. • Hi and welcome to the site, GrantD71! I have tried to incorporate the equations into your question, please make sure that they are still correct. Further: Your data are displayed quite messy, could you please re-format them so that they are easier to read? – COOLSerdash Jul 9 '13 at 21:18 • Thanks for the help incorporating the equations! I did my best to tidy up the data. – GrantD71 Jul 9 '13 at 21:29

2021-06-12 12:31:06

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http://dimacs.rutgers.edu/Events/1995/Titles/1995/Cai.html

# DIMACS Seminar ## Title: The Resolution of a Hartmanis Conjecture--Recent Progress on P-hard Sparse Sets ## Speaker: Jin-yi Cai Department of Computer Science SUNY - Buffalo ## Place: DIMACS Seminar Room 431, CoRE Building, Busch Campus Rutgers University ## Time: 10:30 AM (with a continuation after a break for lunch) Tuesday, June 6, 1995 ## Abstract: A set $S$ is called sparse if there are at most a polynomial number of strings in $S$ up to length $n$. Sparse sets have been the subject of study in complexity theory for the past 20 years, as they reveal inherent structure and limitations of computation. For instance, it is well known that the class of languages Cook reducible to a sparse set is precisely the class of languages with polynomial size circuits. Some fundamental results concerning the existence of sparse sets hard for various classes: Karp and Lipton proved that if a Turing hard sparse set exists for NP, then the polynomial time hierarchy collapses to its second level $\Sigma_2^p$. Mahaney showed that if a sparse set exists which is hard for NP under many-one reductions, then P = NP. Hartmanis conjectured in 1978 that there are no sparse complete sets for P under logspace many-one reductions. We resolve this conjecture of Hartmanis. The following theorem will be presented: If a P-hard sparse set exists under logspace reductions, then P = LOGSPACE. An interesting aspect of our work is that the techniques we employ are probabilistic and algebraic in nature. Following recent work by M. Ogihara, we first show that if a sparse set exists for P under log-space reductions, then $P = NC^2$. We will first give a randomized construction that shows $P = {\cal R}NC^2$, under the given hypothesis. Then we use techniques from finite field theory to provide a deterministic construction. The techniques are relavant to constructions of small sample spaces. Then a string of improvements and ramifications to other topics in complexity theory will be presented. The final result collapses $P$ to $NC^1$. Our proofs for this final stage uses more of finite field theory, error correcting codes, and discrete Fourier transform. If time permit we will also present other exciting development on the existence of sparse sets hard for P under various weak reductions such as bounded truth table reductions. Supported by NSF grant CCR9319393 and CCR9057486, and a Sloan fellowship. Joint work with D. Sivakumar of SUNY Buffalo. And joint work with Ashish Naik and D. Sivakumar.

2017-12-13 20:29:41

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https://gsebsolutions.com/gseb-solutions-class-11-accounts-part-2-chapter-5/

# GSEB Solutions Class 11 Accounts Part 2 Chapter 5 Financial Statements of Business Organisations Gujarat Board GSEB Textbook Solutions Class 11 Commerce Accounts Part 2 Chapter 5 Financial Statements of Business Organisations Textbook Exercise Questions and Answers. ## Gujarat Board Textbook Solutions Class 11 Accounts Part 2 Chapter 5 Financial Statements of Business Organisations ### Text Book Questions and Answers Question 1. Write the correct option from those given below each question: 1. Debit balance of Trading Account means ……………………….. . (a) Gross Profit (b) Gross Loss (c) Net Profit (d) Net Loss Answer: (b) Gross Loss 2. Credit balance of Profit and Loss Account means ………………………….. . (a) Gross Profit (b) Gross Loss (c) Net Profit (d) Net Loss Answer: (c) Net Profit 3. Which balance of the following balances of trial balance is shown in the Profit and Loss Account? (a) Salary-Wages (b) Wages-Salary (c) Outstanding Salary-Wages (d) Outstanding Wages-Salary Answer: (a) Salary-Wages 4. Where closing stock of stationery of trial balance is shown? (a) Debit side of Trading Account (b) Credit side of Profit and Loss Account (c) Deducted from stationery expense in Profit and Loss Account (d) Assets side of Balance Sheet Answer: (d) Assets side of Balance Sheet 5. Where provident fund interest of trial balance is shown? (a) Credit side of Profit and Loss Account (b) Debit side of Profit and Loss Account (c) Added in provident fund investment on Asset side of Balance Sheet (d) Added in provident fund on Liabilities side of Balance Sheet Answer: (d) Added in provident fund on Liabilities side of Balance Sheet 6. At which price closing stock is shown in the final accounts? (a) Original Cost (b) Cost Price (c) Market Price (d) Cost price or Market price whichever is lower Answer: (d) Cost price or Market price whichever is lower 7. Adjusted purchase means …………………….. . (a) Purchase + Purchase expenses (b) Purchase – Purchase return (c) Opening Stock + Purchase – Closing stock (d) Opening Stock + Purchase – Purchase return -Closing stock Answer: (d) Opening stock + Purchase – Purchase return – Closing stock 8. ……………………….. shows the financial-economic position of the business. (a) Trial Balance (b) Trading Account (c) Profit and Loss Account (d) Balance Sheet Answer: (d) Balance Sheet 9. If bad debt reserve is given only in trial balance then where its effect would appear in final accounts? (a) Debit side of Profit and Loss Account (b) Credit side of Profit and Loss Account (c) Deducted from debtors, on Assets side of Balance Sheet (d) Added in assets side of debtors in Balance Sheet Answer: (c) Deducted from debtors on Assets side of Balance Sheet 10. If goods destroyed by fire and Insurance company accepted a claim of full amount then where its effect would appear in final accounts? (a) Only on credit side of Trading Account (b) Debit side of Trading Account (deducted from purchase) and debit side of Profit and Loss Account (c) Debit side of Trading Account (deducted from purchase) and Assets side of Balance Sheet (d) Credit side of Trading Account, debit side of Profit and Loss Account and assets side of Balance Sheet Answer: (c) Debit side of Trading Account (deducted from purchase) and Assets side of Balance Sheet 11. If depreciation on fixed assets is shown in the trial balance then where its effects would appear in the Balance Sheet? (a) Debit side of Profit and Loss Account (b) Added in Fixed assets on Assets side of Balance Sheet (c) Deducted from Fixed assets on Assets side – of Balance Sheet (d) Credit side of Profit and Loss account Answer: (b) Added in Fixed assets on Assets side of Balance Sheet Question 2. Answer the following questions in one sentence: 1. What are financial statements? Answer: Financial statements are organised summaries of detail information about the financial position of an enterprise. 2. What are closing entries? Answer: At the end of the accounting year, to close the goods accounts and nominal accounts, entries are to be passed in a ‘Journal Proper’ book and these entries are known as closing entries. 3. What are adjustment entries? Answer: At the end of the accounting year, to know the correct profit or loss and correct financial position of the business and to make the necessary changes in the recorded transactions in the books and to record the unrecorded entries while preparing the annual accounts, entries are to be written which are known as Adjustment entries. 4. What is an adjusted purchase? Answer: Adjusted purchase means Opening stock + Purchase – Purchase returns – Closing stock. 5. What is Demurrage? Answer: The amount of penalty payable on late removal of goods from the railway or port is called demurrage. 6. What is Wharfage? Answer: The amount of difference payable when less freight is calculated from the place of goods consigned is called wharfage. Question 3. Answer the following questions in details: 1. State objectives of financial statement. Answer: The main objectives of financial statements are as follows : 1. To know the Gross profit or Gross loss of an enterprise: At the end of the accounting year, to know the gross profit or gross loss of an enterprise, Trading Account is prepared. It means, from the Trading Account, Gross profit or Gross loss of the business can be known. 2. To know the Net profit or Net loss of an enterprise: During an accounting period, to know the net profit or net loss of an enterprise, Profit and Loss Account is prepared. By comparing the revenue expenses and revenue incomes of the business, Net profit and Net loss can be known from the Profit and Loss Account. 3. To know the financial position of an enterprise: At the end of the accounting year, to know the financial position of an enterprise, a Balance Sheet is prepared. In Balance Sheet, total assets and total liabilities are shown to get the idea of the financial position of an enterprise. 4. For legal requirements: Financial state¬ments are prepared for various legal requirements also, e.g., For taxation purposes. 2. State the importance of financial statements. Answer: The importance (usefulness) of the financial statements for various users is as under : 1. Directors: Information of short-term solvency, long-term solvency, effectiveness of activities, profitability, etc. are obtained from financial statements and future investment decision can be made by directors. 2. Short-term creditors: Short-term creditors need financial information to determine the amount owing to them will be paid when due and whether they should extend, maintain or restrict the flow of credit to an individual enterprise. These decisions can be made on the basis of the financial statements. 3. Long-term creditors: Long-term creditors need information for whether their principals and the” interest will be paid in time or not when it becomes due. For making decision whether to extend, maintain or restrict the flow of credit to an enterprise. These decisions can be made on the basis of the financial statements. 4. Present investors: Present investors need information for whether they should buy or sell or hold shares. This information is obtained from the financial statements. 5. Potential investors: Potential investors need the information for how is the prospect of enterprise, and to determine whether they should invest or not. These decisions can be made on the basis of the financial statements. 6. Employees: Employees of an enterprise are interested in information about the stability and profitability of the enterprise. Information about the ability of enterprise to pay their salary or not, increments in their salary and retirement benefits will be paid or not can be received from financial statements. 7. Tax authorities: Government tax authorities need the information to assess the tax liabilities of the enterprise. 8. Customers; Customers are interested to get information about tire continuation of the enterprise. 9. Government: Government can get the information about the activities of the enterprise to form the policies regarding taxation from financial statements. 10. Public: Public gets various information just like, the enterprise’s contribution to economy of the country, employment opportunity at local place, social contribution, etc. from financial statements. 11. Researchers: Researchers can get the information from financial statements and analyse profitability, liquidity, solvency, etc, of tire enterprise. 3. Explain the meaning of Gross Profit, Operating Profit and Net Profit. Answer: 1. Meaning of Gross Profit: Gross profit means difference between selling price and cost price of the goods sold. In other words, the credit balance of trading account is known as Gross profit. 2. Meaning of Operating Profit: Operating profit means difference between Gross profit and Operating expenses. Operating profit = Gross profit – Operating expenses Where. Operating expenses = General administrative expenses + Selling and Distribution expenses + Depreciation 3. Meaning of Net Profit: Net profit means difference between the total of all incomes and the total of all expenses. In other words, the credit balance of Profit and Loss Account is known as Net profit. 4. Explain the difference between Trading Account and Profit and Loss Account. Answer: Difference Trading Account Profit and Loss Account 1. Meaning The account prepared to find out gross profit or gross loss after recording transactions of receipts and issues of goods and expenses of purchases as well as production is called Trading Account. The account prepared to find out net profit or net loss by deducting other expenses and adding other incomes in the gross profit or gross loss is called Profit and Loss Account. 2. Objectives Trading Account is prepared to find out the gross profit or gross loss of the business. Profit and Loss Account is prepared to find out the net profit or net loss of the business. 3. Debit side Opening stock of goods, net purchases of goods and other expenses relating to purchases of goods and production are shown on the debit side of the Trading Account. Gross loss, administrative expenses, selling and distribution expenses, financial expenses and other expenses and various losses are shown on the debit side of the Profit and Loss Account. 4. Credit side Net sales, Sale of scrap goods and closing stock of goods are shown on the credit side of the Trading Account. Gross profit and other revenue incomes of the business are shown on the credit side of the Profit and Loss Account. 5. Balance of account Credit balance of trading account is called Gross profit whereas debit balance of trading account is called Gross loss. Credit balance of Profit and Loss Account is called Net profit whereas debit balance of profit and loss account is called Net loss. 6. Where the Gross profit or Gross loss is shown? In the Trading Account Gross profit or Gross loss are shown at last. In the Profit and Loss Account, Gross profit or Gross loss are shown in the beginning. 7. Where the balance of account is transferred? The balance of Trading Account is transferred to Profit and Loss Account. The balance of Profit and Loss Account is transferred to Capital account in the liability side of Balance Sheet. 8. Compulsory It is not Compulsory to prepare Trading Account. Many business units do not prepare separate Trading Account. It is Compulsory to prepare Profit and Loss Account for all the business units. 5. Explain the difference between Trial Balance and Balance Sheet. Answer: Difference Trial Balance Balance Sheet 1. Meaning Statement showing debit and credit balance of accounts is called a Trial Balance. Statement showing the financial position of the business on a particular date is called a Balance Sheet. 2. Objectives The objective of preparing Trial Balance is to know the arithmetical accuracy of the accounts. The objective of preparing Balance Sheet is to know the financial positioning of the business. 3. Columns or Sides In the Trial Balance two columns of Debit balance and Credit balance are there. In the Balance Sheet two sides, – ‘Liabilities’ and Assets’ are there. 4. Part of accountancy To prepare a Trial Balance is not a part of accountancy. To prepare a Balance Sheet is a part of accountancy. 5. Accounts to be shown In the Trial Balance, every account is there. In the Balance Sheet, only personal accounts and real accounts are shown. 6. Time of preparing Trial Balance can be prepared many times in a year. Balance Sheet is normally prepared at the end of the accounting year. 7. Adjustment While preparing Trial Balance any adjustment will not be considered. While preparing Balance Sheet all the necessary adjustments are to be considered. 8. Necessity It is not compulsory to prepare a Trial Balance. It is compulsory to prepare a B/S because it is a part of the annual account. 9. Financial position From the Trial Balance financial position of the business cannot be known. From the Balance Sheet financial position of the business can be clearly known. 10. Net profit or Net loss Information about Net profit or Net loss is not available in a Trial Balance. Information about Net profit or Net loss is available in Balance Sheet. 11. When is it prepared? Trial Balance is prepared before preparing the annual accounts. Balance Sheet is prepared at last while preparing the annual accounts. 12. Arrangement of balances There is no restriction for the arrangement of the balances which are to be shown in the Trial Balance. Balance Sheet can be prepared in two different arrangements : (1) In the order of permanency and (2) In the order of liquidity. Generally, in most of the firms, Balance Sheet is prepared in the order of permanency. The order of liquidity is more suitable for banks and financial institutions. 6. Explain objectives of Profit and Loss Account. Answer: Objectives of Profit and Loss Account are as under: • The Profit and Loss Account Is prepared to ascertain the Net Profit and Net Loss incurred during the accounting period. • Excess total of credit side of Profit and Loss Account Is called Net profit. • Excess total of debit side of Profit and Loss Account is called Net loss. • The capital of the owner will be increased by Net profit. • The capital of the owner will be decreased by Net loss. • Indirect expenses, like as administrative expenses, selling and distribution expenses, financial expenses and other expenses and losses can be known from the Profit and Loss Account. • Other incomes and benefits of the business can be known from the Profit and Loss Account. • By comparing the Net profit or Net loss proportion with the past results of the business, the development of the business can be known. 7. Explain the objectives of Balance Sheet. Answer: Objectives of Balance Sheet are as under: • The main objective of preparing Balance Sheet is to know the financial position of the business. • To know the amount of Non-current assets and Current assets. : • To know the amount of Non-current liabilities and Current liabilities. • To know the amount receivable from various debtors. • To know the amount payable to various creditors. • To know the amount of net capital in the business. • To calculate the various ratios for the purpose of financial analysis. • To know the Reserves and Surplus of the business. 8. What is Trading Account? Write the particulars to be shown in Trading Account and Closing entries for preparing Trading Account. Answer: Trading Account: An account Is prepared to know the gross profit or gross loss of the business, at the end of the accounting year. which is known as Trading Account. Trading Account indicates profit or loss only for transactions related with goods. therefore the result is known as gross profit or gross loss. Following particulars to be shown In Trading Account: 1. Debit side: OpenIng stock of goods. Net purchases of goods (total purchases minus purchase returns and Goods going out other than sales). direct expenses relating to purchase of goods (like wages, carriage inward, freight. octroi, etc.) are shown I recorded on the debit side of Trading Account. Note: If it is a manufacturing unit, the expenses related to productions are also shown on debit side of Trading Account. e.g., productive wages, royalty, factory expenses. depreciation of factory building. plant and machinery, oil, grease, etc. 2. CredIt side: Net sales (total sales minus sales returns), sale of Scrap goods and Closing stock of goods are shown on the Credit side of Trading Account. Closing Entries: Trading account is an account which include the matter which is nothing but a posting of some journal entry. These journal entries are the closing entries for the accounts like purchase of goods, sales, purchase return, sales-return, direct expenses of purchase (Accounts-related with the goods and expenses of purchase), etc. And the Trading Account is prepared with the help of posting of the above accounts. (1) The closing entry, for opening stock, purchase, sales return, direct expenses of the purchase like wages, carriage inward, etc. which have debit balance, is as follow: Trading A/c Dr ………………….. To Opening stock A/c ………………….. To Purchase A/c ………………….. To Sales return A/c ………………….. To Wages A/c ………………….. To Carriage inward A/c ………………….. To Other direct expenses A/c ………………….. (Being the closing entry to close the accounts of debit side of Trading Account.) Effect: As a result of this journal entry, all the accounts which are shown on credit side (which have debit balance) will be closed and to be written on the debit side of the Trading Account. (2) The closing entry for sales, purchase return, goods going out for any other reason other than sales (like stolen away, burnt by lire, withdrawn for personal use, given for charity, given as samples), etc. which have credit balance in the book, is as follows : Sales A/c Dr ………………….. Purchase return A/c Dr ………………….. To Trading A/c ………………….. (Being closing entry to close the accounts of the credit side of Trading account.) Effect: As a result of this journal entry, Sales A/c, Purchase return A/c and goods going out for the other reason will be closed and balance of the concern account will be recorded on credit side of the Trading Account. (3) For closing stock, brought into the books of accounts: Closing stock A/c Dr ………………….. To Trading A/c ………………….. (Being the adjustment entry passed for the closing stock.) Explanation: Closing stock of goods account is not there in any book. At the end of the accounting year, to prepare the final accounts, a list of the goods in stock is prepared and the value of it, is decided. This decided value, normally, is based on purchase value. Therefore, while writing the account regarding closing stock value, the market value or book value whichever is less, is to be considered. For this, a journal entry is to be passed which is known as adjustment entry. For the closing stock, one effect is to be given on the credit side of Trading Account and another effect is to be given on the Assets side of Balance Sheet, because closing stock is considered as an asset. (4) A journal entry to close the Trading Account: If this account shows the credit balance, then it is known as Gross profit and if it shows the debit balance, then it is known as Gross loss. By transferring the Gross profit or Gross loss to Profit and Loss Account, Trading Account will be closed as below: (A) If Gross profit is there : Trading A/c Dr ………………….. To Profit and Loss A/c ………………….. (Being gross profit transferred to Profit and Loss account.) (B) If Gross loss is there : Profit and Loss A/c Dr ………………….. To Trading A/c ………………….. (Being gross loss transferred to Profit and Loss Account.) 9. State the specimen of Balance Sheet in order of permanency and liquidity. Answer: Balance Sheet in order of Permanency Balance Sheet in order of Liquidity 10. What are Final Accounts? State the objectives of preparing Final Accounts. Answer: Final Accounts: At the end of accounting year. 1.0 know the business result and financial position of the business, accounts and statements are prepared. They are known as Final or Annual Accounts. Another meaning of Final Accounts is to prepare the Trading Account. Profit and Loss Account and Balance Sheet, Generally. these types of accounts are prepared at the end of the accounting year, therefore, they are known as Final (Annual) Accounts. But sometimes at the end of six or nine months also these types of the accounts are prepared. Institutes like Bank. prepares such interim accounts at the end of six months also, which are known as Final Accounts. Objectives: According to the meaning, Final (Annual) Accounts have two main objectives: 1. To know the business result and 2. To know the financial position of the business. 1. To know the business result: At the end of the accounting year, to know the result of the business. Trading Account and Profit and Loss Account are prepared. By comparing the expenses and incomes of the business, profit or loss can be found out. From the Trading account Gross profit or Gross loss and from the Profit and Loss Account. Net profit or Net loss can be known. 2. To know the financial position of the business: At the end of the accounting year, a statement is prepared which is known as Balance Sheet. In Balance Sheet. total assets and total liabilities are shown to get the Idea of the financial position of the business. Balance Sheet is a statement showing the financial position of the business. Other objectives: Other objectives of the Final Accounts are explained below: • To know the amount of Net capital in the business. • To know the amount of Non-current Assets and Current Assets. • To know the amount of Non-current liabilities and current liabilities. • To know the amount of Reserves and Surplus. • To know the amount receivable from various debtors. • To know the amount payable to various creditors. • To know the Trading profit. Operating profit and Abnormal gains and losses. • To find out or ascertain the amount of various taxes. i.e.. service tax. income tax. VAT. wealth tax, etc. payable to the State and Central Government. • To calculate the various ratios for the purpose of financial analysis. • To enable businessmen to take policy decisions in respect to future business activities. In the Final Accounts. Trading Account, Profit and Loss Account and a Balance Sheet are prepared. Trading Account and Profit and Loss Account are accounts, while Balance Sheet is statement or a list. Question 4. Pass adjustment entry for the following and also show its effect in final accounts: ( 1 ) Closing stock of ₹ 1,00,000 out of which ₹ 2,000 stationery stock. Out of total goods, goods of ₹ 50,000 required repairing expense of ₹ 2,000. Answer: Adjustment Entry 2. The following expenses are outstanding at the end of the year: Rent-taxes ₹ 5,000; Salary ₹ 3,000. Answer: Adjustment Entry 3. Following revenues are receivable at the end of the year: Trainee employee’s premium ₹ 2,000; Commission ₹ 1,000. Answer: Adjustment Entry 4. Brokerage of ₹ 2,700 is received in advance. Answer: Adjustment Entry 5. Proprietor’s capital in the business is ₹ 3,00,000 on which 12 % interest is payable. Answer: Interest on capital = $$\frac{3,00,000 \times 12 \times 1}{100}$$ = ₹ 36,000 Adjustment Entry 6. Drawings of proprietor after 9 months from the business amounted ₹ 40,000. Calculate interest on drawings at 12 %. Answer: Period for interest on drawings N = 12 months-9 months = 3 months Interest on drawings = $$40,000 \times \frac{12}{100} \times \frac{3}{12}$$ = ₹ 1,200 Adjustment Entry Effect in final accounts: 7. Credit sale of ₹ 10,000 is recorded as credit purchase. Answer: Adjustment Entry 8. Purchase return of 13,000 is recorded as credit sales. Answer: Adjustment Entry 9. Fixed assets of ₹ 1,00,000 is purchased on dt. 1-07-’15. Accounting year of firm is ended as on 31-03-’16. Calculate depreciation at 12%. Answer: Amount of fixed assets = ₹ 1,00,000; Depreciation rate =12%; Period for depreciation = From 1-7-T5 to 31-3-’16 = 9 months Depreciation = $$1,00,000 \times \frac{12}{100} \times \frac{9}{12}$$ = ₹ 9,000 Adjustment Entry 10. Debtors are amounting to ₹ 1,00,000 out of which write off ₹ 10,000 as bad debts, provide 10 % as bad debts reserve and 2 % as discount reserve on debtors. Answer: Necessary calculation : Adjustment Entry 11. Goods of ₹ 10,000 destroyed by fire. Insurance company has accepted a claim of ₹ 8,000. Answer: 12. ₹ 1,000 labour charge of machinery installation is wrongly debited to labour account. Answer: Adjustment Entry Question 5. While preparing final accounts of Suresh for the year ended 31-3-’15, close the following accounts and write journal entries to close the accounts: (1) Wages-Salary A/c : (2) Interest received A/c : (3) Sales A/c: (4) Suresh’s Drawings A/c : Answer: Journal Proper of Suresh Ledger of Suresh Question 6. Prepare final account from the Trial Balance and adjustments of Dipak as on31-3-’15: Trial Balance as on 31-3-’15 Name of the Account Debit ₹ Credit ₹ Capital – Drawings 18,000 3,00,000 Adjusted Purchase – Sales 8,00,000 12,91,000 Goods Return 50,000 – Discount 6,000 8,000 Rent 7,000 – Debtors – Creditors 1,10,000 90,000 Commission 8,000 – Bills 20,000 30,000 Cash Balance 20,000 – Bank Balance 90,000 – Building 1,50,000 – Furniture 40,000 – Machinery 3,00,000 – Wages 60,000 – Carriage Inward 60,000 – 10 % Bank Loan and Bank loan Interest 20,000 2,00,000 Closing Stock 40,000 Office Expenses 1,20,000 Total 19,19,000 19,19,000 Adjustments : (1) Goods of ₹ 12,000 lost due to theft. (2) Goods of ₹ 15,000 distributed as sample. (3) Goods of ₹ 16,000 burnt by fire. (4) Goods of ₹ 1,500 given as charity. Answer: Trading Account of Dipak Explanation: Following are the adjustment entries and effects in final accounts for every adjustment: (1) Adjustment No. 1 : Adjustment entry: Loss due to theft A/c Dr 12,000 To Purchase A/c 12,000 Effect in final accounts: Effect No. 1: On the debit side of Profit and Loss A/c, as loss due to theft – Debit effect Effect No. 2 : On the debit side of Trading A/c, deduct from purchase – Credit effect (2) Adjustment No. 2 : Adjustment entry: Advertisement expense A/c Dr 15,000 To Purchase A/c 15,000 Effect in final accounts: Effect No. 1: On the debit side of Profit and Loss A/c, added to Advertisement expense – Debit effect Effect No. 2: On the debit side of Trading A/c, deduct from purchase – Credit effect (3) Adjustment No. 3 : Adjustment entry: Loss due to fire A/c Dr 16,000 To Purchase A/c 16,000 Effect in final accounts: Effect No. 1: On the debit side of Profit and Loss A/c, as loss due to fire – Debit effect Effect No. 2: On the debit side of Trading A/c, deduct from purchase – Credit effect (4) Adjustment No. 4 : Adjustment entry: Charity expense A/c Dr 1,500 To Purchase A/c 1,500 Effect in final accounts: Effect No. 1: On the debit side of Profit and Loss A/c, as charity expense – Debit effect Effect No. 2: On the debit side of Trading A/c, deduct from purchase – Credit effect Question 7. Prepare final accounts from the Trial Balance and adjustments of Pankaj as on 31 – 3 – ’15 Trial Balance as on 31 – 3 – ’15 Adjustments: (1) Closing Stock of ₹ 1,65,000 out of which market value of 50% of stock is 10 % more and market value of remaining stock of goods is 10 % less. (2) Unrecorded credit purchase ₹ 60,000. (3) Unrecorded credit purchase return ₹ 7,500. . (4) Unrecorded credit sales ₹ 75,000. (5) Unrecorded credit sales return ₹ 22,500. (6) Outstanding wages ₹ 15,000. (7) Goods of ₹ 15,000 destroyed by fire and insurance company accepted a claim of whole amount. (8) Goods of ₹ 7,500 withdrawn for personal use. (9) Labour charges for installation of machinery ₹ 7,500 wrongly debited to labour charges. Answer: Explanation : (1) Adjustment No. 1 : (2) Adjustment No. 2: Unrecorded credit purchase of ₹ 60,000 Effect No. 1: On the debit side of Trading Account, added to purchase. Effect No. 2: On the Liabilities side of Balance Sheet, added to Creditors. (3) Adjustment No. 7 : Effect No. 1: Amount of goods destroyed by fire is deducted from purchase, on the debit side of Trading Account. Effect No. 2: Receivable amount from Insurance company is shown on the Asset side of Balance Sheet, Insurance Company as a debtor. (4) Adjustment No.9: Installation labour charges of ₹ 7,500 has been wrongly debited to wages, so which has been deducted from wages amount, on the debit side of Trading Account and has been added to Machinery amount, on the Assets side of Balance Sheet. Question 8. Following is the Trial Balance of R. K. Stores as on 31-3-’15: Trial Balance as on 31 – 3 – ’15 Name of the Account Debit ₹ Credit ₹ Gross Profit – 3,00,000 Salary 54,000 – General Expenses 6,000 – Tax-Insurance 7,200 – Sundry Debtors 1,20,000 – Closing Stock 13,200 – Bank Overdraft – 6,000 Commission – 9,000 Advertisement Expenses 9,000 – Interest 3,000 – Furniture 48,000 – Building 1,80,000 – Motorcar 60,000 – Capital – 1,42,800 Drawings 6,000 – Bad – debts 3,600 – Bad – debts Reserve – 6,000 Loan – 24,000 Creditors – 12,000 Bills Receivable 3,000 – Bills Payable – 9,600 Carriage-outward 4,000 – Discount given 3,200 – Discount received – 2,400 General Reserve – 30,000 Cash Balance 21,000 – Total 5,41,800 5,41,800 Adjustments: (1) Salary was paid up to 31-12-’14. (2) ₹ 1,200 being insurance premium for the year ending on 30-9-’15. (3) Commission of ₹ 2,000 is receivable. (4) Calculate 10 % interest on Capital and 12 % interest on Drawings. (5 ) Calculate depreciation at 5 % on furniture, at 10 % on building and at 20 % on motorcar. (6) From debtor of ₹ 20,000 write off 50 %. (7) Provide 5 % bad debt reserve. (8) Provide 2 % debtors discount reserve. (9) Transfer ₹ 10,000 to General Reserve. From the above information, prepare final account of R. K. Stores for the year ending as on 31 – 3 – ’15. Answer: Explanation: (1) Adjustment No. 1: Salary ₹ 54,000 shown in the trial balance, which is paid up to 31 – 12-’14, means it is paid for 9 months. ∴ ₹ 54,000 ÷ 9 = ₹ 6,000 is the salary of 1 month. While salary for 3 months, i.e., from 1-1-’15 to 31-3-’15, is not paid. ∴ Unpaid salary for 3 months = ₹ 6,000 × 3 = ₹ 18,000 (2) Adjustment No. 2: Insurance premium ₹ 1,200 is for the year ended on 30-9-’15. Means, from Dt. 1-4-’15 to Dt. 30-9-’15, six months insurance premium is prepaid. ∴ Prepaid insurance premium = $$1,200 \times \frac{6}{12}$$ = ₹ 600 Question 9. Prepare final accounts from the Trial Balance and adjustments of Pushpa Traders as on 31-3 – ’15 : Trial Balance of Pushpa Traders as on 31-3-’15 Name of the Account J.F. Debit ₹ Credit ₹ Drawings – Capital 26,400 3,30,000 Purchase – Sales 3,24,900 8,80,000 Goods Returns 88,000 22,000 Provident Fund and Contribution to Provident Fund 11,000 1,10,000 Provident Fund Investment and Interest on Provident 1,10,000 8,800 Fund Investment Debtors – Creditors 2,20,000 1,65,000 Discount 50,600 15,400 Bad Debts and Bad Debts Reserve 33,000 49,500 Bills 16,500 27,500 Goods stock (1-4-’14) 88,000 – Demurrage 3,300 – Custom duty 21,000 – Trade Expenses 1,00,000 – Cash Balance 10,000 – Bank Balance 35,100 – Fixed Assets (Cost Price ₹ 6,00,000) 4,80,000 – Advertisement Expenses 10,000 – Other Incomes – 19,600 Total 16,27,800 16,27,800 Adjustments: (1) Stock as on 31-3-’15 is ₹ 2,02,000 out of which ₹ 2,000 of stock was for advertisement goods stock and from the remaining stock the market value of 40 % stock is 20 % more. Market value of 30 % stock is less by 20 %. Whereas remaining stock needs to be repaired at the expenses of ₹ 5,000. (2) Goods of ₹ 7,500 given as advertisement. (3 ) Credit sales of ₹ 10,000 wrongly recorded as credit purchase. (4) Write off ₹ 30,000 as bad debts from debtors and provide 10% bad debt reserve. (5 ) Calculate 10 % interest on Capital and 6 % interest on Drawings. (6) Calculate depreciation at 10 % on fixed assets as per straight-line method. Answer: Trading Account of Pushpa Traders Profit and Loss Account of Pushpa Traders Explanations : (1) Adjustment No. 1: Stock of goods on 31-3-’15 ₹ 2,02,000 – Stock of goods for advertisement ₹ 2,000 ∴ Net stock of goods ₹ 2,00,000 (2) Adjustment No. 3: This adjustment is for rectification. Rectification entry: Creditor A/c … Dr 10,000 Debtors A/c … Dr 10,000 To Purchase A/c 10,000 To Sales A/c 10,000 (3) Adjustment No. 6 : Depreciation is to be calculated at 10% on fixed assets of ₹ 6,00,000 by straight-line method. Amount of depreciation = $$₹ 6,00,000 \times \frac{10}{100}$$ = ₹ 60,000. Question 10. Prepare final accounts from the Trial Balance and adjustments of Nirmi as on 31 – 3-’15 : Trial Balance of Nirmi as on 31-3-’15 Name of the Account Debit ₹ Credit ₹ Capital – 2,70,000 Drawings 16,200 – Land and Building 1,80,000 – Machinery 1,26,000 – Furniture 22,500 – Leasehold Building (Date: 1-4-’14 for five years) 45,000 – Sales – 4,50,000 Purchase Return – 10,800 Debtors 81,000 – 12% Loan from Dattu (Date : 1 – 10-’14) – 27,000 Purchase 1,80,000 – Sales return 9,000 – Freight – Octroi 13,500 – Sundry expenses 3,150 – Insurance premium 14,200 – Bad Debts 12,080 – Bad Debts Reserve – 12,600 Discount Reserve on Debtors – 450 Commission received – 6,000 Goods Stock (Date: 1-4-’14) 9,900 – Salary 42,000 – Wages 6,600 – Creditors – 28,200 Dead Stock 4,500 – Bank Overdraft – 18,900 Cash Balance 36,720 – Carriage Inward 6,000 – Carriage Outward 7,500 – Bills 12,000 7,000 Discount 5,100 2,000 Total 8,32,950 8,32,950 Adjustments : (1) Closing stock as on 31-3-’15 was valued at ₹ 50,000. (2) Fire occurred in business on 31-1-’15 due to which goods of ₹ 8,000 were destroyed and the insurance company accepted a claim of 70%. (3) Out of debtors, ₹ 6,000 are not recoverable so they are to be written off. Provide Bad debt reserve 5 % and discount reserve 2 %. (4) Credit purchases of ₹ 6,000 and Credit purchase return of ₹ 1,000 were not recorded. (5 ) Calculate depreciation, at 10 % on fixed assets. (6 ) Insurance premium includes ₹ 3,200 for the next year. (7) 50% commission is received. Answer: Trading Account of Nirmi Profit and Loss Account of Nirmi Balance Sheet of Nirmi as on 31-3-’15 Explanation : (1) As the leasehold building is for 5 years. ∴ $$\frac{1}{5}$$th of its value is written off every year. ∴ Amount written off during the current year =$$\frac{45,000}{5}$$ = ₹ 9,000 (2) 12% loan was taken from Dattu as on 1-10-’14. ∴ Interest on loan will be calculated for 6 months (from 1-10-’14 to 31-3-’15). Interest on loan = $$27,000 \times \frac{12}{100} \times \frac{6}{12}$$ = ₹ 1,620 Outstanding interest on loan = ₹ 1,620 Question 11. Prepare final accounts from the Trial Balance and adjustments of Sajan Readymade Stores as on 31-3-’15. Trial Balance of Sajan Readymade Stores as on 31-3-’15 Name of the Account J.F. Debit ₹ Credit ₹ Capital – 1,08,000 Drawings 4,800 – Opening stock 8,000 – Purchase 70,000 – Sales – 1,30,000 Goods return 6,000 10,000 Salary 30,000 – Audit fees 5,000 – Rent – Taxes – Insurance 4,800 – Stationery – Printing 1,200 – Unpaid Salary – 2,500 Prepaid Insurance Premium 400 – Duty on Import goods 900 – Commission – 800 Debtors – Creditors 29,600 14,000 Building 40,000 – Addition in Building (31-12-’14) 10,000 – Machinery 20,000 – Vehicles 8,000 – Bills 5,000 6,000 Dividend – 1,000 Investment in Ram-Rahim Company’s Shares 10,000 – Advertisement suspense account 4,000 – Furniture 6,000 – Maintenance expense 3,000 – Electricity Expense 3,600 – Bonus 2,500 – Discount 1,000 – Bad Debt Reserve – 1,500 Total 2,73,800 2,73,800 Adjustments: (1) Closing stock is of ₹ 12,600, out of which goods worth ₹ 4,600 requires’ repairing of ₹ 600. Remaining stock’s market value is less by 20 %. (2) Unrecorded credit sales ₹ 4,400. (3) Expense incurred for an advertisement campaign on 1-10-’14 is transferred to advertisement suspense account. This expense is to be written off in 5 years. (4) Vehicles of ₹ 20,000 were purchased on 1-04-’09. Scrap Value of Vehicles is ₹ 4,000 and estimated life is 10 years. Depreciation is to be calculated by straight-line method. (5) Purchase of furniture of ₹ 2,000 is wrongly debited to purchase account. Furniture was purchased on 1-10-’14. Rate of depreciation on furniture is 20%. (6) Calculate interest on capital at 6 %. Addition capital of ₹ 8,000 was brought into business on 1-10-’14. (7) Calculate depreciation on building at 10 % and rate of depreciation on machinery is 20 %. Answer: Trading Account of Sajan Readymade Stores Profit and Loss Account of Sajan Readymade Stores Balance Sheet of Sajan Readymade Stores as on 31 -3- ‘15 Explanation : (1) Adjustment No 1 : ∴ Hence, closing stock has’ been valued at ₹ 10,400 (₹ 4,000 + ₹ 6,400) (2) Adjustment No. 3 : As Advertisement Suspense A/c is to be written off over 5 years. ∴ Annual amount written off = $$\frac{4,000}{5}$$ = ₹ 800 ∴ Amount written off for six months, i.e., from Dt. 1 – 10-’14 to 31 – 3-’15 = $$₹ 800 \times \frac{6}{12}$$ = ₹ 400 (3) Adjustment No. 4: Depreciation is to be calculated on vehicles by straight line method. ∴Amount of annual depreciation for vehicles = $$\frac{\text { Cost price – Scrap value }}{\text { Estimated life }}$$ = $$\frac{20,000-4,000}{10}$$ = $$\frac{16,000}{10}$$ = ₹ 1,600. (4) Adjustment No. 5: First of all, In debit side of Trading A/c, purchase of furniture of ₹ 2,000 is deducted from Purchase A/c and then, in Assets of Balance Sheet, it is added to furniture. Calculation of depreciation on furniture: Depreciation on opening balance = ₹ 6,000 x 20 % = ₹ 1,200 + Depreciation on new purchase furniture of ₹ 2,000 for 6 months = $$2,000 \times \frac{20}{100} \times \frac{6}{12}$$ = ₹ 200 ∴ Total Depreciation on total furniture = ₹ 1,400 (5) Adjustment No. 6: Addition capital of ₹ 8,000 was brought into business on 1-10-’14. ∴ Amount of opening capital on 1 – 4 – ’14 = Total capital – Additional capital = ₹ 1,08,000 – ₹ 8,000 = ₹ 1,00,000 Calculation of interest on capital: Interest on opening capital = ₹ 1,00,000 x 6% = ₹ 6,000 + Interest on addition capital for 6 months, i.e., from 1 – 10-’14 to 31 – 3-15 = $$8,000 \times \frac{6}{100} \times \frac{6}{12}$$ = ₹ 240 ∴ Total interest on total capital = ₹ 6,240 (6) Necessary note: For the bad debts reserve on debtors shown in the Trial Balance, nothing is mentioned in the adjustment, therefore it will be deducted from the debtors on the Assets side in the Balance Sheet. Question 12. Prepare final accounts from the following Trial Balance and adjustments of Baldev as on 31 – 3 – ’16 : Trial Balance of Baldev as on 31-3-’16 Debit Balance Amount ₹ Credit Balance Amount ₹ Drawings 45,000 Trading Account 5,70,000 Fixed Assets 6,75,000 Capital 7,50,000 Office expenses 82,500 Bank overdraft 18,000 Rent 22,500 Traders 3,00,000 Insurance 45,000 Bills payables 37,500 Salaries – Wages 3,75,000 Bad debt reserve 21,000 Customers 2,25,000 Discount received 10,500 Bills receivables 22,500 Outstanding office expenses 3,000 Discount allowed 7,500 Prepaid insurance premium 3,750 Closing Stock 45,000 Cash Balance 22,500 Selling and Distribution expenses 1,20,000 Bonus 18,750 Total 17,10,000 Total 17,10,000 Adjustments: (1) After preparing trading account, it was found that Bhavesh has taken goods for personal use of ₹ 7,500, which is not recorded in the book. Outstanding Carriage inward ₹ 3,750. (2) Calculate interest on capital at 5%. (3) Outstanding Interest on Bank overdraft ₹ 750. (4) After preparing trading account, it was found that ₹ 22,500 received from debtors, which is wrongly credited to sales account. (5) Provide depreciation on fixed assets at 10 %. (6) Unrecorded credit purchases ₹ 12,000. (7) Goods of ₹ 22,500 are destroyed by fire, for which the Insurance company has accepted a claim of 90 % amount. (8) A fixed asset of ₹ 30,000 sold for ₹ 22,500 for cash on Dt. 1-10-’15 which is not recorded in the book. Answer: Adjusted Trading Account of Baldev Profit and Loss Account of Baldev Balance Sheet of Baldev as on 31-3-’16 Question 13. The following balances are taken from the books of Vipul as on 31-3-’15. Prepare final accounts. Name of Account Amount ₹ Name of Account Amount ₹ Capital 2,17,000 Debtors 1,40,000 Drawings 36,000 Creditors 60,000 Sales 6,00,000 Furniture (Dt. 1 – 4 – ’ 14) 1,60,000 Purchase 3,00,000 Addition in Furniture 40,000 Sales return 5,000 (Dt. 1-10-’14) – Purchase return 4,000 Office expenses 30,000 Opening stock 10,000 Bad debts 5,000 Salary (for 11 months) 1,10,000 Bad debt reserve 6,000 10% Loan from bank 1,00,000 Insurance premium 24,000 Interest on 10% loan from bank 5,000 Cash balance 50,000 Bills receivable 6,000 Bank overdraft 18,000 Bills payable 5,000 Commission received 5,000 Investment in 12% Debenture 1,00,000 Interest on 12% Debenture 6,000 Adjustments: (1) Stock of goods is ₹ 1,50,000 at the end of the year. From which the market value of 50 % goods is ₹ 80,000 and the market value of 50 % goods is ₹ 70,000. (2) Credit sales of ₹ 60,000 is not recorded. (3) Calculate 20 % depreciation on furniture. (4) Life Insurance premium of Vipul of ₹ 3,000 is included in the insurance premium. (5) Write off additional bad debts of ₹ 15,000 and provide 5 % bad debt reserve on debtors. (6) Additional capital of ₹ 17,000 brought in the business as on Dt. 1-10-’14. Calculate 10 % interest on capital. (7) Invoice of ₹ 10,000 for purchase is received from the creditor which is not recorded by an error. Answer: Trial Balance of Vipul as on 31-3-’15 Balance Sheet of Vipul as on 31-3-’15 Question 14. As on 31-3-’15, the ratio of capital and reserve is 4:1 in the business of Bhavna. The balances of other accounts on that date are as under. Prepare final accounts from the balances and adjustments. Name of Account Amount ₹ Name of Account Amount ₹ Opening Stock 30,000 Bad debt reserve 6,000 Purchase 1,00,000 Rent paid (₹ 1,200 per month) 12,000 Sales 2,50,000 Carriage inward 4,000 Debtors 1,00,000 Cash balance 30,000 Creditors 20,000 Office expenses 20,000 Machinery 2,00,000 Rent received 3,000 10 % loan taken from Pratibha 50,000 Patents 20,000 (From Dt. 1-10-’14) 2,000 Discount received 2,000 Insurance premium 9,000 Depreciation on furniture 2,000 Advertisement expense 6,000 Furniture 8,000 Adjustments: (1) Closing stock is ₹ 80,000 of which market value of 10 % goods is 20 % less. Goods of ₹ 10,000 needs to be repaired for ₹ 1,000. (2) Goods of ₹ 5,000 are distributed as free sample, which is not recorded. (3) Goods of ₹ 6,000 withdrawn by Bhavna for her personal use, which is recorded in the sales book. Purchase invoice of ₹ 4,000 is not recorded in the purchase book. (4) Insurance premium of ₹ 3,000 paid for the year ending as on 30-06-’15 is included in insurance premium. (5) Out of total debtors a debtor of ₹ 10,000 is declared insolvent and his receiver has declared first and final dividend of 80 paise per rupee. Provide 5 % bad debt reserve on debtors. (6) Calculate 20 % depreciation on machinery. (7) Patents are to be revalued at ₹ 17,000. (8) Office salary of ₹ 1,500 is outstanding which is included in office expenses. Answer: Trial Balance of Bhavna as on 31-3-’15 Debit Balances Amount ₹ Credit Balances Amount ₹ Opening Stock 30,000 Sales 2,50,000 Purchase 1,00,000 Creditors 20,000 Debtors 1,00,000 10% Loan taken from Pratibha (From Dt. 1- 10-14) 50,000 Machinery 2,00,000 Insurance premium 9,000 Bad debt reserve 6,000 Advertisement expense 6,000 Rent received 3,000 Furniture 8,000 Discount received 2,000 Rent paid (₹ 1,200 per month) 12,000 Reserve 42,000 Carriage inward 4,000 Capital 1,68,000 Cash balance 30,000 Office expenses 20,000 Patents 20,000 Depreciation on furniture 2,000 Total 5,41,000 Total 5,41,000 Balance Sheet of Bhavna as on 31-3-’15 Explanation : (1) Before writing capital and reserve amount in Trial Balance. Total of debit balances is ₹ 5,41,000 and total of credit balances is ₹ 3,31,000. So, difference of both total is arrived ₹ 2,10,000. Now according to instruction given, the ratio of Capital and Reserve is 4:1. ∴ Amount of capital = $$2,10,000 \times \frac{4}{5}$$ = ₹ 1,68,000 and Amount of reserve =$$2,10,000 \times \frac{1}{5}$$ = ₹ 42,000 (2) Adjustment No. 1:10% of the stock of ₹ 80,000 is ₹ 8,000 and its market value is less by 20%, i.e, by ₹ 1,600 (8000 x $$\frac{20}{100}$$ ) and required repairing expense is ₹ 1,000. Hence, closing stock has been valued at ₹ 80,000- ₹1,600- ₹ 1,000 = ₹ 77,400 (3) Adjustment No. 2: First effect: On the debit side of Profit and Loss A/c added ₹ 5,000 to Advertisement expense. Second effect: On the debit side of Trading A/c deduct ₹ 5,000 from purchase. (4) Adjustment No. 4: Insurance premium includes ₹ 3,000 for the year ended on 30-06-15. Means, prepaid insurance premium for the three months (from 1-4-15 to 30-6-15) is ₹ 750 (3,000 x $$\frac{3}{12}$$ ). (5) Adjustment No. 5: A debtor of ₹ 10,000 is declared insolvent and his receiver has declared first and final dividend of 80 paise per rupee. It means bad debts is 20 paise per rupee. The total debtors are ₹ 94,000 out of which ₹ 2,000 (20% of ₹ 10,000) is bad debts. Therefore the net debtors are ₹ 92,000 out of which ₹ 8,000 is sure to be received. So no reserve should be kept on this ₹ 8,000. Hence Bad debts reserve should be provided on doubtful debtors ₹ 84,000 (₹ 92,000 – ₹ 8,000) only. Amount of Bad debts reserve = ₹ 84,000 x $$\frac{5}{100}$$ = ₹ 4,200 (6) Adjustment No. 7 : Book value of patents = ₹ 20,000 – Revised value of patents = ₹ 17,000 ∴ Written off amount = ₹ 3,000

2022-08-12 12:20:52

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https://math.stackexchange.com/questions/3095843/can-the-gauss-bonnet-theorem-be-proven-from-stokess-theorem

# Can the Gauss-Bonnet theorem be proven from Stokes's theorem? In a comment to this question, John Ma claims that the Gauss-Bonnet theorem can be proven from Stokes's theorem, but does not explain how. For two dimensions, Stokes's theorem says that for any smooth 2-manifold (i.e. surface) $$S$$ and one-form $$\omega$$ defined on $$S$$, $$\oint_{\partial S} \omega = \iint_S d\omega.$$ I could vaguely imagine coming up with some kind of one-form $$\omega$$ that depends on the metric, such that (a) along the boundary curve $$\omega$$ maps the boundary tangent vector to the geodesic curvature and (b) in the surface interior $$\ast d\omega$$ equals the Gaussian curvature. (In more concrete vector-field language, this corresponds to a vector field $$\vec{\omega}$$ defined over the surface such that (a) on the boundary curve $$\vec{\omega} \cdot d\vec{l}$$ equals the curve's geodesic curvature and (b) in the surface interior $$(\vec{\nabla} \times \vec{\omega}) \cdot d\vec{S}$$ equals the Gaussian curvature.) This would reproduce part of the Gauss-Bonnet formula, but how could you possibly get out the Euler characteristic term? • The proof given by Chern in "A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds" is based on Stokes' theorem. – JHF Feb 1 '19 at 13:24 • For the 2-dimensional G-B theorem, you can see (most of) the argument on p. 105 of my differential geometry text. The local-to-global argument to get to $\chi(M)$ is the standard triangulation argument. If you recognize $\chi$ as the sum of the indices of a vector field, you can turn the proof into a direct argument, taking out little balls $B$ around each zero and seeing that $\int_{\partial B} \bar\omega_{12}$ gives the index of the vector field. Feb 1 '19 at 17:12

2021-11-29 03:42:02

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https://www.bartleby.com/questions-and-answers/3.-a-use-the-putzer-algorithm-theorem-7.1-page-49-to-find-the-atrix-e-when-b-show-how-to-use-the-mat/d0c54891-90f1-47e3-8c48-84d0ee5f8ef6

# 3. (a) Use the Putzer algorithm (Theorem 7.1, page 49) to find the atrix e when (b) Show how to use the matrix eAt in (a) to find the vector r(t) that solves the system (t) Ax(t) and satisfies 1 x(0) = Question Pls explain to me step by step and dont skip any steps. pls write clearly.  i will rate your answer immediately. thanks a lot

2021-03-09 08:16:44

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https://ruor.uottawa.ca/handle/10393/4196

### Cellular responses to ionizing radiation and cisplatin. ##### Description Title: Cellular responses to ionizing radiation and cisplatin. Authors: Dolling, Jo-Anna. Date: 1998 Abstract: This thesis tested the hypothesis that the synergistic effect of cisplatin in combination with radiation was due to cisplatin inhibition of repair of radiation-induced DNA damage. Two model cell systems were used. DNA repair inhibition caused by cisplatin and the fundamental mechanism of DNA double strand break repair were studied in human fibroblast cells. The effect of cisplatin on stress response and the induction of radiation resistance was studied in yeast. It was shown that normal human fibroblasts cells (AG1522), irradiated in the presence or absence of cisplatin adducts have biphasic DNA repair curves with a fast and slow component. When cells were treated with cisplatin immediately before irradiation, fast repair was not affected but slow repair was inhibited. The rate of the slow repair in the presence of cisplatin adducts was ten fold less than the rate in the absence of cisplatin adducts. Cisplatin treatment 24 hours prior to radiation resulted in inhibition of both fast and slow repair. Yeast experiments tested whether defects in DNA repair mechanisms would amplify the radiosensitizing effect of cisplatin. It was shown that cisplatin sensitized cells with a competent recombinational repair mechanism, but did not sensitize cells defective in recombinational repair. It was also shown that under certain circumstances cisplatin did not radiosensitize normal, repair competent cells but induced stress response and cellular radiation resistance. Repair proficient wild type yeast cells became thermal tolerant and radiation resistant two hours after a sublethal cisplatin treatment. Cisplatin pretreatment also suppressed mutations caused by N-methyl-N$\sp\prime$-nitro-N-nitrosoguanidine (MNNG) treatment, a response previously shown in wild type cells with radiation pretreatment. Like radiation, cisplatin-induced stress response did not confer radiation resistance or suppress MNNG mutations in a recombinational repair deficient mutant (rad52). These results support the idea that cisplatin crosslinks in DNA can induce a stress response which subsequently confers radiation resistance, thermal tolerance, and mutation resistance in yeast. The mechanism of this cisplatin-induced resistance was determined to be dependent on an error free recombinational repair pathway. The results obtained in this thesis indicated that error free recombinational repair plays a major role in the interaction between cisplatin and radiation. To further examine error-free recombinational repair in mammalian cells, confocal microscopy in conjunction with fluorescence in situ hybridization was used to show that the distance between homologous chromosome domains was reduced after radiation. The mechanism for homologous chromosome rearrangement following exposure to radiation is not known, however, it is plausible that a recombinational repair process is responsible. Overall, this work has shown that the radiosensitizing effect of cisplatin was due to inhibition of DNA repair processes involving recombinational repair. However, it was also shown that, under specific conditions, cisplatin treatment induced a stress response that conferred cellular radiation resistance. Therefore, the effect of cisplatin in combination with radiation was variable depending upon the cellular processes influenced by cisplatin. URL: http://hdl.handle.net/10393/4196http://dx.doi.org/10.20381/ruor-10143 Collection Thèses, 1910 - 2010 // Theses, 1910 - 2010

2019-02-16 08:11:32

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https://scriptinghelpers.org/questions/40569/how-to-change-character-and-keep-animations-running

Still have questions? Join our Discord server and get real time help. 1 # How to change character and keep animations running? Asked by 2 years ago Ok so I have a idea to make a game where you sorta go around an possess different characters. Ive made a map with a ton of noob npcs that you can possess and control Heres the script. BTW it is a local script but I have filtering enabled off. So you press q to switch but when you switch it works but when you move around it doesnt run the animations such as walking and jumping. If you want to try the place this is the link:https://web.roblox.com/games/672192244/Switch And here's the script: -- Switch script by Wafflecow321 -- in dev local UIS = game:GetService("UserInputService") local Player = game.Players.LocalPlayer local Mouse = Player:GetMouse() local Camera = game.Workspace.CurrentCamera function Click(input,gp) if input.UserInputType == Enum.UserInputType.Keyboard then if input.KeyCode == Enum.KeyCode.Q then if Mouse.Target then if Mouse.Target.Parent:FindFirstChild("Humanoid")and not Mouse.Target:IsDescendantOf(Player.Character)then Player.Character.Archivable = true if Player.Character:FindFirstChildOfClass("Tool")then Player.Character:FindFirstChildOfClass("Tool"):Destroy() end local Char = Player.Character local Clone = Char:Clone() Clone.Parent = workspace print(Mouse.Target.Parent.Name) local Target = Mouse.Target Camera.CameraSubject = Target.Parent Player.Character = Target.Parent end end end end end UIS.InputBegan:connect(Click) I don't rlly care if you copy this but plzz be considerate and give me credit. 0 Goulstem 7980 2 years ago Edited 2 years ago I'm pretty sure if you disable the Animate script inside the character, then re-enable it, the animations should recalibrate. local Char = Player.Character local Clone = Char:Clone() Clone.Parent = workspace local Target = Mouse.Target Camera.CameraSubject = Target.Parent Player.Character = Target.Parent wait(1) local anim = Player.Character:WaitForChild("Animate"); anim.Disabled = true; anim.Disabled = false; Test around with this idea. 0 Thanks that fixed everyting Wafflecow321 274 — 2y

2019-04-25 18:08:20

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https://mathoverflow.net/questions/172129/simple-maps-flat-versus-locally-trivial?noredirect=1

# Simple maps: Flat versus locally trivial In deformation of complex analytic spaces, one usually considers an analytic proper simple surjective map $\varpi: \mathscr{M} \twoheadrightarrow \mathscr{P}$ as an analytic family. However the term simple differs by literature. There are two notions of simple: as a locally trivial map and as a flat map. Are these definitions equivalent? I should mention too that some references define an analytic family using submersions instead of simpleness for the smooth analytic case. But this definition coincides with the first one by Ehresmann's fibration theorem. Maybe the question is trivial, but since I have never seen it written anywhere, I think I should be more careful. EDIT: The locally triviality is in the category of real differentiable manifolds or the category of topological manifolds. This explains why I have cited Ehresmann fibration theorem as an alternative for the statement. In fact, flat maps are not required to be smooth maps in general. For instance, a flat family of smooth curves degenerating to a nodal curve is clearly not locally trivial. However, the answer is still no even if we only consider smooth maps. In fact, there is the following theorem due to Grauert and Fischer, see [Barth-Peters-Van de Ven, Compact Complex Surfaces, Chapter I]: Theorem. A smooth family of compact complex manifold is locally trivial if and only if all its fibers are analytically isomorphic. Now it is possible to give examples of smooth and flat but not locally trivial maps: the so-called Kodaira fibrations, see the same book, Chapter V. These are smooth maps $f \colon X \to C$, where $X$ is a complex surface ad $C$ a smooth curve, such that the fibres are not analytically isomorphic. By Grauert-Fischer theorem, it follows that Kodaira fibrations are not locally trivial maps (i.e., although all their fibres are smooth, they are not complex analytic fibre bundles). Since every smooth fibration of a surface over a curve is automatically flat, this provides the examples we were looking for. Added. If $f \colon X \to Y$ is a flat map in the complex category, it is not true in general that it provides a submersion in the real category. Again, this is because flat map does not imply smooth map. For instance, one can consider a flat map $f \colon X \to \Delta$, where $\Delta \subset \mathbb{C}$ is the unit disk, such that the general fibre is a smooth complex conic and the central fibre is the union of two complex lines intersecting at one point. This map cannot be a submersion because of the Ehresmann theorem: in fact, the topological type of the central fibre is different from the topological type of the general fibre. • Thanks for the answer. What do you mean by analitically isomorphic fibers? If the fibers are isomorphic in the complex sense the deformation is trivial. For the manifolds case the fibers are always diffeomorphic by Ehresmann fibration theorem. – user40276 Jun 18 '14 at 14:17 • I mean that the complex structure does not change in deformation, i.e. that the fibres are isomorphic in the complex sense. If the family is smooth, by Grauert-Fischer this is equivalent to the fact that the family is locally trivial. – Francesco Polizzi Jun 18 '14 at 14:37 • Maybe I'm missing something. But, in my question, I was meaning locally triviality in the category of real manifolds. However, even for the analytic category it seens weird, since Grothendieck defines analytic family using locally triviality in the category of analytic spaces in his paper about Teichmuller theory. Maybe Grothendieck was wrong... – user40276 Jun 18 '14 at 14:48 • Well, nowadays when one talks about deformation theory and says family of analytic varieties usually means flat, not locally trivial. I do not know the Grothendieck paper you are talking about, maybe you should provide more context in your question in order to have a more precise answer. At any rate, flat is surely weaker than locally trivial, as I explained in my answer. – Francesco Polizzi Jun 18 '14 at 15:14 • Here I'm only talking about the analytic category – Francesco Polizzi Jun 18 '14 at 15:20

2021-06-21 19:40:53

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https://www.tutorialspoint.com/narayana-number-in-cplusplus

# Narayana number in C++ The Narayana numbers can be expressed in terms of binomial expression $1/n\binom{n}{k} \binom{n}{k-1}$  Learn more about the Narayana number here. You are given the numbers n and k. Find the Narayana number. It's a straightforward problem having the combinations formula. Let's see the code. ## Algorithm • Initialise the numbers n and k. • Find the Narayana number using the given formula. • Print the resultant number. ## Implementation Following is the implementation of the above algorithm in C++ #include <bits/stdc++.h> using namespace std; int factorial(int n) { int product = 1; for (int i = 2; i <= n; i++) { product *= i; } return product; } int nCr(int n, int r) { return factorial(n) / (factorial(n - r) * factorial(r)); } int main() { int n = 8, k = 5; cout << nCr(n, k) * nCr(n, k - 1) / n << endl; return 0; } ## Output If you run the above code, then you will get the following result. 490 Published on 29-Jun-2021 09:50:39

2022-01-21 03:32:10

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http://www.chegg.com/homework-help/questions-and-answers/-q3277560

## need help calc 3 • here i've denoted theta as a In cylindrical coordinates, we have x = r cos a, y = r sin a, and z = z. In these coordinates, dV = dxdydz = rdrdadz. Now we need to figure out the bounds of the integrals in the new coordinates. Since on the xy plane, we have z = 0, we know that x^2+y^2=4 when z = 0. And so the biggest that x^2+y^2 can be is 4 and the smallest it is is zero. So 0 <= r <= 4. Also 0 <=a<= 2pi. And 0 <= z <= 4-r^2 So our integral becomes: integral (oto2pi) integral (0to4) integral (0to 4-r^2) (r^2 dz dr da) = 2pi integral (0to4) (4-r^2)r^2 dr = 2pi (4^4/3-4^5/5) = 2pi (-1792/15) = -3584pi/15 (or = -750.6312 )

2013-05-21 03:51:32

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https://mathematica.stackexchange.com/questions/40228/mapthread-multiple-functions-onto-multiple-lists

# MapThread multiple functions onto multiple lists I'm trying to learn the functional style which seems to prevail in Mathematica. I'm having trouble accomplishing the following: Let's say I have multiple lists of arbitrary data (using two lists here to keep it simple): a = {1,2,3,4,5,6} b = {1,1,2,2,3,3} I also have multiple arbitrary functions (again using two to keep it simple) which all take the same inputs in the same order, but use them to generate different outputs: f = Function[{u,v},{{u^2,u*v},{-u*v,v^2}}] g = Function[{u,v},{{u^2,1},{-1,v^2}}] I understand how to build lists of results, threading over lists a,b, with MapThread: fOut = MapThread[f,{a,b}] However, because in reality there are dozens of functions (f,g,etc.) and dozens of lists of data (a,b,etc.), I end up with dozens of MapThread commands, each with the same long list of arguments, creating a wall of text that is far from elegant-looking. So I tried to merge it into a single MapThread command, which didn't work: {fOut,gOut} = MapThread[{f,g},{a,b}] Is there a way to MapThread many functions onto many lists of data (assuming each function expects the data in the same order)? If possible, I would like to avoid creating new variables because the functions are intended to be compiled, and I think it would create redundant data. • Does this generate the result you expect: (# @@@ Transpose@{a, b}) & /@ {f, g}? Or even: SetAttributes[{f, g}, Listable]; (# @@ {a, b}) & /@ {f, g}. – István Zachar Jan 11 '14 at 17:28 • That first one does exactly what I want. Thanks! Now I just need to understand what the hell it's doing. – phosgene Jan 11 '14 at 17:35 • You can do : Outer[#1 @@ #2 &, {f, g}, Transpose[{a, b}], 1] – andre314 Jan 11 '14 at 18:02 It is not entirely clear to me what your larger problem looks like. If you have the same set of lists each time and merely want to MapThread a series of functions across them you can use a simple construct such as: a = {1, 2, 3, 4, 5, 6}; b = {1, 1, 2, 2, 3, 3}; MapThread[#, {a, b}] & /@ {f, g} {{f[1, 1], f[2, 1], f[3, 2], f[4, 2], f[5, 3], f[6, 3]}, {g[1, 1], g[2, 1], g[3, 2], g[4, 2], g[5, 3], g[6, 3]}} If you have a more involved operation in mind please describe it in greater detail. • That was exactly what I needed. Of the three suggestions I've seen so far (all of which work), this one has the most concise and easy-to-read syntax, and also the highest (uncompiled) performance by a small margin. – phosgene Jan 11 '14 at 18:23 • @user2790167 If you give a more representative example of your actual operation we may be able to recommend a better approach. For example, MapThread will unpack packed arrays, and can therefore significantly limit performance in some cases. – Mr.Wizard Jan 11 '14 at 18:38 • I'm not using any packed arrays (to my knowledge). I'm actually writing code inside a Compile command. The fundamental operations are floating-point linear algebra. – phosgene Jan 11 '14 at 18:59 • ...including construction of matrices from data (similar to functions f,g in my example). I've already written the whole thing in the procedural style (a wall of text to be sure), and I wanted to make the code shorter and easier to read. – phosgene Jan 11 '14 at 19:08 • Map[MapThread[#,{a,b}]&,{f,g}] compiles seemingly without error. However, when it's called, it fails with this error: "Compiled expression Function[{u,v},{{u^2,u v},{-u v,v^2}}] should be a machine-size real number. >>", then executes the uncompiled version instead, which is an order of magnitude slower. A plain MapThread command makes a good compiled function, but it seems not to like nested Map[MapThread] commands for some reason. – phosgene Jan 11 '14 at 21:58

2019-09-17 03:29:45

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https://stacks.math.columbia.edu/tag/00E4

Lemma 10.17.6. Let $R$ be a ring. Let $f \in R$. The map $R \to R_ f$ induces via the functoriality of $\mathop{\mathrm{Spec}}$ a homeomorphism $\mathop{\mathrm{Spec}}(R_ f) \longrightarrow D(f) \subset \mathop{\mathrm{Spec}}(R).$ The inverse is given by $\mathfrak p \mapsto \mathfrak p \cdot R_ f$. Proof. This is a special case of Lemma 10.17.5. $\square$ There are also: • 4 comment(s) on Section 10.17: The spectrum of a ring In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

2021-07-25 05:42:43

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http://mathhelpforum.com/pre-calculus/128811-limits.html

## Limits Hii ! 1) prove That : $\forall x \in \mathbb{R}^*$ , $\vert x . \sin (\frac{1}{x^2}) \vert \leq \vert x \vert$ - Calculat : $\lim_{x \rightarrow 0} x . \sin (\frac{1}{x^2})$ . 2) prove That : $\forall x \in \mathbb{R}^*$ , $3x-2x^2 < x^2(E(\frac{1}{x}) + E(\frac{2}{x}) ) \leq 3x$ - Calculat : $\lim_{x \rightarrow 0} x^2 ( E(\frac{1}{x}) + E(\frac{2}{x}) )$ $E(x)$ : The Floor of x .

2017-07-22 12:51:02

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http://yutsumura.com/tag/determinant-of-a-matrix/

# Tagged: determinant of a matrix ## Problem 537 Let $A$ and $B$ be $2\times 2$ matrices such that $(AB)^2=O$, where $O$ is the $2\times 2$ zero matrix. Determine whether $(BA)^2$ must be $O$ as well. If so, prove it. If not, give a counter example. ## Problem 509 Using the numbers appearing in $\pi=3.1415926535897932384626433832795028841971693993751058209749\dots$ we construct the matrix $A=\begin{bmatrix} 3 & 14 &1592& 65358\\ 97932& 38462643& 38& 32\\ 7950& 2& 8841& 9716\\ 939937510& 5820& 974& 9 \end{bmatrix}.$ Prove that the matrix $A$ is nonsingular. ## Problem 508 Let $A$ be a square matrix. Prove that the eigenvalues of the transpose $A^{\trans}$ are the same as the eigenvalues of $A$. ## Problem 505 Let $A$ be a singular $2\times 2$ matrix such that $\tr(A)\neq -1$ and let $I$ be the $2\times 2$ identity matrix. Then prove that the inverse matrix of the matrix $I+A$ is given by the following formula: $(I+A)^{-1}=I-\frac{1}{1+\tr(A)}A.$ Using the formula, calculate the inverse matrix of $\begin{bmatrix} 2 & 1\\ 1& 2 \end{bmatrix}$. ## Problem 486 Determine whether there exists a nonsingular matrix $A$ if $A^4=ABA^2+2A^3,$ where $B$ is the following matrix. $B=\begin{bmatrix} -1 & 1 & -1 \\ 0 &-1 &0 \\ 2 & 1 & -4 \end{bmatrix}.$ If such a nonsingular matrix $A$ exists, find the inverse matrix $A^{-1}$. (The Ohio State University, Linear Algebra Final Exam Problem) ## Problem 479 Prove that if $n\times n$ matrices $A$ and $B$ are nonsingular, then the product $AB$ is also a nonsingular matrix. (The Ohio State University, Linear Algebra Final Exam Problem) ## Problem 473 Prove that the determinant of an $n\times n$ skew-symmetric matrix is zero if $n$ is odd. ## Problem 419 (a) Let $A$ be a real orthogonal $n\times n$ matrix. Prove that the length (magnitude) of each eigenvalue of $A$ is $1$ (b) Let $A$ be a real orthogonal $3\times 3$ matrix and suppose that the determinant of $A$ is $1$. Then prove that $A$ has $1$ as an eigenvalue. ## Problem 394 Determine the values of $x$ so that the matrix $A=\begin{bmatrix} 1 & 1 & x \\ 1 &x &x \\ x & x & x \end{bmatrix}$ is invertible. For those values of $x$, find the inverse matrix $A^{-1}$. ## Problem 391 (a) Is the matrix $A=\begin{bmatrix} 1 & 2\\ 0& 3 \end{bmatrix}$ similar to the matrix $B=\begin{bmatrix} 3 & 0\\ 1& 2 \end{bmatrix}$? (b) Is the matrix $A=\begin{bmatrix} 0 & 1\\ 5& 3 \end{bmatrix}$ similar to the matrix $B=\begin{bmatrix} 1 & 2\\ 4& 3 \end{bmatrix}$? (c) Is the matrix $A=\begin{bmatrix} -1 & 6\\ -2& 6 \end{bmatrix}$ similar to the matrix $B=\begin{bmatrix} 3 & 0\\ 0& 2 \end{bmatrix}$? (d) Is the matrix $A=\begin{bmatrix} -1 & 6\\ -2& 6 \end{bmatrix}$ similar to the matrix $B=\begin{bmatrix} 1 & 2\\ -1& 4 \end{bmatrix}$? ## Problem 390 Prove that if $A$ and $B$ are similar matrices, then their determinants are the same. ## Problem 389 (a) A $2 \times 2$ matrix $A$ satisfies $\tr(A^2)=5$ and $\tr(A)=3$. Find $\det(A)$. (b) A $2 \times 2$ matrix has two parallel columns and $\tr(A)=5$. Find $\tr(A^2)$. (c) A $2\times 2$ matrix $A$ has $\det(A)=5$ and positive integer eigenvalues. What is the trace of $A$? (Harvard University, Linear Algebra exam problem) ## Problem 380 Find the determinant of the following matrix $A=\begin{bmatrix} 6 & 2 & 2 & 2 &2 \\ 2 & 6 & 2 & 2 & 2 \\ 2 & 2 & 6 & 2 & 2 \\ 2 & 2 & 2 & 6 & 2 \\ 2 & 2 & 2 & 2 & 6 \end{bmatrix}.$ (Harvard University, Linear Algebra Exam Problem) ## Problem 374 Let $A=\begin{bmatrix} a_0 & a_1 & \dots & a_{n-2} &a_{n-1} \\ a_{n-1} & a_0 & \dots & a_{n-3} & a_{n-2} \\ a_{n-2} & a_{n-1} & \dots & a_{n-4} & a_{n-3} \\ \vdots & \vdots & \dots & \vdots & \vdots \\ a_{2} & a_3 & \dots & a_{0} & a_{1}\\ a_{1} & a_2 & \dots & a_{n-1} & a_{0} \end{bmatrix}$ be a complex $n \times n$ matrix. Such a matrix is called circulant matrix. Then prove that the determinant of the circulant matrix $A$ is given by $\det(A)=\prod_{k=0}^{n-1}(a_0+a_1\zeta^k+a_2 \zeta^{2k}+\cdots+a_{n-1}\zeta^{k(n-1)}),$ where $\zeta=e^{2 \pi i/n}$ is a primitive $n$-th root of unity. ## Problem 363 (a) Find all the eigenvalues and eigenvectors of the matrix $A=\begin{bmatrix} 3 & -2\\ 6& -4 \end{bmatrix}.$ (b) Let $A=\begin{bmatrix} 1 & 0 & 3 \\ 4 &5 &6 \\ 7 & 0 & 9 \end{bmatrix} \text{ and } B=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 &0 \\ 0 & 0 & 4 \end{bmatrix}.$ Then find the value of $\det(A^2B^{-1}A^{-2}B^2).$ (For part (b) without computation, you may assume that $A$ and $B$ are invertible matrices.) ## Problem 338 Each of the following sets are not a subspace of the specified vector space. For each set, give a reason why it is not a subspace. (1) $S_1=\left \{\, \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \in \R^3 \quad \middle | \quad x_1\geq 0 \,\right \}$ in the vector space $\R^3$. (2) $S_2=\left \{\, \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \in \R^3 \quad \middle | \quad x_1-4x_2+5x_3=2 \,\right \}$ in the vector space $\R^3$. (3) $S_3=\left \{\, \begin{bmatrix} x \\ y \end{bmatrix}\in \R^2 \quad \middle | \quad y=x^2 \quad \,\right \}$ in the vector space $\R^2$. (4) Let $P_4$ be the vector space of all polynomials of degree $4$ or less with real coefficients. $S_4=\{ f(x)\in P_4 \mid f(1) \text{ is an integer}\}$ in the vector space $P_4$. (5) $S_5=\{ f(x)\in P_4 \mid f(1) \text{ is a rational number}\}$ in the vector space $P_4$. (6) Let $M_{2 \times 2}$ be the vector space of all $m\times n$ real matrices. $S_6=\{ A\in M_{2\times 2} \mid \det(A) \neq 0\}$ in the vector space $M_{2\times 2}$. (7) $S_7=\{ A\in M_{2\times 2} \mid \det(A)=0\}$ in the vector space $M_{2\times 2}$. (Linear Algebra Exam Problem, the Ohio State University) (8) Let $C[-1, 1]$ be the vector space of all real continuous functions defined on the interval $[a, b]$. $S_8=\{ f(x)\in C[-2,2] \mid f(-1)f(1)=0\}$ in the vector space $C[-2, 2]$. (9) $S_9=\{ f(x) \in C[-1, 1] \mid f(x)\geq 0 \text{ for all } -1\leq x \leq 1\}$ in the vector space $C[-1, 1]$. (10) Let $C^2[a, b]$ be the vector space of all real-valued functions $f(x)$ defined on $[a, b]$, where $f(x), f'(x)$, and $f^{\prime\prime}(x)$ are continuous on $[a, b]$. Here $f'(x), f^{\prime\prime}(x)$ are the first and second derivative of $f(x)$. $S_{10}=\{ f(x) \in C^2[-1, 1] \mid f^{\prime\prime}(x)+f(x)=\sin(x) \text{ for all } -1\leq x \leq 1\}$ in the vector space $C[-1, 1]$. ## Problem 337 Let $A, B$ be complex $2\times 2$ matrices satisfying the relation $A=AB-BA.$ Prove that $A^2=O$, where $O$ is the $2\times 2$ zero matrix. ## Problem 332 Let $G=\GL(n, \R)$ be the general linear group of degree $n$, that is, the group of all $n\times n$ invertible matrices. Consider the subset of $G$ defined by $\SL(n, \R)=\{X\in \GL(n,\R) \mid \det(X)=1\}.$ Prove that $\SL(n, \R)$ is a subgroup of $G$. Furthermore, prove that $\SL(n,\R)$ is a normal subgroup of $G$. The subgroup $\SL(n,\R)$ is called special linear group ## Problem 330 Let $V$ be the vector space of all $n\times n$ real matrices. Let us fix a matrix $A\in V$. Define a map $T: V\to V$ by $T(X)=AX-XA$ for each $X\in V$. (a) Prove that $T:V\to V$ is a linear transformation. (b) Let $B$ be a basis of $V$. Let $P$ be the matrix representation of $T$ with respect to $B$. Find the determinant of $P$. ## Problem 316 Let $n$ be an odd positive integer. Determine whether there exists an $n \times n$ real matrix $A$ such that $A^2+I=O,$ where $I$ is the $n \times n$ identity matrix and $O$ is the $n \times n$ zero matrix. If such a matrix $A$ exists, find an example. If not, prove that there is no such $A$. How about when $n$ is an even positive number?

2017-08-20 00:07:54

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https://bioinformatics.stackexchange.com/questions/2929/joining-scaffolds-to-get-full-genome/2957#2957

# Joining scaffolds to get full genome? I am using Ray to assemble a about 7.2 kb picornavirus genome. I am using k-mer of 55. Following is the exact code that I used. mpiexec -n 1 Ray -k 55 -s 2-CA-SVA-2_S2_L001_R1_001.fastq_q30_trim_LR_15.fasta -o rayd55tr This worked quite well as I got a scaffolds.fasta file with two scaffolds one with 5730 bp and another with 1548 bp. Now, I am confused how I can join those scaffolds to get one linear genome. I joined them manually and blasted just to check and I got something like below :. Is there any tool to join these two contigs together to have one complete linear genome? I have reference genome too if needed. • What did you blast against? Your image just shows a few identical sequences, but we can't interpret any blast results without knowing what was blasted against what. Also, if you have a reference genome, why didn't you use that to assemble the contigs? Nov 25 '17 at 17:15 • Are there any good tools available for reference based contigs joining ? Nov 26 '17 at 7:48 • It is quite important to know what kind of sequencing data you have used for people to provide accurate tips. Nov 30 '17 at 7:56 Ragout worked well for me. It is a reference-based scaffolder. ragout.py --outdir output/ input/ragout.rcp > message.txt 2> error.txt --threads 8 --overwrite The ragout.rcp file contains a 'recipe' with the reference sequence and the contigs in FASTA format.: .references = ensembl .target = assembly ensembl.fasta = ref.fa assembly.fasta = contigs.fa In my case, it reduced the number of contigs 10-fold and increased the N50 10-fold. It added N's between the contigs. • Please consider expanding your answer. How/when does it work well ? How will it help the OP in their case? – llrs Nov 27 '17 at 11:55 • I have added my code and what Ragout did for me. What does 'OP' mean? Nov 27 '17 at 13:52 • Great edit! OP comes from Original Poster to refer the one that asked the question. I hope this will be useful. – llrs Nov 27 '17 at 15:42 In some cases you might consider reference-based scaffolding, as per charlesdarwin's answer. I would argue that in most cases this will only provide limited information, as this will only really provide you with the order of the contigs as it is in your reference, as opposed to how it is in your sampled organism. In that sense it really only provides pseudo-scaffolding that makes your assembly look artificially good. In all cases you will have to check wether your raw data supports your scaffolding solution. Example: you will never be able to call structural variants across contig boundaries if you use reference based scaffolding. I would suggest you try different k-mer sized for your assembly algorithm, and look into dedicated scaffolding tools. Without knowing your type of sequencing data it is hard to suggest anything specific.

2021-09-25 06:16:39

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https://web2.0calc.com/questions/a-used-car-lot-has-120-vehicles-for-sale-a-sample

+0 # A used-car lot has 120 vehicles for sale. A sample of 15 of these vehicles finds that 6 of them have previously been in an accident. +1 530 2 A used-car lot has 120 vehicles for sale. A sample of 15 of these vehicles finds that 6 of them have previously been in an accident. What is the best estimate of the percent of the used-car lot's vehicles that have previously been in an accident? Aug 7, 2021 #1 +36433 +2 6 out of every 15 have been in an accident how many 15's are there in 120?       Eight 8 x  6 = 48  of 120   might have been in anaccident Aug 7, 2021 #2 +364 +4 Hey there, Guest! 120 divided by 15 = 8 8 times 5 = 48 $$\frac{48}{120}$$ equals 40% 40% of the cars were previously damaged in an accident. (120 ÷ 15) ÷ 6 = 40%. Hope this helped! :) ( ﾟдﾟ)つ Bye Aug 7, 2021

2022-09-26 02:47:13

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https://www.mathworks.com/discovery/capm.html

# CAPM ## Capital Asset Pricing Model CAPM (capital asset pricing model) is used to evaluate investment risk and rates of return compared to the overall market. You can use CAPM to price an individual asset, or a portfolio of assets, using a linear model defined as: E(ri)=rƒ+βi(E(rM)- rƒ) Where: E(ri) is the expected return of the asset or portfolio denoted with i. rƒ is the risk-free rate of return. βi (beta) is the sensitivity of returns of asset i to the returns from the market, and is defined as the covariance of returns between the asset i and the market to the market variance. E(rM) is the expected return of the market. Using CAPM, you can calculate the expected return for a given asset by estimating its beta from past performance, the current risk-free (or low-risk) interest rate, and an estimate of the average market return. A common pitfall in estimating beta from historical data sets can arise when the data set is incomplete, or contains missing data, so it is important to have missing data estimation functions to reduce this type of estimation risk for CAPM. For more information, see Statistics and Machine Learning Toolbox and Financial Toolbox.

2016-12-08 22:30:25

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http://openstudy.com/updates/508bff8be4b077c2ef2ea1fa

## A community for students. Sign up today Here's the question you clicked on: ## anonymous 3 years ago can some one help me -24x^2+28/3x-5/6=0 • This Question is Open 1. anonymous $\frac{ -24x^2 + 28 }{ 3x - 5 } * \frac{ 1 }{ 6 } = 0$ it look like that? 2. anonymous yes it does 3. anonymous is that the answer 4. anonymous no... 5. anonymous the problem looks like this -24x^2+28/3x-5/6=0 6. anonymous I took the reciprocal of 6 for it's being divide by another fraction. (if you divide by a fraction you flip it and multiply) 7. anonymous okay thanks 8. anonymous multiply $\frac{ -24x^2 + 28 }{ 3x - 5 } * \frac{ 1 }{ 6 } = 0$ and what does it look like? #### Ask your own question Sign Up Find more explanations on OpenStudy Privacy Policy

2016-05-28 02:07:46

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https://www.gban.net/2018/07/06/pericardial-mesothelioma-and-exposure-to-asbestos/

# Pericardial mesothelioma and exposure to asbestos by Francisco Báez Baquet Posted on July 6, 2018 By Francisco Báez Baquet Mesothelioma -in any of its possible settlements-, in real or supposed absence of previous exposure to asbestos, remains one of the most current topics in the medical literature -see, for example: Batahar et al. (2016) -. Extreme rigor, at the time of being able to affirm, with the maximum possible security to reach, in the current state of scientific knowledge, if indeed it is, in each case considered, a real etiological absence of asbestos -or not-, it is, in our opinion, an inescapable requirement of scientific honesty, with tangible repercussions, even outside the purely academic sphere. The asbestos affects the entire cardiovascular system, including all its tissues and constituent organs, and therefore also the pericardium. See, in this respect, our work: Cardiovascular pathologies in exposed to asbestos                                                          «Rebellion», 06/15/2015 / 06/16/2015 http://www.rebelion.org/noticia.php?id=199971 (I) http://www.rebelion.org/noticia.php?id=199972 (II) The question is also addressed in our work: The other heads of the Hydra. Special presentations of mesothelioma «Rebelión», 10-10-2015 http://www.rebelion.org/noticia.php?id=204286 Reading this previous article of ours, we consider it highly recommended, we would say essential, for the full understanding of the whole issue, including such essential aspects, such as the consideration of pericardial mesothelioma as an occupational disease. The pericardial effusion, originated by asbestos, is treated in: Trogrlic et al. (1997). In Mirabella (1992), the author it states that “asbestos has a deleterious effect on the pericardial serosa.” Referring specifically to the causal nexus regarding pericardial mesothelioma, several papers postulate it, either generically, expressing the opinion of the respective authors, or referring it to the specific case treated in each of those articles. We will now review some of them, starting with those in which such a causal link is more unquestionable. In Okumura et al. (1980), the authors, in the “Summary” of their work, say: “The patient had been working in an asbestos factory for four years, from 16 years. Five years ago she complained of sputum and cough, and was treated for chronic bronchitis. As of March 1977, when he was 53 years old, hydrothorax and ascites increased, his weight decreased and he was hospitalized for cachexia. The clinical diagnosis of diffuse malignant mesothelioma was made based on the presence of atypical cells in effusions. The atypical cells showed positive colloidal iron staining test and positive hyaluronidase digestion test. Asbestos bodies were found in the sputum. The patient died in February 1978. The post-mortem examination confirmed asbestosis and mesothelioma, which spread over the pleura, the pericardial sac, the diaphragm, the peritoneum and the pancreas. In addition, bronchial-alveolar lung cancer was found in the lower lobe of the left lung. Electron beam diffraction revealed that asbestos was amosite (brown asbestos).” To highlight for our part, that in the process of certification of the previous exposure to asbestos, several of the forecasts postulated in our protocol, included in our work, were included: Asbestos and paratesticular mesothelioma                                                                      «Rebelión», 06/01/2017 https://www.rebelion.org/noticia.php?id=221280 In relation to our text, we deem it appropriate to make an indent here to indicate the omission of a sign of involvement, immediate and non-invasive execution, which is the observation of an eventual cyanosis in the patient, noting at the same time, the limitations that the interpretation of such a symptom must inevitably present, and which consist in the wide margin of subjectivity and discretion in its observation (in practice, it is a sign of unviable quantification), and in the non-universality of its possibility application, because of the racial characteristic, consisting of the diversity of skin tones, adding to it the degree to which it has been daily sunny, and, eventually, even taking into account the different degree of personal hygiene , used by the patient. Once all the above is concluded, let’s return to the central content of our dissertation. Similar to what was said before, regarding the coincidences noticed with respect to the forecasts included in our protocol of verification of evidences of a possible previous exposure to asbestos, and abounding in the same coincidence of criteria with respect to the precise observations to be able to confirm this previous exposure , in Burazor et al. (2014), specifies: “Signs of diseases related to asbestos can be observed, such as calcified pleural plaques, diffuse pleural thickening and interstitial fibrosis”. On the contrary, the histological confirmation of the absence of causal link between pericardial mesothelioma and asbestos, we will have it in: Ashouri et al. (1993). In Contreras et al. (1985), the authors confirm the absence of a previous exposure to asbestos, through, exclusively, the inexistence of a history of exposure, and indirectly crediting, therefore, the lack of other elements of evidence, which could have been similarly used, and which would be those listed in the corresponding protocol, inserted in our previously mentioned work on paratesticular mesothelioma, and which we will now detail again -see: Chiappino & Bertazzi (1980) – : Anamnesis. Preferably, documented. In the case of Spain, through the so-called “work life” (curriculum of successive jobs). In the case of those who have already ceased their work (retired or deceased), collecting it themselves, in the case of the former, or through their families, in the case of the latter. If this were impossible, due to a regulatory impediment, it would be necessary to fight politically so that the obstacle could be rectified. The companies registered in the aforementioned “working life”, have to be investigated, in order to deduct their corresponding ascriptions to their respective economic or industrial sectors, for, by taking them into consideration, and the history of possible lawsuits by exposure to asbestos in these companies, to infer the possible occupational exposure to asbestos, by the patient. The adequate complement to this investigation should consist of being able to determine the respective mortality rate attributable to the staff of each of these companies with known or suspected links to the industrial use of asbestos, in comparison with the mortality corresponding to the generality of the country. It is an epidemiological tool whose importance goes beyond the scope of application related to asbestos etiology, allowing to identify, in general, those companies whose working environment conditions have been determining this increase in the mortality rate; including those situations in which the union representatives of the workers intuit that “something strange” may have been happening in a certain company or workplace. In the specific case of Spain, all this could not be addressed, except on the basis of the data to be supplied, for that purpose, by the same official body that extends the “working lives”, that is, by the INSS (National Institute of the Social Security), for being the depositary of the same ones, with free access to them, and with the suitable computer, organizational resources, and of facultative personnel, to be able to do it. With this exhibition, we are reiterating, once again, in our writings, the imperative demand that such a possibility, perfectly feasible, be made tangible in the reality. Clinical examination. Visual check of acropachy, or of cyanosis. Auscultation, in order to detect the presence of possible inspiratory basal crackles. Preferably, with permanent graphic registration of its representative curve. Analysis by optical microscopy of the presence, and eventual quantification, of “asbestos bodies” in sputum, urine and feces. See: Alderisio et al. (1996), Bignon et al. (1973), Billon-Galland (2012), Boatman (1983), Boatman et al. (1983), Capellaro et al. (1997), Cunningham et al. (1976), Davies et al. (2004), Farley et al. (1977), Finn & Hallenbeck (1984) & (1985), Guille min et al. (1989), Hallenbeck et al. (1990), McDonald et al. (1992), McLarty et al. (1980), Modin et al. (1982), Paris et al. (2002), Pettazzoni et al. (2007), Roggli et al. (1983), Scansetti et al. (1996), Smith & Naylor (1972), Sulotto et al. (1997), Teschler et al. (1996), Tomatis et al. (2005), Wyss (1953), Zaina et al. (2016). Evaluation of pulmonary function, to be able to eventually show, the possible existence of a restrictive or mixed pattern. Evaluation of gaseous diffusion, to the same effects. Radiological evidence. Pleural plaques. Pleural thickening. Affectation of lung parenchyma (incipient asbestosis). Other possible alterations (atelectasis, bronchiectasis, obliteration of costophrenic angles, etc.). Electronic microscopy. In his case, verification, by means of electronic microscopy, in tissues of the investigated organ, that in the present opportunity would be the pericardium, of the possible presence, quantifying it, of asbestos fibers. In Morinaga et al. (1988), the authors present a single case of pericardial mesothelioma in which the presence of asbestos could be detected in situ. Only if there is a negative result in each of these potential evidences, with no exceptions (except the logical ones, depending on the situation contemplated in each case), it could be concluded with full foundation, that no evidence of previous exposure to asbestos has been found. Satisfying yourself with the mere memory evoked by the patient or their relatives, does not guarantee an authentic fidelity with regard to what actually happened, with the academic rigor required in some research work, to publish in specialized professional journals, and constitutive of the corresponding medical bibliography. The protocol is based on a tripod of evidence classes: An improved anamnesis, endowed with a better exhaustiveness and depth in the information gathered, going to the opportune source, and fully exploiting its possibilities to identify work situations in which it can reasonably be presumed to imply a potential presence of asbestos in the environment of the successive work centers in which the patient could be exposed, possibly with a possible reflection in the mortality rate of the corresponding company at each opportunity. Analytical tests capable of detecting the possible presence of asbestos fibers and / or “asbestos bodies”, quantifying them, both in sputum, urine and feces, by optical microscopy, as well as in the tissues of the settlement organ of the asbestos-related pathology object of the investigation, and that in the present opportunity it would consist in the tissues of the pericardial mesothelioma itself, looking, in this last histological material, for the direct presence of the fibers, by means of electronic microscopy. Evidence of alterations, pathognomonic signs, which may eventually reveal the presence, in a situation of co-morbidity, of other morbid asbestos-related manifestations (incipient asbestosis, pleural plaques, benign pleural thickening, respiratory alterations, etc.). Obviously, the relevance of the application of the aforementioned protocol, is not limited to the specific case of the works to be published, on the specific pathology consisting of pericardial mesothelioma, but also refer to those of all cases of mesothelioma, whatever its settlement, and also as regards other asbestos-related malignancies, such as lung cancer, cancers of the gastro-intestinal tract, cancer of the larynx, cancer of the ovaries, etc. With regard to the first thing -mesotheliomas, in any settlement- we will say that in Delgermaa et al. (2011), work entitled “Global deaths by mesothelioma, notified to the World Health Organization between 1994 and 2008,” states: “The distribution of the disease by anatomical site was: pleura, 41.3%; Peritoneum, 4.5%; Pericardium, 0.3%; And unspecified sites, 43.1% “. In the “Conclusion” of the “Summary” of this work, it closes the same, with the following sentence: “The different temporal trends observed between countries may be an early indication that the burden of disease is slowly changing towards those who have used asbestos more recently.” Similarly, in Maltoni et al. (1991), the authors make up a cohort of affected by mesothelioma based in their respective settlements, having mediated exposure to asbestos, with the following composition: 78 pleural (94%), 4 peritoneal (4.8%), and 1 pericardial (1.2%). In Kakar et al. (2006), the authors express their opinion that in order to trigger pericardial mesothelioma, comparatively higher doses of exposure are required than those required for the outcrop of mesothelioma in the rest of the settlement sites. This would explain its reciprocally lower rate. The involvement of the pericardium by another pathology other than mesothelioma, and in relation to a previous exposure to asbestos, is addressed in Cooper et al. (1996). In Cucchi (2003), the author recounts a case of pericardial mesothelioma, in which the patient, by his profession as a firefighter, was already showing us the high probability of having a previous occupational exposure to asbestos. The existence of another asbestos-related pathology -pericardial thickening-, with settlement in the same type of organic tissue and anatomical structure -the pericardium- reinforce the plausibility of the actual existence of the same etiology, referred to mesothelioma with the referred Settlement: Al Jarad et al. (1993). In Davies et al. (1991), the authors report a case of pericardial effusion and constrictive pericarditis, induced by asbestos. Therefore, even if it were not a case of pericardial mesothelioma, the factual background makes plausible the eventuality of a future drift towards malignancy, of the aforementioned clinical picture. Pericardial mesothelioma, in co-morbidity with other asbestos-related malignancies, will be found in the cases described in: An et al. (2009), Filho et al. (2015) -in animal-, Nojiri et al. (2009). The same, but in co-morbidity with malignant pathology not related to the exposure to asbestos, we will have it in: Kunakov et al. (1989). In Raeside et al. (2016), the authors, referring to their patient, express themselves in these terms: “… he may have been exposed to asbestos in the farm premises during his work as a farmer”. The causal link between environmental exposure to asbestos and pericardial mesothelioma is recognized in: Arslan et al. (2012). Although the authors do not expressly express themselves about this possibility, we will have a job – Eker et al. (1989) – in which, because it refers to a case that occurred in a country, such as Turkey, where geological outcrops abound, both asbestos and erionite, the probability that indeed, that may have been the route of contamination, etiological responsible for the case that arose. The asbestos etiology of pericardial mesothelioma is assumed by the authors of the following works: Beck et al. (1982), Burke & Virmani (1995), Fujiwara et al (2005) -job exposure-, Horie et al. (2010), Kahn et al. (1980), Mensi et al. (2010), Nojiri et al. (2009), Oc et al. (2012), Oreopoulos et al. (1999), Rizzardi et al. (2010), Roggli (1981), Sharma & Katechis (2011), Thomason et al. (1994). A remarkable and exceptional case of direct contamination, by asbestos, of the pericardium, through a surgical maneuver, generating an iatrogenic exposure, is described in Churg et al. (1978). We transcribe the manifested in this respect in our work: Sufrir por sanar (I) – Padecimientos iatrogénicos asociados al tratamiento o al diagnóstico de las patologías del amianto / Rebelión. 23-04-2015 Suffering to heal (I) – Iatrogenic disorders associated with the treatment or diagnosis of asbestos pathologies / Rebellion . 04-23-2015 http://www.rebelion.org/noticia.php?id=197976 and: (II) – «Rebellion». 25-04-2015 http://www.rebelion.org/noticia.php?id=197977 : “In Churg et al. (1978), a case of pericardial mesothelioma is reported in a patient who, 15 years earlier, had been treated for angina pectoris by depositing a mix of asbestos dust and fiberglass in the pericardial cavity, a performance that, in 1963, it should have been avoided, bearing in mind the evidences of all kinds that already existed, about the carcinogenic power of asbestos fibers “. Mesothelioma metastases, located in the heart and / or pericardium, are relatively frequent, given that the aggressiveness of the aforementioned asbestos-related malignant pathology is conditioned, among other factors, by its high propensity to generate metastasis: Silvestri et al. (1997). Pericardial mesothelioma is recorded in several animals: Balli et al. (2003), Bollo et al. (2011), Carnine et al. (1977), Ceribasi et al. (2013), Chandra & Mansfield (1999), Closa et al. (1999), Colbourne et al. (1992), Filho et al. (2015), Ikede et al. (1980), Ledecká et al. (2010), Machida et al. (2004), McCleery et al. (2015), McDonough et al. (1992), Movassaghi et al. (2009), Nash & Kaliner (1984), Takasu et al. (2006), Wiedner et al. (2008), Yamamoto et al. (2013). As it is known, mesothelioma in animals has been considered as sentinel episode of an environmental risk by asbestos: Ardizzone et al. (2014), Backer et al. (2001), Bukowski & Wartenberg (1997), De Nardo (1996 -2 refs.-), (1997), (2003) & (2004), De Nardo et al. (2004), Reif (2011). This does not imply, in any way, that every case of pericardial mesothelioma in animals has to be considered as evidence in favor of the causal link between asbestos and mesothelioma based on the aforementioned settlement, but the truth is that at least for some of the authors who reported such cases of pericardial mesothelioma in animals, the reality of the causal link is assumed. So we will have, for example, that in Bollo et al. (2011), the authors state in the following terms: “Since he was born, the lion was housed overnight in a cage covered by boards made of cement and asbestos fibers. Therefore, a relationship between the inhalation of asbestos fibers and the lesion can easily be raised, as has already been described in humans.”. See also: Ceribasi et al. (2013), Closa et al. (1999). For pericardial mesothelioma and pleural mesothelioma, both in the hamster, infection with the SV40 virus has been postulated as an alternative etiology: Hubbard et al. (1997). Another alternative etiology, of iatrogenic nature, is attributed to pericardial mesothelioma: previous irradiation. See: Small et al. (2008), Velissaris et al. (2001), Yıldırım et al. (2010). We do not hide the evidence that, without denying it categorically, nevertheless there are several works that come to question the veracity of an etiology for asbestos, of the pericardial mesothelioma: Ali et al. (2014), Fazekas et al. (1991), Grebenc et al. (2000), Hoey et al. (2016), Karadžić et al. (2005), Kayatta et al. (2013), Lagrotteria et al. (2005), Lingamfelter et al. (2009), Llewellyn (1987), Montesinos et al. (2012), Morteza (2013), Nilsson & Rasmuson (2009), Patel & Sheppard (2010), Restrepo et al. (2013), Yıldırım et al. (2010). It seems pertinent to ask the question, that if each of these authors (and as far as possible, since in some cases dealing with works referring to post-mortem findings), they will have tried to stick as much as possible to the postulated protocol in our previous work, and here again recalled, to discern whether there has been evidence available, or not, of a previous exposure to asbestos, by the patient. At the same time, and insofar as such completeness has not occurred, it can be conjectured whether, in the opposite case, the respective authors concerned would not, logically, have changed their position, changing it in its opposite. Bibliography The access link to the Dropbox file, which contains it, is then provided:

2023-01-28 09:14:12

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http://www.reddit.com/user/ZombieLurker1

[–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on I told myself I wasn't going to bother with this anymore, but since your tone has calmed down some I'll just leave with this. Wanting something, no matter how badly does not mean you are feeling a sense of entitlement. Believing you are owed or have the right to something, does mean you feel you have a sense of entitlement. The people here can bitch, complain, yell to the stars that the Standalone isn't here and show their distaste for the game not being released... but that does not make them entitled. There are a lot of other words to describe their behavior but entitled is not one of them. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on Oh my! So threatening! Lets resort to cursing! I showed you how the word entitled is properly used and then I also demonstrated how you used it incorrectly and pointed out how it doesn't make any sense. Wanting control over when the Alpha releases (Not entitled) and believing you have the right over control of the Alpha (Entitled) are two separate things and you basically cement my point. So glad you finally can admit it since the words did come out of your mouth. Hold on let me see if I can quote it. People want the release of Standalone. If they could control the release they would release it now. = Impatient. Go back to school ShirtGames. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on They are passionate about the game. They want to know when they can play it or at the very least when they cannot play it. There's no point in wishing they'll be able to play it during the holiday break from school/work/whatever if there is little certainty that the game will release! It's not a hard concept to understand. They just want something more than vague answers and false hope. Last, and this is the final thing for the night so you and your buddy ShirtGames can go have some bromancing.... You try to act superior by siding with the development team and calling anyone who questions or challenges the development team "entitled." Then you call me a moron (Questioning my intelligence) and then you try to get all StepBrothers on me with asking if I was high... out of all that you focus on thinking I'm insulted because you asked if I was high? You're seriously not all there. :) Alllllll this because you don't know how to use the word entitled! What a night. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on Wow, you two are really dense! Reading comprehension is another one of your weak areas! I can't stay up any longer and waste my time educating you two. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on I've been following the development off and on from the beginning. When a developer says "We really want a soft release" you would think that meant doing things like... I don't know, probably not purposely hyping the community by posting "Hype train" videos as if the games release was imminent and/or soon; also words frequently stated by the development team. I know you are challenged with your vocabulary so do I need to bother going over the definition of imminent or soon? Lastly, they dangle the game by saying ... "One X gets fixed, the game will be ready for release." This has been done on multiple occasions and there is always something else they have to accomplish first. It's dangling because it keeps people at the edge of their seats waiting for the moment that item is fixed, or implemented, or whatever the case and when that time comes they are let down with another excuse on why they cannot release it. You're pulling at straws. There's not a single person that thinks they can control the release date. All the conspiracy theories, release date theories, pictures and videos about release date are just to keep their spirits up and have a good time. Then the dark cloud (people like you) come along and just try to knock them off because they're disappointed by your gods and you feel the need to defend them. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on You're entitled to your opinion. Also translates to. You have the right to your opinion. See how that works? You think you're entitled to have the standalone right now. Translates to You think you're entitled to have the standalone right now that you will inevitably pay for if that happens and thus be entitled to play it. See what a mess that is? Doesn't quite make sense but I get it. I know, I know... Saying "Stop being entitled!" Just has a ring to it that exudes supremacy. The word you're looking for is impatient, like I said. Have a goodnight though. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on You used free to define your usage of entitlement which I told you was incorrect. Sorry to burst your bubble. You have no argument here. I suppose I'm high, or maybe I took the "You have no argument here." as your rally cry for your victory? I'm really lost on you. I gave you the definition of entitlement and yet you still try to give me your spin on it. There is no "Unless there is some form of such and such" That is not how the word works. Entitlement is about believing you have the right to something, simple as that. A person does have the right to something they purchase, which no one is questioning correct? So you're trying to take a word and misuse it. Simple. As I said, just because they want the game RIGHT NOW does not mean they feel they are entitled to the game. They are just impatient. So now you've called me a moron, accused me of being high, it seems you're awfully fond of insulting people? I guess you are the internet badass? [–] -1 points0 points  (0 children) sorry, this has been archived and can no longer be voted on I love just watching the community interact. Since we live in a society that likes labels and titles I made some up. :) Which one are you? The Extremists: Devoted, Passionate, Impatient. They just want to play the game in any shape or form. They hang on every word the development team says, create conspiracy theories, and just want to explore the new DayZ. The Zealots: Defensive, Snobbish, Loves to use the term Entitled. They hate the Extremists with a furious passion. Very defensive of the Development team and try to act as if they are patient happy-go-lucky but are nearly as on the edge of their seats as the Extremists. The Lurkers: Patient observers. Mostly users who visit the news sites for news, some may not even be registered users. Others who like to talk about the game, make suggestions or talk about newly added features they've seen. [–] -1 points0 points  (0 children) sorry, this has been archived and can no longer be voted on Is that really the roadmap of an Alpha though? Disappearing loot is a common thing in the mod, not that gamebreaking or preventing people from having a meaningful experience. Crashing, unless super common, can be a problem. As others have mentioned and from what we've experienced in the mod is that the community is incredibly resilient. I just like discussing about the game and I do a lot of ball busting but you gotta draw the line somewhere Dean or else you'll always find a reason why something isn't perfect enough to release the game. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on Such animosity towards your fellow community members over a game... I'm not sure how you self proclaim "won" the argument. Unless the community is demanding they get this game for free, as in its their right to own this game for whatever reason without purchasing it, then they are in no way shape or form acting "entitled." [–] -1 points0 points  (0 children) sorry, this has been archived and can no longer be voted on Whining bitches who won't stop insulting the team? Well when the Development team taunts them with hype videos and pictures and dangles the game in front of their faces with "Once we do this... once we do that..." I can't say I blame them for being a little upset. I'm sure some are more vocal than others for the simple fact that they know there is a high chance that the development team will read it but why do you feel empowered to defend the development team and insult them? (The community) You still can't grasp the concept of how that word is used I see. People want to play the game, they want it released right now... that doesn't make them entitled. Impatient yes, entitled no. [–] 14 points15 points  (0 children) sorry, this has been archived and can no longer be voted on I've never been a fan of the modding community or private hives to be honest. This game in my opinion should be treated like games like Eve, WoW, etc and just keep it as secure and genuine as possible. If someone wants to mod the game they should do that to Arma 3. Just my .02 [–] -5 points-4 points  (0 children) sorry, this has been archived and can no longer be voted on Ummm, that is the argument you're going with? Entitlement would be if people say Dean owes them the standalone because they purchased Arma II specifically for the mod. Entitlement has nothing to do with people wanting to play the standalone in its current state despite its flaws. The reason I said "free" was because no one has the right to play the game unless they purchase it, and no one is asking to have the game for free. People like yourself just go around anytime anyone questions why the game isn't out, has any criticism, or overall shows disappointment the first thing I've noticed is you call them entitled. It's the wrong use of the word for starters, as I mentioned (though you're entitled to disagree ;) ) as well as just makes you out to be a brown nosing snob. [–] -1 points0 points  (0 children) sorry, this has been archived and can no longer be voted on Base game $60 + Generally 4 Expansion Map Packs at$15 each = $60 ... Total$120? Or buy the yearly season pass ($50?) and basically prepay for the DLC for a grand total of$110. I could be a little off on the expansion packs as I have a personal no purchasing policy towards DLC. [–] 0 points1 point  (0 children) sorry, this has been archived and can no longer be voted on Price points have not been confirmed but my money is on $35. Speechless. by in dayz [–] 1 point2 points (0 children) sorry, this has been archived and can no longer be voted on Hicks I must admit that you are the most refreshing part of the development team. Very calm and collected but still a fun personality. [–] -6 points-5 points (0 children) sorry, this has been archived and can no longer be voted on en·ti·tle·ment noun -ˈtī-təl-mənt\ : the condition of having a right to have, do, or get something : the feeling or belief that you deserve to be given something (such as special privileges) : a type of financial help provided by the government for members of a particular group No one expects DayZ for free. All I see are people who want to play a game they are passionate about. Speechless. by in dayz [–] 0 points1 point (0 children) sorry, this has been archived and can no longer be voted on Stop using the word entitled. This has got to be the biggest misused word of this entire forum. en·ti·tle enˈtītl/ verb past tense: entitled; past participle: entitled 1. give (someone) a legal right or a just claim to receive or do something. "employees are normally entitled to severance pay" synonyms: qualify, make eligible, authorize, allow, permit; More enable, empower "this pass entitles you to visit the museum" 2. give (something, esp. a text or work of art) a particular title. "an article entitled “The Harried Society.”" en·ti·tle transitive verb \in-ˈtī-təl, en-\ : to give a title to (something, such as a book) : to give a right to (someone) [–] 2 points3 points (0 children) sorry, this has been archived and can no longer be voted on The flashlights were really disappointing. Just like in the mod it's nearly impossible to loot indoors in the dark because the lighting doesn't disperse indoors properly. Though in their defense they didn't do much to the flashlights but soften up its beam to make it look more organic and I imagine that it's still a WIP. [–] -2 points-1 points (0 children) sorry, this has been archived and can no longer be voted on I'm more focusing on the fact that using "entitled" , "entitlement" , and "self entitlement" make absolutely no sense and the fact that people use these terms to describe other people so much on this forum is really stupid which in turn just makes you look like some elitist snob. Speechless. by in dayz [–] 0 points1 point (0 children) sorry, this has been archived and can no longer be voted on They do need more people to really test their work, unless they wouldn't have asked if it was ok to bring on the content creators and such. The developers do need to decide when enough is enough, and Dean has admitted this as well, and just put it in the hands of the consumers to pick apart. The problem is, and a double edged sword, is that the CEO of Bohemia has left this all in the hands of Dean with no oversight really and given him free reign. Great for creativity but bad for overall direction. Speechless. by in dayz [–] -2 points-1 points (0 children) sorry, this has been archived and can no longer be voted on You won't know what will occur when 100k people log into the game, until they do. That's why you have an Alpha. The more you fix and add things to make sure the game is solid and playable... it's no longer really an Alpha. Sorry... maybe you were trying to be witty and make sense and I didn't get it. ;) [–] 1 point2 points (0 children) sorry, this has been archived and can no longer be voted on Call of Duty is the same game every year, and it doesn't take them that long to develop. They wait to release one every year so they can milk it with 4 DLC packs ($120 every year per person, or \$110 if you have the season pass...) and then they launch a new game and repeat. It's a cash cow because society must have the latest and greatest and are too blind to see they are only buying the same ole game in a newer skin. Kudos for them I guess. [–] -1 points0 points  (0 children) sorry, this has been archived and can no longer be voted on I really don't understand why everyone who brown-noses uses the word "entitled/entitlement" etc in all its various forms when anyone says how much they want to play the game. No one is asking for the game for free, they will all be paying customers so they will have the "right" to play the game if they pay... or rather they are entitled to play the game. Stop trying to be some elitist snob. [–] 21 points22 points  (0 children) sorry, this has been archived and can no longer be voted on This is your major flaw in how you communicate with the community. It's not a matter of "If you say it won't be out by the end of the year, people will think it'll be out Jan 1st." That's ridiculous. The problem is you consistently give them the impression that it's "Soon" or "Imminent" and that if you verify or fix whatever your main goal is at that very moment then it's a green light for release; which again history shows you are hesitant to do. You say things like we'll implement this or fix that and then we're ready to go and then something else always comes up and the community is seeing the reasons for it to not be that detrimental. The mod in all its forms, even currently is very well unplayable to some with its FPS issues, script prevention issues, etc... Yet there is an astounding collective of over 25 billion hours played. I'm just an outside looking in type of person and not someone pounding at Dean's door demanding the game. Just taking the whole picture in perspective.

2015-05-25 22:40:03

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http://crypto.stackexchange.com/tags/pairings/new

# Tag Info I use multiplicative notation for $\mathbb{G}_1$ and $\mathbb{G_2}$ (as in your question) as this may make it a bit clearer for you. Lets say the groups are of prime order $p$ and and lets consider your elements w.r.t. bases $g_1$ and $g_2$. Lets write your elements $x_1$ and $x_3$ as $g_1^{a_1}$ and $g_1^{a_2}$ and $x_2$ and $x_4$ as $g_2^{b_1}$ and ... For clarity, I will use an additive notation in the groups $\mathbb{G}_1$ and $\mathbb{G}_2$, and denote group elements with the "$x$" letter, not "$e$". For all $x_1, x_3 \in \mathbb{G}_1$ and $x_2, x_4 \in \mathbb{G}_2$, we have the following: \begin{eqnarray*} e(x_1 + x_3, x_2 + x_4) &=& e(x_1, x_2 + x_4) e(x_3, x_2 + x_4) \\ &=& e(x_1, ...

2014-09-02 12:11:25

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http://compgroups.net/comp.databases.ms-access/text-field-only-for-text-no-numbers/1452182

f #### text field only for text - no numbers Hi I would like some help about the following : I have a text field and I don't want it contains any numbers. How can I limit this situation ? TIA Paulo 0 amigo.alf (1) 10/15/2003 10:56:15 PM comp.databases.ms-access 42670 articles. 0 followers. 2 Replies 841 Views Similar Articles [PageSpeed] 46 "Paulo Rodrigues" <amigo.alf@netvisao.pt> wrote in message news:<newscache$kgmtmh$bb1$1@newsfront4.netvisao.pt>... > Hi > > I would like some help about the following : > > I have a text field and I don't want it contains any numbers. How can I > limit > this situation ? > > So far, I couldn't find literature exacly about this here in the newsgroup. > > TIA > Paulo Paulo, the online help is your FRIEND. Private Sub Text0_KeyPress(KeyAscii As Integer) If KeyAscii >= 48 And KeyAscii <= 57 Then KeyAscii = 0 End If End Sub Just put this code in the KeyPress event of whatever text field you do not want to contain numbers. OR you could glue thumbtacks to the number keys on all your users keyboards... 0 pietlinden (2926) 10/16/2003 1:49:29 AM Thought I'd add my 2 cents worth. Avoid magic numbers, especially when you can use builtin VBA constants. The following is a little more intuitive to read and a future developer does not have to lookup 48 and 57 to see exactly what is being blocked. Private Sub Text2_KeyPress(KeyAscii As Integer) 'Cancel any numeric keys If KeyAscii >= vbKey0 And KeyAscii <= vbKey9 Then KeyAscii = 0 End If End Sub The above solution does not stop the user from cutting and pasting a numeric character. Its often the small things that get you. <g> I have a couple of generic functions, which do stop the user from pasting banned characters and it also allows you to add a series of non consecutive banned characters such as spaces or quotes or commas etc. Both functions could be modified for speed but I'm lazy and they work so I've never bothered tweaking them. Pieter's solution is much faster but does not allow you to easily add a newly banned character for numerous text boxes by modifying one constant in one place. I couldn't find the functions, so I rewrote them. You should test them if you use them and limit the length of the string to the maximum length of the field. This will slow down enough to be painful with a huge field so use it sparingly. You can also trap the "paste" using API calls and check the string at this point, which will speed things up considerably but all of this is overkill for 99% of applications. Have fun. Can you tell I'm bored? I go sailing in two days for four weeks so I'm just killing time at work. 'String of banned characters for text boxes Const fstrBANNED = "0123456789" 'Maximum text box field length Const flngMAX_LENGTH As Long = 255 Private Sub Text0_Change() StripBannedChars Text0 End Sub Private Sub Text0_KeyPress(KeyAscii As Integer) CancelBannedKey KeyAscii, fstrBANNED End Sub Public Sub CancelBannedKey( _ ByRef rintKeyASCII As Integer, _ ByVal vstrBanned As String) '******************************************************** 'Purpose: Cancels the key press for all banned ' characters specified in the supplied string '******************************************************** 'Loop through every character in the supplied string While Len(vstrBanned) > 0 'If the key pressed is the specified key, cancel it If rintKeyASCII = _ Asc(Left(vstrBanned, 1)) Then rintKeyASCII = 0 'Strip the leading character vstrBanned = Right(vstrBanned, Len(vstrBanned) - 1) Wend 'more characters End Sub Private Function strStripBannedChars( _ ByVal vstrSource As String, _ ByVal vstrBanned As String) As String '******************************************************** 'Purpose: Strips all banned characters from the ' supplied source string '******************************************************** 'Loop through every character in the supplied string While Len(vstrBanned) > 0 'Replace any occurrence of each banned 'character with an empty string vstrSource = Replace(vstrSource, _ Left(vstrBanned, 1), vbNullString) 'Strip the leading character from the banned characters vstrBanned = Right(vstrBanned, Len(vstrBanned) - 1) Wend 'more characters strStripBannedChars = vstrSource End Function Public Sub StripBannedChars(ByVal vtxt As TextBox, _ Optional ByVal vlngMaxLength As Long = flngMAX_LENGTH) '******************************************************** 'Purpose: Strips all banned characters from the supplied ' textbox. The cursor returns to the start of ' the textbox if banned characters are found. '******************************************************** Dim strSource As String Dim strStripped As String 'The source string to be tested for banned characters strSource = vtxt.Text 'The source string with banned characters removed strStripped = strStripBannedChars(strSource, fstrBANNED) 'If the source string has any banned characters 'remove them. This will trigger this function 'again. Beware of recursive event triggers! If strSource <> strStripped Then vtxt.Text = Left(strStripped, vlngMaxLength) End If 'Finished with the local pointer Set vtxt = Nothing End Sub 0 10/16/2003 6:53:45 AM Reply: Similar Artilces: text-text Wondering how what I input to my UTF-8 terminal gets passed along through my patched [1] trn ... Cyrillic: А Б В Г Д Е Ж З И Й К Л М Н О П а б в г д е ж з и й к л м н о п IPA: ᴀ ᴁ ᴂ ᴃ ᴄ ᴅ ᴆ ᴇ ᴈ ᴉ ᴊ ᴋ ᴌ ᴍ ᴎ ᴏ ɀ Ɂ ɂ Ƀ Ʉ Ʌ Ɇ ɇ Ɉ ɉ Ɋ ɋ Ɍ ɍ Ɏ ɏ [1] https://groups.google.com/d/msg/comp.sys.raspberry-pi/7Z37Hdrm0DM/6aqD-reXFzAJ ... text + text What is "text + text" supposed to do right now? It doesn't seem very useful to me. What about making "text + text" as an equivalent for "text || text"? Most strongly-typed programming languages do this. And MS SQL Server too, I think (CMIIW). -- dave ---------------------------(end of broadcast)--------------------------- TIP 1: subscribe and unsubscribe commands go to majordomo@postgresql.org Am Freitag, 8. Oktober 2004 12:57 schrieb David Garamond: > What is "text + text" supposed to do right now? Nothing. > What about making "text + text" as an equivalent for "text > || text"? Most strongly-typed programming languages do this. And MS SQL > Server too, I think (CMIIW). What would this gain except for bloat? It's not like SQL is utterly compatible with any programming language; users will still have to learn all the operators anyway. -- Peter Eisentraut http://developer.postgresql.org/~petere/ ---------------------------(end of broadcast)--------------------------- TIP 9: the planner will ignore your desire to choose an index scan if your joining column's datatypes do not match Peter Eisentraut wrote: >>What is "text + text" supposed to do right now? > > Nothing. Then are these bugs? (7.4.5 and 8.0.0beta1 give same results). Frankly, the current behaviour is quite strange to me. ------------------ =... Unbound text box, text>255, MS Access/PostgreSQL Hello. I have the following problem with MS Access/PostgreSQL combination: There is a form in Access that has an unbound text box, used for entering a commentary of a batch of records. There is a DAO Append Query that has a parameter that is passed from the text box using parameter of DAO QueryDef object. I adjusted B7 parameter (Text as LongVarchar) in connection string (ODBC driver) to 1, so that Access links PostgreSQL Text fields as Memo fields in Access. The intention was to be able to enter unlimited length commentary into the field. But, although I can enter unlimited text by using... rich text in text field I am using GUIDE for my UI work. (MATLAB 2009b) I would like to display some rich-text (font size change, bold, underline etc) inside a panel. Can I put some rich-text, using html tags, in a text field? For example: <html><b> this is bold </b></html> I know you can do it in table headers. Thank you. ... Text filtering in a text field Hi, am new to SKILL and would like to do some text checking and filtering for illegal characters in the text field. Meaning I have a text field in my form that is only to be with text, not any of the symbols (i.e. ~!@#$%^&* and so on). When the user input and saved the fields, those characters won't be allowed to be saved. What will be the best way to filter out only text? Only numbers? Terence <terrylau77@gmail.com> writes: > Hi, am new to SKILL and would like to do some text checking and > filtering for illegal characters in the text field. Meaning I have a > text f... How to convert Number Field to Text Field I'm newbie in Filemaker, currently I'm using Filemaker pro v 6.01 on Windows XP. I have a small problem. I'm trying to make a solution for Hotel Rate. I want to change the USD. 0.00 to "Included" for breakfast rate which already included in the room rate. Anybody can help, will be much appreciated. Thanks. "Adhie" <priyadi77@yahoo.com> wrote in message news:ba1b5c27.0404080446.21e110b2@posting.google.com... > I'm newbie in Filemaker, currently I'm using Filemaker pro v 6.01 on > Windows XP. I have a small problem. I'm trying to make a ... How to import a tab delimited text file into MS Access database Hi, I have the following task to be done in VC++ 6.0. I have a tab delimited text file that needs to be imported into a MS Access table. The table is created and the table structure is defined using DAO methods. So now I have to fill this table with the data in the text files. For a few rows in the text file, the number of columns could be less than the number of columns in the table. Can anyone please post me the code to do this. Thanks a ton in advance. Pradeep wrote: > I have the following task to be done in VC++ 6.0. We'd be happy to give you the VBA code, but do you really want ... Text file with numbers and text, want to just read numbers I have a series of text files I want to read. The files begin with header information. The number of rows of header information changes, there is no commenting symbol such as %%, and the header information sometimes has numbers such as a date or a time. I want to read in the number and only the numbers. This is an example of a file: (Again, the header info changes, different # of lines, different text) Vector Signal [Measurement4]: 09/27/2006, 09:05:24 Units: EU Time Real 0 0.053732 9.6e-005 0.11968 0.000192 0.085483 0.000288 ... Forcing a New Line in a Text Field in MS Access using VB Heya! I feel I'm beating an old horse to death with this question but I can't get around the problem. I want to update a text field on a form with a string from a VB module. I need enter/linefeeds in the string. I've tried: Chr(10) & Chr(13) Chr(13) & Chr(10 vbnewline vbcrlf none of which seem to work. I've set the properties for the text box to [Enter Key Behavior] = 'New Line In Field' and [Can Grow] = 'yes'. At the moment, my code looks like this: celsql = celsql _ & "Program: " & encname _ ... Sorting a Text field like a Number Field I have a table with around 18,000 records in it. One of the fields is a Text field, but 85% of the things in that field is a number (The other 15% is a number with a text suffix). I was wondering if there was an easy way to Sort this field as if it were a number (because, when it sorts as text it looks like this... 1 11 12 14 2 21 24 3 35 So far, the only thing I came up with was to make a query with this expression... TempSection: CDbl([Section]) But that either produces a #Error for those rows where the Section has a text character in there or it won't even open the query in datasheet view because of Data type mismatch in criteria expression. What can I do? Can I create an iif statement to catch that error? or Something? Thanks! -- Nathan Try this: sc:iif(isnumeric(x!y),cdbl(x!y),0) where X is table and Y is field. Sort on this but display y. This will place all fields containing text at the top and then sort numbers. If you want all text fields at the bottom then change 0 to 99999999. If you really need to sort the text contianing fields as well you will need a funtion to extract the numeric part and use that as the arguement to cdbl. You wouldn't need the iif function then. Good Luck Ira Solomon On 5 Oct 2003 16:31:25 -0700, ngiven@hotmail.com (Nathan Given) wrote: >I have a table with around 18,000 records in it. One of the fields is >a Text field, but 85% of the things in that fiel... Get the real type of columns from MS Access databases(OLEObject, text, memo, numeric) Hello, I made one application that opens MS Access databases.And I have one problem.How can I find the real data type of columns(text, memo, OLEObject, numeric) like it is into Access.I tried with resultSetMetaData.getColumnType(columnIndex) but I receive java.sql.Types.I have two columns that contains OLEObjects(images).But I receive two different types for columns : VARCHAR once, and for second column SMALLINT.I only want to see the types like in Access(OLEObjects, Text, Numeric, Memo...).Thanks in advance! Best regards, Calin Pop ... problem with importing text with number and text i am trying to import a csv file (~49000 rows x 52 cols) with numbers text and characters in it and not getting through. xlsread works fine with all my data except the first column of data which is a time stamp. it converts the time stamps into a constant value through the entire column. To add to the problem, when opened as a text file, every row of the file starts with a comma. I got very close with textscan/textread with all the data coming in but all the rows are transposed into one column one above the other ( imagine 49000 rows 52 cells long transposed one above the other in one column c... Insert text file in a text field ... Hallo, I have 2 questions: 1) How can I insert a text file into a TEXT field of a table (by an sql instruction) ? 2) How can I insert a microsoft word file into a BLOB field of a table (by an sql instruction) ? Please, could you help me ? Thank you . Fab. On Thu, 18 Oct 2007 06:41:52 -0700, electric_r@yahoo.it wrote: > Hallo, > > I have 2 questions: > > 1) How can I insert a text file into a TEXT field of a table (by an > sql instruction) ? > > 2) How can I insert a microsoft word file into a BLOB field of a table > (by an sql instruction) ? > > Please, could you help me ? This is a task for the application program, not the database itself. -- A way of life that is odd or even erratic but interferes with no rights or interests of others is not to be condemned because it is different. -- Chief Justice Warren E. Burger electric_r@yahoo.it wrote: > Hallo, > > I have 2 questions: > > 1) How can I insert a text file into a TEXT field of a table (by an > sql instruction) ? > > 2) How can I insert a microsoft word file into a BLOB field of a table > (by an sql instruction) ? > > Please, could you help me ? > > Thank you . > > Fab. Look at the LOAD_FILE() function in the manual On 18 Oct, 14:41, electri...@yahoo.it wrote: > Hallo, > > I have 2 questions: > > 1) How can I insert a text file into a TEXT field of a table (by an > sql instruction) ? > > 2) How can... Accessing text form fields name=field[label] I'm pretty much a JavaScript novice. I'm good at learning by example and changing those examples to suit my needs. That said .... ..... I have some select fields in a form I created for a database search that I am unable to figure out how to access. (The search is implemented in Php/MySQL.) The user enters search values for: name, address1, city, .... etc., ..... and for each of these they also select whether the search should look for the field to be equal to, not equal to, Like, or Not Like the value in the database. So in the form I have: <input type=text name=city> in combination with <select name=func[city]> <option value='='>=</option> <option value='!='>!=</option> <option value='LIKE'>LIKE</option> <option value='!='NOT LIKE>NOT LIKE</option> </select> For an example, this search could be to find an entry "WHERE city $func[city]]$city. (Php - e.g., WHERE city = 'Denver'). This works fine - in Php. I use similar combinations for name, address, etc., ... Okay, here's the JavaScript problem. For the Reset action I have a JavaScript function to Reset all the form fields. I want to Reset the selected indexes for the "func" fields (func[name], func[city], func[state], ...) using a loop that goes through the associative array, "func." I cannot find the right syntax to address them as an array and I am beg... reading in file with text and numbers to be able to access numbers Hi. I am trying to read in a file that was created by another application. The first two lines of this file are composed of text that I don't need. Following are 100 lines of numbers that I do need. Any idea on how to load this file without making an overly specific script? The number of rows of numbers the other application generates varies. Thank you for any tips! Look at the TEXTREAD function. One of the options is 'headerlines', to tell it the number of lines to skip at the beginning of the file. So you would do something like this: n = textread('myfile.txt','... Wrapping Text I'm trying to export an Access table to a pipe-delimited text file (with no text qualifier) and it keeps wrapping the text for one of the tables. None of the fields are particularly long, so I'm not sure why it's doing this. Any ideas how I can stop it from wrapping the text in the text file? -- Message posted via AccessMonster.com http://www.accessmonster.com/Uwe/Forums.aspx/databases-ms-access/200803/1 Leviathan wrote: >I'm trying to export an Access table to a pipe-delimited text file (with no >text qualifier) and it keeps wrapping the text for one of the tables. N... Old ms-access file, showing wrong text in access xp Dear sirs: I've one old .mdb file ( since 97). now when I open it, it converts most of text to strange unicode characters. can I stop this conversion and ask access to just show original non-unicode characters? Thanks Bijan ... Musatov exposes R.S.A. vulnerability: Blue highlight black text truncates black background text turning it white black foreground text remains in field. 505152535455565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f7071 72737475767778797a7b7c7d7e7f808182838485868788898a8b8c8d8e8f909192939495969 798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3 505152535455565758595a5b5c5d5e5f606162HMAC/SHA-256 Large Correct: Superposition of lines 1 and 4 will correct R.S.A. example: http://il8n.co/test.html ... Quickly adding text to a mysql text field that is NOT empty Hi all Is there a way to insert text into a mysql text field that already has text into it; without having first to extract the existing data and append the new text to that string variable and then insert the new string. Basically i'm looking for a way to do it with a single query not 2 (one being a select to gather existing data). Please help! I could have sworn I already replied to this but it appears that it did not go through, but anyway; you want to modify the contents of an existing field without having to fetch it using a query, yes? This is possible through the use of MySQL&#... Text from required text box to read-only text box Hello, I am fairly new to JavaScript and its use in Acrobat Professional. My situation is this: I have a form with a text box field which is required for the user to enter his/her name. I would like the required text box to display the name in all caps. I also need the user's name to appear in a read-only text box later in the form, which I would like to have the first letter of the user's first, middle initial, and last names to be capitalized. I would also like to have all required fields on the form highlighted in yellow, but the highlighting not printed. Lastly, I would like the... Surrounding text with text I was wondering if it was possible to surround a text body with text like so: +--------------+ |ABCDEFGHIJKLM | |H N| |A Main Body O| |L Text goes P| |B here Q| |-=+_ZYXWVUTSR | | | | | | | | | +--------------+ This seems far-fetched, but just curious. I suppose that I could just move stuff around by hand in the GIMP later on, but there's probably a {better,more {extensible,clean}} way of doing it from (La)TeX. -FreeSmith ptjm@interlog.com (Patrick TJ McPhee) wrote in message news:<bffbhe$per$1@news.eusc.inter.net>... > Peter Flynn had an example like that, which he either posted here or > posted a link here. It was something to do with a certificate -- try > searching for his name and that word in google. > > It wouldn't be hard to do with metapost. I have a macro called `pathalong' > which puts text along an arbitrary path. Well, it's been a while, but I finally finished it. It's a little job I was doing for an upcoming wedding. At any rate, I used pstricks to make the text go along a path, along with a couple of hacks for sizing (from graphicx) and kerning along the line (from soul). Here's the code (don't laugh): CAUTION:THIS CODE MAY MAKE YOU WRETCH ---SNIP--- \documentclass{article} \usepackage{graphicx} \usepackage{pstricks,pst-text,nopageno} \usepackage[width=8.5in]{geometry} \usepackage{soul} \begin{document} \thispagestyle{empty} \set... Windows 7 style Text Fields backgound text Hi is there a way to get a background text in entry fields (text presenters) in the entry area itself - that disappears when you start typing - i.e. Windows 7 style. (Is there any special name / buzzword for that feature ?) Regards Sanjay Sanjay, >is there a way to get a background text in entry fields (text >presenters) in the entry area itself - that disappears when you start >typing - i.e. Windows 7 style. If you don't mind the test being selected then this should work. Select all the following and evaluate in a workspace... sh := Shell show. sh v... Sorting Numbers in a Text Field One field in my database contains the dosage of medicines. It's a text field since I have to include the units. Here's a list of what might be in the field: 10 mg 20 mg 50 mg 100 mg When I sort I want them to appear as I listed them above. However, they appear as 10 mg 100 mg 20 mg 50 mg Any suggestions for solving this problem? Rich This question has been answered multi times before. You have entered the numbers in a text field so they are sorted on their ascii value and not on their numeric value. Put the numbers in a number field, leave the mg part out (since it is always mg... Updating A Text String In A Text Field With An Update Query If I have the following string in a text field of a table: "This is a test" can I create an update query that will change, say, the string "is" to "xyz" in the two locations where it occurs or would this require VBA? Thanks, Sheldon Potolsky Use an Update query. Something like this: UPDATE Table1 SET [F1] = Replace([F1], "is", "xyz") WHERE [F1] Like "*is*"; -- Allen Browne - Microsoft MVP. Perth, Western Australia Tips for Access users - http://allenbrowne.com/tips.html Reply to group, rather than allenbrowne at mvps ... Web resources about - text field only for text - no numbers - comp.databases.ms-access Number - Wikipedia, the free encyclopedia A number is a mathematical object used to count , label, and measure . In mathematics , the definition of number has been extended over the years ... Number - Wikipedia, the free encyclopedia A number is a mathematical object used to count , label, and measure . In mathematics , the definition of number has been extended over the years ... Queensland suburbs house the highest number of drug labs in Australia Dangerous backyard labs in Queensland pose dangers beyond drugs. Mathematicians stunned by 'unrandomness' discovery of prime numbers The infinite world of prime numbers just got a little more finite, after a pair of mathematicians discovered the prime number sequence isn't ... Mathematicians stunned by 'unrandomness' discovery of prime numbers The infinite world of prime numbers just got a little more finite, after a pair of mathematicians discovered the prime number sequence isn't ... Rooster amnesty declared to reduce Hobart's growing number of rogue fowl Hobart's chicken owners are asked to surrender unwanted roosters to a special amnesty at the city's showgrounds. Girlish Number TV Anime Casts Sayaka Senbongi, Kaede Hondo, Yui Ishikawa Series centering on on idol voice actresses to air on TBS, BS-TBS A huge number of short bets on Ocado went horribly wrong this morning Ocado stock popped up 7% this morning after the company reported stronger than expected sales. This is good news for the company, and good news ... International Student Numbers At U.S. Colleges Grew At The Fastest Rate In 35 Years Overseas enrollments are a lucrative source of tuition fees for U.S. colleges, and NYU is leading the charge to recruit more. Seoul: Number of North Korean cyberattacks doubled in month SEOUL, South Korea (AP) — South Korea's spy agency told lawmakers Friday that the number of North Korean cyberattacks on the South has doubled ... Resources last updated: 3/16/2016 1:10:07 AM

2019-05-23 20:52:14

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https://www.cheenta.com/pigeonhole-principle/

How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances? Pigeonhole Principle “The Pigeonhole principle” ~ Students who have never heard may think that it is a joke. The pigeonhole principle is one of the simplest but most useful ideas in mathematics. Let’s learn the Pigeonhole Principle with some applications. Pigeonhole Principle Definition: In Discrete Mathematics, the pigeonhole principle states that if we must put N + 1 or more pigeons into N Pigeon Holes, then some pigeonholes must contain two or more pigeons. Example: If Kn+ 1 (where k is a positive integer) pigeons are distributed among n holes than some hole contains at least k + 1 pigeons. Applications of Pigeonhole Principle: This principle is applicable in many fields like Number Theory, Probability, Algorithms, Geometry, etc. Problems and Solutions: Problem 1 A bag contains beads of two colours: black and white. What is the smallest number of beads which must be drawn from the bag, without looking so that among these beads, two are of the same colour? Solution: We can draw three beads from bags. If there were no more than one bead of each colour among these, then there would be no more than two beads altogether. This is obvious and contradicts the fact that we have chosen their beads. On the other hand, it is clear that choosing two beads is not enough. Here the beads play the role of pigeons, and the colours (black and white) play the role of pigeonhole. Problem 2 Find the minimum number of students in a class such that three of them are born in the same month? Solution: Number of month n =12 According to the given condition, K+1 = 3 K = 2 M = kn +1 = 2*12 + 1 = 25. Problem 3 Show that from any three integers, one can always choose two so that $a^3$b – a$b^3$ is divisible by 10. Solution: We can factories the term $a^3$b – a$b^3$ = ab(a + b)(a - b), which is always even, irrespective of the pair of integers we choose. If one of three integers from the above factors is in the form of 5k, which is a multiple of 5, then our result is proved. If none of the integers is a multiple of 5 then the chosen integers should be in the form of (5k)+-(1) and (5k)+-(2) respectively. Clearly, two of these three numbers in the above factors from the given expression should lie in one of the above two, which follows by the virtue of this principle. These two integers are the ones such that their sum and difference is always divisible by 5. Hence, our result is proved. Problem 4 If n is a positive integer not divisible by 2 or 5 then n has a multiple made up of 1's. Watch the solution:

2021-11-30 12:05:40

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https://tomasp.net/blog/tag/links/

TP # Learn F# at TechMesh and SkillsMetter Autumn is a busy period and I already invited you to a couple of interesting events, but there are two more events that you definitely should not miss. In only two weeks, you can come to two-day Progressive F# Tutorials packed with tutorials for both F# beginners and experts. At the beginning of December, the TechMesh Conference comes with three days of talks about alternative (and future) technologies. I'll be speaking at both Progressive F# Tutorials and TechMesh and I'm also doing a tutorial at TechMesh, so if you want to learn about F#, type providers in F# 3.0 and financial computing with F#, here are some talks that you should not miss... Published: Sunday, 21 October 2012, 4:53 PM # F# Courses and Talks for Autumn 2012 (I.) Similarly to the last year, I already have a number of F# events planned for the end of the summer and autumn that I'd like to invite you to! The Visual Studio 2012 has been completed recently and it comes with F# 3.0. For me, this means two things. Firstly, it is the second Visual Studio version of F#, which means that functional programming is worth taking seriously. Secondly, F# 3.0 comes with type providers, which is a killer feature for working with data. No matter if you're a C# programmer now to functional programming or if you're an F# user in the real-world, I hope you can find some interesting and useful event below! The two main things that I'm going to be involved in are SkilsMatter trainings in London and New York and a few events at the biggest functional conference (ICFP) in Copenhagen... Published: Wednesday, 8 August 2012, 3:47 AM # Asynchronous client/server in F# (QCon 2012) Last week, I gave a talk on asynchronous programming in F# at London QCon 2012. The talk was a part of The Rise of Scala & Functional Programming track organized by Charles Humble. Reactive and asynchronous programming was a topic that was repeated a couple of times during the whole session - Sadek Drobi talked about non-blocking reactive web framework Play2 and Damien Katz talked about Erlang and CouchDB. I used the one hour slot to implement "Rectangle Drawing App" - a simple application that shows how to write complete client-server application just using F#. On the server-side, I used asynchronous workflows to write HTTP server with an F# agent. On the client-side, I used asynchronous workflows to express user interface logic and the Pit project to run F# code as JavaScript that works everywhere. The app definitely had a huge commercial potential: Published: Monday, 12 March 2012, 1:09 AM Tags: presentations, functional, asynchronous, f#, links If you have been following my blog, you've probably already heard of joinads. It is a research extension of F# computation expressions (or monads in Haskell). The extension makes computation expressions more useful in domains like parallel, concurrent and reactive programming. However, it can be used for any type of computation including, for example, parsers. If you're interested in detailed description, you can find it in two academic papers that I blogged about previously: PADL 2011 and Haskell 2011. The extension adds a keyword match! - as the syntax suggests, it is akin to pattern matching using match, but instead of pattern matching on values, you can pattern match on computations like Async<'T> (or on other monadic values). Just like other features of computation expressions, the match! syntax is translated to applications of several methods defined by the computation builder. I won't say more about joinads in this post, because you can now easily try joinads yourself... Published: Monday, 13 February 2012, 4:21 PM # F# courses and talks (Autumn 2011) The end of the summer holiday season is getting closer. Luckily, I was in Prague last week so I actually noticed there was summer this year! After a few quiet months, the autumn is going to be quite busy. Microsoft's //build/ conference will reveal the future of software development for Windows, but great things are going on in the F# world too. Don Syme is going to talk about F# Information Rich Programming at Progressive F# Tutorials in November, which should reveal more about F# 3.0 and type providers! I have quite a few speaking engagements planned already, so if you want to learn about functional programming in .NET (and become a better C# programmer) or about F# and asynchronous programming, here are a few events that you may be interested in... Published: Friday, 26 August 2011, 3:04 AM # Real-World F# Articles on MSDN More than a year ago, Mike Stephens from Manning (who was also behind my Real-World Functional Programming book) asked me if I'd be interested in collaborating on a project for MSDN. The idea was to collaborate with Microsoft on creating some additional content for the official F# Documentation. A few days ago, the new content appeared on MSDN, so I finally have an excuse for the recent lack of blogging! Although the content contains a large number of new articles that are not based on my book, you can find it in the MSDN section named after my book, right under Visual F#. If you can't wait to check it out, here are all the links: While working on the articles, I also wrote about a few topics that we didn't use in the final version. You'll see them on my blog in the next few days, as soon as I edit them into a blog post form. Continue reading for more information about individual chapters. Published: Wednesday, 10 August 2011, 4:38 AM Tags: functional, web, asynchronous, parallel, links, f#, c# # MonoDevelop & Teaching F# & QCon tutorial Point of sale application from QCon tutorial It appears that I have been doing a lot more talking than writing in the last two months. I'm hoping to change this direction and I have two articles almost ready, so stay tuned! I was also posting all my interesting F# snippets to fssnip.net, which has grown quite a bit since I announced it in the last blog post. Thanks to everybody who submitted their snippets already and I'm looking forward to more! By the way, you can now run snippets using tryfs.net by clicking at "Load in TryF#" button. In the meantime, the queue with talk materials that I wanted to post on my blog has grown to 3. I talked about F# in MonoDevelop in the Mono room at FOSDEM in February, then I did an online talk for the Community for F# . Finally, this week, I did a tutorial on F# with Phil Trelford at QCon in London (to fill in for Michael Stal due to unexpected health reasons). Before I move on to writing about my recent experiments with LINQ, you can find materials from all of the recent talks below... Published: Wednesday, 9 March 2011, 4:01 PM # Announcing F# snippets web site When writing F# programs, I often write some nice code snippet or some useful helper function that I'd like to share with the F# community. Unfortunately, my blog posts are usually longer and more elaborate, so I never get to blogging about it. Now that I have a twitter (follow me if you don't already) I thought I could just post the snippet somewhere, but there was no good web site for posting F# snippets - until now! • If you can't wait any further, then go directly to the new F# snippets web site at fssnip.net. The web site uses my earlier project F# Web Snippets to format F# source code. It highlights colors and adds JavaScript tooltips using services provided by the F# compiler, which means that you'll get almost the same experience as when reading code in Visual Studio. I also wanted to make the page a repository of browsable snippets, so you can use it in two ways... Published: Sunday, 12 December 2010, 2:19 AM # F# in Education & Concurrency with Agents November was quite a busy month for me. First, I traveled to Cambridge (the "new one" in Massachusetts :-)) to present my work on the F# plugin for MonoDevelop at the F# in Education workshop. Shortly after getting back to London, I started working on a presentation about Concurrent Programming with Agents at the F#unctional Londoners meeting. Now that both of the events are over, I'd like to write a short summary and also finally publish my slides and demos. In addition, both of the events were recorded (thanks to External Research group at MSR and SkillsMatter), so if you missed them, you can watch the recording... Both of the events were really great and I had a chance to meet quite a few interesting people. One of the things that make F# great is the community around it. I think that one unique aspect of the F# community is its diversity. The same language is appealing to high school teachers, academics and researchers as well as software developers and technical directors from the industry. This combination is really valuable for both sides. It helps to transfer ideas from research to practice it gives researchers clear picture of problems in the industry that deserve their attention. Published: Tuesday, 30 November 2010, 7:18 PM # Reactive, parallel and concurrent programming in F# (PADL 2011) Don Syme blogged about a paper on the F# Asynchrounous Programming Model that I helped to write. Without any doubt, the asynchronous programming features of F# are one of the reason for its success and also influence other teams in Microsoft. However, I'm very glad that there is now also an academic paper that makes this idea accessible to the academic community. I believe that the ideas could evolve in interesting ways when used in other programming languages and also, it is now easier to create research projects that build on top of the F# model. Don already mentioned that we have another paper accepted at PADL. The paper describes work that started during my internship at Microsoft Research in 2009. It presents a simple language extension for computation expressions that makes them even more useful in some reactive, concurrent and parallel programming models. Note that this is only a research project and there are currently no plans to support the extension in the F# language (although, if there will, eventually, be an open-source F# release, then you'll hear about the extension again...) ### Joinads: A retargetable control-flow construct for reactive, parallel and concurrent programming Modern challenges led to a design of a wide range of programming models for reactive, parallel and concurrent programming, but these are often difficult to encode in general purpose languages. We present an abstract type of computations called joinads together with a syntactic language extension that aims to make it easier to use joinads in modern functional languages. Our extension generalizes pattern matching to work on abstract computations. It keeps a familiar syntax and semantics of pattern matching making it easy to reason about code, even in a non-standard programming model. We demonstrate our extension using three important programming models – a reactive model based on events; a concurrent model based on join calculus and a parallel model using futures. All three models are implemented as libraries that benefit from our syntactic extension. This makes them easier to use and also opens space for exploring new useful programming models. The paper can still be revised before the final publication, so any comments and suggestions for improvement are largely welcome. You can contact me either via comments (below) or using email at tomas@tomasp.net. I would be also quite interested to hear from anybody who would like to implement similar feature in other programming languages (for example Haskell or Scala). Published: Monday, 25 October 2010, 12:00 AM # Recording and samples from my Reactive F# talk Almost a week ago, I posted an invitation to my F# talk at the F#unctional Londoners user group. The theme of my talk was reactive programming, which was also a topic of my Master's thesis (defended earlier in June), so I really enjoyed talking about it. In the talk, I discussed the two approaches that you can use for developing reactive applications in F# (using examples in Silverlight): • Declarative (or data-flow oriented) allows you to describe "what" should be done with data that your component receives from various events (such as mouse position etc.) This can be written using F# event combinators such as Event.map and Event.scan. • Imperative (or control-flow oriented) - in this style, we describe various states of the component (e.g. semaphore with green, orange and red) and describe transitions between the states. This can be written using F# asynchronous workflows and the AwaitObservable primitive (which you can get as part of the source code). Thanks to the folks from SkillsMatter who provided place for the meetup and helped with the organization, the talk was also recorded and is already available online! Below, you can also get all the nice Silverlight demos that I used during the talk... Thanks again to Carolyn Miller and Phil Trelford for organizing the talk and also to Don Syme for taking me to the airport in the early morning (at 4 AM...) after the talk. Published: Sunday, 27 June 2010, 2:49 PM Tags: universe, presentations, functional, f#, links # Calculating with infinite sequences on MSDN About a year ago, I wrote an article about using lazy computations in C# 3.0. It was published by the C# Community PM Charlie Calvert at the C# Developer Center. The article was a first of two articles where I wanted to demonstrate that C# 3.0 can be used for implementing useful constructs known from functional languages. I realized that I never posted the link to the second article to my blog, so you can find the annotation and link below. However, I remembered about these two articles because I was just working on chapters 11 and 12 of the Real-world Functional Programming in .NET book that I’m writing. Lazy values, which were the topic of my first article, are discussed in the second part of chapter 11 and IEnumerable and F# sequences are the topic for the first part of chapter 12. Because I already wrote two articles on this topic, I had to think really hard to find better (and still simple enough) examples where these concepts are useful in practice. I also finally have enough space to show how these two concepts relate and talk about some interesting background – for example in Haskell, lazy sequences are in fact just ordinary lists that are lazy thanks to the Haskell nature. A year ago, I definitely wouldn’t believe that today, I’ll be writing about the same topics, but this time as part of a book that has partly the same goal as these two articles – to show that functional programming ideas are really useful in the real-world and can enrich your programming toolbox (no matter whether you’re using C# or F# language). Anyway, here is the link to the second article – as usual when I look at something that I worked on a long time ago, I think I should rewrite it to make it better :-), but it still gives you an idea what is the book that I’m working on about... Published: Thursday, 13 November 2008, 2:36 AM Tags: c#, functional, universe, writing, links # Thesis: Client-side Scripting using Meta-programming I realized that I haven’t yet posted a link to my Bachelor Thesis, which I partially worked on during my visit in Microsoft Research and which I successfully defended last year. The thesis is about a client/server web framework for F# called F# WebTools, which I already mentioned here and its abstract is following: “Ajax” programming is becoming a de-facto standard for certain types of web applications, but unfortunately developing this kind of application is a difficult task. Developers have to deal with problems like a language impedance mismatch, limited execution runtime in web browser on the client-side and no integration between client and server-side parts that are developed as a two independent applications, but typically form a single and homogenous application. In this work we present the first project that deals with all three mentioned problems but which still integrates with existing web technologies such as ASP.NET on the server and JavaScript on the client. We use the F# language for writing both client and server-side part of the web application, which makes it possible to develop client-side code in a type-safe programming language using a subset of the F# library, and we provide a way to write both server-side and client-side code as a part of single homogeneous type defining the web page logic. The code is executed heterogeneously, part as JavaScript on the client, and part as native code on the server. Finally we use monadic syntax for the separation of client and server-side code, tracking this separation through the F# type system. The full text is available here: Client side scripting using meta-programming (PDF, 1.31MB) Published: Monday, 17 March 2008, 10:07 AM Tags: random thoughts, universe, web, links # Phalanger at Lang.NET Symposium Last week I attended the Lang.NET Symposium and I also did a short presentation about Phalanger (below you can find the demos and slides from my talk). By the way – during the trip from Prague to Seattle I missed a connecting flight from Paris, so I had one day to visit Paris and since I was traveling on Saturday I actually quite enjoyed it :-), so that’s where the picture comes from. Overall it was really a fantastic event with many great talks from many interesting people. I hope that there will be recordings as a last year, so I won’t comment every topic that I found interesting (that would be really a long post). But just quickly – people from Microsoft often talked about DLR (dynamic language runtime) related topics, which was interesting as we’re planning to look at DLR in Phalanger. Luckily, Wez Furlong from the PHP community was there too, so we discussed how we could work on “PHP on DLR” project together (see also our mailing list). There were also two talks about F# (from Luke Hoban and Harry Pierson), and it was a lot of fun to hang out with them. Finally, Erik Meijer presented the Volta project, which I was particularly interested in as it shares many goals and ideas with my F# Web Tools. Non-Microsoft talks covered wider range of topics including Mono and Moonlight project (by Miguel de Icaza) and I actually had a chance to talk with Miguel about Phalanger and we even tried running the Helicopter sample on Moonlight – there were some issues, but it seems quite promising, so I hope to have the sample running on Moonlight on Linux quite soon! Miguel mentioned that the installation of Moonlight is currently a bit painful (due to some issues with media codecs), but it should be fixed in next few weeks, so I hope to be able to try it on my machine too! Published: Saturday, 2 February 2008, 11:51 AM # Lazy Computation in C# on MSDN I think that one of the interesting things about C# 3.0 is that it gives you the ability to use many techniques known from functional languages (like Haskell or F#). Most of the articles about C# 3.0 and LINQ focus on the queries and LINQ to SQL, but I believe that using these functional techniques deserve some attention as well. This is why I'm very happy that my article about one of these techniques - representing lazy computations - is now available at the C# Developer Center. I would like to thank to Charlie Calvert [^], who is the Community Program Manager for C# and who edited and published my article there. Here is the annotation: Most of the programming languages used in practice (including for example C#, VB.NET, C++, Python or Java) employ so called eager evaluation, which means that the program evaluates all expression and statements in the order in which they are written, so all the preceding statements and expressions are evaluated before executing the next piece of code. This, for example, means that all arguments to a method call are evaluated before calling the method. Sometimes it may be useful to delay an execution of some code until the result is actually needed, either because the result may not be needed at all (but we can’t tell that before executing some computation) or because we don’t want to block the program for a long time by executing all computations in advance and instead we want to execute the computations later, when we will actually need the result. In this article we will look how these lazy computations can be written in C# (using some of the new language features from version 3.0). We will first implement a Lazy class to represent this kind of computation, then look at a few simple examples to demonstrate how the class can be used, and finally we will examine one slightly more complicated, but practically useful application. You can read the complete article here: Lazy Computation in C# [^] Published: Saturday, 6 October 2007, 1:29 AM

2023-03-28 15:49:49

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http://tex.stackexchange.com/questions/89986/what-is-the-easiest-way-to-see-default-spaces-with-respect-to-ex-and-em-in

# What is the easiest way to see default “spaces” with respect to “ex” and “em” in the book class? What is the easiest way to see default "spaces" with respect to "ex" and "em" in the book class? I mean by spaces all horizontal and vertical spaces such as: 1. the space before and after the section headings in the text 2. the space between the captions and the text after it 3. the space between the header and the main text 4. the space between the figures and their caption 5. the space between the footnotes at the bottom of the pages and so on. I'm using xelatex and TeX Live 2012 on Win7. - See, for instance, page 132 of lshort. In your command line, type texdoc lshort –  hpesoj626 Jan 9 '13 at 10:45 @hpesoj626 I want the default values, not the customized values of the lshort. Also, I want a complete list. –  Sisabe Jan 9 '13 at 10:49 @Sisabe lshort documents LaTeX2e, which is the version of LaTeX in use. Therefore you find there the default values documented. –  tohecz Jan 9 '13 at 11:00 @tohecz I want the values as a list. –  Sisabe Jan 9 '13 at 11:02 @Sisabe There is no such list of all distances. List all of them you are interested in and we will provide a code to show them. –  tohecz Jan 9 '13 at 11:04 This answer makes use of Philippe Goutet's \convertto macro in What are the various units (ex, in, pt, etc.) expressed in mm?. ## Code %http://tex.stackexchange.com/questions/89986/what-is-the-easiest-way-to-see-default-spaces-with-respect-to-ex-and-em-in#89986 \documentclass{book} \usepackage{array} \makeatletter \def\convertto#1#2{\strip@pt\dimexpr #2*65536/\number\dimexpr 1#1} \makeatother \begin{document} \begin{tabular} {>{\def\colunit{pt}}l >{\convertto{pt}{\rowlength}}l >{\def\colunit{em}}l<{\convertto{em}{\rowlength}}l <{\convertto{ex}{\rowlength}}} \multicolumn{1}{l}{} & \multicolumn{1}{l}{\textbf{pt}} & \multicolumn{1}{l}{\textbf{em}} & \multicolumn{1}{l}{\textbf{ex}}\\ \gdef\rowlength{\lineskip} \verb!\lineskip! & & & \\ \gdef\rowlength{\baselineskip} \verb!\baselineskip! & & & \\ \gdef\rowlength{\belowcaptionskip} \verb!\belowcaptionskip! & & & \\ \gdef\rowlength{\abovedisplayskip} \verb!\abovedisplayskip! & & & \\ \gdef\rowlength{\belowdisplayskip} \verb!\belowdisplayskip! & & & \\ \gdef\rowlength{\abovedisplayskip} \verb!\abovedisplayskip! & & & \\ \gdef\rowlength{\abovedisplayshortskip} \verb!\abovedisplayshortskip! & & & \\ \gdef\rowlength{\belowdisplayshortskip} \verb!\belowdisplayshortskip! & & & \\ \gdef\rowlength{\parskip} \verb!\parskip! & & & \\ \gdef\rowlength{\textfloatsep} \verb!\textfloatsep! & & & \\ \gdef\rowlength{\intextsep} \verb!\intextsep! & & & \\ \gdef\rowlength{\floatsep} \verb!\floatsep! & & & \\ \gdef\rowlength{\textheight} \verb!\textheight! & & & \\ \gdef\rowlength{\textwidth} \verb!\textwidth! & & & \\ \gdef\rowlength{\parindent} \verb!\parindent! & & & \\ \gdef\rowlength{\oddsidemargin} \verb!\oddsidemargin! & & & \\ \gdef\rowlength{\evensidemargin} \verb!\evensidemargin! & & & \\ \gdef\rowlength{\marginparsep} \verb!\marginparsep! & & & \\ \gdef\rowlength{\topmargin} \verb!\topmargin! & & & \\ \gdef\rowlength{\marginparwidth} \verb!\marginparwidth! & & & \\ \gdef\rowlength{\marginparpush} \verb!\marginparpush! & & & \\ \end{tabular} \end{document} - belowdisplayskip comes twice instead of belowdisplayshortskip. –  devendra Jan 9 '13 at 13:14 @devendra thanks. Edited. :) –  hpesoj626 Jan 9 '13 at 13:20 For the page layout ones, use the package \usepackage{layout} and add the command \layout into the document body: \documentclass{article} \usepackage{layout} \begin{document} \layout \end{document} The others can be displayed as well, but a list of those you want is necessary. - The following code uses printlen package and I typically use it to see all the parameters of interest to me. Modify the code for other parameters. Use uselengthunit to change the unit you are interested in. Unfortunately, printlen doesn't provide lengths in em and ex. However, you could convert pt to ex and em for a given fontsize. \documentclass{report} \usepackage{printlen} % \begin{document} {\Large \textsc{Vertical}}\\ \uselengthunit{pt} \verb|\lineskip|~~\the\lineskip\\ \verb|\baselineskip|~~\the\baselineskip\\ \verb|\baselinestretch|~~\baselinestretch\\ \verb|\abovecaptionskip|~~\printlength{\abovecaptionskip}\\ \verb|\belowcaptionskip|~~\printlength{\belowcaptionskip}\\ \verb|\abovedisplayskip|~~\printlength{\abovedisplayskip}\\ \verb|\belowdisplayskip|~~\printlength{\belowdisplayskip}\\ \verb|\abovedisplayshortskip|~~\printlength{\abovedisplayshortskip}\\ \verb|\belowdisplayshortskip|~~\printlength{\belowdisplayshortskip}\\ \verb|\parskip|~~\printlength{\parskip}\\ \verb|\textfloatsep|~~\printlength{\textfloatsep}\\ \verb|\intextsep|~~\printlength{\intextsep}\\ \verb|\floatsep|~~\printlength{\floatsep}\\ \verb|\textheight|~~\printlength{\textheight}\\ %\verb|\textwidth|~~\printlength{\textwidth}\\ \vspace{15pt} {\Large \textsc{Horizontal}}\\ \verb|\textwidth|~~\printlength{\textwidth}\\ \verb|\parindent|~~\printlength{\parindent}\\ %\verb|\textwidth|~~\printlength{\textwidth}\\ \vspace{15pt} {\Large \textsc{Misc.}}\\ \verb|\textfraction|~~\textfraction\\ \verb|\topfraction|~~\topfraction\\ \verb|\floatpagefraction|~~\floatpagefraction\\ \verb|\clubpenalty|~~\printlength{\clubpenalty}\\ \verb|\widowpenalty|~~\printlength{\widowpenalty}\\ \verb|\displaywidowpenalty|~~\printlength{\displaywidowpenalty}\\ \verb|\tolerance|~~\printlength{\tolerance}\\ \verb|\pretolerance|~~\printlength{\pretolerance}\\ \verb|\emergencystretch|~~\printlength{\emergencystretch}\\ %\verb|\textwidth|~~\textwidth\\ \end{document} - 1- Are these values dependent on the font size of the text? 2- Why the \belowcaptionskip is zero? It's not zero, it's about 1.5 cm. –  Sisabe Jan 9 '13 at 11:30 Some values like baselineskip etc. are font dependent while others like textfraction are not. Space between caption and the text below includes among other things textfloatsep. So thats why you are seeing space below caption. –  devendra Jan 9 '13 at 11:38 @Sisabe \belowcaptionskip is zero. It is \textfloatsep and \floatsep adding the space. –  tohecz Jan 9 '13 at 12:12 @devendra Is there a way to know which one is font dependent and which one is not? –  Sisabe Jan 9 '13 at 12:15 @devendra -- while baselineskip is generally dependent on font size, it is usually not dependent on the x-height (ex). some fonts have relatively large x-height (e.g. lucida), while others (e.g. bembo) have a smaller x-height for the same nominal font size. on the other hand, textwidth should sometimes be dependent on font size; if you've ever tried to read legal "boilerplate" you will understand why -- having very small print in very long lines is a disincentive to read the content. (experience does count.) –  barbara beeton Jan 9 '13 at 14:14

2014-09-03 04:51:23

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http://clay6.com/qa/74965/a-circular-coil-expands-radially-in-a-region-of-magnetic-field-and-no-elect

Comment Share Q) A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. The can be cause (a) The magnetic field is constant (b) The magnetic field is in the same plane as the circular coil and it may or may not vary (c) The magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. (d) There is constant magnetic field in the perpendicular (to the plane of the coil) direction When a circular coil expands radially in a region of magnetic field, induced $emf$ developed is \begin{align*}\; \; \; \; \; \; e& =Blv \\ & = B \times rate\; of\; charge\; of\; area \end{align*} It is given that the magnetic field B is in a plane perpendicular to the plane of the circular coil. Since e=0, magnetic field should be in the plane of circular coil so that its component which perpendicular to plane of coil is zero. If the magnetic of the magnetic field decrease with the magnetic flux linked with the coil, then $e = \frac{d \phi}{dt}$= 0

2019-12-12 11:35:01

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https://standards.globalspec.com/std/10277543/jis-construction-i-hdbk

JSA - JIS CONSTRUCTION I HDBK JIS Machine Construction I Handbook active, Most Current Organization: JSA Publication Date: 1 January 2018 Status: active Document History JIS CONSTRUCTION I HDBK January 1, 2018 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2017 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2016 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2015 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2013 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2013 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2012 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2011 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2010 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2009 JIS CONSTRUCTION I HANDBOOK A description is not available for this item.

2019-04-22 22:46:23

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http://openstudy.com/updates/5611c5b0e4b0af5cf2f0352b

## anonymous one year ago Given a 13-card bridge hand has been dealt from a standard deck of 52 cards, what is the probability of having a) exactly 6 hearts? b) exactly 7 hearts, three diamonds, two clubs, and one spade? 1. anonymous exactly 6 hearts means 6 hearts and 7 other stuff do you know how many hearts are in the deck? 2. anonymous 13 3. anonymous ok so 13 hearts to choose 6 from and 39 other stuff to choose 7 from 4. anonymous $\huge \frac{\binom{13}{6}\binom{39}{7}}{\binom{52}{13}}$ s the quick answer 5. anonymous so is it 0.042%? 6. anonymous how would be work?

2017-01-24 21:57:37

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https://www.gamedev.net/forums/topic/335770-vertex-fvf-classes-static-members/

# Vertex FVF classes... static members? This topic is 4582 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Ok, if I create a series of classes for my vertex data, like Simplevertex, VertexTextureColorNormal etc, would I be able to place a static variable in the class with the value for the FVF? struct SimpleVertex { static long FVF = fvf values; float x,y,z; float nx,ny,nz; float r,g,b,a; }; or does that screw up the data during buffering? It would be really nice to just use SimpleVertex::FVF where I needed the FVF for the class. ##### Share on other sites You will be OK doing that. I would stick to the SDK data type for an FVF though, which is DWORD (AFAIK unsigned long). ***edit*** The static FVF is OK but the rest of your vertex structure looks wrong. float x, y, z is ok for the vertex position. float nx, ny, nz is ok for the normal. not sure about the color data though (r,g, b, a) as floats. I think the color data type should be D3DCOLOR (DWORD) Also I think the ordering of the (non static) structure members should be different. Try this: struct SimpleVertex { float x, y, z; // position D3DCOLOR diffuse; // diffuse color float nx, ny, nz; // normal static DWORD FVF; }; DWORD SimpleVertex::FVF = D3DFVF_XYZ|D3DFVF_DIFFUSE|D3DFVF_NORMAL; Also you can set the r, g, b, a values for the color using the D3DCOLOR_RGBA macro: v.diffuse = D3DCOLOR_RGBA(r,g,b,a); r, g, b,a values here should be between 0 and 255. HTH, Cambo_frog [Edited by - Cambo_frog on July 30, 2005 3:07:53 PM] ##### Share on other sites The note on diffuse is correct - it's a DWORD, too. However, normals do come before diffuse when using FVF buffers. ##### Share on other sites I wasn't so much concerned with the datatypes, because I still have to look those up for every vertex definition. But thanks anyways!

2018-02-21 23:18:18

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http://mathoverflow.net/questions/77206/mathematical-programming-with-other-algebras-than-linear

# Mathematical Programming with other Algebras than Linear Linear Programming is strongly entwined with linear algebra, as are many of its generalizations under the heading of mathematical programming / convex optimization. What analogies are there for convex optimization techniques outside of vector spaces dealt with in linear algebra. For example, Gaussian Elimination is generalized by Buchberger's algorithm for finding Groebner bases (or so I'm told); is there any algorithm that has a relationship with Buchberger's analogous to the Simplex Method's relationship with Gaussian Elimination? - did you already check out: math.berkeley.edu/~philipp/CAG-seminar.html –  Suvrit Oct 5 '11 at 9:20

2015-04-02 01:53:08

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https://tex.stackexchange.com/questions/558712/bold-small-caps-with-lualatex/558715

# Bold small caps with Lualatex Referring to this tread: How to use fontspec and also have small bold caps with LuaLaTeX?, I've a font with real small caps, but the same problem too. Please, compile this simple code: \documentclass{article} \usepackage{fontspec} \usepackage[italian]{babel} \babelfont[italian]{rm}{EB Garamond} % \setmainfont{EB Garamond} \begin{document} Quel \textbf{ramo del \textsc{lago} di Como}, che volge a \textbf{\textsc{mezzogiorno}} \end{document} So, the solution is not You need to choose a font family that has bold small caps for it has... Is it so hard to have bold small caps? It works adding \setmainfont{EB Garamond}, but I think it's not a good idea to make a xelatex and lualatex fruit salad ... Thank you • “The solution is not: You need to choose a font family that has bold small caps” Yes it is (-1). What kind of answer did you expect? – Henri Menke Aug 15 '20 at 8:06 • Does this answer your question? Missing bold and italic font in XeLaTeX – Henri Menke Aug 15 '20 at 8:07 • What does it mean to "make a xelatex and lualatex fruit salad"? Is something holding you back from using LuaLaTeX? – Mico Aug 15 '20 at 8:19 • My font family has bold small caps (and EB Garamond in my MWE too), but I don't obtain them with the above code. I don't need fake bold! Moreover, I'm using Lualatex, and - if I'm not wrong- there is no \setmainfont for Lualatex (but for Xelatex). But if I don't add \setmainfontI don't obtain the bold sc, so I'm looking for a "pure" Lualatex solution – user41063 Aug 15 '20 at 9:47 \setmainfont is not a command meant only for xelatex. It is a command from fontspec for both engines. babel has its own command to set fonts (which also can be used with both engines). In your case the optional argument [italian] disables the small caps because of two reasons: At first with the optional argument babel doesn't directly load the font but only prepares it for the language. And at second because babel doesn't set like fontspec the default bold series to b which it should imho do so I will report it. As the series is bx it triggers a substituation and so you loose small caps (which perhaps shouldn't happen too ...). I suggest to remove the language, it doesn't make much sense as the font doesn't know it anyway, and to add a series declarations (this requires a current latex) for now. \documentclass{article} \usepackage{fontspec} \DeclareFontSeriesDefault[rm]{bf}{b} \usepackage[italian]{babel} \babelfont{rm}{EB Garamond} \begin{document} Quel \textbf{ramo del \textsc{lago} di Como}, che volge a \textbf{\textsc{mezzogiorno}} \end{document} • ah ok, now I understand better the meaning of \setmainfont. Only, sometimes I have to add a language for I use more (Italian, Greek...). Now I'll try your solution, thank you – user41063 Aug 15 '20 at 9:52 • I managed to isolate the bug (which was far from trivial), and it will get fixed in the next release. – Javier Bezos Aug 26 '20 at 10:30 • @JavierBezos but actually I think that my remark that babel should use b is not accurate -- the series to use is far from trivial (that's why I didn't report it at the end). – Ulrike Fischer Aug 26 '20 at 10:33 • @UlrikeFischer Actually, babel is agnostic about the default series. It sets nothing (afaik) and just loads fontspec and defines the family. But there are some problems in the way languages are selected when the document starts, which, to be honest, I don't fully understand yet. I thought I'd found a solution, but it doesn't work with \nofiles 😖. – Javier Bezos Aug 26 '20 at 11:07

2021-08-03 04:12:11

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http://n-dim.de/tutorial/webscraping-with-rvest.html

Hydrologists use isotope signatures of precipitation water as a tracer to follow water flow pathways in the ground and in rivers. The International Atomic Energy Ageny (IAEA) has setup a Global Network of Isotopes in Precipitation (GNIP). We will have a look into this data set in this tutorial series about working with isotope data. First thing we have to do is to download the data from their website. Of course we want to autotmate this! We will use a webscraping package called rvest to get this done. Goals: • download all the .csv files Challenges: • master the login page form • implement file download which is not explicitly implemented in the rvest package • do everything in a tidy dataframe In this post we will give you a short theoretical background as a motivation about why we want to work with this data. Then we will show you how to download the data with rvest step by step. In follow-up tutorials linked to this tutorial we will show you: • how to derive the Local Meteoric Water Line (LMWL) for all stations with linear regression • how to show the variation of parameters on an interactive map • make correllations between the isotope signatures and parameters like longitude, latitude, elevation and climatic variables # Theoretical Background Water containts not only the usual $H$ and $O$ atoms. It contains also small amounts of the slightly heavier isotopes $^2H$ and $^{18}O$. Isotopes are atoms containing one or multiple additional neutrons in the core than the more abundant variety of the atom. Because of their slightly heavier mass (compare table below), they behave different from the abundant $H$ and $O$ isotopes. This shows mainly when the water evaporates or condensates: The heavier isotopes are slightly less likely to evaporate and a bit more likely to condensate before the lighter isotopes. Hence water that stems from evaporation (like clouds generally do) are depleted in the heavy isotopes (compared to the water remaining in the ocean). When clouds rain off, the water remaining in the cloud get’s even more depleted of the heavy isotopes, since these condensate and rain down first. isotope name neutrons natural abundance* molecular weight stability $^1H$ Protium 0 $99.988\, \%$ $1.0078\, u$ stable $^2H$ Deuterium 1 $0.012\, \%$ $2.0141\, u$ stable $^3H$ Tritium 2 $10^{−15}\, \%$ $3.0160\, u$ decays $^{16}O$   8 $99.76\,\%$ $15.994\, u$ stable $^{17}O$   9 $0.04\,\%$ $16.999\, u$ stable $^{18}O$   10 $0.20\,\%$ $17.999\, u$ stable * abundance varies slightly in different water bodies (ocean, groundwater, river, cloud) Due to this fractionation of the isotopes researchers can measure a difference in the isotope “fingerprint” of rainwater and water on the ground. The atmospheric fingerprint varies a lot, depending on the temperature and humidity conditions when the vater evaporated and during the time it traveled through the atmosphere. Water on the ground is a more stable mix of isotopes. Therefore every rain event brings in a new pulse of water with different isotope signature. Hence the $H$ and $O$ isotopes can be utilized as a natural tracer to visualize the flow pathways the water takes after raining down to the ground. Following the water with the isotope signature of the last rainfall shows reasearchers where the precipitation water ended up. Measuring a mixed signature between the ground water and the precipitation water means that the former stored water and the fresh water have mixed. Since isotopes don’t chemically react, decay or get bound, they are also a very useful tracer. In the end they still are water and behave like water in most ways. The International Atomic Energy Ageny (IAEA) has setup a Global Network of Isotopes in Precipitation (GNIP). They maintain a database where measurements from different institutions from all over the world are gathered together and made available for everyone to use. The database access system is called WISER (Water Isotope System for Data Analysis, Visualization, and Electronic Retrieval). You have to register at websso.iaea.org, but then it is free to use for everyone (they just ask for your name, thats it). They also provide a similar database for isotopes signatures in rivers, the Global Network of Isotopes in Rivers (GNIR). # How is the server set up? Generally the database can be accessed with the follwoing link: https://nucleus.iaea.org/wiser/gnip.php?ll_latlon=&ur_latlon=&country=&wmo_region=&date_start=1953&date_end=2016&iso_o18=on&iso_h2=on&result_start=0&result_end=1000&action=Search This page is only accessable for registered users, hence if you are not logged in you get redirected to the login page. If you haven’t done this register to create an account. If you visit the page and fiddle around with the form to select the region, the isotopes and other options, you can see how the url changes with these options. It is the usual syntax of the http request-response protocol GET: You have • country= for selecting the country (for example country=Germany) • wmo_region= which you can give a number (like wmo_region=6 for the european wmo region) • with date_start= and date_end= you can define the date range. Just give it a year • iso_018=on, iso_h2=on and iso_h3=on define which isotopes have to have been measured at the stations you want to select • result_start=0 and result_end=1000 define how many enries are shown on one page. You have the option to set result_end to 10, 20, 30 and 1000 (The 1000 corresponds to the “All” button on the page). Setting it to 1000 comes handy to download all available files (although if you select the whole world you end up with even more than a thousand stations). What we are looking for are the $^{18}O$ and $^2H$ isotopes. So we set iso_018=on&iso_h2=on and leave iso_h3 out. We aks for stations of the whole world by setting wmo_region= and leaving it without any number. Add the end we have to add action=Search to initiate the search for stations. The url above is already setup with these options. # What is rvest? rvest is a package for webscraping—extracting content from web pages. It is not only about downloading files from the internet, but crawling through web pages, finding certain links inside the page and follow them to the next page and so on. You can select elements of the page by their DOM (their html structure), their id or class selectors. Then you can not only extract the text of the page, but also the html attributes like the href= of a link or the src= of an image (which contain the url of the link and the image respectively). Let’s go ahead and install rvest: After installing we have to laod it: To be able to access the data or even display the station list, we have to be logged in. After loggin in we have to maintain this login information when going to different pages. In rvest this is done by establishing a session and passing the session info to the next commands. If you try to surf to the above mentioned link without beeing logged in you find yourself beeing redirected to another page with the following url: With rvest we will establish a session with the link to the login page: We then have to fill in the login form. First we extract the form: Let’s have a look: You see one input field for 'User' and one for 'PASSWORD'. We then fill these out: Of course you first have to store a variable with username and the password: Next we do something we learned from this stackoverflow answer to prevent an (cryptic) error when submitting the form: Now we are ready to submit the form: We save a new session with the return of the form submission. The return is a redirect to the original page (the page with the station list). We now are logged in with a cookie stored in our session and are redirected to the page we originally intended to view. # Extract station list With the session stored under nucl2 we now can extract the data from the table displayed on the page. We use [[3]] to extract the third table. # Convert to tidy data.frame We want to work with a tidy data.frame (also called tibble). A data.frame stores observations (the rows) in variables (the colums). Each column can have a different data type (like integer, character, logical, etc.). Have a look at help(typeof) to learn more about object types. What the rows of a column are not allowed to contain is other object classes like list or matrix. Consult help(class) to learn the difference between an object class and the object type. Therefore traditionally everyone tended to introduce a new variable (for example data <- list()) to store data that don’t fit into the data.frame. The problem is, there is no direct link between the data.frame (let’s say it is called stations) and the data stored in the list called data. If we change one of the objects (for example we drop some rows of the data.frame), the other object doesn’t change. So later on we cannot link the rows of the table to the elements of the list. With a tibble we can store all the data we will later download in a column of the station list. This way we maintain a constant link between the data and the station list. Let’s convert the station data.frame to a tibble. The package tibble is automatically loaded when loading the package dplyr (which contains additional useful functions like mutate for working with tidy data). Convert the station list: If we display the tibble you see the difference to a data.frame: With the mutate() function we can introduce new columns. Here we replace the column WMO Code: With this we add back the leading 0s of the WMO Code that where stripped in the table read process. We now extract all links from the page: With the part css="a" we extract all html <a></a> elements (the syntax for inserting links into html pages). The following shows the links in one row of the station list: Of course we only want the links referencing a csv file. All csv links have “csv “ in the link text. So we make a list about which fo the links contain the keyword “csv”: Now we extract the href attribute of all links linking a csv file (note how we use is_csv_link here): The extracted links we add into the station list with mutate: For the download we need a destination file name for every csv file. We will use the station WMO code for this: We now are ready to download the data. We use a loop over all the csv_links. Because we can’t pass the session info to download.file() we will use a different approach to download the files: With the command jump_to() we maintain the session while following the links. We then write the content of the loaded link to a file with writeBin() (the idea came from this stackoverflow answer). We set Sys.sleep(1) to prevent sending too many request in short time to the server. Some servers deny service when we send requests in sequence too fast. Finally we want to add the station data to our tidy data.frame. For reading we use the package readr, which reads csv files a lot faster and reads it directly into a tibble. Advantage of the latter is for example, that column names get preserved in the format they have in the csv file. We also need the function map of the purr package. map is an apply function that can be executed on the elements of a vector. Install these packages with install.packages("readr") and install.packages("purrr"). To check what we have done just now we display the data for the first station: Finally have a look with what a “tidy dataframe” we ended up with: # The short version Using the pipe operator %>% very often you can get rid of a lot of the temporary variables and compact the code quite a lot:

2019-01-19 17:17:00

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https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-8-rational-functions-8-1-model-inverse-and-joint-variation-8-1-exercises-problem-solving-page-556/40a

## Algebra 2 (1st Edition) $f=64.3249482 \dfrac{\sqrt T}{Ld}$ General equation for inverse variation is given by $y=\dfrac{k}{x}$ Here, we have $f=k \dfrac{\sqrt T}{Ld}$ ...(1) Plug the data, we have $262=k \dfrac{\sqrt {670}}{(62)(0.1025)}$ and $K \approx 64.3249482$ Thus, the equation (1) becomes: $f=64.3249482 \dfrac{\sqrt T}{Ld}$

2022-07-07 13:45:38

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https://math.stackexchange.com/questions/439101/are-epimorphisms-stable-under-pullback-in-balanced-categories-with-epimorphic-im

# Are epimorphisms stable under pullback in balanced categories with epimorphic images? Suppose that $\mathcal{C}$ is a balanced category with epimorphic images, that is, every bimorphism is an isomorphism, every morphism has an image and the image factorization is an epi-mono factorization. Under such hypotheses, is it true that epimorphisms are stable under pullback (if it exists)? Or at least that $f(f^{-1}(S)) = S$, if it's defined, where $f : A \rightarrow B$ is an epimorphism and $S$ is a subobject of $B$? I believe both should be false, but I was not able to provide a counterexample.

2019-08-21 12:06:38

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https://mathoverflow.net/questions/368067/smallest-ordinal-alpha-such-that-l-cap-pl-alpha-is-uncountable

# smallest ordinal $\alpha$ such that $L \cap P(L_\alpha)$ is uncountable Let $$V$$ denote the von Neumann universe and $$L$$ Gödel's constructible universe. For any set $$X$$, let $$P(X)$$ denote the power set of $$X$$. Assume that $$0^\sharp$$ exists (and ZFC). What is the smallest ordinal $$\alpha$$ such that $$L \cap P(L_{\alpha})$$ is uncountable? (If $$V = L$$, then $$\alpha = \omega$$, but if $$0^\sharp$$ exists, then $$\alpha > \omega$$.) • It’s $\omega_1$. Aug 1, 2020 at 5:46 • I suspected so. Do you have a reference for a theorem that implies this? Aug 1, 2020 at 5:55 • If $0^\sharp$ exists, then every cardinal is inaccessible in L. Aug 1, 2020 at 6:04 • Ah, so $L \cap V_\alpha$ is countable for all countable $\alpha$, too, since $L \cap V_\alpha$ is the $V_\alpha$ of $L$. Thank you. Aug 1, 2020 at 6:08 • In ZFC alone, the $\alpha$ in the title can be described as: (1) If genuine $\omega_1$ is a successor cardinal of $L$, then $\alpha$ is its immediate predecessor cardinal of $L$. (2) If genuine $\omega_1$ is a limit (and therefore inaccessible) cardinal of $L$, then it is equal to $\alpha$. The additional hypothesis that $0^\#$ exists implies that case (2) occurs. Aug 1, 2020 at 14:22 We have in $$L$$, for each (infinite) $$\alpha$$, the following bijections: • $$f_\alpha:\alpha\rightarrow L_\alpha$$. • $$g_\alpha: \mathcal{P}(L_\alpha)^L=\mathcal{P}(L_\alpha)\cap L\rightarrow L_{(\vert\alpha\vert^+)^L}$$. Hence $$\vert\mathcal{P}(L_\alpha)^L\vert=\vert(\vert\alpha\vert^+)^L\vert$$. Now assuming $$0^\sharp$$ we have that $$\omega_1^V$$ is a limit cardinal in $$L$$, so for each $$\alpha<\omega_1^V$$ we have $$\vert\mathcal{P}(L_\alpha)^L\vert=\aleph_0$$. So the answer to your question is $$\omega_1^V$$. Note that all this requires is that $$\omega_1^V$$ be a limit cardinal in $$L$$. More generally, let $$\kappa$$ be the supremum of the $$L$$-cardinals whose $$L$$-successor is $$<\omega_1^V$$; then the $$\kappa$$th level of $$L$$ is the first whose $$L$$-powerset is truly uncountable. • OK, except I think you meant $P(L_\alpha)^L = L \cap P(L_\alpha)$, not $P(L_\alpha)^L = P(\alpha) \cap L$. Aug 3, 2020 at 0:30 • @JesseElliott Whoops, quite right - fixed! Aug 3, 2020 at 0:36

2023-02-01 15:35:24

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https://www.r-bloggers.com/cross-validation-for-kernel-density-estimation/

# Cross Validation for Kernel Density Estimation October 1, 2014 By (This article was first published on Freakonometrics » R-english, and kindly contributed to R-bloggers) In a post publihed in July, I mentioned the so called the Goldilocks principle, in the context of kermel density estimation, and bandwidth selection. The bandwith should not be too small (the variance would be too large) and it should not be too large (the bias would be too large). Another standard method to select the bandwith, as mentioned this afternoon in class is the cross-validation technique (described in Chiu (1991)). Here, we would like to minimize The integral can be writen Since the third component is constant, we have to minimize the expected value of the sum of the first two. The idea is to approximate it as which can easily be computed. Consider here some sample, with 50 observations, from a Gaussian distribution, ```> set.seed(1) > X=rnorm(50)``` From Silverman’s rule of thumb (which should be appropriate here since the sample has a Gaussian sample) the optimal bandwidth is ```> 1.06*sd(X)*length(X)^(-1/5) [1] 0.4030127``` Using the cross-validation technique mentioned above, compute ```> J=function(h){ + fhat=Vectorize(function(x) density(X,from=x,to=x,n=1,bw=h)\$y) + fhati=Vectorize(function(i) density(X[-i],from=X[i],to=X[i],n=1,bw=h)\$y) + F=fhati(1:length(X)) + return(integrate(function(x) fhat(x)^2,-Inf,Inf)\$value-2*mean(F)) + } > vx=seq(.1,1,by=.01) > vy=Vectorize(J)(vx) > df=data.frame(vx,vy) > library(ggplot2) > qplot(vx,vy,geom="line",data=df)``` The function has the following shape and the optimal value is ```> optimize(J,interval=c(.1,1)) \$minimum [1] 0.4687553 \$objective [1] -0.3355477``` Note that, indeed, it is close to Siverman’s optimal bandwidth. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

2018-08-15 22:33:41

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https://www.isa-afp.org/entries/Special_Function_Bounds.html

# Real-Valued Special Functions: Upper and Lower Bounds Title: Real-Valued Special Functions: Upper and Lower Bounds Author: Lawrence C. Paulson Submission date: 2014-08-29 Abstract: This development proves upper and lower bounds for several familiar real-valued functions. For sin, cos, exp and sqrt, it defines and verifies infinite families of upper and lower bounds, mostly based on Taylor series expansions. For arctan, ln and exp, it verifies a finite collection of upper and lower bounds, originally obtained from the functions' continued fraction expansions using the computer algebra system Maple. A common theme in these proofs is to take the difference between a function and its approximation, which should be zero at one point, and then consider the sign of the derivative. The immediate purpose of this development is to verify axioms used by MetiTarski, an automatic theorem prover for real-valued special functions. Crucial to MetiTarski's operation is the provision of upper and lower bounds for each function of interest. BibTeX: @article{Special_Function_Bounds-AFP, author = {Lawrence C. Paulson}, title = {Real-Valued Special Functions: Upper and Lower Bounds}, journal = {Archive of Formal Proofs}, month = aug, year = 2014, note = {\url{https://isa-afp.org/entries/Special_Function_Bounds.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Sturm_Sequences

2021-01-16 12:19:48

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https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-10-10-1-matrices-and-systems-of-equations-10-1-exercises-page-711/81

# Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 711: 81 x = 1 y = 0 z = 4 w = -2 #### Work Step by Step The reduced row-echelon form of the matrix is: $\begin{bmatrix} 1 & 0 & 0 & 0 & |1\\ 0 & 1 & 0 & 0 & |0\\ 0 & 0 & 1 & 0 & |4\\ 0 & 0 & 0 & 1 & |-2\\ \end{bmatrix}$ From reduced row-echelon form the solution is simple: x = 1 y = 0 z = 4 w = -2 After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

2020-01-26 20:17:06

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http://clay6.com/qa/1731/true-or-false-a-binary-operation-on-a-set-has-always-the-identity-element-

Browse Questions True or False: A binary operation on a set has always the identity element. Toolbox: • An identify element 'e' is defined binary operation * meet A if $e \in A$ and $a*e=a=e*a$ for $a\in A$ Let * on set of natural number be defined by $a *b =a-b \qquad a,b \in N$ Let $a-b =a$ $b=a-a=0$ $(ie) b=0 \notin N$ Therfore there does not exist any element 'e' in N such that $a*e=e *a =a$ Identify element does not exists for bianry operation * The given statement is 'False'

2017-01-17 15:25:53

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https://puzzling.stackexchange.com/questions/100830/a-mix-of-2048-and-match-3

# A mix of 2048 and Match 3 I was playing a game and thought of this problem: ## Rules 1. There are 4 distinct tiles on a $$6\times6$$ grid. The game starts out with one block on the board. 2. You can shift all the tiles in one of the four cardinal directions (north, south, west, east) until they hit a wall or a tile. 3. After every move, a new tile appears on the grid. 4. After all tiles have been shifted, if three or more same tiles line up orthogonally (not diagonally), these blocks disappear. (The tiles will not continue to shift.) This game is basically a mix of 2048 and Match 3. Here is an example screenshot. The player can shift the tiles down and the 3 green H-tiles will be removed from the game: Question: Is it guaranteed to never lose in this game? and if yes, is there a strategy? • Are you allowed to make a move which does not shift any of the existing tiles (because they're already up against that wall) but only generates a new one? 2048 doesn't allow this in general – dspyz Aug 6 at 1:00 • Cool game! I may try to implement it at one stage. – Dmitry Kamenetsky Aug 6 at 1:47 • @dspyz Yes - creator of the game says it is intended – u-ndefined Aug 6 at 3:58 • After the green tiles have disappeared will those above them continue to fall? – Paul Panzer Aug 6 at 9:56 • @PaulPanzer Nope – u-ndefined Aug 7 at 3:41 Not even close to a full answer but I'd like to share an "educated conjecture": Sorry fleshbags but you are at the computer's mercy! Heuristics: The following broad strategy looks promising to me for the computer not to allow a single tile to evaporate: Let us assume the last vertical push was to the top and the last horizontal one was to the left. The computer's strategy would be to work $$2\times2$$ block by $$2\times2$$ block, from top left to top right and then double row by double row. Ideally, each $$2\times2$$ block would contain all four colors (in any arrangement); it would follow trivially that the player cannot get anything done. One can easily check by hand that the computer can make sure of that for the first two blocks; afterwards small deviations must be factored in: For the first double row I think the best the computer can get is the left and the right blocks complete and the middle block having three colors, the equal tiles placed diagonally to each other. (Doing this exercise is what makes me feel that even the damage the player can do by shearing our $$2\times2$$ blocks can be controlled.) Note that this is still good enough for the human not to get a chance of scoring. My gut feeling is that when relaxed in this or similar fashion the $$2\times2$$ blocks can be kept "colorful" enough to thwart the player. A full proof may require (fittingly) a computer to cover all cases. The $$2\times2$$ block invariant may be good enough to keep the combinatorial explosion at bay and manageable.

2020-10-01 13:49:11

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