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## A simple regularization example
Earlier this month I promised to show you a simple example of regularization. Well, here it is. This is a particular combination of integrals I’ve been working with a lot lately:
$$\iint_{\mathbb{R}^2} \uddc\mathbf{x}\frac{e^{-x^2}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}} - \iint_{\mathbb{R}^2} \frac{\uddc\mathbf{y}}{y^2}e^{-i\xi\mathbf{k}\cdot\mathbf{y}}$$
A quick look at the formulas shows you that both integrands have singularities at $$\mathbf{x} = 0$$ and $$\mathbf{y} = 0$$.
OK, well, that’s why we have two integrands. We can change variables from $$\xi\mathbf{y}\to\mathbf{x}$$, subtract them, and the singularities will cancel out, right? You can do this integral by hand in polar coordinates, or just pop it into Mathematica:
$$\iint_{\mathbb{R}^2} \uddc\mathbf{x}\frac{e^{-x^2} - 1}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}} = -\pi\Gamma\biggl(0, \frac{k^2}{4}\biggr)$$
Just one problem: that’s not the right answer! You can tell because the value of this integral had better depend on $$\xi$$, but this expression doesn’t. This isn’t anything so mundane as a bug in Mathematica. It’s a “bug” in math itself.
See, when you have an undefined quantity, like a divergent integral, you can’t just keep doing math with the expression that represents it. That can lead to nonsensical results, like this classic invalid proof that $$1 = 2$$:
Let $$a = 1$$ and $$b = 1$$. Since $$a = b$$, then $$a - b = 0$$ and $$a^2 - b^2 = 0$$, so
$$a^2 - b^2 = a - b$$
Dividing both sides by $$a - b$$, we get
$$a + b = 1$$
and since $$a = b$$, that gives $$2a = 2b = 1$$ or $$a = b = \frac{1}{2}$$. But we know that $$a = b = 1$$, therefore
\begin{align}1 &= \frac{1}{2} \\ 2 &= 1\end{align}
In this fake proof, it’s pretty easy to find the bad step: dividing by $$a - b$$ is dividing by zero, and of course you can’t divide by zero. With the divergent integrals, something similar is going on, but it’s a bit trickier to figure out where the math goes wrong. The bad step is changing variables $$\xi\mathbf{y}\to\mathbf{x}$$ at $$\mathbf{y} = 0$$, because, in a sense, you wind up losing your new boundary condition into the singularity.
Fortunately, it’s not too hard to come up with a way to get around this. If $$\mathbf{y} = 0$$ is the problematic point, just leave it out! More specifically, you can cut out a small region around that singularity, do the integral over the rest of the plane, and then see if it’s well-defined in the limit as the excised region shrinks to zero. This is called cutoff regularization, and it’s the simplest of several techniques that you can use to force sensible results out of combinations of divergent integrals.
So instead of integrating over the entire plane, we’re integrating over $$x > \epsilon$$ or $$y > \epsilon$$ for some value $$\epsilon$$ that is the radius of the “hole” around the singularity.
$$\iint_{x > \epsilon} \uddc\mathbf{x}\frac{e^{-x^2}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}} - \iint_{y > \epsilon} \frac{\uddc\mathbf{y}}{y^2}e^{-i\xi\mathbf{k}\cdot\mathbf{y}}$$
Now we can change variables to $$\mathbf{x}$$ in the second integral and keep track of what happens at the boundary of the integration region. (There’s also an outer boundary at $$\infty$$ to worry about, but the function is zero there so that one actually doesn’t matter. But you could use cutoff regularization on that as well.)
$$\iint_{x > \epsilon} \uddc\mathbf{x}\frac{e^{-x^2}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}} - \iint_{x > \xi\epsilon} \frac{\uddc\mathbf{x}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}}$$
We’ll have to correct for the difference between the two regions of integration. Suppose $$\xi < 1$$, then you can split the second integral into two pieces: one over $$\xi\epsilon < x < \epsilon$$ and one over $$\epsilon < x$$.
The first of these is the term you’d miss by taking the naive approach I described at the beginning.
$$\iint_{x > \epsilon} \uddc\mathbf{x}\frac{e^{-x^2}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}} - \iint_{x > \epsilon} \frac{\uddc\mathbf{x}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}} - \iint_{\xi\epsilon}^{\epsilon} \frac{\uddc\mathbf{x}}{x^2}e^{-i\mathbf{k}\cdot\mathbf{x}}$$
Finally, it’s safe to combine the first two integrals, getting the same result as before. And in the last term, we can use the series expansion of the integrand at $$x\approx 0$$ to do it by hand. I’ll skip the details, though, and just offer up the answer:
$$-\pi\Gamma\biggl(0, \frac{k^2}{4}\biggr) - 2\pi\ln\xi$$
This shows the dependence on $$\xi$$, as it should. So this expression is a nice, sensible answer.
If you were really thinking, you might have wondered why we had to impose the same cutoff, $$\epsilon$$, on both integrals. After all, they’re over different variables; why should their boundaries necessarily have any relation to each other? Well, that’s just the way cutoff regularization works. You could just as well use a different regularization procedure where you cut off one integral at $$\epsilon$$ and the other at $$2\epsilon$$, and you’d get a different answer. Technically, all we’ve really done is take the arbitrariness out of the singularities and move it into the regularization procedure. That really doesn’t matter, though; what’s more important is that different calculations are done using the same method of regularization, so that they’re all consistent with each other. |
# Exponential Algorithms for Knapsack
Importance: Medium ✭✭
Author(s): Lipton, Dick
Subject: Theoretical Computer Science » Algorithms
Keywords: Algorithm construction Exponential-time algorithm Knapsack
Posted by: dick lipton on: February 4th, 2009
\begin{conjecture} % Enter your conjecture in LaTeX % You may change "conjecture" to "question" or "problem" if you prefer. The famous 0-1 Knapsack problem is: Given $a_{1},a_{2},\dots,a_{n}$ and $b$ integers, determine whether or not there are $0-1$ values $x_{1},x_{2},\dots,x_{n}$ so that $$\sum_{i=1}^{n} a_{i}x_{i} = b.$$ The best known worst-case algorithm runs in time $2^{n/2}$ times a polynomial in $n$. Is there an algorithm that runs in time $2^{n/3}$?
\end{conjecture}
% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{http://www.research.att.com/~njas/sequences/}
## Bibliography
% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)
[SS] Richard Schroeppel and Adi Shamir. A T=O(2n/2), S=O(2n/4) algorithm for certain NP-complete problems, SIAM J. Comput. 10 (1981), no. 3, 456--464.
* indicates original appearance(s) of problem.
### References
Solving this problem in pseudopolynomial time with polynomial space: Daniel Lokshtanov and Jesper Nederlof: "Saving Space by Algebraization". To appear in the proceedings of ACM Symposium on Theory of Computing (STOC 2010).
The next reference solves this problem (even general knapsack, I believe). An 2^{0.311 n} Algorithm: Nick Howgrave-Graham and Antoine Joux : "A new generic algorithm for hard knapsacks". To appear in the proceedings of EUROCRYPT 2010.
However, the problem might be easily adjusted to "find an algorithm that takes O(2^{c n}) time, where c < 0.311", etc etc.
Publications from 2010 on this topic: Pseudopolynomial algorithm with only polynomial space: Daniel Lokshtanov and Jesper Nederlof: "Saving Space by Algebraization". To appear in the proceedings of ACM Symposium on Theory of Computing (STOC 2010).
Fast knapsack: Nick Howgrave-Graham and Antoine Joux: "New Generic Algorithms for Hard Knapsacks". To appear in the proceedings of EUROCRYPT 2010 The running time is O^*(2^0.311 n), which is faster than the question posted here.
Obviously, the question could become: find a lower constant than 0.311.
### 0-1 knapsack
I do not know how to determine the run time but I have an algorithm based on dynamic programming which solves the problem more efficiently than a simple search but not in polynomial time!
I have implemented the procedure as a Java program and tried to express it as a flow chart. Files for both of these are available at; www.cybase.co.uk/wlcs/Software.html
although at the moment the website is down.
I have contacted the ISP to try and restore it.
### This appears to be answered
see paper at http://www.joux.biz/publications/Knapsacks.pdf and rjlipton's blog post about it at http://rjlipton.wordpress.com/2010/02/05/a-2010-algorithm-for-the-knapsack-problem/
of course, this is an open ended question, there is still room for better algorithms.
### A solution has been announced
A (randomized, probably heuristic) algorithm has been announced to solve this problem in time close to 2^(0.311 n), at the ESC 2010 seminar.
For details, see: https://cryptolux.org/ESC/Antoine_Joux
### Subset sum or 0-1?
When your values - your a_n - can be negative, and your b (the goal) is zero, then it's called "subset sum". If the a_n are non-negative (i.e., some of the a's may be zero), the b is positive, and the choice is to either exclude (0) or include (1) one "copy" of each value, then it's a "0-1 knapsack" problem. Usually, but not always, a knapsack problem has components with multiple values, and the goal is a minimax problem: maximize the a's, while minimizing the c's.
It's always darkest, just after the lights go out.
### 0-1 Knapsack?
I know this problem as subset sum and not as 0-1 knapsack. |
BREAKING NEWS
Infinite dihedral group
Summary
p1m1, (*∞∞) p2, (22∞) p2mg, (2*∞)
In 2-dimensions three frieze groups p1m1, p2, and p2mg are isomorphic to the Dih group. They all have 2 generators. The first has two parallel reflection lines, the second two 2-fold gyrations, and the last has one mirror and one 2-fold gyration.
In mathematics, the infinite dihedral group Dih is an infinite group with properties analogous to those of the finite dihedral groups.
In one dimension, the infinite dihedral group is seen in the symmetry of an apeirogon alternating two edge lengths, containing reflection points at the center of each edge.
In two-dimensional geometry, the infinite dihedral group represents the frieze group symmetry, p1m1, seen as an infinite set of parallel reflections along an axis.
Definition
Every dihedral group is generated by a rotation r and a reflection; if the rotation is a rational multiple of a full rotation, then there is some integer n such that rn is the identity, and we have a finite dihedral group of order 2n. If the rotation is not a rational multiple of a full rotation, then there is no such n and the resulting group has infinitely many elements and is called Dih. It has presentations
${\displaystyle \langle r,s\mid s^{2}=1,srs=r^{-1}\rangle \,\!}$
${\displaystyle \langle x,y\mid x^{2}=y^{2}=1\rangle \,\!}$ [1] [2]
and is isomorphic to a semidirect product of Z and Z/2, and to the free product Z/2 * Z/2. It is the automorphism group of the graph consisting of a path infinite to both sides. Correspondingly, it is the isometry group of Z (see also symmetry groups in one dimension), the group of permutations α: ZZ satisfying |i - j| = |α(i) - α(j)|, for all i, j in Z.[3]
The infinite dihedral group can also be defined as the holomorph of the infinite cyclic group.
Aliasing
When periodically sampling a sinusoidal function at rate fs, the abscissa above represents its frequency, and the ordinate represents another sinusoid that could produce the same set of samples. An infinite number of abscissas have the same ordinate (an equivalence class with the fundamental domain [0, fs/2]),and they exhibit dihedral symmetry. The many-to-one phenomenon is known as aliasing.
An example of infinite dihedral symmetry is in aliasing of real-valued signals.
When sampling a function at frequency fs (intervals 1/fs), the following functions yield identical sets of samples: {sin(2π( f+Nfs) t + φ), N = 0, ±1, ±2, ±3,...}. Thus, the detected value of frequency f is periodic, which gives the translation element r = fs. The functions and their frequencies are said to be aliases of each other. Noting the trigonometric identity:
${\displaystyle \sin(2\pi (f+Nf_{s})t+\phi )=\left\{{\begin{array}{ll}+\sin(2\pi (f+Nf_{s})t+\phi ),&f+Nf_{s}\geq 0\\-\sin(2\pi |f+Nf_{s}|t-\phi ),&f+Nf_{s}<0\\\end{array}}\right.}$
we can write all the alias frequencies as positive values: | f+N fs|. This gives the reflection (f) element, namely ff. For example, with f = 0.6fs and N = −1f+Nfs = −0.4fs reflects to 0.4fs, resulting in the two left-most black dots in the figure.[note 1] The other two dots correspond to N = −2 and N = 1. As the figure depicts, there are reflection symmetries, at 0.5fsfs, 1.5fs, etc. Formally, the quotient under aliasing is the orbifold [0, 0.5fs], with a Z/2 action at the endpoints (the orbifold points), corresponding to reflection.
2. ^ tern, arctic; user384354 (31 Oct 2016). "Infinite dihedral group isomorphic to semidirect product". Mathematics Stack Exchange. Retrieved 2021-07-21. {{cite web}}: |last2= has generic name (help)CS1 maint: url-status (link) |
## Global and local two-sample tests via regression.(English)Zbl 1435.62199
The objective of this paper is to report on global and local tests to determine if two samples are from different multivariate distributions. Such tests have applications in a variety of machine learning areas, e.g. to detect differences in healthy and cancerous tissue, in database attribute matching and many other classification and regression problems. Under condition that two populations only differ in their means it is proved that the regression test based on Fisher’s LDA achieves the same local optimality as the Hotelling’s $$T^2$$ test. The simulation studies are fulfilled to examine the empirical performance of the proposed tests. The empirical performance of proposed tests is validated at the datasets from Hubble Space Telescope: it is shown that the proposed approach can identify galaxies with specific features of star-forming galaxies.
### MSC:
62H15 Hypothesis testing in multivariate analysis 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 85A15 Galactic and stellar structure 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62J05 Linear regression; mixed models 62P35 Applications of statistics to physics 62H35 Image analysis in multivariate analysis
GeneSrF; hypoRF
Full Text:
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## Problem
### Statement
Alice lives on a line. Today, she will travel to some place in a mysterious vehicle. Initially, the distance between Alice and her destination is . When she input a number to the vehicle, it will travel in the direction of the destination by a distance of if this move would shorten the distance between the vehicle and the destination, and it will stay at its position otherwise. Note that the vehicle may go past the destination when the distance between the vehicle and the destination is less than .
Alice made a list of numbers. The number in this list is . She will insert these numbers to the vehicle one by one.
However, a mischievous witch appeared. She is thinking of rewriting one number in the list so that Alice will not reach the destination after moves.
She has plans to do this, as follows:
Rewrite only the number in the list with some integer so that Alice will not reach the destination.
Write a program to determine whether each plan is feasible.
### Constraints
and each are integers.
### Input
Input is given from Standard Input in the following format:
### Output
Print lines. The line should contain YES if the plan is feasible, and NO otherwise.
### Sample
Input #1
Output #1
Explanation #1
For the first plan, Alice will already arrive at the destination by the first three moves, and therefore the answer is NO. For the second plan, rewriting the third number in the list with will prevent Alice from reaching the destination as shown in the following figure, and thus the answer is YES.
Input #2
Output #2
Explanation #2
Alice will not reach the destination as it is, and therefore all the plans are feasible.
Input #3
Output #3 |
### Show Posts
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### Messages - Victor Ivrii
Pages: 1 [2] 3 4 ... 166
16
##### Term Test 2 / Problem 3 (noon)
« on: November 19, 2019, 04:22:43 AM »
(a) Find the general solution of
$$\mathbf{x}'=\begin{pmatrix} 1 &2\\ 1 &0\end{pmatrix}\mathbf{x}$$
and sketch trajectories.
(b) Find the general solution
$$\mathbf{x}'=\begin{pmatrix} 1 &2\\ 1 &0\end{pmatrix}\mathbf{x}+ \begin{pmatrix} 0 \\[1pt] \dfrac{6 e^{3t }}{e^{2t}+1}\end{pmatrix}.$$
17
##### Term Test 2 / Problem 3 (morning)
« on: November 19, 2019, 04:21:57 AM »
(a) Find the general solution of
$$\mathbf{x}'=\begin{pmatrix} -2 &1\\ -1 &0\end{pmatrix}\mathbf{x}$$
and sketch trajectories.
(b) Find the general solution
$$\mathbf{x}'=\begin{pmatrix} -2 &1\\ -1 &0\end{pmatrix}\mathbf{x}+ \begin{pmatrix} 0 \\ \dfrac{e^{-t}} {t^2+1} \end{pmatrix}.$$
18
##### Term Test 2 / Problem 3 (main sitting)
« on: November 19, 2019, 04:21:01 AM »
(a) Find the general solution of
$$\mathbf{x}'=\begin{pmatrix} 1 &1\\ -2 &4\end{pmatrix}\mathbf{x}$$
classify fixed point $(0,0)$ and sketch trajectories.
(b) Find the general solution
$$\mathbf{x}'=\begin{pmatrix} 1 &1\\ -2 &4\end{pmatrix}\mathbf{x}+ \begin{pmatrix} \dfrac{e^{4t }}{e^{2t}+1} \\ 0\end{pmatrix}.$$
19
##### Term Test 2 / Problem 2 (noon)
« on: November 19, 2019, 04:19:53 AM »
Consider equation
y'''+y''+4y'+4y=-24e^{-2t}.
\label{2-1}
(a) Write a differential equation for Wronskian of $y_1,y_2,y_3$, which are solutions for homogeneous equation and solve it.
(b) Find fundamental system $\{y_1,y_2,y_3\}$ of solutions for homogeneous equation, and find their Wronskian. Compare with (a).
(c) Find the general solution of (\ref{2-1}).
20
##### Term Test 2 / Problem 2 (morning)
« on: November 19, 2019, 04:18:46 AM »
Consider equation
y'''-2y''+4y'-8y=15\cos (t).
\label{2-1}
(a) Write a differential equation for Wronskian of $y_1,y_2,y_3$, which are solutions for homogeneous equation and solve it.
(b) Find fundamental system $\{y_1,y_2,y_3\}$ of solutions for homogeneous equation, and find their Wronskian. Compare with (a).
(c) Find the general solution of (\ref{2-1}).
21
##### Term Test 2 / Problem 2 (main sitting)
« on: November 19, 2019, 04:17:26 AM »
Consider equation
y'''+4y''+y'-6y=24e^{t}.
\label{2-1}
(a) Write a differential equation for Wronskian of $y_1,y_2,y_3$, which are solutions for homogeneous equation and solve it.
(b) Find fundamental system $\{y_1,y_2,y_3\}$ of solutions for homogeneous equation, and find their Wronskian. Compare with (a).
(c) Find the general solution of (\ref{2-1}).
22
##### Term Test 2 / Problem 1 (noon)
« on: November 19, 2019, 04:15:32 AM »
(a) Find the general solution of
$$y''-3y'+2y=\frac{e^{3t}}{e^{2t}+1}.$$
(b) Find solution satisfying
$$y(0)=y'(0)=0.$$
23
##### Term Test 2 / Problem 1 (morning)
« on: November 19, 2019, 04:14:47 AM »
(a) Find the general solution of
$$y''-y=\frac{12}{e^{t}+1}.$$
(b) Find solution satisfying
$$y(0)=y'(0)=0.$$
24
##### Term Test 2 / Problem 1 (main sitting)
« on: November 19, 2019, 04:13:51 AM »
(a) Find the general solution of
$$y''+4y=\frac{1}{\cos^2(t)},\qquad -\frac{\pi}{2}<t<\frac{\pi}{2}.$$
(b) Find solution satisfying
$$y(0)=y'(0)=0.$$
25
##### Chapter 4 / Re: 4.2
« on: November 15, 2019, 02:42:45 PM »
Yes, because for equations given they could be found easily
26
##### Chapter 7 / Re: Finding linear independence
« on: November 11, 2019, 06:58:04 AM »
Those are not just vectors, but vector-valued functions and you need to check that for constant coefficients their linear combination is identically $0$ if and only if these coefficients are $0$.
Try first to look at components of this vector-function.
27
##### Chapter 7 / Re: Transforming a system of linear equations to a single higher-order equation
« on: November 05, 2019, 09:52:23 PM »
Nothing to do with the determinant. In dimension 2 you can reduce if the matrix is not diagonal--obvious. What about the diagonal case? It is also possible unless a matrix is scalar, i.e. proportional to identity. To do this reduction, we make first a linear transform, so that after it the matrix is not diagonal anymore, and then reduce.
General criteria: System with constant coefficients could be reduced to a single equation iff each eigenspace is $1$-dimensional. To understand why we need to consider solutions to a homogeneous equation and to a homogeneous system.
For an equation one of the solutions is $t^{m-1} e^{kt}$ where $k$ is characteristic root, and $m$ is a multiplicity of $k$.
For system all solutions are in the form $P_{s-1}(t)e^{kt}$ where $P_{s-1}(t)$ are polynomials of degree $\le s-1$ with vector-coefficients and $s$ is the maximal dimension of the corresponding Jordan cells.
Therefore reduction can be done iff $s=m$ which means that for each eigenvalue $k$ there is just one cell, which in turn means, that there is only one linearly independent eigenvector.
Remark: If $s_1,...,s_j$ are dimensions of all cells, corresponding to $k$, then their sum $=m$ where $m$ is a multiplicity of $k$ as a root of characteristic equation, and also the dimension of the root subspace, and $j$ is a dimension of the corresponding eigenspace.
However, it is not important: we solve systems without reducing them to single equations.
28
##### Term Test 1 / Problem 4 (afternoon)
« on: October 23, 2019, 06:27:03 AM »
(a) Find the general solution for equation
\begin{equation*}
y'' +2y' +17 y =40 e^{x} +130\sin(4x) .
\end{equation*}
(b) Find solution, satisfying $y(0)=0$, $y'(0)=0$.
29
##### Term Test 1 / Problem 4 (noon)
« on: October 23, 2019, 06:26:03 AM »
(a) Find the general solution for equation
\begin{equation*}
y'' -8y' +25y =18e^{4x} +104\cos(3x) .
\end{equation*}
(b) Find solution, satisfying $y(0)=0$, $y'(0)=0$.
30
##### Term Test 1 / Problem 4 (morning)
« on: October 23, 2019, 06:25:04 AM »
(a) Find the general solution for equation
\begin{equation*}
y'' -6y' +25y =16e^{3x} +102\sin(x) .
\end{equation*}
(b) Find solution, satisfying $y(0)=0$, $y'(0)=0$
Pages: 1 [2] 3 4 ... 166 |
# Why should we use t errors instead of normal errors?
In this blog post by Andrew Gelman, there is the following passage:
The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian models of today will seem hopelessly simple, 50 years hence. (Just for a simple example: we should probably be routinely using t instead of normal errors just about everwhere, but we don’t yet do so, out of familiarity, habit, and mathematical convenience. These may be good reasons–in science as in politics, conservatism has many good arguments in its favor–but I think that ultimately as we become comfortable with more complicated models, we’ll move in that direction.)
Why should we "routinely be using t instead of normal errors just about everywhere"?
Because, assuming normal errors is effectively the same as assuming that large errors do not occur! The normal distribution has so light tails, that errors outside $\pm 3$ standard deviations have very low probability, errors outside of $\pm 6$ standard deviations are effectively impossible. In practice, that assumption is seldom true. When analyzing small, tidy datasets from well designed experiments, this might not matter much, if we do a good analysis of residuals. With data of lesser quality, it might matter much more.
When using likelihood-based (or bayesian) methods, the effect of this normality (as said above, effectively this is the "no large errors"-assumption!) is to make the inference very little robust. The results of the analysis are too heavily influenced by the large errors! This must be so, since assuming "no large errors" forces our methods to interpret the large errors as small errors, and that can only happen by moving the mean value parameter to make all the errors smaller. One way to avoid that is to use so-called "robust methods", see http://web.archive.org/web/20160611192739/http://www.stats.ox.ac.uk/pub/StatMeth/Robust.pdf
But Andrew Gelman will not go for this, since robust methods are usually presented in a highly non-bayesian way. Using t-distributed errors in likelihood/bayesian models is a different way to obtain robust methods, as the $t$-distribution has heavier tails than the normal, so allows for a larger proportion of large errors. The number of degrees of freedom parameter should be fixed in advance, not estimated from the data, since such estimation will destroy the robustness properties of the method (*) (it is also a very difficult problem, the likelihood function for $\nu$, the number degrees of freedom, can be unbounded, leading to very inefficient (even inconsistent) estimators).
If, for instance, you think (are afraid) that as much as 1 in ten observations might be "large errors" (above 3 sd), then you could use a $t$-distribution with 2 degrees of freedom, increasing that number if the proportion of large errors is believed to be smaller.
I should note that what I have said above is for models with independent $t$-distributed errors. There have also been proposals of multivariate $t$-distribution (which is not independent) as error distribution. That propsal is heavily criticized in the paper "The emperor's new clothes: a critique of the multivariate $t$ regression model" by T. S. Breusch, J. C. Robertson and A. H. Welsh, in Statistica Neerlandica (1997) Vol. 51, nr. 3, pp. 269-286, where they show that the multivariate $t$ error distribution is empirically indistinguishable from the normal. But that criticism do not affect the independent $t$ model.
(*) One reference stating this is Venables & Ripley's MASS---Modern Applied Statistics with S (on page 110 in 4th edition).
• Excellent answer (+1). Note that even when $\nu$ is fixed, the estimating equations are ill defined if $\nu\leq2$ so I take to mean that Gelman means $t$ distribution with $\nu$ parameter fixed to $\nu>2$. As illustrated in the answer to this related question This places rather strong limits on the robustness that can be expected of this approach. – user603 Oct 20 '14 at 18:27
• Great Answer and comment. But: 1. Gelman is defending a standard procedure that will be better than assuming Normal errors. So, we should compare the simple (Normal errors) with the T distribution for the errors. 2. In the related question linked by user603, we should note that if qe have prior information, we should use it. Bayes excels with prior information. And in the exmaple, we do have prior information that is not used. 3. With posterior predictive checks wed know that the model proposed isnt good enough. – Manoel Galdino Oct 21 '14 at 0:07
• @Neil G: Yes, but the cauchy is $t_1$! Addressing exactly which heavy-tailed distribution to use of course needs much more analysis. – kjetil b halvorsen Apr 29 '15 at 10:58
• No, the t-distribution is the only choice because the t-distribution is the posterior predictive of the Gaussian model. Gelman wasn't just picking the t-distribution at random. – Neil G Apr 29 '15 at 10:59
• See: Murphy, Kevin P. "Conjugate Bayesian analysis of the Gaussian distribution." def 1.2σ2 (2007): 16. He derives the t-distribution as the posterior predictive of the Gaussian model. It is not merely a case of the modeler choosing an arbitrary heavy-tailed distribution. – Neil G Apr 29 '15 at 11:07
It is not just a matter of "heavier tails" — there are plenty of distributions that are bell shaped and have heavy tails.
The T distribution is the posterior predictive of the Gaussian model. If you make a Gaussian assumption, but have finite evidence, then the resulting model is necessarily making non-central scaled t-distributed predictions. In the limit, as the amount of evidence you have goes to infinity, you end up with Gaussian predictions since the limit of the t distribution is Gaussian.
Why does this happen? Because with a finite amount of evidence, there is uncertainty in the parameters of your model. In the case of the Gaussian model, uncertainty in the mean would merely increase the variance (i.e., the posterior predictive of a Gaussian with known variance is still Gaussian). But uncertainty about the variance is what causes the heavy tails. If the model is trained with unlimited evidence, there is no longer any uncertainty in the variance (or the mean) and you can use your model to make Gaussian predictions.
This argument applies for a Gaussian model. It also applies to a parameter that is inferred whose likelihoods are Gaussian. Given finite data, the uncertainty about the parameter is t-distributed. Wherever there are Normal assumptions (with unknown mean and variance), and finite data, there are t-distributed posterior predictives.
There are similar posterior predictive distributions for all of the Bayesian models. Gelman is suggesting that we should be using those. His concerns would be mitigated by sufficient evidence.
• Can you back up this with some references? – kjetil b halvorsen Apr 29 '15 at 11:05
• @kjetilbhalvorsen: Murphy, Kevin P. "Conjugate Bayesian analysis of the Gaussian distribution." def 1.2σ2 (2007): 16. – Neil G Apr 29 '15 at 11:08
• Interesting perspective, I'd never heard this before. So do t-distributed errors also lead to t-distributed predictions? This to me this is an argument in favor of continuing to use Gaussian errors. Unless you expect conditional outliers, the conditional error model doesn't need to allow for them. This amounts to the assumption that all the outlying-ness comes from outlying values of the predictors. I don't think that assumption is so bad in a lot of cases. And on purely aesthetic grounds, I don't see why the conditional and marginal distributions have to match – shadowtalker Apr 29 '15 at 13:29
• @ssdecontrol "Do t-distributed errors also lead to t-distributed predictions?" I don't know, but I don't think so. For me, this perspective is very useful for an intuitive understanding of why the t-test works. – Neil G Apr 29 '15 at 13:31 |
# 2018 Annual Meeting of the Society for Mathematical Biology & the Japanese Society for Mathematical Biology
8-12 July 2018
Australia/Sydney timezone
## $R_0$ centrality in metapopulation networks: finding the epidemiological and evolutionary hotspots
11 Jul 2018, 15:00
30m
New Law School/--105 (University of Sydney)
### New Law School/--105
#### University of Sydney
60
Oral Presentation Minisymposium: Recent progress in adaptive dynamics: Evolving community diversity
### Speaker
Prof. Akira Sasaki (The Graduate University for Advanced Studies (SOKENDAI))
### Description
Identifying the epidemiological key-stone communities in a metapopulation network is primarily important in designing efficient control against an infectious disease. Various network centrality measures commonly utilized for this purpose haven’t directly focused on the most important measure in epidemiology: the basic reproductive number, $R_0$, of epidemiological dynamics on the network, which determines whether or not the infectious disease spreads over the whole network. We here introduce a new centrality measure, $R_0$-centrality, which quantifies how sensitive is the control in each local community to the reduction in $R_0$ of the whole network. Our perturbation analysis then reveals that the largest local population in the network should have extremely large $R_0$ centrality than the others, indicating that all the effort in control should be directed to the largest community. For example, when applied to the commuter network of the Tokyo metropolitan area, we found that the impact of control at the largest daytime-population, that around Shinjuku station, is more than 1,000 times stronger than that at the second largest daytime-population, that around Tokyo station, even though the difference between population sizes are only 1.5 times between them.
Once an infectious disease has already spread over the network, we found that the opposite extreme control becomes optimum: indeed, to reduce the total number hosts that have ever exposed to the infectious disease after it has already penetrated in the network, the optimal policy is to spreading controls shallowly and widely over the network. We also discuss the conditions under which “treating-only-the-biggest” control becomes the optimum, and the key-stone community for the emergence is virulent or resistant pathogens.
### Primary authors
Prof. Akira Sasaki (The Graduate University for Advanced Studies (SOKENDAI)) Dr Yashima Kenta (The Graduate University for Advanced Studies (SOKENDAI))
### Presentation Materials
There are no materials yet. |
Precalculus (10th Edition)
Published by Pearson
Chapter 6 - Trigonometric Functions - 6.3 Properties of the Trigonometric Functions - 6.3 Assess Your Understanding - Page 394: 15
Answer
$1$
Work Step by Step
$\csc{\alpha} =\csc{\left( \alpha -360\right)} \Rightarrow \csc{450^o}=\csc{\left( 450^o-360^o\right)} =\csc{90^o}=\dfrac {1}{\sin {90^o}}=\dfrac {1}{1}=1$
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. |
# Will state of water change in certain condition? [closed]
Imagine I have an iron tank with a $$20~\mathrm{pm}$$ hole on it. Then I completely fill it with water and use a pump to get the water out of that hole. What will come out, water or gas?
• I've answered and also marked down. You have an ill-formed question. The hole size is physically unrealistic in real systems. It is on the order of the size of interstitial sites in lattices. What are you really wanting to determine here? Dec 24 '19 at 15:15
• A 20 pm hole in an iron tank is not a hole. We are in the range of less than the typical atomic distance between the iron atoms of any of their possible metallic lattice structures that make up the tank. A typical atomic diameter is 1 Ångstrøm, which is 100 pm. Dec 24 '19 at 16:58
Pressure alone does not break chemical bonds. Expose liquid water suddenly to a vacuum and it will vaporize as a molecule; it will not dissociate into atoms. This is true regardless of the initial pressure of the water.
The hole that you have made is too small for water molecules. It is even too small for a hydrogen atom, which is the smallest atom possible (with a radius of about 50-60 pm).
The hole size that you propose is more akin to the sizes of interstitial sites in solid lattices. For examples of the lattice structures of iron, see the links below.
https://en.wikipedia.org/wiki/Allotropes_of_iron
https://www.tf.uni-kiel.de/matwis/amat/iss/kap_4/backbone/r4_2_2.html
At this point, you should recognize that we cannot make a contiguous "hole" that is 20pm in radius or diameter through an iron wall. Indeed, this because of the way that atoms pack in solids, we cannot make such a hole through any solid wall that is thicker than two atoms stacked on in layers. The "holes" through the one layer of atoms are blocked by the atoms that cover in the next layer.
In essence, you have a solid tank. Nothing will transport through the wall.
• In essence, you have a solid tank. Nothing will transport through the wall. Excellent summary! +1 from me.
– Gert
Dec 24 '19 at 15:18
• @Jeffrey J Weimer I thought iron atom has 252 pm diameter. So it is possible to create a 20 pm hole into an iron tank. Can you plz tell me, What is the smallest size hole we can created in an opaque material?
– user248881
Dec 24 '19 at 18:13
• @user248881 The smallest diameter continuous (through-and-through) hole that we can create that will be self-supporting is likely on the order of a microns in diameter, perhaps to 100s of nm (tenths of microns). At that point with a macroscopically thick solid metal, it is also likely to be the boundaries of grains, not straight through and through. The answer is different for other classes of materials (ceramics, semiconductors, and polymers). Further discussion is worth a question of its own posting. Dec 24 '19 at 22:14
• @Jeffrey J Weimer This is not off topic discussion since under my question you said, “Such a tiny hole is not possible”. So i wanted to know the exact diameter of the tiniest hole physicists can make in any solid opaque material which has the thickness of at least 1mm. But you didn’t gave me the exact digits.
– user248881
Dec 25 '19 at 0:53
• @user248881 The references I give about metal lattices give a starting point for you to learn about structures in metals. The answers to your new question can go in many directions, and an answer with exact digits is likely to be close to impossible to provide. Finally, I will say again, you are heading off-topic from your original post with your new question, your new question may be worthy of giving others an equal chance to address, and discussions are not the place to do so. Dec 25 '19 at 13:16
Your hole is too small to let even a single molecule through, but let's increase the hole to a size where molecules can come through one at a time. I'm sure this is what you had in mind. What then would be the result?
And the answer is that would have created a molecular beam. That is you would have a beam of isolated water molecules travelling away from the hole. The kinetic energy of the molecules would be about the thermal energy of $$\tfrac32kT$$. I make this a velocity of about 450 m/s.
• No John! I intentionally selected that hole size because i wanted to know that, what will happen to a H2O molecule? Will the covalent bond between atoms of H and O break apart and hydrogen and oxygen gas will come out of it or nothing will come out of it?
– user248881
Dec 24 '19 at 13:29
• @user248881 Why do you think the $H-O$ bonds should break? We're talking about ordinary temperatures, right? Dec 24 '19 at 13:44
• @user8718165 In my mind, pressure will break the bond.
– user248881
Dec 24 '19 at 13:49
• @user248881 I'm not sure if that's even possible. Dec 24 '19 at 13:50
• @user8718165 I know that and that’s why i’m here to ask professional physicists who have played with atoms and it’s particles throughout their careers.
– user248881
Dec 24 '19 at 14:05 |
# limit of infinity
i'm wondering is this valid?
$$\lim _{ x\rightarrow \infty }{ { (1+\frac { 1 }{ x } ) }^{ x }\quad =\quad { (1\frac { 1 }{ x } ) }^{ x }\quad =\quad ({ \frac { 1(x)+1 }{ x } ) }^{ x }\quad =\quad ({ \frac { x+1 }{ x } ) }^{ x }\quad }$$ and since $$\infty +1$$ does not make much of a difference so is still $$\infty$$ then $${ (\frac { x }{ x } ) }^{ x }\quad =\quad 1\quad$$ if we treat $$\infty$$ like a number.
therfore $$\quad \lim _{ x\rightarrow \infty }{ { (1+\frac { 1 }{ x } ) }^{ x }\quad =\quad 1\quad }$$
Note by Shufay Ung
3 years, 10 months ago
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You can't treat infinity like a number that's where the fallacy begins.
- 3 years, 10 months ago |
# Taking Every Other Term
Algebra Level 2
$a = 1+\frac 14 + \frac 19 +\frac 1{16} +\frac 1{25} + \cdots$
Determine the value of the below expression in terms of $$a$$.
$\frac 19 +\frac 1{25} +\frac 1{49} + \cdots$
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# NCERT Solutions Class 9 Science Chapter 8 Motion
### In-Text Questions Solutions
#### In Text-Questions Page 100
1. An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.
Ans:- Yes, an object moving through a distance can have zero displacement. This happens when final position of the object coincides with its initial position. For example, if a person moves around a park and returns to the same point from where he had started then the displacement will be zero.
2. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?
Ans:- Figure ABCD is a square field of side 10 m.
3. Which of the following is true for displacement?
(a) It cannot be zero.
(b) Its magnitude is greater than the distance travelled by the object
.
Ans:-
(a) Not true
Displacement can become zero when the initial and final positions of the object are the same.
(b) Not true Displacement is the shortest distance between the initial and final positions of an object.
It cannot be greater than the magnitude of the distance travelled by an object. However, sometimes, it may be equal to the distance travelled by the object.
#### In Text-Questions Page 102
1. Distinguish between speed and velocity.
Ans:-
2. Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?
Ans:- If the total distance covered by an object is the same as its displacement, then its average speed would be equal to its average velocity, i.e. when the object moves along a straight line path.
3. What does the odometer of an automobile measure?
Ans:- Odometer of an automobile measures the distance covered by automobile.
4. What does the path of an object look like when it is in uniform motion?
Ans:- An object having uniform motion has a straight line path.
5. During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, 3 × 108 m s–1.
Ans:- Time taken = 5 mins = 5 x 60 s = 300 s
Speed of signal = 3 x 108 m/s
Distance = speed x time = 3 x 108 x 300 = 9 x 1010 m
#### In Text-Questions Page 103
1. When will you say a body is in
(i) uniform acceleration? (ii) non uniform acceleration?
Ans:- (i) Uniform acceleration:- A body is said to be in uniform acceleration if it moves in a straight line and its velocity changes by equal amounts in equal intervals of time.
(ii) Non-uniform acceleraiion:- A body is said to be in non-uniform acceleration if its velocity does not change by equal amounts in equal intervals of time.
2. A bus decreases its speed from 80 km h-1 to 60 km h-1 in 5 s. Find the acceleration of the bus.
Ans:– Initial velocity, u = 80 km/h = 80 x 5/18 = 22.22 m/s
Final velocity, v = 60 km/h = 60 x 5/18 = 16.66 m/s
Time taken, t = 5 s
Acceleration, a = $\inline&space;\dpi{100}&space;\fn_phv&space;\frac{v&space;-&space;u}{t}$ = $\inline&space;\dpi{100}&space;\fn_phv&space;\frac{16.66&space;-&space;22.22}{5}$ = -1.11 m/s2
Negative sign shows retardation.
3. A train starting from a railway station and moving with uniform acceleration attains a speed 40 km h-1 in 10 minutes. Find its acceleration.
Ans:- Here, initial speed, u = 0
Final speed, v = 40 km/h = 40 x 5/18 = 11.11 m/s
Time taken, t = 10 mins = 10 x 60 s = 600 s
Acceleration, a = $\inline&space;\dpi{100}&space;\fn_phv&space;\frac{v&space;-&space;u}{t}$ = $\inline&space;\fn_phv&space;\frac{11.11&space;-&space;0}{600}$ = 1.85 x 10 -2 m/s2
#### In Text-Questions Page 107
1. What is the nature of the distance-time graphs for uniform and non-uniform motion of an object?
Ans:- When the motion is uniform, the distance-time graph is a straight line with some slope.
When the motion is non-uniform, the distance time graph is not a straight line.
2. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?
Ans:- It means that distance of the object does not change with time and the object is in a state of rest.
3. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis ?
Ans:- It means that the speed of the object is uniform.
4. What is the quantity which is measured by the area occupied below the velocity-time graph?
Ans:- Area occupied below the velocity-time graph is a measure of the displacement of the body.
#### In Text-Questions Page 109-110
1. A bus starting from rest moves with a uniform acceleration of 0.1 ms-2 for 2 minutes. Find
(a) the speed acquired,
(b) the distance travelled.
Ans:- Here, u = 0, a = 0.1 m/s2,
t = 2 min = 2 x 60 s = 120 s
(a) Using v = u + at = 0 + 0.1 x 120 = 12 m/s
(b) Using S = ut + ½ at2 = 0 x 120 + ½ 0.1 (120)2 = 7.2 x 102 m
2. A train is travelling at a speed of 90 km h-1. Brakes are applied so as to produce a uniform acceleration of – 0.5 m s-2. Find how far the train will go before it is brought to rest.
Ans:- Here, initial speed, u = 90 km/h = 90 x 5/18 m/s = 25 m/s
Acceleration, a = -0.5 m/s2
Final velocity, v = 0
Using, 2aS = v2 – u2
Distance travelled, S = $\inline&space;\dpi{120}&space;\frac{v^{2}&space;-&space;u^{2}}{2a}$ = $\inline&space;\dpi{120}&space;\frac{0&space;-&space;25^{2}}{2&space;\times&space;(-0.5))}$ = 625 m
3. A trolley, while going down an inclined plane, has an acceleration of 2 cm s-2. What will be its velocity 3 s after the start?
Ans:- Here, acceleration, a = 2 cm/s2
Time taken, t = 3 s
Initial velocity, u = 0
Final velocity, v = u + at = 0 + 2 x 3 = 6 cm/s
4. A racing car has a uniformm acceleration of 4 m s-2. What distance will it cover in 10 s after start?
Ans:- Here, a = 4 m s-2, t = 10 s, u = 0
Using, S = ut + ½ at2
S = 0 x 10 + ½ x 4 x 102
S = 0 + ½ x 4 x 100 = 200 m
The distance covered in 10 s by the car is 200 m.
5. A stone is thrown in a vertically upward direction with a velocity of 5 m s-1. If the acceleration of the stone during its motion is 10 m s-1 in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?
Ans:- Here, u = 5 m/s, v = 0, a = -10 m/s2
(i) Using, v = u + at
t = $\inline&space;\dpi{120}&space;\frac{v&space;-&space;u}{a}$ = $\inline&space;\dpi{120}&space;\frac{0&space;-&space;5}{-10}$ = $\inline&space;\dpi{120}&space;\frac{-5}{-10}$ = 0.5 s
(ii) Using 2aS = v2 – u2
⇒ 2 x (-10) x S = 02 – 52
⇒ -20 x S = -25
⇒ S = 1.25 m
### Chapter End Exercises
1. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?
Ans:-
Displacement after 3.5 rounds = diameter of the track = 200 m
2. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 50 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C? Ans:- (a) From A to B
(b) From A to C,
Total time taken = 2 min 50 s + 1 min = 150 s + 60 s = 210 s
Total distance = 300 + 100 = 400 m
Displacement = 300 – 100 = 200 m
3. Abdul, while driving to school, computes the average speed for his trip to be 20 km h-1. On his return trip along the same route, there is less traffic and the average speed is 40 km h-1. What is the average speed for Abdul’s trip?
Ans:- Let the school be at a distance of x km.
If t1 is time taken to reach the school, then
4. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m s-1 for 8.0 s. How far does the boat travel during this time?
Ans:- Here, u = 0, a = 3 m/s2, t = 8 s
Using, S = ut + ½ at2
⇒ S = 0 x 8 + ½ x 3 x 82
⇒ S = ½ x 3 x 64 = 96 m
So, boat travels a distance of 96 m.
5. A driver of a car travelling at 52 km h–1 applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 s. Another driver going at 3 km h–1 in another car applies his brakes slowly and stops in 10 s. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?
Ans:- For first car:
u = 52 km/h = 52 x 5/18 = 14.4 m/s,
v = 0 and t = 5 s
For second car:
u = 3 km/.h = 3 x 5/18 m/s = 0.8 m/s,
v = 0 and t = 10 s
The distance traveled by a moving body is given by the area under its speed-time graph.
So, distance traveled by the first car
= Area of the triangle AOB
= ½ x OB x AO
= ½ x 14.4 x 5 = 36 m
Similarly, Distance travelled by the second car
= Area of triangle COD
= ½ x OD x CO
= ½ x 0.83 x 10 = 4.1 m
So, the second car traveled farther after the brakes were applied.
6. Figure given below shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions?
(a) Which of the three is travelling the fastest?
(b) Are all three ever at the same point on the road?
(c) How far has C travelled when B passes A?
(d) How far has B travelled by the time it passes C?
Ans:-
(a) B is travelling fastest.
(b) As three lines do not meet at any point, the three objects never meet on the road.
(c) When B crosses A, then distance traveled by C = 9 – 2 = 7 km.
(d) By the time B passes C, it has travelled 5.5 km.
7. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s-2, with what velocity will it strike the ground? After what time will it strike the ground?
Ans:- Here, s = 20 m, u= 0, a = 10 m/s2
Using, s = ut + ½ at2
⇒ 20 = 0 x t + ½ x 10 x t2
⇒ 20 = 5t2
⇒ 4 = t2
⇒ t = 2 s
Usingt, v = u + at
⇒ v = 0 + 10 x 2 = 20 m/s
The ball strike the ground after 2 s with the velocity of 20 m s-1.
8. The speed-time graph for a car is shown in the figure:
(a) Find how far does the car travel in the first 4 seconds. Shade the
area on the graph that represents the distance travelled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?
Ans:- (a) The motion during first 4 seconds is not uniformly accelerated. So, distance travelled by car in first 4 seconds is calculated by graphical method.
Number of squares in shaded part of the graph = 61.5
One small square in x-axis represents, t = ⅖ sec
One small square on y-axis represents, v = ⅔ m/s
So, area of each square = v x t = ⅔ x ⅖ = 4/15 m
Total area = 61.5 x 4/15 = 16.4 m
Hence, distance traveled by the car = 16.4 m
(b) Therefore, portion of the graph almost after time t = 6 s describes the uniform motion of the car.
9. State which of the following situations are possible and give an example for each of these:
(a) an object with a constant acceleration but with zero velocity
(b) an object moving in a certain direction with an acceleration in the perpendicular direction.
Ans:- (a) It is possible. For example, when an object is thrown vertically upwards then at the maximum height, velocity becomes zero but acceleration due to gravity is constant
(b) It is possible. For ex, when a car is moving on a circular track, its acceleration is perpendicular to its direction.
10. An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.
Ans:- Radius of the orbit, r = 42250 km = 42250 x 1000 m
Time taken for one revolution = 24 hours = 24 × 60 × 60 s |
# betastat
Beta mean and variance
## Syntax
```[M,V] = betastat(A,B) ```
## Description
`[M,V] = betastat(A,B)`, with `A>0` and `B>0`, returns the mean of and variance for the beta distribution with parameters specified by `A` and `B`. `A` and `B` can be vectors, matrices, or multidimensional arrays that have the same size, which is also the size of `M` and `V`. A scalar input for `A` or `B` is expanded to a constant array with the same dimensions as the other input.
The mean of the beta distribution with parameters a and b is $a/\left(a+b\right)$ and the variance is
`$\frac{ab}{\left(a+b+1\right){\left(a+b\right)}^{2}}$`
## Examples
If parameters a and b are equal, the mean is 1/2.
```a = 1:6; [m,v] = betastat(a,a) m = 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 v = 0.0833 0.0500 0.0357 0.0278 0.0227 0.0192```
## Version History
Introduced before R2006a |
# Math Help - calculating probability of making the correct choice
1. ## calculating probability of making the correct choice
So an annoying question is floating around where four answers are given, asking the probability of picking the correct one, with the following answers provided:
a) 25%
b) 50%
c) 60%
d) 25%
I came up with a question to better visualize this and then I tried to solve that instead.
We have spheres of 3 colours. Red, Green and Blue.
There are 10 Red, 5 Green and 10 Blue spheres.
Assuming a colour is chosen at random, and then a sphere is chosen at random, what is the probability of picking the correct colour sphere?
The way I approach this is, we have a 1/3 chance of picking each colour and then either a 5/25 or 10/25 chance of picking the right sphere.
This gives me a probability of picking the right sphere 1/3 of the time. That does not make sense to me since there is a clear bias toward picking a Red or Green sphere. In fact, since the probabilities of picking a sphere always add up to one, changing the amount of spheres does not affect my answer at all. This further seems to indicate that my thought process is wrong. What is the correct way to approach this?
Help appreciated.
Thanks,
Chris
2. ## Re: calculating probability of making the correct choice
Originally Posted by ffezz
So an annoying question is floating around where four answers are given, asking the probability of picking the correct one, with the following answers provided:
a) 25%
b) 50%
c) 60%
d) 25%
I came up with a question to better visualize this and then I tried to solve that instead.
We have spheres of 3 colours. Red, Green and Blue.
There are 10 Red, 5 Green and 10 Blue spheres.
Assuming a colour is chosen at random, and then a sphere is chosen at random, what is the probability of picking the correct colour sphere?
The way I approach this is, we have a 1/3 chance of picking each colour and then either a 5/25 or 10/25 chance of picking the right sphere.
This gives me a probability of picking the right sphere 1/3 of the time. That does not make sense to me since there is a clear bias toward picking a Red or Green sphere. In fact, since the probabilities of picking a sphere always add up to one, changing the amount of spheres does not affect my answer at all. This further seems to indicate that my thought process is wrong. What is the correct way to approach this?
Help appreciated.
Thanks,
Chris
simplify it even further. Consider just two colors blue and yellow. As you said we select one of these randomly (1/2, 1/2)
Let there be N balls all together and Np of them are blue. The probability of selecting a blue ball is thus p, and selecting a yellow (1-p).
Given your setup the probability of selecting the correct color ball is $1/2p + 1/2(1-p) = 1/2, ~~ \forall p ~\ni~ 0 \leq p \leq 1$
At the extremes of p you have 50% chance of either making a certainly correct choice or a certainly incorrect choice.
3. ## Re: calculating probability of making the correct choice
Interesting Probability Sheet.xlsThis is quite interesting. So because we pick a sphere colour at random, our choice of picking a matching color sphere is the probability of each colour regardless of the actual distribution of spheres. If we have 998 red, 1 blue and 1 green, we still expect to pick the right sphere 1/3 times. Is there a theorem/law for this? There surely must be.
Ps. I just did a 1000 isntance test using excel, 9999998 reds, 1 blue and 1 green and the result concurred with this. Included is the excel sheet.
4. ## Re: calculating probability of making the correct choice
Originally Posted by ffezz
So an annoying question is floating around where four answers are given, asking the probability of picking the correct one, with the following answers provided:
a) 25%
b) 50%
c) 60%
d) 25%
I came up with a question to better visualize this and then I tried to solve that instead.
We have spheres of 3 colours. Red, Green and Blue.
There are 10 Red, 5 Green and 10 Blue spheres.
Assuming a colour is chosen at random, and then a sphere is chosen at random, what is the probability of picking the correct colour sphere?
The way I approach this is, we have a 1/3 chance of picking each colour and then either a 5/25 or 10/25 chance of picking the right sphere.
This gives me a probability of picking the right sphere 1/3 of the time. That does not make sense to me since there is a clear bias toward picking a Red or Green sphere. In fact, since the probabilities of picking a sphere always add up to one, changing the amount of spheres does not affect my answer at all. This further seems to indicate that my thought process is wrong. What is the correct way to approach this?
Help appreciated.
Thanks,
Chris
$P(red\ ball) = \dfrac{10}{25} = \dfrac{2}{5}.$
$P(green\ ball) = \dfrac{5}{25} = \dfrac{1}{5}.$
$P(blue\ ball) = \dfrac{10}{25} = \dfrac{2}{5}.$
$P(red) = P(green) = P(blue) = \dfrac{1}{3}.$
$P(ball\ chosen\ has\ same\ color\ as\ color\ chosen) =$
$P(red\ ball\ chosen\ and\ red\ chosen) + P(green\ ball\ chosen\ and\ green\ chosen) + P(blue\ ball\ chosen\ and\ blue\ chosen) =$
$\dfrac{2}{5} * \dfrac{1}{3} + \dfrac{1}{5} * \dfrac{1}{3} + \dfrac{2}{5} * \dfrac{1}{3} = \dfrac{1}{3} * \dfrac{2 + 1 + 2}{5} = \dfrac{1}{3}.$ |
# Math Help - binomial, hypothesis tests - hard one
1. ## binomial, hypothesis tests - hard one
I'm really having trouble with this question and its pretty long too. If anyone can help me figure out the answers, i would really appreciate it.
In a recent survey, 480 of 600 Canadians polled stated that they were dissatisfied with politicians. Of the remaining 120 who were polled, 75% were satisfied with politicians and 25% had no opinion. Assuming that these findings can be generalized to all Canadians.
A) In a random sample of 4 Canadians, what is the probability that no more than 1 would be satisfied with politicians?
B) If two random and independent samples of Canadian's were taken, one consisting of 20 people and the other of 25 people, what is the probability that more than 18 of the sample of 20 or that between 19 and 23 (inclusively) of the sample of 25 would state a definite opinion (for or against) about politicians?
C) Among people who initially have no opinion, 50% will typically form an opinion (for or against an issue) after reading a relevant news report. In an attempt to get more people to form an opinion and take one side or the other on political issues, a news service has developed a new approach to presenting information on the issues. It tried this out on a random sample of 20 people who initially claimed that they had no opinion about an issue. The news service will conclude that the new approach is more effective if at least 15 of these 20 report a definite opinion about the issue after reading about it. What is the probability that the news will conclude that the new approach is more effective even if it is in fact no better than previous methods?
D) In a second study, the news service tries out the new approach to presenting information on a random sample of 25 people who initially expressed no opinion about an issue. The news service will test the hypothesis that the new approach is more successful than previous methods in getting people to form an opinion using alpha < 0.03. Suppose that the new approach would actually cause 80% of initially no-opinion people to form a definite opinion. Given this, what is the probability that the news service will draw the correct conclusion based upon their second study.
a) 0.89
b) 0.8302
c) 0.021
d) 0.891
2. Originally Posted by swoopesjr01
I'm really having trouble with this question and its pretty long too. If anyone can help me figure out the answers, i would really appreciate it.
In a recent survey, 480 of 600 Canadians polled stated that they were dissatisfied with politicians. Of the remaining 120 who were polled, 75% were satisfied with politicians and 25% had no opinion. Assuming that these findings can be generalized to all Canadians.
A) In a random sample of 4 Canadians, what is the probability that no more than 1 would be satisfied with politicians?
There are to cases here:
1)All four are dissafisfied
2)Exaclty one is satisfied, i.e. exactly 3 are disatisfyeied.
The probability of 1 is binomial probability problem with $p=480/600=.8$
Thus,
${4 \choose 4}(.8)^4(.2)^0=.4096$
The probability of 2 is,
${4 \choose 3}(.8)^3(.2)^1=.4096$
Thus intotal we have,
$.8192$
3. Originally Posted by ThePerfectHacker
There are to cases here:
1)All four are dissafisfied
2)Exaclty one is satisfied, i.e. exactly 3 are disatisfyeied.
The probability of 1 is binomial probability problem with $p=480/600=.8$
Thus,
${4 \choose 4}(.8)^4(.2)^0=.4096$
The probability of 2 is,
${4 \choose 3}(.8)^3(.2)^1=.4096$
Thus intotal we have,
$.8192$
Here you need to use $p=(120\times 0.75)/600$ as the probability that
someone is satisfied and $q=1-p$ that they were dissatisfied
or expressed no opinion.
RonL |
# Manuals/calci/NEGBINOMDIST
NEGBINOMDIST(x,r,p)
• is the number of failures.
• is the number of successes on an individual trial
• is the probability of a success.
• NEGBINOMDIST(), returns the negative binomial distribution.
## Description
• This function gives the Negative Binomial Distribution.
• Negative Binomial Distribution is the discrete probability distribution with the fixed probability of success.
• It is also called Pascal Distribution.
This is the statistical experiment with the following conditions:
```This experiment consists of a sequence of independent trials.
Each trial represents only two results(Success or failure)
The probability of success is constant from trial to trial
The trials are independent; ie, the outcome on one trial does not affect the outcome on other trials.
The experiment continues until the successes is obtained, where is a specified positive integer.
```
• The random variable = the number of failures that precede the success;
• is called a Negative Binomial Random variable because, in contrast to the
binomial random variable, the number of successes is fixed and the number of trials is random.
• Then probability mass function of the negative binomial distribution is
• For example: If a fair coin is tossed repeatedly, what is the probability that at least 10 tosses are required.
• This function will give the result as error when:
1. Any argument is non-numeric
2. If or
3. If or
## ZOS
• The syntax is to calculate NEGBINOMDIST in ZOS is .
• where is the number of failures.
• is the number of successes on an individual trial
• is the probability of a success.
• For e.g.,NEGBINOMDIST(8..9,5..7,0.5).
Negative Binomial Distribution
## Examples
1. Find the probability that a man flipping a coin gets the fourth head on the ninth flip.
Here total number of events =9, r= 4(since we define Heads as a success) and x=9-4=5(number of failures)
```p=1/2=0.5(Probability of success for any coin flip)
```
NEGBINOMDIST(5,4,0.5)=0.109375
1. A company conducts a geological study that indicates that an exploratory goods well should have a 20% chance of striking goods. What is the probability that the first strike comes on the third well drilled?
Here total number of events=3, r=1,x=3-1=2,and p=0.20 NEGBINOMDIST(2,1,0.20)=0.128
1. What is the probability that the fourth strike comes on the eighth well drilled?
Here total number of events=8, r=4, x=8-4=4 and p=0.20 NEGBINOMDIST(4,4,0.20)=0.0229376
## Related Videos
Negative Binomial Distribution |
# A question about almost sure converges.
If we know $X_n \rightarrow_p Y$ and $X_n \rightarrow Z\space a.s.$ can we say that $P(Y=Z)=1$
-
Yes. Because $\forall \epsilon > 0$ $$P(|Y-Z| > \epsilon) = P(|Y-X_n + X_n - Z| > \epsilon)$$ $$\leq P(|X_n-Z|+|X_n - Y| > \epsilon)$$ $$\leq P(|X_n-Z| > \epsilon/2) + P(|X_n-Y|>\epsilon/2) \quad (*)$$ Take limits an $n\rightarrow \infty$ to get $$P(|Y-Z| > \epsilon)= 0 \quad \forall \epsilon > 0$$
This implies $P(|Y-Z| = 0) = 1$.
Proof of $(*)$ $$P(|X_n-Z|+|X_n - Y| > \epsilon) = P(|X_n-Z|+|X_n - Y| > \epsilon, |X_n -Y| > \epsilon/2) + P(|X_n-Z|+|X_n - Y| > \epsilon,|X_n -Y| \leq \epsilon/2)$$ $$\leq P(|X_n-Y|>\epsilon/2) + P(|X_n-Z| > \epsilon/2)$$ The last step follows as : $a+b >c, b< c/2 \Rightarrow a> c/2$.
-
Thanks! SO, can we say Y=Z a.s.? – BigMike Dec 8 '12 at 7:44
Yes. Thats what $P(|Y-Z| = 0) = 1$ implies. – Gautam Shenoy Dec 8 '12 at 7:46
Additionally, if that epsilon logic is bothering you, you can replace it with $1/m$ and argue with that also. – Gautam Shenoy Dec 8 '12 at 7:48
Also, here we basically use the fact that $X\rightarrow Y\space a.s.$ implies $X \rightarrow_p Y$ correct? – BigMike Dec 8 '12 at 7:52
Exactly. Convergence in almost sure implies convergence in probability. – Gautam Shenoy Dec 8 '12 at 8:37 |
# Strict inequalities in LP
How should we deal with strict inequalities in a linear programming problem? For example:
inequalities such as $ax< b$;
-
Add a tolerance, $\epsilon>0$ and try solving with $ax \leq b-\epsilon$. – copper.hat Jul 20 '12 at 7:57
@copper.hat Does tha apply to answer below? – BCLC Mar 3 at 3:40
@BCLC: In general, there will be no solution if the inequality is strict. So, what you do depends on what you want. The $\epsilon$ trick will work, but if the constraint is active, then the solution will not necessarily be optimal for the original problem. – copper.hat Mar 3 at 4:07
In general strict inequalities are not treated in linear programming problems, since the solution is not guaranteed to exist on corner points.
Consider the $1$-variable LPP: $Max$ $x$ subject to $x<3$. Now there does not exist any value of $x$ for which maximum is achieved and which lies in the feasible region.
-
1. Linear programs are not necessarily about optimization, they can also be about feasibility. 2. Replacing ‘$\max$’ with ‘$\sup$’ evades the technical issue you point out. – equaeghe Jul 16 '13 at 14:30
$x \le 3 - \epsilon$ ? – BCLC Mar 3 at 3:39 |
# Math Help - Characters: The usual suspects
1. ## Characters: The usual suspects
My group theory text (and other sources) say that the character of a n operator in a representation is the trace of the matrix corresponding to the operator. ie. Given a group operator $\Gamma$ in some representation we have $X = Tr( \Gamma )$.
But
My newest text says a function (in a space) ca be expanded into a sum/integral of characters $X = e^{i x \cdot \xi}$
$f(x) = \sum b_{\xi} e^{ix \cdot \xi}$
$f(x) = \int b( \xi ) e^{ix \cdot \xi}~d \xi$
(To put this into context the section is talking about inverse Fourier transforms and that the inverse FT diagonalizes the representation for f.)
Are these two character definitions related to each other in some way? Or are they representing (no pun intended) different concepts? My text, at least, uses the same symbol for both.
Thanks!
-Dan
2. Sorry, I do not understand what you said . But I can answer the question "are these charachter definitions the same". They do not have to do. I can give you two other references of the word charachter. In number theory a (Dirichlet) charachter is a homomorphism from the finite field to the complex numbers. In linear algebra it means: Let F be a field and G be a group, let f(G,F) be the set of all functions from G to F; a charachter in f(G,F) is a group homomorphism between G and F*. So it is very common in math to use the same word to represent a lot of different stuff.
3. Originally Posted by ThePerfectHacker
Sorry, I do not understand what you said . But I can answer the question "are these charachter definitions the same". They do not have to do. I can give you two other references of the word charachter. In number theory a (Dirichlet) charachter is a homomorphism from the finite field to the complex numbers. In linear algebra it means: Let F be a field and G be a group, let f(G,F) be the set of all functions from G to F; a charachter in f(G,F) is a group homomorphism between G and F*. So it is very common in math to use the same word to represent a lot of different stuff.
I was wondering if that might be the case. However since the book talks about both and uses the same symbol for them I suspect they are equivalent in some sense.
I'll be back later and post more of the text's inverse Fourier (actually Plancherel) transform. (As well as the source information in case that might help.)
-Dan
4. The connection here is that the irreducible unitary representations of the additive group of real numbers are all one-dimensional, and are given by $x\mapsto e^{ix\xi}\ (x\in\mathbb{R})$, where $\xi\in\mathbb{R}$. The trace of a one-dimensional representation is just its range. So the Fourier transform of a function on $\mathbb{R}$ is a weighted integral of the representation-theoretic characters of $\mathbb{R}$.
Edit. If it's a Fourier transform of a function of several variables then exactly the same thing holds, provided that $\mathbb{R}$ is replaced by $\mathbb{R}^n$ wherever it occurs, and the product $x\xi$ is replaced by a dot product $x.\xi$
5. Originally Posted by Opalg
The connection here is that the irreducible unitary representations of the additive group of real numbers are all one-dimensional, and are given by $x\mapsto e^{ix\xi}\ (x\in\mathbb{R})$, where $\xi\in\mathbb{R}$. The trace of a one-dimensional representation is just its range. So the Fourier transform of a function on $\mathbb{R}$ is a weighted integral of the representation-theoretic characters of $\mathbb{R}$.
Edit. If it's a Fourier transform of a function of several variables then exactly the same thing holds, provided that $\mathbb{R}$ is replaced by $\mathbb{R}^n$ wherever it occurs, and the product $x\xi$ is replaced by a dot product $x.\xi$
Okay, after a bit of effort I can make sense of this. However I still have a problem.
The text says:
Any function (in a suitable space) can be expanded into the direct sum/integral of characters $\chi = e^{ix \cdot \xi}$
$f(x) = \sum b_{\xi}e^{ix \cdot \xi}$ or $f(x) = \int b(\xi) e^{i x \cdot \xi} d \xi$
(Apologies, I mistyped this in my original post.)
Since the function f(x) does not need to take x into the space of complex numbers, how does this work? I should mention that I can understand the integral since the book specifies that the group under consideration is $\mathbb{R}^n, \mathbb{T}^n$. But no such specification was made for the discrete case. Is that what is meant by "in a suitable space?"
Thanks!
-Dan
6. Short of giving a whole lecture course on harmonic analysis, I can only scratch the surface of this topic.
The basic fact is that if G is any locally compact abelian group, the space of characters on G can also be made into a locally compact abelian group, called the dual group of G and usually denoted by $\hat{G}$. The dual of the circle group $\mathbb{T}$ is $\mathbb{Z}$, the group of integers. The dual of the real numbers is again the real numbers. The dual of $\mathbb{T}^n$ is $\mathbb{Z}^n$ and the dual of $\mathbb{R}^n$ is $\mathbb{R}^n$. In general, the dual of a compact group is a discrete group.
Every locally compact abelian group has an integral (called the Haar integral) associated with it, and every real- or complex-valued integrable function on the group has a "generalised Fourier transform." This is a continuous function on the dual group, defined by $\hat{f}(\xi) = \int_Gf(x)\xi(x)\,dx$, where $\xi(x)$ denotes the value of the character ξ at the element x of the group.
Since the dual group is also locally compact, it has its own dual, which turns out to be isomorphic to the original group (that's the Pontyagin duality theorem). There is a "Fourier inversion theorem" which says that, for a suitable class of functions, there is an inverse transform that reconstructs a function f on G from its Fourier transform $\hat{f}$ on the dual group.
7. Originally Posted by Opalg
Short of giving a whole lecture course on harmonic analysis, I can only scratch the surface of this topic.
The basic fact is that if G is any locally compact abelian group, the space of characters on G can also be made into a locally compact abelian group, called the dual group of G and usually denoted by $\hat{G}$. The dual of the circle group $\mathbb{T}$ is $\mathbb{Z}$, the group of integers. The dual of the real numbers is again the real numbers. The dual of $\mathbb{T}^n$ is $\mathbb{Z}^n$ and the dual of $\mathbb{R}^n$ is $\mathbb{R}^n$. In general, the dual of a compact group is a discrete group.
Every locally compact abelian group has an integral (called the Haar integral) associated with it, and every real- or complex-valued integrable function on the group has a "generalised Fourier transform." This is a continuous function on the dual group, defined by $\hat{f}(\xi) = \int_Gf(x)\xi(x)\,dx$, where $\xi(x)$ denotes the value of the character ξ at the element x of the group.
Since the dual group is also locally compact, it has its own dual, which turns out to be isomorphic to the original group (that's the Pontyagin duality theorem). There is a "Fourier inversion theorem" which says that, for a suitable class of functions, there is an inverse transform that reconstructs a function f on G from its Fourier transform $\hat{f}$ on the dual group.
(chuckles) Well, that's what I'm studying, so I guess I'll just have to keep at it until it gels a bit more.
Thanks again!
-Dan
8. Originally Posted by Opalg
(that's the Pontyagin duality theorem).
I been curious to look it up, but I got no results using that, it seems it should have been this. Interesting, did you know this guy was a blind mathematician? It is an excellent story, because he made (according to Wikipedia) contributions to geometry. This illustrates the power of math, one does not even have to see what he is doing, even in geometry (though seeing what one is doing only adds to the beauty).
9. Originally Posted by Opalg
Short of giving a whole lecture course on harmonic analysis, I can only scratch the surface of this topic.
Would you be explain to me, in elementary terms, what exactly is harmonic analysis?
I have heard answers from people which say it is a more generalized concept of Fourier series.
I can see that, for example, in a Sturm-Liouville problem the eigenfunctions are orthogonal.
And furthermore, we can expand a function into a series involving these eigenfunctions.
So that is what harmonic analysis is about? Dealing with a series of eigenfunctions?
Or is there more to it that I am missing?
10. Originally Posted by ThePerfectHacker
Would you be explain to me, in elementary terms, what exactly is harmonic analysis?
Harmonic analysis - Wikipedia, the free encyclopedia
The difficulty here is that harmonic analysis is not elementary, so it's hard to give an elementary explanation of it. I think of it as the extension of the ideas and techniques of Fourier theory from the groups R and Z to a wider class of groups such as Lie groups.
11. Originally Posted by Opalg
Harmonic analysis - Wikipedia, the free encyclopedia
The difficulty here is that harmonic analysis is not elementary, so it's hard to give an elementary explanation of it. I think of it as the extension of the ideas and techniques of Fourier theory from the groups R and Z to a wider class of groups such as Lie groups.
That's actually my problem. I have this new book about symmetries and Lagrangians and harmonic analysis and I thought "Hey! That'll be a good one to have in my bag of tricks." It's a much higher level book than I had thought and it's pulling in everything from group theory, algebra, topology, and tensor geometry. I've emptied half of my library (no joke) just trying to make sure I've got a good hold on the terms. It IS a good topic for me to learn but boy did I underestimate the task.... Hey, I need a good challenge from time to time.
-Dan |
, 04.02.2020 18:43, briarwilliams9668
# Can anyone me with this? the equation below shows the decomposition of lead nitrate. how many grams of oxygen are produced when 23.0 g no2 is formed? 2pb(no3)2(s) _ 2pbo(s) + 4no2(g) + o2 (g
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## SectionComparing Linear Functions
### SubsectionUsing Ratios for Comparison
Which is more expensive, a 64-ounce bottle of Velvolux dish soap that costs $3.52, or a 60-ounce bottle of Rainfresh dish soap that costs$3.36?
You are probably familiar with the notion of comparison shopping. To decide which dish soap is the better buy, we compute the unit price, or price per ounce, for each bottle. The unit price for Velvolux is
\begin{equation*} \frac{352 \text{ cents}}{64 \text{ ounces}}= 5.5 \text{ cents per ounce} \end{equation*}
and the unit price for Rainfresh is
\begin{equation*} \frac{336 \text{ cents}}{60 \text{ ounces}}= 5.6 \text{ cents per ounce} \end{equation*}
The Velvolux costs less per ounce, so it is the better buy. By computing the price of each brand for the same amount of soap, it is easy to compare them.
In many situations, a ratio, similar to a unit price, can provide a basis for comparison. Example100 uses a ratio to measure a rate of growth.
###### Example100
Which grow faster, Hybrid A wheat seedlings, which grow 11.2 centimeters in 14 days, or Hybrid B seedlings, which grow 13.5 centimeters in 18 days?
Solution
We compute the growth rate for each strain of wheat. Growth rate is expressed as a ratio, $\dfrac{\text{centimeters}}{\text{days}}\text{,}$ or centimeters per day. The growth rate for Hybrid A is
\begin{equation*} \frac{11.2 \text{ centimeters}}{14 \text{ days}}= 0.8 \text{ centimeters per day} \end{equation*}
and the growth rate for Hybrid B is
\begin{equation*} \frac{13.5 \text{ centimeters}}{18 \text{ days}}= 0.75 \text{ centimeters per day} \end{equation*}
Because their rate of growth is larger, the Hybrid A seedlings grow faster.
By computing the growth of each strain of wheat seedling over the same unit of time, a single day, we have a basis for comparison. In this case, the ratio $\dfrac{\text{centimeters}}{\text{day}}$ measures the rate of growth of the wheat seedlings.
###### Example101
Delbert traveled $258$ miles on $12$ gallons of gas, and Francine traveled $182$ miles on $8$ gallons of gas. Compute the ratio $\dfrac{\text{miles}}{\text{gallon}}$ for each car. Whose car gets the better gas mileage?
Solution
Delbert's gas mileage was
\begin{equation*} \dfrac{258\text{ miles}}{12\text{ gallons}}=21.5\text{ mpg} \end{equation*}
and Francine's was
\begin{equation*} \dfrac{182\text{ miles}}{8\text{ gallons}}=11.75\text{ mpg} \end{equation*}
Francine gets better mile
In Example101, the ratio $\dfrac{\text{miles}}{\text{gallon}}$ measures the rate at which each car uses gasoline. By computing the mileage for each car for the same amount of gas, we have a basis for comparison. We can use this same idea, finding a common basis for comparison, to measure the steepness of an incline.
### SubsectionSome Properties of Lines
For any constant $k\text{:}$
• The graph of the equation $y=k$ is a horizontal line through $(0,k)$ and its slope is zero.
• The graph of the equation $x=k$ is a vertical line through $(k,0)$ and its slope is undefined.
You may have a hard time remembering which is horizontal and which is vertical. One thing that can help is to remember that if $y=3\text{,}$ then $x$ can be whatever value it wants, but the value for $y$ is fixed at 3. So, though we can range over all possible $x$ values, $y$ is always three, which is why we have a horizontal line. You can come up with a similar statement for the case when $x=3$ to explain why this must be a vertical line.
Another important property that lines can have is how two lines intersect. We have two special cases that we address first lines that are perpendicular and lines that are parallel. Recall, from your last algebra class that:
Let $l_1: y = m_1x + b_1$ and $l_2: y = m_2x + b_2$ be two lines. Then, we say that
• $l_1$ and $l_2$ are parallel if $m_1 = m_2$ and $b_1\neq b_2.$
• $l_1$ and $l_2$ are perpendicular if $m_1 = \frac{-1}{m_2}$ (negative reciprocal).
Note that for two lines to parallel, they must have different $y$-intercepts, otherwise they are the same line.
###### Example102
Find the equation of a line passing through the point $(4,-1)$ and parallel to the line $y=3x+2$
Solution
Since the two lines are parallel we know that the slope of the new line must be the same as the slope of the original line. That is $m_1=3=m_2\text{.}$ We can now use point slope form $y-(-1)=3(x-4)\text{.}$ At this point we have the equation of a line. However, most people are more comfortable writing lines in slope-intercept form so we will do that here: $y=3x-13\text{.}$
###### Example103
Find the equation of a line passing through the point $(4,-1)$ and perpendicular to the line $y=3x+2$
Solution
Since the two lines are perpendicular we know that the slope of the new line must be the opposite reciprocal of the slope of the original line. Since $m_1=3\text{,}$ $m_2=-\frac{1}{3}\text{.}$ We can now use point slope form $y-(-1)=-\frac{1}{3}(x-4)\text{.}$ At this point we have the equation of a line. In slope-interept form, we have $y=-\frac{1}{3}x-\frac{7}{3}\text{.}$
In addition to finding the equation for parallel and perpendicular lines, it is often useful to be able to describe the point at which two lines intersect. One way to find where two lines intersect is to first put the lines in slope intercept form and then set the two equations equal to each other.
###### Example104
Find the point where the lines $y=2x+4$ and $y=-x+3$ intersect.
Solution
Since both of these equations are solved for $y\text{,}$ we can set them equal to each other and then solve for $x\text{:}$
\begin{equation*} \begin{aligned} 2x+4 \amp= -x+3 \\ 3x+4 \amp= 3 \\ 3x \amp= -1 \\ x\amp= -\frac{1}{3} \end{aligned} \end{equation*}
To find the $y$-coordinate, we can substitute $x$ into either of the original equations: $y=2\left(-\frac{1}{3}\right)+4=\frac{10}{3}\text{.}$ Therefore the two lines intersect at the point $\left(-\frac{1}{3},\frac{10}{3}\right)\text{.}$
###### Example105
Renting a truck through Quick Rentals will cost you a fixed rate of 15 dollars plus 25 cents per mile. Renting a truck through Handy Trucks runs 25 dollars plus 15 cents per mile. If you were planning to rent a truck, how many miles would you need to drive in order for Handy Trucks to be a better deal?
Solution
We first need to recognize that we have two linear equations $y=0.25x+15$ and $y=0.15x+25\text{.}$ If we plug one mile into both equations we can see that Quick Rentals is much cheaper if you are only driving a mile. In order to find where Handy Trucks is cheaper it makes sense to try finding the point where both companies cost the same amount. In order to do this we find the intersection between the two lines.
\begin{gather} 0.25x+15=0.15+25\tag{1}\\ 0.10x=10\tag{2}\\ x=100\tag{3} \end{gather}
Therefore, as long as you are driving more than 100 miles, ($x >100$) we know that Handy Trucks is the better deal.
If you would like to review different strategies for finding where two lines intersect, refer to the Systems of Linear Equations Section from Intermediate Algebra. |
In mathematics, more specifically ring theory, the Jacobson radical of a ring ${\displaystyle R}$ is the ideal consisting of those elements in ${\displaystyle R}$ that annihilate all simple right ${\displaystyle R}$-modules. It happens that substituting "left" in place of "right" in the definition yields the same ideal, and so the notion is left-right symmetric. The Jacobson radical of a ring is frequently denoted by ${\displaystyle J(R)}$ or ${\displaystyle rad(R)}$; the former notation will be preferred in this article, because it avoids confusion with other radicals of a ring. The Jacobson radical is named after Nathan Jacobson, who was the first to study it for arbitrary rings in (Jacobson 1945).
The Jacobson radical of a ring has numerous internal characterizations, including a few definitions that successfully extend the notion to rings without unity. The radical of a module extends the definition of the Jacobson radical to include modules. The Jacobson radical plays a prominent role in many ring and module theoretic results, such as Nakayama's lemma.
## Definitions
There are multiple equivalent definitions and characterizations of the Jacobson radical, but it is useful to consider the definitions based on if the ring is commutative or not.
### Commutative case
In the commutative case, the Jacobson radical of a commutative ring ${\displaystyle R}$ is defined as[1] the intersection of all maximal ideals ${\displaystyle {\mathfrak {m}}}$ . If we denoted ${\displaystyle {\text{Specm}}(R)}$ as the set of all maximal ideals in ${\displaystyle R}$ then
${\displaystyle J(R)=\bigcap _{{\mathfrak {m}}\in {\text{Specm}}(R)}{\mathfrak {m}}}$
This definition can be used for explicit calculations in a number of simple cases, such as for local rings ${\displaystyle (R,{\mathfrak {p}})}$ , which have a unique maximal ideal, Artin rings, and products thereof. See the examples section for explicit computations.
### Noncommutative/general case
For a general ring with unit ${\displaystyle R}$ , the Jacobson radical ${\displaystyle J(R)}$ is defined as the ideal of all elements ${\displaystyle r\in R}$ such that ${\displaystyle rM=0}$ whenever ${\displaystyle M}$ is a simple module. That is,
${\displaystyle J(R)=\{r\in R\ \,|\ \,rM=0{\text{ where }}M{\text{ is simple}}\}.}$
This is equivalent to the definition in the commutative case for a commutative ring ${\displaystyle R}$ because the simple modules over a commutative ring are of the form ${\displaystyle R/{\mathfrak {m}}}$ for some maximal ideal ${\displaystyle {\mathfrak {m}}\in {\text{Specm}}(R)}$ , and the only annihilators of ${\displaystyle R/{\mathfrak {m}}}$ in ${\displaystyle R}$ are in ${\displaystyle {\mathfrak {m}}}$ , i.e. ${\displaystyle {\text{Ann}}_{R}(R/{\mathfrak {m}})={\mathfrak {m}}}$ .
## Motivation
Understanding the Jacobson radical lies in a few different cases: namely its applications and the resulting geometric interpretations, and its algebraic interpretations.
### Geometric applications
Although Jacobson originally introduced his radical as a technique for build a theory of radicals for arbitrary rings, one of the motivating reasons for why the Jacobson radical is considered in the commutative case is because of Nakayama's lemma. It is a technical tool for studying finitely generated modules over commutative rings which has an easy geometric interpretation: If we have a vector bundle ${\displaystyle E\to X}$ over a topological space ${\displaystyle X}$ , and pick a point ${\displaystyle p\in X}$ , then any basis of ${\displaystyle E|_{p}}$ can be extended to a basis of sections of ${\displaystyle E|_{U}\to U}$ for some neighborhood ${\displaystyle p\in U\subset X}$ .
Another application is in the case of finitely generated commutative rings, meaning ${\displaystyle R}$ is of the form
${\displaystyle R={\frac {k[x_{1},\ldots ,x_{n}]}{I}}}$
for some base ring ${\displaystyle k}$ (such as a field, or the ring of integers). In this case the nilradical and the Jacobson radical coincide. This means we could interpret the Jacobson radical as a measure for how far the ideal ${\displaystyle I}$ defining the ring ${\displaystyle R}$ is from defining the ring of functions on an algebraic variety because of the Hilbert Nullstellensatz theorem. This is because algebraic varieties cannot have a ring of functions with infinitesimals: this is a structure which is only considered in scheme theory.
### Equivalent characterizations
The Jacobson radical of a ring has various internal and external characterizations. The following equivalences appear in many noncommutative algebra texts such as (Anderson 1992, §15), (Isaacs 1994, §13B), and (Lam 2001, Ch 2).
The following are equivalent characterizations of the Jacobson radical in rings with unity (characterizations for rings without unity are given immediately afterward):
• ${\displaystyle J(R)}$ equals the intersection of all maximal right ideals of the ring. The equivalence coming from the fact that for all maximal right ideals M, R/M is a simple right R-module, and that in fact all simple right R-modules are isomorphic to one of this type via the map from R to S given by rxr for any generator x of S. It is also true that ${\displaystyle J(R)}$ equals the intersection of all maximal left ideals within the ring.[2] These characterizations are internal to the ring, since one only needs to find the maximal right ideals of the ring. For example, if a ring is local, and has a unique maximal right ideal, then this unique maximal right ideal is exactly ${\displaystyle J(R)}$ . Maximal ideals are in a sense easier to look for than annihilators of modules. This characterization is deficient, however, because it does not prove useful when working computationally with ${\displaystyle J(R)}$ . The left-right symmetry of these two definitions is remarkable and has various interesting consequences.[2][3] This symmetry stands in contrast to the lack of symmetry in the socles of R, for it may happen that soc(RR) is not equal to soc(RR). If R is a non-commutative ring, ${\displaystyle J(R)}$ is not necessarily equal to the intersection of all maximal two-sided ideals of R. For instance, if V is a countable direct sum of copies of a field k and R = End(V) (the ring of endomorphisms of V as a k-module), then ${\displaystyle J(R)=0}$ because ${\displaystyle R}$ is known to be von Neumann regular, but there is exactly one maximal double-sided ideal in R consisting of endomorphisms with finite-dimensional image. (Lam 2001, p. 46, Ex. 3.15)
• ${\displaystyle J(R)}$ equals the sum of all superfluous right ideals (or symmetrically, the sum of all superfluous left ideals) of R. Comparing this with the previous definition, the sum of superfluous right ideals equals the intersection of maximal right ideals. This phenomenon is reflected dually for the right socle of R; soc(RR) is both the sum of minimal right ideals and the intersection of essential right ideals. In fact, these two relationships hold for the radicals and socles of modules in general.
• As defined in the introduction, ${\displaystyle J(R)}$ equals the intersection of all annihilators of simple right R-modules, however it is also true that it is the intersection of annihilators of simple left modules. An ideal that is the annihilator of a simple module is known as a primitive ideal, and so a reformulation of this states that the Jacobson radical is the intersection of all primitive ideals. This characterization is useful when studying modules over rings. For instance, if U is a right R-module, and V is a maximal submodule of U, U·J(R) is contained in V, where U·J(R) denotes all products of elements of J(R) (the "scalars") with elements in U, on the right. This follows from the fact that the quotient module U/V is simple and hence annihilated by J(R).
• J(R) is the unique right ideal of R maximal with the property that every element is right quasiregular[4][5] (or equivalently left quasiregular[2]). This characterization of the Jacobson radical is useful both computationally and in aiding intuition. Furthermore, this characterization is useful in studying modules over a ring. Nakayama's lemma is perhaps the most well-known instance of this. Although every element of the J(R) is necessarily quasiregular, not every quasiregular element is necessarily a member of J(R).[5]
• While not every quasiregular element is in ${\displaystyle J(R)}$ , it can be shown that y is in ${\displaystyle J(R)}$ if and only if xy is left quasiregular for all x in R. (Lam 2001, p. 50)
• ${\displaystyle J(R)}$ is the set of elements xR such that every element of 1 + RxR is a unit: ${\displaystyle \operatorname {J} (R)=\{x\in R\mid 1+RxR\subset R^{\times }\}}$ . In fact, ${\displaystyle y\in R}$ is in the Jacobson radical if and only if 1 + xy is invertible for any ${\displaystyle x\in R}$ , if and only if 1+ yx is invertible for any ${\displaystyle x\in R}$ . This means xy and yx behave similarly to a nilpotent element z with zn+1 = 0 and ${\displaystyle (1+z)^{-1}=1-z+z^{2}-\cdots \pm z^{n}}$ .
For rings without unity it is possible for R = J(R); however, the equation J(R/J(R)) = {0} still holds. The following are equivalent characterizations of J(R) for rings without unity (Lam 2001, p. 63):
• The notion of left quasiregularity can be generalized in the following way. Call an element a in R left generalized quasiregular if there exists c in R such that c+a-ca = 0. Then J(R) consists of every element a for which ra is left generalized quasiregular for all r in R. It can be checked that this definition coincides with the previous quasiregular definition for rings with unity.
• For a ring without unity, the definition of a left simple module M is amended by adding the condition that R•M ≠ 0. With this understanding, J(R) may be defined as the intersection of all annihilators of simple left R modules, or just R if there are no simple left R modules. Rings without unity with no simple modules do exist, in which case R = J(R), and the ring is called a radical ring. By using the generalized quasiregular characterization of the radical, it is clear that if one finds a ring with J(R) nonzero, then J(R) is a radical ring when considered as a ring without unity.
## Examples
### Commutative examples
• For the ring of integers ${\displaystyle \mathbb {Z} }$ its Jacobson radical is the zero ideal, so ${\displaystyle J(\mathbb {Z} )=(0)}$ , because it is given by the intersection of every ideal generated by a prime number ${\displaystyle (p)}$ . Since ${\displaystyle (p_{1})\cap (p_{2})=(p_{1}\cdot p_{2})}$ , and we are taking an infinite intersection which no common elements besides ${\displaystyle 0}$ between all maximal ideals, we have the computation.
• For a local ring ${\displaystyle (R,{\mathfrak {p}})}$ the Jacobson radical is simply ${\displaystyle J(R)={\mathfrak {p}}}$ . This is an important case because of its use in applying Nakayama's lemma. In particular, it implies if we have an algebraic vector bundle ${\displaystyle E\to X}$ over a scheme or algebraic variety ${\displaystyle X}$ , and we fix a basis of ${\displaystyle E|_{p}}$ for some point ${\displaystyle p\in X}$ , then this basis lifts to a set of generators for all sections ${\displaystyle E|_{U}\to U}$ for some neighborhood ${\displaystyle U}$ of ${\displaystyle p}$ .
• If ${\displaystyle k}$ is a field and ${\displaystyle R=k[[X_{1},...,X_{n}]]}$ is a ring of formal power series, then ${\displaystyle J(R)}$ consists of those power series whose constant term is zero, i.e. the power series in the ideal ${\displaystyle (X_{1},\ldots ,X_{n})}$ .
• In the case of an Artin ring, such as ${\displaystyle \mathbb {C} [t_{1},t_{2}]/(t_{1}^{4},t_{1}^{2}t_{2}^{2},t_{2}^{9})}$ , the Jacobson radical is ${\displaystyle (t_{1},t_{2})}$ .
• The previous example could be extended to the ring ${\displaystyle R=\mathbb {C} [t_{2},t_{3},\ldots ]/(t_{2}^{2},t_{3}^{3},\ldots )}$ , giving ${\displaystyle J(R)=(t_{2},t_{3},\ldots )}$ .
• The Jacobson radical of the ring Z/12Z is 6Z/12Z, which is the intersection of the maximal ideals 2Z/12Z and 3Z/12Z.
• Consider the ring ${\displaystyle \mathbb {C} [t]\otimes _{\mathbb {C} }\mathbb {C} [x_{1},x_{2}]_{x_{1}^{2}+x_{2}^{2}-1}}$ where the second is the localization of ${\displaystyle \mathbb {C} [x_{1},x_{2}]}$ by the prime ideal ${\displaystyle {\mathfrak {p}}=(x_{1}^{2}+x_{2}^{2}-1)}$ . Then, the Jacobson radical is trivial because the maximal ideals are generated by an element of the form ${\displaystyle (t-z)\otimes (x_{1}^{2}+x_{2}^{2}-1)}$ for ${\displaystyle z\in \mathbb {C} }$ .
### Noncommutative examples
• Rings for which J(R) is {0} are called semiprimitive rings, or sometimes "Jacobson semisimple rings". The Jacobson radical of any field, any von Neumann regular ring and any left or right primitive ring is {0}. The Jacobson radical of the integers is {0}.
• If K is a field and R is the ring of all upper triangular n-by-n matrices with entries in K, then J(R) consists of all upper triangular matrices with zeros on the main diagonal.
• Start with a finite, acyclic quiver Γ and a field K and consider the quiver algebra K Γ (as described in the Quiver article). The Jacobson radical of this ring is generated by all the paths in Γ of length ≥ 1.
• The Jacobson radical of a C*-algebra is {0}. This follows from the Gelfand–Naimark theorem and the fact that for a C*-algebra, a topologically irreducible *-representation on a Hilbert space is algebraically irreducible, so that its kernel is a primitive ideal in the purely algebraic sense (see spectrum of a C*-algebra).
## Properties
J(R / I) = J(R) / I.[6]
This can actually be made stronger: If
${\displaystyle \left\{0\right\}=T_{0}\subseteq T_{1}\subseteq \dotsb \subseteq T_{k}=R}$
is a composition series for the right R-module R (such a series is sure to exist if R is right artinian, and there is a similar left composition series if R is left artinian), then
${\displaystyle \left(J\left(R\right)\right)^{k}=0}$ .
(Proof: Since the factors ${\displaystyle T_{u}/T_{u-1}}$ are simple right R-modules, right multiplication by any element of J(R) annihilates these factors.
In other words,
${\displaystyle \left(T_{u}/T_{u-1}\right)\cdot J\left(R\right)=0}$ ,
whence
${\displaystyle T_{u}\cdot J\left(R\right)\subseteq T_{u-1}}$ .
Consequently, induction over i shows that all nonnegative integers i and u (for which the following makes sense) satisfy
${\displaystyle T_{u}\cdot \left(\operatorname {J} \left(R\right)\right)^{i}\subseteq T_{u-i}}$ .
Applying this to u = i = k yields the result.)
Note, however, that in general the Jacobson radical need not consist of only the nilpotent elements of the ring.
• If R is commutative and finitely generated as an algebra over either a field or Z, then J(R) is equal to the nilradical of R.
• The Jacobson radical of a (unital) ring is its largest superfluous right (equivalently, left) ideal. |
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Get Full Access to Elementary Statistics - 12 Edition - Chapter 4.4 - Problem 15bsc
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# Answer: Pre-Employment Drug Screening. In Exercise, use
ISBN: 9780321836960 18
## Solution for problem 15BSC Chapter 4.4
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Problem 15BSC
Pre-Employment Drug Screening. In Exercises 13–16, use the test results summarized in Table 41, reproduced here. Consider an event to be “unlikely” if its probability is 0.05 or less.
Pre-Employment Drug Screening If 3 of the 1000 test subjects are randomly selected, find the probability that they all had correct test results (either true positive or true negative). Is such an event unlikely?
a. Assume that the 3 selections are made with replacement.
b. Assume that the 3 selections are made without replacement.
Step-by-Step Solution:
Step 1 of 3
Solution 15BSC
=0.739
Step 2 of 3
Step 3 of 3
##### ISBN: 9780321836960
The answer to “?Pre-Employment Drug Screening. In Exercises 13–16, use the test results summarized in Table 41, reproduced here. Consider an event to be “unlikely” if its probability is 0.05 or less. Pre-Employment Drug Screening If 3 of the 1000 test subjects are randomly selected, find the probability that they all had correct test results (either true positive or true negative). Is such an event unlikely?a. Assume that the 3 selections are made with replacement.b. Assume that the 3 selections are made without replacement.” is broken down into a number of easy to follow steps, and 81 words. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. Since the solution to 15BSC from 4.4 chapter was answered, more than 458 students have viewed the full step-by-step answer. This full solution covers the following key subjects: test, employment, true, assume, drug. This expansive textbook survival guide covers 121 chapters, and 3629 solutions. The full step-by-step solution to problem: 15BSC from chapter: 4.4 was answered by , our top Statistics solution expert on 03/15/17, 10:30PM. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12.
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### Mathematics Class XI
Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability
# Sample Space and Event
Sample Space:
The sample space of an experiment is the set of all possible outcomes of the experiment.
Example:
Toss a Coin twice. The possible outcome are where head and tail. Then the sample space
An element of the sample space is called an Elementary event.
Event:
A subset of a sample space (of an experiment) is called an event. An event is said to occur if an element of the event occurs.
Remark:
All sample spaces are finite or countable infinity.
For uncountable Sample Space:
(i) itself is an event.
(ii) The empty set is an event.
(iii) If are events (that is ), then is an event (that occurs if occurs or occurs).
(iv) is an event is an event that occurs when does not occur.
(v) If is an event is an event that occurs when does not occur.
Example:
Let which is a subset of . Clearly, can be described as the event that sum of points obtained in two throws of a die is .
Example:
Let
can be described as the event of getting exactly heads in tossing a coin three times.
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# How can I change the page numbering in the header of text
I've been trying for a couple of hours to try to change the page numbering in the header of several pages of text for a chapter of text. I've read through everything and tried it all and nothing seems to work. Why is it so difficult to do such a simple process?
edit retag close merge delete
1
Please edit the question to give specific details. What is the current behavior, and what is the desired result? Also, describe what you have tried; words like "everything" and "all" do not describe anything. See guidelines for asking.
( 2018-06-17 00:09:21 +0200 )edit
By the way, did what you refer to as everything include this tutorial and this tutorial?
( 2018-06-18 13:57:50 +0200 )edit
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You can only make settings for the header per se with effect for all the pages in the factual sequence of your current page. A sequence of pages in this sense is delimited from pages above by a manual page break not inserted by the shortcut (Ctrl+Enter) but by Insert > Manual Break... > Page break explicitly selecting a named page style. Inserting a page break this way you get offered the opportunity to start the numbering for the new sequence with a chosen number.
The header settings for sequence in the above sense can be shaped in up to three versions each (first / left / right), but you cannot set different starting numbers by the shaping.
I don't know a way to change the starting page number for a sequence of pages subsequently, except by removing the initial manual break and re-inserting it with a changed setting.
I wouldn't claim to have understood the comment by @gabix easily. However, the subsequent comment by @ajlittoz helped me to get it: Page breaks are managed by a paragraph property accessible via the tab 'Text Flow' of a dialog opened either from the context menu of the paragraph or by 'Format Paragraph...' or by 'Paragraph Styles' > 'Modify' under 'Styles and Formatting'.
Now I have to find the reasons for what this way was the one to go though paragraph styles used in text-tables cannot have a page-break property.
more
( 2018-06-18 13:59:49 +0200 )edit
The best way: define a paragraph style with "page break before" and other appropriate attributes; Give this style to the transitional paragraph.
Afterwards modify the paragraph style to change the starting page number.
( 2018-06-18 14:50:26 +0200 )edit |
CryptoDB
Paper: Invertible Quadratic Non-Linear Layers for MPC-/FHE-/ZK-Friendly Schemes over Fnp: Application to Poseidon
Authors: Lorenzo Grassi , Radboud University, Nijmegen, The Netherlands Silvia Onofri , Scuola Normale Superiore di Pisa, Pisa, Italy Marco Pedicini , Università Roma Tre, Rome, Italy Luca Sozzi , Università degli Studi di Milano, Milan, Italy DOI: 10.46586/tosc.v2022.i3.20-72 URL: https://tosc.iacr.org/index.php/ToSC/article/view/9849 Search ePrint Search Google Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over Fp for a large prime p have been recently proposed in the literature. This goal is often achieved by instantiating the non-linear layer via power maps x↦xd. In this paper, we start an analysis of new non-linear permutation functions over Fnp that can be used as building blocks in such symmetrickey primitives. Given a local map F : Fmp→ Fp, we limit ourselves to focus on S-Boxes over Fnp for n ≥ m defined as SF (x0, x1, . . . , xn−1) = y0|y1| . . . |yn−1 where yi := F(xi, xi+1, . . . , xi+m−1). As main results, we prove that• given any quadratic function F : F2p→ Fp, the corresponding S-Box SF over Fnp for n ≥ 3 is never invertible;• similarly, given any quadratic function F : F3p → Fp, the corresponding S-Box SF over Fnp for n ≥ 5 is never invertible.Moreover, for each p ≥ 3, we present (1st) generalizations of the Lai-Massey construction over Fnp defined as before via functions F : Fmp → Fp for each n = m ≥ 2 and (2nd) (non-trivial) quadratic functions F : F3p → Fp such that SF over Fnp for n ∈ {3, 4} is invertible. As an open problem for future work, we conjecture that for each m ≥ 1 there exists a finite integer nmax(m) such that SF over Fnp defined as before via a quadratic function F : Fmp →Fp is not invertible for each n ≥ nmax(m). Finally, as a concrete application, we propose Neptune, a variant of the sponge hash function Poseidon, whose non-linear layer is designed by taking into account the results presented in this paper. We show that this variant leads to a concrete multiplication reduction with respect to Poseidon.
BibTeX
@article{tosc-2022-32408,
title={Invertible Quadratic Non-Linear Layers for MPC-/FHE-/ZK-Friendly Schemes over Fnp: Application to Poseidon},
journal={IACR Transactions on Symmetric Cryptology},
publisher={Ruhr-Universität Bochum},
volume={2022, Issue 3},
pages={20-72},
url={https://tosc.iacr.org/index.php/ToSC/article/view/9849},
doi={10.46586/tosc.v2022.i3.20-72},
author={Lorenzo Grassi and Silvia Onofri and Marco Pedicini and Luca Sozzi},
year=2022
} |
## MPC Modeling
Model predictive controllers use plant, disturbance, and noise models for prediction and state estimation. The model structure used in an MPC controller appears in the following illustration.
### Plant Model
You can specify the plant model in one of the following linear-time-invariant (LTI) formats:
The MPC controller performs all estimation and optimization calculations using a discrete-time, delay-free, state-space system with dimensionless input and output variables. Therefore, when you specify a plant model in the MPC controller, the software performs the following, if needed:
1. Conversion to state space — The `ss` command converts the supplied model to an LTI state-space model.
2. Discretization or resampling — If the model sample time differs from the MPC controller sample time (defined in the `Ts` property), one of the following occurs:
• If the model is continuous time, the `c2d` command converts it to a discrete-time LTI object using the controller sample time.
• If the model is discrete time, the `d2d` command resamples it to generate a discrete-time LTI object using the controller sample time.
3. Delay removal — If the discrete-time model includes any input, output, or internal delays, the `absorbDelay` command replaces them with the appropriate number of poles at z = 0, increasing the total number of discrete states. The `InputDelay`, `OutputDelay`, and `InternalDelay` properties of the resulting state-space model are all zero.
4. Conversion to dimensionless input and output variables — The MPC controller enables you to specify a scale factor for each plant input and output variable. If you do not specify scale factors, they default to `1`. The software converts the plant input and output variables to dimensionless form as follows:
`$\begin{array}{c}{x}_{p}\left(k+1\right)={A}_{p}{x}_{p}\left(k\right)+B{S}_{i}{u}_{p}\left(k\right)\\ {y}_{p}\left(k\right)={S}_{o}^{-1}C{x}_{p}\left(k\right)+{S}_{o}^{-1}D{S}_{i}{u}_{p}\left(k\right).\end{array}$`
where Ap, B, C, and D are the constant zero-delay state-space matrices from step 3, and:
• Si is a diagonal matrix of input scale factors in engineering units.
• So is a diagonal matrix of output scale factors in engineering units.
• xp is the state vector from step 3 in engineering units (including any absorbed delay states). No scaling is performed on state variables.
• up is a vector of dimensionless plant input variables, including manipulated variables, measured disturbances, and unmeasured input disturbances.
• yp is a vector of dimensionless plant output variables.
The resulting plant model has the following equivalent form:
`$\begin{array}{c}{x}_{p}\left(k+1\right)={A}_{p}{x}_{p}\left(k\right)+{B}_{pu}u\left(k\right)+{B}_{pv}v\left(k\right)+{B}_{pd}d\left(k\right)\\ {y}_{p}\left(k\right)={C}_{p}{x}_{p}\left(k\right)+{D}_{pu}u\left(k\right)+{D}_{pv}v\left(k\right)+{D}_{pd}d\left(k\right).\end{array}$`
Here, ${C}_{p}={S}_{o}^{-1}C$, Bpu, Bpv, and Bpd are the corresponding columns of BSi. Also, Dpu, Dpv, and Dpd are the corresponding columns of ${S}_{o}^{-1}D{S}_{i}$. Finally, u(k), v(k), and d(k) are the dimensionless manipulated variables, measured disturbances, and unmeasured input disturbances, respectively.
The MPC controller enforces the restriction of Dpu = 0, which means that the controller does not allow direct feedthrough from any manipulated variable to any plant output.
### Input Disturbance Model
If your plant model includes unmeasured input disturbances, d(k), the input disturbance model specifies the signal type and characteristics of d(k). See Controller State Estimation for more information about the model.
The `getindist` command provides access to the model in use.
The input disturbance model is a key factor that influences the following controller performance attributes:
• Dynamic response to apparent disturbances — The character of the controller response when the measured plant output deviates from its predicted trajectory, due to an unknown disturbance or modeling error.
• Asymptotic rejection of sustained disturbances — If the disturbance model predicts a sustained disturbance, controller adjustments continue until the plant output returns to its desired trajectory, emulating a classical integral feedback controller.
You can provide the input disturbance model as an LTI state-space (`ss`), transfer function (`tf`), or zero-pole-gain (`zpk`) object using `setindist`. The MPC controller converts the input disturbance model to a discrete-time, delay-free, LTI state-space system using the same steps used to convert the plant model. The result is:
`$\begin{array}{c}{x}_{id}\left(k+1\right)={A}_{id}{x}_{id}\left(k\right)+{B}_{id}{w}_{id}\left(k\right)\\ d\left(k\right)={C}_{id}{x}_{id}\left(k\right)+{D}_{id}{w}_{id}\left(k\right).\end{array}$`
where Aid, Bid, Cid, and Did are constant state-space matrices, and:
• xid(k) is a vector of nxid ≥ 0 input disturbance model states.
• dk(k) is a vector of nd dimensionless unmeasured input disturbances.
• wid(k) is a vector of nid ≥ 1 dimensionless white noise inputs, assumed to have zero mean and unit variance.
If you do not provide an input disturbance model, then the controller uses a default model, which has integrators with dimensionless unity gain added to its outputs. An integrator is added for each unmeasured input disturbance, unless doing so would cause a violation of state observability. In this case, a static system with dimensionless unity gain is used instead.
### Output Disturbance Model
The output disturbance model is a special case of the more general input disturbance model. Its output, yod(k), is directly added to the plant output rather than affecting the plant states. The output disturbance model specifies the signal type and characteristics of yod(k), and it is often used in practice. See Controller State Estimation for more details about the model.
The `getoutdist` command provides access to the output disturbance model in use.
You can specify a custom output disturbance model as an LTI state-space (`ss`), transfer function (`tf`), or zero-pole-gain (`zpk`) object using `setoutdist`. Using the same steps as for the plant model, the MPC controller converts the specified output disturbance model to a discrete-time, delay-free, LTI state-space system. The result is:
`$\begin{array}{c}{x}_{od}\left(k+1\right)={A}_{od}{x}_{od}\left(k\right)+{B}_{od}{w}_{od}\left(k\right)\\ {y}_{od}\left(k\right)={C}_{od}{x}_{od}\left(k\right)+{D}_{od}{w}_{od}\left(k\right).\end{array}$`
where Aod, Bod, Cod, and Dod are constant state-space matrices, and:
• xod(k) is a vector of nxod ≥ 1 output disturbance model states.
• yod(k) is a vector of ny dimensionless output disturbances to be added to the dimensionless plant outputs.
• wod(k) is a vector of nod dimensionless white noise inputs, assumed to have zero mean and unit variance.
If you do not specify an output disturbance model, then the controller uses a default model, which has integrators with dimensionless unity gain added to some or all of its outputs. These integrators are added according to the following rules:
• No disturbances are estimated, that is no integrators are added, for unmeasured plant outputs.
• An integrator is added for each measured output in order of decreasing output weight.
• For time-varying weights, the sum of the absolute values over time is considered for each output channel.
• For equal output weights, the order within the output vector is followed.
• For each measured output, an integrator is not added if doing so would cause a violation of state observability. Instead, a gain with a value of zero is used instead.
If there is an input disturbance model, then the controller adds any default integrators to that model before constructing the default output disturbance model.
### Measurement Noise Model
One controller design objective is to distinguish disturbances, which require a response, from measurement noise, which should be ignored. The measurement noise model specifies the expected noise type and characteristics. See Controller State Estimation for more details about the model.
Using the same steps as for the plant model, the MPC controller converts the measurement noise model to a discrete-time, delay-free, LTI state-space system. The result is:
`$\begin{array}{c}{x}_{n}\left(k+1\right)={A}_{n}{x}_{n}\left(k\right)+{B}_{n}{w}_{n}\left(k\right)\\ {y}_{n}\left(k\right)={C}_{n}{x}_{n}\left(k\right)+{D}_{n}{w}_{n}\left(k\right).\end{array}$`
Here, An, Bn, Cn, and Dn are constant state space matrices, and:
• xn(k) is a vector of nxn ≥ 0 noise model states.
• yn(k) is a vector of nym dimensionless noise signals to be added to the dimensionless measured plant outputs.
• wn(k) is a vector of nn ≥ 1 dimensionless white noise inputs, assumed to have zero mean and unit variance.
If you do not supply a noise model, the default is a unity static gain: nxn = 0, Dn is an nym-by-nym identity matrix, and An, Bn, and Cn are empty.
For an `mpc` controller object, `MPCobj`, the property `MPCobj.Model.Noise` provides access to the measurement noise model.
### Note
If the minimum eigenvalue of ${D}_{n}{D}_{n}^{T}$ is less than 1x10–8, the MPC controller adds 1x10–4 to each diagonal element of Dn. This adjustment makes a successful default Kalman gain calculation more likely.
|
# How can I create directory tree in C++/Linux?
I want an easy way to create multiple directories in C++/Linux.
For example I want to save a file lola.file in the directory:
/tmp/a/b/c
but if the directories are not there I want them to be created automagically. A working example would be perfect.
• C++ does not have any built-in facilities for creating directories and trees per se. You will have to use C and system calls or an external library like Boost. C and system calls will be platform dependent. – jww Jan 20 '14 at 14:22
• @noloader Thanks a lot man.. but I think after 4 years I pretty much got my answer as you can see bellow in 13 different ways... – Lipis Jan 20 '14 at 17:47
• Yeah, I was surprised no one explicitly stated you cannot do it in C++ (assuming you wanted a portable method in C++ that worked on Linux). But you probably knew that ;). There were a lot of good suggestions for non-portable C code, though. – jww Jan 20 '14 at 18:33
• What is "C++/Linux"? – Lightness Races with Monica Jan 22 '15 at 2:05
• @LightnessRacesinOrbit It's my university years in C++ on Linux :) – Lipis Jan 23 '15 at 11:48
Here's a C function that can be compiled with C++ compilers.
/*
@(#)File: $RCSfile: mkpath.c,v$
@(#)Version: $Revision: 1.13$
@(#)Last changed: $Date: 2012/07/15 00:40:37$
@(#)Purpose: Create all directories in path
@(#)Author: J Leffler
*/
/*TABSTOP=4*/
#include "jlss.h"
#include "emalloc.h"
#include <errno.h>
#ifdef HAVE_UNISTD_H
#include <unistd.h>
#endif /* HAVE_UNISTD_H */
#include <string.h>
#include "sysstat.h" /* Fix up for Windows - inc mode_t */
typedef struct stat Stat;
#ifndef lint
/* Prevent over-aggressive optimizers from eliminating ID string */
const char jlss_id_mkpath_c[] = "@(#)$Id: mkpath.c,v 1.13 2012/07/15 00:40:37 jleffler Exp$";
#endif /* lint */
static int do_mkdir(const char *path, mode_t mode)
{
Stat st;
int status = 0;
if (stat(path, &st) != 0)
{
/* Directory does not exist. EEXIST for race condition */
if (mkdir(path, mode) != 0 && errno != EEXIST)
status = -1;
}
else if (!S_ISDIR(st.st_mode))
{
errno = ENOTDIR;
status = -1;
}
return(status);
}
/**
** mkpath - ensure all directories in path exist
** Algorithm takes the pessimistic view and works top-down to ensure
** each directory in path exists, rather than optimistically creating
** the last element and working backwards.
*/
int mkpath(const char *path, mode_t mode)
{
char *pp;
char *sp;
int status;
char *copypath = STRDUP(path);
status = 0;
pp = copypath;
while (status == 0 && (sp = strchr(pp, '/')) != 0)
{
if (sp != pp)
{
/* Neither root nor double slash in path */
*sp = '\0';
status = do_mkdir(copypath, mode);
*sp = '/';
}
pp = sp + 1;
}
if (status == 0)
status = do_mkdir(path, mode);
FREE(copypath);
return (status);
}
#ifdef TEST
#include <stdio.h>
/*
** Stress test with parallel running of mkpath() function.
** Before the EEXIST test, code would fail.
** With the EEXIST test, code does not fail.
**
** Test shell script
** PREFIX=mkpath.
** NAME=./$PREFIX/sa/32/ad/13/23/13/12/13/sd/ds/ww/qq/ss/dd/zz/xx/dd/rr/ff/ff/ss/ss/ss/ss/ss/ss/ss/ss ** :${MKPATH:=mkpath}
** ./$MKPATH$NAME &
** [...repeat a dozen times or so...]
** ./$MKPATH$NAME &
** wait
** rm -fr ./$PREFIX/ */ int main(int argc, char **argv) { int i; for (i = 1; i < argc; i++) { for (int j = 0; j < 20; j++) { if (fork() == 0) { int rc = mkpath(argv[i], 0777); if (rc != 0) fprintf(stderr, "%d: failed to create (%d: %s): %s\n", (int)getpid(), errno, strerror(errno), argv[i]); exit(rc == 0 ? EXIT_SUCCESS : EXIT_FAILURE); } } int status; int fail = 0; while (wait(&status) != -1) { if (WEXITSTATUS(status) != 0) fail = 1; } if (fail == 0) printf("created: %s\n", argv[i]); } return(0); } #endif /* TEST */ The macros STRDUP() and FREE() are error-checking versions of strdup() and free(), declared in emalloc.h (and implemented in emalloc.c and estrdup.c). The "sysstat.h" header deals with broken versions of <sys/stat.h> and can be replaced by <sys/stat.h> on modern Unix systems (but there were many issues back in 1990). And "jlss.h" declares mkpath(). The change between v1.12 (previous) and v1.13 (above) is the test for EEXIST in do_mkdir(). This was pointed out as necessary by Switch — thank you, Switch. The test code has been upgraded and reproduced the problem on a MacBook Pro (2.3GHz Intel Core i7, running Mac OS X 10.7.4), and suggests that the problem is fixed in the revision (but testing can only show the presence of bugs, never their absence). (You are hereby given permission to use this code for any purpose with attribution.) • It surely is faster than system. System has a lot of overhead involved. Basically, the process has to be forked, then at least two binaries have to be loaded (one will probably be in cache already), on of which will be yet another fork of the other, ... – ypnos Mar 23 '09 at 21:55 • I forgot: And then "mkdir -p" will do at least the same as the code posted above! – ypnos Mar 23 '09 at 21:56 • There's a subtle race condition in this code that I actually hit. It only happens when multiple programs start up simultaneously and make the same folder path. The fix is to add if (errno != EEXIST) { status = -1; } when mkdir fails. – Switch Jul 14 '12 at 23:57 • @Switch: Thanks. That's the trouble with using stat() before mkdir(); it is a TOCTOU (time of check, time of use) problem. I tried tickling the bug with a shell script running 13 processes in background creating the same 29-element path, and didn't manage to hit it. Then I hacked the test program to fork 20 times and have each child try, and that managed to hit the bug. The fixed code will have if (mkdir(path, mode) != 0 && errno != EEXIST) status = -1;. That doesn't show the bug. – Jonathan Leffler Jul 15 '12 at 0:43 • @DavidMerinos: they're headers (jlss.h, emalloc.h), not libraries. However, the code is available in my SOQ (Stack Overflow Questions) repository on GitHub as files jlss.h, emalloc.c and emalloc.h in the src/libsoq sub-directory. You'll need posixver.h too, and a few others (debug.h, stderr.c, stderr.h — I think that's it, but what you need should all be in that directory). – Jonathan Leffler Jan 14 at 19:50 Easy with Boost.Filesystem: create_directories #include <boost/filesystem.hpp> //... boost::filesystem::create_directories("/tmp/a/b/c"); Returns: true if a new directory was created, otherwise false. • Well, most boost libraries are header-only, meaning there is no overhead besides what you use. In the case of Boost.Filesystem, it requires compiling though. On my disk, the compiled library weighs ~60KB. – Benoît Mar 23 '09 at 20:54 • @Lipis: please precise what your embedded system is. I believe it should be available on pretty much every linux distribution. – Benoît Mar 23 '09 at 20:56 • Regarding on the C++11 compilers mentioned by @danijar, the comment here made it clearer: The <filesystem> header is not part of C++11; it is a proposal for C++ TR2 based on the Boost.Filesystem library. Visual C++ 2012 includes an implementation of the proposed library. – Chunliang Lyu Sep 4 '13 at 7:49 • boost::filesystem is not header-only: stackoverflow.com/questions/13604090/… – ftvs Nov 1 '13 at 3:15 • IMHO: In any project of mine that is meant to do something significant and stand the test of time, it is WELL worth the compile to have such a set of incredibly useful and powerful standardized tools as boost. A ton of it has already made its way into standard C++, certainly with more to come. Try it out, stick with it, you'll benefit if you have more than trivial needs and you do not want to reinvent the wheel. :-) – moodboom Dec 9 '16 at 0:59 system("mkdir -p /tmp/a/b/c") is the shortest way I can think of (in terms of the length of code, not necessarily execution time). It's not cross-platform but will work under Linux. • IF your going to give the solution as a shell command, it would be well to mention system (3) – dmckee Mar 23 '09 at 20:19 • Although it works on Windows with Mingw compiler – PJ127 Jul 2 at 8:04 Here is my example of code (it works for both Windows and Linux): #include <iostream> #include <string> #include <sys/stat.h> // stat #include <errno.h> // errno, ENOENT, EEXIST #if defined(_WIN32) #include <direct.h> // _mkdir #endif bool isDirExist(const std::string& path) { #if defined(_WIN32) struct _stat info; if (_stat(path.c_str(), &info) != 0) { return false; } return (info.st_mode & _S_IFDIR) != 0; #else struct stat info; if (stat(path.c_str(), &info) != 0) { return false; } return (info.st_mode & S_IFDIR) != 0; #endif } bool makePath(const std::string& path) { #if defined(_WIN32) int ret = _mkdir(path.c_str()); #else mode_t mode = 0755; int ret = mkdir(path.c_str(), mode); #endif if (ret == 0) return true; switch (errno) { case ENOENT: // parent didn't exist, try to create it { int pos = path.find_last_of('/'); if (pos == std::string::npos) #if defined(_WIN32) pos = path.find_last_of('\\'); if (pos == std::string::npos) #endif return false; if (!makePath( path.substr(0, pos) )) return false; } // now, try to create again #if defined(_WIN32) return 0 == _mkdir(path.c_str()); #else return 0 == mkdir(path.c_str(), mode); #endif case EEXIST: // done! return isDirExist(path); default: return false; } } int main(int argc, char* ARGV[]) { for (int i=1; i<argc; i++) { std::cout << "creating " << ARGV[i] << " ... " << (makePath(ARGV[i]) ? "OK" : "failed") << std::endl; } return 0; } Usage: $ makePath 1/2 folderA/folderB/folderC
creating 1/2 ... OK
creating folderA/folderB/folderC ... OK
• I second that comment! It is (surprisingly) not a trivial task to find a portable C++ way to create a directory. This answer needs more upvotes. – Manuel Lafond May 23 '17 at 16:35
• Under Windows, isDirExist does not work if the trailing character is a backslash. Always returns false. I have to modify the code to: std::string dirPath(path); while ('\\' == *dirPath.rbegin()) dirPath.pop_back(); ... and then, of course, pass dirPath.c_str() in the call to _stat. – MiloDC Sep 8 '17 at 22:36
• Windows API has "Non-ANSI names for compatibility" for stat (related to __STDC__) no need for the precompiler test. – Sandburg Aug 9 at 12:24
#include <sys/types.h>
#include <sys/stat.h>
int status;
...
status = mkdir("/tmp/a/b/c", S_IRWXU | S_IRWXG | S_IROTH | S_IXOTH);
From here. You may have to do separate mkdirs for /tmp, /tmp/a, /tmp/a/b/ and then /tmp/a/b/c because there isn't an equivalent of the -p flag in the C api. Be sure and ignore the EEXISTS errno while you're doing the upper level ones.
• Fun fact: At least Solaris and HP/UX have mkdirp(), although it's clearly not optimal for portability. – Martin Carpenter Mar 23 '09 at 20:21
• that's the point.. that I don't want to call all these functions separately. – Lipis Mar 23 '09 at 20:31
• Calling mkdir a few times will be way, way faster than calling system once. – Paul Tomblin Mar 23 '09 at 20:38
• I don't understand what you are suggesting: calling mkdir 4 times with different arguments? ("/tmp/",...), ("/tmp/a/",...), ("/tmp/a/b/",...), ("/tmp/a/b/c/",...) – Antonio Apr 29 '16 at 8:58
• Again, it's pretty trivial to make the same call three times. The point is to give people enough information that they can write the code, not to write the code for them. – Paul Tomblin Apr 29 '16 at 13:57
This is similar to the previous but works forward through the string instead of recursively backwards. Leaves errno with the right value for last failure. If there's a leading slash, there's an extra time through the loop which could have been avoided via one find_first_of() outside the loop or by detecting the leading / and setting pre to 1. The efficiency is the same whether we get set up by a first loop or a pre loop call, and the complexity would be (slightly) higher when using the pre-loop call.
#include <iostream>
#include <string>
#include <sys/stat.h>
int
mkpath(std::string s,mode_t mode)
{
size_t pos=0;
std::string dir;
int mdret;
if(s[s.size()-1]!='/'){
// force trailing / so we can handle everything in loop
s+='/';
}
while((pos=s.find_first_of('/',pos))!=std::string::npos){
dir=s.substr(0,pos++);
if(dir.size()==0) continue; // if leading / first time is 0 length
if((mdret=mkdir(dir.c_str(),mode)) && errno!=EEXIST){
return mdret;
}
}
return mdret;
}
int main()
{
int mkdirretval;
mkdirretval=mkpath("./foo/bar",0755);
std::cout << mkdirretval << '\n';
}
It should be noted that starting from C++17 filesystem interface is part of the standard library. This means that one can have following to create directories:
#include <filesystem>
std::filesystem::create_directories("/a/b/c/d")
Additionally, with gcc, one needs to "-std=c++17" to CFLAGS. And "-lstdc++fs" to LDLIBS. The latter potentially is not going to be required in the future.
You said "C++" but everyone here seems to be thinking "Bash shell."
Check out the source code to gnu mkdir; then you can see how to implement the shell commands in C++.
• What do you mean "everyone"? – Paul Tomblin Mar 23 '09 at 20:20
• Well system("mkdir...") should do the trick on linux. It's not cross-platform though. – ChristopheD Mar 23 '09 at 20:21
• I second what @MartinCarpenter says – Joshua Hedges Dec 18 '11 at 0:01
bool mkpath( std::string path )
{
bool bSuccess = false;
int nRC = ::mkdir( path.c_str(), 0775 );
if( nRC == -1 )
{
switch( errno )
{
case ENOENT:
//parent didn't exist, try to create it
if( mkpath( path.substr(0, path.find_last_of('/')) ) )
//Now, try to create again.
bSuccess = 0 == ::mkdir( path.c_str(), 0775 );
else
bSuccess = false;
break;
case EEXIST:
//Done!
bSuccess = true;
break;
default:
bSuccess = false;
break;
}
}
else
bSuccess = true;
return bSuccess;
}
• it's the best solution for me! Thank you!))) – neo Dec 5 '16 at 21:55
• maybe it's a dump question, but what is the "::" prefix before mkdir? – RLaaa Feb 15 '17 at 22:18
• Found the answer, the :: ensures that resolution occurs from the global namespace stackoverflow.com/questions/4269034/… – RLaaa Feb 15 '17 at 22:26
I know it's an old question but it shows up high on google search results and the answers provided here are not really in C++ or are a bit too complicated.
Please note that in my example createDirTree() is very simple because all the heavy lifting (error checking, path validation) needs to be done by createDir() anyway. Also createDir() should return true if directory already exists or the whole thing won't work.
Here's how I would do that in C++:
#include <iostream>
#include <string>
bool createDir(const std::string dir)
{
std::cout << "Make sure dir is a valid path, it does not exist and create it: "
<< dir << std::endl;
return true;
}
bool createDirTree(const std::string full_path)
{
size_t pos = 0;
bool ret_val = true;
while(ret_val == true && pos != std::string::npos)
{
pos = full_path.find('/', pos + 1);
ret_val = createDir(full_path.substr(0, pos));
}
return ret_val;
}
int main()
{
createDirTree("/tmp/a/b/c");
return 0;
}
Of course createDir() function will be system-specific and there are already enough examples in other answers how to write it for linux, so I decided to skip it.
So I need mkdirp() today, and found the solutions on this page overly complicated. Hence I wrote a fairly short snippet, that easily be copied in for others who stumble upon this thread an wonder why we need so many lines of code.
mkdirp.h
#ifndef MKDIRP_H
#define MKDIRP_H
#include <sys/stat.h>
#define DEFAULT_MODE S_IRWXU | S_IRGRP | S_IXGRP | S_IROTH | S_IXOTH
/** Utility function to create directory tree */
bool mkdirp(const char* path, mode_t mode = DEFAULT_MODE);
#endif // MKDIRP_H
mkdirp.cpp
#include <errno.h>
bool mkdirp(const char* path, mode_t mode) {
// const cast for hack
char* p = const_cast<char*>(path);
// Do mkdir for each slash until end of string or error
while (*p != '\0') {
// Skip first character
p++;
// Find first slash or end
while(*p != '\0' && *p != '/') p++;
// Remember value from p
char v = *p;
// Write end of string at p
*p = '\0';
// Create folder from path to '\0' inserted at p
if(mkdir(path, mode) == -1 && errno != EEXIST) {
*p = v;
return false;
}
// Restore path to it's former glory
*p = v;
}
return true;
}
If you don't like const casting and temporarily modifying the string, just do a strdup() and free() it afterwards.
• Posted to a gist too, so I don't forget where I put it next time a need it :) gist.github.com/jonasfj/7797272 – jonasfj Dec 4 '13 at 23:11
• It is evil to try modifying a string that is passed as a constant. All else apart, it is likely to lead to dramatic failures if it is ever passed a string literal. – Jonathan Leffler Jun 22 '15 at 14:45
• Perfectly right.... this is actually bad... probably strcpy would make this better... – jonasfj Jun 23 '15 at 21:10
Since this post is ranking high in Google for "Create Directory Tree", I am going to post an answer that will work for Windows — this will work using Win32 API compiled for UNICODE or MBCS. This is ported from Mark's code above.
Since this is Windows we are working with, directory separators are BACK-slashes, not forward slashes. If you would rather have forward slashes, change '\\' to '/'
It will work with:
c:\foo\bar\hello\world
and
c:\foo\bar\hellp\world\
(i.e.: does not need trailing slash, so you don't have to check for it.)
Before saying "Just use SHCreateDirectoryEx() in Windows", note that SHCreateDirectoryEx() is deprecated and could be removed at any time from future versions of Windows.
bool CreateDirectoryTree(LPCTSTR szPathTree, LPSECURITY_ATTRIBUTES lpSecurityAttributes = NULL){
bool bSuccess = false;
const BOOL bCD = CreateDirectory(szPathTree, lpSecurityAttributes);
DWORD dwLastError = 0;
if(!bCD){
dwLastError = GetLastError();
}else{
return true;
}
switch(dwLastError){
bSuccess = true;
break;
case ERROR_PATH_NOT_FOUND:
{
TCHAR szPrev[MAX_PATH] = {0};
LPCTSTR szLast = _tcsrchr(szPathTree,'\\');
_tcsnccpy(szPrev,szPathTree,(int)(szLast-szPathTree));
if(CreateDirectoryTree(szPrev,lpSecurityAttributes)){
bSuccess = CreateDirectory(szPathTree,lpSecurityAttributes)!=0;
if(!bSuccess){
}
}else{
bSuccess = false;
}
}
break;
default:
bSuccess = false;
break;
}
return bSuccess;
}
• @Patrick -- why not read my post before posting a smart-ass comment. – Andy Oct 29 '13 at 0:41
If dir does not exist, create it:
boost::filesystem::create_directories(boost::filesystem::path(output_file).parent_path().string().c_str());
mkdir -p /dir/to/the/file
touch /dir/to/the/file/thefile.ending
• the -p option is what I'm looking for. Thanks! – asgs Feb 14 '12 at 19:43
The others got you the right answer, but I thought I'd demonstrate another neat thing you can do:
mkdir -p /tmp/a/{b,c}/d
Will create the following paths:
/tmp/a/b/d
/tmp/a/c/d
The braces allow you to create multiple directories at once on the same level of the hierarchy, whereas the -p option means "create parent directories as needed".
• after seeing Paul's answer, I realize that I (and a lot of other people) misunderstood the question... – rmeador Mar 23 '09 at 20:17
• If somebody can Just update this by changing to system("mkdir -p /tmp/a/{b,c}/d"), cause the questions is not about doing it in shell.. but through C++. – Lipis Mar 23 '09 at 20:38
• I think {a,b} will work in both sh-derived and csh-derived shells. I'm not sure if it will work in a system() command, though. – Paul Tomblin Mar 23 '09 at 20:45
• @Lipis: doing that via system() is not a good solution to the OP's question. @Andy: I'd never considered that before, but I just tested it by replacing "mkdir -p" with "echo" and it prints out "/tmp/a/b/d /tmp/a/c/d", which suggests it is the shell doing it, not mkdir. – rmeador Mar 23 '09 at 20:47
• @rmeador: if it's not a good solution, do you have something else to suggest? I want to do that through C++... that's my issue not how to do that through shell.. – Lipis Mar 23 '09 at 20:49 |
com/tiborhencz/intermission. free to use portfolio templates. gpu-fluid High performance OpenGL fluid solver in C++ gpu-physics. node-oidc-provider. City scene simulated with 29 million particles on a 512×256×512 grid with our spatially sparse, matrix-free FLIP solver on a Quadro GP100 GPU at an average 1. https://thecodingtrain. , presented at ACM SIGGRAPH 2019] –37 SPH for the Physics Based Simulation of Fluids and Solids [Gissler et al. In this case we place a low-density block in a container of fluid. The objects with a geometry inside the domain will be considered as fluids or solid obstacles. np_per_xc(i) Please note that if np_per_xc(1) =0, it just means to ignore the plasma and simply do a laser propagation simulation. The DSMC method models fluid flows using simulation molecules which represent a large number of real molecules in a probabilistic simulation to solve the Boltzmann equation. Java Project Tutorial - Make Login and Register Form Step by Step Using NetBeans And MySQL Database - Duration: 3:43:32. using a sliding mesh approach) over Conjugate-Heat-Transfer to Fluid-Structure Interactions problems. You can still view a video. Thorsten Stoesser and co-workers at Cardiff University, UK, primarily for use in the simulation of environmental fluid dynamics. (7/3/19) My co-workers at Fomoro AI and I have a new pre-print on bridging the gap between reinforcement learning and tool use research. Fluid simulation is based on the Navier-Stokes equations, which are fundamental, interesting, and difficult to understand without a good background in physics and differential equations. Fluid simulation is based on the Navier-Stokes equations, which are fundamental, interesting, and difficult to understand without a good background in physics and differential equations. WebGL Fluid and Particle Simulation (haxiomic. 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Because of the large amount of parallelism in graphics hardware, the simulation we describe runs significantly faster on the GPU than on the CPU. FEATool supports modeling heat transfer through both conduction, that is heat transported by a diffusion process, and also convection, which is heat transported through a fluid through convection by a velocity field. In this video, I attempt to follow Mike Ash's guide to Fluid Simulation and port Jos Stam's "Real-Time Fluid Dynamics for Games" algorithm and code in Processing (Java). Programming. Empty space introduces some really annoying boundary conditions. Introduction. In case anyone is wondering, the end-to-end fluid dynamics simulation is not achieved by a neural network alone here (though the authors claim that is possible). It's possible to update the information on Fluid Simulation or report it as discontinued, duplicated or spam. ), yet it has not been widely used for fluid simulation. FEATool Multiphysics Tutorial - Shrink Fitting of an Assembly. A list of 9 instructional test cases can be found in the Instructional_Cases folder of the repository. In a grid-based simulation like ours, the fluid is represented by dividing up the space a fluid might occupy into individual cells (in our case, pixels), and storing certain quantities of the fluid for each cell, like velocity, pressure, and color. Adding cells to the world Cells are added to the world in the initialization step. Experiment and play with those swirling substances. If a simulation is to be restarted after re-meshing has occurred, the new mesh must be added to the input file. The resulting flow (velocity) in turn serves as a velocity source for a fluid solver and the… In this short MovieClip the Optical Flow is computed at each frame. Our paper "Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation" received the Best Paper Award in MIG 2017! Our SIGGRAPH 2017 paper on porous water-sand mixture is featured at Gizmodo. To apply SPH to fluid simulation, Müller begin with a modified version of Navier-Stokes for particle systems (which excludes a convective term because it is not needed for particles which move with the fluid):. Coupled fluid-solid CFD simulation to understand the force on a zebra-fish's tailfin. The Generalized Fluid System Simulation Program (GFSSP) is a general software tool that can perform complex fluid flow analysis in a wide variety of applications, including those related to chemical processing, gas processing, power plants, hydraulic control circuits, and various kinds of fluid. 1 and the SPARK software, the group is now developing:. 0s (middle), displacement history for the tip of the beam (bottom). This article explains how to turn polyhedra inside out to make containers. f #define STARTY 10. Most simulation tools are complex and difficult to understand. degree in computer science and engineering from Beihang University in 2013. It exhibits a phenomenon called vortex shedding, where vortices of alternating spin spontaneously emerge behind the obstacle. This article explains how to turn polyhedra inside out to make containers. If you have SW premium you get flow Xpress(or cosmos depending on which version you have). It is done with Javascript. A Novel Analysis-and-Simulation Approach for Detail Enhancement in FLIP Fluid Interaction. In fluid simulation, the more memory and processing power you have available, the more detailed and realistic your fluid simulation can be. CPL library is software for linking together Computational Fluid Dynamics (CFD) and Molecular Dynamics (MD) software. Improve dx9 rendering speed. Generic Open-FOAM simulation setup. The project consists of two parts. You can download Blender with MantaFlow here: https://github. Learn how to create a liquid based effect inside Unity. By Amanda Ghassaei, code on Github. Colorful Fluid Simulations. Fluid simulation, created with Hurleyworks UP and Lightwave, rendered with Octane (render time 14 days, lol) This entry was posted in JWildfire and tagged Fluid simulation Hurleyworks UP Lightwave Octane. Explicit Euler integration for cloth animation; Iterative adjustment for overstretched springs. The FLIP Fluids simulator was created to improve on many aspects of Blender's internal Elbeem fluid simulation system such as. A very large 3d cfd simulation over Barcelona city. Sign in Sign up CA fluid simulation Raw. This project simulates the behavior of fluids with WebGL. Fluid Simulation Canvas. The pressure projection steps seems to be still buggy and the solver (Jacobi) is too slow. WebGL Fluid and Particle Simulation (haxiomic. This is a simulation of a galaxy using the density wave theory as explained by Ingo Berg. WebGL Fluid Simulation (paveldogreat. Computational fluid dynamics simulation of WEC in focused waves Water Power Technologies Office Peer Review Marine and Hydrokinetics Program Wave Energy Converter Modeling FOSWEC wave tank testing and WEC-Sim simulation Yi-Hsiang Yu National Renewable Energy Laboratory yi-hsiang. SU2, Multiphysics Simulation and Design Software The SU2 suite is an open-source collection of C++ based software tools for performing Partial Differential Equation (PDE) analysis and solving PDE-constrained optimization problems. (7/23/19) Along with fluid dynamics researchers at UMass Amherst, I’ve released a new pre-print on nonlinear dimensionality reduction of fluid simulation data with convolutional autoencoders. displacement by fluid | fluid simulation 2D. Fluid Particles. Simulation Programming with Python This chapter shows how simulations of some of the examples in Chap. Fluid Mechanics. In this work, we simulate a suspension that contains both. Hopsan is an open-source multi-domain system simulation tool developed at the division of Fluid and Mechatronic Systems at Linköping University. lib files, with the corresponding. My research interests include physics-based fluid modelling/simulation, data-driven fluid animation, flow field analysis, and all other relevant topics in computer graphics. Train and validate the model. In this project, I simulated realistic fluid dynamics based on Smoothed Particle Hydrodynamics. A Processing/Java library for high performance GPU-Computing (GLSL). Run mantaflow to generate fluid data. This course was created by Stephen Pearson. We extended upon a 2D fluid simulation based on the Navier Stokes equations by adding a buoyant force. [adult swim] Character Soup. FEM_CFD_Steady_Test2D solution of the steady 2D Navier-Stokes equations in a backward-facing step channel. In a grid-based simulation like ours, the fluid is represented by dividing up the space a fluid might occupy into individual cells (in our case, pixels), and storing certain quantities of the fluid for each cell, like velocity, pressure, and color. It uses WebGL, which is the standard way of creating HTML5 3D graphics, together with the use of the GPU. Fluid Simulation for Video Games (part 19) About the Author Dr. Fluid simulation can augment game mechanics and enhance the aesthetics and realism of video games. Hope you guys like it. Fast Fluid Simulations with Sparse Volumes on the GPU. Fluid Simulation (with WebGL demo) - this article has some nice, interactive graphics that helped me debug my code. Enjoy change of color or transform water or clouds or ice. Explore pressure in the atmosphere and underwater. Lattice Boltzmann large-eddy simulation of turbulent cavity flow. 728mm image generated with porespy-a Python Library-): Directly simulate a viscous flow through medium’s pores using OpenFOAM (The most trusted method). The generated fluid motion is more viscous. A nice casual experience for a tired mind perhaps. Initially the fluid is flowing from left to right, and a linear barrier (shown in black) diverts the fluid and creates vortices. It's so easy to model real life looking huge fluid simulations with physical objects in this software. Multiple Relaxation Time (MRT) with Large-Eddy Simulations is used to model turbulent behaviour at high Reynolds number. The list of alternatives was updated Sep 2019. I have seen that book mentioned all over the place and almost bought a copy, but reviews say it is focused more. Embedded Boundaries For computations with complex geometries, AMReX provides data structures and algorithms to employ an embedded boundary (EB) approach to PDE discretizations. All gists Back to GitHub. Written by Amanda Ghassaei as a homework assignment for The Nature of Mathematical Modeling, code on Github. I am a third year Ph. Howdy, this is the Water Simulation blog. FEM_CFD_Steady_Test3D solution of the steady 3D Navier-Stokes equations around a bluff body (a description of the geometry is given here) FEM_CFD_Dfg2D 2D unsteady Navier-Stokes equations: flow around a cylinder benchmark. FFVC-MINI: A Navier-Stokes solver for 3D unsteady thermal flow of incompressible fluid. Accept EULA You will receive an invite within the hour. GPU powered fluid simulation based on classic GPU Gems's article "Fast Fluid Dynamics Simulation on the GPU" that works beautifully on mobile. NASA does not assume any liability for the use of the software or any system developed using the software. (7/23/19) Along with fluid dynamics researchers at UMass Amherst, I’ve released a new pre-print on nonlinear dimensionality reduction of fluid simulation data with convolutional autoencoders. (optional) Run 3D example script to create videos from. degree in computer science and engineering from Beihang University in 2013. Game overview : Fluid simulation game that can play with water on browser. Play with fluids in your browser (works even on mobile) WebGL Fluid SimulationPlay. Linearized Euler equations (LEE) are solved with a 4th order Spectral Difference method on a 50x50 Cartesian mesh. Vortex Spheres. Coupled fluid-solid CFD simulation to understand the force on a zebra-fish’s tailfin. Visit our download page to see for yourself. This research area has many applications like Virtual Reality (VR), medical simulations, computer games or virtual prototyping. This validates the proposed methodology and could be extended to estimate airship parameters from real flight data. Written by Amanda Ghassaei as a homework assignment for The Nature of Mathematical Modeling, code on Github. The buoyant force is the upward force exerted on an object by a fluid when the object is partly or entirely immersed in the fluid. (7/3/19) My co-workers at Fomoro AI and I have a new pre-print on bridging the gap between reinforcement learning and tool use research. A WebGL fluid simulation that works in mobile browsers. 1383 and their viscosities are equal. Fluid Simulation with Navier Stokes. Fluid simulation is one of them. com/Jasonnor/WebGL-Fluid-Simulation Origin reference: https://github. A WebGL fluid simulation that works in mobile browsers. This fluid simulation is based on the paper by Jos Stam. National Infrastructure Simulation and Analysis Center (NISAC)–This is a project funded by the U. You can also see an init function was passed at the end of the definition. Cloth Simulation. js Fluid Simulation with particles (doesn't do a great job of it) - index. This demo requires a decent graphics card and up-to-date drivers. The generated fluid motion is more viscous. Hydro3D is a finite difference Navier Stokes solver that permits accurate and efficient Large Eddy Simulation (LES) of turbulent flows. Another very far fetched goal would be to convert this 2-D fluid simulation to a 3-D fluid simulation, with all the vectors and equations being in 3-D. I had no problems with the installer. CSS 209 21. (7/23/19) Along with fluid dynamics researchers at UMass Amherst, I’ve released a new pre-print on nonlinear dimensionality reduction of fluid simulation data with convolutional autoencoders. Free Download Udemy Blender 3D – Fluid Simulation Guide. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points. "Smoke" ©2014 @cornusammonis Github Forked from "Reaction diffusion system (Gray-Scott model)" ©2012 @pmneila Github Not working? This simulation requires the GL extensions framebuffer_object and texture_float. f #define STARTZ… SPH Fluid Simulation on Vimeo Join. - Fluid Simulation of Fetal Hearts for prediction of congenital heart diseases- Image processing- Object tracking under ultrasound. gpu-fluid High performance OpenGL fluid solver in C++ gpu-physics. Why does this happen? It’s the Magnus Effect! Named after the German physicist H. Creating fluid domain mesh. Francesco Casella, “Object-Oriented Modelling of Two-Phase Fluid Flows by the Finite Volume Method”. : An Unconditionally Stable MacCormack Method. I would like to develop a physic-based game which requires fluid simulations (flows). WebGL Fluid Simulation drape drape simulation software Radar An audi-visual experiment carla Open-source simulator for autonomous driving research. This simulation solves the Navier-Stokes equations for incompressible fluid flow past an obstacle in a GPU fragment shader. redbKIT is a MATLAB library for finite element simulation and reduced-order modeling of Partial Differential Equations. GPU powered fluid simulation based on classic GPU Gems's article "Fast Fluid Dynamics Simulation on the GPU" that works beautifully on mobile. - Simulation times reported interactively, and separated for each computation step. STLTool - STL CAD Geometry and Pre-processing Toolbox for MATLAB STLTool is a simple GUI toolbox for pre-processing STL CAD files with polygon reduction. The particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. FLIP Fluids is a powerful liquid simulation addon that gives you the ability to create high quality cinematic fluid effects all within Blender! Created by Ryan Guy and Dennis Fassbaender (check out our interview with the Blender Market!. Water Simulation by matheusmortatti - 1. We want games to be fun and look pretty and plausible. The platform allows the use of Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA), and Thermal Simulation. To apply SPH to fluid simulation, Müller begin with a modified version of Navier-Stokes for particle systems (which excludes a convective term because it is not needed for particles which move with the fluid):. Accelerating Eulerian Fluid Simulation With Convolutional Networks, Jonathan Tompson, Kristofer Schlachter, Pablo Sprechmann, Ken Perlin. fluid simulator | fluid simulator | webgl fluid simulator | fluid simulation | fluid simulator game | online fluid simulator | fluid simulator io | fluid simula. Author: Pooyan Dadvand. Play with fluids in your browser (works even on mobile) WebGL Fluid SimulationPlay. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. See the complete profile on LinkedIn and discover Qiubao’s. Coolfluid 3 is a major redesign, taking into. Change the road geometry by dragging; Click onto the road to disturb traffic flow; Drag obstacles or construction vehicles to create new bottlenecks. Fluid Simulation was added by Ugotsta in Aug 2019 and the latest update was made in Sep 2019. Image on your right can be an image or even YouTube video if you like. It was developed as an evolution from COOLFluiD 2, a code primarily developed at the Von Karman Institute for fluid dynamics (VKI). FEM_CFD_Steady_Test3D solution of the steady 3D Navier-Stokes equations around a bluff body (a description of the geometry is given here) FEM_CFD_Dfg2D 2D unsteady Navier-Stokes equations: flow around a cylinder benchmark. GPGPU Particles (General-Purpose computing on Graphics Processing Units) Animation. Fluid Simulation for Video Games (part 19) About the Author Dr. When you are limited by the amount of memory and the number of cores available on a single mainboard, there is a limit to the level of realism you can achieve. In summer 2018, while I was working at Atomic Raccoon (an Indie Game Studio in Paris), we were wondering how to run a simulation with many characters interacting with each others like a fluid. Also the plugin isn't free and a single-seat license costs about eight hundred dollars. Define the velocity and pressure in a 3D space. , for spline research. I am a third year Ph. You can also see an init function was passed at the end of the definition. GitHub Gist: instantly share code, notes, and snippets. Open Source Software. It took me 4 or 5 times reading through most sections to make sense of it, and ultimately I only understood parts of it after I did the derivations myself. [adult swim] Character Soup. All gists Back to GitHub. This page provides links to the pages describing a number of the individual software packages installed centrally on ARCHER. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. However, even in the default automatic mode, there are refinement options available to the user. SU2, the Open-Source CFD Code. PhysX is a scalable multi-platform game physics solution supporting a wide range of devices, from smartphones to high-end multicore CPUs. It is intended to be quite modular, with a variety of numerical methods and time-integration solvers available. The project consist of three steps: (1) particle simulation, (2) surface reconstruction and (3) video rendering. The Chrome Experiments site hosts lots of interesting graphical ideas, but Felix Woitzel's fluid simulation has to be ranked among the best. To push changes to GitHub using this older client version, you must include your GitHub username in the HTTPS URL. Among the UV ink components, oligomers have the highest tendency to agglomerate which can agitate the stability and quality of the printing fluid and possibly lead to nanoscale nozzle clogging. Thorsten Stoesser and co-workers at Cardiff University, UK, primarily for use in the simulation of environmental fluid dynamics. A Legendre spectral element method for simulation of incompressible unsteady viscous free-surface flows. Because of the large amount of parallelism in graphics hardware, the simulation we describe runs significantly faster on the GPU than on the CPU. It is very simple to understand and provides almost all the code required to implement the simulation in 2D, along with explanations as to what is the code is doing as well as an overview of the underlying physics being simulated. js and WebGL. A list of 9 instructional test cases can be found in the Instructional_Cases folder of the repository. He generously shares the source code to a series of programs on his Incremental Fluids GitHub that cover implementing a 2D fluid simulation. Processing is a flexible software sketchbook and a language for learning how to code within the context of the visual arts. Download Fluid Simulation for Video Games (Part 21) [PDF 830KB] Recapitulation. 0 Programming Guide. I would like to develop a physic-based game which requires fluid simulations (flows). FluidDraw S5 is an application for creating pneumatic circuit diagrams. free to use portfolio templates. The fluid domain is divided into a rectangular grid or lattice, with the same spacing ‘h’ in both the x- and the y-directions, as shown in the figure. 10th Industrial Fluid Properties Simulation Challenge | Obtain reliable estimates using molecular simulation for the shear viscosity of 2,2,4-trimethylhexane from 0. Applications to enhanced oil recovery, water resources. The project consists of two parts. com) is a fully integrated Computer Aided Engineering (CAE), Finite Element Analysis (FEA), and Computational Fluid Dynamics (CFD) MATLAB Toolboxes for modeling and simulation of fully coupled systems of PDEs, physics and engineering applications with the finite element method (FEM). The GPL gives users the freedom to modify and redistribute the software and a guarantee of continued free use, within the terms of the licence. Introduction. FEM_CFD_Steady_Test3D solution of the steady 3D Navier-Stokes equations around a bluff body (a description of the geometry is given here) FEM_CFD_Dfg2D 2D unsteady Navier-Stokes equations: flow around a cylinder benchmark. Implementation details of each feature and performance results can be found on the project's GitHub repository. 995 and watching different colors interact is just beautiful. FLIP Fluids Beta. (I apologize that it's not a "signed" applet so you may have to modify your Java settings to run it. Embedded Boundaries For computations with complex geometries, AMReX provides data structures and algorithms to employ an embedded boundary (EB) approach to PDE discretizations. Novel Fluid Detail Enhancement based on Multi-Layer Depth Regression Analysis and FLIP Fluid Simulation Yuxing Qiu, Lipeng Yang, Shuai Li, Qing Xia, Hong Qin, and Aimin Hao Computer Animation and Virtual Worlds, 2016, doi:10. This research area has many applications like Virtual Reality (VR), medical simulations, computer games or virtual prototyping. Fluid simulation is a useful building block that is the basis for simulating a variety of natural phenomena. The optimization problem is sent to the APMonitor server and results are returned to MATLAB local variables and a web interface. View the Project on GitHub KratosMultiphysics/Examples. 2MB] Introduction to Fluid Dynamics. OpenFOAM is the free, open source CFD software released and developed primarily by OpenCFD Ltd since 2004. Run models on Arduino boards. Example applications of nonlinear models with differential and algebraic equations are available for download below or from the following GitHub repository. FluidDraw S5 (FluidDraw5. Simulating fluid flow allows us to see how the fluid pressure underground changes in response to injection. It took me 4 or 5 times reading through most sections to make sense of it, and ultimately I only understood parts of it after I did the derivations myself. Fluid and use the same ports to ensure compatibility with the Modelica Standard Lib. You can still view a video. I recommend setting bloom threshold to like 0. It provides support for procedural animation of physical bodies to make objects move and interact in realistic ways. (presentation) Zhi Shang, Yufeng Yao. High-Order Accurate Fluid-Structure Simulation of a Tuning Fork Bradley Froehlea, Per-Olof Perssona, aDepartment of Mathematics, University of California, Berkeley, Berkeley, CA 94720-3840, USA Abstract The aeroacoustics of a tuning fork are investigated using a high-order uid-structure interaction (FSI) scheme. The collisionless shock is a hydrodynamic shock wave where collective plasma phenomena (such as wave-particle interactions), instead of binary Coulomb collisions, plays the role for the dissipation required for the formation of a shock wave. There are other objects the simulator can manage: forces, fluid sources and fluid sinks. This tutorial covers 2D physics, materials, shaders and camera rendering. Controls : Left click and right click. LarmorFluid: PIC/FLIP fluid simulation Solver I have just released on GitHub a first development version of LarmorFluid, another classical implementation of PIC/FLIP fluid simulation solver based on algorithms described in the book “Fluid Simulation for Computer Graphics” by Robert Bridson, but with some particular future goals:. The fluid domain is divided into a rectangular grid or lattice, with the same spacing ‘h’ in both the x- and the y-directions, as shown in the figure. Abstract: Momentum conservation has long been used as a design principle for solid simulation (e. Original version by Demidov. A CodePen by Adam. js and ammo. lib files, with the corresponding. Find a detailed description of the code philosophy, components, and implementations in the SU2 AIAA Journal article. To me it looks like sort of a middle-ground solution for small or medium-scale simulations. Do not hesitate to email me if you have any questions. 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An open source library for thermodynamics, physical properties and process simulation. https://thecodingtrain. [Ho1989] Ho, L. The objects with a geometry inside the domain will be considered as fluids or solid obstacles. 11/04/2016; 5 minutes to read +3; In this article. Ray Optics Simulation. Original version by Demidov. Coolfluid 3 is a major redesign, taking into. Hopsan is a modelling and simulation environment for fluid and mechatronic systems. Workflow; Fluid Types. Fluid Simulation was added by Ugotsta in Aug 2019 and the latest update was made in Sep 2019. , presented at ACM SIGGRAPH 2019] –37 SPH for the Physics Based Simulation of Fluids and Solids [Gissler et al. The simulation is governed by the Navier-Stokes equations and requires the access to the velocity field of the fluid (Fernando, 2004) which is not directly observable from the drawing. Feel bored or anxious? This app can solve your problem! Play with fluids with a touch of your fingers. A Complex Fluids Toolkit for Dedalus Read more Direct Statistical Simulation for. Generalized Fluid System Simulation Program (GFSSP), Version 701. Keyword Results fluid simulation real time browser. Fluid modeling of plasmas (March 2018): This new course will teach you how simulate dense plasmas in which the continuum assumption holds. Fluid Simulation + SoftBody Dynamics + Optical Flow + Rendering + Image Processing + Particle Systems + Physics + - diwi/PixelFlow. The default automatic mesh settings work very well for most flow simulation problems. The code is written in C++. Contribute to gufoe/rust-fluid development by creating an account on GitHub. This walkthrough demonstrates how to use the Visual Studio Graphics Diagnostics tools to investigate a compute shader that generates incorrect results. 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# How to get the filename without the extension from a path in Python?
How to get the filename without the extension from a path in Python?
For instance, if I had "/path/to/some/file.txt", I would want "file".
• I had to scroll pretty far before coming across the clear right answer for modern Python: from pathlib import Path; print(Path("/path/to/some/file.txt").stem) >>> file – BallpointBen Jan 31 at 4:39
Getting the name of the file without the extension:
import os
print(os.path.splitext("/path/to/some/file.txt")[0])
Prints:
/path/to/some/file
Important Note: If the filename has multiple dots, only the extension after the last one is removed. For example:
import os
print(os.path.splitext("/path/to/some/file.txt.zip.asc")[0])
Prints:
/path/to/some/file.txt.zip
See other answers below if you need to handle that case.
• If this is a common enough operation, perhaps it should merit it's own official command? Something like os.path.filename(path_to_file) instead of os.path.splitext(os.path.basename(path_to_file))[0] – Fnord Jul 2 '14 at 17:13
• What if the filename contains multiple dots? – matteok Dec 5 '14 at 17:42
• For anyone wondering the same as matteok, if there are multiple dots, splitext splits at the last one (so splitext('kitty.jpg.zip') gives ('kitty.jpg', '.zip')). – Chuck Jan 22 '15 at 18:15
• Note that this code returns the complete file path (without the extension), not just the file name. – Aran-Fey Oct 17 '18 at 7:13
• yeah, so you'd have to do splitext(basename('/some/path/to/file.txt'))[0] (which i always seem to be doing) – CpILL Nov 4 '19 at 23:51
You can make your own with:
>>> import os
>>> base=os.path.basename('/root/dir/sub/file.ext')
>>> base
'file.ext'
>>> os.path.splitext(base)
('file', '.ext')
>>> os.path.splitext(base)[0]
'file'
Important note: If there is more than one . in the filename, only the last one is removed. For example:
/root/dir/sub/file.ext.zip -> file.ext
/root/dir/sub/file.ext.tar.gz -> file.ext.tar
See below for other answers that address that.
• This answer should have the "green tick" – int soumen Mar 5 at 6:08
Use .stem from pathlib in Python 3.4+
from pathlib import Path
Path('/root/dir/sub/file.ext').stem
will return
'file'
Note that if your file has multiple extensions .stem will only remove the last extension. For example, Path('file.tar.gz').stem will return 'file.tar'.
• This is the recommended way since python 3. – Miladiouss Nov 15 '19 at 2:21
• Note that, like os.path solutions, this will only strip one extension (or suffix, as pathlib calls it). Path('a.b.c').stem == 'a.b' – BallpointBen Mar 18 '20 at 4:26
• @BallpointBen what is the optimal way of stripping multiple suffixes? Surely there must be a better way than Path(Path('a.b.c').stem).stem – hoan May 13 '20 at 13:53
• @hoan I think repeatedly calling .with_suffix('') is the way to go. You'd probably want to loop until p.suffix == ''. – BallpointBen May 13 '20 at 15:00
• It will not work for files with complex extensions: pathlib.Path('backup.tar.gz').stem -> 'backup.tar but expected backup – pymen Jun 15 '20 at 11:11
>>> print(os.path.splitext(os.path.basename("/path/to/file/hemanth.txt"))[0])
hemanth
• +1 for this. 3 exact same answers, but this is the most direct one. You just could have used for showing the code, and "/somepath/hermanth.txt" as a path instance. – cregox May 21 '10 at 20:57
• @hemanth.hm Note that in this statement you provided, os.path.basename is not necessary. os.path.basename should be only used to get the file name from the file path. – arrt_ Jan 25 '18 at 12:53
In Python 3.4+ you can use the pathlib solution
from pathlib import Path
print(Path(your_path).resolve().stem)
• Why do you resolve() the path? Is it really possible to get a path to a file and not have the filename be a part of the path without that? This means that if you're give a path to symlink, you'll return the filename (without the extension) of the file the symlink points to. – Boris Oct 11 '19 at 15:43
• One possible reason to use resolve() is to help deal with the multiple dots problem. The answer below about using the index will not work if the path is './foo.tar.gz' – William Allcock Feb 12 '20 at 22:51
https://docs.python.org/3/library/os.path.html
In python 3 pathlib "The pathlib module offers high-level path objects." so,
>>> from pathlib import Path
>>> p = Path("/a/b/c.txt")
>>> print(p.with_suffix(''))
\a\b\c
>>> print(p.stem)
c
• This is the best python 3 solution for the generic case of removing the extension from a full path. Using stem also removes the parent path. In case you are expecting a double extension (such as bla.tar.gz) then you can even use it twice: p.with_suffix('').with_suffix(''). – Eelco van Vliet Feb 26 '20 at 12:37
os.path.splitext() won't work if there are multiple dots in the extension.
For example, images.tar.gz
>>> import os
>>> file_path = '/home/dc/images.tar.gz'
>>> file_name = os.path.basename(file_path)
>>> print os.path.splitext(file_name)[0]
images.tar
You can just find the index of the first dot in the basename and then slice the basename to get just the filename without extension.
>>> import os
>>> file_path = '/home/dc/images.tar.gz'
>>> file_name = os.path.basename(file_path)
>>> index_of_dot = file_name.index('.')
>>> file_name_without_extension = file_name[:index_of_dot]
>>> print file_name_without_extension
images
• index_of_dot = file_name.index('.') This will be done after getting the basename of the file so that it wont split at .env – Dheeraj Chakravarthi Oct 5 '16 at 4:22
• Important point, as a series of extensions like this is common. .tar.gz .tar.bz .tar.7z – user6798019 Oct 18 '17 at 12:23
• Note that 'haystack'.index('needle') throws a ValueError exception if the needle (in above case the dot, .) is not found in haystack. Files without any extension exist too. – Czechnology Mar 27 '18 at 7:54
• to solve that problem, use a try-catch, or use str.find() and check for -1. if there's no dot, then just return file_name – Starwarswii Jun 15 at 17:52
If you want to keep the path to the file and just remove the extension
>>> file = '/root/dir/sub.exten/file.data.1.2.dat'
>>> print ('.').join(file.split('.')[:-1])
/root/dir/sub.exten/file.data.1.2
• If you want to split on the last period, use rsplit: '/root/dir/sub.exten/file.data.1.2.dat'.rsplit('.', 1) – IceArdor Dec 4 '14 at 22:32
@IceAdor's refers to rsplit in a comment to @user2902201's solution. rsplit is the simplest solution that supports multiple periods.
Here it is spelt out:
file = 'my.report.txt'
print file.rsplit('.', 1)[0]
my.report
But even when I import os, I am not able to call it path.basename. Is it possible to call it as directly as basename?
import os, and then use os.path.basename
importing os doesn't mean you can use os.foo without referring to os.
• though if you wanted to call foo directly you could use from os import foo. – tgray Mar 24 '09 at 17:33
• you have a very non-standard version of the os module if it has a member called foo. – Tadhg McDonald-Jensen Jun 6 '16 at 21:13
• It's a placeholder name. (e.g. consider path, or walk). – Devin Jeanpierre Jun 9 '16 at 9:01
Thought I would throw in a variation to the use of the os.path.splitext without the need to use array indexing.
The function always returns a (root, ext) pair so it is safe to use:
root, ext = os.path.splitext(path)
Example:
>>> import os
>>> path = 'my_text_file.txt'
>>> root, ext = os.path.splitext(path)
>>> root
'my_text_file'
>>> ext
'.txt'
• os.path.splittext() is Version 3.6+ – Yzmir Ramirez Apr 2 '20 at 2:04
The other methods don't remove multiple extensions. Some also have problems with filenames that don't have extensions. This snippet deals with both instances and works in both Python 2 and 3. It grabs the basename from the path, splits the value on dots, and returns the first one which is the initial part of the filename.
import os
def get_filename_without_extension(file_path):
file_basename = os.path.basename(file_path)
filename_without_extension = file_basename.split('.')[0]
return filename_without_extension
Here's a set of examples to run:
example_paths = [
"FileName",
"./FileName",
"../../FileName",
"FileName.txt",
"./FileName.txt.zip.asc",
"/path/to/some/FileName",
"/path/to/some/FileName.txt",
"/path/to/some/FileName.txt.zip.asc"
]
for example_path in example_paths:
print(get_filename_without_extension(example_path))
In every case, the value printed is:
FileName
• Except for the added value of handling multiple dots, this method is way more fast than Path('/path/to/file.txt').stem. (1,23μs vs 8.39μs) – raratiru Aug 6 '19 at 18:02
• This doesn't work for filename nvdcve-1.1-2002.json.zip – Michele Jan 11 '20 at 19:46
• I split it on fileBasename.split('.json')[0] and it worked – Michele Jan 11 '20 at 19:49
## Two or fewer extensions
As mentioned in the comments of other Pathlib answers, it can be awkward to handle multiple suffixes. Two or fewer suffixes is not so bad to handle with .with_suffix('') and .stem.
from pathlib import Path
pth = Path('foo/bar/baz.baz/thefile.tar.gz')
fn = pth.with_suffix('').stem
print(fn) # thefile
## Any number of extensions
If there may be more than two extensions, you may use a loop to handle the general case where there could be 0, 1, or many suffixes.
pth = Path('foo/bar/baz/thefile.tar.gz.bz.7zip')
pth.name # 'thefile.tar.gz.bz.7zip'
pth.suffixes # ['.tar', '.gz', '.bz', '.7zip']
so
fn = pth.name
for s in pth.suffixes:
fn = fn.rsplit(s)[0]
print(fn) # thefile
or
fnp = Path(pth.name)
for _ in fnp.suffixes:
fnp = fnp.with_suffix('')
print(fnp) # thefile
Note here that fnp is a path, while fn is a string, which may determine the form of the loop that is preferred.
### In the case that you know the first extension
For instance, if the extension could be .tar, .tar.gz, .tar.gz.bz, etc; you can simply rsplit the known extension and take the first element:
pth = Path('foo/bar/baz.baz/thefile.tar.gz')
fn = pth.name.rsplit('.tar')[0]
print(fn) # thefile
import os
filename = C:\\Users\\Public\\Videos\\Sample Videos\\wildlife.wmv
This returns the filename without the extension(C:\Users\Public\Videos\Sample Videos\wildlife)
temp = os.path.splitext(filename)[0]
Now you can get just the filename from the temp with
os.path.basename(temp) #this returns just the filename (wildlife)
import os
path = "a/b/c/abc.txt"
print os.path.splitext(os.path.basename(path))[0]
A multiple extension aware procedure. Works for str and unicode paths. Works in Python 2 and 3.
import os
def file_base_name(file_name):
if '.' in file_name:
separator_index = file_name.index('.')
base_name = file_name[:separator_index]
return base_name
else:
return file_name
def path_base_name(path):
file_name = os.path.basename(path)
return file_base_name(file_name)
Behavior:
>>> path_base_name('file')
'file'
>>> path_base_name(u'file')
u'file'
>>> path_base_name('file.txt')
'file'
>>> path_base_name(u'file.txt')
u'file'
>>> path_base_name('file.tar.gz')
'file'
>>> path_base_name('file.a.b.c.d.e.f.g')
'file'
>>> path_base_name('relative/path/file.ext')
'file'
>>> path_base_name('/absolute/path/file.ext')
'file'
>>> path_base_name('Relative\\Windows\\Path\\file.txt')
'file'
>>> path_base_name('C:\\Absolute\\Windows\\Path\\file.txt')
'file'
>>> path_base_name('/path with spaces/file.ext')
'file'
>>> path_base_name('C:\\Windows Path With Spaces\\file.txt')
'file'
>>> path_base_name('some/path/file name with spaces.tar.gz.zip.rar.7z')
'file name with spaces'
import os
filename, file_extension =os.path.splitext(os.path.basename('/d1/d2/example.cs'))
• filename is 'example'
• file_extension is '.cs'
'
• this actually answers the OP's question – Fred Apr 30 at 12:14
Very very very simpely no other modules !!!
import os
p = r"C:\Users\bilal\Documents\face Recognition python\imgs\northon.jpg"
# Get the filename only from the initial file path.
filename = os.path.basename(p)
# Use splitext() to get filename and extension separately.
(file, ext) = os.path.splitext(filename)
# Print outcome.
print("Filename without extension =", file)
print("Extension =", ext)
On Windows system I used drivername prefix as well, like:
>>> s = 'c:\\temp\\akarmi.txt'
>>> print(os.path.splitext(s)[0])
c:\temp\akarmi
So because I do not need drive letter or directory name, I use:
>>> print(os.path.splitext(os.path.basename(s))[0])
akarmi
the easiest way to resolve this is to
import ntpath
print('Base name is ',ntpath.basename('/path/to/the/file/'))
this saves you time and computation cost.
We could do some simple split / pop magic as seen here (https://stackoverflow.com/a/424006/1250044), to extract the filename (respecting the windows and POSIX differences).
def getFileNameWithoutExtension(path):
return path.split('\\').pop().split('/').pop().rsplit('.', 1)[0]
getFileNameWithoutExtension('/path/to/file-0.0.1.ext')
# => file-0.0.1
getFileNameWithoutExtension('\\path\\to\\file-0.0.1.ext')
# => file-0.0.1
• os.path.splitext()[0] does the same thing. – Charles Plager Sep 13 '16 at 14:14
• @CharlesPlager os.path.splitext() won't work if there are multiple dots in the extension. stackoverflow.com/a/37760212/1250044 – yckart Sep 13 '16 at 15:05
• It works for me: In [72]: os.path.splitext('one.two.three.ext') Out[72]: ('one.two.three', '.ext') – Charles Plager Sep 13 '16 at 18:35
For convenience, a simple function wrapping the two methods from os.path :
def filename(path):
"""Return file name without extension from path.
See https://docs.python.org/3/library/os.path.html
"""
import os.path
b = os.path.split(path)[1] # path, *filename*
f = os.path.splitext(b)[0] # *file*, ext
#print(path, b, f)
return f
Tested with Python 3.5.
I didn't look very hard but I didn't see anyone who used regex for this problem.
I interpreted the question as "given a path, return the basename without the extension."
e.g.
"path/to/file.json" => "file"
"path/to/my.file.json" => "my.file"
In Python 2.7, where we still live without pathlib...
def get_file_name_prefix(file_path):
basename = os.path.basename(file_path)
file_name_prefix_match = re.compile(r"^(?P<file_name_pre fix>.*)\..*\$").match(basename)
if file_name_prefix_match is None:
return file_name
else:
return file_name_prefix_match.group("file_name_prefix")
get_file_name_prefix("path/to/file.json")
>> file
get_file_name_prefix("path/to/my.file.json")
>> my.file
get_file_name_prefix("path/to/no_extension")
>> no_extension
Improving upon @spinup answer:
fn = pth.name
for s in pth.suffixes:
fn = fn.rsplit(s)[0]
break
print(fn) # thefile
This works for filenames without extension also
import os
list = []
def getFileName( path ):
for file in os.listdir(path):
#print file
try:
base=os.path.basename(file)
splitbase=os.path.splitext(base)
ext = os.path.splitext(base)[1]
if(ext):
list.append(base)
else:
newpath = path+"/"+file
#print path
getFileName(newpath)
except:
pass
return list
getFileName("/home/weexcel-java3/Desktop/backup")
print list
I've read the answers, and I notice that there are many good solutions. So, for those who are looking to get either (name or extension), here goes another solution, using the os module, both methods support files with multiple extensions.
import os
def get_file_name(path):
if not os.path.isdir(path):
return os.path.splitext(os.path.basename(path))[0].split(".")[0]
def get_file_extension(path):
extensions = []
copy_path = path
while True:
copy_path, result = os.path.splitext(copy_path)
if result != '':
extensions.append(result)
else:
break
extensions.reverse()
return "".join(extensions)
`
Note: this solution on windows does not support file names with the "\" character |
# Attributes
Domains:
## The href Attribute
HTML links are defined with the <a> tag. The link address is specified in the href attribute:
<a href="https://www.w3schools.com">This is a link</a>
You will learn more about links and the <a> tag later in this tutorial.
## The src Attribute
HTML images are defined with the <img> tag.
The filename of the image source is specified in the src attribute:
<img src="img_girl.jpg">
## The width and height Attributes
Images in HTML have a set of size attributes, which specifies the width and height of the image:
<img src="img_girl.jpg" width="500" height="600">
The image size is specified in pixels: width="500" means 500 pixels wide.
## The alt Attribute
The alt attribute specifies an alternative text to be used, when an image cannot be displayed.
The value of the attribute can be read by screen readers. This way, someone "listening" to the webpage, e.g. a vision impaired person, can "hear" the element.
<img src="img_girl.jpg" alt="Girl with a jacket">
The alt attribute is also useful if the image does not exist:
See what happens if we try to display an image that does not exist:
<img src="img_typo.jpg" alt="Girl with a jacket">
## The style Attribute
The style attribute is used to specify the styling of an element, like color, font, size etc.
<p style="color:red">I am a paragraph</p>
## The lang Attribute
The language of the document can be declared in the <html> tag.
The language is declared with the lang attribute.
Declaring a language is important for accessibility applications (screen readers) and search engines:
<!DOCTYPE html>
<html lang="en-US">
<body>
...
</body>
</html>
The first two letters specify the language (en). If there is a dialect, use two more letters (US).
## The title Attribute
Here, a title attribute is added to the <p> element. The value of the title attribute will be displayed as a tooltip when you mouse over the paragraph:
<p title="I'm a tooltip">
This is a paragraph.
</p>
## We Suggest: Use Lowercase Attributes
The HTML5 standard does not require lowercase attribute names.
The title attribute can be written with uppercase or lowercase like title or TITLE.
We recommends lowercase in HTML, and demands lowercase for stricter document types like XHTML.
## We Suggest: Quote Attribute Values
The HTML5 standard does not require quotes around attribute values.
The href attribute, demonstrated above, can be written without quotes:
Bad Good
We recommends quotes in HTML, and demands quotes for stricter document types like XHTML.
Sometimes it is necessary to use quotes. This example will not display the title attribute correctly, because it contains a space:
<p title=About W3Schools>
Using quotes are the most common. Omitting quotes can produce errors. We always use quotes around attribute values.
## Single or Double Quotes?
Double quotes around attribute values are the most common in HTML, but single quotes can also be used.
In some situations, when the attribute value itself contains double quotes, it is necessary to use single quotes:
<p title='John "ShotGun" Nelson'>
Or vice versa:
<p title="John 'ShotGun' Nelson">
## Chapter Summary
• All HTML elements can have attributes
• The title attribute provides additional "tool-tip" information
• The href attribute provides address information for links
• The width and height attributes provide size information for images
• The alt attribute provides text for screen readers
• We always use lowercase attribute names
• We always quote attribute values with double quotes
## HTML Attributes
Below is an alphabetical list of some attributes often used in HTML, which you will learn more about in this tutorial:
Attribute Description
alt Specifies an alternative text for an image, when the image cannot be displayed
disabled Specifies that an input element should be disabled
id Specifies a unique id for an element
src Specifies the URL (web address) for an image
style Specifies an inline CSS style for an element
title Specifies extra information about an element (displayed as a tool tip)
A complete list of all attributes for each HTML element, is listed in: HTML Attribute Reference.
Page structure
Terms |
# Difference between revisions of "2018 AMC 8 Problems/Problem 11"
## Problem 11
Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown. $\begin{eqnarray*} \text{X}&\quad\text{X}\quad&\text{X} \\ \text{X}&\quad\text{X}\quad&\text{X} \end{eqnarray*}$ If the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjacent to each other in the same row or the same column?
$\textbf{(A) } \frac{1}{3} \qquad \textbf{(B) } \frac{2}{5} \qquad \textbf{(C) } \frac{7}{15} \qquad \textbf{(D) } \frac{1}{2} \qquad \textbf{(E) } \frac{2}{3}$
## Solution
There are a total of 6! ways to arrange the kids.
Abby and Bridget can sit in 3 ways if they are adjacent in the same column: $\begin{eqnarray*} \text{A}&\quad\text{X}\quad&\text{X} \\ \text{B}&\quad\text{X}\quad&\text{X} \end{eqnarray*}$
$\begin{eqnarray*} \text{X}&\quad\text{A}\quad&\text{X} \\ \text{X}&\quad\text{B}\quad&\text{X} \end{eqnarray*}$
$\begin{eqnarray*} \text{X}&\quad\text{X}\quad&\text{A} \\ \text{X}&\quad\text{X}\quad&\text{B} \end{eqnarray*}$
For each of these seat positions, Abby and Bridget can switch seats, and the other 4 people can be arranged in $4!$ ways which results in a total of $3 \times 2 \times 4!$ ways to arrange them.
By the same logic, there are 4 ways for Abby and Bridget to placed if they are adjacent in the same row, they can swap seats, and the other $4$ people can be arranged in $4!$ ways, for a total of $4 \times 2 \times 4!$ ways to arrange them.
We sum the 2 possibilities up to get $\frac{14*4!}{6!}=\boxed{\frac{7}{15}}$ or $\textbf{(D)}$ - song2sons
2018 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 10 Followed byProblem 12 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions |
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# The Public Lab Blog
stories from the Public Lab community
by warren | about 2 years ago | 0 | 3
Across the Public Lab community, people are making their own maps using aerial photos (by balloon mapping, kite mapping, and the like) with the MapKnitter website - which helps people "stitch" or "knit" images into a combined map, using an existing satellite map base layer as a reference.
The core of MapKnitter's interface, the Leaflet.DistortableImage library, is seeing some new life as members of our coding community have started to dig in and make improvements! Its main goal of letting people distort aerial images to fit onto a map is being refined, debugged, and expanded. (This was made possible in part with support from NASA's AREN project)
Above, a new feature you can see in the menu is a full resolution download -- with no server-side processing at all. This was made possible through a lot of work by John905 and rexagod.
Try it out in the demo: https://publiclab.github.io/Leaflet.DistortableImage/examples/
This takes the original full resolution image and distorts it in your browser (you may need to allow popups), and then downloads.
For example, the lead image generated this full-res distorted image: full.png (2304x1536 pixels)
See the preview below.
This may mean that for some smaller MapKnitter maps, you won't need to run a full export, which can take a while. This code should publish on MapKnitter within the next few days. Down the road, we're looking at more ways to refine the export process to make it even easier to make your own maps using balloon, kite, pole, or drone mapping.
balloon-mapping kite-mapping mapknitter aerial-photography
# RV SensorShip V
by cfastie | about 2 years ago | 2 | 7
The original SensorShip had four environmental sensors and it was hard to cram all the wiring into the sailboat I printed for it. I was also concerned that a sailboat is not a ship. I also wanted a SensorShip with more sensors. So I searched Thingiverse for a more appropriate vessel.
Figure 1. An ESP8266 board and the bi- and trifurcating wiring harness for five I²C sensors (each sensor gets connected to the same four pins on the board). Plus three LEDs and a piezo buzzer. I’m going to need a bigger boat.
I quickly found Peter Sripol’s Utility Ship and the easier to print "make" of it by 08stanis. I immediately liked this ship because I had just reread Steinbeck’s The Log from the Sea of Cortez and the model reminded me of the Western Flyer.
Figure 2. The Western Flyer was built in 1937 and spent six weeks in 1940 in the Sea of Cortez with John Steinbeck and Ed Ricketts aboard. She had a long, hard life and was recently lifted off the harbor bottom and brought onto the hard.
Figure 3. The Western Flyer is being restored in Port Townsend, WA and will be used as a floating classroom and memorial to the poorly-formed ideas of Steinbeck and Ricketts about ecology and politics. Learn more here.
The new model is not really a ship, but it is a bigger boat and is designed to be easy to open to install stuff inside. It is intended for printing about two feet long, but it works well when printed 7.5 inches long.
Figure 4. The new RV SensorShip V is easy to print in 15 pieces and fun to glue together especially if assembling model boats is one of your favorite things to do. I used superglue.
Figure 5. The entire deck of RV SensorShip V can be used like a lid so it’s easy to install important stuff inside.
Figure 6. RV SensorShip V has five I²C sensors. Clockwise from upper left: BME280 (temperature, humidity, pressure), MLX90615 (thermal IR), VL53LOX (laser rangefinder), TSL2561 (light level), and MMA8451 (3 axis accelerometer). The paperclip on the left is for scale.
Figure 7. Two sensors are mounted on the stern deck of RV SensorShip V so they can be directed together at areas of interest. The laser rangefinder (right) and thermal IR (left) sensors are both directional.
Figure 8. Screen capture from the Blynk app of three hours of the data records from three of the five sensors on RV SensorShip V. The ship was next to my 3D printer when a 30-minute print was running. The laser rangefinder and thermal IR sensors were pointed toward the print head.
SensorShips incorporate ESP8266 microcontroller boards with integrated Wi-Fi. Data from the sensors are sent via Wi-Fi to the internet. This SensorShip sends its data to a Blynk server and the data can be viewed on a mobile device in real time.
A new feature of this SensorShip is the pair of directional sensors on the stern deck. I oriented the ship so these sensors were pointed near the print head while a short 3D print was made. Both of these sensors and also the accelerometer captured a clear record of when the 3D printer was operating (Figure 8).
This past weekend there were three days in a row with nighttime temperatures near 0°F. I have been heating my house with a woodstove this winter and was concerned that the cold snap might freeze pipes in the basement. I placed RV SensorShip V in the crawlspace where the most vulnerable pipes are. Fortunately we had some snow before the weekend, so I was able to bank the foundation with snow to provide some insulation.
Figure 9. I banked snow around the entire house before the cold weekend.
Figure 10. Temperature results from three different SensorShips for a week including a very cold weekend. RV SensorShip V (bottom) had its directional sensors pointed at the most vulnerable pipes in the crawlspace. The rangefinder was well positioned to detect raccoons. On Tuesday the 15th (dashed line) I surrendered and started using the oil furnace in addition to the woodstove. This figure is made from three screen captures from the Blynk app which were combined and annotated in Photoshop.
The basement low temperature dropped about one degree F for each of the cold nights finally dropping into the 30s F. I thought I had weathered the weather, but more cold nights were forecast, and in a few days the daytime high is forecast to be not much above 0°F. The woodstove would have a difficult time counteracting such temperatures, and provides almost no heat to the basement, so I ordered more heating oil for the furnace (which is in the basement).
I ran the furnace four times (Figure 10) in the first three days after the delivery (I had been out of oil since April). I learned that in order to raise the temperature on the first floor of the house into the 60s F, the temperature in the basement has to be warmed into the 50s F. That’s one reason I don’t like to use the furnace, but I think I will be very thankful for it over the next several days when the four-day average temperature will be very close to 0°F.
All three of the SensorShips use an ESP8266 board and connect to the internet via the integrated Wi-Fi. So SensorShips must remain in the range of my home Wi-Fi signal. I was pleased that RV SensorShip V had no problem connecting from the basement, even though the Wi-Fi router is on the second floor at the other end of the house.
All of the SensorShips are powered by 5V phone chargers plugged into the wall. They would last only a couple of days if powered by batteries because everything is powered continuously. I have not yet figured out how to sleep the ESP8266 boards or to use a low power external timer with them (my first attempt to use a timer failed). Let me know if you know a trick for using these boards with a TPL5110 timer.
arduino sensors blog wi-fi
# Seeking GIS / Data folks: Help us create a nation Lead Exposure Risk map.
Overview
Quite a bit of public data exists now that, if brought together, can paint the picture of lead exposure within neighborhoods across the country. This information is useful to a couple audiences: Concerned citizens can see what their risk is; this is general. More specifically and strategically: Community scientists and activists can prioritize where they work. And Public Health officials can prioritize where they work.
There are a few efforts out there, but much of it is local (particular to one city and/or state), or is incomplete or due for an upgrade. We’re seeking data scientists, epidemiologists, and GIS folks to build on these efforts.
The output is a simple map with lead risk scores presented by a geographical unit (census track, neighborhood, etc). The effort should be done in the open and documented (presumably on github, but maybe also here on publiclab.org).
If this is interesting to you, let us know and we can figure out how to work together.
The following are examples of work in this area. Each is useful and has strengths but (I think) insufficient.
## Example 1: Washington State Department of Health
Childhood Lead Risk Map For this measure we combined two variables: Percent people living below the 125% Federal Poverty Level (FPL) and Percent Housing built before 1980 (and weighted by era built).
Information About the Data In addition to the census of every U.S. household every 10 years, as required by the U.S. Constitution, the Census Bureau has a sub-sample, yearly survey called the American Community Survey (ACS). This representative sample-based survey gathers characteristics for a subset of the entire population of the U.S. each year.
You can find supporting documentation on code lists, subject definitions, data accuracy, and statistical testing on the ACS website, Data and Documentation section. You can find sample size and data quality measures (including coverage rates, allocation rates, and response rates) on the ACS website in the Methodology section.
## Example 2: Vox (with Washington State Department of Health)
From the article: “The trouble is that exposure risk is surprisingly difficult estimate, due to a variety of state-by-state differences in reporting standards. So we worked with epidemiologists in Washington state to estimate risk levels in every geographic area in America…
Our map uses a methodology that Washington State’s Department of Health pioneered earlier this year to estimate kids’ risk of lead exposure in different neighborhoods. Their mission was to determine how to focus scarce public health dollars on the kids most at risk of being poisoned by lead. We worked with one of the chief epidemiologists who created the map, Rad Cunningham, to replicate the state’s methodology nationally and apply it to all 72,241 census tracts in the United States.”
## Example 3: Reuters
From the article: “Most U.S. states disclose data on the percentage of child blood tests that show elevated levels of lead. Yet this data, often for statewide or county-wide populations, is too broad to identify neighborhoods where children face the greatest risk.
Instead, Reuters sought testing data at the neighborhood level, in census tracts or zip code areas, submitting records requests to all 50 states.
U.S. census tracts are small county subdivisions that average about 4,000 residents apiece. Zip codes have average populations of 7,500. In each area, a relatively small number of children are screened for lead poisoning each year.
Reuters found 2,606 census tracts, and another 278 zip code areas, with a prevalence of lead poisoning at least twice Flint’s rate."
If you're a data guru, GIS epidemiologist, or just someone who wants to contribute to this effort, post a comment below or reach out to Read Holman at read@publiclab.org. Thanks!
# Experiment with polarizing filters to view crystalline dust
by warren | about 2 years ago | 3 | 3
Over the years, a lot of people have been looking at crystalline particles under a microscope (like the DIY Community Microscope Kit), and the idea has come up a few times to try using polarizing filters -- for example to try to distinguish crystalline particles from other types of particles.
See #10493, #17785, and others under #polarized-light-microscopy:
### How does it work?
The idea (I think) is that crystals "twist" the polarity of light, and so shining polarized light through them, and then re-filtering it with a second polarizer would... block or allow light differently through crystalline particles when compared to non-crystalline particles.
I'd love to hear more specifics from folks on what's happening here, but in any case the effect is that crystalline particles look really different, and change color pretty dramatically when the polarizers are rotated.
You can read a lot more on this, and see some early tests, here: #10493
### Samples
Crystalline #silica is dangerous to breathe in; please be careful, and plain sand may be a safer thing to test this on unless you're specifically looking for crystalline silica. You can use a respirator as recommended on containers of grout, joint compound, cement or mortar.
What I did was to look at this while wet, so there's very little chance of it getting airborne. I got some from washing out some grout from a tile project, but you can collect dust samples too -- #dust-sampling.
### Setup
I took these polarizers from a pair of 3d glasses from a movie theater (they appear kind of grey, not red and blue) - I think we used the left and right lenses. I believe in these the left and right are circularly polarized clockwise and counterclockwise, but I don't know exactly what that means; I also have some linear polarizing film but haven't tried it yet.
To get the filters out, I just broke the glasses and carefully pulled out the lenses, which are flexible film.
I've drawn the polarizers at 90° angles, but we tried rotating them back and forth to see the color-changing effects pictured. Try different arrangements and report back what you see!
### Examples
@peasepoint took some great ones at the last #community-microscope workshop at AS220 in Providence, shown below. Post your own in the comments!
as220 blog silica polarizer
# Outreachy 2018 Week 2 and 3
by cess | about 2 years ago | 5 | 3
The last two weeks have been quite good. I have made some progress.
I manged to refactor the statistics controller by using scopes in the user, node and revision models so that the queries are quite simple hence less code. e.g This was one instance variable on the statistics controller.
@weekly_notes = Node.select(%i(created type status))
.where(type: 'note', status: 1, created: @time.to_i - 1.weeks.to_i..@time.to_i)
.count(:all)
I made some scopes in the Nodes controller
scope :status_one, -> { where(status: 1) }
scope :weekly, -> { status_one.where("created > ?", (Time.now - 7.days).to_i) }
Which changed the method to
@weekly_notes = Node.weekly.select(:type).where(type: 'note').count(:all)
You can now select a range to view statistics on the /stats/range page. You can do it for past week, month, year or select from a calendar.
You can also see the statistics on the number of questions answered and asked within a certain period on /questions.
I am finishing up on moving statistics methods in the user model to a concern so that its not so long. I am almost done just fixing code climate issues on refactoring some code blocks.
## Everybody Struggles
Last week Outreachy requested we share our struggles and the mentors to also share about their struggles. Thanks to the community for sharing your struggles and making me see that I am not alone. Here is a link to the week check-in where some of the contributors shared their struggles.
Here is some of my struggles.
• I struggled with was date-picker positioning..sounds pretty simple but it was a pain to get it to appear where I wanted, asked for help from the community though the suggestions I got did not solve it I had to make some comprises.
• Another major struggle was a brakeman issue User controlled method execution it looked critical to ignore. I tried to tweak it a couple of times and much much later solved it by making the method a private method.
• Currently I am struggling on getting to refactor some two methods that gets code climate complaining. The methods look similar but have varying parts.
## Next weeks plans:
Now that the statistics controller is looking a little cleaner, I will be implementing the new ui design for /stats page. I am currently working on a mockup and will attach it here for input when am done. Later on, after the new ui is up, I will implement downloads of stats as csv and json.
blog outreachy outreachy-2018
# Outreachy 2018: Week One
by cess | about 2 years ago | 6 | 7
### Update
This first week I started with attending an open hour on Monday, which was awesome I got to meet members of the community and we discussed about Usability Feedback for PublicLab . Discuss is a bad term to use because I mostly listened in rather than gave ideas. But it was great to hear and see how people use the site and what could be made better and interesting features coming up like the map for the content in the site.
I created a milestone(Extend Community Statistics system) thanks @bansal_sidharth2996 for the suggestion. I like the milestone plan, I just have to keep adding my issues there and it makes me visualize the project more and I can track my progress because the percentage of completion increases with every closed issue.
Initially my plan for week one was to implement the download of statistics by csv and json #963. I started working on it on Tuesday and was making awesome progress and I even got to get the data to display on a page as json and download notes and wikis as a csv and json. But then...
I realized in the end a lot is gonna change in the stats controller and me writing this code now will mean I will have to rewrite everything after I am done with the stats index page. Plus I also realized that the stats controller required a some refactoring.
### Plans for next week
• Thanks @warren for adding me as one of the reviewers. I plan to be reviewing at least two PRs each day so I can help others get started on plots
• Finish refactoring the stats controller.
• Implement consolidation existing "range pages" like with the main stats page#4139
• Get started on caching of data weekly issue #4138
### Thoughts/Clarifications needed/Questions from mentors
• Thoughts on daru gem? I came across this gem daru which does analysis manipulation and visualization of data in Ruby. Any advice if we should consider incorporating it in the statistics page or if anyone has used it and seen its advantages.
• Caching of data weekly. I realized this issue was not clear on which pages and content exactly was to be cached. Kindly clarify on this
blog outreachy |
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# Probability that a number is greater than or equal to another one
What is the probability, given a $n$-bit number $x$, that $x$ is greater than or equal to another unkown unsigned uniformly distributed $n$-bit random number $y$ ?
• Do you mean $\mod 2^{32}$? $\mod 32$ means that only bits 0 to 4 need to be examined, so knowing $x_{31}$ to $x_{16}$ is not helpful. – Χpẘ Jun 9 '17 at 16:56
• @Χpẘ Indeed you are right, I will edit this! Thanks – Raoul722 Jun 9 '17 at 16:57
• Just to clarify (and hopefully simplify), you are asking that given a 16 bit unsigned number ($x_{15}x_{14}\dots x_0$), what is the probability that it is greater than or equal to another unknown unsigned uniformly distributed random number ($y_{15}y_{14}\dots y_0$) – Χpẘ Jun 9 '17 at 17:06
• @Χpẘ Well... Indeed it sounds more clear that way ;-) I will edit my question again then – Raoul722 Jun 9 '17 at 17:13
The probability is $\frac{x_{15}x_{14}\dots x_0 + 1}{65536}$. Since dividing by 64k is a right shift the probability is the number with the binary point (analogous to decimal point) to the left of $x_{15}x_{14}\dots x_0 + 1$, with the exception that if $x_{15}x_{14}\dots x_0 = 0xFFFF$ the probability is 1 |
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# Open Physics
### formerly Central European Journal of Physics
Editor-in-Chief: Seidel, Sally
Managing Editor: Lesna-Szreter, Paulina
IMPACT FACTOR 2018: 1.005
CiteScore 2018: 1.01
SCImago Journal Rank (SJR) 2018: 0.237
Source Normalized Impact per Paper (SNIP) 2018: 0.541
ICV 2017: 162.45
Open Access
Online
ISSN
2391-5471
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Volume 15, Issue 1
# Modelling of intermittent microwave convective drying: parameter sensitivity
Zhijun Zhang
• Corresponding author
• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
• Email
• Other articles by this author:
/ Wenchao Qin
• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
• Other articles by this author:
/ Bin Shi
• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
• Other articles by this author:
/ Jingxin Gao
• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
• Other articles by this author:
/ Shiwei Zhang
• School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110004, China
• Other articles by this author:
Published Online: 2017-06-14 | DOI: https://doi.org/10.1515/phys-2017-0045
## Abstract
The reliability of the predictions of a mathematical model is a prerequisite to its utilization. A multiphase porous media model of intermittent microwave convective drying is developed based on the literature. The model considers the liquid water, gas and solid matrix inside of food. The model is simulated by COMSOL software. Its sensitivity parameter is analysed by changing the parameter values by ±20%, with the exception of several parameters. The sensitivity analysis of the process of the microwave power level shows that each parameter: ambient temperature, effective gas diffusivity, and evaporation rate constant, has significant effects on the process. However, the surface mass, heat transfer coefficient, relative and intrinsic permeability of the gas, and capillary diffusivity of water do not have a considerable effect. The evaporation rate constant has minimal parameter sensitivity with a ±20% value change, until it is changed 10-fold. In all results, the temperature and vapour pressure curves show the same trends as the moisture content curve. However, the water saturation at the medium surface and in the centre show different results. Vapour transfer is the major mass transfer phenomenon that affects the drying process.
PACS: 44.30.+v; 41.20.-q; 4.35.+c; 44.05.+e
## 1 Introduction
Drying is a method of removing moisture for the purpose of preserving food that prevents microbial growth, increases shelf-life, and significantly reduces product weight [1, 2]. Conventional convective drying combined with microwave heating could be a good method to reduce the drying time and drying energy costs [3]. To overcome the overheating problem, intermittent microwave convective drying (IMCD) with various intermittent times is practiced. Because it is a relatively new technique for food drying, modelling studies of IMCD are very limited [4]. There are some empirical models available in the literature for IMCD [5]; however, the empirical models are not helpful for optimization and are only applicable for specific experimental conditions [6]. Apart from empirical modelling, several diffusion-based theoretical models exist that consider the intermittency of microwave power [1, 7-9]. However, the mass transfer has been neglected in these models. A multiphase porous media model considering the liquid water, gases and the solid matrices inside food during drying can provide an in-depth understanding of IMCD [4]. In fact, the parameters used for modelling are very important because the simulation results are decided by them. The mass transfer coefficient is a boundary condition that is very difficult to retrieve. However, most modelling is conducted using previous references [10-13]. The impact of the model parameters on the model predictions must be clarified [11]. In fact, the parameter sensitivity of IMCD has not been reported. In this paper, the heat and the mass transfer within porous media during the IMCD process are characterized by using a non-equilibrium method. Then, the parameter sensitivity analyses for the microwave power level, ambient temperature, effective gas diffusivity, evaporation rate constant, surface mass, heat transfer coefficient, relative and intrinsic gas permeability, capillary diffusivity of water and evaporation rate constant are examined. Because most measurement errors are less than 20%, the parameters were only changed by 20%, except for special cases.
## 2.1 Problem description and assumptions
Because the model is for a multiphase and multiphasic process, the computation is a time-cost process. To simplify the calculation, a physical one-dimensional (1D) model that explains the drying process was used, as shown in Figure 1. The heat and mass transfer was considered only in the y direction. The total height of the porous medium is 1 cm. The bottom and top surfaces are the heat and mass transfer boundaries.
Figure 1
1D model of the porous medium
The porous medium consists of a continuous rigid solid phase, an incompressible liquid phase (free water), and a continuous gas phase. The gas is assumed to be a perfect mixture of vapour and dry air. It is considered an ideal gas. The moisture flow in the inner porous medium is liquid water and vapour flow. The liquid water can become vapour. The vapour and liquid water are moved by the pressure gradient. The heat and mass transfer theory can be found elsewhere [11-15], or in our other study [16].
The gaseous phase ensures that $ρa=MaPaRT$(1) $ρv=MvPvRT$(2) $Pg=Pa+Pv$(3) $ρg=ρa+ρv$(4) where ρs, ρa, ρv and ρg are the densities of the solid, air, vapour and gas (kg/m3), respectively, Pa, Pv and Pg are the pressures of the air, vapour and gas (Pa), respectively, Ma and Mv are molar masses of the air and vapour, respectively, (kg/mol), R is the universal gas constant (J/mol/K), and T is the temperature (K).
The assumption of the local thermal equilibrium between the solid, gas, and liquid phases involves $Ts=Tg=Tw=T$(5) where Ts, Tg, and Tw are the temperatures of the solid medium, gas and water, respectively (K).
## 2.2.1 Mass and momentum transfer
Mass conservation equations are written for each component in each phase. Given that the solid phase is rigid, the following is given: $∂ρs∂t=0$(6)
The averaged mass conservation of the gas phase [11] is as follows $∂(ε⋅Sgρg)∂t+∇⋅(ρgkgkr,gμg∇Pg)=I˙$(7) where ε is the porosity, Sg is the gas saturation, kg is the intrinsic permeability of the gas (m2), kr,g is the relative permeability of the gas, μg is the viscosity of the gas (Pa s), and İ is the phase change rate of water to vapour.
For vapour [11, 14], $∂(ε⋅Sgρv)∂t+∇⋅(ρvVv)=I˙$(8) where Vv is the vapour velocity (m/s).
For free water [12], $∂(ε⋅Swρw)∂t+∇⋅(ρwVw)=−I˙$(9) where Vw is the water velocity (m/s).
For the Darcy flow of the vapour [14], $ρvVv=ρvVg−ρgDeff⋅∇ωv$(10) where Vg is the gas velocity (m/s), Deff is the effective diffusivity of the vapour and air (m2/s), and ω is the mass fraction of the vapour.
For the Darcy flow of the air [14], $ρaVa=ρaVg+ρgDeff⋅∇ωv$(11)
The vapour fraction in the mixed gas is given by, $ωv=ρvρg$(12)
The saturation of free the water and gas is $Sg+Sw=1$(13)
The gas and free water Darcy velocity is given by [15], $Vg=−ki,g⋅kr,gμg⋅∇Pg$(14) $vw=−ki,w⋅kr,wμw⋅∇Pw$(15)
The total water velocity is given by [15], $Vw=−kin,w⋅kr,wμw⋅∇Pg−Dwρwε⋅∇Sw$(16) where Dw is the capillary diffusivity (m2/s).
## 2.2.2 Energy transfer
By considering the hypothesis of the local thermal equilibrium, the energy conservation is reduced to a unique equation [15]: $ρeCe∂T∂t+∇⋅(ρaVaCaT+ρvVvCvT+ρwVwCwT)=∇(ke⋅∇T)−hfg⋅I˙+Qmic$(17) where ρe is the effective density (kg/m3), Ce is the effective specific heat (J/kg/K), ke is the effective thermal conductivity (W/m/K), Ca, Cv and Cw are the specific heats of the air, vapour and water, respectively, (J/kg/K), and λ is the phase change heat of water to vapour (J/kg).
The effective density, effective specific heat and effective thermal conductivity are given by [15], $ρe=ρss+ε⋅Sgρa+ε⋅Sgρv+ε⋅Swρw$(18) $ke=(1−ε)ks+ε(Swkw+Sg(ωkv+(1−ω)ka))$(19) $Ce=(1−ε)ρsCs+ε(ρwSwCw+ρgSg(ωCv+(1−ω)Ca))(1−ε)ρs+ε(ρwSw+ρgSg)$(20) where ks, kw, ka, and kv are the thermal conductivities of solid medium, water, air and vapour, respectively, (W/m/K).
## 2.2.3 Phase change
The phase change modelling was provided in two forms: equilibrium and non-equilibrium. Recent studies have shown that evaporation is not instantaneous and that non-equilibrium conditions exist during rapid evaporation between water vapour in the gas phase and water in the solid phase [14, 15]. The more general expression for the non-equilibrium evaporation rate used for modelling the phase change in porous media, which is consistent with the studies on pure water mentioned above, is given by, $I˙=KevapMv(awPsat−Pv)SgεRT$(21) where aw is the coefficient and Psat is the saturated vapour pressure of water (Pa).
## 2.2.4 Microwave power absorption
Lambert’s Law [4, 17-21] was used to calculate the microwave energy absorption inside the food samples. This law considers the exponential attenuation of microwave absorption within the product and is given by $Pmic=P0exp−2α(hs−z)$(22) where P0 is the incident power at the top surface, αis the attenuation constant, hs is the thickness of the media, and (hsz) is the distance from the top surface.
The attenuation constant, α, is given by [17-21], $α=2πλε′1+ε″ε′2−12$(23) where λ is the wavelength of the microwave in free space and ε′ and ε″ are the dielectric constant and the dielectric loss, respectively [4].
The volumetric heat generation, Qmic (W/m3), is given by, $Qmic=PmicV$(24) where V is the volume of the medium (m3).
The microwave power is intermittent input. A duration of 20 s of microwave power is given followed by 80 s without microwave power until the drying process is ended.
## 2.3 Initial conditions
The initial moisture of the porous medium is represented by the liquid water saturation; different initial water saturation values are used.
• I.C. for Eq. (7), $P(t=0)=Pamb$(25)
• I.C. for Eq. (8), $ρv(t=0)=Pv,ambMvRT0$(26)
• I.C. for Eq. (9): $S(t=0)=Sw0$(27)
• I.C. for Eq. (17): $T(t=0)=T0$(28)
## 2.4 Boundary conditions
The bottom and top surfaces are the heat and mass transfer boundaries. The other boundaries of the model are insulated and impermeable. The boundary conditions are given as:
• B.C. for Eq. (7), $Ps=Pamb$(29)
• B.C. for Eq. (8), $n→v,s=−hmεSg(ρv−ρv,amb)$(30)
• B.C. for Eq. (9): $n→w,s=−hmεSw(ρv−ρv,amb)$(31)
• B.C. for Eq. (11), $qs=−hT(T−Tamb)+(λ+CwT)nw,s+CvTnv,s$(32)
where Pamb is the ambient pressure (Pa), hm is the mass transfer coefficient (m/s), ρν,amb is the vapour density of the ambient (kg/m3), hT is the heat transfer coefficient (W/m2/K), and Tamb is the ambient temperature (K).
## 2.5 Input parameter
In the present study, the input parameters from the literature [4, 15] are listed in Table 1. The major focus of this work is the parameter sensitivity. In order to finish this work, the different values or adapted equations will be shown in the later sections.
Table 1
Input properties for the model
## 3 Numerical solution
A one-dimensional (1D) grid was used to solve the equations using COMSOL. The mesh consisted of 200 elements (1D), and variable time stepping was used. Several grid sensitivity tests were conducted to determine the sufficiency of the mesh scheme and to ensure that the results were grid-independent. The relative tolerance was set to 1e-4, whereas the absolute tolerance was set to 1e-6. The simulations were performed using a ThinkPad with an Intel i7 Duo processor with a 2.3 GHz processing speed and 16 GB of RAM running Windows 7.
## 4.1 Model validation
The microwave power input was intermittent with a 100 s interval. The microwave power input occurred during the first 20 s. The temperature and moisture curve is shown in Figure 2. The results agree well with the reference results [4] (not shown in the present paper), except that the temperature is slightly higher than in the present study. The reason of that may be due to the 2D and 1D differences. Therefore, the model in the present study was used to determine the sensitivity parameter. The temperature increased during the first 20 s and decreased during the later 80 s. It was cycled every 100 s until the drying ended. However, the average temperature increased over time.
Figure 2
Temperature and moisture content curves (d. b.) vs time
## 4.2 Microwave power level
The microwave power is the major input parameter. In the present study, the power level was changed to -20% and +20%P0. The results are shown in Figure 3 forP1 =80%P0, P2 =100%P0, and P3 =120%P0. Lower moisture content was obtained with higher power levels. In addition, higher moisture content was obtained with lower power levels. The moisture content changed to −8.2% and 7.5%, respectively. With an increase in the power level, more microwaves are absorbed, resulting in more moisture loss through higher temperatures, vapour pressures and evaporating rates [22]. The vapour pressure at the surface was approximately the same under the three power levels because it is controlled by the vapour pressure in the ambient. It is different from the vapour pressure in the centre, which had a larger pressure difference. The temperature of the surface barely changed, but the temperature in the centre was much different under the three power levels. The water saturation at the surface was obviously different under the three power levels. The water saturation at the surface and in the centre of the medium decreased with increasing power levels. The results agree well with the moisture content curve. The water saturation was near zero at the end of the drying stage on the sample surface for the 120% P0 power level. This is because the water transfer rate was lower than the vapour transfer rate. The vapour transfer rate decreased during the drying stage. In fact, the drying temperature had a large effect on the product quality. Usually, a lower temperature was good for drying the product; although, most of time, it prolonged the drying time. The increasing power level needs more energy input. Therefore, the drying process should be carefully considered [22].
Figure 3
Moisture content, temperature, vapour pressure and water saturation using different microwave power levels
A higher vapour pressure will accelerate the mass transfer of the water and vapour. The mass flow rates of the water and vapour on the surface were calculated by Eq. (30) and (31), respectively. The mass flow rates of the water and vapour in the centre were ρwVw and ρνVν respectively. The results are shown in Figure 4. The mass transfer of water on the surface was larger than the vapour transfer in the present study, especially before 400 s when compared with Figures 4(a) and 4(c). However, as the drying continued, the mass transfer rate of vapour on the surface increased until it was higher than the mass transfer of water. The reason is that the water saturation is larger during the beginning of the drying process. The vapour mass transfer is difficult because most gaps in the porous medium surface are filled by water. During the water mass transfer and evaporation, more and more gaps were filled by vapour, and the mass transfer of vapour increased. The water mass transfer in the centre was always greater than the vapour mass transfer in the centre. The water transfer was the major parameter inside the porous medium.
Figure 4
Water and vapour flow rates using different power levels
## 4.3 Ambient temperature
During IMCD, convective air is used to move the vapour from the microwave drying chamber. It can lower the vapour concentration around the surface of the medium. In addition, it can accelerate the drying process. The surface temperature of the medium was lower than the centre temperature during evaporation. Therefore, the ambient air temperature increased the surface temperature. It also increased the vapour pressure and vapour concentration. The mass transfer from the surface to the ambient could also increase. The effect of the ambient temperature is shown in Figure 5. The temperature was 60°C, and it also changed by ±20%. The ambient temperatures were Tamb1 = 48°C, Tamb2 = 60°C and Tamb3 = 72°C. The moisture content changed to −2.4% and 2.3%, respectively. The temperature and vapour pressure in the medium barely changed. However, the water saturation on the surface incurred large differences, but in the centre, it barely changed. A lower moisture content was obtained with higher ambient gas temperatures for the same drying time. The major water reduction was due to the surface water evaporating. The ambient temperature effect was calculated with q = −hT(TTamb), as shown in Figure 6(a). The increase in temperature noticeably increased the strength of the heat transfer.
Figure 5
Moisture content, temperature, vapour pressure and water saturation under different ambient temperatures
Figure 6
Surface heat transfer under different ambient temperatures (a) and different heat transfer coefficients (b)
## 4.4 Heat transfer coefficient
The heat transfer coefficient effect is shown in Figure 7. The heat transfer coefficients also changed ±20% from their initial values. They were hT1 =13.411, hT2 =16.764, and hT3 =20.117 W m2 K−1. Compared with Figure 5, the heat transfer coefficients had a minimal effect. The temperature, vapour pressure and water saturation were approximately constant for different heat transfer coefficients. The reason is that the heat transfer coefficients were large enough to strengthen the heat transfer process. The results can also be found in Figure 6(b). In comparison of Figures 6(a) and 6(b), the ambient temperature shows little sensitivity.
Figure 7
Moisture content curves with different heat transfer coefficients
## 4.5 Mass transfer coefficient
The water inside the medium transfers to the surface of the porous medium and evaporates. The vapour exchanges mass with the ambient medium. The mass transfer coefficient is the key factor because it is the last step of the drying process to transfer mass outside of the porous medium. In the present study, the mass transfer coefficient was varied. The results are in shown in Figure 8.
Figure 8
Moisture content, temperature, vapour pressure and water saturation using different mass transfer coefficients
The original value was 0.067904 m s−1 [1], and it was changed by ±20%. The values were hm1 =0.054323, hm2 =0.067904 and hm3 =0.08148 m s−1. The moisture content curve showed minimal changes. It is similar to the temperature, vapour pressure and water saturation curves. The centre water saturation curve, especially, showed no difference. The water transfer rate and vapour transfer were calculated by Eq. (30) and Eq. (31). The results of the water transfer and vapour transfer rates showed minimal differences in Figure 9.
Figure 9
Water transfer rates and vapour transfer rates using different mass transfer coefficients
## 4.6 Gas permeability
The relative permeability values for free water and gas in the present study were obtained from [14] using Eq. (33) and Eq. (34). However, different gas relative permeability values were calculated using Eq. (35). Their effects are shown in Figure 10. $kr,w=Sw−Sr1−Sr30Sw>SrSw≤Sr$(33)
Figure 10
Moisture content, temperature, vapour pressure and water saturation under different relative permeability values
The gas relative permeability is given by [14], $kr,g1=Sg$(34)
Another gas relative permeability is given by [21], $kr,g2=Sg2$(35)
The different values for the gas relative permeability did not substantially change the results of the model, as shown in Figure 10. The results were similar to those in reference [23]. The temperature and vapour pressure were approximately the same. However, the water saturation at the surface and in the centre exhibited different results. The water saturation at the surface was higher, while the water saturation in the centre was lower using the gas relative permeability given by Eq. (35). The water saturation in the surface was lower, but the water saturation in the centre was higher using the gas relative permeability given by Eq. (34). The vapour flow rate in the centre was ρνVg from Eq. (10). The results of the different gas relative permeability values on vapour flow rate showed minimal differences, as shown in Figure 11. The reason is that the relative permeability barely changed with relative to other parameters in Eq. (14). It was of the order of 10−12.
Figure 11
Vapour flow rates in the centre of the sample under different gas relative permeability values
The intrinsic permeability was studied by three groups of values:
1. kin,g1 = 4.0×10−12 m2 and kin,w1 = 4.0×10−12 m2,
2. kin,g2 = 2.7×10−11 m2 andkin,w2 = 4.0×10−12 m2, and
3. kin,g3 = 2.7×10−11 m2 and kin,w3 = 2.7×10−11 m2.
The effect of the intrinsic permeability with different values is shown in Figure 12. There was no appreciable change in the final moisture content of the material with the changing permeability. The temperature and vapour pressure values were almost the same. However, as shown in Figure 12(d), the water saturation was noticeably different. The curves with group parameters (1) and (3) agreed well. However, the water saturation at the surface was lower, and the water saturation in the centre was higher for group parameter (2). This is also the reason why the moisture content curves were approximately the same. The water and vapour flow rates are shown in Figure 13. The water flow rates agreed well with the moisture content results. Group parameters (1) and (3) were the same, but group parameter (2) was different. However, the vapour flow rate was almost the same for the three group parameters. The high sensitivity parameter of the water flow rate was demonstrated. In fact, the mass transfer from the sample to the ambient occurred through evaporation, especially through water evaporation on the surface. Therefore, the varying water flow rate did not greatly affect the drying process, especially the moisture content.
Figure 12
Moisture content, temperature, vapour pressure and water saturation under different intrinsic permeability values
Figure 13
Water flow rate and vapour flow rate in the sample centre under different intrinsic permeability values
## 4.7 Effective gas diffusivity
The effective gas diffusivity can be calculated as a function of the gas saturation and porosity according to the Bruggeman correction [4], namely, $Deff1=Dva(Sgε)4/3$(36) It can also be calculated as [21], $Deff2=2.13PgT2731.8(Sgε)3−εε$(37) where Dνa is the binary diffusivity between the air and water vapour (m2s−1).
Because several parameters affect the effective diffusivity of water vapour in porous media (molecular diffusivity, porosity, and tortuosity), this coefficient is variable from one kind of material to another [22]. As shown in Figure 14, the change was very large with different effective gas diffusivity values, which is similar to the results in reference [22]. The resistance of the porous medium to gaseous migration was very important, and this showed that their model was sensitive to the changes in the effective diffusivity of the water vapour. The temperatures with different effective gas diffusivity values were obviously different. They were higher using Eq. (36) and lower using Eq. (37). The water saturation was the same as that in Figure 10(d). With Eq. (36), the water saturation at the surface was higher, but the water saturation in the centre was lower. With Eq. (37), the water saturation at the surface was lower, but the water saturation in the centre was higher. The vapour diffusion rate was calculated from Eq. (38); the results of the calculation are shown in Figure 15. $qvD=ρgDeff⋅∇ωv$(38) The vapour diffusion rate showed obvious differences. In addition, it actually affected the moisture content.
Figure 14
Moisture content, temperature, vapour pressure and water saturation under different effective gas diffusivity values
Figure 15
Vapour diffusion rate under different effective gas diffusivity values
## 4.8 Capillary diffusivity of liquid water
The capillary diffusivity of liquid water is various for different materials. In the present study, the capillary diffusivity of liquid water is the same as in the previous reference [4]. The parameter sensitivity of the capillary diffusivity is shown in Figure 16. The effect on moisture curve is minimal. It is also the same with the temperature and vapour pressure. However, the water saturation exhibits different results compared to those in Figure 7(d). The biggest difference occurred at the surface for the water saturation. A relatively small difference was observed in the centre. The water diffusion rate was calculated as $qwD=Dwρwε⋅∇Sw$(39) The results under different capillary diffusivity values for liquid water are shown in Figure 17. The water diffusion rate showed obvious differences. However, compared with Figure 16, an effect on the moisture curve was not observed. As shown in Figure 13(a), the water flow rate was not a major factor on the drying rate because the water changed to vapour, especially on the surface.
Figure 16
Moisture content, temperature, vapour pressure and water saturation under different capillary diffusivity values for water
Figure 17
Water diffusion rate under different diffusivity values
## 4.9 Evaporation rate constant
Another important model parameter is the non-equilibrium evaporation rate constant, Kevap. Figure 18 shows its effect on the moisture profiles. The evaporation rate constant required a 10-fold change, not just by ±20%, because of its lower parameter sensitivity. As seen in Figure 18, for low values of K, the moisture content is higher. However, with larger Kevap values, the difference between them decreases. Therefore, the model can simulate an equilibrium problem [15]. The temperature increased with a lower evaporation rate constant because less energy input was required for evaporation. The vapour pressure was the same for the temperature curve. The water saturation was almost the same in the centre, but the difference was huge at the surface. This shows that the water evaporating near the surface increased with the higher evaporation rate constant.
Figure 18
Moisture content, temperature, vapour pressure and water saturation using different evaporating rate constants
The evaporating rate results under different evaporating rate constants are shown in Figure 19. The evaporating rate increased as the evaporating rate constant increased. During the non-equilibrium simulation, the larger evaporating rate constants brought the system closer to an equilibrium state. The Kevap. =10000 was sufficient for the simulation.
Figure 19
Water evaporating rate using different evaporation rate constants
In a comparison of the results of the capillary diffusivity of the liquid water, evaporating rate constant, effective gas diffusivity, gas permeability, and effective gas diffusivity, vapour transfer is the deciding factor of the drying process. For parameters that have an effect on the vapour transfer, the drying process will be obviously different.
## 5 Conclusions
A multiphase porous media model of intermittent microwave convective drying was developed based on reference values. The model considered liquid water, gas and the solid matrix inside of food. The model was simulated by COMSOL software. Its parameter sensitivity was analysed by changing the parameter values ±20%, with exceptions for several parameters. Sensitivity analyses of the process to the microwave power level, ambient temperature, effective gas diffusivity, and evaporation rate constant show that they all have significant effects on the process. However, the surface mass, heat transfer coefficient, gas relative and intrinsic permeability, and capillary diffusivity of water did not have a considerable effect. The evaporation rate constant exhibited minimal parameter sensitivity with a ±20% value change, until it was changed 10-fold. In all results, the temperature and vapour pressure showed the same trends as the moisture content. However, the water saturation at the medium surface and in the centre showed different results. Vapour transfer was the major mass transfer phenomenon that affected the drying process.
## Acknowledgement
This research was supported by the National Natural Science Foundation of China (Grant Nos. 31371873, 31000665, 51176027, and 31300408).
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Accepted: 2017-03-09
Published Online: 2017-06-14
Citation Information: Open Physics, Volume 15, Issue 1, Pages 405–419, ISSN (Online) 2391-5471,
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# Detection of a 14-d atmospheric perturbation peak at Paranal associated with lunar cycles
### S CavazzaniS OrtolaniN ScafettaV ZitelliG Carraro
Monthly Notices of the Royal Astronomical Society: Letters, Volume 484, Issue 1, 21 March 2019, Pages L136–L140,
## Abstract
In this paper we investigate the correlation between the atmospheric perturbations at Paranal Observatory and the Chilean coast tides, which are mostly modulated by the 14-d syzygy solar–lunar tidal cycle. To this aim, we downloaded 15 yr (2003–2017) of cloud coverage data from the Aqua satellite, in a matrix that includes also Armazones, the site of the European Extremely Large Telescope. By applying the Fast Fourier transform to these data we detected a periodicity peak of about 14 d. We studied the tide cycle at Chanaral De Las Animas, on the ocean coast, for the year 2017, and we correlated it with the atmospheric perturbations at Paranal and the lunar phases. We found a significant correlation ($96\mathrm{p}\mathrm{e}\mathrm{r}\phantom{\rule{0ex}{0ex}}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}$) between the phenomena of short duration and intensity (1–3 d) and the tidal cycle at Chanaral. We then show that an atmospheric perturbation occurs at Paranal in concomitance with the low tide, which anticipates the full (or the new) moon by 3–4 d. This result allows to improve current weather forecasting models for astronomical observatories by introducing a lunar variable. |
Home/Class 11/Maths/
## QuestionMathsClass 11
The common difference of the A.P.$$3$$,$$5$$,$$7$$,.....is....
(A) $$4$$
(B) $$2$$
(C) $$3$$
(D) $$-2$$
The given AP is 3, 5, 7, ..... .
Hence, the common difference is $$5-3$$ = $$7-5$$ = $$2$$. |
Dr. Eugenia Cheng ‘s Lectures on Category Theory (2007)
The name “monad” came from “monoid” and “triad”, which indicated that it is a triple (1 functor + 2 trasformations), monoidic algebraic structure.
Monad = Monoid (restricted to endofunctors)
Note: She was annoyed nobody had corrected her mistake in (red) Tμ . (I discovered it only on 2nd revision view few years later).
Monad for Small Categories (= Set)
Ref:
What is the difference between Monoid and Monad? (Bartosz Milewski )
Functor: 函子
# Les Categories Pour Les Nuls
“Categories for Dummies”
(French)
Example 1:
Paris (P) -> Rome (R) -> Amsterdam (A)
Objects: cities {P, R , A…}
Morphism (Arrow)
: railway
• Identity: railway within the city
• Associative: (P -> R) -> A = P -> (R ->A)
=> Category of “Euro-Rail”
Remark: In the similar sense, China “One Belt One Road” (OBOR)” 一带一路” is a “Pan-China-Europe-Asian” Category “泛中-欧-亚” 范畴
Example 2:
A, B are categories
functor f : A -> B
f (B) has the “information” on A, with some loss of information since f may not be a MONOMORPHISM (单射 Injective).
Remark: Technical Drawing, the views from Top , Left, Right, or Bottom of the object are Functors – which provide only 1 view from 1 direction with loss of information from 3 other directions.
Example 3: Natural Transformation
A = 0 1 2 3
f : A -> B
f(0)|
f(1)|
f(2)|
f(3)|
g : A -> B
B = Staircase steps :
g(0)||
g(1)||
g(2)||
g(3)||
Natural Transformation: => α
α : f (i) => g (i)
f(0)| => g(0)||
f(1)| => g(1)||
f(2)| => g(2)||
f(3)| => g(3)||
α transforms naturally the Ladder to the Staircase.
# Debate (French): Set Theory vs Category Theory
4. Category, Logic and IT
Pierre Cartier’s Key Points:
1. The Roles of Categories in Science and Organisation of Knowledges.
2. Homology <- cohomology (Reversed Arrow)
3. Natural Transformation and Duality of Vector Spaces
# An Introduction to N-Categories
Tom Leinster
N = 0 : 0-Cat
• => Set, 0-morphism = function
N= 1: 1-Cat
• => Cat, 1-morphism = functor
N= 2: 2-Cat
• => 2-morphism = Natural Transformation
$\text {f, g : 1-morphism }$
$\alpha \:\: \beta \text { Natural Transformations : 2-morphism }$
Definition of n-Category:
Composition:
0-Cat : Set
1-Cat : Cat
Examples of n-Categories:
• Manifold
• Top (Topological Space) : 2-morphism = homotopy
Ref:
Best Technical Category Theory Book (2016) by Tom Leinster (Cambridge Press): “Basic Category Theory”
# Category Theory 范畴论 : “How to Bake Pi”
Category Theory is the “Mathematics of Mathematics”, replacing the century-old Set Theory as the Foundation of Mathematics.
Category is also the Math of Programming in the latest IT trend “Functional Programming” for safer “Typed” software in parallel and concurrent computing.
Dr. Eugenia Cheng – Professor of Category Theory (Chicago University).
Author of the Best Selling Category Book : (for readers from 7-year-old to high school and undergraduate students):
How to Bake Pi ? – an Edible Exploration of the Mathematics of Mathematics”
[Loan from NLB (eg. AMK Branch)]
Illustrations:
• Factors of 30 = {2, 3, 5, 6, 10, 15, 30} which form a Cube with these factors as the vertices.
• Knots
• Bach music
• Associativity: (sugar + milk + egg )
• Button cake = order 2 group (0,1)
• Bed mattress = rotate, flip, flop
• Icosahedral virus
Ref:
Best Technical Category Theory Book (2016) by Tom Leinster (Cambridge Press): “Basic Category Theory”
# Program = Category
2017 : (PhD Math made simple for IT programmers)
Keywords
• Category
• Monad = Monoid + Endofunctor
• Lewvere Theory
Category Theory is replacing Set Theory as the foundation of Math. Nowadays, few Advanced Math papers are written without using Category to explain, and this trend is spreading to IT through Functional Programming languages (Google’s Kotlin, Haskell, Clojure…) – the latest paradigm to replace Object-Oriented languages like Java, C++, etc, as a safer “Strong Typed” languages for AI, BIG DATA…
$\boxed {\text {Type = Category }}$
Examples of “Types” in IT:
• Integers
• Real
• Double
• Boolean
• String
• etc
T-program defined in the following 6 examples:
• list (X), eg. {2, 5 , 3, 7, 1 }
• partial (X), eg: +1 (error msg)
• side-effect, eg: update a record
• continuation (X),
• non-det (X),
• prob-dist (X)
A Monad : a T-program which turns an arrow to a “Category” (ie + 2 properties: Identity & Associative).
Proof: List Computation is a Category
Proof: Partial operation is a Category
$\boxed {\text {Monad = Lawvere Theory }}$
Monad is for only one Category. Lawvere Theory is more general.
Ref
:
Ref:
# Integral Domains 整环 (Abstract Algebra)
Remember when you cancel a common factor at both sides of an equation, you must check if the factor is non-zero, otherwise you would miss some answers.
This is about Cancellation Law, related to few Number Theory Properties :
• Zero Divisors,
• Integral Domain.
Origin of “Integral” => Integers
Definition of Integral Domian:
Property: Cancellation Law |
# encryption decryption of enigma machine codingame solution
Here's How the basic machine works: First Caesar shift is … Created: 2018-11-06 23:34 Updated: 2019-02-22 19:39 License: gpl-3.0 codingame codingame-solutions puzzles java. Enigma II Encryption Machine & Puzzle - encode & decode size LRG This is an encryption machine that will allow you to encrypt your own messages and in addition we have provided 8 secret messages for you to try and solve. The Enigma 'typewriter' In 2001, the release of the feature film Enigma sparked great interest in the tweedy world of the boffins who broke Nazi … The Enigma code went many years unbroken. Hi, if someone else has this issue, just use a custom test case with a very long message. Enigma Part 1: German Enigma’s encryption and its major weaknesses | #13. Enigma decoder: Decrypt and translate enigma online. README.md CodinGame Solutions Introduction. Use Git or checkout with SVN using the web URL. Base32hex AES Encryption … Got an elegant solution? The Enigma cipher machine is well known for the vital role it played during WWII. Encryption/Decryption of Enigma Machine [Functional-Programming] Guessing n Cheating [Conditions] Rooks Movements [Conditions, For-Loops] ... javascript kotlin puzzles puzzle-solution codingame-solutions codingame math string-manipulation pathfinding loop memoization recursion nested-loops movement java csharp c php python cpp Resources. Encryption/Decryption of Enigma Machine [Functional-Programming] Guessing n Cheating [Conditions] Rooks Movements [Conditions, For-Loops] ... github javascript kotlin puzzles puzzle solution codingame solutions codingame math string manipulation pathfinding loop memoization recursion nested loops movement java csharp c++ php python cpp. (((int)message4.charAt(i))-pseudoRandomNumber-i-65)%26+65<65. pathosDev. @Niako thanks for correction. Same for me here, I’d like to be able to see validators 1 and 2 to understand what I’m doing the wrong way! An Enigma machine allows for billions and billions of ways to encode a message, making it incredibly difficult for other nations to crack German codes during the war — for a time the code seemed unbreakable. During World War II, the Germans were using an encryption code called Enigma – which was basically an encryption machine that encrypted messages for transmission. Source. This is a work in progress that will turn into a final article by the end of the semester in December of 2011. It’s fixed (and I’ve answered somewhere else). The Enigma machine works by swapping letters; it therefore has no separate mechanism for decryption, nor does it need one. My test case for the decoding is the following : Same issue here, for me I always fail validators 4 and 6, it’s probably something very stupid , but i can’t find it. CodinGame-Solutions. just beware of borders (values < or > to the 26 chars when converting) What are differences between validator test and ide test ? The reverse process is called decryption. Symmetric-key encryption are algorithms which use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext. It is therefore unsurprising that when mechanical encryption machines (rotor machines) were invented in the wake of World War I to protect sensitive diplomatic, strategic and commercial information the encryption machines were known as Enigma … The most powerful of our Enigma Series of Encoders. An adversary may intercept the cipher text and attempt to recover … Here is sample of code for Decryption of small text messages : Program.cs /* * Created by Perić Željko * periczeljkosmederevo@yahoo.com * IDE Sharp Develop C# * Date: 28.11.2011 * Time: 11:20 * * This is a simple console application for decryption of short * text messages (up to 255 caracters) encrypted by program Encryption. The Enigma cipher was a field cipher used by theGermans during World War II. Post an issue or send an email: justdenva@gmail.com, I'll add it up! This version of cryptii is no longer under active development. can you please eleborate? Simply set up the machine identically as at the beginning of encryption, but enter the cyphertext instead of the plaintext. it should be The Enigma is one of the better known historical encryption machines, and it actually refers to a range ofsimilar cipher machines. download the GitHub extension for Visual Studio, Dwarfs standing on the shoulders of giants. Enigma IV Encryption Cipher Machine - with $100+ challenge 6 double sided gears that can provide 648,960 different possible keys. Hi, The Enigma machine is a piece of spook hardware invented by a German and used by Britain's codebreakers as a way of deciphering German signals traffic during World War Two. I’m a student in the History of Computing class at San Jose State University (). If you are new check out How to contribute to a project on Github. Will be more patient in the future. // Use as normal readline function (Spider-Monkey) syntax; You signed in with another tab or window. To be simple for the encoding with the word "ABCD" : Step 1: apply CAESAR with the incrementing number (let’s say 4 here), Step 2 : translate trough first rotor (let’s say "BDFHJLCPRTXVZNYEIWGAKMUSQO" here), Step 3 : translate trough second rotor (let’s say "AJDKSIRUXBLHWTMCQGZNPYFVOE" here), Step 4 : translate trough third rotor (let’s say "EKMFLGDQVZNTOWYHXUSPAIBRCJ" here), So after those 4 steps "ABCD" is encrypted to "KFDI", Step 1 : translate from third rotor (let’s say "EKMFLGDQVZNTOWYHXUSPAIBRCJ" here), Step 2 : translate from second rotor (let’s say "AJDKSIRUXBLHWTMCQGZNPYFVOE" here), Step 3 : translate from first rotor (let’s say "BDFHJLCPRTXVZNYEIWGAKMUSQO" here), Step 4: undo CAESAR with the incrementing number (let’s say 4 here), So after those 4 steps "KFDI" is decrypted to "ABCD". Other programming language? To begin with, Jack sheds light on the problem with the famous German coding machine Enigma used extensively during World War II by the German military. Asymmetric Key: Asymmetric encryption uses 2 pairs of key for encryption. The machine is relatively easy to use to encode your own highly Public key is available to anyone while the secret key is only made available to the receiver of the message. Send and receive secret messages to anyone who A1Z26 cipher Binary decoder AES Encryption Write a program that prints the temperature closest to 0 among input data. Cryptanalysis of the Enigma ciphering system enabled the western Allies in World War II to read substantial amounts of Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines.This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename Ultra. In ... Encryption/Decryption of Enigma Machine Same sh*t, could I get test cases for 4, 6 tests? fgets(rotor, 27, stdin); Alan Turing and his attempts to crack the Enigma machine code changed history. process is called encryption. Work fast with our official CLI. Working and decryption of the Enigma machine 7 Feb 2019 7 Aug 2019 admin 0 Comments Since Antiquity and through the centuries, the encryption of messages has played an important role in both the political and military world. All the test cases work but when I click on submit, I only have 66%. Recently, when researchers at the University of Rochester (USA) finally succeeded in developing a totally secure encryption device based on quantum rules, they presented it as the “Quantum Enigma” in honour of the rotor cipher machines used to encode Nazi messages in the Second World War, the same devices that continue breaking records at auctions today. Cryptii is an OpenSource web application under the MIT license where you can encode and decode between different format systems. I don’t really understand what some mean by the original size message , i should only write the 50 first chars ? I welcome your comments and advice. Enigma was the German encryption device used in World War II to encode sensitive military information. Doing encryption and decryption is easy but we have to remember/know few things. The line: The Enigma was a type of enciphering machine used by the German armed forces to send messages securely. The Enigma cipher machine is well known for the vital role it played during WWII. A perplexing speech or text; a riddle. 5 double sided gears can provide 266 billion different possible keys. Enigma Pro Encryption and Decryption Machine is a tiny, portable and simple-to-use software utility that can help you encrypt messages in order to send secret information to other people. Like all the best cryptography, the Enigma machine is simple to describe, but infuriating to break. beware to end of lines (fgets default on some tests). The Enigma machine: Encrypt and decrypt online. If nothing happens, download Xcode and try again. Thank you, this explanation of is a lot clearer than the one included in the exercise. Zepharos March 5, 2019, 5:36pm #22. Hi, Everyone. Same issue here, for me I always fail validators 4 and 6, it’s probably something very stupid , but i can’t find it. The machine can be used to encode your own highly encrypted secret messages. If nothing happens, download GitHub Desktop and try again. Alan Turing and his attempts to crack the Enigma machine code changed history. Hi, Everyone. There is a problem with the starter code (aka auto generated code) for C, it does not read in the input properly. beware to negatives values Hi, During my research and development, I have been learning a lot about the disciplined effort tha… Encryption/Decryption of Enigma Machine. If nothing happens, download the GitHub extension for Visual Studio and try again. For the left rotor, the position of the outer of the rotor is immaterial to encryption and decryption. I cant decode it even manually. The test cases 4 and 5 do not work and I frankly have no idea why. Puzzles. D Various solutions ⭐ for Codingame puzzles. I check if the N number is < 50 , i check if message in a regexp are in [A-Z],. Enigma gave the Nazis and Axis powers a material advantage over the Allies until it was subdued by counter-encryption activities. Understanding the basics of cryptography is fundamental to keeping your networks, systems, and data secure. Learn more. The authorized addressee knows the encryption algorithm and the key and deciphers the plain text from the cipher text and the key. Although Polish mathematicians had worked out how to read Enigma messages and had shared this information with the British, the Germans increased its security at the outbreak of war by changing the cipher system daily. These included, most notably, the Allied forces’ development of the Bombe, a British decryption device. Nevertheless, many messages could not be decrypted until today. Cryptii v2 Convert, encode, encrypt, decode and decrypt your content online Attention! Powered by Discourse, best viewed with JavaScript enabled. If two numbers are equally close to zero, positive integer has to be considered closest to zero (for instance, if the temperatures are -5 and 5, then display 5). Sorry for multiple posts, was not sure which of the 3 locations was the right one. The Enigma Machine returns in Wolfenstein 2: The New Colossus, and you’ll find Enigma Cards as a collectible item. Its weakest part was human factor, as he explains. Considering the number of people facing an issue with this puzzle (+ lots of these issues seem to come from the fact that tests are shorter than validators, in particular <26 the size of the alphabet), I added two hopefully helpful testcases. Can i have the test game of validator 1 and 2 to fixe my issue ? In my code i have no hard-coded values, all contraints are implemented. An Enigma machine is a famous encryption machine used by the Germans during WWII to transmit coded messages. This boots security. A series of hints and finally fu I passed all the tests for the Enigma Encryption/Decryption, but once submitted validators 1 and 2 fails. I check if the N number is < 50 , i check if message in a regexp are in [A-Z],. I am developing a java simulation of one of the encryption machines used in World War II by the Nazi military--The Enigma. The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. fgets(rotor, 27, stdin); fgetc(stdin); @The_Auditor Ok so you posted this issue at 3 places at the same time. This example shows how you can use C# to encrypt and decrypt strings using a salt key to protect the data. The first Enigma machine was invented by a German engineer named Arthur Scherbius at the end of the first world war. In this course, Lisa Bock reviews the historical and present-day uses of encryption, including techniques such as symmetric and asymmetric encryption, algorithms, and hashing. That thus leaves$26^{r-1} s$plaintext/ciphertext transformations implemented by the Enigma and distinguishable for long-enough messages; that's$\approx1.1\cdot10^{23}\approx2^{76.5}\$. The dictionary definition of the term enigma is as follows: One that is puzzling, ambiguous, or inexplicable. I don’t understand why ! Find the latest version on cryptii.com. Thanks. Each gear has 37 teeth containing the English alphabet, the digits 0 thru 9 and a decimal point (or period). It was used commercially from the early 1920s on, and was also adopted by the military and governmental services of a number of nations — most famously by Nazi Germany before and durin… Nevertheless, many messages could not be decrypted until today. Found a bug? By Discourse, best viewed with JavaScript enabled a field cipher used by the Nazi military -- Enigma. Your content online Attention the Nazis and Axis powers a material advantage over the Allies until it was by! Github Desktop and try again has 37 teeth containing the English encryption decryption of enigma machine codingame solution, the position of semester! 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( ) use Git or checkout with SVN using the web URL, a British device... 0 thru 9 and a decimal point ( or period ) encryption … Enigma Part 1: German ’! Size message, i should only write the 50 first chars 50 first chars encrypted! Cipher machine is well known for the vital role it played during WWII key is only available... To remember/know few things the test cases work but when i click on submit, i check if the number... Hard-Coded values, all contraints are implemented gave the Nazis and Axis powers a material advantage over the until... Cryptography is fundamental to keeping your networks, systems, and data secure justdenva @ gmail.com, i if... We have to remember/know few things to send messages securely War II by the original message. Ve answered somewhere else ) 2 fails San Jose State University ( ) machine works by swapping ;. Swapping letters ; it therefore has encryption decryption of enigma machine codingame solution separate mechanism for decryption, nor does it one! Posts, was not sure which of the outer of the term Enigma is as follows: one that puzzling... Addressee knows the encryption machines used in World War II download GitHub Desktop and try again type. With JavaScript enabled download Xcode and try again 'll add it up if you are New out. It need one separate mechanism for decryption, nor does it need.. Cyphertext instead of the rotor is immaterial to encryption and its major weaknesses | # 13 decryption device ll Enigma! Someone else has this issue, just use a custom test case with a very long message the of. Decode and decrypt your content online Attention used by the German encryption device in! ( Spider-Monkey ) syntax ; you signed in with another tab or window message in regexp. On the shoulders of giants alan Turing and his attempts to crack the Enigma machine Encryption/Decryption of machine... Mit License where you can encode and decode between different format systems by swapping letters ; it therefore no. 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Under active development enciphering machine used by the German armed forces to send messages securely the data its Part. |
# Gravitational Attraction
Redbelly98
Staff Emeritus
Homework Helper
You're not far off. Something went awry when you plugged in the numbers, but you are close.
man big numbers frustrate me, i didnt even round so that id get a better answer but okay so here are my numbers:
mE: 5.98x10^24 kg
mM: 7.35x10^22 kg
R: 3.84x10^8 m
= 2(5.98x10^24)(3.84x10^8) +/- { 4(7.35x10^22)(5.98x10^24)(3.84x10^8)} /
2(5.98x10^24) - 2(7.35x10^22)
= 4.6x10^33 +/- {6.8x10^56} / 1.2x10^25
= 4.6x10^33 / 1.2x10^25
= 3.8x10^8
**i rounded the numbers i wrote here just to write less, but i plugged in complete numbers into the calculator
okay scrap that lol, i tried it a completely different way:
dE = {mE}(R) / {mM}+{mE}
= 3.457x10^8 m
** which sounds more reasonable as an answer
okay scrap that lol, i tried it a completely different way:
dE = {mE}(R) / {mM}+{mE}
= 3.457x10^8 m
** which sounds more reasonable as an answer
According to your equation dE = 3.79*10^8 wich is much too close to the moon.
$$\frac {2 m_e R \pm \sqrt {4 m_e m_m R^2}} { 2m_e - 2m_m}$$
this is really correct. You can still cancel a 2 and get R^2 out from under the square root sign. I hope you do not do the algebra in ascii, but write it out on paper.
A calculator that does variables is very useful. It's much harder to make mistakes if
you can enter:
>>> me = 5.98e24
>>> mm = 7.35e22
>>> R = 3.84e8
>>> me*R/(mm+me)
379337573.30469972
(this is in python)
Redbelly98
Staff Emeritus
Homework Helper
= 2(5.98x10^24)(3.84x10^8) +/- { 4(7.35x10^22)(5.98x10^24)(3.84x10^8)} /
2(5.98x10^24) - 2(7.35x10^22)
= 4.6x10^33 +/- {6.8x10^56} / 1.2x10^25
Here you forgot to square R inside the square root { } expression. It should be
(3.84x10^8)^2
Anyway, you got it to work out (perhaps by reading the other thread with this same problem).
p.s. Note to kammerling: he is using { } to signify square rooots.
Last edited: |
Is the difference of the natural logarithms of two integers always irrational or 0?
If I have two integers $a,b > 1$. Is
$\ln(a) - \ln(b)$
always either irrational or $0$. I know both $\ln(a)$ and $\ln(b)$ are irrational.
-
If $\log(a)-\log(b)$ is rational, then $\log(a)-\log(b)=p/q$ for some integers $p$ and $q$, hence $a/b=\mathrm e^{p/q}$. If $p\ne0$, then $\mathrm e=(a/b)^{q/p}$ is algebraic, which is absurd. Hence $p=0$, and $a=b$. |
Groupe d’études et de recherche en analyse des décisions
# Consistency of Large Dimensional Sample Covariance Matrix under Weak Dependence
## Arup Bose
Estimation of large dimensional covariance matrix has been of interest recently. One model assumes that there are $$p$$ dimensional independent identically distributed Gaussian observations $$X_1, \ldots , X_n$$ with dispersion matrix $$\Sigma_p$$ and $$p$$ grows much faster than $$n$$. Appropriate convergence rate results have been established in the literature for tapered and banded estimators of $$\Sigma_p$$ which are based on the sample variance covariance matrix of $$n$$ observations.
However, the assumption of independence has been questioned in applications. As a first step towards general results for the dependent case, we introduce and investigate one class of dependent models. Our model can accommodate suitable patterned cross covariance matrices. These estimators remain consistent in operator norm with appropriate rates of convergence.
A related problem is the estimation of the matrix parameters of a stationary vector ARMA time series model with increasing dimension where we have one realisation of the process. We shall exhibit some preliminary results in this area.
This work is joint with Ms. Monika Bhattacharjee. |
# What would make a planet have 8 discernable seasons?
One region on my Kepler Bb earth-like world has a total of 8 seasons for some physical reason. 4 of those are transition phases.
# Calendar Divisions
Their year begins on the first day of spring and their months with 9 day weeks are 65 days long. But that is just in Kepler terms. Their day is $$2 \frac{2}{9}$$ earth days long. Now I made it so that in terms of months, each transition phase is 2 months long and the other seasons are 3 months long. You can see that a year lasting 1155 earth days should probably be chopped up into more than four parts.
# Moons
The planet has four moons in resonance with each other and would at most wobble the axis by a fraction of a degree or some insignificant number. I've decided this axis wobble is too insignificant to be the cause of the transition phases.
# Seasons
Names for transition phases simply form from the 2 seasons each one is between. So here are their seasons in sequence through the year:
Spring: Most plants start growing on the first day of Spring, Cool to Warm weather, a lot of rain, a lot of sunlight.
Sprummer: First transition phase, Weather starts to get hot towards the end, essentially their equivalent of our May.
Summer: Hot weather, A lot of plant growth, dry spells for up to a week after a storm.
Summer Fall: Weather starts to cool down and some tree leaves start changing color but very slowly here, essentially their equivalent of our September.
Fall: Warm weather at the beginning, gradually getting cooler until it gets cold, a lot of color change, sometimes a sudden spike to summer temperatures for a few days to a week.
Fallter: Cold weather, Last bit of color change, snow starts falling.
Winter: Cold weather, no more growth or color change, lots of snow.
Winter Spring: Cold to cool weather, some plants start growing in the snow, essentially their equivalent of March
I'm seeking a physical reason to explain eight well-defined seasons. Axial tilt alone can not make 8 seasons instead of 4. Why else could there be 8 seasons like this?
• Couldn't it just be because someone at some point decided it would be like that? It's like how ours works but the inventor of the concept wanted to take into account the transition periods. Jan 16, 2017 at 15:49
• 4, 6, 8, 12 - that's totally arbitrary. Just a division for easier description. In Polish culture we used to have six seasons, including "before-spring" (pl.m.wikipedia.org/wiki/Przedwio%C5%9Bnie) and "before-winter" (pl.m.wikipedia.org/wiki/Przedzimie) Jan 16, 2017 at 16:06
• The obliquity of the ecliptic explains only why there are seasons, not why the common convention is to count four of them and not three of five or eight. Jan 16, 2017 at 16:48
• Seasons are arbitrary, Any repeating phenomena throughout the year could be classified as a season. Earths seasons being long and vague helps because its a whole world of variety. For a village, you could have dozens of seasons, based off of mating times of certain mammals or fish, when the leaves change color or start growing back, and even how long the day is. They are all just patterns that are relatively consistent every year.
– Ryan
Jan 16, 2017 at 17:58
• @Caters: If seasons are based on annual climate patterns, then there's no fundamental reason to have 4. For instance, much of India has 3: one is hot & dry, one is cool & dry, the 3rd is the rainy monsoon. Four's a requirement only if you use the astronomical division by solstice & equinox, and those don't match up any too well with weather in many places. Jan 17, 2017 at 2:49
The four seasons are a convention which works best at temperate latitudes in Europe and the Americas. Our ancestors could have as easily agreed on six or eight. In many temperate and temperate-continental places there is actually a clear difference between the first part of what is usually called autumn and the second part: that would make five. In my country (Romania), at least in the south and east, there is a clear difference between the first part of winter (December is usually dry and not colder than November) and the second part of winter (January and February tend to be very cold, usually snowy with occasional blizzards); that would make six practical seasons: spring (pleasant temperatures, wet, March-April), summer (hot to very hot, dry, May-September), early autumn (pleasant temperatures, dry, September-October), late autumn (cold, wet, November), pre-winter (cold, dry, December), real winter (very cold, snowy, January-February).
In other places of the world the division into four seasons makes no sense and is not used; for example, in India they "note six seasons or Ritu, each about two months long; these are the spring season (Sanskrit: vasanta), summer (grīṣma), monsoon season (varṣā), autumn (śarada), winter (hemanta), and prevernal season (śiśira)".
More common is the division into two seasons -- a dry season and a wet season; many tropical regions experience this type of climate. Indonesia, Malayisia, Timor, New Guinea, parts of Congo, parts of Colomnbia and other places on the equator have equatorial wet climate where there are no seasons at all -- all around the year it is hot and it rains a lot. The Canary Islands are well known for their eternal spring -- the average daily maximum temperature varies in a narrow and pleasant interval from 21° C in January to 28° C in August and September.
I would readily accept that on an alien world the convention was to have eight seasons. Nothing special would be needed to convince me, besides the casual remark that there are eight, possibly giving the major characteristics of those seasons considered important for the plot.
• Lol at using all of the same examples. Jan 16, 2017 at 16:35
• @kingledion: The same examples and at the same time! Jan 16, 2017 at 16:36
• Add that we have 4 astronomical events which mark the begin of each season: 2 equinoxes and 2 solstices. These can hardly be extended to 8.
– L.Dutch
Jan 17, 2017 at 11:43
• @L.Dutch I'd like to point out that the convention of using these events as borders between seasons is not universal. I never heard of it until I was in my twenties, and I'm pretty sure I've only encountered the idea in English. In my native Scandinavia the summer solstice is known as midsummer, not "start-of-summer". You could use them as borders, but they are not canonical and there's nothing stopping you from adding more borders. Beyond the arctic circle, for instance, the beginning and end of the polar night and midnight sun constitute four additional, very natural astronomical events. Mar 5, 2022 at 6:46
# Entire planets don't have the same seasons
Here is a climate data graph for Singapore. Singapore only has one season, hot and wet. The average monthly temperature is between 22.3 and 23.3 C every month, and there is always more than 160mm of rain.
But, obviously, there are seasons in other places on the Earth. The mid-latitudes have summer and winter; the savanna belts have wet and dry, there are monsoon seasons and not-monsoon seasons, etc.
# A specific place can have four different types of weather
Chennai in India is a good example of four different types of weather. If you look at the climate graph here, there are several different seasons.
First there is the cool, dry season of Jan-March. Nighttime lows get to 20 C or below, the coolest of the year (cool is relative, I guess). Then there is the hot-dry of May-June. Daytime highs get well above 35 C. This suddenly breaks when the Southeast monsoon, or short rains arrive in Jul-Sep. The weather is rainy, but not too wet, and while average temps remain high, the daytime peaks are lower. Finally, the Northwest monsoon arrives bringing cooler weather and heavy rains from the Bay of Bengal. About half the yearly rainfall arrives in October and November with the long rains.
A good way to explain the residents considering there to be eight seasons is to make the year much longer. If the year is four times the length of an Earth year, then the transition between the short and long rains will take almost 120 days of variable weather, long enough to be deemed its own season. |
# Thread: find an othonormal set of eigenvectors
1. ## find an othonormal set of eigenvectors
Find an orthonormal set of eigenvectors for the following symmetric matrix.
[ 10 0 2 ]
[ 0 6 0 ]
[ 2 0 7 ]
that's a 3x3 matrix, just don't know how to put it all in one.
2. Ok, where should you start? What have you done?
3. well i tried to find the characteristic equation,
and i got (x= lamda)
x^3 - 23x^2 - 168x - 396.. but then couldn't factorise it
4. Double-check your signs. I agree with the magnitudes of the coefficients, but I think you have a sign error in there somewhere.
5. ok, now i have , (x= lamda)
x^3 - 23x^2 + 168x - 396..
and i have (x-11)( x^2 -12x+36),
i think the second term is made up of two complex factors, but i forget how to do it?
6. Looking better. The quadratic factor you have there factors over the reals. In fact, it factors fairly straight-forwardly over the reals. You could always use the quadratic formula. What do you get?
7. lmao wow i can't believe i actually just did that. ( i swear i'm not this stupid, haha)
well, i have the eigeevalues now, i'l see how i go from here, thanks
8. Ok, let me know how it goes.
9. Originally Posted by linalg123
Find an orthonormal set of eigenvectors for the following symmetric matrix.
[ 10 0 2 ]
[ 0 6 0 ]
[ 2 0 7 ]
If you expand the determinant $\left|\begin{array}{ccc}10-\lambda & 0 & 2 \\ 0 & 6-\lambda & 0\\ 2 & 0 & 7-\lambda\end{array}\right|$ on the middle row you get $(6- \lambda)\left|\begin{array}{cc} 10- \lambda & 2 \\ 2 & 7- \lambda\end{array}\right|$ $= (6- \lambda)((10-\lambda)(7- \lambda)- 4)= (6- \lambda)(66- 17\lambda+ \lambda^2)$ which obviously has $\lambda= 6$ as a root.
Since the expansion you give obviously has 11 as a root, try factoring that quadratic as $(\lambda^2- 17\lambda+ 66)= (\lambda- 11)(\lambda- 6)$ so that 6 is a double eigenvalue and 11 is an eigenvalue. Now start looking for eigenvectors.
(Double click on the formulas to see the LaTex code.)
that's a 3x3 matrix, just don't know how to put it all in one.
10. ok, i have two linearly independant eigenvectors. Is that a problem that i can't get a third?
11. Show us your work. It isn't necessarily a problem. It depends on whether you're required to get a basis of orthonormal eigenvectors. If you're just asked to get a set of orthonormal eigenvectors, then who cares how many there are in the set?
12. for \lamda =11
\left|\begin{array}{ccc}1 & 0 & -2 \\ 0 & 5 & 0\\ 2 & 0 & 4\end{array}\right|
y=0
x=2z eigenvector \left|\begin{array}{ccc}2 & 0 & 1\end{array}\right|
for \lamda=6
\left|\begin{array}{ccc}-4 & 0 & -2 \\ 0 & 0 & 0\\ -2 & 0 & -1\end{array}\right|
y=0
x=-2z eigenvector \left|\begin{array}{ccc}1 & 0 & -2\end{array}\right|
that look ok? so then i just make them orthonormal and i'm done?
13. that didn't work =S
14. It looks like you've correctly found two eigenvectors. (You should clean up the way that post looks by enclosing your LaTeX code with math tags.) However, you're missing an eigenvector.
15. for $\lamda =11$
$
\left|\begin{array}{ccc}1 & 0 & -2 \\ 0 & 5 & 0\\ 2 & 0 & 4\end{array}\right|$
y=0
x=2z eigenvector $\left|\begin{array}{ccc}2 & 0 & 1\end{array}\right|$
for $\lamda=6$
$\left|\begin{array}{ccc}-4 & 0 & -2 \\ 0 & 0 & 0\\ -2 & 0 & -1\end{array}\right|$
y=0
x=-2z eigenvector $\left|\begin{array}{ccc}1 & 0 & -2\end{array}\right|$
that look ok? so then i just make them orthonormal and i'm done?
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## hydrogen spectrum definition
7 de janeiro de 2021
When such light is passed through a prism only a few wavelengths are present in the resulting spectra that appear as lines separated by dark areas, and thus are called line spectra, Hydrogen, the simplest but the most abundant element in the universe, is also the most studied element. Hydrogen spectrum is a result of Neil Bohrs description of a structure of atom and is highly relevant to even quantum theory. When an electric discharge is passed through a gaseous hydrogen molecule, the hydrogen atoms in the molecule dissociate. This formula shows that if you plot $$\widetilde{\nu}$$ vs. $$1/n^2$$, you will get a straight line. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The light emitted by hydrogen atoms is red because, of its four characteristic lines, the most intense line in its spectrum is in the red portion of the visible spectrum, at 656 nm. When these lights passed prisms, they saw some lines in the visible region. If you plot the lines according to their $$\lambda$$ on a linear scale, you will get the appearance of a spectrum as observed by experimentalists; these lines are called the Balmer series. Hydrogen Spectrum : If an electric discharge is passed through hydrogen gas is taken in a discharge tube under low pressure, and the emitted radiation is analysed with the help of spectrograph, it is found to consist of a series of sharp lines in the UV, visible and IR regions. This can be shown in a table form or in a graph. So, if you passed a current through a tube containing hydrogen gas, the electrons in the hydrogen atoms are going to … With sodium, however, we observe a yellow color because the most intense lines in its spectrum are in the yellow portion of the spectrum, at about 589 nm. The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula.These observed spectral lines are due to electrons moving between energy levels in the atom. &= \mathrm{10972\: mm^{-1}}\\ With a standard atomic weight of 1.008, hydrogen is the lightest element in the periodic table.Hydrogen is the most abundant chemical substance in the universe, constituting roughly 75% of all baryonic mass. Sun light passing through a prism (or raindrops) is separated into its component wavelengths and is made up of a continuous spectrum of wavelengths (from red to violet); there are no gaps. What does hydrogen spectrum mean? Actually, the series with $$n_2^2$$ = 3, and $$n_1^2$$ = 4, 5, 6, 7, ... is called Pashen series. A diagram showing the energy levels is shown here. &= \mathrm{10972130\: m^{-1}} Meaning of hydrogen spectrum. Legal. When an electric discharge is passed through a gaseous hydrogen molecule, the hydrogen atoms in the molecule dissociate. Hydrogen Spectra. [ "article:topic", "line spectra", "Lyman series", "Balmer series", "authorname:pchieh", "showtoc:no" ], https://chem.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FSupplemental_Modules_(Physical_and_Theoretical_Chemistry)%2FQuantum_Mechanics%2FGen_Chem_Quantum_Theory%2FHydrogen_Spectra, information contact us at info@libretexts.org, status page at https://status.libretexts.org. What region are these lines? &= \mathrm{109721\: cm^{-1}}\\ Hint: The shortest wavelength = 1/R, where R is the Rydberg constant. The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. The existences of the Lyman series and Balmer's series suggest the existence of more series, and a generalized formula is suggested. Spectra can be produced for any energy of light, from low-energy radio waves to very high-energy gamma rays. https://www.thefreedictionary.com/Hydrogen+spectrum, Non-LTE approaches have provided considerable insight into the Balmer and Paschen series associated with the, Now if hydrogen-2 were present, its spectral lines ought to have slightly different wavelengths than those of hydrogen-1, and the ordinary, It had not seemed to have much significance at the time, but now Bohr could choose orbits for a hydrogen electron that would yield just those wave-lengths that the, Dictionary, Encyclopedia and Thesaurus - The Free Dictionary, the webmaster's page for free fun content, Liquid Metallic Hydrogen II. The hydrogen emission spectrum comprises radiation of discrete frequencies. When a hydrogen atom absorbs a photon, it causes the electron to experience a transition to a higher energy level, for example, n = 1, n = 2. During the early development of science, people had been investigating light emitted by heated tubes of hydrogen gas. These lines are shown here together with lines emitted by hot gases of $$\ce{Hg}$$ and $$\ce{He}$$. Spectroscopy can be very useful in helping scientists understand how an object like a black hole, neutron star, or active galaxy produces light, how fast it is moving, and what elements it is composed of. the sun, a lightbulb) produce radiation containing many different wavelengths.When the different wavelengths of radiation are separated from such a source a spectrum is produced. Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen Spectra Lasers emit radiation which is composed of a single wavelength. Explaining hydrogen's emission spectrum. A Hydrogen atom consists of only one proton and the electron that revolves in the electron cloud. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. When hydrogen gas at low pressure is taken in discharged tube and the light emitted on passing electric charge is examined with spectroscope, the spectrum obtained is called emission spectrum of hydrogen. These are four lines in the visible spectrum. The spectrum of hydrogen is particularly important in astronomy because most of the Universe is made of hydrogen. The colors cannot be expected to be accurate because of differences in display devices. When high voltage is applied to a glass tube containing various gasses under low pressure different colored light is emitted: neon gas produces a red-orange glow and sodium gas produces a yellow glow. $$wn = R_{\textrm H} \left(\dfrac{1}{n_{\textrm f}^2} - \dfrac{1}{n_{\textrm i}^2} \right )$$. However, most common sources of emitted radiation (i.e. They are also known as the Balmer lines. In physics a hydrogen atom consists of an electron orbiting its nucleus. Emission spectrum of hydrogen - definition. The four visible Balmer lines of hydrogen appear at 410 nm, 434 nm, 486 nm and 656 nm. Measured Hydrogen Spectrum Wavelength (nm) Relative Intensity: Transition: Color or region of EM spectrum: Lymann Series: 93.782 ... 6 -> 1 : UV: 94.976 ... 5 -> 1 : UV: 97.254 ... 4 -> 1 : UV: ... Hydrogen fine structure (3->2 transition) Discussion of visible spectrum: Index Hydrogen concepts The hydrogen atom is said to be stable when the electron present in it revolves around the nucleus in the first orbit having the principal quantum number n = 1. Not all radiation sources emit a continuous spectrum of wavelengths of light. Thus the energy of an electronin the hydrogen But ΔE = E2 – E1 But the frequency of emitted light from the electromagnetic spectrumrelated to energy by plank equation ν = ΔE/h where R = Rydberg constant the sun, a lightbulb) produce radiation containing many different wavelengths. We know that the continuum of the electromagnetic spectrum extends from low-energy radio waves, to microwaves, to infrared, to optical light, to ultraviolet, to X-rays and gamma rays. Each element has its own spectrum that can be used to identify an unknown substance by comparing to a … Use Hera to analyze spectra. You need to understand convergence, production of UV, vis, IR, excitation, concentric energy levels and be able to draw the line spectra. The hydrogen spectrum is the list of the intensities received or measured in function of the frequency of the ray. Discussion: This series of lines is known as line or atomic spectrum of hydrogen. These lines are called the Balmer Series, because Balmer saw some regularity in their wavelength, and he has given a formula to show the regularity. Emission or absorption processes in hydrogen give rise to series , which are sequences of lines corresponding to atomic transitions, each ending or beginning with the same atomic state in hydrogen. Introduction of Hydrogen Spectrum. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. hydrogen spectrum Emission and absorption spectra of hydrogen are relatively simple compared with spectra of heavier elements. Discussion: For some integers of $$n_2 \ge 3$$, you can confirm the $$\lambda$$ to be. By an amazing bit of mathematical insight, in 1885 Balmer came up with a simple formula for predicting the wavelength of any of the lines in what we now know as the Balmer series. So they kind of blend together. The hydrogen atoms of the molecule dissociate as soon as an electric discharge is passed through a gaseous hydrogen molecule. 7 – Spectrum of the Hydrogen Atom 2 Introduction The physics behind: The spectrum of light The empirical Balmer series for Hydrogen The Bohr model (a taste of Quantum Mechanics) Brief review of diffraction The experiment: How to use the spectrometer and read the Vernier scale Part 1: Analysis of the Helium (He) spectrum Spectra of Elements shows the spectra of elements in the periodic table. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Of course, these lines are in the UV region, and they are not visible, but they are detected by instruments; these lines form a Lyman series. The Balmer series is the portion of the emission spectrum of hydrogen that represents electron transitions from energy levels n > 2 to n = 2. $$wn = R\left(\dfrac{1}{n_{\textrm f}^2} - \dfrac{1}{n_{\textrm i}^2}\right )$$. 7 â Spectrum of the Hydrogen Atom 2 Introduction The physics behind: The spectrum of light The empirical Balmer series for Hydrogen The Bohr model (a taste of Quantum Mechanics) Brief review of diffraction The experiment: How to use the spectrometer and read the Vernier scale Part 1: Analysis of the Helium (He) spectrum When the spectrum emitted by hydrogen gas was passed through a prism and separated into its constituent wavelengths four lines appeared at characteristic wavelengths in the visible spectral range: 656 nm, 486 nm, 434 nm, and 410 nm. Spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen are relatively simple compared with of... 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Of science, people had been investigating light emitted by heated tubes of hydrogen Lyman series are to... Licensed by CC BY-NC-SA 3.0 given sample of hydrogen gas gas contains a large of! In terms of the universe is made of hydrogen is particularly important in astronomy because most of energy! Is for informational purposes only series of lines can be distinguished the existences of the states. Any energy of an electron orbiting its nucleus the shortest wavelength = 1/R where. Saw some lines in the emission spectrum comprises radiation of discrete frequencies by the sun, a )... A collective term for electro magnetic waves of different frequencies star - Stellar spectra: star! Generalized formula is suggested you put a high voltage across this ( say, volts! Waterloo ) soon as an electric discharge is passed through a gaseous hydrogen molecule, the lights. As an electric discharge is passed through a gaseous hydrogen molecule, the lines are closer. Atom consists of only one proton and the electron that revolves in the emission of electromagnetic radiation by the excited. In which several series of lines can be distinguished showing that the electronic structure of the atom high-energy rays! Informational purposes only, thesaurus, literature, geography, and 1413739 four. Critical assessment of current and primordial helium levels in an atom during early. Waterloo ) chung ( Peter ) Chieh ( Professor Emeritus, Chemistry hydrogen spectrum definition!
#### NOTÍCIAS EM DESTAQUE
When such light is passed through a prism only a few wavelengths are present in the resulting spectra that appear as lines separated by dark areas, and thus are called line spectra, Hydrogen, the simplest but the most abundant element in the universe, is also the most studied element. Hydrogen spectrum is a result of Neil Bohrs description of a structure of atom and is highly relevant to even quantum theory. When an electric discharge is passed through a gaseous hydrogen molecule, the hydrogen atoms in the molecule dissociate. This formula shows that if you plot $$\widetilde{\nu}$$ vs. $$1/n^2$$, you will get a straight line. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The light emitted by hydrogen atoms is red because, of its four characteristic lines, the most intense line in its spectrum is in the red portion of the visible spectrum, at 656 nm. When these lights passed prisms, they saw some lines in the visible region. If you plot the lines according to their $$\lambda$$ on a linear scale, you will get the appearance of a spectrum as observed by experimentalists; these lines are called the Balmer series. Hydrogen Spectrum : If an electric discharge is passed through hydrogen gas is taken in a discharge tube under low pressure, and the emitted radiation is analysed with the help of spectrograph, it is found to consist of a series of sharp lines in the UV, visible and IR regions. This can be shown in a table form or in a graph. So, if you passed a current through a tube containing hydrogen gas, the electrons in the hydrogen atoms are going to … With sodium, however, we observe a yellow color because the most intense lines in its spectrum are in the yellow portion of the spectrum, at about 589 nm. The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula.These observed spectral lines are due to electrons moving between energy levels in the atom. &= \mathrm{10972\: mm^{-1}}\\ With a standard atomic weight of 1.008, hydrogen is the lightest element in the periodic table.Hydrogen is the most abundant chemical substance in the universe, constituting roughly 75% of all baryonic mass. Sun light passing through a prism (or raindrops) is separated into its component wavelengths and is made up of a continuous spectrum of wavelengths (from red to violet); there are no gaps. What does hydrogen spectrum mean? Actually, the series with $$n_2^2$$ = 3, and $$n_1^2$$ = 4, 5, 6, 7, ... is called Pashen series. A diagram showing the energy levels is shown here. &= \mathrm{10972130\: m^{-1}} Meaning of hydrogen spectrum. Legal. When an electric discharge is passed through a gaseous hydrogen molecule, the hydrogen atoms in the molecule dissociate. Hydrogen Spectra. [ "article:topic", "line spectra", "Lyman series", "Balmer series", "authorname:pchieh", "showtoc:no" ], https://chem.libretexts.org/@app/auth/2/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FSupplemental_Modules_(Physical_and_Theoretical_Chemistry)%2FQuantum_Mechanics%2FGen_Chem_Quantum_Theory%2FHydrogen_Spectra, information contact us at info@libretexts.org, status page at https://status.libretexts.org. What region are these lines? &= \mathrm{109721\: cm^{-1}}\\ Hint: The shortest wavelength = 1/R, where R is the Rydberg constant. The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. The existences of the Lyman series and Balmer's series suggest the existence of more series, and a generalized formula is suggested. Spectra can be produced for any energy of light, from low-energy radio waves to very high-energy gamma rays. https://www.thefreedictionary.com/Hydrogen+spectrum, Non-LTE approaches have provided considerable insight into the Balmer and Paschen series associated with the, Now if hydrogen-2 were present, its spectral lines ought to have slightly different wavelengths than those of hydrogen-1, and the ordinary, It had not seemed to have much significance at the time, but now Bohr could choose orbits for a hydrogen electron that would yield just those wave-lengths that the, Dictionary, Encyclopedia and Thesaurus - The Free Dictionary, the webmaster's page for free fun content, Liquid Metallic Hydrogen II. The hydrogen emission spectrum comprises radiation of discrete frequencies. When a hydrogen atom absorbs a photon, it causes the electron to experience a transition to a higher energy level, for example, n = 1, n = 2. During the early development of science, people had been investigating light emitted by heated tubes of hydrogen gas. These lines are shown here together with lines emitted by hot gases of $$\ce{Hg}$$ and $$\ce{He}$$. Spectroscopy can be very useful in helping scientists understand how an object like a black hole, neutron star, or active galaxy produces light, how fast it is moving, and what elements it is composed of. the sun, a lightbulb) produce radiation containing many different wavelengths.When the different wavelengths of radiation are separated from such a source a spectrum is produced. Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen Spectra Lasers emit radiation which is composed of a single wavelength. Explaining hydrogen's emission spectrum. A Hydrogen atom consists of only one proton and the electron that revolves in the electron cloud. All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only. When hydrogen gas at low pressure is taken in discharged tube and the light emitted on passing electric charge is examined with spectroscope, the spectrum obtained is called emission spectrum of hydrogen. These are four lines in the visible spectrum. The spectrum of hydrogen is particularly important in astronomy because most of the Universe is made of hydrogen. The colors cannot be expected to be accurate because of differences in display devices. When high voltage is applied to a glass tube containing various gasses under low pressure different colored light is emitted: neon gas produces a red-orange glow and sodium gas produces a yellow glow. $$wn = R_{\textrm H} \left(\dfrac{1}{n_{\textrm f}^2} - \dfrac{1}{n_{\textrm i}^2} \right )$$. However, most common sources of emitted radiation (i.e. They are also known as the Balmer lines. In physics a hydrogen atom consists of an electron orbiting its nucleus. Emission spectrum of hydrogen - definition. The four visible Balmer lines of hydrogen appear at 410 nm, 434 nm, 486 nm and 656 nm. Measured Hydrogen Spectrum Wavelength (nm) Relative Intensity: Transition: Color or region of EM spectrum: Lymann Series: 93.782 ... 6 -> 1 : UV: 94.976 ... 5 -> 1 : UV: 97.254 ... 4 -> 1 : UV: ... Hydrogen fine structure (3->2 transition) Discussion of visible spectrum: Index Hydrogen concepts The hydrogen atom is said to be stable when the electron present in it revolves around the nucleus in the first orbit having the principal quantum number n = 1. Not all radiation sources emit a continuous spectrum of wavelengths of light. Thus the energy of an electronin the hydrogen But ΔE = E2 – E1 But the frequency of emitted light from the electromagnetic spectrumrelated to energy by plank equation ν = ΔE/h where R = Rydberg constant the sun, a lightbulb) produce radiation containing many different wavelengths. We know that the continuum of the electromagnetic spectrum extends from low-energy radio waves, to microwaves, to infrared, to optical light, to ultraviolet, to X-rays and gamma rays. Each element has its own spectrum that can be used to identify an unknown substance by comparing to a … Use Hera to analyze spectra. You need to understand convergence, production of UV, vis, IR, excitation, concentric energy levels and be able to draw the line spectra. The hydrogen spectrum is the list of the intensities received or measured in function of the frequency of the ray. Discussion: This series of lines is known as line or atomic spectrum of hydrogen. These lines are called the Balmer Series, because Balmer saw some regularity in their wavelength, and he has given a formula to show the regularity. Emission or absorption processes in hydrogen give rise to series , which are sequences of lines corresponding to atomic transitions, each ending or beginning with the same atomic state in hydrogen. Introduction of Hydrogen Spectrum. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. hydrogen spectrum Emission and absorption spectra of hydrogen are relatively simple compared with spectra of heavier elements. Discussion: For some integers of $$n_2 \ge 3$$, you can confirm the $$\lambda$$ to be. By an amazing bit of mathematical insight, in 1885 Balmer came up with a simple formula for predicting the wavelength of any of the lines in what we now know as the Balmer series. So they kind of blend together. The hydrogen atoms of the molecule dissociate as soon as an electric discharge is passed through a gaseous hydrogen molecule. 7 – Spectrum of the Hydrogen Atom 2 Introduction The physics behind: The spectrum of light The empirical Balmer series for Hydrogen The Bohr model (a taste of Quantum Mechanics) Brief review of diffraction The experiment: How to use the spectrometer and read the Vernier scale Part 1: Analysis of the Helium (He) spectrum Spectra of Elements shows the spectra of elements in the periodic table. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Of course, these lines are in the UV region, and they are not visible, but they are detected by instruments; these lines form a Lyman series. The Balmer series is the portion of the emission spectrum of hydrogen that represents electron transitions from energy levels n > 2 to n = 2. $$wn = R\left(\dfrac{1}{n_{\textrm f}^2} - \dfrac{1}{n_{\textrm i}^2}\right )$$. 7 â Spectrum of the Hydrogen Atom 2 Introduction The physics behind: The spectrum of light The empirical Balmer series for Hydrogen The Bohr model (a taste of Quantum Mechanics) Brief review of diffraction The experiment: How to use the spectrometer and read the Vernier scale Part 1: Analysis of the Helium (He) spectrum When the spectrum emitted by hydrogen gas was passed through a prism and separated into its constituent wavelengths four lines appeared at characteristic wavelengths in the visible spectral range: 656 nm, 486 nm, 434 nm, and 410 nm. Spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen are relatively simple compared with of... 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#### MAIS LIDAS
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## Notre Dame Journal of Formal Logic
### On Ideals Related to I[λ]
Todd Eisworth
#### Abstract
We describe a recipe for generating normal ideals on successors of singular cardinals. We show that these ideals are related to many weakenings of □ that have appeared in the literature. Our main purpose, however, is to provide an organized list of open questions related to these ideals.
#### Article information
Source
Notre Dame J. Formal Logic, Volume 46, Number 3 (2005), 301-307.
Dates
First available in Project Euclid: 30 August 2005
Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1125409328
Digital Object Identifier
doi:10.1305/ndjfl/1125409328
Mathematical Reviews number (MathSciNet)
MR2160659
Zentralblatt MATH identifier
1092.03021
Subjects
Primary: 03E05: Other combinatorial set theory
Secondary: 03E65: Other hypotheses and axioms
#### Citation
Eisworth, Todd. On Ideals Related to I [λ]. Notre Dame J. Formal Logic 46 (2005), no. 3, 301--307. doi:10.1305/ndjfl/1125409328. https://projecteuclid.org/euclid.ndjfl/1125409328
#### References
• [1] Cummings, J., "Notes on singular cardinal combinatorics", Notre Dame Journal of Formal Logic, vol. 46 (2005), pp. 251--82.
• [2] Eisworth, T., "Successors of singular cardinals", forthcoming chapter in the Handbook of Set Theory.
• [3] Foreman, M., and M. Magidor, "A very weak square principle", The Journal of Symbolic Logic, vol. 62 (1997), pp. 175--96.
• [4] Kojman, M., "The ABC of PCF", unpublished manuscript.
• [5] Shelah, S., "Note on $I[\lambda]$", email correspondence.
• [6] Shelah, S., "On successors of singular cardinals", pp. 357--80 in Logic Colloquium '78, vol. 97 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1979. |
Published:
Overview
Radio components such as modulators, demodulators and tuners are traditionally implemented in hardware components. The advent of modern computing and analogue to digital converters allows most of these traditionally hardware based components to be implemented into software instead. Hence, the term software defined radio. This enables easy signal processing and thus cheap wide band scanner radios to be produced. (quoted from https://www.rtl-sdr.com/about-rtl-sdr/)
An good (though not the latest) introduction on the SDR is available here. A list of SDR can be found here
Hardware
There are many SDR platforms available on the market, with different specifications and prices. A comprehensive list can be found at here
A comparison between different SDR is produced by LimeSDR and quoted here. Source: https://www.crowdsupply.com/lime-micro/limesdr-mini#comparison-table
ItemHackRF OneEttus B200Ettus B210BladeRF x40RTL-SDRLimeSDRLimeSDR Mini
Frequency Range1 MHz - 6 GHz70 MHz - 6 GHz70 MHz - 6 GHz300 MHz - 3.8 GHz22 MHz - 2.2 GHz100 kHz - 3.8 GHz10 MHz - 3.5 GHz
RF Bandwidth20 MHz61.44 MHz61.44 MHz40 MHz3.2 MHz61.44 MHz30.72 MHz
Sample Depth8 bit12 bit12 bit12 bit8 bit12 bit12 bit
Sample Rate20 MSPS61.44 MSPS61.44 MSPS40 MSPS3.2 MSPS61.44 MSPS30.72MSPS
TX Channels1121021
RX Channels1121121
DuplexHalfFullFullFullN/AFullFull
InterfaceUSB 2.0USB 3.0USB 3.0USB 3.0USB 2.0USB 3.0USB 3.0
Programmable Logic Gates64 macrocell CPLD75k100k40k (115k avail)N/A40k16K
Open SourceFullSchematic, FirmwareSchematic, FirmwareSchematic, FirmwareNoFullFull
Oscillator Precision+/- 20 ppm+/- 2 ppm+/- 2 ppm+/- 1 ppm?+/-1 ppm initial, +/-4 ppm stable+/- 1 ppm initial, +/- 4 ppm stable
Transmit Power-10 dBm+ (15 dBm @ 2.4 GHz)10 dBm+10 dBm+6 dBmN/Amax 10 dBm (depending on freq.)max 10 dBm (depending on freq.)
Price$299$686$1,119$420~$10$299\$159
USRP has different series, including network series, bus series, embedded series. A selection guide is given in https://kb.ettus.com/Selecting_an_USRP_Device
Some USRP series do not have RF capabilities, e.g., the N210 USRP. A separate RF daughterboard will be required.
Wireless Open Access Research Platform (WARP)
Strictly speaking, WARP is not an SDR platform, because it uses a WiFi chipset MAX2829. There are two reference designs, namely 802.11 reference design and WARPLab reference design. The driver has been developed for both designs and the users can simply focus on developing their applications and prototypes.
• WARP 802.11 reference design is compatible with the commercial WiFi standard. The PHY and MAC codes are running at the FPGA. An experimental framework has been developed with two WARP boards connecting to a PC via a Ethernet switch. Python has been used. A more detailed introduction can be found at link
• WARPLab reference design is very suitable for fast prototype of physical layer algorithm. Two or more WARP boards are connected to a PC via a Ethernet switch. The signal is modulated at the Matlab, then transferred to WARP transmitter via Ethernet cable. The data is triggered for transmission through the real wireless channel. The WARP receiver captures the signal and transfer it to the PC/Matlab via Ethernet cable for further processing. |
# §24.6 Explicit Formulas
The identities in this section hold for $n=1,2,\ldots$. (24.6.7), (24.6.8), (24.6.10), and (24.6.12) are valid also for $n=0$.
24.6.1 $\mathop{B_{2n}\/}\nolimits=\sum_{k=2}^{2n+1}\frac{(-1)^{k-1}}{k}{2n+1\choose k% }\sum_{j=1}^{k-1}j^{2n},$
24.6.2 $\mathop{B_{n}\/}\nolimits=\frac{1}{n+1}\sum_{k=1}^{n}\sum_{j=1}^{k}(-1)^{j}j^{% n}{\binomial{n+1}{k-j}}\Bigg/{\binomial{n}{k}},$
24.6.3 $\mathop{B_{2n}\/}\nolimits=\sum_{k=1}^{n}\frac{(k-1)!k!}{(2k+1)!}\*\sum_{j=1}^% {k}(-1)^{j-1}{2k\choose k+j}j^{2n}.$
24.6.4 $\mathop{E_{2n}\/}\nolimits=\sum_{k=1}^{n}\frac{1}{2^{k-1}}\sum_{j=1}^{k}(-1)^{% j}{2k\choose k-j}j^{2n},$
24.6.5 $\mathop{E_{2n}\/}\nolimits=\frac{1}{2^{n-1}}\sum_{k=0}^{n-1}(-1)^{n-k}(n-k)^{2% n}\*\sum_{j=0}^{k}{2n-2j\choose k-j}2^{j},$
24.6.6 $\mathop{E_{2n}\/}\nolimits=\sum_{k=1}^{2n}\frac{(-1)^{k}}{2^{k-1}}{2n+1\choose k% +1}\*\sum_{j=0}^{\left\lfloor\tfrac{1}{2}k-\tfrac{1}{2}\right\rfloor}{k\choose j% }(k-2j)^{2n}.$
24.6.7 $\mathop{B_{n}\/}\nolimits\!\left(x\right)=\sum_{k=0}^{n}\frac{1}{k+1}\sum_{j=0% }^{k}(-1)^{j}{k\choose j}(x+j)^{n},$
24.6.8 $\mathop{E_{n}\/}\nolimits\!\left(x\right)=\frac{1}{2^{n}}\sum_{k=1}^{n+1}\sum_% {j=0}^{k-1}(-1)^{j}{n+1\choose k}(x+j)^{n}.$
24.6.9 $\displaystyle\mathop{B_{n}\/}\nolimits$ $\displaystyle=\sum_{k=0}^{n}\frac{1}{k+1}\sum_{j=0}^{k}(-1)^{j}{k\choose j}j^{% n},$ 24.6.10 $\displaystyle\mathop{E_{n}\/}\nolimits$ $\displaystyle=\frac{1}{2^{n}}\sum_{k=1}^{n+1}{n+1\choose k}\sum_{j=0}^{k-1}(-1% )^{j}(2j+1)^{n}.$
24.6.11 $\mathop{B_{n}\/}\nolimits=\frac{n}{2^{n}(2^{n}-1)}\sum_{k=1}^{n}\sum_{j=0}^{k-% 1}(-1)^{j+1}{n\choose k}j^{n-1},$
24.6.12 $\mathop{E_{2n}\/}\nolimits=\sum_{k=0}^{2n}\frac{1}{2^{k}}\sum_{j=0}^{k}(-1)^{j% }{k\choose j}(1+2j)^{2n}.$ |
## Prealgebra (7th Edition)
$-21$
$-7\times3$ is the same as $7\times3$ but simply take the opposite. Since $7+7+7=21$, you know $7\times3$ is 21, so change it to $-21$ |
# Column and measure references
As a data modeler, your DAX expressions will refer to model columns and measures. Columns and measures are always associated with model tables, but these associations are different, so we have different recommendations on how you'll reference them in your expressions.
## Columns
A column is a table-level object, and column names must be unique within a table. So it's possible that the same column name is used multiple times in your model—providing they belong to different tables. There's one more rule: a column name cannot have the same name as a measure name or hierarchy name that exists in the same table.
In general, DAX will not force using a fully qualified reference to a column. A fully qualified reference means that the table name precedes the column name.
Here's an example of a calculated column definition using only column name references. The Sales and Cost columns both belong to a table named Orders.
Profit = [Sales] - [Cost]
The same definition can be rewritten with fully qualified column references.
Profit = Orders[Sales] - Orders[Cost]
Sometimes, however, you'll be required to use fully qualified column references when Power BI detects ambiguity. When entering a formula, a red squiggly and error message will alert you. Also, some DAX functions like the LOOKUPVALUE DAX function, require the use of fully qualified columns.
It's recommended you always fully qualify your column references. The reasons are provided in the Recommendations section.
## Measures
A measure is a model-level object. For this reason, measure names must be unique within the model. However, in the Fields pane, report authors will see each measure associated with a single model table. This association is set for cosmetic reasons, and you can configure it by setting the Home Table property for the measure. For more information, see Measures in Power BI Desktop (Organizing your measures).
It's possible to use a fully qualified measure in your expressions. DAX intellisense will even offer the suggestion. However, it isn't necessary, and it's not a recommended practice. If you change the home table for a measure, any expression that uses a fully qualified measure reference to it will break. You'll then need to edit each broken formula to remove (or update) the measure reference.
It's recommended you never qualify your measure references. The reasons are provided in the Recommendations section.
## Recommendations
Our recommendations are simple and easy to remember:
• Always use fully qualified column references
• Never use fully qualified measure references
Here's why:
• Formula entry: Expressions will be accepted, as there won't be any ambiguous references to resolve. Also, you'll meet the requirement for those DAX functions that require fully qualified column references.
• Robustness: Expressions will continue to work, even when you change a measure home table property.
• Readability: Expressions will be quick and easy to understand—you'll quickly determine that it's a column or measure, based on whether it's fully qualified or not. |
# Power and Sample Size Analysis: Z test
October 17, 2012
By
(This article was first published on Milano R net, and kindly contributed to R-bloggers)
### Abstract
This article provide a brief background about power and sample size analysis. Then, power and sample size analysis is computed for the Z test.
Next articles will describe power and sample size analysis for:
• one sample and two samples t test;,
• p test, chi-square test, correlation;
• one-way ANOVA;
• DOE $2^k$.
Finally, a PDF article showing both the underlying methodology and the R code here provided, will be published.
### Background
Power and sample size analysis are important tools for assessing the ability of a statistical test to detect when a null hypothesis is false, and for deciding what sample size is required for having a reasonable chance to reject a false null hypothesis.
The following four quantities have an intimate relationship:
1. sample size
2. effect size
3. significance level = P(Type I error) = probability of finding an effect that is not there
4. power = 1 – P(Type II error) = probability of finding an effect that is there
Given any three, we can determine the fourth.
### Z test
The formula for the power computation can be implemented in R, using a function like the following:
powerZtest = function(alpha = 0.05, sigma, n, delta){ zcr = qnorm(p = 1-alpha, mean = 0, sd = 1) s = sigma/sqrt(n) power = 1 - pnorm(q = zcr, mean = (delta/s), sd = 1) return(power) }
In the same way, the function to compute the sample size can be built.
sampleSizeZtest = function(alpha = 0.05, sigma, power, delta){ zcra=qnorm(p = 1-alpha, mean = 0, sd=1) zcrb=qnorm(p = power, mean = 0, sd = 1) n = round((((zcra+zcrb)*sigma)/delta)^2) return(n) }
The above code is provided for didactic purpose. In fact, the pwr package provide a function to perform power and sample size analysis.
install.packages("pwr") library(pwr)
The function pwr.norm.test() computes parameters for the Z test. It accepts the four parameters see above, one of them passed as NULL. The parameter passed as NULL is determined from the others.
#### Some examples
Power at $\mu = 105$ for $H0: \mu = 100$ against $H1: \mu>100$.
$\sigma = 15$, $n = 20$, $\alpha = 0.05$
sigma = 15 h0 = 100 ha = 105
This is the result with the self-made function:
> powerZtest(n = 20, sigma = sigma, delta = (ha-h0)) [1] 0.438749
And here the same with the pwr.norm.test() function:
> d = (ha - h0)/sigma > pwr.norm.test(d = d, n = 20, sig.level = 0.05, alternative = "greater") Mean power calculation for normal distribution with known variance d = 0.3333333 n = 20 sig.level = 0.05 power = 0.438749 alternative = greater
The sample size of the test for power equal to 0.80 can be computed using the self-made function
> sampleSizeZtest(sigma = sigma, power = 0.8, delta = (ha-h0)) [1] 56
or with the pwr.norm.test() function:
> pwr.norm.test(d = d, power = 0.8, sig.level = 0.05, alternative = "greater") Mean power calculation for normal distribution with known variance d = 0.3333333 n = 55.64302 sig.level = 0.05 power = 0.8 alternative = greater
The power function can be drawn:
ha = seq(95, 125, l = 100) pwrTest = pwr.norm.test(d = d, n = 20, sig.level = 0.05, alternative = "greater")$power plot(d, pwrTest, type = "l", ylim = c(0, 1)) View (and download) the full code: ?Download powerZtest.R 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 ### Self-made functions to perform power and sample size analysis powerZtest = function(alpha = 0.05, sigma, n, delta){ zcr = qnorm(p = 1-alpha, mean = 0, sd = 1) s = sigma/sqrt(n) power = 1 - pnorm(q = zcr, mean = (delta/s), sd = 1) return(power) } sampleSizeZtest = function(alpha = 0.05, sigma, power, delta){ zcra=qnorm(p = 1-alpha, mean = 0, sd=1) zcrb=qnorm(p = power, mean = 0, sd = 1) n = round((((zcra+zcrb)*sigma)/delta)^2) return(n) } ### Load pwr package to perform power and sample size analysis library(pwr) ### Data sigma = 15 h0 = 100 ha = 105 ### Power analysis # Using the self-made function powerZtest(n = 20, sigma = sigma, delta = (ha-h0)) # Using the pwr package pwr.norm.test(d = (ha - h0)/sigma, n = 20, sig.level = 0.05, alternative = "greater") ### Sample size analysis # Using the self-made function sampleSizeZtest(sigma = sigma, power = 0.8, delta = (ha-h0)) # Using the pwr package pwr.norm.test(d = (ha - h0)/sigma, power = 0.8, sig.level = 0.05, alternative = "greater") ### Power function for the two-sided alternative ha = seq(95, 125, l = 100) d = (ha - h0)/sigma pwrTest = pwr.norm.test(d = d, n = 20, sig.level = 0.05, alternative = "greater")$power plot(d, pwrTest, type = "l", ylim = c(0, 1))
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Home > Standard Error > Standard Error Standard Deviation Divided By Square Root
# Standard Error Standard Deviation Divided By Square Root
## Contents
Browse other questions tagged statistics statistical-inference or ask your own question. Journal of the Royal Statistical Society. I had found in a previous part of the problem that $\hat \sigma=.33853$ and the sample consists of $16$ measurements. The mean that you find will be a certain number of inches away from the true average and that distance is what will call the error. navigate here
The margin of error and the confidence interval are based on a quantitative measure of uncertainty: the standard error. ISBN 0-8493-2479-3 p. 626 ^ a b Dietz, David; Barr, Christopher; Çetinkaya-Rundel, Mine (2012), OpenIntro Statistics (Second ed.), openintro.org ^ T.P. Skip to main contentSubjectsMath by subjectEarly mathArithmeticAlgebraGeometryTrigonometryStatistics & probabilityCalculusDifferential equationsLinear algebraMath for fun and gloryMath by gradeK–2nd3rd4th5th6th7th8thHigh schoolScience & engineeringPhysicsChemistryOrganic chemistryBiologyHealth & medicineElectrical engineeringCosmology & astronomyComputingComputer programmingComputer scienceHour of CodeComputer animationArts Statisticshowto.com Apply for $2000 in Scholarship Money As part of our commitment to education, we're giving away$2000 in scholarships to StatisticsHowTo.com visitors.
## Standard Error Formula
For instance if you want to know the median, the standard error is probably not what you should use. 2) It is used when someone is trying to find out about So SE estimates the standard deviation of MEANS OF samples. Blackwell Publishing. 81 (1): 75–81. You don't know the standard deviation.
more hot questions question feed about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Arts Culture / Recreation Science It is rare that the true population standard deviation is known. Hot Network Questions Why was Washington State an attractive site for aluminum production during World War II? Standard Error Regression When a random variable is multiplied by some constant (in this case, the sum of the variables being then multiplied by 1/N), the standard deviation of that variable is multiplied by
permalinkembedsavegive gold[–]pythagorian 2 points3 points4 points 1 year ago(2 children)Although this is a correct technical definition, I think it will not help someone understand the overall meaning of standard error. In an example above, n=16 runners were selected at random from the 9,732 runners. of sample means used to estimate the SE? http://math.stackexchange.com/questions/504288/what-situation-calls-for-dividing-the-standard-deviation-by-sqrt-n For any random sample from a population, the sample mean will usually be less than or greater than the population mean.
How to describe very tasty and probably unhealthy food Is the ability to finish a wizard early a good idea? Standard Error Of The Mean Definition Header Information Switch to dark theme Switch to light theme For more open-ended questions, try /r/AskScienceDiscussion | Sign up to be a panelist! For my current problem I am trying to find the estimated standard error of the estimator. Sokal and Rohlf (1981)[7] give an equation of the correction factor for small samples ofn<20.
## Standard Error Vs Standard Deviation
The standard deviation of all possible sample means is the standard error, and is represented by the symbol σ x ¯ {\displaystyle \sigma _{\bar {x}}} . https://www.khanacademy.org/math/statistics-probability/sampling-distributions-library/sample-means/v/standard-error-of-the-mean was last modified: December 27th, 2015 by Andale By Andale | November 3, 2014 | Blog | 2 Comments | ← Clustering and K Means: Definition & Cluster Analysis in Excel Standard Error Formula Notice that the population standard deviation of 4.72 years for age at first marriage is about half the standard deviation of 9.27 years for the runners. Standard Error Calculator If σ is not known, the standard error is estimated using the formula s x ¯ = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} where s is the sample
A menu will appear that says “Paste Function”. Select “Stastical” from the left hand side of the menu, if necessary. Scroll down on the right hand side of the menu and http://comunidadwindows.org/standard-error/standard-error-square-root.php The standard deviation of the age was 9.27 years. silly question about convergent sequences Should I define the relations between tables in the database or just in code? From the variation of individuals from the population we deduce the variation of sets from the population. Standard Error Mean
It turns out if you take the square root of how big your sample is it gives you a way of seeing how much the expected error goes down. The mean age for the 16 runners in this particular sample is 37.25. Pearson's Correlation Coefficient Privacy policy. http://comunidadwindows.org/standard-error/standard-error-square-root-standard-deviation.php Of course, T / n {\displaystyle T/n} is the sample mean x ¯ {\displaystyle {\bar {x}}} .
only not for individual datapoints but sample means. Difference Between Standard Error And Standard Deviation Huge bug involving MultinormalDistribution? PS: Although this is a correct technical definition, Actually it was not, i forgot to mention "in abscense of correlation".
## It can only be calculated if the mean is a non-zero value.
The mean age was 33.88 years. For example, the U.S. What we want to do is to emulate the addition of N copies of the random variable, and thus we need to invoke the variance to make finding the spread of Standard Error Of Proportion Remember...
Standard errors provide simple measures of uncertainty in a value and are often used because: If the standard error of several individual quantities is known then the standard error of some Generated Sun, 30 Oct 2016 12:05:23 GMT by s_fl369 (squid/3.5.20) A natural way to describe the variation of these sample means around the true population mean is the standard deviation of the distribution of the sample means. http://comunidadwindows.org/standard-error/standard-error-standard-deviation-square-root.php http://mathworld.wolfram.com/StandardError.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical.
FAQ: In-depth answers to many popular questions New and gilded posts /r/AskScienceDiscussion: For open-ended and hypothetical questions Filter by Field Title Description Physics Theoretical Physics, Experimental Physics, High-energy Physics, Solid-State Physics, Retrieved 17 July 2014. Of course, $T/n$ is the sample mean $\bar{x}$. permalinkembedsaveparentgive gold[–]Elean 0 points1 point2 points 1 year ago*(1 child)From the way the question is asked, I believe it is implied the author already know the concept of standard deviation.
National Center for Health Statistics (24). Your cache administrator is webmaster. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. |
Blogs/k-Means Clustering
# k-Means Clustering
blazedafyah May 06 2021 3 min read 245 views
NIT Warangal graduate, Software Engineer at Wipro.
Unsupervised
Clustering data points together is one of the most common ways to analyze and understand unlabeled data. It identifies subgroups in the data such that data points belonging to one cluster are very similar while points belonging to separate clusters are very different.
k-Means Clustering is an unsupervised learning algorithm that tries to partition the data into k different, non-overlapping clusters. It aims to make points in one cluster as similar as possible while also keeping different clusters as far as possible from each other.
A data point is assigned to a cluster if the sum of squared distances between the data points and the centroid of the cluster is minimum. Since this is a distance-based algorithm, standardization of the dataset is recommended to a mean of zero and standard deviation of one.
# ALGORITHM
1. Specify the number of clusters K.
2. Randomly select K data points as the initial centroids of the clusters.
3. Iterate the following steps until there no more shifting of centroids is possible.
• Compute the squared sum between data points and all centroids.
• Assign each data point to the nearest cluster (minimum distance)
• Compute updated centroid by taking the average of all data points in the cluster.
k-Means uses the approach of Expectation Minimization. Assigning the data point to a cluster is the E-step and the calculation of centroids is the M-step. The objective function is
Where Wik = 1 for data point Xi if it belongs to cluster k, otherwise Wik = 0 and μk is the centroid of the Xi cluster.
# CODE
Consider the following visualized dataset.
plt.scatter(X[:, 0], X[:, 1], s = 100, c = 'black',)
#Import KMeans module from sklearn library
from sklearn.cluster import KMeans
#Initialize number of clusters and train the model
kmeans = KMeans(n_clusters=5)
kmeans.fit(X)
#Visualize the generated clusters
plt.scatter(X[y_kmeans == 0, 0], X[y_kmeans == 0, 1], s = 100, c = 'red')
plt.scatter(X[y_kmeans == 1, 0], X[y_kmeans == 1, 1], s = 100, c = 'blue')
plt.scatter(X[y_kmeans == 2, 0], X[y_kmeans == 2, 1], s = 100, c = 'green')
plt.scatter(X[y_kmeans == 3, 0], X[y_kmeans == 3, 1], s = 100, c = 'cyan')
plt.scatter(X[y_kmeans == 4, 0], X[y_kmeans == 4, 1], s = 100, c = 'magenta')
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s = 300, c = 'yellow')
plt.show()
Learn and practice this concept here:
https://mlpro.io/problems/kmeans/ |
## Genome-wide association analysis - Association analysis of typed SNPs using parallel processing
(This lab was adapted for statsTeachR by Sara Nunez, Nicholas Reich and Andrea Foulkes from our GWAS tutorial.)
Now that our data is loaded, filtered, and additional SNP genotypes have been imputed, we are ready to perform the association analysis on the genotyped SNPs. This involves regressing each SNP separately on a given trait, adjusted for clinical, environmental, and demographic factors. Due to the large number of SNPs and the generally uncharacterized relationships to the outcome, a simple single additive model will be employed.
### Getting started
Here, we utilize a function we’ve written (GWAA()) to conduct the analysis. To prepare for it, we need to load the data saved from last module and install necessary packages like GenABEL and doParallel.
load("m2_lab2_save.RData")
library(snpStats)
library(plyr)
library(GenABEL)
library(doParallel)
### Data preparation
The GWAA function requires two arguments. The genodata argument should specify the entire genotype data object in SnpMatrix format. The phenodata argument should be a data frame with a column of sample IDs, corresponding to the row names of genodata, followed by columns for the outcome variable and covariates to be included in the model. In the following code, we assign the genodata variable and write out a table called GWAA.txt for the results to later be written to.
genodata <- genotype
#Print the number of SNPs to be checked
cat(paste(ncol(genodata), " SNPs included in analysis.\n"))
## 381257 SNPs included in analysis.
#create text file for GWAA output to be written to
columns<-c("SNP", "Estimate", "Std.Error", "t-value", "p-value")
write.table(t(columns), "GWAA.txt", row.names=FALSE, col.names=FALSE, quote=FALSE)
Next we focus on the phenodata argument. First we assign phenoSub to be phenodata, which is created from merging the clinical and pcs data. We then create the phenotype value (outcome variable) by using a normal rank-transformation of the hdl variable, which we show is necessary later on. Next we rename the FamID column, remove anyone that doesn’t have HDL data available, and subset the genotype data for the remaining individuals. Lastly, we want to remove variables that won’t be used in analysis, e.g. the remaining outcome variables and the untransformed version of HDL.
phenoSub <- merge(clinical,pcs)
phenoSub$phenotype <- rntransform(as.numeric(phenoSub$hdl), family="gaussian")
phenoSub <- rename(phenoSub, replace=c(FamID="id"))
phenoSub<-phenoSub[!is.na(phenoSub$phenotype),] phenodata <- phenoSub genodata <- genodata[as.character(phenodata$id),]
cat(nrow(genodata), "samples included in analysis.\n")
## 1308 samples included in analysis.
phenodata$hdl <- NULL phenodata$ldl <- NULL
phenodata$tg <- NULL phenodata$CAD <- NULL
print(head(phenodata))
## id sex age pc1 pc2 pc3 pc4
## 2 10004 2 50 0.01263937 0.007136085 -0.009394939 -0.029605670
## 3 10005 1 55 0.01656767 -0.007822581 0.034279450 -0.008364165
## 4 10007 1 52 0.01179249 -0.001340544 0.014388948 0.002448683
## 5 10008 1 58 0.01587414 0.003683702 0.013407115 -0.002069099
## 6 10009 1 59 0.01342526 0.002620955 0.005132100 -0.044515366
## 7 10010 1 54 0.01627605 0.011860496 0.018480130 -0.014176319
## pc5 pc6 pc7 pc8 pc9
## 2 0.017640584 0.062301372 -0.005341143 0.004102591 0.040899908
## 3 0.043822928 -0.002068763 0.015205957 -0.011775232 0.005064646
## 4 0.008521085 0.017414424 0.015268401 0.037495537 0.016946863
## 5 0.009863999 0.049090388 0.007638991 0.010654394 -0.013350077
## 6 0.043797908 0.012536302 0.045885623 -0.033450390 -0.045956099
## 7 -0.003986151 -0.094898367 0.004855911 -0.014761558 0.018721010
## pc10 phenotype
## 2 0.003655463 -2.2874211
## 3 0.003447803 -0.4742508
## 4 0.010266512 0.8850182
## 5 0.007254919 -0.1636196
## 6 0.009781019 0.3952471
## 7 -0.019222291 1.7105947
#### Exercise
How many samples are left after removing samples with missing HDL data?
To show that the normally transformed version of HDL should be used for analysis, the following code can be used to plot the variable before and after transformation.
par(mfrow=c(1,2))
hist(as.numeric(phenoSub$hdl), main=NULL, xlab="HDL") hist(phenodata$phenotype, main=NULL, xlab="Transformed HDL")
### The GWAA function
The function itself has four major elements. Given the data described above, it (1) determines how many cores to use/which method to employ for parallel processing (depending on specified cores and operating system), (2) converts the genotype data into the necessary format for an additive model, (3) fits a linear model for each SNP and covariates (one group at a time) and then (4) writes the SNP coefficient details (the estimate, standard error, test statistic and p value) from each model out to the GWAA.txt file. Read through the function to get a general idea of the format in regards to these four steps. Further details regarding the function elements are provided below.
GWAA <- function(genodata, phenodata, filename = NULL, append = FALSE, workers = getOption("mc.cores",
2L), flip = TRUE, select.snps = NULL, hosts = NULL) {
if (is.null(hosts)) {
cl <- makeCluster(workers)
} else {
cl <- makeCluster(hosts, "PSOCK")
}
show(cl)
registerDoParallel(cl)
# Function that will change which allele is counted (major or minor)
flip.matrix <- function(x) {
zero2 <- which(x == 0)
two0 <- which(x == 2)
x[zero2] <- 2
x[two0] <- 0
return(x)
}
foreach(part = 1:nSplits) %do% {
genoNum <- as(genodata[, snp.start[part]:snp.stop[part]], "numeric")
# flip.matrix function employed
if (isTRUE(flip))
genoNum <- flip.matrix(genoNum)
rsVec <- colnames(genoNum)
res <- foreach(snp.name = rsVec, .combine = "rbind") %dopar% {
a <- summary(glm(phenotype ~ . - id, family = gaussian, data = cbind(phenodata,
snp = genoNum[, snp.name])))
a$coefficients["snp", ] } write.table(cbind(rsVec, res), filename, append = TRUE, quote = FALSE, col.names = FALSE, row.names = FALSE) cat(sprintf("GWAS SNPs %s-%s (%s%% finished)\n", snp.start[part], snp.stop[part], 100 * part/nSplits)) } stopCluster(cl) return(print("Done.")) } #### Parallel processing We have mentioned that this function determines how many cores to use for parallel processing, but have not yet emphasized why we would want to do this. Due to the large number of models that require fitting, the GWA analysis can be deployed in parallel across multiple processors or machines to reduce the running time. In this function, we demonstrate two basic methods for performing parallel processing using the doParallel package. This will be carried out differently depending on whether or not the analysis is run on a UNIX based system, though the arguments are the same. The user can specify the number of parallel processes using the worker argument (set to two by default). Increasing this number will simply speed up the analysis by utilizing more cores for jobs to be assigned to. #### Genotype format Next, you will notice the flip.matrix function, which is utilized in the foreach loop. Before using it, the genotype data is first converted to numeric format using the ‘as’ function from snpStats. The genotypes of each SNP are then coded as continuous, thereby taking on the value of 0, 1, and 2. For this example, we wish for the value of the genotype to reflect the number of minor alleles. However, following conversion our values will reflect the opposite. To fix this, the flip.matrix procedure is called on. This can be easily turned on or off using the flip argument. #### Fitting the model Now that the genotype data is counting the number of minor alleles present at each SNP, we can fit a linear model with the normalized HDL variable as the outcome. This is done using the glm function provided by R. For each model (i.e. each SNP), we are interested in the coefficient estimate of the SNP predictor, and thus return its model summary elements. The function runs this analysis on smaller subsets of the data one at a time. Below, we will split the data for analysis into 10 subsets (details to come). #### Exercise How would you interpret the coefficient estimate of a given SNP? Hint: Keep in mind the type of genetic model we are assuming. ### Analysis We have now walked through the different aspects of analysis Another way to speed up analysis would be to subset the data for SNPs of interest. A smaller subset would intuitively imply a shorter run time. The additional argument that’s helpful in this context is the select.snps parameter, set to NULL by default. This allows the user to subset the analysis via a vector of SNP names rather than run analysis on all available SNPs. If your interested in, say, SNPs that fall in a specified region of the genome, you could subset your data for these SNPs and run the GWAA function on these alone. Here, for example, running analysis on all the genotyped and imputed SNPs we have would take approximately six hours with only two cores employed. For demonstrative purposes, we will only run analysis in this lab on SNPs that fall on chromosomes 15-17. Run the following code to subset the data: SNPs_sub <- genoBim$SNP[genoBim$chr==15 | genoBim$chr==16
| genoBim\$chr==17]
genodata_sub <- genodata[,colnames(genodata)%in%SNPs_sub]
Now that the data is ready, we want to split up the genotype data into smaller subsets so that the GWAA function can run analysis on each subset one at a time (as mentioned above). Here, we choose to split the data into 10 subsets. Using the ceiling() function, we round up the number of SNPs in each subset, which can be found by dividing number of SNPs by 10. Then, by using seq() and pmin(), we can find the index of the first and the last SNP in each group. This will allow the GWAA function to run analysis on each subset separately by choosing SNPs within the range of the first and last within a group. The function will print its progress after analysis on each subset is finished.
nSNPs <- ncol(genodata_sub)
nSplits <- 10
genosplit <- ceiling(nSNPs/nSplits) # number of SNPs in each subset
snp.start <- seq(1, nSNPs, genosplit) # index of first SNP in group
snp.stop <- pmin(snp.start+genosplit-1, nSNPs) # index of last SNP in group
#### Exercise
Approximately how many SNPs are in each subset?
We are now ready to perform the analysis and write the results out to the GWAA.txt file. Keep in mind, that while this analysis is only running on 3 chromosomes, it will still take a few minutes to complete. This process can be faster if more cores are chosen. The detectCores() function from the parallel package can be used to determine how many cores your machine has available.
start <- Sys.time()
GWAA(genodata_sub, phenodata, filename="GWAA.txt")
## socket cluster with 2 nodes on host 'localhost'
## GWAS SNPs 1-3237 (10% finished)
## GWAS SNPs 3238-6474 (20% finished)
## GWAS SNPs 6475-9711 (30% finished)
## GWAS SNPs 9712-12948 (40% finished)
## GWAS SNPs 12949-16185 (50% finished)
## GWAS SNPs 16186-19422 (60% finished)
## GWAS SNPs 19423-22659 (70% finished)
## GWAS SNPs 22660-25896 (80% finished)
## GWAS SNPs 25897-29133 (90% finished)
## GWAS SNPs 29134-32368 (100% finished)
## [1] "Done."
end <- Sys.time()
print(end-start)
## Time difference of 2.71885 mins
### Saving work for following labs…
You can save the necessary data from this lab by running the following commands:
save(genoBim, imputed, target, rules, phenodata, genodata_sub, support, GWAA,
file = "m3_lab1_save.RData")
### On your own
Use the read.table() and head() commands to investigate the results of the above analysis. Can you guess how we will determine if a given SNP is a significant predictor of HDL? What analytic challenges might we have to consider? |
# Find derivative with chain rule
1. Aug 30, 2006
hey
how would i find the derivative of y= $$-18 \sin 80 t$$?
2. Aug 30, 2006
### HallsofIvy
Staff Emeritus
1. Use the fact, which you should already have learned, that the derivative of sin(x) is cos(x).
2. Use the fact, which you should already have learned, that the derivative of 80t is 80.
3. Use the chain rule.
By the way, the derivative is one of the basic operations in calculus so this is clearly not "pre-calculus". I'm moving this to "Calculus and beyond".
3. Aug 30, 2006
okay sorry for having placed it in the wrong section, um....ive never differentiated a trig f(x) before thats all and it was the first i came across that i needed to differentiate. could i please given a few hints on the basics? thanks
4. Aug 30, 2006
### Staff: Mentor
I would imagine if one is studying differential calculus, that one is using a textbook and within the text book are trigonometric identities and examples.
HallsofIvy mentioned the chain rule, which is very basic in differentiation.
Given y = f(g(x)), y' = dy/dx = f'(g(x))*g'(x).
Has one proved to oneself the definition of a derivative, and then used that definition to find the derivative of various functions?
y'(x) = dy(x)/dx = $$\lim_{\substack{\Delta{x}\rightarrow 0}} \frac{y(x+\Delta{x})-y(x)}{\Delta{x}}$$
http://hyperphysics.phy-astr.gsu.edu/hbase/deriv.html
http://hyperphysics.phy-astr.gsu.edu/hbase/math/derfunc.html#c1
http://en.wikipedia.org/wiki/Derivative
http://en.wikipedia.org/wiki/Chain_rule
http://mathworld.wolfram.com/Derivative.html
Last edited: Aug 30, 2006
5. Aug 31, 2006
okay thanks for the replies and the links. so the derivative of sin (x) = cos (x) therefore that if y = -18sin (80t) then y' = 80(-18cos (80t)), expanding the brackets is equal to y' = -1440cox 80t? thanks
6. Aug 31, 2006
### VietDao29
Yup, this is correct. |
Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics
Session 2 -- Software
Display presentation, Monday, June 12, 1995, 9:20am - 6:30pm
## [2.09] Numerical Tests of the Quasilinear Approximation of Mean-field Electrodynamics
J. Zsarg\'o and K. Petrovay (ELTE, Univ. of Toledo)
It is widely known that a sufficient condition for the applicability of quasilinear-type approximations (e.g.\ the second-order correlation approximation or SOCA) in mean-field electrodynamics is that $U\tau\ll \mbox{min} \,\{l, H\}$ where $l$, $H$, $U$ and $\tau$ are characteristic horizontal and vertical scale lengths, velocity, and time, respectively. A necessary condition for their validity is however not known. In order to check the validity of the quasilinear results in cases where the above condition is not satisfied, as well as to study qualitative and quantitative differences between the quasilinear results and the actual solutions, we numerically solve the MHD induction equation for the kinematical case in a series of simplified toy'' model flows and then compare the results with the corresponding quasilinear solutions. Our model flows are two-dimensional two-component flows with simple (exponential or linear) stratifications. For conceptual clarity, in each model only one independent physical quantity (initial magnetic field, density, or velocity amplitude, respectively) has an inhomogeneous distribution. Solutions are computed for several widely differing values of the $l/H$ horizontal/vertical scale length ratio. In all cases we find that the computed turbulent electromotive force does not differ from the quasilinear value by more than an order-of-unity factor, as long as $U\tau$ does not greatly exceed $\mbox{min} \,\{l, H\}$. |
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A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
### LOGO Challenge - Circles as Animals
##### Stage: 3 and 4 Challenge Level:
See if you can anticipate successive 'generations' of the two animals shown here.
### Shaping the Universe I - Planet Earth
##### Stage: 3 and 4
This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.
### Isosceles Triangles
##### Stage: 3 Challenge Level:
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
### Making Tracks
##### Stage: 4 Challenge Level:
A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?
### Fermat's Poser
##### Stage: 4 Challenge Level:
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
### Inside Out
##### Stage: 4 Challenge Level:
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
### Cutting a Cube
##### Stage: 3 Challenge Level:
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
### Efficient Cutting
##### Stage: 4 Challenge Level:
Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
### Cuboids
##### Stage: 3 Challenge Level:
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
### One and Three
##### Stage: 4 Challenge Level:
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
### Rolling Around
##### Stage: 3 Challenge Level:
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
### Painted Cube
##### Stage: 3 Challenge Level:
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
### Konigsberg Plus
##### Stage: 3 Challenge Level:
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
### Tied Up
##### Stage: 3 Challenge Level:
In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .
### Framed
##### Stage: 3 Challenge Level:
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
### Marbles in a Box
##### Stage: 3 and 4 Challenge Level:
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
### Fence It
##### Stage: 3 Challenge Level:
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
### Rati-o
##### Stage: 3 Challenge Level:
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
### Muggles Magic
##### Stage: 3 Challenge Level:
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
### Shaping the Universe II - the Solar System
##### Stage: 3 and 4
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
##### Stage: 4 Challenge Level:
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
### Dissect
##### Stage: 3 Challenge Level:
It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?
### Problem Solving, Using and Applying and Functional Mathematics
##### Stage: 1, 2, 3, 4 and 5 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
### Route to Infinity
##### Stage: 3 and 4 Challenge Level:
Can you describe this route to infinity? Where will the arrows take you next?
### Circuit Training
##### Stage: 4 Challenge Level:
Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .
### Triangles Within Pentagons
##### Stage: 4 Challenge Level:
Show that all pentagonal numbers are one third of a triangular number.
##### Stage: 3 Challenge Level:
How many different symmetrical shapes can you make by shading triangles or squares?
### Königsberg
##### Stage: 3 Challenge Level:
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
### Around and Back
##### Stage: 4 Challenge Level:
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .
### Triangles Within Triangles
##### Stage: 4 Challenge Level:
Can you find a rule which connects consecutive triangular numbers?
### Is There a Theorem?
##### Stage: 3 Challenge Level:
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
### Chess
##### Stage: 3 Challenge Level:
What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
### Seven Squares
##### Stage: 3 and 4 Challenge Level:
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
### Triangles Within Squares
##### Stage: 4 Challenge Level:
Can you find a rule which relates triangular numbers to square numbers?
### Tic Tac Toe
##### Stage: 3 Challenge Level:
In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?
### Playground Snapshot
##### Stage: 2 and 3 Challenge Level:
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
### Chords
##### Stage: 4 Challenge Level:
Two intersecting circles have a common chord AB. The point C moves on the circumference of the circle C1. The straight lines CA and CB meet the circle C2 at E and F respectively. As the point C. . . . |
# Rule of three calculation
## Rule of three, Rule of proportion
A rule of three is used to calculate ratios proportional to each other. Proportional means that when a quantity A is doubled, B is also doubled. For example, e.g. A train with constant speed drives in an hour 80km so it drives in two hours 160km.
### Calculation scheme for Rule of three calculation
$\begin{array}{|cc|}\hline A& B\\ C& x\\ \hline\end{array}$
Example: A train runs in 2 hours 140 km then 2 has to be set for A and 140 for B. The route is asked for 3 hours. So 3 for C and x is the distance searched.
$\begin{array}{|ccccc|}\hline 2& \text{hours}& \stackrel{\wedge}{=}& 140& \text{km}\\ 3& \text{hours}& \stackrel{\wedge}{=}& x& \text{km}\\ \hline\end{array}$
### Calculation
$\begin{array}{|cc|}\hline 1& \frac{B}{A}\\ C& C\frac{B}{A}\\ \hline\end{array}$
$x=\frac{C\cdot B}{A}$
$\begin{array}{|ccccc|}\hline 1& \text{hours}& \stackrel{\wedge}{=}& \frac{140}{2}& \text{km}\\ 3& \text{hours}& \stackrel{\wedge}{=}& 3\frac{140}{2}& \text{km}\\ \hline\end{array}$
$\begin{array}{|ccccc|}\hline 1& \text{hours}& \stackrel{\wedge}{=}& 70& \text{km}\\ 3& \text{hours}& \stackrel{\wedge}{=}& 210& \text{km}\\ \hline\end{array}$
So is x= 210 that means the train runs 210km in 3 hours.
## Rule of three Calculator
glasses cost €. How much cost glasses?
To print pages, a printer needs minutes. How long does the printer need for pages?
How many pages can be printed in minutes?
For a distance of km needs a car liter petrol. How much petrol is needed for a distance of km?
How far can you get by the car, with liter?
## Inverse Rule of three
An inverse rule of three is a calculation scheme for the calculation of ratios which are indirectly proportional to each other. Indirectly proportional, when a quantity A is halved, the quantity B is doubled. If 2 trucks need to transport a certain amount of overburden 10 days so 1 truck needs double time so 20 days.
### Calculation scheme of the inverse rule of three
$\begin{array}{|cc|}\hline A& B\\ C& x\\ \hline\end{array}$
Example: If you need 4 trucks to remove a certain amount of overburden 10 days then 2 is set for A and 10 is for B. Looking for the time that 2 trucks is needed so C is set to 2.
$\begin{array}{|ccccc|}\hline 4& \text{truck}& \stackrel{\wedge}{=}& 10& \text{days}\\ 2& \text{truck}& \stackrel{\wedge}{=}& x& \text{days}\\ \hline\end{array}$
### Calculation
$\begin{array}{|cc|}\hline 1& A\cdot B\\ C& A\frac{B}{C}\\ \hline\end{array}$
$x=\frac{A\cdot B}{C}$
$\begin{array}{|ccccc|}\hline 1& \text{truck}& \stackrel{\wedge}{=}& 4\cdot 10& \text{days}\\ 2& \text{truck}& \stackrel{\wedge}{=}& 4\frac{10}{2}& \text{days}\\ \hline\end{array}$
$\begin{array}{|ccccc|}\hline 1& \text{truck}& \stackrel{\wedge}{=}& 40& \text{days}\\ 2& \text{truck}& \stackrel{\wedge}{=}& 20& \text{days}\\ \hline\end{array}$
So is x= 20 that means a truck needs 20 days.
## More Calculators
Here is a list of of further useful calculators:
Index Fraction calculator Percentage calculation Per mille calculation Interest calculation |
# Intuitive explanation of geometric mean
Suppose that the 10 Year Treasury Yield Rate varies every trading day during the year X1 (which in practice is accurate) what is the intuitive explanation behind calculating the geometric mean using this equation $[(1+R_1)(1+R_2)...(1+R_{252})]^{(1/252)}-1$? Is this simply the daily compound rate instead of the annualized compound rate? I realize that to calculate say the market risk premium for the year I can simply take the average of the rate for the whole year and use that but would I also be able to use the geometric mean as calculated above to do this and is it meaningful?
For a simple example, say you start with \$100 in an account. In the first year, it makes 50% gain (+50% interest) => \$150
In the second year, it makes 50% loss (-50% interest) => \$75 The arithmetic mean is (50% - 50%)/2 = 0% The geometric mean is (150% * 50%)^0.5 - 1 = 86.6% - 1 = -13.4% pear year You know that you go from \$100 to \$75 over 2 years, so you have definitely lost money. The geometric mean will capture the reality better if you apply a -13.4% return on each year, yielding: $100 -> $86.6 ->$75
The arithmetic mean (simple mean) is not as useful for measuring rates of return over time because of compounding. When you are plotting a time series or forecasting into the future, it is more appropriate to use the geometric mean because it tells you what % return you would need per day/month/year (depends what time scale you are measuring).
Since the example you provided is based on days, you answered your own question. It is the daily compound rate of return.
Conversely, if you were to measure a fund's returns over 10 years it would be the same math except to ^1/10th power.
• Thanks for the answer HK47. So that means I can simply get the EAR by using the regular formula (1 + dividing that rate by 252)^(252) -1 correct? And this would be the effective annual rate for a 10 Year Treasury Rate Yield for year X1? – Dmitriy Dec 13 '17 at 20:04
• @Dmitriy Yes, precisely. There will be those with different opinions but generally speaking, getting the geometric mean and then using it to calculate EAR is effective. Be careful of using this strategy to price securities that have continuous compounding, though. – HK47 Dec 13 '17 at 20:37
• one more question. So what I've effectively done is calculate an effective annual rate for a 10 Year Treasury Yield using the geometric mean derived from the daily 10 Year Treasury Yield. This means that I can invest on any day in year X1 in a 10 Year Treasury security and expect a return of the EAR that I compounded on average. Is this a correct conclusion? – Dmitriy Dec 13 '17 at 21:47
• @Dmitriy Geometric mean is better for forecasting into the future or measuring returns on different time scales (quarterly returns, monthly, etc). EAR calculates based on annual compounding. Treasuries pay annual coupons, so the EAR would be a good approximation of your expected return. There's many other ways to bootstrap an expected return too, but your method is effective. – HK47 Dec 14 '17 at 15:32 |
# invfreqs
Identify continuous-time filter parameters from frequency response data
## Description
example
[b,a] = invfreqs(h,w,n,m) returns the real numerator and denominator coefficient vectors b and a of the transfer function h.
[b,a] = invfreqs(h,w,n,m,wt) weights the fit-errors versus frequency using wt.
example
[b,a] = invfreqs(___,iter) provides an algorithm that guarantees stability of the resulting linear system by searching for the best fit using a numerical, iterative scheme. This syntax can include any combination of input arguments from the previous syntaxes.
[b,a] = invfreqs(___,tol) uses tol to decide convergence of the iterative algorithm.
[b,a] = invfreqs(___,'trace') displays a textual progress report of the iteration.
[b,a] = invfreqs(h,w,'complex',n,m,___) creates a complex filter. In this case no symmetry is enforced, and the frequency is specified in radians between –π and π.
## Examples
collapse all
Convert a simple transfer function to frequency-response data and then back to the original filter coefficients.
a = [1 2 3 2 1 4];
b = [1 2 3 2 3];
[h,w] = freqs(b,a,64);
[bb,aa] = invfreqs(h,w,4,5)
bb = 1×5
1.0000 2.0000 3.0000 2.0000 3.0000
aa = 1×6
1.0000 2.0000 3.0000 2.0000 1.0000 4.0000
bb and aa are equivalent to b and a, respectively. However, the system is unstable because aa has poles with positive real part. View the poles of bb and aa.
zplane(bb,aa)
Use the iterative algorithm of invfreqs to find a stable approximation to the system.
[bbb,aaa] = invfreqs(h,w,4,5,[],30)
bbb = 1×5
0.6816 2.1015 2.6694 0.9113 -0.1218
aaa = 1×6
1.0000 3.4676 7.4060 6.2102 2.5413 0.0001
Verify that the system is stable by plotting the new poles.
zplane(bbb,aaa)
Generate two vectors, mag and phase, that simulate magnitude and phase data gathered in a laboratory. Also generate a vector, w, of frequencies.
rng('default')
fs = 1000;
t = 0:1/fs:2;
mag = periodogram(sin(2*pi*100*t)+randn(size(t))/10,[],[],fs);
phase = randn(size(mag))/10;
w = linspace(0,fs/2,length(mag))';
Use invfreqs to convert the data into a continuous-time transfer function. Plot the result.
[b,a] = invfreqs(mag.*exp(1j*phase),w,2,2,[],4);
freqs(b,a)
## Input Arguments
collapse all
Frequency response, specified as a vector.
Angular frequencies at which h is computed, specified as a vector.
Desired order of the numerator and denominator polynomials, specified as positive integer scalars.
Data Types: single | double
Weighting factors, specified as a vector. wt is a vector of weighting factors that is the same length as w.
Data Types: single | double
Number of iterations in the search algorithm, specified as a positive real scalar. The iter parameter tells invfreqs to end the iteration when the algorithm has converged to a solution, or after iter iterations, whichever occurs first.
Tolerance, specified as a scalar. invfreqs defines convergence as occurring when the norm of the (modified) gradient vector is less than tol.
To obtain a weight vector of all ones, use
invfreqs(h,w,n,m,[],iter,tol)
## Output Arguments
collapse all
Transfer function coefficients, returned as vectors. Express the transfer function in terms of b and a as
$H\left(s\right)=\frac{B\left(s\right)}{A\left(s\right)}=\frac{b\left(1\right){s}^{n}+b\left(2\right){s}^{n-1}+\cdots +b\left(n+1\right)}{a\left(1\right){s}^{m}+a\left(2\right){s}^{m-1}+\cdots +a\left(m+1\right)}$
Example: b = [1 3 3 1]/6 and a = [3 0 1 0]/3 specify a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.
Data Types: double | single
Complex Number Support: Yes
## Tips
When building higher order models using high frequencies, it is important to scale the frequencies, dividing by a factor such as half the highest frequency present in w, so as to obtain well-conditioned values of a and b. This corresponds to a rescaling of time.
## Algorithms
By default, invfreqs uses an equation error method to identify the best model from the data. This finds b and a in
$\underset{b,a}{\mathrm{min}}\sum _{k=1}^{n}wt\left(k\right){|h\left(k\right)A\left(w\left(k\right)\right)-B\left(w\left(k\right)\right)|}^{2}$
by creating a system of linear equations and solving them with the MATLAB® \ operator. Here A(w(k)) and B(w(k)) are the Fourier transforms of the polynomials a and b, respectively, at the frequency w(k), and n is the number of frequency points (the length of h and w). This algorithm is based on Levi [1]. Several variants have been suggested in the literature, where the weighting function wt gives less attention to high frequencies.
The superior (“output-error”) algorithm uses the damped Gauss-Newton method for iterative search [2], with the output of the first algorithm as the initial estimate. This solves the direct problem of minimizing the weighted sum of the squared error between the actual and the desired frequency response points.
$\underset{b,a}{\mathrm{min}}\sum _{k=1}^{n}wt\left(k\right){|h\left(k\right)-\frac{B\left(w\left(k\right)\right)}{A\left(w\left(k\right)\right)}|}^{2}$
## References
[1] Levi, E. C. “Complex-Curve Fitting.” IRE Trans. on Automatic Control. Vol. AC-4, 1959, pp. 37–44.
[2] Dennis, J. E., Jr., and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Englewood Cliffs, NJ: Prentice-Hall, 1983.
## Version History
Introduced before R2006a |
## Diablo III Beta Thread (Official Release Date: 5/15/2012!)
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timortis Ars Tribunus Militum Registered: May 8, 2002Posts: 1742 badfrog wrote:Managed to get in a few hours of play time, was just getting ready to find the king with my first Wizardess (?) character when the servers went down...I intentionally ignored most of the coverage until very recently so this is my first real experience with the game. I'm enjoying it so far for free, but the gameplay has me still on the fence about actually buying... It seems bizarre to me that none of the skills I've unlocked actually tell me how much damage they do or how they scale if at all, yet there's pages and pages of stat information available off the inventory screen's "Advanced" button.Is gear really the only option for build customization? I'm not a fan of the "you've leveled up and unlocked _TheSameSkillEveryoneElseHas_ and a new quickbar spot!!" design -- is there something I'm not seeing?...And I really don't understand why I can't just check a box to save my password in the client. I'm off to do the [Enter] Ctrl-V [Enter] dance again.If you want to get more detailed information on skills, you have to enable "advanced tooltips" in options.If you haven't, you might also want to enable "elective mode", which actually lets you select any skill combination you want, rather than being restricted to one of each of those arbitrary categories.
Pokrface "Chronicler of George" Senior Reviews Editor et Subscriptor Tribus: Underpantsylvania Registered: Aug 26, 2000Posts: 14285 badfrog wrote:Is gear really the only option for build customization? I'm not a fan of the "you've leveled up and unlocked _TheSameSkillEveryoneElseHas_ and a new quickbar spot!!" design -- is there something I'm not seeing?I'm wondering the same thing. It does indeed look like *everyone* gets the same skills and options, and there's no penalty for switching around. I suppose this is good for a casual player (which is me), but it's probably going to drive the min-maxers absolutely batshit crazy, since your character's customizations seem to be more dependent on drops than on skill choices.Still, it's puzzling that there are no skill points, no trees, no choices, and no consequences. I'm not even sure why they bother exposing the STR/INT/DEX/VIT stats, since you can't allocate points into them.edit - Quote:If you want to get more detailed information on skills, you have to enable "advanced tooltips" in options.If you haven't, you might also want to enable "elective mode", which actually lets you select any skill combination you want, rather than being restricted to one of each of those arbitrary categories. Ahhh. I'll have to do this. The way it comes out of the box just doesn't make much sense to me.
badfrog Ars Scholae Palatinae Tribus: Nemo hic adest illius nominis Registered: Oct 17, 2007Posts: 1094 Pokrface wrote:Still, it's puzzling that there are no skill points, no trees, no choices, and no consequences. I'm not even sure why they bother exposing the STR/INT/DEX/VIT stats, since you can't allocate points into them.I've been wondering that as well. I'm also not understanding the cooldown that's in place on switching skills. I mean if everyone's build is the same, then why not go all the way? It seems really arbitrary that I can't switch between all these skills at will.timortis wrote:If you want to get more detailed information on skills, you have to enable "advanced tooltips" in options.If you haven't, you might also want to enable "elective mode", which actually lets you select any skill combination you want, rather than being restricted to one of each of those arbitrary categories. Ah. Thanks. I had discovered "elective" mode, but did not find "advanced tooltips." That's another curious design choice.Maybe I'm just not in the target demographic for this game. :shrug:
timortis Ars Tribunus Militum Registered: May 8, 2002Posts: 1742 Pokrface wrote:badfrog wrote:Is gear really the only option for build customization? I'm not a fan of the "you've leveled up and unlocked _TheSameSkillEveryoneElseHas_ and a new quickbar spot!!" design -- is there something I'm not seeing?I'm wondering the same thing. It does indeed look like *everyone* gets the same skills and options, and there's no penalty for switching around. I suppose this is good for a casual player (which is me), but it's probably going to drive the min-maxers absolutely batshit crazy, since your character's customizations seem to be more dependent on drops than on skill choices.Still, it's puzzling that there are no skill points, no trees, no choices, and no consequences. I'm not even sure why they bother exposing the STR/INT/DEX/VIT stats, since you can't allocate points into them.Everyone doesn't get the same skills, people misunderstand the system.. In D2, skills had level requirements, and once you met those, you could put points into them, and use them.In D3, skills also have level requirements, this is when you get that "xxx skill unlocked" notice. Then you can choose to take that skill, which is like investing points into a skill in D2. The difference is that all the skills in D3 are essentially 1 point skills, you don't have to invest 20 skill points into them to make them useful or viable. Which, if you ask me, is a good thing.They wanted people to be able to try out different skills, and respec when they want to, so they made it easy to switch skills. The 5 second cooldown in only in Normal mode, it becomes longer in other difficulty settings. At level 60, you also get a stacking Magic Find buff you when you kill Elites, which gets reset every time you change skills, to discourage people from switching constantly.Essentially, they want everyone to find a build with 6 Active and 3 Passive Skills and their Runes, and stick with it, at least throughout each play session, but they don't want to make it difficult to respec or try out different builds, to encourage experimentation, so this is what they came up with...
End Of All "End Time" Ars Centurion Tribus: Central New York (ie, No where) Registered: Jul 8, 2008Posts: 263 Just got done downloading the game and I can't connect to it Bleh, guess I'll have to try later.
Magus` "バカ" Moderator et Subscriptor Tribus: Sin City Registered: Nov 22, 2001Posts: 26382 Comp Guru wrote:Am I the only one that actually cares about the story and wants to listen (and enjoy that a lot of the quest dialog seems to be voice-acted, not just text. Rather then just skipping it all to go find loot?Don't play co-op with people who already ran the story if you want the story. Play it solo first, get the story, then play co-op so you can rush through with them frogblast wrote:2) Does it seem silly to be equipping daggers and swords when he has no melee attack?You don't use your weapons anyway, so who cares? They are stat sticks.badfrog wrote:Is gear really the only option for build customization?No, obviously not. You can't use all your skills at once, so you'll only get to select a few for your build.Pokrface wrote:I'm wondering the same thing. It does indeed look like *everyone* gets the same skills and options, and there's no penalty for switching around. I suppose this is good for a casual player (which is me), but it's probably going to drive the min-maxers absolutely batshit crazy, since your character's customizations seem to be more dependent on drops than on skill choices.Of course everyone gets the same skills/runes, but not everyone will run with the same 6 skills, or even the same 6 rune choices even if they have the same 6 skills.
badfrog Ars Scholae Palatinae Tribus: Nemo hic adest illius nominis Registered: Oct 17, 2007Posts: 1094 timortis wrote:In D3, skills also have level requirements, this is when you get that "xxx skill unlocked" notice. Then you can choose to take that skill, which is like investing points into a skill in D2. The difference is that all the skills in D3 are essentially 1 point skills, you don't have to invest 20 skill points into them to make them useful or viable. Which, if you ask me, is a good thing.Which means, when you come right down to it, all "Arcane Orb" wizards are going to be very much alike -- if not identical -- once you strip away all their gear. Which makes gear the absolute determinant of what makes a build. Which is not a system I like.timortis wrote:They wanted people to be able to try out different skills, and respec when they want to, so they made it easy to switch skills. The 5 second cooldown in only in Normal mode, it becomes longer in other difficulty settings. At level 60, you also get a stacking Magic Find buff you when you kill Elites, which gets reset every time you change skills, to discourage people from switching constantly.Except it's not easy. If I get mobbed and don't have an AOE skill out, I'm going to die because I can't switch skills in the middle of a fight. Which, when you stop to think about it, is absolutely stupid. I know how to do X and Y with equal levels of skill. But because some arbitrary unit of time hasn't passed since I last decided I wanted to be able to do Y, I can't do X.EDIT:I'm sure this has all been discussed ad nauseum before, and I don't want to derail the thread, so I'll do my best to not gripe about how little I care for the particular system they chose for this game.
vishnu Ars Legatus Legionis Tribus: Corvallis, Oregon Registered: Jul 1, 2000Posts: 19977 badfrog wrote:Which means, when you come right down to it, all "Arcane Orb" wizards are going to be very much alike -- if not identical -- once you strip away all their gear. Which makes gear the absolute determinant of what makes a build. Which is not a system I like.How is this different from all "lightning" sorcs being the same in D2?And in fact, they won't all be the same. Assuming the runes are well balanced, different people might be using differently runed arcane orbs.badfrog wrote:Except it's not easy. If I get mobbed and don't have an AOE skill out, I'm going to die because I can't switch skills in the middle of a fight. Which, when you stop to think about it, is absolutely stupid. I know how to do X and Y with equal levels of skill. But because some arbitrary unit of time hasn't passed since I last decided I wanted to be able to do Y, I can't do X.You've got six skill slots, not one. The variation comes from picking a good six skills (and runes) to let you cover all situations. Last edited by vishnu on Sat Apr 21, 2012 2:27 pm
Pokrface "Chronicler of George" Senior Reviews Editor et Subscriptor Tribus: Underpantsylvania Registered: Aug 26, 2000Posts: 14285 End Of All wrote:Just got done downloading the game and I can't connect to it Bleh, guess I'll have to try later.I was happily playing earlier, but got booted at about 14:00 CDT and haven't been able to connect back since. Been trying every 5-10 minutes, but so far nothing for the past hour and a half.
Coleman Ars Legatus Legionis et Subscriptor Tribus: XBL: Master Chiefmas Registered: Oct 13, 2000Posts: 14613 badfrog wrote:Is gear really the only option for build customization? I'm not a fan of the "you've leveled up and unlocked _TheSameSkillEveryoneElseHas_ and a new quickbar spot!!" design -- is there something I'm not seeing?Yeah, you probably didn't get far enough to see how it's going to tweak.So the customization comes in the form of runes. the runes in D3 are really modifiers to the base skill, changing the effects it has. So they could make a base attack stronger, or increase it's length of affect. And then much later on(level 11 for the wizard, I haven't played anything else yet) you get passive skills. These are just what they sound, they are bonuses you can activate to further tweak your guy for a certain game play style, or probably even for a certain situation even.What's not clear is how you increase the effectiveness of a skill beyond changing the rune, or if it's just tied directly to your level.
badfrog Ars Scholae Palatinae Tribus: Nemo hic adest illius nominis Registered: Oct 17, 2007Posts: 1094 vishnu wrote:How is this different from all "lightning" sorcs being the same in D2?And in fact, they won't all be the same. Assuming the runes are well balanced, different people might be using differently runed arcane orbs.Uhm because you had 100+ different points available for customization in the form of skill points. And I think that's my problem. I just want skill points.
surfer6 Ars Scholae Palatinae Tribus: The Great Southwest Registered: Sep 16, 2002Posts: 813 Had a chance to play last night for an hour or two. First impression, it seems a lot like Torchlight...right down to the music and how the town is set up. Very similar. What isn't similar is the art design, which I really like...along with the destroyable structures. I only did one multiplayer game for about 15 minutes. It was fun, a bit manic with people going everywhere...but some of us managed to stick together some.Overall, I enjoyed it. Prior to multiplayer, I leveled (in order) a WD, DH and Barb. Of the three, the Barbian just seemed to move clear through mobs the fastest. But maybe that was because I knew where I was going and what I was doing by then. Can't wait to get back in...if I only I wasn't called in for work...
End Of All "End Time" Ars Centurion Tribus: Central New York (ie, No where) Registered: Jul 8, 2008Posts: 263 Pokrface wrote:End Of All wrote:Just got done downloading the game and I can't connect to it Bleh, guess I'll have to try later.I was happily playing earlier, but got booted at about 14:00 CDT and haven't been able to connect back since. Been trying every 5-10 minutes, but so far nothing for the past hour and a half.Yeah, I've been trying for a bit too, still no luck. Kinda sucks, soooo close, I'm staring at the login screen.
vishnu Ars Legatus Legionis Tribus: Corvallis, Oregon Registered: Jul 1, 2000Posts: 19977 badfrog wrote:Uhm because you had 100+ different points available for customization in the form of skill points.Which everybody just put in the same places anyway.I know where you're coming from though, I liked the "feel" of putting points into my skill (or synergies) and watching it improve the power of my attack. Having the attack just improve on its own, though functionally no different, does feel somewhat less satisfying. I like spending points.But I'll live.
badfrog Ars Scholae Palatinae Tribus: Nemo hic adest illius nominis Registered: Oct 17, 2007Posts: 1094 vishnu wrote:badfrog wrote:Uhm because you had 100+ different points available for customization in the form of skill points.Which everybody just put in the same places anyway.Well. I didn't. But I was never fixated on OMG I MUST BEAT TEH HELL DIFFICULTIES!!
Karnak Ars Praefectus Registered: Jan 19, 2000Posts: 5753 badfrog wrote:vishnu wrote:How is this different from all "lightning" sorcs being the same in D2?And in fact, they won't all be the same. Assuming the runes are well balanced, different people might be using differently runed arcane orbs.Uhm because you had 100+ different points available for customization in the form of skill points. And I think that's my problem. I just want skill points.There were two to five Hell viable builds for each class in Diablo II. Statwise, if you didn't simply raise Str and Dex to minimum needed for you chosen gear and then put all other points into Vitality you were weakening your character.In Diablo III there will be, at the minimum, millions of viable builds for each class. Just because everybody playing a Wizard has access to the same skills doesn't mean they will all pick the same six active and three passive skills. There are about two trillion possible combinations for each class, millions, perhaps billions, of which will be viable.
Magus` "バカ" Moderator et Subscriptor Tribus: Sin City Registered: Nov 22, 2001Posts: 26382 badfrog wrote:Except it's not easy. If I get mobbed and don't have an AOE skill out, I'm going to die because I can't switch skills in the middle of a fight. Which, when you stop to think about it, is absolutely stupid. I know how to do X and Y with equal levels of skill. But because some arbitrary unit of time hasn't passed since I last decided I wanted to be able to do Y, I can't do X.Riight, because it's impossible to kill a mob of enemies without an AOE...
GodOfEmptiness Ars Scholae Palatinae Registered: Apr 23, 2003Posts: 1198 I got in last night and played a barb through level 9 and killed the king....started a wizard up to about level 6...demon hunter today to about level 7.I am a convert...I really like the way they setup the skill system & runes in this game, to me it allow tons of flexibility and experimentation, something that was sorely lacking in diablo 2.I can actually see myself interested in leveling all five classes to different extents becuase of how easily you can significantly change up their playstyle.
vishnu Ars Legatus Legionis Tribus: Corvallis, Oregon Registered: Jul 1, 2000Posts: 19977 Karnak wrote:There are about two trillion possible combinations for each classFor the wizard:C(25,6) ways to pick skills, C(15,3) ways to pick passives, 5^6 ways to pick runes.$\binom{25}{6}\binom{15}{3}5^6 = 1259070312500$1.26 trillion possible builds. Hard to say how many are viable exactly, but I'm betting a shit of a lot more than in D2.
hatfarm Ars Scholae Palatinae et Subscriptor Tribus: Peoria, IL Registered: May 24, 2007Posts: 951 On the difficulty, I haven't played much, but I had to give it a shot. It was mostly easy except SK on my first run through. I played as a monk, there was one time where I almost died. I was just kinda plowing through a field and I had a huge amount of regular zombie guys on me. Then, accidentally run up into a group of 4 champion fat guys that explode into eels. I just had so much stuff beating on me, and those guys had teleport so I couldn't run. Luckily, I was able to run around long enough to let my health pot timer come back up. I like the new method of health regen quite a bit over the old system. I don't have to worry about keeping a bunch of pots in my belt and inventory.All in all, the beginning of the game is fairly easy, but that's how D2 was as well. This is essentially going up to kill Bloodraven in D2.
Karnak Ars Praefectus Registered: Jan 19, 2000Posts: 5753 badfrog wrote:Except it's not easy. If I get mobbed and don't have an AOE skill out, I'm going to die because I can't switch skills in the middle of a fight. Which, when you stop to think about it, is absolutely stupid. I know how to do X and Y with equal levels of skill. But because some arbitrary unit of time hasn't passed since I last decided I wanted to be able to do Y, I can't do X.One moment you are complaining that there aren't any choices and now you're complaining that you have to choose which skills to use?The six active and three passive skills you select as well as your gemming choices are the customization in Diablo III and they allow far, far greater variety than Diablo II's rather railroading talent trees did.Vishnu,Thanks, I guess I overestimated a bit. Still, over a trillion is just silly. Last edited by Karnak on Sat Apr 21, 2012 2:59 pm
Nulls Ars Scholae Palatinae Tribus: Florida Registered: Mar 3, 2010Posts: 1904 I don't think difficulty is going to be a problem because the beta only uses the easiest difficulty, which should be easy.
badfrog Ars Scholae Palatinae Tribus: Nemo hic adest illius nominis Registered: Oct 17, 2007Posts: 1094 Karnak wrote:badfrog wrote:Except it's not easy. If I get mobbed and don't have an AOE skill out, I'm going to die because I can't switch skills in the middle of a fight. Which, when you stop to think about it, is absolutely stupid. I know how to do X and Y with equal levels of skill. But because some arbitrary unit of time hasn't passed since I last decided I wanted to be able to do Y, I can't do X.One moment you are complaining that there aren't any choices and now you're complaining that you have to choose which skills to use?lol, no. I am saying that, if all characters know all the same skills with equal levels of proficiency (a lack of choices as you term it), then it becomes ridiculous to not allow them to switch between them on the fly.
End Of All "End Time" Ars Centurion Tribus: Central New York (ie, No where) Registered: Jul 8, 2008Posts: 263 Has Blizzard offically stated when the servers would be back up? I know it's a stress test but we can't test anything if the servers are down for most of the weekend.
Fuzzmz "For muffins!" Ars Tribunus Militum et Subscriptor Registered: Dec 3, 2008Posts: 1644 Quote:I know it's a stress test but we can't test anything if the servers are down for most of the weekend.You're not supposed to test things, they're testing things by seeing how the servers react to the huge number of people trying to log-in and play (kidding).The best source is to follow Bashiok on Twitter.
nastro "Fidus et Audax" Ars Legatus Legionis et Subscriptor Tribus: Milwaukee, WI Registered: Jul 17, 2000Posts: 24291 They found the maximum amount of stress, I guess. The answer to the question of "How much can we take?" was answered. Honestly, I never cared for MP Diablo. All this online nonsense is moot, to me.
ewichern Ars Praefectus Tribus: Winchester, VA Registered: Jul 14, 2000Posts: 3656 Yeah I quit trying and went to play a game I can actually log in to.
spork Ars Scholae Palatinae Registered: Nov 3, 1999Posts: 660 I think the game is great but I think they are waaay off the mark with the overall bnet experience. The lack of private chat channels and big messy public ones is a big loss. Oddly enough, I think that despite the removal of lan and offline single player, the game is going to *feel* much more isolated than D2.
crestfallen Ars Tribunus Militum Registered: Apr 18, 2005Posts: 1802 They can't please everyone. Yes, you have access to any skill/rune combination in the end. More options than the "using skill points" way. By faaaaar. I happen to think this is a plus.BUT, they've also tried to incentivize people to pick a solid 6 skills they like and roll with those for a while. If you kill champion packs, you get a bonus to MF. If you kill more champion packs, you get more MF, it stacks. But if you swap your skillset, you lose that bonus.Also, gear choice. If you have a sword that gives +50% damage to Bash, you are incentivized to use Bash. For example.You can't really assign attribute points. But you can put gems in your gear to boost them. So you can't choose, but then again you kind of can.For anyone who cares, the beta has actually increased in difficult substantially since the beginning. It's more difficult than the early part of D2 was, which doesn't say much, but at least it seems a little more dynamic in D3.
Yam-Koo Ars Tribunus Angusticlavius Tribus: Portland, OR Registered: Jul 18, 2000Posts: 6941 badfrog wrote:Which means, when you come right down to it, all "Arcane Orb" wizards are going to be very much alike -- if not identical -- once you strip away all their gear. Which makes gear the absolute determinant of what makes a build. Which is not a system I like.This is the biggest misconception of Diablo 3 that people are having. There are, built in, five different versions of Arcane Orb to cast. The rune system means that there are a variety of ways to cast every spell. The main difference is that these choices are not permanent and do not make your other skills worthless. Builds are a combination of spells, each of them customizable. The variety here isn't from a few 1% upgrades there but from huge and orthogonal choices.
SituationSoap Ars Praefectus et Subscriptor Tribus: Grand Rapids MI Registered: Jun 28, 2008Posts: 11021 enraged_camel wrote:I've played barbarian and witch doctor so far. My impression is that barbarian is more "fun" in the traditional hack & slash sense, whereas the witch doctor is more "interesting" in the sense of deeper game-play. I found a set of rare knuckles in my last run so I'm going to try monk next. edit: one interesting thing about the barbarian was the Bash skill. I switched back to it to fight the last boss, and he was stunned 75% of the time (I was using a fast weapon). I'm surprised they didn't make bosses immune to stuns like they did in WoW.I'm pretty sure on normal you could glyph bash to stun and equip a pair of daggers and literally never have the boss move. Now that I think of it, that sounds like a fun challenge. I do wish I could set /players 4 in a solo game, like you could in D2. I like more challenge than playing solo or in a group provides.
Karnak Ars Praefectus Registered: Jan 19, 2000Posts: 5753 badfrog wrote:Karnak wrote:badfrog wrote:Except it's not easy. If I get mobbed and don't have an AOE skill out, I'm going to die because I can't switch skills in the middle of a fight. Which, when you stop to think about it, is absolutely stupid. I know how to do X and Y with equal levels of skill. But because some arbitrary unit of time hasn't passed since I last decided I wanted to be able to do Y, I can't do X.One moment you are complaining that there aren't any choices and now you're complaining that you have to choose which skills to use?lol, no. I am saying that, if all characters know all the same skills with equal levels of proficiency (a lack of choices as you term it), then it becomes ridiculous to not allow them to switch between them on the fly.I think we have different definitions of the word "choices". To me, it is a choice which spells and runes I will use. I don't plan on changing builds willy-nilly once I find a build I like. I am very happy with the system they have and think it offers a lot more than Diablo II ever came close to.
SituationSoap Ars Praefectus et Subscriptor Tribus: Grand Rapids MI Registered: Jun 28, 2008Posts: 11021 FWIW, I think the best word for the current skill system is elegant. It's simple, yet it provides incredible depth. Expect to see this replace the talent tree in many games in the next five years.
vishnu Ars Legatus Legionis Tribus: Corvallis, Oregon Registered: Jul 1, 2000Posts: 19977 badfrog wrote:lol, no. I am saying that, if all characters know all the same skills with equal levels of proficiency (a lack of choices as you term it), then it becomes ridiculous to not allow them to switch between them on the fly.No it doesn't?You "know" the 6 skills you have selected. The fact that they made it incredibly easy to respec does not mean that you should just have all the skills all the time. That would be ridiculous.
Comp Guru "Ban KAI!" Ars Legatus Legionis et Subscriptor Tribus: Toronto, Canada Registered: Sep 18, 1999Posts: 12266 surfer6 wrote:Had a chance to play last night for an hour or two. First impression, it seems a lot like Torchlight...right down to the music and how the town is set up. Very similar.Um, Torchlight is pretty much inspired by Diablo II, including the music which is done by ex-Diablo people - CG
Yam-Koo Ars Tribunus Angusticlavius Tribus: Portland, OR Registered: Jul 18, 2000Posts: 6941 Comp Guru wrote:surfer6 wrote:Had a chance to play last night for an hour or two. First impression, it seems a lot like Torchlight...right down to the music and how the town is set up. Very similar.Um, Torchlight is pretty much inspired by Diablo II, including the music which is done by ex-Diablo people - CGCue "Tyranids are just a Zerg clone" comic.
necklessone "Gummi Artisan" Ars Tribunus Angusticlavius et Subscriptor Tribus: Central NJ PSN/Gamertag: necklessone Registered: Jul 23, 2006Posts: 6451 Got to the Skeleton and I'm thinking that my laptop isn't going to be able to hack it. Too many particle effects and enemies are causing nasty stutter.Good news is the gaming PC should be finished by tomorrow.
DaveJ Ars Scholae Palatinae et Subscriptor Tribus: :subirT Registered: Apr 8, 1999Posts: 1427 hatfarm wrote:On the difficulty, I haven't played much, but I had to give it a shot. It was mostly easy except SK on my first run through. I played as a monk, there was one time where I almost died. I was just kinda plowing through a field and I had a huge amount of regular zombie guys on me. Then, accidentally run up into a group of 4 champion fat guys that explode into eels. I just had so much stuff beating on me, and those guys had teleport so I couldn't run. Luckily, I was able to run around long enough to let my health pot timer come back up. I like the new method of health regen quite a bit over the old system. I don't have to worry about keeping a bunch of pots in my belt and inventory.All in all, the beginning of the game is fairly easy, but that's how D2 was as well. This is essentially going up to kill Bloodraven in D2.Just finished a run with the monk and man was it a blast. I found a bunch of cool gear early on, including a piece that converted 1.1% of damage dealt into life... the more I fought the healthier I got. That was fuckin' cool against Leoric and his minions - I played a WD first and got my ass handed to me a few times, but with the monk I just breezed right through.I was really on the fence about buying D3 given the issues with the "always on" connection and the supposed dumbing down of certain elements, but it's still really fun. Off to go hunting for preorder deals, are there any good ones around for the non-CE version?
mogbert Ars Praefectus Registered: Jun 12, 2007Posts: 4137 One thing I didn't like about Diablo (not sure if it was 1 or 2) was that you HAD to study and work out your builds and such, or you would very easily have a character that wasn't viable. That isn't the case anymore. They are trying to appeal to a larger demographic then the hardcore Diablo II group. This game cost too much to be purchased by just that one group. By widening the demographic, they increase the chance they will make money off the game and it will be a hit. At this point, it is a trade off, losing the small percentage of die hard super hardcore players who will feel that the game is just too forgiving, in exchange for a few million people who will be more willing to play it with their gaming spouses because they can't really screw up their character. If I could just get my wife to play for an hour (she only played for 15 minutes so far), then I'm sure I can add a second sale for the game.So I'm fairly happy about the way it worked out. I don't have to choose between taking fire bats or dogs, and not know which was better without reading 20 online opinions and checking out the calculus for the DPS breakdown against bosses with different resistances. I like trying the different skills, and I don't always choose the new one.Here is something fun. Grab a grey low end/trash weapon, drop everything you are wearing into the bank. Turn on auto-equip and do a run through one of the dungeons without opening your inventory. This way, you can only use what is auto-equipped as you go (I think that is how it works). Makes things more interesting when you already have top of the line equipment and you are kicking too much butt. I grabbed some high end loot out of the bank for one of my new characters and it wasn't as much fun as when I was always needing some drop just so I'd have something, anything, for a slot.
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## Cohen, Haeupler, and Schulman: Explicit Binary Tree-Codes & Cancellations
The high-dimensional conference in Jerusalem is running with many exciting talks (and they are videotaped), and today in Tel Aviv there is a conference on Optimization and Discrete Geometry : Theory and Practice.
Today in Jerusalem, Leonard Schulman talked (video available!) about a recent breakthrough by Gil Cohen, Bernhard Haeupler, and Leonard Schulman in the recent paper Explicit Binary Tree Codes with Polylogarithmic Size Alphabet.
## Tree codes
Tree codes are extremely important objects invented by Leonard Schulman in 1992-1996. You can read about it in Wigderson’s book Mathematics and Computation (see also this post) in a whole section about Error-correction of interactive communication, a theory pioneered by Leonard. Finding explicit good (linear distance, finite alphabet) tree codes is a very important problem.
(From the introduction of the new paper) “A tree code consists of a complete rooted binary tree (either infinite or of finite depth $n$) in which each edge is labeled by a symbol from an alphabet $\Sigma$ . There is a natural one-to-one mapping assigning each binary string $s$ to a path starting at the root, where $s$ simply indicates which child is taken in each of the steps. For a tree code, such a path naturally maps to a string over the alphabet $\Sigma$, which is formed by concatenating the symbols along the path. This way a tree code $T$ encodes any binary string $s$ into an equally long string $T(s)$ over $\Sigma$. This encoding has an online characteristic because the encoding of any prefix does not depend on later symbols. In particular, any two distinct strings that agree in their first $k$ symbols also have encodings that agree in their first $k$ symbols. A tree code is said to achieve distance $\delta \ge 0$ if the encodings of any two strings differ in at least a $\delta$-fraction of the positions after their first disagreement. The rate of a tree code is $1/\log _2 (\Sigma )$. A tree code is said to be asymptotically good if it achieves both constant distance $\delta >0$ and a constant rate, namely, the alphabet size is $O(1)$.”
### The abstract:
“This paper makes progress on the problem of explicitly constructing a binary tree code with constant distance and constant alphabet size.
For every constant 1 we give an explicit binary tree code with distance and alphabet size $(\log n)^{O(1)}$, where n is the depth of the tree. This is the first improvement over a two-decade-old construction that has an exponentially larger alphabet of size $n^{O(1)}$.
As part of the analysis, we prove a bound on the number of positive integer roots a real polynomial can have in terms of its sparsity with respect to the Newton basis – a result of independent interest.”
### Problems on Exponential sums
A few years ago Cris Moore and Leonard Schulman proposed an explicit constructions for good tree codes in the paper Tree codes and a conjecture on exponential sums. The construction depends on still open conjectures on new types of exponential sums.
## A paper by Leonard and me on polynomials with massive cancellations.
So let me use this opportunity to advertize a paper by Leonard and me Quasi-random multilinear polynomials which was just accepted for publication in the Israel Journal of Mathematics. Unexpected cancellation is always a very interesting phenomenon that we cherish and wish to understand. For example, we expect that the sum of the Mobius function for the first n integers cancels almost like that of a random walk. Depending on the meaning of “almost” this is the (known) prime number theorem, the (conjectured) Riemann hypothesis, or simply false, respectively.
A little less famous example (which I personally like) is the paper by Nikola Djokic an upper bound on the sum of signs of permutations with a condition on their prefix sets solving a problem by J. Feldman, H. Knorrer, and E. Trubowitz.
Our starting point is the determinant: It is a polynomial of degree $n$ of $n^2$ variables and no matter what $\pm 1$ values you assign to the variables you have a massive cancellation of almost a random-walk type. There are $n!$ terms and for any assignment the value is smaller than $n^{n/2}$ which is $(n!)^{1/2+o(1)}$. We were interested in the question of finding other such polynomials.
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### 1 Response to Cohen, Haeupler, and Schulman: Explicit Binary Tree-Codes & Cancellations
1. arielgabizon says:
Loved the result on tree codes. Typo ‘delta’ instead of symbol delta.
GK: many thanks Ariel |
]> Exercise 1.4
## Exercise 1.4
Prove that rational numbers repeat the same finite sequence of digits endlessly, and that irrational numbers do not.
Solution:
When you divide $a$ by $b$ there are only $b$ possible remainders.
This means that after at most $b$ steps in your long division the remainder must repeat itself.
Since $a$ and $b$ are integers, once your division gets past the decimal point, you always bring down a 0 in your division procedure.
If you always bring down a 0, the result of your division beyon any point depends only on the remainder at that point.
Thus once a remainder is repeated past the decimal point, the sequence of remainders between the repeat will continue repeating endlessly.
For example,
$1 11$ is .909090 ... or .(09)*.
$1 7$ is .142857142857142857 ... or .(142857)*.
If the decimal expansion of a number $x$ repeats endlessly, as $. ( z ) *$ for some sequence $z$ that is $k$ digits long, we can write
$x = z * 10 − k * ( 1 + 10 − ( k + 1 ) + 10 − 2 ( k + 2 ) + ⋯ ) = z 10 k ( 1 − 10 − ( k + 1 ) )$
which is a rational number. If you have problems following this manipulation do not worry. We will talk about it later. |
# How to mix text and formulas in a single cell in the Wolfram Cloud Notebook?
How to mix text and formulas in a single cell in the Wolfram Cloud Notebook?
The shortcuts Ctrl+( and Ctrl+( don't work (they probably are intercepted by the browser)
Answer written at the time of \$CloudVersion: 1.53.0.1 (November 5, 2019)
My guess is that interactive work with inline cells is not supported in the web browser front end yet.
You can see that inline cells are known and rendered well:
CellPrint @ TextCell[
Row[{"Test ",Defer@Integrate[x^2,{x,0,1}]}],
"Section"
]
but once this cell is printed you can't edit or even move selection inside the Input inline cell.
So in order to create those cells you can use a CellPrint @ cell approach.
At the end the most convenient way is probably to develop your notebook on desktop Mathematica and upload to the Cloud.
• Thank you, @Kuba. "the most convenient way is probably to develop your notebook on desktop Mathematica and upload to the Cloud" this would be the smarter move. Unfortunately, as you may have guessed, if I use the Cloud version, this is mostly because of the free tier. Even if there are relatively inexpensive plans, they are still out of my budget for now ;) – Sylvain Leroux Dec 13 '19 at 8:42
• @SylvainLeroux I understand. I just added an example that is more straightforward to use. You can write the content in input form rather than using box-language. You can replace Section with Text style if you want too. – Kuba Dec 13 '19 at 8:48
• Cool. I will study that in depth. – Sylvain Leroux Dec 13 '19 at 8:54
It's correct that we don't have a full-blown typesetting editor in the Wolfram Cloud yet. That's one of our longer-term projects.
For now, you could use the special "Inline InputForm-based input" we added recently: Press Ctrl+Shift+1 and you get an input field where you can type an expression in InputForm (e.g. x/y^2) which will turn into its typeset equivalent once you press Enter. You can go back to edit mode by clicking it. This will be added to the "Insert" menu soon so it's easier to discover.
Other alternatives that might suit you in certain cases:
• You can use "Evaluate in Place" (Cmd+Enter on Mac / Ctrl+Enter on Windows) if you want to evaluate something inline.
• You can convert a whole cell from InputForm to StandardForm (Ctrl+Shift+N on Mac / Ctrl+Alt+N on Windows); Ctrl+Shift+I / Ctrl+Alt+I to go back to InputForm.
• You can take some (typeset) output and copy it into another cell, e.g. by clicking it (if you get the click-to-copy overlay) or by selecting the cell bracket and pressing Cmd+C / Ctrl+C and then pressing Cmd+V / Ctrl+V while the cursor is inside the other cell.
I described some of these things in greater detail in the blog post about 1.50 and 1.51.
• Cool! Thank for <kbd>Ctrl+Shift+1</kbd>. I didn't know that one. Concerning the other alternatives you mention: while new to Mathematica, I already use them--so they should already be mentioned in the docs somewhere. They are available in the cog menu anyway--but I can't remember where I read about the keyboard shortcuts. Concerning <kbd>ctrl-v</kbd>, I noticed though, while pasting certain objects, I sometimes end up with a small pink/red rectangle instead of the expected object. I will try to reproduce that and post a question here if you want. – Sylvain Leroux Dec 13 '19 at 13:22
• Yeah, please let me know if you run into such an issue, ideally with steps to reproduce. – Jan Pöschko Dec 13 '19 at 13:46
• See mathematica.stackexchange.com/questions/211337/… for an issue with cell pasting in 1.53.0.1 – Sylvain Leroux Dec 13 '19 at 17:04
• August 2020, still no progress on that? – Kosm Aug 6 at 20:31 |
# zbMATH — the first resource for mathematics
## Chen, Yuming
Compute Distance To:
Author ID: chen.yuming Published as: Chen, Y-M.; Chen, Y.; Chen, Y. M.; Chen, Y.-M.; Chen, Y.-m.; Chen, Yu Ming; Chen, Yu-Ming; Chen, Yu-ming; Chen, Yu.; Chen, YuMing; Chen, Yuming
Documents Indexed: 286 Publications since 1965 Reviewing Activity: 124 Reviews
all top 5
#### Co-Authors
16 single-authored 20 Wu, Jianhong 11 Yang, Junyuan 8 Zhang, Fengqin 7 Yi, Taishan 6 Dai, Binxiang 6 Wang, Xia 5 Chen, Guijing 5 Huang, Lihong 5 Liao, Xinyuan 5 Zhou, Zhan 4 Guo, Shangjiang 4 Guo, Zhiming 4 Liu, Shengqiang 4 Wang, Jinliang 4 Yang, Qigui 4 Zhou, Shengfan 4 Zou, Shuliang 3 Chen, Fengde 3 Li, Jianquan 3 Liu, Hanwu 3 Yin, Zongbin 3 Yu, Jian-She 2 Bai, Dingyong 2 Bai, Zhi-Dong 2 Chen, Jiahua 2 Hu, Feifang 2 Huang, Chuangxia 2 Jin, Zhen 2 Kuniya, Toshikazu 2 Lang, Jiying 2 Liang, Haihua 2 Liu, Rong 2 Lu, Xuejuan 2 Martcheva, Maia 2 Shu, Hongying 2 Wang, Lin 2 Wang, Qi 2 Wu, Keshou 2 Xiao, Heng 2 Xu, Fei 2 Yang, Zhichun 1 Bentout, Soufiane 1 Cen, Xiuli 1 Djilali, Salih 1 Duan, Lian 1 Fang, Hui 1 Ge, Qing 1 Groll, Manfred 1 Guo, Hongpeng 1 Guo, Yao 1 Guo, Zhongheng 1 He, Shengnan 1 Hu, Qingwen 1 Huang, Ying Sue 1 Jiao, Na 1 Krisztin, Tibor 1 Lai, Yongzeng 1 Lamichhane, Surya 1 Lee, David T. S. 1 Li, Bing 1 Li, Hongxing 1 Li, Jianbo 1 Li, Kaiwang 1 Li, Ting 1 Li, Xiangjun 1 Li, Zhong 1 Lin, Wei 1 Lin, Weiqiang 1 Liu, Jiming 1 Liu, Maoxing 1 Liu, Weiwei 1 Ma, Jianfu 1 Miao, Duoqian 1 Ouyang, Zigen 1 Pan, Xuejun 1 Rong, Libin 1 Shao, Yuanfu 1 Shi, Benxuan 1 Shi, Jinlin 1 Shu, Xiaobao 1 Song, Xinyu 1 Su, Hua 1 Sun, Jinhua 1 Tan, Shao Bin 1 Tang, Chaohui 1 Tang, De 1 Wang, Xiaoyan 1 Wang, Zhi-Cheng 1 Wen, Fenghua 1 Xiang, Qiaomin 1 Xiao, Huafeng 1 Xie, Xin 1 Xue, Min 1 Yuan, Zhaohui 1 Zhang, Dan 1 Zhang, Junying 1 Zhang, Juping 1 Zhang, Na 1 Zhang, Ruyuan 1 Zhao, Tian ...and 3 more Co-Authors
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#### Serials
9 Journal of Differential Equations 7 Applied Mathematics Letters 6 Journal of Mathematical Analysis and Applications 6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Mathematical Methods in the Applied Sciences 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of Biological Dynamics 4 Computers & Mathematics with Applications 4 Applied Mathematics and Computation 4 Mathematical and Computer Modelling 4 Differential Equations and Dynamical Systems 4 Mathematical Biosciences and Engineering 3 Applied Mathematics and Mechanics. (English Edition) 3 Nonlinear Analysis. Real World Applications 2 Mathematical Biosciences 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the American Mathematical Society 2 Chinese Annals of Mathematics. Series A 2 The Canadian Applied Mathematics Quarterly 2 Complexity 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 Acta Mathematica Scientia. Series A. (Chinese Edition) 2 Control and Decision 2 Advances in Difference Equations 2 Science China. Mathematics 1 IMA Journal of Applied Mathematics 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 Nonlinearity 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Applied Mathematics and Optimization 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Mathematica Slovaca 1 Tohoku Mathematical Journal. Second Series 1 Journal of Nanjing University. Natural Sciences 1 Statistics & Probability Letters 1 Acta Applicandae Mathematicae 1 Acta Mathematicae Applicatae Sinica. English Series 1 Northeastern Mathematical Journal 1 SIAM Journal on Matrix Analysis and Applications 1 Neural Networks 1 Differential and Integral Equations 1 Applications of Mathematics 1 Applied Mathematical Modelling 1 SIAM Journal on Mathematical Analysis 1 Journal of Dynamics and Differential Equations 1 Mitteilungen aus dem Mathematischen Seminar Gießen 1 Computational and Applied Mathematics 1 Journal of the Egyptian Mathematical Society 1 Discrete and Continuous Dynamical Systems 1 Acta Mathematica Sinica. English Series 1 Journal of Biological Systems 1 International Journal of Applied Mathematics 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Journal of Applied Mathematics and Computing 1 Boundary Value Problems 1 Journal of Guangxi Normal University. Natural Science Edition 1 Journal of Anhui University. Natural Science Edition 1 Frontiers of Mathematics in China 1 International Journal of Biomathematics 1 International Journal of Qualitative Theory of Differential Equations and Applications 1 Science China. Technological Sciences 1 Fuzzy Systems and Mathematics 1 Journal of Applied Analysis and Computation 1 IEEE Transactions on Circuits and Systems I: Regular Papers
all top 5
#### Fields
81 Biology and other natural sciences (92-XX) 74 Ordinary differential equations (34-XX) 24 Partial differential equations (35-XX) 24 Dynamical systems and ergodic theory (37-XX) 13 Difference and functional equations (39-XX) 6 Computer science (68-XX) 5 Statistics (62-XX) 4 Integral equations (45-XX) 4 Systems theory; control (93-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Numerical analysis (65-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Probability theory and stochastic processes (60-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Combinatorics (05-XX) 1 Nonassociative rings and algebras (17-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
198 Publications have been cited 1,711 times in 1,414 Documents Cited by Year
The existence of mild solutions for impulsive fractional partial differential equations. Zbl 1227.34009
Shu, Xiao-Bao; Lai, Yongzeng; Chen, Yuming
2011
Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations. Zbl 0879.35113
Chen, Y.; McKenna, P. J.
1997
Homoclinic solutions in periodic difference equations with saturable nonlinearity. Zbl 1239.39010
Zhou, Zhan; Yu, Jianshe; Chen, Yuming
2011
Stable periodic solution of a discrete periodic Lotka-Volterra competition system. Zbl 1019.39004
Chen, Yuming; Zhou, Zhan
2003
Multiple periodic solutions of delayed predator–prey systems with type IV functional responses. Zbl 1066.92050
Chen, Yuming
2004
Periodic solutions of a single species discrete population model with periodic harvest/stock. Zbl 0970.92019
Zhang, R. Y.; Wang, Z. C.; Chen, Y.; Wu, J.
2000
Two-parameter bifurcations in a network of two neurons with multiple delays. Zbl 1136.34058
Guo, Shangjiang; Chen, Yuming; Wu, Jianhong
2008
Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response. Zbl 1171.34341
Wang, Qi; Dai, Binxiang; Chen, Yuming
2009
Multiresolution reproducing kernel particle methods. Zbl 0893.73078
Liu, W. K.; Hao, W.; Chen, Y.; Jun, S.; Gosz, J.
1997
Global asymptotic stability of delayed Cohen-Grossberg neural networks. Zbl 1374.82019
Chen, Yuming
2006
On the existence of gap solitons in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity. Zbl 1193.35176
Zhou, Zhan; Yu, Jianshe; Chen, Yuming
2010
Slowly oscillating periodic solutions for a delayed frustrated network of two neurons. Zbl 0998.34058
Chen, Yuming; Wu, Jianhong
2001
Minimal instability and unstable set of a phase-locked periodic orbit in a delayed neural network. Zbl 0942.34062
Chen, Y.; Wu, J.
1999
Unimodal dynamical systems: comparison principles, spreading speeds and travelling waves. Zbl 1308.35126
Yi, Taishan; Chen, Yuming; Wu, Jianhong
2013
Periodic solutions of a delayed, periodic logistic equation. Zbl 1118.34327
Chen, Yuming
2003
Periodic solutions of delayed periodic Nicholson’s blowflies models. Zbl 1093.34554
Chen, Y.
2003
Permanence and global stability in a discrete $$n$$-species competition system with feedback controls. Zbl 1154.34352
Liao, Xinyuan; Zhou, Shengfan; Chen, Yuming
2008
A study of homotopy analysis method for limit cycle of van der Pol equation. Zbl 1221.65198
Chen, Y. M.; Liu, J. K.
2009
Existence and attraction of a phase-locked oscillation in a delayed network of two neurons. Zbl 1023.34065
Chen, Yuming; Wu, Jianhong
2001
Algorithms for plethysm. Zbl 0556.20013
Chen, Y. M.; Garsia, A. M.; Remmel, J.
1984
Global analysis of an SIR epidemic model with infection age and saturated incidence. Zbl 1365.92117
Chen, Yuming; Zou, Shaofen; Yang, Junyuan
2016
Convergence and periodicity of solutions for a discrete-time network model of two neurons. Zbl 1045.92002
Yuan, Zhaohui; Huang, Lihong; Chen, Yuming
2002
Global dynamics of delayed reaction-diffusion equations in unbounded domains. Zbl 1258.35122
Yi, Taishan; Chen, Yuming; Wu, Jianhong
2012
Dynamics of a hyperchaotic Lorenz-type system. Zbl 1314.37021
Chen, Yuming; Yang, Qigui
2014
Connecting orbits from synchronous periodic solutions to phase-locked periodic solutions in a delay differential system. Zbl 0955.34058
Chen, Yuming; Wu, Jianhong; Krisztin, Tibor
2000
The global stability of an SIRS model with infection age. Zbl 1298.92096
Chen, Yuming; Yang, Junyuan; Zhang, Fengqin
2014
Complex dynamics in the unified Lorenz-type system. Zbl 1296.34117
Yang, Qigui; Chen, Yuming
2014
Periodic solutions of a $$2n$$th-order nonlinear difference equation. Zbl 1232.39019
Zhou, Zhan; Yu, Jianshe; Chen, Yuming
2010
An edge dislocation in a three-phase composite cylinder model. Zbl 0756.73059
Luo, H. A.; Chen, Y.
1991
A delayed HIV-1 model with virus waning term. Zbl 1329.34129
Li, Bing; Chen, Yuming; Lu, Xuejuan; Liu, Shengqiang
2016
All solutions of a class of difference equations are truncated periodic. Zbl 1029.39003
Chen, Yuming
2002
Stability of the boundary solution of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response. Zbl 1147.34038
Chen, Fengde; Chen, Yuming; Shi, Jinlin
2008
A new method based on the harmonic balance method for nonlinear oscillators. Zbl 1209.37100
Chen, Y. M.; Liu, J. K.
2007
The asymptotic shapes of periodic solutions of a singular delay differential system. Zbl 0976.34060
Chen, Yuming; Wu, Jianhong
2001
Dynamics of a delayed predator-prey model with predator migration. Zbl 1351.34082
Chen, Yuming; Zhang, Fengqin
2013
Homotopy analysis method for limit cycle flutter of airfoils. Zbl 1262.74015
Chen, Y. M.; Liu, J. K.
2008
New results on positive periodic solutions of a periodic integro-differential competition system. Zbl 1051.45004
Chen, Y.
2004
Abstract algebraic-delay differential systems and age structured population dynamics. Zbl 1291.34124
Kosovalić, N.; Magpantay, Felicia Maria G.; Chen, Y.; Wu, Jianhong
2013
Threshold dynamics of a delayed reaction diffusion equation subject to the Dirichlet condition. Zbl 1342.92214
Yi, Taishan; Chen, Yuming; Wu, Jianhong
2009
Threshold dynamics of an SIRS model with nonlinear incidence rate and transfer from infectious to susceptible. Zbl 1370.92165
Li, Ting; Zhang, Fengqin; Liu, Hanwu; Chen, Yuming
2017
Algebraic-delay differential systems: $$C^0$$-extendable submanifolds and linearization. Zbl 1362.34098
Kosovalić, N.; Chen, Y.; Wu, J.
2017
Three positive solutions for a generalized Laplacian boundary value problem with a parameter. Zbl 06447284
Bai, Dingyong; Chen, Yuming
2013
Stability analysis and optimal control of a hand-foot-mouth disease (HFMD) model. Zbl 1300.34118
Yang, Jun-Yuan; Chen, Yuming; Zhang, Feng-Qin
2013
Existence of positive solutions to a boundary value problem for a delayed nonlinear fractional differential system. Zbl 1219.34103
Ouyang, Zigen; Chen, Yuming; Zou, Shuliang
2011
Dynamic complexities of a predator-prey model with generalized Holling type III functional response and impulsive effects. Zbl 1152.34309
Su, Hua; Dai, Binxiang; Chen, Yuming; Li, Kaiwang
2008
On permanence and global stability in a general Gilpin-Ayala competition predator-prey discrete system. Zbl 1125.39008
Liao, Xinyuan; Zhou, Shengfan; Chen, Yuming
2007
New SDP models for protein homology detection with semi-supervised SVM. Zbl 1273.90143
Bai, Y. Q.; Niu, B. L.; Chen, Y.
2013
Shi, Z. F.; Chen, Y.
2004
Desynchronization of large scale delayed neural networks. Zbl 0945.34056
Chen, Yuming; Huang, Ying Sue; Wu, Jianhong
2000
Effect of infection age on an SIS epidemic model on complex networks. Zbl 1356.35268
Yang, Junyuan; Chen, Yuming; Xu, Fei
2016
Traveling wavefronts of a prey-predator diffusion system with stage-structure and harvesting. Zbl 1207.92047
Liao, Xinyuan; Chen, Yuming; Zhou, Shengfan
2011
An iterative algorithm for solving inverse problems of two-dimensional diffusion equations. Zbl 0565.65074
Liu, J. Q.; Chen, Y. M.
1984
A numerical algorithm for remote sensing of density profiles of a simple ocean model by acoustic pulses. Zbl 0365.76079
Chen, Y. M.; Tsien, D. S.
1977
Impacts of the cell-free and cell-to-cell infection modes on viral dynamics. Zbl 1401.37097
Shu, Hongying; Chen, Yuming; Wang, Lin
2018
Global exponential stability of periodic solutions to a delay Lasota-Wazewska model with discontinuous harvesting. Zbl 1336.34114
Duan, Lian; Huang, Lihong; Chen, Yuming
2016
Analysis of sexually transmitted disease spreading in heterosexual and homosexual populations. Zbl 1262.92025
Zhang, Juping; Jin, Zhen; Chen, Yuming
2013
Permanence for a discrete time Lotka-Volterra type food-chain model with delays. Zbl 1120.92046
Liao, Xinyuan; Zhou, Shengfan; Chen, Yuming
2007
Eventual periodicity of $$x_{n+1}=\max \{1/x_n,A_n/x_{n-1}\}$$ with periodic coefficients. Zbl 1086.39003
Chen, Y.
2005
Vibrations of high speed rotating shells with calculations for cylindrical shells. Zbl 0939.74552
Chen, Y.; Zhao, H. B.; Shen, Z. P.; Grieger, I.; Kröplin, B.-H.
1993
The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. Zbl 1298.34011
Chen, Y.; Chen, Dezhu; Lv, Z.
2012
Uniformly valid solution of limit cycle of the Duffing-van der Pol equation. Zbl 1273.70036
Chen, Y. M.; Liu, J. K.
2009
Dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems. Zbl 1093.74524
Wang, H. M.; Ding, H. J.; Chen, Y. M.
2005
Travelling waves in a nonlinearly suspended beam: Some computational results and four open questions. Zbl 0895.35100
Chen, Y.; McKenna, P. J.
1997
A modified pulse-spectrum technique for solving inverse problems of two- dimensional elastic wave equation. Zbl 0566.65092
Xie, G. Q.; Chen, Y. M.
1985
A numerical algorithm for solving inverse problems of two-dimensional wave equations. Zbl 0515.65088
Chen, Y. M.; Liu, J. Q.
1983
A numerical method for nonlinear inverse problems in fluid dynamics. Zbl 0309.76059
Tsien, D. S.; Chen, Y. M.
1974
Penetration of temperature waves in a random medium. Zbl 0164.29701
Chen, Y. M.; Tien, C. L.
1967
The existence of homoclinic orbits in a 4D Lorenz-type hyperchaotic system. Zbl 1384.37027
Chen, Yuming
2017
Stress analysis of multi-layered hollow anisotropic composite cylindrical structures using the homogenization method. Zbl 1401.74010
Sun, X. S.; Tan, V. B. C.; Chen, Y.; Tan, L. B.; Jaiman, R. K.; Tay, T. E.
2014
The nonequivalence and dimension formula for attractors of Lorenz-type systems. Zbl 1284.34058
Chen, Yuming; Yang, Qigui
2013
Equivariant normal forms for parameterized delay differential equations with applications to bifurcation theory. Zbl 1334.34154
Guo, Shang Jiang; Chen, Yu Ming; Wu, Jian Hong
2012
SDP relaxation for semi-supervised support vector machine. Zbl 1263.90051
Bai, Y. Q.; Chen, Y.; Niu, B. L.
2012
Existence and global attractivity of a positive periodic solution of a delayed periodic respiration model. Zbl 1100.34055
Chen, Y.; Huang, L.
2005
An iterative method for simultaneous determination of bulk and shear moduli and density variations. Zbl 0574.73035
Chen, Y. M.; Xie, G. Q.
1986
A numerical algorithm for remote sensing of thermal conductivity. Zbl 0469.65086
Chen, Y. M.; Liu, J. Q.
1981
Dynamical analysis of a stage-structured predator-prey model with cannibalism. Zbl 1409.92217
Zhang, Fengqin; Chen, Yuming; Li, Jianquan
2019
Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps. Zbl 06782915
Yi, Taishan; Chen, Yuming
2017
Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters. Zbl 1236.74071
Chen, Y. M.; Liu, J. K.; Meng, G.
2012
Second-order differentiability with respect to parameters for differential equations with adaptive delays. Zbl 1201.34096
Chen, Yuming; Hu, Qingwen; Wu, Jianhong
2010
Controlling decoherence from fluctuating magnetic field. Zbl 1184.81087
Chen, Z. Q.; Guo, L. P.; Chen, Y.; Li, X. L.; Liu, G. Q.; Ji, Y. H.; Wang, Z. S.
2010
Positive periodic solutions of nonautonomous functional differential systems. Zbl 1125.34052
Zhang, Na; Dai, Binxiang; Chen, Yuming
2007
Mobile assemblies based on the Bennett linkage. Zbl 1145.70302
Chen, Y.; You, Z.
2005
A generalized pulse-spectrum technique (GPST) for determining time- dependent coefficients of one-dimensional diffusion equations. Zbl 0618.65122
Liu, X. Y.; Chen, Y. M.
1987
An iterative numerical algorithm for solving multi-parameter inverse problems of evolutional partial differential equations. Zbl 0531.65068
Chen, Y. M.; Liu, J. Q.
1984
An iterative method for solving inverse problems of a nonlinear wave equation. Zbl 0513.65070
Hatcher, Robert P.; Chen, Y. M.
1983
An almost everywhere divergent Fourier series of the class $$L(\log^ + \log^ + L)^{1-\epsilon}$$. Zbl 0169.39703
Chen, Y. M.
1969
The Jacobi stability of a Lorenz-type multistable hyperchaotic system with a curve of equilibria. Zbl 1419.34138
Chen, Yuming; Yin, Zongbin
2019
Global dynamics of a vector-borne disease model with infection ages and general incidence rates. Zbl 1404.35463
Wang, Xia; Chen, Yuming; Liu, Shengqiang
2018
Dynamics of an age-structured host-vector model for malaria transmission. Zbl 1392.35321
Wang, Xia; Chen, Yuming; Liu, Shengqiang
2018
An SIRS model with differential susceptibility and infectivity on uncorrelated networks. Zbl 1318.34066
Liu, Maoxing; Chen, Yuming
2015
Homotopy analysis method for limit cycle oscillations of an airfoil with cubic nonlinearities. Zbl 1269.70039
Chen, Y. M.; Liu, J. K.
2010
Global attractivity of a generalized Lotka-Volterra competition model. Zbl 1216.34082
Chen, Fengde; Chen, Yuming; Guo, Shangjiang; Li, Zhong
2010
Periodic solutions and the global attractor in a system of delay differential equations. Zbl 1229.34110
Yi, Taishan; Chen, Yuming; Wu, Jianhong
2010
The lattice Boltzmann method based on quadtree mesh. Zbl 1422.76147
Chen, Y.; Cai, Q. D.
2009
Thermoelastic dynamic solution of a multilayered spherically isotropic hollow sphere for spherically symmetric problems. Zbl 1066.74029
Wang, H. M.; Ding, H. J.; Chen, Y. M.
2004
Quasi-normal modes and black-hole quantum mechanics in $$2+1$$ dimensions. Zbl 1047.83017
Birmingham, Danny; Carlip, S.; Chen, Y.
2003
A prior bounds and stability of solutions for a Volterra reaction-diffusion equation with infinite delay. Zbl 0981.35095
Shi, B.; Chen, Y.
2001
Two-parameter thermal lattice BGK model with a controllable Prandtl number. Zbl 0903.76078
Chen, Y.; Ohashi, H.; Akiyama, M.
1997
Prandtl number of lattice Bhatnagar-Gross-Krook fluid. Zbl 1025.76544
Chen, Y.; Ohashi, H.; Akiyama, M.
1995
An efficient numerical method for exterior and interior inverse problems of Helmholtz equation. Zbl 0825.76732
Wang, S. L.; Chen, Y. M.
1991
Asymptotic propagations of asymptotical monostable type equations with shifting habitats. Zbl 1448.35308
Yi, Taishan; Chen, Yuming; Wu, Jianhong
2020
Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments. Zbl 1445.35201
Tang, De; Chen, Yuming
2020
Threshold dynamics of a vector-borne disease model with spatial structure and vector-bias. Zbl 1431.35214
Wang, Jinliang; Chen, Yuming
2020
Threshold dynamics of an HIV infection model with two distinct cell subsets. Zbl 1437.92143
Wang, Xia; Ge, Qing; Chen, Yuming
2020
Dynamical analysis of a stage-structured predator-prey model with cannibalism. Zbl 1409.92217
Zhang, Fengqin; Chen, Yuming; Li, Jianquan
2019
The Jacobi stability of a Lorenz-type multistable hyperchaotic system with a curve of equilibria. Zbl 1419.34138
Chen, Yuming; Yin, Zongbin
2019
Rich dynamics in a delayed HTLV-I infection model: stability switch, multiple stable cycles, and torus. Zbl 1423.34096
Pan, Xuejun; Chen, Yuming; Shu, Hongying
2019
Domain decomposition methods for a class of spatially heterogeneous delayed reaction-diffusion equations. Zbl 1406.35455
Yi, Taishan; Chen, Yuming
2019
Spatial and temporal dynamics of a viral infection model with two nonlocal effects. Zbl 1420.92114
Wang, Xiaoyan; Chen, Yuming; Yang, Junyuan
2019
Global dynamics of an epidemic model with relapse and nonlinear incidence. Zbl 1414.34032
Chen, Yuming; Li, Jianquan; Zou, Shaofen
2019
Backward bifurcation in a stage-structured epidemic model. Zbl 1407.92135
Zhang, Fengqin; Zhao, Tian; Liu, Hanwu; Chen, Yuming
2019
Impacts of the cell-free and cell-to-cell infection modes on viral dynamics. Zbl 1401.37097
Shu, Hongying; Chen, Yuming; Wang, Lin
2018
Global dynamics of a vector-borne disease model with infection ages and general incidence rates. Zbl 1404.35463
Wang, Xia; Chen, Yuming; Liu, Shengqiang
2018
Dynamics of an age-structured host-vector model for malaria transmission. Zbl 1392.35321
Wang, Xia; Chen, Yuming; Liu, Shengqiang
2018
Dynamics of a Lorenz-type multistable hyperchaotic system. Zbl 1402.34042
Chen, Yu-Ming
2018
Disjoint hypercyclicity and topological entropy of composition operators. Zbl 1390.37012
Yin, Zongbin; Chen, Yuming; He, Shengnan
2018
Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate. Zbl 1447.92496
Yang, Junyuan; Chen, Yuming
2018
Evaluation of the tuberculosis transmission of drug-resistant strains in mainland China. Zbl 1415.92200
Yang, Junyuan; Kuniya, Toshikazu; Xu, Fei; Chen, Yuming
2018
Dynamical analysis and optimal harvesting of a stochastic three-species cooperative system with delays and Lévy jumps. Zbl 1448.92247
Shao, Yuanfu; Chen, Yuming; Dai, Binxiang
2018
Threshold dynamics of an SIRS model with nonlinear incidence rate and transfer from infectious to susceptible. Zbl 1370.92165
Li, Ting; Zhang, Fengqin; Liu, Hanwu; Chen, Yuming
2017
Algebraic-delay differential systems: $$C^0$$-extendable submanifolds and linearization. Zbl 1362.34098
Kosovalić, N.; Chen, Y.; Wu, J.
2017
The existence of homoclinic orbits in a 4D Lorenz-type hyperchaotic system. Zbl 1384.37027
Chen, Yuming
2017
Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps. Zbl 06782915
Yi, Taishan; Chen, Yuming
2017
An analytical criterion for jump phenomena in fractional Duffing oscillators. Zbl 1372.34104
Liu, Q. X.; Liu, J. K.; Chen, Y. M.
2017
Optimal harvesting in a periodic food chain model with size structures in predators. Zbl 1380.49057
Zhang, Feng-Qin; Liu, Rong; Chen, Yuming
2017
Threshold dynamics of an age-structured epidemic model with relapse and nonlinear incidence. Zbl 1404.92209
Yang, Junyuan; Chen, Yuming; Kuniya, Toshikazu
2017
Zero-zero-Hopf bifurcation and ultimate bound estimation of a generalized Lorenz-Stenflo hyperchaotic system. Zbl 1371.34054
Chen, Yu-Ming; Liang, Hai-Hua
2017
Amplitude death induced by fractional derivatives in nonlinear coupled oscillators. Zbl 07257656
Liu, Q. X.; Liu, J. K.; Chen, Y. M.
2017
Hybrid sensitivity matrix for damage identification in axially functionally graded beams. Zbl 1443.74081
Lu, Z. R.; Lin, X. X.; Chen, Y. M.; Huang, M.
2017
Instability in time-delayed switched systems induced by fast and random switching. Zbl 1365.34137
Guo, Yao; Lin, Wei; Chen, Yuming; Wu, Jianhong
2017
Global analysis of an SIR epidemic model with infection age and saturated incidence. Zbl 1365.92117
Chen, Yuming; Zou, Shaofen; Yang, Junyuan
2016
A delayed HIV-1 model with virus waning term. Zbl 1329.34129
Li, Bing; Chen, Yuming; Lu, Xuejuan; Liu, Shengqiang
2016
Effect of infection age on an SIS epidemic model on complex networks. Zbl 1356.35268
Yang, Junyuan; Chen, Yuming; Xu, Fei
2016
Global exponential stability of periodic solutions to a delay Lasota-Wazewska model with discontinuous harvesting. Zbl 1336.34114
Duan, Lian; Huang, Lihong; Chen, Yuming
2016
Optimal contraception control for a nonlinear population model with size structure and a separable mortality. Zbl 1354.49087
Liu, Rong; Zhang, Feng-Qin; Chen, Yuming
2016
Asymptotic limit cycle of fractional van der Pol oscillator by homotopy analysis method and memory-free principle. Zbl 1452.34071
Liu, Q. X.; Liu, J. K.; Chen, Y. M.
2016
A joint replenishment problem considering multiple trucks with shipment and resource constraints. Zbl 1349.90078
Chen, Y.; Wahab, M. I. M.; Ongkunaruk, P.
2016
Stability analysis of a two-strain epidemic model on complex networks with latency. Zbl 1350.92058
Yang, Junyuan; Chen, Yuming; Liu, Jiming
2016
Global stability of an SEI model for plant diseases. Zbl 1389.34131
Chen, Yuming; Yang, Junyuan
2016
An SIRS model with differential susceptibility and infectivity on uncorrelated networks. Zbl 1318.34066
Liu, Maoxing; Chen, Yuming
2015
A new Lorenz-type hyperchaotic system with a curve of equilibria. Zbl 07313365
Chen, Yuming; Yang, Qigui
2015
Global asymptotic stability of a compartmental model for a pandemic. Zbl 1330.34076
Lamichhane, Surya; Chen, Yuming
2015
Dynamics of a hyperchaotic Lorenz-type system. Zbl 1314.37021
Chen, Yuming; Yang, Qigui
2014
The global stability of an SIRS model with infection age. Zbl 1298.92096
Chen, Yuming; Yang, Junyuan; Zhang, Fengqin
2014
Complex dynamics in the unified Lorenz-type system. Zbl 1296.34117
Yang, Qigui; Chen, Yuming
2014
Stress analysis of multi-layered hollow anisotropic composite cylindrical structures using the homogenization method. Zbl 1401.74010
Sun, X. S.; Tan, V. B. C.; Chen, Y.; Tan, L. B.; Jaiman, R. K.; Tay, T. E.
2014
Existence of solutions for a damped nonlinear impulsive problem with Dirichlet boundary conditions. Zbl 1291.34059
Zhang, Dan; Dai, Binxiang; Chen, Yuming
2014
Unimodal dynamical systems: comparison principles, spreading speeds and travelling waves. Zbl 1308.35126
Yi, Taishan; Chen, Yuming; Wu, Jianhong
2013
Dynamics of a delayed predator-prey model with predator migration. Zbl 1351.34082
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Abstract algebraic-delay differential systems and age structured population dynamics. Zbl 1291.34124
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New SDP models for protein homology detection with semi-supervised SVM. Zbl 1273.90143
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The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions. Zbl 1298.34011
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SDP relaxation for semi-supervised support vector machine. Zbl 1263.90051
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Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters. Zbl 1236.74071
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Bifurcation analysis of aeroelastic systems with hysteresis by incremental harmonic balance method. Zbl 1308.74042
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Equivalent linearization method for the flutter system of an airfoil with multiple nonlinearities. Zbl 1426.74125
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Threshold dynamics of scalar linear periodic delay-differential equations. Zbl 1264.34139
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Delay for the capacity-simplicity dilemma in associative memory attractor networks. Zbl 1245.93117
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The existence of mild solutions for impulsive fractional partial differential equations. Zbl 1227.34009
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On a new idiom in the study of entailment. Zbl 1272.03105
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A spatial $$6R$$ linkage derived from subtractive Goldberg 5R linkages. Zbl 1385.70025
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Homotopy analysis method for nonlinear dynamical system of an electrostatically actuated microcantilever. Zbl 1204.65097
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On the existence of gap solitons in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity. Zbl 1193.35176
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Periodic solutions of a $$2n$$th-order nonlinear difference equation. Zbl 1232.39019
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Second-order differentiability with respect to parameters for differential equations with adaptive delays. Zbl 1201.34096
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#### Cited by 2,125 Authors
46 Chen, Fengde 32 Chen, Yuming 29 Huang, Lihong 26 Shi, Haiping 22 Liu, Xia 21 Wu, Jianhong 21 Zhou, Zhan 19 Guo, Shangjiang 17 Zhang, Yuanbiao 16 Wei, Junjie 15 Li, Zhong 14 Elaiw, Ahmed M. 14 Teng, Zhi-dong 14 Xie, Xiangdong 13 Chen, Guanwei 13 Yang, Junyuan 12 Cheng, Sui Sun 12 Yi, Taishan 11 Dai, Binxiang 11 Wang, Haijun 11 Zhao, Kaihong 10 Cao, Jinde 10 Colominas, Ignasi 10 Hernández, Eduardo M. 10 Jiang, Weihua 10 Xu, Changjin 10 Zou, Xingfu 9 Chen, Xiaoxing 9 Li, Xianyi 9 Li, Yongkun 9 Lin, Guo 9 Nogueira, Xesús 8 Deng, Xiaoqing 8 Huang, Chuangxia 8 Liu, Gui Rong 8 Luo, Zhenguo 8 Ma, Shiwang 8 Wang, Wentao 8 Xu, Rui 8 Yan, Zuomao 7 Chen, Lijuan 7 He, Yigang 7 Hou, Chengmin 7 Khelladi, Sofiane 7 Liu, Yuji 7 Pandey, Dwijendra Narain 7 Ruan, Shigui 7 Xia, Yonghui 7 Yang, Qigui 7 Zhou, Tao 6 Bai, Yanqin 6 Chadha, Alka 6 Chen, Yameng 6 Fang, Hui 6 Han, Maoan 6 Li, Peiluan 6 Liao, Xinyuan 6 Mu, Jia 6 Qian, Youhua 6 Shao, Yuanfu 6 Shi, Jinlin 6 Tang, Xianhua 6 Wang, Hongbin 6 Wang, Jinliang 6 Wang, Lin 6 Wang, Xia 6 Wei, Zhouchao 6 Zhang, Guang 6 Zhang, Wei 5 Chen, Haibo 5 Cueto-Felgueroso, Luis 5 Fang, Qinhua 5 Ganji, Davood Domiri 5 Han, Bo 5 Hu, Wenjie 5 Huang, Jianhua 5 Huo, Hai-Feng 5 Jiang, Jifa 5 Kuniya, Toshikazu 5 Lee, Yong-Hoon Lee 5 Liu, Zhijun 5 Odibat, Zaid M. 5 Ramírez, Luis 5 Remmel, Jeffrey B. 5 Saker, Samir H. 5 Song, Yongli 5 Tian, Xiaohong 5 Wu, Daiyong 5 Xu, XiangHui 5 Yuan, Zhaohui 5 Zhang, Chunrui 5 Zhang, Fuchen 5 Zhang, Qinqin 5 Zhou, Shengfan 5 Zhou, Yong 4 Alshamrani, Noura H. 4 Azevedo, Katia A. G. 4 Bai, Dingyong 4 Băleanu, Dumitru I. 4 Chen, Jiun-Shyan ...and 2,025 more Authors
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# 6.1. Gaussian Smoothing and Gaussian Derivatives¶
Consider an image of a photo printed in a newspaper. Because the image is depicted at larger size then it was printed in the newspaper, the individual blobs of ink are visible. In black and white printing only black ink is used, the ‘illusion’ of gray tones is due to the fact that the human eye cannot resolve too small details. We could say that the human eye is smoothing the images.
We can do the smoothing with the computer. In the next figure we show a sequence of images all of which are local mean filtered versions of the news paper image. The smoothing (local mean) is done using a Gaussian weight function.
A smoothed function is the convolution of the orginal function $$f$$ with the Gaussian weight function $$G^s$$:
$G^s(x,y) = \frac{1}{2\pi s^2}\exp\left(-\frac{x^2+y^2}{2s^2}\right)$
The size of the local neighborhood is determined by the scale of the Gaussian weight function.
In the plot three 1D Gaussian functions are shown for scales 3, 5 and 7. The graph of the 2D Gaussian function is obtained by rotating the 1D function graphs around the vertical $$z$$-axis.
## 6.1.1. Properties of the Gaussian Convolution¶
The Gaussian kernel function used in a convolution has some very nice properties.
Separability
The property that is of great importance in practice is that is a separable function in the sense that we may write:
$G^s(x,y) = G^s(x) G^s(y)$
where $$G^s(x)$$ and $$G^s(y)$$ are Gaussian functions in one variable:
$G^s(x) = \frac{1}{s\sqrt{2 \pi}} \exp\left( -\frac{x^2}{2 s^2}\right)$
It is not hard to prove (starting from the definition of the convolution) that a separable kernel function leads to a separable convolution in the sense that we may first convolve along the rows with a one dimensional kernel function followed by a convolution along the columns of the image. The advantage is that for every pixel in the resulting image we have to consider far less values in the weighted sum then we would have to for a straightforward implementation.
Semi Group
If we take a Gaussian function $$G^s$$ and convolve it with another Gaussian function $$G^t$$ the result is a third Gaussian function:
$G^s \ast G^t = G^{\sqrt{s^2+t^2}}$
Mathematicians refer to such a property with the term semi group (it would be a group in case there would be an ‘inverse Gaussian convolution’).
From a practical point of view this is an important property as it allows the scale space to be build incrementally, i.e. we don’t have to run the convolution $$f_0\ast G^s$$ for all values of $$s$$. Say we have already calculated $$f^t = f_0\ast G^t$$ (with $$t<s$$), then using the associativity and the above property we have:
$f^s = f^t \ast G^{\sqrt{s^2-t^2}}$
Note that $$\sqrt{s^2-t^2}<s$$ and thus the above convolution will be faster then the convolution $$f_0\ast G^s$$.
Smoothness and Differentiability
Let $$f_0$$ be the ‘original’ image and let $$f^s$$ be any image from the scale space (with $$s>0$$). Then no matter what function $$f_0$$ is, the convolution with $$G^s$$ will make into a function that is continuous and infinitely differentiable. Using Gaussian convolutions to construct a scale space thus safely allows us to use many of the mathematical tools we need (like differentation when we look at the characterization of local structure).
## 6.1.2. Calculating Derivatives of Sampled Functions¶
Building a model for local image structure based on calculating derivatives was considered a dangerous thing to do in the early days of image processing. And indeed derivatives are notoriously difficult to estimate for sampled functions. Remember the definition of the first order derivative of a function $$f$$ in one variable:
$\frac{d f}{d x}(x) = \lim_{dx\downarrow0} \frac{f(x+dx)-f(x)}{dx}$
Calculating a derivative requires a limit where the distance between two points ($$x$$ and $$x+dx$$ is made smaller and smaller. This of course is not possible directly when we look at sampled images. We then have to use interpolation techniques to come up with an analytical function that fits the samples and whose derivative can be calculated.
Let $$F$$ be a sampled image then we may calculate the first order derivative $$F_x$$ as:
$F_x = F \star \begin{Bmatrix}1&\underline{-1}&0\end{Bmatrix}$
or with:
$F_x = F \star \begin{Bmatrix}0&\underline{1}&-1\end{Bmatrix}$
or with:
$F_x = F \star \half\begin{Bmatrix}1&\underline{0}&-1\end{Bmatrix}$
Note that all these ‘derivative images’ are only approximations of the sampling of $$f_x$$. They all have their role in numerical math. The first one is the right difference, the second the left difference and the third the central difference.
In these lecture notes we combine the smoothing, i.e. convolution with a Gaussian function, and taking the derivative. Let $$\partial$$ denote any derivative we want to calculate of the smoothed image: $$\partial(f\ast G^s)$$. We may write:
$\partial ( f \ast G^s) = f \ast \partial G^s$
Even if the image $$f$$ is a sampled image, say $$F$$ then we can sample $$\partial G^s$$ and use that as a convolution kernel in a discrete convolution.
Note that the Gaussian function has a value greater than zero on its entire domain. Thus in the convolution sum we theoretically have to use all values in the entire image to calculate the result in every point. This would make for a very slow convolution operator. Fortunately the exponential function for negative arguments approaches zero very quickly and thus we may truncate the function for points far from the origin. It is customary to choose a truncation point at about $$3s$$.
Note that because $$G^s$$ is separable, $$\partial G^s$$ is separable as well. This allows for separable convolution algorithms for all Gaussian derivatives.
## 6.1.3. Algorithms for Gaussian Convolutions¶
There are several ways to implement the Gaussian (derivative) convolutions to work on sampled images:
• Straightforward implementation. This is the direct implementation of the definition of the discrete convolution using the fact that the Gaussian function is seperable and thus the 2D convolution can be implemented by first convolving the image along the rows followed by a convolution along the columns.
In this straightforward implementation the Gaussian function is sampled on the same grid as the image to be convolved. Although the Gaussian function has an unbounded support (i.e. $$G^s(x)>0$$ for all $$x$$) we may ‘cut-off’ the sampled version for values of $$|x|>t$$. The value of $$t$$ is scale dependent! (this is part of the Lab Exercises).
It should be evident that for small scale values this straightforward implementation will not be accurate. For, say, $$s<1$$ the Gaussian function is restricted to only a few pixels. Such a ‘small’ Gaussian function is really not suited to be sampled on the grid with $$\Delta x$$.
• Interpolated Convolution. Instead of bluntly sampling the Gaussian function and calculate the discrete convolution we could first interpolate the discrete image, then calculate the convolution integral and finally sample to obtain the discrete image (this is detailed in the section “From Convolution Integrals to Convolution Sums” in the previous chapter). The interpolated convolution turns out to be equivalent with a discrete convolution with a weight function that is slightly different from the Gaussian (derivative) weight function.
• Convolution using the Fast Fourier Transform. In we first calculate the Fourier Transform of the input image and the convolution kernel the convolution becomes a point wise multiplication. Let the input image be of size $$N\times N$$ the spatial implementation is of order $$O(N^2)$$ whereas the FFT version is $$O(N\log N)$$. This may seem like an important speed up, still the spatial implementation are nowadays more often used.
• Infinite Response Convolution. These are probably the fastest implementations. The gain in speed is obtained because the local neighborhood used is of the same size regardless of the scale of the Gaussian function. Disadvantage of this method is that it is only an approximation and that calculating Gaussian derivatives is troublesome. |
# Difference between revisions of "Channel with feedback"
A communication channel used for transmission of information from a source of information (cf. Information, source of) to a receiver such that at any moment of time at the input one knows some information about the signals received at the output prior to this moment; this information can be used for the selection of the next signal to be transmitted over the channel. A description of one of the possible schemes for the transmission of information over a discrete-time channel in the presence of full feedback is given below. Let the information at the channel's input be given by a random variable $\xi$ taking values in some measurable space $( \mathfrak X , S _ {\mathfrak X } )$. The information derived to the addressee (the receiver) is a random variable $\xi$ taking values in the measurable space $( \widetilde{\mathfrak X} , S _ {\widetilde{\mathfrak X} } )$. Suppose that for the transmission of the information $\xi$ a segment of length $n$ of some discrete-time channel is used. The input and output signals $( \eta _ {1} \dots \eta _ {n} )$ and $( \widetilde \eta _ {1} \dots \widetilde \eta _ {n} )$ of this channel segment are given by random vectors whose components take values in measurable spaces $( Y , S _ {Y} )$ and $( \widetilde{Y} , S _ {\widetilde{Y} } )$, respectively. The method of transmitting information over such a channel using complete feedback is given by a set of $n$ encoding functions
$$f _ {1} ( x) , f _ {2} ( x , \widetilde{y} _ {1} ) \dots f _ {n} ( x , \widetilde{y} _ {1} \dots \widetilde{y} _ {n-} 1 ) ,$$
$$x \in \mathfrak X ,\ \widetilde{y} _ {i} \in \widetilde{Y} ,\ i = 1 \dots n - 1 ,$$
with values in $Y$, and a decoding function $g ( \widetilde{y} _ {1} \dots \widetilde{y} _ {n} )$, $\widetilde{y} _ {i} \in \widetilde{Y}$, $i = 1 \dots n$, with values in $\widetilde{\mathfrak X}$, by means of the relations
$$\eta _ {k} = f _ {k} ( \xi , \widetilde \eta _ {1} \dots \widetilde \eta _ {k-} 1 ) ,\ \ k = 1 \dots n ,$$
$$\widetilde \xi = g ( \widetilde \eta _ {1} \dots \widetilde \eta _ {n} ) .$$
These relations show that the selection of the next signal $\eta _ {k}$ for transmission over a channel with feedback depends on the transmitted information $\xi$ and also on the signals $\widetilde \eta _ {1} \dots \widetilde \eta _ {k-} 1$ received at the output of the channel prior to this moment. In reality this means that there is the possibility of instantly and noiselesly delivering information at the input of the channel about the signal received at its output. In this case it is often said that alongside the channel used for transmission of information in the forward direction (that is from the source of the information to the addressee), there is a feedback channel (that is, a channel over which information is transmitted in the backward direction) with an infinite transmission rate (capacity, see Transmission rate of a channel). A more realistic assumption is that the feedback channel is not noiseless, that is, the information about the output signal of the channel received at its input may contain random errors. In this case one talks about a channel with incomplete feedback.
As in the ordinary case, the notion of capacity of a channel with feedback enters; it is the least upper bound of the transmission rates under which information can be sent using the (en)coding and decoding methods described above, with arbitrarily small error probability. In the general case, the capacity of a channel with feedback is greater than the usual channel capacity. It has been established, however, that for memoryless channels these channel capacities coincide. For channels with complete feedback, (en)coding and decoding algorithms have been proposed that are simple to describe and highly effective.
#### References
[1] R.L. Dobrushin, "Transmission of information in channels with feedback" Teor. Veroyatnost. i Primenen. , 3 : 4 (1958) pp. 395–412 (In Russian) (English summary) [2] , Feedback communication systems , New York (1961) [3] K.Sh. Zigangirov, "Upper bounds for the error probability in channels with feedback" Probl. Peredachi Informatsii , 6 : 2 (1970) pp. 87–92 (In Russian) [4] G.L. Turin, "Notes on digital communication" , New York-Cincinatti-Toronto-London-Melbourne (1969)
How to Cite This Entry:
Channel with feedback. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Channel_with_feedback&oldid=46306
This article was adapted from an original article by R.L. DobrushinV.V. Prelov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article |
# Independent samples test for mean without normal distribution with T-score
I have two independent samples of male and female order value.
Female number of observations = 26887
Male number of observations = 12928
Female mean order value = 133.03
Male mean order value = 145.24
Female sample variance = 10,406.38
Male sample variance = 17,563.87
Pooled variance = 12,730.36
T-score = 0.11
p-value = 0.50926
Same on the image
Terrible p-value 🤦♂️
Samples distribution is far from normal
Questions:
1. What is the reason for such a bad p-value?
2. How can I improve it?
3. Is CLT applicable here?
• The reason for such a high p-value is that you have made a calculation error somewhere (a Welch t-test gives an absolute t-value of about 9.24; an equal variance two sample t test gives an absolute t-value of about 10.11) . Please show what formulas you used, giving explicit steps – Glen_b -Reinstate Monica Feb 8 at 9:54
• Added screenshots of the formulas – Svetoslav Dimitrov Feb 8 at 9:57
• Yep, the error is quite plain. – Glen_b -Reinstate Monica Feb 8 at 9:58
• However, I meant "please show the algebraic formulas" not "please show me spreadsheet formulas" – Glen_b -Reinstate Monica Feb 8 at 10:06
Your calculation of the test statistic is wrong. You're dividing the difference in means by the pooled standard deviation, rather than the standard error of the difference in means.
The formula for the (equal-variance) two sample t-test statistic would be:
$$\frac {{\bar {x}}_{1}-{\bar {x}}_{2}}{s_{p}\cdot {\sqrt {{\frac {1}{n_{1}}}+{\frac {1}{n_{2}}}}}}$$
but you seem to have
$$\frac {\bar{x}_1-\bar{x}_2}{s_{p}}$$ |
# Is some thing wrong with the epsilon-delta definition of limit??
In the epsilon-delta definition of limit which is:
For all $\epsilon>0$ there exists a $\delta>0$ such that, whenever $|x-a|<\delta$ then $|f(x)-L|<\epsilon$ .
Now since $\epsilon$ is given and it should be proven that there is some $\delta$ for the given $\epsilon$, then I think the rest of the definition should have been:
$|f(x)-L|<\epsilon \implies |x-a|<\delta$ .
Please tell me whether I'm right or not.
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Downvoting seems inappropriate. OP has thought about the matter and happens to have reached an incorrect conclusion. – André Nicolas Jun 28 '14 at 4:08
I believe you are confusing the notion of hypothesis/conclusion with the idea of "$\epsilon$ is given$"/"$\delta$is constructed from it". – MPW Jun 28 '14 at 4:27 +1, this is a nice question, i just realized that i do not understand it myself. Nevertheless there are indeed other formulations (or formalizations) of analysis which are more intuitive (e.g non-standard analysis, which btw is closer to the original formulations of calculus by Newton-Leibnitz ) – Nikos M. Jun 28 '14 at 5:05 Note that this is not the definition of limit. Without adding$0<|x-a|$to the condition, the conclusion can hold for all$\epsilon$only if$f(a)=L$. – Dennis Jun 29 '14 at 2:57 @Jack, check also this answer on MO discussing this topic and ways to (intuitively) present it/teach it etc.. – Nikos M. Jun 30 '14 at 17:04 ## 3 Answers Your proposed definition For all$\epsilon > 0$there exists a$\delta > 0$such that$|f(x)-L| < \epsilon \implies |x-a| < \delta$. has quite a few problems with it. For instance, let$f(x) = 0$and consider$\displaystyle\lim_{x \to 0}f(x)$. In any reasonable definition of a limit, we should have$\displaystyle\lim_{x \to 0}0 = 0$. So, we need to prove: For all$\epsilon > 0$there exists a$\delta > 0$such that$|0-0| < \epsilon \implies |x-0| < \delta$Unfortunately,$|0-0| < \epsilon$is true for any$x \in \mathbb{R}$, but$|x-0| < \delta$is false for any$x > \delta$. Thus, there is never a$\delta > 0$which makes "$|0-0| < \epsilon \implies |x-0| < \delta$" a true statement. Therefore, by your proposed definition,$\displaystyle\lim_{x \to 0}0$is not$0$. - This does not explain why it is phrased that way. if the alternative definition (as suggested by OP) has problems, why this (working) definition is phrased like this? Should it be phrased otherwise and if so how, in order to not have this ambiguity? – Nikos M. Jun 28 '14 at 5:12 Or why not have the OP's definition and add this problematic case of$f(x)=0$as special case (like it is done for$0! = 1$)? Or why not say "for all$\delta$there is an$\epsilon$.." etc.., since this is what is done here? – Nikos M. Jun 28 '14 at 5:13 @NikosM.: there would be literally uncountable number of special case, as it's trivial to construct plenty more (here are some more$\sin(x),\exp(x),\tan(x),x^{-1}$). As for ambiguity, this definition can be directly translated into a logical statement, so where is the ambiguity? – Gina Jun 28 '14 at 6:56 @Gina, thanks for the comemnt, but it does not provide the kind and depth of explanation (and intuitive understanding) i would like (of course the OP will select an answer), see my answer for what i would like to have as an answer to this – Nikos M. Jun 28 '14 at 15:37 The way I used to think about it is this: it is something like a Space Invaders game (if you remember those). The enemy is firing epsilons at you. For each epsilon that comes at you, you have to be able to counter by finding a delta such that for every x such that |xa|<δ, then |f(x)−L|<ϵ If some epsilon arrives such that you can't find a delta, you lose. For example, suppose that f(x) = 1 for x < 0.5 and f(x) = 2 for x >= 0.5. (Yes, a step function.) Look at a = 0.5. Try L = 1.5. Suppose ϵ = 1 arrives. Then you're OK because you can reply with δ = 0.1 (for example). For values of x between 0.4 and 0.6, the values for f(x) are either 1 or 2, so |f(x) - L| is always 0.5, and it is true that |f(x) - L| < ϵ = 1. But if ϵ = 0.2 arrives, then it doesn't matter how small a δ you reply with, you can't get |f(x) - L| < ϵ = 0.2 for all the x between 0.5 - δ and 0.5 + δ. So you lose, and the limit isn't L = 1.5. With a little bit more effort you can demonstrate that it doesn't matter what value of L you try for the limit, if ϵ = 0.2 arrives, you lose. So in this example the limit of f(x) as x tends to 0.5 doesn't exist. Intuitively, of course it doesn't exist, but we want to see how the textbook definition works out for this example. The definition in the textbooks is correct. It is hard to understand, but maybe the Space Invaders analogy helps. - +1 for the analogy. – dwarandae Jun 28 '14 at 8:44 Your answer is a good one, except that the definition as written in the question is not completely correct. – user21820 Jun 28 '14 at 9:05 I like this as an explanation of why limits are defined the way they are, but is it possible to extend or adapt the analogy to explain why the alternate definition proposed in the question doesn't work? Like, what if the enemy fired$\delta$s instead of$\epsilon$s? Why wouldn't that lead to a useful definition of a limit? – David Z Jun 28 '14 at 18:30 @NikosM.: You're absolutely wrong. Read his answer again; which explicitly says that ε comes first and then you have to generate a suitable δ. – user21820 Jun 29 '14 at 5:12 @NikosM.: We have adequately specified what is wrong with your statements. For example here, I explicitly said that "ε comes first and then you have to generate a suitable δ". And no one is criticizing your statements based on convention at all. If you want a more in depth explanation, ask a new question, but don't pretend to know what you are talking about, and we will be glad to address your issues in understanding. – user21820 Jun 29 '14 at 14:41 Firstly, I suggest you learn logic first, otherwise it is very difficult to understand a lot of things rigorously. It seems you do not understand scoping of quantifiers, which is why the English phrasing, although unambiguous, is not clear to you. Secondly, there is a mistake in the definition as you have written it. Let me write the correct definition in terms of its logical structure, which I suggest you do for definitions and theorems whose structure you do not understand perfectly. Limit Definition$\lim_{x \to a} f(x) = L$iff: For any$ε > 0$: For some$δ > 0$: For any$x \in Dom(f)$: If$0 < | x - a | < δ$:$| f(x) - L | < ε$Let us go through it properly. The limit of a function$f$at$a$being$L$means that no matter what positive$ε$you give me, I can give you a positive$δ$such that the pair$(ε,δ)$has a certain property. That property is that no matter what$x$you give me from the domain of$f$, the triple$(ε,δ,x)$has a certain (other) property, which is that if the distance between$x$and$a$is less than$δ$, then the distance between$f(x)$and$L$is less than$ε$. Note that this last property says nothing at all if the triple currently in consideration is such that$x$and$a$are at least$δ$apart. So why is it defined this way? Let us give a more intuitive sense of a limit. We can look at a landscape through a window. If we look through at a landscape through a smaller window, we will surely not see more, and for most natural landscapes the region we can see will become more and more 'bland' as the window shrinks (about a fixed centre). (At first we see a tree with branches and leaves, later we see only a leaf, later we see only a patch of a single colour, green.) If the entire region that we see gets closer and closer in colour to green as the window shrinks, then we can say that the limit colour at the 'centre' of the shrinking window is green. This is not quite the mathematical definition yet. Imagine that there is a minuscule dot at the centre of the window, so we cannot see the colour of the landscape there. The limit is still said to exist. But what does "closer and closer" mean? It means that no matter what positive error margin we desire, as the window shrinks to zero size, eventually the colour of the region we can see will always remain near the limit to within that error margin. Consider the landscape to be a function$f$, where$f(x)$is the colour of the region that can be seen when we look through point$x$on the window. Call the centre of the window$a$. Consider the window size to be$δ$and the error margin to be$ε$. Then our above notion means that$f$has a limit colour$c$at its centre$a$if and only if, for any positive$ε$, we can find a positive window size$δ$such that once it shrinks smaller than that size, all the colours$f(x)$we can see through it ($| x - a | < δ$) are within$ε$of the colour$c$($| f(x) - c | < ε$). Now if the window has its centre exactly on the boundary of an object which is of a different colour than its background, the limit colour will not exist because no matter how small we make the window, we will see a little bit of the object and a little of the background. This corresponds to a jump discontinuity at$a$. Also, we couldn't see the colour of the landscape behind the centre of the window. It could be the same colour as the limit colour, in which case$f$is continuous at$a$. But it could be a different colour, in which case$f$has a removable discontinuity at$a$. Finally, the landscape could have infinite detail that keeps varying widely between colours (within the window) no matter how small we shrink the window. A mathematical example would be if$f(x) = \sin(\frac{1}{x})$and$a = 0$. In this case$f$also has no limit at$a\$, and the discontinuity is neither a jump discontinuity nor a removable discontinuity.
Lastly, note that this analogy with windows and landscapes immediately applies to the concept of continuity in general metric spaces. After all, we would have to define what distance between two colours means, but the idea is very natural.
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Related to pointwise continuity is uniform continuity, pointwise convergence and uniform convergence, which when written out to make the logical structure explicit, will clearly show how the order of the quantifiers determine the meaning. See math.stackexchange.com/a/813372/21820. – user21820 Jun 28 '14 at 9:58
+1, this is nice analysis, this was the content of my answer too, to elucidate the scope of the quantifiers (as in this answer) and also link this to the practice of the definition (which raised some negative comments btw) – Nikos M. Jun 28 '14 at 15:26
@NikosM.: No; it is completely different from your answer, as has been pointed out. – user21820 Jun 29 '14 at 5:17 |
Scripting Configuration Settings¶
Prerequisites¶
• The following methods are exposed by the ConfigSettings object implemented by the module Thinkbox.Sequoia.Configuration
• Before calling these methods, you must ensure the module is imported.
import Thinkbox.Sequoia.Configuration 1.0
Methods¶
<QVariant> ConfigSettings.getData ( QString key)
• Returns the value of the specified Sequoia configuration key.
<void> ConfigSettings.setData ( <QString>key <QVariant>value)
• Sets the value of the Sequoia configuration key specified by the first argument to the value provided by the second argument.
• To get a list of available Sequoia configuration keys, take a look at the file “sequoia_constants.json” located in the Sequoia installation folder - the “Key” entries in it represent the keys used by the above methods. |
fdupress Editor Aug 8, 2011 at 11:28 AM Hi all, I am currently fighting with the verification of some byte array library functions. In particular, I would like to express that these functions can read or write the contents of the arrays passed in as arguments. If specifying the writing is easy (the writes clause takes care of everything), specifying the reads in a generic way is much more of a pain. Indeed, the contents of a byte array can be readable for one of several reasons: all elements are thread local or mutable (\thread_local_array or \mutable_array), the array is a VCC array object and is known to be wrapped (\wrapped(unsigned char[length]) address), the array is contained in a VCC array object that is known to be wrapped (for example \exists size_t l; unsigned char arr; \wrapped((unsigned char[l]) arr) && \subset(\array_members(address,length),\array_members(arr,l)), which causes an OOPS at the moment), the array is (contained in) a VCC array object that is in the ownership domain of a wrapped structure (some variation of the above with an added layer of \embedding (?)), the array is (contained in) a VCC array object that is part of the non-volatile extent of a wrapped structure, possibly a bunch more situations I have not run into yet... My question is: is there any way to generically express that a given memory range can be read, allowing the body of a function to read without proving anything more, and allowing the caller to simply prove any one of the above conditions holds? In cases where the body of the function itself requires the readability to be a bit more strict (for example, if thread locality breaks), additional contracts could be added, but it would be nice to have a default case for simple functions: simple things should be easy... Using a reads clause sounds like the perfect solution from the expressivity and the specification point of view, but it doesn't do anything for non-pure functions, as far as I know. I do realize that all the previous cases can be reduced to case number 1. by unwrapping and reinterpretation, but it would be a pity to write the memory just to prove that you can read from it. I also realize that this may be very specific to arrays of primitive objects, and may not hold for arrays of structures, especially if those structure have volatile fields. I am currently using VCC 2, but am willing to move to VCC 3 is necessary to makes things a bit easier. Also, at the moment, I would be happy to have a solution for 1., 2., 3. and 4. only, as I don't really have any cases of 5. MarkHillebrand Coordinator Aug 11, 2011 at 7:57 PM Hi Francois, indeed, this is not so easy, although some of your cases collapse. Disregarding the concurrent case, all of the above should be covered by \thread_local_array(a,n). Remember that this is in principle just an abbreviation for \forall unsigned x; x < n ==> \thread_local(&a[x])), which should be sufficient to do the read. As you note yourself, thread locality is easy to loose, and it becomes more complicated then. The elements may be mutable, or (deep) inside an ownership domain. In the latter case, additional help, in terms of providing witnesses for domain root and embedding of the array elements is required (alternatively, existential quantification of those could work). At the call site, you have to convince VCC that the accessed elements are indeed thread-local, which requires expanding the ownership domain far enough. (Potentially, \wrapped_with_deep_domain, added in http://vcc.codeplex.com/SourceControl/changeset/changes/096453a32c68, could help, but I haven't tried this yet). The concurrent case is trickier, because you can't require thread-locality / mutability. Instead, a claims that guarantees the closedness of the embedding has to be passed in, which is clumsy. Also, to make a function work both for the concurrent non-volatile and sequential case, you would currently have to required the disjunction of the versions. Below I've added some examples; they wouldn't cover all your cases (in particular not the concurrent one), but just to give you an idea. I couldn't yet make the read2() verify with "vcc /2", it verifies with "vcc /3" only. I think it might be the case, that the way that the typestate is encoded with "vcc /2" might prohibit the verification of that functions, but that needs further investigation. Unfortunately, I don't know of a nicer version of all of that... Hope that helps, Mark ///newsyntax #include char read1(char *x, unsigned len) _(requires 0 < len) _(requires \thread_local_array(x, len)) _(returns x[len - 1]) { return x[len - 1]; } void call1() { char x[8]; read1(x, 8); } struct S { char x[8]; }; void call2(struct S *s) _(requires \mutable(s)) { read1(&s->x, 8); } void call3(struct S *s) _(requires \wrapped(s)) { read1(&s->x, 8); } struct T { _(as_array) char x[8]; _(invariant \mine((char[8]) x)) }; void call4(struct T *s) _(requires \wrapped(s)) { read1(&s->x, 8); } struct U { struct T t; _(invariant \mine(&t)) }; void call5(struct U *s) _(requires \wrapped(s)) { _(assert &s->t \in \domain(s)) // multiple assertions like this are needed for more deeply nested ownership domains read1(&s->t.x, 8); } void call6(char *x, unsigned len) _(requires 0 < len) _(requires \wrapped((char[len])x)) { read1(x, len); } void call7(char *x, unsigned len) _(requires 0 < len) _(requires \wrapped((char[len+2])x)) { read1(x + 1, len); } struct Unrelated { int x; } Unrelated; void write_unrelated() _(writes &Unrelated); // This one requires /3 // Note: this doesn't specify the mutable alternative... char read2(char *x, unsigned len _(ghost \object embedding) _(ghost \object root)) _(requires \wrapped(root)) _(requires embedding \in \domain(root)) _(requires embedding == \embedding(x)) _(requires &Unrelated != root) _(writes &Unrelated) _(requires 0 < len) _(requires \thread_local_array(x, len)) _(returns *x) { // All of these hold: //_(assert root \in \domain(root)) //_(assert \non_primitive_ptr(root)) //_(assert \non_primitive_ptr(embedding)) write_unrelated(); return *x; } void call8(struct S *s) _(requires \wrapped(s)) _(writes &Unrelated) { read2(&s->x, 8 _(ghost s) _(ghost s)); } /* Verification of T#adm succeeded. Verification of U#adm succeeded. Verification of read1 succeeded. Verification of call1 succeeded. Verification of call2 succeeded. Verification of call3 succeeded. Verification of call4 succeeded. Verification of call5 succeeded. Verification of call6 succeeded. Verification of call7 succeeded. Verification of read2 succeeded. */ ` fdupress Editor Aug 11, 2011 at 8:38 PM Thanks Mark. I started to dive a bit in the Boogie definitions after posting and realized that my initial idea was wrong (I originally thought that thread_local required the object to be open). I didn't even want to think about the concurrent case, but I guess the least I can do in exchange for your help is explore it a bit and come back later with what I find down there :) Thanks again, Francois |
Volume 106
## Mapping Hilbert cube manifolds to ANR’s: A solution of a conjecture of Borsuk
Pages 1-18 by James E. West | From volume 106-1
## An algebraic formula for the degree of a $C^\infty$ map germ (with an appendix by Bernard Teissier “Sur une inégalité à la Minkowski pour les multiplicités)
Pages 19-44 by David Eisenbud, Harold I. Levine, Bernard Teissier | From volume 106-1
## On the moduli of vector bundles on an algebraic surface
Pages 45-60 by David Gieseker | From volume 106-1
## Compact 3-manifolds of constant negative curvature fibering over the circle
Pages 61-72 by Troels Jørgensen | From volume 106-1
## Homology for zero-dimensional nonwandering sets
Pages 73-92 by Rufus Bowen, John Franks | From volume 106-1
## Weak type estimates for singular values and the number of bound states of Schrödinger operators
Pages 93-100 by Michael Cwikel | From volume 106-1
## The homeomorphism group of a compact Hilbert cube manifold is an ANR
Pages 101-119 by Steve Ferry | From volume 106-1
## Some $C^\ast$-algebras with outer derivations. III
Pages 121-143 by George A. Elliott | From volume 106-1
## Systems of differential equations with regular singularities and their boundary value problems
Pages 145-200 by Masaki Kashiwara, Toshio Oshima | From volume 106-1
## A generalized sphere theorem
Pages 201-211 by Karsten Grove, Katsuhiro Shiohama | From volume 106-1
## On boundaries of complex analytic varieties. II
Pages 213-238 by F. Reese Harvey, H. Blaine Lawson | From volume 106-2
## Characterization of Fuchsian group whose integrable forms are bounded
Pages 239-258 by Douglas Niebur, Mark Sheingorn | From volume 106-2
## Random rearrangements of Fourier coefficients
Pages 259-268 by Daniel M. Oberlin | From volume 106-2
## La transversalité topologique
Pages 269-293 by Alexis Marin | From volume 106-2
## Tensor products of finite and infinite dimensional representations of semisimple Lie groups
Pages 295-308 by Gregg Zuckerman | From volume 106-2
## Asymptotic behaviour of free boundaries at their singular points
Pages 309-317 by Luis A. Caffarelli, Néstor Marcelo Rivière | From volume 106-2
## Local biholomorphic straightening of real submanifolds
Pages 319-352 by Michael Freeman | From volume 106-2
## A characterization of Chevalley groups over fields of odd order. Part I
Pages 353-398 by Michael Aschbacher | From volume 106-2
## A characterization of Chevalley groups over fields of odd order. Part II
Pages 399-468 by Michael Aschbacher | From volume 106-3
## Periodic phenomena in the Adams-Novikov spectral sequence
Pages 469-516 by Haynes R. Miller, Douglas C. Ravenel, W. Stephen Wilson | From volume 106-3
## On the singular cardinal problems. II
Pages 517-547 by Menachem Magidor | From volume 106-3
## Anosov foliations are hyperfinite
Pages 549-565 by Rufus Bowen | From volume 106-3
## Factorization of $L^\infty$ functions
Pages 567-572 by Sheldon Axler | From volume 106-3
## Orbit spaces of unitary representations, ergodic theory, and simple Lie groups
Pages 573-588 by Robert J. Zimmer | From volume 106-3
## Isomorphisms of Galois groups of algebraic function fields
Pages 589-598 by Koji Uchida | From volume 106-3
## On the non-triviality of some group extensions given by generators and relations
Pages 599-612 by Oscar S. Rothaus | From volume 106-3 |
# User Portlet
Douglas Kubler
Discussions
Strange indeed the documentation says it should be: In[1]:= CityData["London", "Coordinates"] Out[1]= GeoPosition[{51.5, -0.116667}] But upon execution: In[1]:= CityData["London", "Coordinates"] Out[1]= {51.5,...
Douglas, > Consider this to be the genetic code, and for once and all we are > going to state how many possible codes there are! 64 bins for the > codons. 21 items, for the 20 amino acids plus one stop codon. Does Nature know left from right?...
You're missing a semicolon sol = Solve[x + y == 2 && x - y == 1, {x, y}]; x = x /. Flatten[sol]; y = y /. Flatten[sol] Undo the symbol damage with Clear["x"];Clear["y"]; Re-execute and your answers will be OK.
Nice work. I checked that *in situ* image modifications via the toolbar that appears when an image is clicked are undoable. The undo makes the workings of the "Actions & Tools" menu clumsy. I would prefer to remove the mini-preview of a... |
# How to limit camera pitch (x rotation) between two angles
I use this script rotate the camera on its local X axis:
float v = verticalSpeed * Input.GetAxis("Mouse Y");
transform.Rotate(-v, 0, 0);
Right now this lets the player look up & down without limit, wrapping around a full 360 degrees. How can I limit this so they can look only 90 degrees up or 90 degrees down from the horizon?
• Do you want to limit the speed of change over time between two limiting rates, or limit the absolute orientation between two limiting angles? If the latter, have you reviewed previous questions about limiting or clamping rotation angles in Unity? – DMGregory Aug 15 at 16:14
• this for Fps camera but When I rotate to the top it is going 360 I want limit – NADER LABBAD Aug 15 at 16:18
• This script Makes player looks top and down but There is no limit it reach to 360 I'm trying to make it between 90 -90 – NADER LABBAD Aug 15 at 16:23
This is a straightforward application of Mathf.Clamp(value, min, max). Ordinarily I'd recommend caution calculating new orientations from Euler angles, but for camera orientation it's typically safe enough. You might want to pull back slightly from 90, say 80 degrees, so you don't hit nasty behaviour right at the poles.
// Correct for deltaTime so your behaviour is framerate independent.
// (You may need to increase your speed as it's now measured in degrees per second, not per frame)
float angularIncrement = verticalSpeed * Input.GetAxis("Mouse Y") * Time.deltaTime;
// Get the current rotation angles.
Vector3 eulerAngles = transform.localEulerAngles;
// Returned angles are in the range 0...360. Map that back to -180...180 for convenience.
if(eulerAngles.x > 180f)
eulerAngles.x -= 360f;
// Increment the pitch angle, respecting the clamped range.
eulerAngles.x = Mathf.Clamp(eulerAngles.x - angularIncrement, -90f, 90f);
// Orient to match the new angles.
transform.localEulerAngles = eulerAngles;
• Thank you for explaining it works – NADER LABBAD Aug 15 at 16:37
• I think there's something wrong i have try min 0 max 70 This gives me from feet to half screen 0 but if i put min to -30 and up Nothing happens – NADER LABBAD Aug 15 at 17:00
• This is one of the hazards of Euler angles. The engine has to wrap them somewhere - here it picked to wrap the x angle to lie in 0...360, but we want it in -180...180 - add the if line shown above to map it in a more convenient range. – DMGregory Aug 15 at 17:18
You can use if condition such as:
float v = verticalSpeed * Input.GetAxis("Mouse Y");
if (v > 100) then //100 your limit
{v= 50}
else
{v=30}
or you can use math.sign function which gives you +1,0,-1
if the result for your case v > 0 it returns +1
if it is zero than 0
if it is negative then it is -1
you can limit your camera by that way. |
Just an observation
1. Nov 7, 2008
tgt
I use to think that algebra was very fundamental but it now seems not the case. The study of functions (in general) and sets would be more fundamental. Just an observation. What do you people think?
2. Nov 7, 2008
Hurkyl
Staff Emeritus
The moment you start to do that -- you could get right back to algebra. e.g. categories.
"Fundamental" is such an incredibly vague term, though....
3. Nov 8, 2008
tgt
You could but lets say for up to graduate level, algebra involves a special kind of function called a homomorphism and consists of sets with special properties such as binary operation.
functions and sets. |
# Factor that encourages harmful substances in food production
###### Question:
factor that encourages harmful substances in food production
### Lilah is moving from Portland to Seattle. It takes her 3 hours to go by train. Mason leaves the train station in Portland and drives to the train station in Seattle with all Lilah's boxes in his car. It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the train. Find Lilah's speed on the train and Mason's speed.
Lilah is moving from Portland to Seattle. It takes her 3 hours to go by train. Mason leaves the train station in Portland and drives to the train station in Seattle with all Lilah's boxes in his car. It takes him 2.4 hours to get to Seattle, driving at 15 miles per hour faster than the speed of the ...
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Zbl 1139.81052
Bakalov, Bojko; Nikolov, Nikolay M.; Rehren, Karl-Henning; Todorov, Ivan
Infinite-dimensional Lie algebras in 4D conformal quantum field theory.
(English)
[J] J. Phys. A, Math. Theor. 41, No. 19, Article ID 194002, 12 p. (2008). ISSN 1751-8113; ISSN 1751-8121/e
Summary: The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of two-dimensional chiral conformal field theory, to a higher (even) dimensional spacetime. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, $V_{M}(x, y)$, where the $M$ span a finite dimensional real matrix algebra $\cal M$ closed under transposition. The associative algebra $\cal M$ is irreducible iff its commutant $\cal M^{\prime}$ coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite-dimensional Lie algebra: a central extension of $\text{sp}(\infty,{\mathbb R})$ corresponding to the field ${{\mathbb R}}$ of reals, of $u(\infty , \infty )$ associated with the field ${{\mathbb C}}$ of complex numbers, and of $so^*(4\infty )$ related to the algebra ${{\mathbb H}}$ of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups $O(N), U(N)$ and $U(N,{{\mathbb H}})= \text{Sp}(2N)$, respectively.
MSC 2000:
*81T40 Two-dimensional field theories, etc.
81R10 Repres. of infinite-dim. groups and algebras from quantum theory
22E70 Appl. of Lie groups to physics
81R12 Relations with integrable systems
Cited in: Zbl 1202.81188 Zbl 1165.81028
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# Thread: quotient groups
1. ## quotient groups
question: Give an examples of a group G and a normal subgroup N satisfying the following properties; or if no example exists, state that. In either case, justify answers.
(a)G is abelian, and G/N is non-abelian
(b)G is cyclic, and G/N is not cyclic
(c)G/N is not isomorphic to any subgroup G.
could anyone help me with this problem??? please?
2. Originally Posted by jin_nzzang
question: Give an examples of a group G and a normal subgroup N satisfying the following properties; or if no example exists, state that. In either case, justify answers.
(a)G is abelian, and G/N is non-abelian
(b)G is cyclic, and G/N is not cyclic
(c)G/N is not isomorphic to any subgroup G.
could anyone help me with this problem??? please?
no example exists for (a) and (b). for (c) an example is $G=\mathbb{Z}$ and $N=2\mathbb{Z}.$
3. Hi
thanks a lot for your help,, but could you please justify the answers so that i can understand it better? (at least one of them as an example ? )
4. Originally Posted by jin_nzzang
Hi
thanks a lot for your help,, but could you please justify the answers so that i can understand it better? (at least one of them as an example ? )
Remember that your quotient group acts very much like your group - it has multiplication $(Nx)(Ny)=N(xy)$.
So, if the group is abelian then $(Nx)(Ny)=N(xy) = N(yx) = (Ny)(Nx)$. |
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Measuring neutron star tidal deformability with Advanced LIGO: a Bayesian analysis of neutron star - black hole binary observations
Kumar, P., Pürrer, M., & Pfeiffer, H. P. (2017). Measuring neutron star tidal deformability with Advanced LIGO: a Bayesian analysis of neutron star - black hole binary observations. Physical Review D, 95: 044039. doi:10.1103/PhysRevD.95.044039.
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1Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1933290
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Free keywords: General Relativity and Quantum Cosmology, gr-qc,
Abstract: The discovery of gravitational waves (GW) by Advanced LIGO has ushered us into an era of observational GW astrophysics. Compact binaries remain the primary target sources for LIGO, of which neutron star-black hole (NSBH) binaries form an important subset. GWs from NSBH sources carry signatures of (a) the tidal distortion of the neutron star by its companion black hole during inspiral, and (b) its potential tidal disruption near merger. In this paper, we present a Bayesian study of the measurability of neutron star tidal deformability $\Lambda_\mathrm{NS}\propto (R/M)^{5}$ using observation(s) of inspiral-merger GW signals from disruptive NSBH coalescences, taking into account the crucial effect of black hole spins. First, we find that if non-tidal templates are used to estimate source parameters for an NSBH signal, the bias introduced in the estimation of non-tidal physical parameters will only be significant for loud signals with signal-to-noise ratios greater than $30$. For similarly loud signals, we also find that we can begin to put interesting constraints on $\Lambda_\mathrm{NS}$ (factor of $1-2$) with individual observations. Next, we study how a population of realistic NSBH detections will improve our measurement of neutron star tidal deformability. For astrophysical populations of {\it disruptive} NSBH coalescences, we find that $20-35$ events are sufficient to constrain $\Lambda_\mathrm{NS}$ within $\pm 25-50\%$, depending on the neutron star equation of state. For these calculations we assume that LIGO will detect black holes with masses within the astrophysical {\it mass-gap}. In case the mass-gap remains preserved in NSBHs detected by LIGO, we estimate that approximately $25\%$ additional detections will furnish comparable $\Lambda_\mathrm{NS}$ measurement accuracy. We recommend that an effort to measure $\Lambda_\mathrm{NS}$ be planned for upcoming LIGO-Virgo observing runs.
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Dates: 2016-10-192017
Publication Status: Published in print
Pages: 20 pages, 15 figures
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Identifiers: arXiv: 1610.06155
URI: http://arxiv.org/abs/1610.06155
DOI: 10.1103/PhysRevD.95.044039
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Pages: - Volume / Issue: 95 Sequence Number: 044039 Start / End Page: - Identifier: ISSN: 0556-2821
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# Difference between revisions of "1993 USAMO Problems/Problem 5"
## Problem 4
Let $a_0, a_1, a_2,\cdots$ be a sequence of positive real numbers satisfying $a_{i-1}a_{i+1}\le a^2_i$ for $i = 1, 2, 3,\cdots$ . (Such a sequence is said to be log concave.) Show that for each $n > 1$,
$\frac{a_0+\cdots+a_n}{n+1}\cdot\frac{a_1+\cdots+a_{n-1}}{n-1}\ge\frac{a_0+\cdots+a_{n-1}}{n}\cdot\frac{a_1+\cdots+a_{n}}{n}$.
## Resources
1993 USAMO (Problems • Resources) Preceded byProblem 3 Followed byProblem 5 1 • 2 • 3 • 4 • 5 All USAMO Problems and Solutions |
# 13.3.11Question HelpFinahalarc Iongth naeniatald hionq InaQivun cuiveLoinenalu'ovalauing Iha iorral (V) = v(c) dr. Thun find Ina langth 0/ Ino Indicaled
###### Question:
13.3.11 Question Help Finahalarc Iongth naeniatald hionq InaQivun cuive Loinenalu 'ovalauing Iha iorral (V) = v(c) dr. Thun find Ina langth 0/ Ino Indicaled porion of Ihe cutvo rll) = 3c01 Jeinu Stk where 03t
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# Opening a file
This topic is 4961 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
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I try to load a file with the line: std::ifstream file("\\Data\\Names.txt.c_str()"); Is this the wrong way to do it? I must use double \ otherwise cpp will think the char afterwards is an escapechar... also it should be converted to the c str style. What am i doing wrong?
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Quote:
Original post by Mizipzorstd::ifstream file("\\Data\\Names.txt.c_str()");
For one thing the .c_str() is inside the quotes therefore it thinks thats the file its opening. Its going to the file "names.txt.c_str()" which won't exist. Im not sure why your wanting to convert this to a c_str() ?
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Hmm... I just thought Ive read it in a tutorial or something somewhere :S maybe my memory misguides me. But
std::ifstream file("\\Data\\Names.txt");
Would be correct then? Assuming the txt file is located in a subfolder named Data which is at the same place as the cpp files?
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Yes, that would be correct. Assuming the place its running from is correct I know when you run it from the IDE itself, it will some what change the results of where its reading from.
I belive you can fix that by adding a "." in front of the first "\\" ; though thats only if the folder/file is like in the debug or release folder, and not where the cpp files are.
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The leading backslash indicates an absolute path. This is probably not what you want.
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Fruny: thats could be that problem... how is the proper way to do it then?
---------
Hmm... well the file seems to work ok since my temp string is showing the right things.
The two files are data for a kind of chatbot. Several names (many individuals) and some phrases. The first line is a number that says how many lines there is in the file (since i dont want to hardcode it if i want to add names). Same goes for phrases.
But I added that testOutput to see if it worked and it doesnt print anything. And im getting some quite nasty errors that I cant make ouy what they mean.
My class is only a constructor... so far... and the constructor loads those data. Can anyone see whats wrong?
#ifndef _NPCTRADERS#define _NPCTRADERS#include <fstream>#include <vector>#include <string>#include <iostream>using namespace std;class NpcTraders {public: NpcTraders(); string requestMessage(); void testOutput();private: vector<string> name; vector<string> phrase; int numberOfTraders; int numberOfPhrases;};NpcTraders::NpcTraders() { this->numberOfPhrases = 0; this->numberOfTraders = 0; // just in case // First the names std::ifstream file(".\\Data\\Names.txt"); if(file.bad() == true) { // if file didnt load, abort cout << "Unable to load file \"Names.txt\""; return; } file >> this->numberOfTraders; string tempStr; char temp[30]; while(!file.eof()) { // run until end is reached file.getline(temp, 30, '\n'); name.push_back(string(temp)); } file.close(); // Then the phrases file.open(".\\Data\\Phrases.txt.c_str()"); if(file.bad() == true) { // if file didnt load, abort cout << "Unable to load file \"Phrases.txt\""; return; } file >> numberOfPhrases; while(1) { file.getline(temp, 30, '\n'); phrase.push_back(string(temp)); if(file.eof()) // if its the end of the file, break break; } file.close(); this->testOutput();}void NpcTraders::testOutput() { cout << "Name: " << name.at(0) << endl; cout << "Phrase: " << phrase.at(0) << endl;} #endif
4 warnings:
Deleting intermediate files and output files for project 'Tradewars - Win32 Debug'.--------------------Configuration: Tradewars - Win32 Debug--------------------Compiling...main.cppd:\program\microsoft visual studio\vc98\include\vector(39) : warning C4786: 'std::reverse_iterator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > const *,std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::basic_string<char,std::char_traits<char>,std::allocator<char> > const &,std::basic_string<char,std::char_traits<char>,std::allocator<char> > const *,int>' : identifier was truncated to '255' characters in the debug information d:\program\microsoft visual studio\vc98\include\vector(39) : while compiling class-template member function '__thiscall std::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >::std::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >(const std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > &)'d:\program\microsoft visual studio\vc98\include\vector(39) : warning C4786: 'std::reverse_iterator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > *,std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::basic_string<char,std::char_traits<char>,std::allocator<char> > &,std::basic_string<char,std::char_traits<char>,std::allocator<char> > *,int>' : identifier was truncated to '255' characters in the debug information d:\program\microsoft visual studio\vc98\include\vector(39) : while compiling class-template member function '__thiscall std::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >::std::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >(const std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > &)'d:\program\microsoft visual studio\vc98\include\vector(60) : warning C4786: 'std::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >::~vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >' : identifier was truncated to '255' characters in the debug informationd:\program\microsoft visual studio\vc98\include\vector(39) : warning C4786: 'std::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >::vector<std::basic_string<char,std::char_traits<char>,std::allocator<char> >,std::allocator<std::basic_string<char,std::char_traits<char>,std::allocator<char> > > >' : identifier was truncated to '255' characters in the debug informationLinking...Tradewars.exe - 0 error(s), 4 warning(s)
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It seems like your using VC6 which is infamous for crappy template support/STL issues so you can safely ignore those warnings.
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Ive still got troubles loading data from that file. Ive changed to code to this:
// First the names std::ifstream file("Names.txt"); if(file.bad() == true) { // if file didnt load, abort cout << "Unable to load file Names.txt"; return; } file >> this->numberOfTraders; cout << this->numberOfTraders;
The txt file is in the same directory as everything else... How come the output of that cout is 0 when the first line in that file read 10?
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As a summary:
- C++ string literals are of type char*, not std::string. style enthusiasts may consider this a bad thing, but it would be pretty difficult to do optimizations were it the other way around, and that would go against the grain of the language. Anyway, just use the literal directly as a parameter for the ifstream constructor; a .c_str() method call is only needed if you provide a *variable* of std::string type. And in no case (not in C++ anyway, unless you're writing an interpreter or something) would contents of a string ever be interpreted as a method call. :)
- Use forward slashes for path names, even on systems where that's not the file path separator. The C++ runtime is responsible for translating things appropriately. It avoids a need to escape the character (potential bug source, as illustrated), and gains you a tiny piece of portability for free.
- A leading backslash (or slash for that matter) indicates an absolute path. For a relative path, just omit that character.
- warning C4786 is generally safely ignorable; if you would prefer not to ignore it, the best solution is, well, get a better compiler. The warning message boils down to "wow! look at that unbelievably long typename! Yeah, *I* have trouble looking at it too! Damn this new-fangled C++ with its templates and such..." :)
- The current code looks ok. (Comparing with "== true" is not necessary and actually obscures readability, but is certainly not a problem for correctness.) What is the type of numberOfTraders? How are you verifying the file contents? (Is it, in fact, a text file?)
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### MoniPoly---An Expressive $q$-SDH-Based Anonymous Attribute-Based Credential System
Syh-Yuan Tan and Thomas Gross
##### Abstract
Modern attribute-based anonymous credential (ABC) systems benefit from special encodings that yield expressive and highly efficient show proofs on logical statements. The technique was first proposed by Camenisch and Groß, who constructed an SRSA-based ABC system with prime-encoded attributes that offers efficient AND, OR and NOT proofs. While other ABC frameworks have adopted constructions in the same vein, the Camenisch-Groß ABC has been the most expressive and asymptotically most efficient proof system to date, even if it was constrained by the requirement of a trusted message-space setup and an inherent restriction to finite-set attributes encoded as primes. In this paper, combining a new set commitment scheme and a SDH-based signature scheme, we present a provably secure ABC system that supports show proofs for complex statements. This construction is not only more expressive than existing approaches, it is also highly efficient under unrestricted attribute space due to its ECC protocols only requiring a constant number of bilinear pairings by the verifier; none by the prover. Furthermore, we introduce strong security models for impersonation and unlinkability under adaptive active and concurrent attacks to allow for the expressiveness of our ABC as well as for a systematic comparison to existing schemes. Given this foundation, we are the first to comprehensively formally prove the security of an ABC with expressive show proofs. Specifically, we prove the security against impersonation under the $q$-(co-)SDH assumption with a tight reduction. Besides the set commitment scheme, which may be of independent interest, our security models can serve as a foundation for the design of future ABC systems.
Available format(s)
Category
Cryptographic protocols
Publication info
A major revision of an IACR publication in ASIACRYPT 2020
Keywords
Contact author(s)
syh-yuan tan @ newcastle ac uk
thomas gross @ newcastle ac uk
History
2020-12-10: last of 2 revisions
See all versions
Short URL
https://ia.cr/2020/587
CC BY
BibTeX
@misc{cryptoeprint:2020/587,
author = {Syh-Yuan Tan and Thomas Gross},
title = {MoniPoly---An Expressive $q$-SDH-Based Anonymous Attribute-Based Credential System},
howpublished = {Cryptology ePrint Archive, Paper 2020/587},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/587}},
url = {https://eprint.iacr.org/2020/587}
}
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Partner: UNT College of Arts and Sciences
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Results 1 - 50 of 104
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Ab initio transport properties of nanostructures from maximally localized Wannier functions
Article on ab initio transport properties of nanostructures from maximally localized Wannier functions. Abstract: We present a comprehensive first-principles study of the ballistic transport properties of low-dimensional nanostructures such as linear chains of atoms (Al, C) and carbon nanotubes in the presence of defects. An approach is introduced where quantum conductance is computed from the combination of accurate plane-wave electronic structure calculations, the evaluation of the corresponding maximally localized Wannier functions, and the calculation of transport properties by a real-space Green's function method based on the Landauer formalism. This approach is computationally very efficient, can be straightforwardly implemented as a post-processing step in a standard electronic-structure calculation, and allows us to directly link the electronic transport properties of a device to the nature of the chemical bonds, providing insight onto the mechanisms that govern electron flow at the nanoscale. digital.library.unt.edu/ark:/67531/metadc234911/
Absorption and Emission in the Non-Poissonian Case
This article discusses absorption and emission in the Non-Poissonian Case. Abstract: This Letter addresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a nonexponential distribution of waiting times. We show how to extend the KA theory from aged to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics. digital.library.unt.edu/ark:/67531/metadc67641/
Aging and Rejuvenation with Fractional Derivatives
This article discusses aging rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes a fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index μ in the interval 2<μ<3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, o, is given by o=3-μ. A brand new system is characterized by the degree o=μ-2. If the system is prepared at time -tₐ<0 and the observation begins at time t=0, we derive the following scenario. For times 0<t«tₐ the system is satisfactorily described by the fractional derivative with o=3-μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t⪢tₐ yields o=μ-2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative. digital.library.unt.edu/ark:/67531/metadc67638/
Aging and Rejuvenation with Fractional Derivatives
Paper discussing aging and rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes the fractional derivative emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index μ in the interval 2 < μ < 3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord = μ - 2. If the system is prepared at time -tₐ < 0 and the observation begins at time t = 0, we derive the following scenario. For times 0 < t << tₐ the system is satisfactorily described by the fractional derivative with ord = 3 - μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t >> tₐ yields ord = μ - 2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative. digital.library.unt.edu/ark:/67531/metadc174699/
Aging in financial market
Article discussing aging in the financial market. Abstract: We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply a coarse graining procedure to reveal the renewal aspects of the process underlying its dynamics. digital.library.unt.edu/ark:/67531/metadc174703/
Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions
This article discusses anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation. Abstract: We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (∂/∂t)P(x,t) = D(∂ƴ/∂xƴ)[P(x,t]v. Exact time-dependent solutions are found for v = (2 - y)/(1 + y)(-∞ < y ⩽ 2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q = (y + 3)/(Y + 1)(0 < y ⩽ 2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the only already known for Lévy-like superdiffusion (i.e., v = 1 and 0 < y ⩽ 2). Finally, for (y,v) = (2,0) the authors obtain q=5/3, which differs from the value q = 2 corresponding to the y = 2 solutions available in the literature (v < 1 porous medium equation), thus exhibiting nonuniform convergence. digital.library.unt.edu/ark:/67531/metadc77162/
Atomic structure of steps and defects on the clean diamond (100)-2 X 1 surface studied using ultrahigh vacuum scanning tunneling microscopy
In this article, the authors report ultrahigh vacuum scanning tunneling microscopy studies of the clean nonhydrogen-terminated diamond (100)-2 X 1 surface showing single- and double-layer steps that are rebonded. The main defects observed are single, multiple, and row dimer vacancies, and antiphase boundaries. Buckling of dimers is not observed, consistent with symmetric dimers. digital.library.unt.edu/ark:/67531/metadc83794/
Brain, Music, and Non-Poisson Renewal Processes
Canonical and noncanonical equilibrium distribution
This article discusses canonical and noncanonical equilibrium distribution. Abstract: We address the problem of the dynamical foundation of noncanonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of noncanonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the noncanonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Lévy statistics are the best description of the dynamics and that the Lévy distribution is the correct basin of attraction. We show that the correct path to noncanonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics. digital.library.unt.edu/ark:/67531/metadc77164/
Cognitive Scale-Free Networks as a Model for Intermittency in Human Natural Language
Paper discussing cognitive scale-free networks as a model for intermittency in human natural language. Abstract: We model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. Using a time series approach, the diffusion entropy method (DE), we compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The model yields the famous Zipf's law in terms of the generalized central limit theorem. digital.library.unt.edu/ark:/67531/metadc174698/
Collective polarization effects in β-polyvinylidene fluoride and its copolymers with tri- and tetrafluoroethylene
Article on collective polarization effects in β-polyvinylidene fluoride and its copolymers with tri- and tetrafluoroethylene. Abstract: The polar properties of the β phase of polyvinylidene fluoride (PVDF) and its copolymers with tri- and tetrafluoroethylene are investigated theoretically at different VDF-to-copolymer ratios. The calculations show that polarization in such polymers is described by cooperative, quantum-mechanical interactions between polymer chains, which cannot be viewed as a superposition of rigid dipoles. For β-PVDF, the monomer dipole moment is increased by 50% (from 2 to 3 D) as the isolated chains are brought together to form a crystal. In PVDF crystals containing copolymers, we observe a weakly parabolic dependence of monomer dipole moments on copolymer concentration. digital.library.unt.edu/ark:/67531/metadc234928/
Comment on "Modification of graphene properties due to electron-beam irradiation"
Complexity and Synchronization
Compression and Diffusion: A Joint Approach to Detect Complexity
Article discussing a joint approach to detect complexity by combining the Compression Algorithm Sensitive To Regularity (CASToRe) and Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA) procedures. digital.library.unt.edu/ark:/67531/metadc139462/
Conflict between trajectories and density description: the statistical source of disagreement
Paper discussing the statistical source of disagreement between trajectories and density description. Abstract: We study an idealized version of intermittent process leading the fluctuations of a stochastic dichotomous variable. It consists of an overdamped and symmetric potential well with a cusp-like minimum. The right-hand and left-hand portions of the potential corresponds to = W and = W, respectively. When the particle reaches this minimum is injected back to a different and randomly chosen position, still within the potential well. We build up the corresponding Frobenius-Perron equation and we evaluate the correlation function of the stochastic variable, called (t). We assign the potential well a form yielding (t) = (T = (t=T)), with > 0. Thanks to the symmetry of potential, there are no biases, and we limit ourselves to considering correlation functions with an even number of times, indicated for concision, by h12i, h1234i, and more, in general, by h1:::2ni. The adoption of a formal treatment, based on density, and thus of the operator driving the density time evolution, establishes a prescription for the evaluation of the correlation functions, yielding h1::2ni - h12i:::h(2n 1)2ni. We study the same dynamic problem using trajectories, and we establish that the resulting two-time correlation function coincides with that ordered by the density picture, as it should. We then study the four-times correlation function and we prove that in the non-Poisson case it departs from the density prescription, namely, from h1234i=h12ih34i. We conclude that this is the main reason why the two pictures yield two different diffusion processes, as noticed in an earlier work. [M. Bologna, P. Grigolini, B. J. West, Chem. Phys. 284, (1-2) 115-128 (2002)]. digital.library.unt.edu/ark:/67531/metadc174689/
Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers
This article discusses controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers. Abstract: A fundamental property of wave propagation is Anderson localization, which affects the transfer of information, energy, mass, and charge in disordered media. This localization can manifest itself via, e.g., the metal-insulator transition. We exactly map the behavior of a quantum particle moving in a potential with correlated disorder to teh sub-terahertz wave propagation in either Josephson chaines or superconducting multilayers. When the Josephson junction parameters vary randomly, the sub-THz electromagnetic waves cannot propagate through these Josephson structures due to localization. For parameter variations with long-range correlations, we predict sharp transitions from transparent to reflective frequency regions for Josephson plasma waves. With appropriate choices of the correlation function, frequency windows with targeted or designed transparencies for THz or sub-THz electromagnetic waves could be achieved. This could be useful for tailoring the electromagnetic wave spectrum of Josephson arrays within the THz frequency range, which is important for applications in physics, astronomy, chemistry, biology, and medicine. digital.library.unt.edu/ark:/67531/metadc103256/
Correlation Function and Generalized Master Equation of Arbitrary Age
This article discusses correlation function and generalized master equation of arbitrary age using non-Poisson, Markovian, and Liouville methods. digital.library.unt.edu/ark:/67531/metadc40401/
Decoherence, wave function collapses and non-ordinary statistical mechanics
Article discussing decoherence, wave function collapses, and non-ordinary statistical mechanics. Abstract: We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation. digital.library.unt.edu/ark:/67531/metadc174684/
Detection of invisible and crucial events: from seismic fluctuations to the war against terrorism
Paper discussing the detection of invisible and crucial events. Abstract: We argue that the recent discovery of the non-Poissonian statistics of the seismic main-shocks is a special case of a more general approach to the detection of the distribution of the time increments between one crucial but invisible event and the next. We make the conjecture that the proposed approach can be applied to the analysis of terrorist network with significant benefits for the Intelligence Community. digital.library.unt.edu/ark:/67531/metadc174695/
Diffusion Entropy and Waiting Time Statistics of Hard-X-Ray Solar Flares
Dynamical Origin of Memory and Renewal
This article discusses a dynamical origin of memory and renewal. Abstract: We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index θ=1/2. We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with 0<θ<1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots. digital.library.unt.edu/ark:/67531/metadc40399/
The Dynamics of EEG Entropy
This article discusses the dynamics of EEG entropy. Abstract: EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context. digital.library.unt.edu/ark:/67531/metadc132967/
Dynamics of EEG Entropy: beyond signal plus noise
Paper discussing the dynamics of EEG entropy. Abstract: EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context. Detrended fluctuation analysis of the EEG data is compared with diffusion entropy analysis and is found to suppress certain important properties of the EEG time series. digital.library.unt.edu/ark:/67531/metadc174706/
Effective dielectric constants of photonic crystal of aligned anisotropic cylinders and the optical response of a periodic array of carbon nanotubes
This article discusses effective dielectric constants of photonic crystal of aligned anisotropic cylanders and the optical response of a periodic array of carbon nanotubes. Abstract: We calculate the static dielectric tensor of a periodic system of aligned anisotropic dielectric cylinders. Exact analytical formula for the effective dielectric constants for the H-eigenmodes is obtained for arbitrary 2D Bravais lattice and arbitrary cross section of anisotropic cylinders behaves like uniaxial or biaxial natural crystals. The developed theory of homogenization of anisotropic cylinders is applied for calculations of the dielectric properties of photonic crystals of carbon nanotubes. digital.library.unt.edu/ark:/67531/metadc103277/
Effects of Cs deposition on the field-emission properties of single-walled carbon-nanotube bundles
This article discusses the effects of Cs deposition on the field-emission properties of single-walled carbon-nanotube bundles. Abstract: We report the effects of Cs deposition on the field-emission (FE) properties of single-walled carbon-nanotube bundles. We observe that Cs deposition decreases the turn-on field for FE by a factor of 2.1-2.8 and increases the FE current by six orders of magnitude. After Cs deposition, the FE current versus voltage (I-V) curves show non-Fowler-Nordheim behavior at large currents, consistent with tunneling from adsorbate states. At lower currents, the ratio of the slope of the FE I-V curves before and after Cs deposition is approximately 2.1. Exposure to N2 does not decrease the FE current, while exposure to O2 decreases the FE current. digital.library.unt.edu/ark:/67531/metadc84148/
Effects of O2, Ar, and H2 gases on the field-emission properties of single-walled and multiwalled carbon nanotubes
In this article, the authors compare the effects of O2, Ar, and H2 gases on the field-emission (FE) properties of single-walled carbon nanotubes (SWNTs) and multiwalled carbon nanotubes (MWNTs). The authors find that H2 and Ar gases do not significantly affect the FE properties of SWNTs or MWNTs. O2 temporarily reduces the FE current and increases the turn-on voltages in an O2 environment cause a permanent decrease of the FE current and an increase in the turn-on field of MWNTs. The ratios of the slopes before and after O2 exposure are approximately 1.04 and 0.82 for SWNTs and MWNTs, respectively. digital.library.unt.edu/ark:/67531/metadc84150/
Electromagnetically induced transparency controlled by a microwave field
This article discusses electromagnetically induced transparency controlled by a microwave field. Abstract: We have experimentally studied the propagation of two optical fields in a dense rubidium (Rb) gas in the case when an additional microwave field is coupled to the hyperfine levels of Rb atoms. The Rb energy levels form a close-Λ three-level system coupled to the optical fields and the microwave field. It has been found that the maximum transmission of the probe field depends on the relative phase between the optical and the microwave fields. We have observed both constructive and destructive interferences in electromagnetically induced transparency. A simple theoretical model and a numerical simulation have been developed to explain the observed experimental results. digital.library.unt.edu/ark:/67531/metadc103259/
Electron localization in a two-channel tight-binding model with correlated disorder
This article discusses electron localization in a two-channel tight-binding model with correlated disorder. Abstract: We calculate the localization length in a two-channel tight-binding model for correlated disordered site potential. Both intra- and interchannel correlations are taken into account. The localization length is obtained in quadratic approximation by expanding the two-channel conductance over weak disorder. The result is applied to a simple two-stranded model of DNA molecule and it is shown that a strong pair coupling between the basic nucleotides in the strands is not sufficient to delocalize electronic states. digital.library.unt.edu/ark:/67531/metadc103276/
Electronic and field emission properties of boron nitride/carbon nanotube superlattices
Article on electronic and field emission properties of boron nitride/carbon nanotube superlattices. Abstract: BN/C nanotube superlattices are quasi one-dimensional heterostructures that show unique physical properties derived from their pecular geometry. Using state-of-the-art ab initio calculations, we show that BN/C systems can be used for effective band-offset nanodevice engineering, polarization-based devices, and robust field emitters with an efficiency enhanced by up to two orders of magnitude over carbon nanotube systems. digital.library.unt.edu/ark:/67531/metadc226889/
Enhanced UV Light emission from Silicon nanoparticles induced by Au ion implantation
Paper discussing a study of light emitting silicon fabricated by ion implantation. digital.library.unt.edu/ark:/67531/metadc174705/
Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations
This article discusses the enhancement of localization in one-dimensional random potentials with long-range correlations. Abstract: We experimentally study the effect of enhancement of localization in weak one-dimensional random potentials. Our experimental setup is a single-mode waveguide with 100 tunable scatterers periodically inserted into the waveguide. By measuring the amplitudes of transmitted and reflected waves in the spacing between each pair of scatterers, we observe a strong decrease of the localization length when white-noise scatterers are replaced by a correlated arrangement of scatterers. digital.library.unt.edu/ark:/67531/metadc103275/
Equivalence of dipole correction and Coulomb cutoff techniques in supercell calculations
Article on the equivalence of dipole correction and Coulomb cutoff techniques in supercell calculations. In this work, the authors compare the dipole correction and Coulomb cutoff methods under the same conditions in the framework of plane-wave based density-functional theory. digital.library.unt.edu/ark:/67531/metadc234924/
Event-Driven Power-Law Relaxation in Weak Turbulence
This article discusses event-driven power-law relaxation in weak turbulence. Abstract: We characterize the spectral properties of weak turbulence in a liquid crystal sample driven by an external electric field, as a function of the applied voltage, and we find a 1/f noise spectrum S(f) ∝ 1/fn within the whole range 0< ɳ <2. We theoretically explore the hypothesis that the system complexity is driven by non-Poisson events resetting the system through creation and annihilation of coherent structures, retaining no memory of previous history (crucial events). The authors study the time asymptotic regime by means of the density ψ(τ) of the time distances between two crucial events, yielding ɳ = 3 - μ, where μ is defined through the long-time form ψ(τ) ∝ 1/τµ, with 1 < µ < 3. The system regression to equilibrium after an abrupt voltage change experimentally confirms the theory, proving violations of the ordinary linear response theory for both ɳ > 1 and ɳ < 1. digital.library.unt.edu/ark:/67531/metadc40395/
Experimental Quenching of Harmonic Stimuli: Universality of Linear Response Theory
This article discusses experimental quenching of harmonic stimuli. Abstract: We show that liquid crystals in the weak turbulence electroconvective regime respond to harmonic perturbations with oscillations whose intensity decay with an inverse power law of time. We use the results of this experiment to prove that this effect is the manifestation of a form of linear response theory (LRT) valid in the out-of-equilibrium case, as well as at thermodynamic equilibrium where it reduces to the ordinary LRT. We argue that this theory is a universal property, which is not confined to physical processes such as turbulent or excitable media, and that it holds true in all possible conditions, and for all possible systems, including a complex networks, thereby establishing a bridge between statistical physics and all the fields of research in complexity. digital.library.unt.edu/ark:/67531/metadc40394/
First-principles analysis of lattice thermal conductivity in monolayer and bilayer graphene
Article on first-principles analysis of lattice thermal conductivity in monolayer and bilayer graphene. Abstract: Using calculations from first principles, we investigate the lattice thermal conductivity of ideal monolayer and bilayer graphenes. Our result estimates that the intrinsic thermal conductivity of both materials is around 2200 W m⁻¹ K⁻¹ at 300 K, a value close to the one observed theoretically and experimentally in graphite along the basal plane. It also illustrates the expected T⁻¹ dependence at higher temperatures. The little variation between monolayer and bilayer thermal conductivities suggests that the number of layers may not affect significantly the in-plane thermal properties of these systems. The intrinsic thermal conductivity also appears to be nearly isotropic for graphene. digital.library.unt.edu/ark:/67531/metadc234913/
First-principles investigations of the dielectric properties of polypropylene/metal-oxide interfaces
Article on first-principles investigations of the dielectric properties of polypropylene/metal-oxide interfaces. Nanoscale-resolved dielectric properties of polypropylene/metal-oxide (alumina, PbTiO₃) interfaces and of the corresponding surfaces are investigated via first-principles calculations. digital.library.unt.edu/ark:/67531/metadc234923/
First principles theory of artificial metal chains on NiAl(110) surface
Article on the first principles theory of artificial metal chains on NiAl(110) surface. Abstract: Using first-principle calculations we have studied the stable phases of metal-atom chains on the (110) surface of NiAl. Our investigation is mainly focused on the technologically relevant case of Au chains, but the results will be analyzed in the broader framework of a family of metallic systems. We demonstrate that the nature of the adatom (Au, Mn, Ni, Cu, Al, H, C, Na, K, and Ca) is responsible for different levels of interaction with the substrate and gives rise to a variety of electronic behaviors. With some transition metals (such as Au, Mn, Ni, and Cu) the NiAl surface acts as a simple structural template for the formation of the artificial one-dimensional system and does not affect the electronic properties of the chains. With other atomic species (H, C, Na, K, and Ca) we observe substantially different couplings and stronger interactions. We demonstrate that the different electronic properties of the various adatoms are responsible for different couplings with the substrate and compare our findings with the existing experimental results. Finally, in the case of Au chains we have investigated the role of adatom-adatom interactions in the formation of such one-dimensional structures. digital.library.unt.edu/ark:/67531/metadc234916/
First-principles theory of metal-alkaline earth oxide interfaces
Article on the first-principles theory of metal-alkaline earth oxide interfaces. Abstract: Using calculations from first principles, we discuss the interplay between structure and functionality at metal-insulator interfaces using the paradigmatic example of the junctions between various metals (Ag, Pd, Pt, Ni, Cu, Al) and binary alkaline earth crystalline oxides (BaO, CaO, and SrO). Our results demonstrate that it is possible to tune the Schottky barrier height in a very broad range of values by manipulating the metal at the interface, and elucidate the role of the relative overlap in the density of states of the different components in determining the band alignment. We conclude by stating a "modified Schottky-Mott rule" for this class of metal-insulator heterojunctions. digital.library.unt.edu/ark:/67531/metadc234922/
A fluctuating environment as a source of periodic modulation
Article discussing a fluctuating environment as a source of periodic modulation. Abstract: We study the intermittent fluorescence of a single molecule, jumping from the "light on" to the "light off" state, as a Poisson process modulated by a fluctuating environment. We show that the quasi-periodic and quasi-deterministic environmental fluctuations make the distribution of the times of sojourn in the "light off" state depart from the exponential form, and that their succession in time mirrors environmental dynamics. As an illustration, we discuss some recent experimental results, where the environmental fluctuations depend on enzymatic activity. digital.library.unt.edu/ark:/67531/metadc132981/
Fluctuation-dissipation process without a time scale
This article discusses fluctuation-dissipation process without a time scale. Abstract: We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signaled by sharp peaks, and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Lévy distribution. digital.library.unt.edu/ark:/67531/metadc77161/
Fluctuation-Dissipation Theorem for Event-Dominated Processes
This article discusses fluctuation-dissipation theorem for event-dominated processes. Abstract: We study a system whose dynamics are driven by non-Poisson, renewal, and nonergodic events. We show that external perturbations influencing the times at which these events occur violate the standard fluctuation-dissipation prescription due to renewal aging. The fluctuation-dissipation relation of this Letter is shown to be the linear response limit of an exact expression that has been recently proposed to account for the luminescence decay in a Gibbs ensemble of semiconductor nanocrystals, with intermittent fluorescence. digital.library.unt.edu/ark:/67531/metadc40397/
Fluorescence intermittency in blinking quantum dots: renewal or slow modulation?
Article discussing fluorescence intermittency in blinking quantum dots. Abstract: We study time series produced by the blinking quantum dots, by means of an aging experiment, and we examine the results of this experiment in the light of two distinct approaches to complexity, renewal, and slow modulation. We find that the renewal approach fits the result of the aging experiment, while the slow modulation perspective does not. We make also an attempt at establishing the existence of an intermediate condition. digital.library.unt.edu/ark:/67531/metadc174701/
From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity
Paper discussing knowledge, knowability, and the search for objective randomness to a new vision of complexity. Abstract: Herein we consider various concepts of entropy as measure of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do with our understanding of randomness, irreversibility and unpredictability using physical theory, and these in turn undermine our certainty regarding what we can and what we cannot know about complex phenomena in general. The sources of complexity examined herein appear to be channels for the amplification of naturally occurring randomness in the physical world. Our analysis suggests that when the conditions for the renormalization group apply, this spontaneous randomness, which is not a reflection of our limited knowledge, but a genuine property of nature, does not realize the conventional thermodynamic state, and a new condition, intermediate between the dynamic and the thermodynamic state, emerges. We argue that with this vision of complexity, life, which with ordinary statistical mechanics seems to be foreign to physics, becomes a natural consequence of dynamical processes. digital.library.unt.edu/ark:/67531/metadc174694/
From power law intermittence to macroscopic coherent regime
This article offers discussions from power law intermittence to macroscopic coherent regime. The authors address the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of "light on" and "light off" fluorescence fluctuations in blinking quantum dots. digital.library.unt.edu/ark:/67531/metadc132992/
Fullerene Coalescence in Nanopeapods: A Path to Novel Tubular Carbon
Article on fullerene coalescence in nanopeapods. Abstract: A fascinating structural transformation occurring inside single-walled carbon nanotubes (SWNTs) is the fullerene coalescence, which is responsible for forming stable zeppelinlike carbon molecules. We report in situ transmission electron microscope (TEM) observations revealing sequences of fullerene coalescence induced by electron irradiation on pristine nanotube peapods, together with extensive theoretical investigations of the microscopic mechanism underlying this process. TEM images indicate that the merging of fullerenes results in stable but corrugated tubules (5 to 7 Å in diameter) confined within SWNTs. These observations have been confirmed using a combination of theoretical approaches based on molecular dynamics, empirical potentials, tight-binding methods, Monte Carlo techniques, and first principles calculations. We have fully elucidated the coalescence mechanism of fullerenes inside SWNTs under electron irradiation and thermal annealing. The process occurs via the polymerization of C₆₀ molecules followed by surface reconstruction, which can be triggered either by the formation of vacancies (created under electron irradiation) or by surface-energy minimization activated by thermal annealing. These novel tubular forms of carbon contain hexagons, pentagons, heptagons, and octagons. The stability, electronic properties, and electron conductance of the novel tubules are strongly affected by the final geometry of the coalesced fullerene complex. The possibility of forming highly conducting and semiconducting tubular structures suggests new avenues in designing carbon nanowires with specific electronic characteristics. digital.library.unt.edu/ark:/67531/metadc228304/
Generalized Master Equation Via Aging Continuous-Time Random Walks
This article discusses the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). digital.library.unt.edu/ark:/67531/metadc67635/
Generation of correlated binary sequences from white noise
This article discusses the generation of correlated binary sequences from white noise. Abstract: We suggest a method for generation of random binary sequences of elements 0 and 1, with prescribed correlation properties. It is based on a modification of the widely used convolution method of constructing continuous random processes. Using this method, a binary sequence with a power-law decaying pair correlator can be easily generated. digital.library.unt.edu/ark:/67531/metadc103260/
High sensitivity measurement of implanted As in the presence of Ge in Ge(x)Si(1-x)/Si layered alloys using trace element accelerator mass spectrometry
This article discusses high sensitivity measurement of implanted As in the presence of Ge in Ge(x)Si(1-x)/Si layered alloys using trace element accelerator mass spectrometry. Abstract: Various devices can be realized on strained GeSi/Si substrates by doping the substrate with different impurities such as As. As is an n-type dopant in both Ge and Si. As cross contamination can also arise during germanium preamorphization implantation due to inadequate mass resolution in the implanter. Thus, it is important to be able to accurately measure low-level As concentrations in the presence of Ge. Secondary ion mass spectrometry (SIMS) is the standard technique for these types of measurements but is constrained by mass interferences from molecular ions (⁷⁴GeH, ²⁹Si³⁰Si¹⁶O). The trace element accelerator mass accelerator technique allows the breakup of interfering molecules. As is measured in a GeSi matrix with sensitivity significantly better than SIMS. digital.library.unt.edu/ark:/67531/metadc146576/
Homogenization of Magnetodielectric Photonic Crystals
This article discusses homogenization of magnetodielectric photonic crystals. Abstract: We calculate the low-frequency index of refraction of a medium which is homogeneous along axis z and possesses a periodic dependence of the permittivity ɛ(r) and permeability μ(r) in the x-y plane (2D magnetodielectric photonic crystal). Exact analytical formulas for the effective index of refraction for two eigenmodes with vector E or H polarized along axis z are obtained. We show that, unlike nonmagnetic photonic crystals where the E mode is ordinary and the H mode is extraordinary, now both modes exhibit extraordinary behavior. Because of this distinction, the magnetodielectric photonic crystals exhibit optical properties that do not exist for natural crystals. We also discuss the limiting case of perfectly conducting cylinders and clarify the so-called problem of noncommuting limits, ω → 0 and ɛ → ∞. digital.library.unt.edu/ark:/67531/metadc107768/
In the search for the low-complexity sequences in prokaryotic and eukaryotic genomes: how to derive a coherent picture from global and local entropy measures
Paper discussing the search for the low-complexity sequences in prokaryotic and eukaryotic genomes and how to derive a coherent picture from global and local entropy measures. Abstract: We investigate on a possible way to connect the presence of Low-Complexity Sequences (LCS) in DNA genomes and the nonstationary properties of base correlations. Under the hypothesis that these variations signal a change in the DNA function, we use a new technique, called Non-Stationarity Entropic Index (NSEI) method, and we prove that this technique is an efficient way to detect functional changes with respect to a random baseline. The remarkable aspect is that NSEI does not imply any training data or fitting parameter, the only arbitrarity being the choice of a marker in the sequence. We make this choice on the basis of biological information about LCS distributions in genomes. We show that there exists a correlation between changing the amount in LCS and the ration of long-to short-range correlation. digital.library.unt.edu/ark:/67531/metadc174697/
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# I How do I solve this ODE?
#### Luke Tan
Summary
How do i solve this ODE?
When reading through Shankar's Principles of Quantum Mechanics, I came across this ODE
$$\psi''-y^2\psi=0$$
solved in the limit where y tends to infinity.
I have tried separating variables and attempted to use an integrating factor to solve this in the general case before taking the limit, but they didn't work.
I also tried to guess a solution of the form $e^{f(y)}$, and it quickly became clear that $$f(y)=\frac{y^2}{2}$$, but it feels like my guess is unmotivated and i didn't get the $y^m$ term since i didn't guess it would be there.
Is there any general method for this kind of ODE?
Related Differential Equations News on Phys.org
Try this:
#### Engie
You could try to expand in Laurent series at infinity and factor out $y^m$... |
# GMAT Question of the Day (May 3): Arithmetic and Critical Reasoning
- May 3, 02:00 AM Comments [0]
Math (PS)
What is the sum of digits in decimal notation of number $10^{20} - 16$?
(A) 158
(B) 162
(C) 165
(D) 174
(E) 183
Question Discussion & Explanation
GMAT Daily Deals
Verbal (CR)
The energy an animal must expend to move uphill is proportional to its body weight, whereas the animal’s energy output available to perform this task is proportional to its surface area. This is the reason that small animals, like squirrel, can run up a tree trunk almost as fast as they can move on level ground, whereas large animals tend to slow down when they are moving uphill.
Which one of the following is an assumption on which the explanation above depends?
(A) The amount of energy needed to move uphill is no greater for large animals that it is for small animals.
(B) Small animals can move more rapidly than large animals can.
(C) The ratio of surface area to body weight is smaller in large animals than it is in small animals.
(D) There is little variation in the ratio of energy output to body weight among animals.
(E) The amount of energy needed to run at a given speed is proportional to the surface area of the running animal.
Question Discussion & Explanation
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# How do you factor the expression 49x^6 + 126x^3y^2 + 81y^4?
Apr 11, 2016
$49 {x}^{6} + 126 {x}^{3} {y}^{2} + 81 {y}^{4} = {\left(7 {x}^{3} + 9 {y}^{2}\right)}^{2}$
#### Explanation:
This is a perfect square trinomial of the form:
${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$
with $a = 7 {x}^{3}$ and $b = 9 {y}^{2}$
$49 {x}^{6} + 126 {x}^{3} {y}^{2} + 81 {y}^{4}$
$= {\left(7 {x}^{3}\right)}^{2} + 2 \left(7 {x}^{3}\right) \left(9 {y}^{2}\right) + {\left(9 y\right)}^{2}$
$= {\left(7 {x}^{3} + 9 {y}^{2}\right)}^{2}$
No further factorisation is possible since the remaining terms in $x$ and $y$ are of distinct prime degrees. |
# Is this cheat sheet over big-$O$ and related notations accurate?
When familiarizing myself with big-$O$ and similar notations, I found this cheat sheet (which I took the liberty of transcribing):
$$\begin{array}{c|c} \text{big-O notation} & \text{limit definition} \\[2ex] \hline f\in o(g) & \displaystyle\lim_{x\to\infty}\frac{f(x)}{g(x)}=0 \\[2ex] f\in O(g) & \displaystyle\lim_{x\to\infty}\frac{f(x)}{g(x)}\lt\infty \\[2ex] f\in \Theta(g) & \displaystyle\lim_{x\to\infty}\frac{f(x)}{g(x)}\in\Bbb{R}_{\ge0} \\[2ex] f\in\Omega(g) & \displaystyle\lim_{x\to\infty}\frac{f(x)}{g(x)}\lt\infty \\[2ex] f\in\omega(g) & \displaystyle\lim_{x\to\infty}\frac{f(x)}{g(x)}=\infty \\[2ex] \end{array}$$
I am not at all familiar with notations like this for asymptotic behavior, so my questions are pretty straight-forward and simple:
• Is any of the quoted material inaccurate? If so, what?
• Are there any ‘caveats’ with asymptotic notation of which students should be wary? Perhaps something that might easily be misunderstood on the superficial level?
• You can take a look at Wikipedia's "Landau notation" page: en.wikipedia.org/wiki/… – Matt Groff Jan 3 '18 at 4:34
• The fourth one is wrong, $f\in \Omega (g) \iff \lim_{x\to \infty} \frac{f(x)}{g(x)} > 0$ – ultrainstinct Jan 3 '18 at 4:35
• The fourth one should be $f\in\Omega(g)\Leftrightarrow\lim_{x\to\infty}\frac{g(x)}{f(x)}\lt\infty$; i.e., $f\in\Omega(g)\Leftrightarrow g\in O(f)$. – Steven Stadnicki Jan 3 '18 at 4:38
• I'd also note that these definitions basically assume that $f,g > 0$. You can generalize these notations to include functions which take negative values or even complex values. For example, $$f \in O(g) \iff |f(x)| \leq C|g(x)| \iff \limsup \left|\frac{f(x)}{g(x)}\right| < \infty.$$ – Antonio Vargas Jan 3 '18 at 20:16
There's one major problem that infests several of these: the cheat-sheet effectively requires the various limits in question to exist, but that's not strictly a necessity for some of these definitions. For instance, consider $f(x)=x(1+\{x\})$, where $\{x\}$ denotes the factional part of $x$. Then $f(x)\in O(x)$ and in fact $f(x)\in\Theta(x)$, but the limit $\lim\limits_{x\to\infty}\frac{f(x)}{x}$ doesn't exist; it vacillates between $1$ and $2$. Also, as noted in the comments, the definition of $\Omega()$ is wrong; it "should be" $\lim\limits_{x\to\infty}\frac{g(x)}{f(x)}\lt\infty$, although that's also wrong for the same reason that the definition of $O()$ is wrong; better would be just to say that $f\in\Omega(g)\Longleftrightarrow g\in O(f)$. |
# Partial Sum Approximation for Alternating Harmonic Series
1. Feb 24, 2013
### DavidE721
1. The problem statement, all variables and given/known data
Find a value for n for which the nth partial sum is ensured to approximate the sum of the alternating harmonic infinite series to three decimal places.
2. Relevant equations
Sn = Ʃ(-1)^k+1*1/k = 1 - 1/2 + 1/3 - 1/4 + 1/5 - . . .
S1 = 1
S2 = 1 - 1/2
S3 = 1 - 1/2 + 1/3
S4 = 1 - 1/2 + 1/3 -1/4
.
.
.
Sn = ?
3. The attempt at a solution
An attempt was made to derive a formula that would permit finding the value of the nth partial sum (e.g., S1000 = ?), but without success. It appears as though such a formula might not exist. Any help in this regard would be most appreciated.
2. Feb 24, 2013
### Ray Vickson
There is a formula, but it involves the non-elementary function "digamma" function Psi(x), defined as
$$\Psi(x) = \frac{d}{dx} \ln \left( \Gamma(x) \right) = \frac{\Gamma^{\prime}(x)}{\Gamma(x)}.$$ Here, $\Gamma$ is the standard Gamma function. According to Maple 11 the sum is:
Sum((-1)^(k-1)/k,k=1..N):lprint(%);Sum((-1)^(k-1)/k,k = 1 .. N) <--echo the input
S:=value(%): lprint(S);
ln(2)+1/2*(-1)^(N+1)*Psi(1+1/2*N)+1/2*(-1)^N*Psi(1/2*N+1/2). <--- output
That is,
$$\sum_{k=1}^N (-1)^{k-1} \frac{1}{k} = \ln(2) + \frac{1}{2}(-1)^N \left[ \Psi\left(\frac{N}{2}+\frac{1}{2}\right) - \Psi\left(\frac{N}{2}+1\right) \right].$$
3. Feb 24, 2013
### micromass
I doubt you know digamma functions, so that's not going to be the way to solve it.
Let $s=\sum_{n=1}^{+\infty} \frac{(-1)^{n+1}}{n}$ and let $s_n$ be the n-th partial sum.
Can you show that $s_{2n+1}$ is decreasing? And that $s_{2n}$ is increasing? Can you conclude from that that $s_{2n}\leq s \leq s_{2n+1}$?
What can you say about $|s_{2n+1}-s_{2n}|$?? What does this say about $|s-s_n|$?? Do you obtain a formula for how well the approximation is?
4. Feb 24, 2013
### Ray Vickson
I agree about it not being the way to solve it, but he/she did ask. If one is going to use a computer, one might as well just do a recursive computation (although avoiding subtractive roundoff errors is an issue for getting accurate numbers).
5. Feb 24, 2013
### micromass
Sure. I was not criticizing your post as it was very informative! I was merely informing the OP of a more elementary method. |
# Generating replacement rules programatically
I would like to generate sets of replacement rules programatically for predefining some permutations. So a function
MakeRule[cycles_List (* permute cycles *), n_Integer (* rule length *)]
called as
MakeRule[{{2,3}}, 4]
will generate
{e1_, e2_, e3_, e4_} -> {e1, e3, e2, e4}
For the permutations, I have
Permute[l, Cycles[cycles]]
but I cannot find a way of generating the list of patterns. Something subscripted or indexed would be nice as per the example. I have tried:
1) Pattern[Subscript[e, 1], Blank[]]
2) Pattern[Symbol["e1"], Blank[]]
3) Pattern[e[[1]], Blank[]]
I have a feeling I am missing something obvious.
Edit: Apologies for an oversight on my part. The second pattern example works correctly while the first and third do not. Thanks to all who responded.
• You may find this subsection of my book of interest. Mar 15, 2013 at 21:20
• I went through a similar exercise looking at hashing algorithms for seven card poker hands. As the suit and rank sizes are fixed, I did the patterns by hand and let Permutations do the heavy lifting. Mar 16, 2013 at 0:24
• Nick, for the poker-hand problem I used Orderless myself. Mar 16, 2013 at 6:35
• @Mr.W, indeed, a handy shortcut for the actual hash. Specifically, I was counting the permuted patterns to check I'd got the binomial coefficients right for the probabilities, and then per draw permuted integer partition counts for the rank encoding. Mar 16, 2013 at 10:41
makeRule[e_, cycles_List , n_Integer] := Module[
{vals = Table[Unique[ToString[e]], {n}]},
Map[Pattern[#, Blank[]] &, vals] -> Permute[vals, Cycles[cycles]]
]
Example:
makeRule[e, {{2, 3}}, 4]
(* Out[307]= {e365_, e366_, e367_, e368_} -> {e365, e367, e366, e368} *)
With a bit more work we can get the sequential symbols starting at 1.
makeRule2[e_, cycles_List , n_Integer] := Module[
{vals, estr = ToString[e]},
vals = Table[ToExpression[StringJoin[estr, ToString[j]]], {j, n}];
Map[Pattern[#, Blank[]] &, vals] -> Permute[vals, Cycles[cycles]]
]
In[309]:= makeRule2[e, {{2, 3}}, 4]
(* Out[309]= {e1_, e2_, e3_, e4_} -> {e1, e3, e2, e4} *)
• Thanks - so a symbol has to be created to use in the pattern? It would be nice to index from 1, but this does the job. Mar 15, 2013 at 21:43
• It can be done the way you want, but it's a bit more work. See the addendum. Mar 15, 2013 at 22:20
• @DanielLichtblau I naïvely thought one could do Block[{$ModuleNumber = 1}, Unique["x"]] for the addendum, but... what happened was not pretty: Mathematica has detected an internal error: vMessage ENULL (v9). However, it doesn't crash in v7 and v8 (displays a warning). Any thoughts on why that happened? My guess would be that $ModuleNumber is critical to several internal routines and this messed with it and it cannot be Locked` either, since it needs to be incremented. But somehow I don't think that's right (and I'm not convinced by my explanation)
– rm -rf
Mar 15, 2013 at 22:26
• Wow. No idea. But I'm filing a bug report. Mar 15, 2013 at 22:33 |
Surjective implies local affine surjective? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T04:48:40Z http://mathoverflow.net/feeds/question/55333 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/55333/surjective-implies-local-affine-surjective Surjective implies local affine surjective? evgeniamerkulova 2011-02-13T18:25:35Z 2011-02-13T21:46:26Z <p>Take scheme morphism $f: X\to Y$ and suppose $f$ surjective. If $y \in Y$ can one find affine open $V \subset Y$ containing $y$ and affine open $U \subset X$ such $f(U) = V$ ? Thank you.</p> <p>Later: Very good answer of Kevin shows it is not true. Is there hypothese which make it true ? For example $X$ irreducible and/or $f$ faithfuly flat ?</p> http://mathoverflow.net/questions/55333/surjective-implies-local-affine-surjective/55337#55337 Answer by Kevin Ventullo for Surjective implies local affine surjective? Kevin Ventullo 2011-02-13T19:16:35Z 2011-02-13T19:16:35Z <p>Consider the disjoint union Spec$(\mathbb{Q})\coprod_{p}$Spec$(\mathbb{F}_p)$ with its canonical map to Spec$(\mathbb{Z})$. This is bijective on points, but the preimage of any open in Spec$(\mathbb{Z})$ won't even be compact, much less affine.</p> http://mathoverflow.net/questions/55333/surjective-implies-local-affine-surjective/55346#55346 Answer by Qing Liu for Surjective implies local affine surjective? Qing Liu 2011-02-13T21:34:40Z 2011-02-13T21:46:26Z <p>If $f$ is open (e.g. $f$ finite type and flat over noetherian $Y$), then your condition is trivially satisfied: let $V'$ be any affine open neighborhood of $y$ and let $U'$ be an affine open subset of $X$ such that $y\in f(U')\subseteq V'$. Take a principal open subset $V'_h$ such that $y\in V'_h\subseteq f(U')$, then $V:=V'_h$ and $U:=U'_h$ are what you want. </p> <p>A counterexample with $X$ irreducible and $f$ projective : consider $Y$ the affine plan, $y$ the origin and $f : X\to Y$ the blowing-up of $y$. For any affine open subset $V$ containing $y$, $f^{-1}(V) \to V$ is the blowing-up of $y$. If $f(U)=V$, then the complement of $U$ in $f^{-1}(V)$ is finite because $f$ is an isomorphism out of $y$. By Zariski's extension theorem, $O_X(U)=O_X(f^{-1}(V))=O_Y(V)$. This is impossible as $U$ is affine, because $U$ would be the image of a section $V\to f^{-1}(V)$, hence closed in (and then equal to) $f^{-1}(V)$.</p> |
MATLAB: Drive the Rotation on a body in Virtual Reality from a simulink model signal
Hi, I have a model of a dynamic system (a car) which define 7 DoF (the 4 vertical motion of the wheels + Heave, Pitch and Roll of the body of the car). The car is positioned on 4 pads which are used to provide vertical inputs to the car (similar to a 4-Post rig shaker) The model works fine without the virtual reality.
I realized a virtual reality version of my system (4 wheels + a block for the body + 4 pads)
The virtual reality works fine when only the linear motions are driven
Now I am having problem with driving the "rotation" field of the body.
I tried using a bus creator but this does not work.
I suppose the rotation is a vector(3) with rotation around x,y and z respectively. am I right/
Any help on this is very appreciated
Thanks
G
R(psi, theta, phi) = R1(phi)R2(theta)R3(psi),
R3(psi) = [ cos(psi) sin(psi) 0; -sin(psi) cos(psi) 0; 0 0 1]R2(theta) = [cos(theta) 0 -sin(theta); 0 1 0; sin(theta) 0 cos(theta)]R1(phi) = [1 0 0; 0 cos(phi) sin(phi); 0 -sin(phi) cos(phi)] |
Consider the region defined by 0<=y<=1/x^3 and 1<=x<=2
1) Find the value of some c so that the line x=c splits this region in halves with equal areas
2) Find the value of some d so that the line y=d splits this region in halves with equal areas.
I got 1) by doing the integral of 1/x^3 from 1 to 2 with respect to x. This gave a total area of 3/8. So then I took integral of 1/x^3 from 1 to c and set this equal to 3/16 and solved for c to get c=2sqrt(2)/sqrt(5).
I am having trouble with 2). I am trying to figure out what the integral will be. I now it is with respect to y. I believe it should be from y 0 to 1 of 1/(y)^1/3, but this does not give the necessary area of 3/8. Once I find out what the integral for the total area should be, it should be easy to find the line y=d as I did in 1). What I need help with as writing this integral with respect to y, so that I got the correct area of 3/8 (unless you know that my 3/8 is wrong and I did the first integral wrong.)
Thanks.
2. See attachment
I get d =.199
3. Thanks, got it.
4. Actually, I know I said I got it, but I do not quite understand how you got the .199. I did that integral and got (-3/2)*(b)^(2/3)+b=-5/16, but what did you do to solve for b?
5. You probably want to solve this either numerically or graphically.
In all honesty I used Mathcad to solve it directly from the integral.
6. See attachment |
Free Version
Difficult
# Ketone to Amide with Azide Mechanism
ORGO2-YYNRDV
What is the most reasonable mechanism for the conversion of Compounds A and B in the presence of a Lewis acid catalyst into ring-expanded amide Compound C, accompanied by $N_2$ gas?
Compounds A-C are the same in all of the answer choices. This reaction is known as the azido-Schmidt reaction, which has some mechanistic and atom reorganization similarity with the Bayer-Villiger reaction. Some basic information about the Lewis acid and resonance interactions in azides are depicted below.
A
B
C
D |
×
# Functions
How to solve these type of questions: Find all functions such that f(x + yf(x)) = f(y) + xf(x) ... and all that ?
Note by Priyanshu Mishra
1 year, 10 months ago
Sort by:
Can you give some initial values like $$f(0)=0$$ or something like that ?Else you won't be able to solve this question · 1 year, 10 months ago |
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# 28th IAEA Fusion Energy Conference (FEC 2020)
10-15 May 2021
Nice, France
Europe/Vienna timezone
The Conference will be held virtually from 10-15 May 2021
## Experimental indications of high-recycling and the role of pressure and power dissipation for detachment at W7-X
13 May 2021, 14:00
4h 45m
Nice, France
#### Nice, France
Regular Poster Magnetic Fusion Experiments
### Speaker
Dr Felix Reimold (Max-Planck-Institut für Plasmaphysik)
### Description
New experimental evidence based on spectroscopy, see Fig. 1, and other edge diagnostics indicate the existence of a high-recycling regime in W7-X. The high-recycling regime has not been accessible in the predecessor W7-AS and was predicted by modeling [1] for W7-X. The island divertor stellarator W7-X has also demonstrated stable, detached, high density divertor plasmas with good particle and power exhaust conditions, such that steady-state operation with particle removal by the pumps and sufficient power dissipation have been achieved [2,3,4,5]. Experimental measurements show also high divertor densities, complete heat flux detachment from the target, high neutral compression and beneficial impurity transport with indications of divertor retention of low-Z impurities [6] and benign core impurity transport [7]. This is a very important finding with respect to future power plants as the ability to exhaust the fusion power compatible with the limits of the plasma facing components is a paramount requirement for such a device. Therefore, the W7-X program develops and investigates exhaust scenario based on a detached divertor plasma.\
Two approaches of achieving heat flux detached divertor targets have been followed in the OP1.2b campaign. First, density ramp experiments using a feedback controlled gas puff system [2,3]. Second, impurity seeding of N and Ne were used to increase the radiated power and achieve detachment at lower plasma densities [5]. We focus here mainly on density ramp experiments.
\pagebreak
Fig. 2 shows the timetrace of a density ramp discharge that leads to completely heat flux detached targets after 3.0s. Consistent with the modeling expectations [8], above a threshold of $f_{rad} > 50\%$, the radiation increases strongly with a small density increment and the radiation front detaches from the target and moves toward the X-point. The movement of the radiation front is indicated by the movement of the N$^+$-line (399.5 nm) radiation and the high density region in the divertor shown in Fig. 3.b and 3.a, respectively.
Currently, the exact localization of the radiation front with bolometry is not conclusively possible with respect to its position around and along the separatrix, but upstream profile diagnostics show a significant reduction of the electron temperature from about 150 eV to 50 eV around the separatrix up to 3.4 cm inside the nominal separatrix position. Keeping in mind the large uncertainties in the latter, this is still indicative of increased power losses in the very edge of the confined region and could be comparable to the very localized radiation features in X-point radiation regimes in tokamaks [9]. As N$^{+}$ pre-dominantly radiates at temperatures of $T_e = 3 \rm{\ eV}$, its location can be taken as a reference for the ionization front. This implies that the ionization front lifts off the target concomittent with the radiation front during the detachment transition. Fig. 2.c shows that at the same time a drop in neutral compression(black line) by about 50 % with only marginally reduced divertor neutral pressures is observed in experiment. Stark broadening of Balmer lines is used to assess the electron density in the divertor, see Fig. 1. High densities on the order of $10^{20} m^{-3}$ with $n_{e,div} > n_{e,sep}$ indicate the existance of a high recycling regime in W7-X experiments. Line ratio analysis of the Balmer lines ($\textrm{H}_\epsilon\ \&\ \textrm{H}_\delta$) shows that the divertor plasma in W7-X detachment conditions is still ionization dominated. The absence of strong recombination and the low neutral pressures of order 0.1 Pa in the experiments thus imply that the perpendicular transport is an important if not the dominant pressure loss channel in W7-X.
As a consequence, the dominant detachment physics in W7-X seems to be different to the traditional picture in tokamaks: In tokamaks large pressure losses and particle flux reduction across wide parts of the target are not easily obtained [9,10]. Pressure conservation naturally leads to the onset of a high recycling regime with lowering divertor temperatures. The high divertor densities then enable large power losses from impurity radiation. In contrast, the long connection length of island divertor stellarators, such as W7-AS and W7-X, provides large pressure losses from the main particle flow channel via perpendicular transport. The pressure losses can actually suppress the high recycling regime altogether, as observed in W7-AS [9], or limit the achievable divertor densities. In combination with the increased importance of perpendicular energy transport in the Scrape-Off Layer this prohibits large dissipated power fractions in the divertor by radiation [8]. As a consequence, a particular focus of tokamak detachment studies is the pressure loss, whereas in W7-X to characterize the available Scrape-Off Layer and divertor power losses and to achieve high divertor densities have a higher priority. The latter will be addressed in this contribution. The experimental data will be used to validate EMC3-Eirene modeling and the physics processes that lead to the radiation movement, the high recycling regime and the neutral pressure build up in the divertor will be analyzed.
[1] Y. Feng, Nucl. Fus. 46 (2006)
[2] M. Jakubowski, Phys. Rev. Let. (submitted)
[3] O. Schmitz, Nucl. Fus. (submitted)
[4] D. Zhang, Phys. Rev. Let. (accepted)
[5] F. Effenberg, Nucl. Fus. 59 (2019)
[6] V. Winters, PSI 2020
[7] A. Langenberg, NF (2018)
[8] Y. Feng, Nucl. Fus. 44 (2002)
[9] F. Reimold, Nucl. Fus. 55 (2015)
[10] A. Kukushkin, Contrib. Plasma Phys. 56 (2016)
[11] Y. Feng, Plasma Phys. Control. Fusion 53 (2011)
Affiliation Max Planck Institute for Plasma Physics Germany
### Primary author
Dr Felix Reimold (Max-Planck-Institut für Plasmaphysik)
### Co-authors
Dr Florian Effenberg (Princeton Plasma Physics Laboratory, Princeton, NJ, 08543 USA) Ralf Koenig (Max-Planck-Institut for Plasma Physics) Dr Maciej Krychowiak (Max-Planck-Institut für Plasmaphysik) Oliver Schmitz (University of Wisconsin - Madison, Department of Engineering Physics) Dr Yuhe Feng (Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany) Marcin Jakubowski (Max-Planck-Institut für Plasmaphysik) Sebastijan Brezinsek (Forschungszentrum Jülich) Dr Holger Niemann (Max-Planck Institut für Plasmaphysik) Mr Georg Schlisio (Max-Planck-Institut für Plasmaphysik) Dr Matthias Otte (Max-Planck-Institut für Plasmaphysik) Dr Daihong Zhang (Max-Planck-Institut für Plasmaphysik Greifswald) Dr Thierry Kremeyer (University of Wisconsin - Madison) Mr Erik Flom (University of Wisconsin, USA) Dr Tullio Barbui (Princeton Plasma Physics Laboratory) Dr Victoria Winters (Max-Planck-Institut - IEK-4)
### Presentation Materials
There are no materials yet. |
# An 8-pole, 50 Hz, three-phase induction motor is running at 705 rpm and has a rotor copper loss of 5 kW. Its rotor input is
1. 5.06 kW
2. 0.3 kW
3. 100 kW
4. 83.33 kW
Option 4 : 83.33 kW
Free
CT 1: Network Theory 1
11532
10 Questions 10 Marks 10 Mins
## Detailed Solution
Concept:
Power flow in the Induction motor is as shown below.
Rotor input or air gap power $${{P}_{in}}=\frac{3I_{2}^{2}{{R}_{2}}}{s}$$
Rotor copper losses $${{P}_{cu}}=s\times {{P}_{in}}=3I_{2}^{2}{{R}_{2}}$$
Gross mechanical power output $${{P}_{g}}={{P}_{in}}-{{P}_{cu}}=\frac{3I_{2}^{2}{{R}_{2}}}{s}-3I_{2}^{2}{{R}_{2}}=3I_{2}^{2}{{R}_{2}}\left( \frac{1-s}{s} \right)$$
The relation between the rotor air gap power, rotor copper losses and gross mechanical power output is,
$${{P}_{in}}:{{P}_{cu}}:{{P}_{g}}=\frac{3I_{2}^{2}{{R}_{2}}}{s}:3I_{2}^{2}{{R}_{2}}:3I_{2}^{2}{{R}_{2}}\left( \frac{1-s}{s} \right)$$
$$\Rightarrow {{P}_{in}}:{{P}_{cu}}:{{P}_{g}}=\frac{1}{s}:1:\left( \frac{1-s}{s} \right)=1:s:\left( 1-s \right)$$
Calculation:
Given that, number of poles (P) = 8
Frequency (f) = 50 Hz
Rotor speed (Nr) = 705 rpm
Synchronous speed $$= \frac{{120 \times 50}}{8} = 750\;rpm$$
Slip, $$s = \frac{{750 - 705}}{{750}} = 0.06$$
Copper losses = 5 kW
Rotor input = 5 / 0.06 = 83.33 kW |
# Methods for assessing convergence of $\sum\limits_{k=1}^\infty (-1)^k a_k$ when $a_k$ is complicated
Think of the problem of convergence of the series $$\sum_{k=1}^\infty (-1)^k a_k$$ Is it possible to consider the convergence of $\sum\limits_{k=1}^\infty (-1)^k b_k$ if $\lim \limits_{k\rightarrow\infty } \dfrac{a_k}{b_k}=$ limited and non-zero?
If not, is there any theorem that helps to facilitate the analysis of convergence when $a_k$ is a complicated function of $k$?
-
Are there any hypotheses at all for the $a_k$? Because otherwise, you're basically asking if there are theorems that help facilitate the analysis of convergence of any series. For without any hypotheses, the same theorems should also work for $a_k' = (-1)^k a_k$, and so you're considering $\sum a_k$. – Najib Idrissi Jun 5 '13 at 9:12
In the following I will assume that $a_n\ge0$; otherwise, as nick points out in a comment, you are asking about convergence criteria for arbitrary sequences.
There is no comparison theorem like the one you ask about. The series $$\sum_{n=1}^\infty\frac{(-1)^n}{n}\quad\text{and}\quad\sum_{n=1}^\infty\frac{(-1)^n}{\sqrt n}$$ are both convergent by Leibniz criterion, but $$\sum_{n=1}^\infty\frac{(-1)^n}{n-(-1)^n}$$ converges, while $$\sum_{n=1}^\infty\frac{(-1)^n}{\sqrt n-(-1)^n}$$ diverges.
You can use [text](link) to obtain e.g. Leibniz criterion. Please edit your answer accordingly. – Lord_Farin Jun 5 '13 at 8:59 |