darklight03/StackMIAsub huggingface dataset:
I was working on a lab in class drawing Free Body Diagrams. The problem required we drew an FBD of a ball that is in the motion of being thrown. I drew a slightly diagonal line labelled Applied Force, a vertical line straight down labelled Gravity, and a line opposite of Gravity labelled Normal Force. I was told that there is no normal force at all in this situation, and that the only two forces are gravity and applied force. I was confused because I thought that the ball was being held up by the hand (acting as a surface) which provided a normal force while still being pushed by the hand in the positive direction resulting in an applied force. So in this situation, would the ball have any normal force at all acting on it?
I'm a huge Pulp Fiction fan, and the following is one of my favorite scenes, but it also irks me. (source: IMDB) Jules: [Jules shoots the man on the couch] I'm sorry, did I break your concentration? I didn't mean to do that. Please, continue, you were saying something about best intentions. What's the matter? Oh, you were finished! Well, allow me to retort. What does Marsellus Wallace look like? Can a question be a retort to something? I see retort defined as (dictionary.reference.com): to reply to, usually in a sharp or retaliatory way; reply in kind to. to return (an accusation, epithet, etc.) upon the person uttering it. to answer (an argument or the like) by another to the contrary. All the above suggest some sort of a reply. But can a retort be a question, or even a counter-question ?
Break comes to a close, and you, a renowned mathematics professor, step into a grand lecture hall to deliver the first lecture of the semester on topology. This is an introductory course. Half of the students cannot even pronounce homeomorphism. As you look around the room, a bead of sweat works its way across your brow. All you can think of is the possibility that the entire class will fail, and you will be mocked by the other professors. Then you take a sip of water and pull yourself together. You pick up a fresh (but not too fresh) piece of chalk, write your name across the board--effectively marking your territory--and address the class. How do you introduce a class of undergraduate students to the field of topology? I am looking for a creative, but precise explanation of the field and the most fundamental topological concepts. Diagrams and metaphors are welcome.
Can a sentence like this: "I don't know who the first man that made such and such thing in such and such place was," be grammatically correct if we don't put "was" at the end of the long phrase, that is, if we write: "I don't know who was the first man that made such and such thing in such and such place"? I can see in Google Books examples that in such cases the verb is often put after the wh-word, but I don't know if there is a grammar rule to support this. Some examples: "We do not know who was the first man who ascended above a poor and humble people to become Egypt's first king ..." "... we do not know what was the ultimate judgment of the various members of the community ..." "I do not know who was the first to suggest a connection between the problem of free will and the breakdown ..." "I do not know what was the date of this change in me, nor of the train of ideas ..." "We do not know what was the primitive text from which Codex Bezae derived its Latin or its Greek ..." "We do not know what was the practice in the days of the monarchy, but the story of Athaliah shows ..."
I'm writing a paper about an algorithm that I have developed. Just for illustration, I will say that the method name is "quicksort". My question is about the usage of the in the following context: This paper proposes quicksort, a novel and fast algorithm. The advantage of quicksort is that... My question is whether I should use "The advantage of the quicksort..." or "The advantage of quicksort". I am also looking for resources explaining the usage of the in this context. [Meta] Usually, to check if a certain sentence is correct, I search Google using wildcards. However, in this case, the correct answer is depends on the context. I have also tried to find a answer in the following book but without success: Science Research Writing: A Guide for Non-Native Speakers of English.
I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture onto Sci. Computing/Applied Maths, but I'm worried my inadequacy (as quite personally, unfortunate lack of interest) for Lin. Alg. will prevent me from being successful in topics such as Numerical Analysis, Algebra, as well as Scientific Computing. Does anyone in the applied maths field/experience with applied maths have any advice on what I should do? That is, what else is there like Calculus/DEs that will help me in this field? Or do i just need to buck up and get on my Lin. Alg. horse in order to get remotely close to where I want to go? I appreciate any and all input.
I was looking for a synonym of spontaneous, and voluntary naturally came to my mind. In an attempt to understand the difference between them, I tried to google spontaneous vs voluntary. To my surprise, nothing really interesting popped up from search results. Then I decided to look them up respectively. As expected, voluntary is listed as a synonym of spontaneous according to many online resources, and vice versa. However, to my great shock, involuntary is also listed as a synonym of spontaneous by major online dictionaries. Although the fact does not necessarily imply voluntary and involuntary are synonyms, I continued to look further into voluntary vs involuntary due to confusion. I found that a voluntary action is something that is done voluntarily or with meaning to do so, while an involuntary action on the other hand is done automatically. Now I'm even more confused. The word automatically just reminds me of spontaneously, convincing me to believe involuntary is indeed a synonym of spontaneous while voluntary seems less so. Could someone please justify or explain the contradictions mentioned above? I'm totally lost.
Suppose we have a contact process on a finite lattice. I'm asked to give a heuristic argument for the fact that the extinction time for the contact process is exponential in the size of the lattice when it is in the supercritical phase, and logarithmic in the size of the lattice when it is subcritical. The supercritical phase means that on the infinite lattice, the infection never goes extinct almost surely. I really don't know why this is the case. I get that the extinction time in the supercritical phase will grow rapidly, because if you make your lattice larger, the number of infected nodes grows. Because all these nodes are infected and they infect other nodes quickly (because of the supercritical phase), the other nodes will stay infected much longer. But is there any reason why this should be exponential (or logarithmic in the other case)?
Motivation: If I start with the group axioms and drop the requirement that I have inverses, I get the monoid axioms. If I proceed to drop the requirement that I have an identity, I get the semigroup axioms. If I then drop the requirement of associativity, I get the magma axioms. If I drop the operation, I get the set axioms. A map preserving the monoid structure is a "monoid homomorphism;" a map preserving the semigroup structure is a "semigroup homomorphism;" etc. Question: Now suppose I start with the topological space axioms and start dropping conditions. Do the resulting sets of axioms have names? What about the maps preserving such structure -- do they have names? In particular, what about the smallest case of a sets equipped with some subset of their powersets, together with functions such that the preimage of a designated set is a designated set?
There is a challenge involving a lemon floating in a jug of water which seems impossible to beat. I've noticed it in several pubs of Edinburgh. The challenge is as follows: There is a jug half filled with water. Floating in the water, there's a lemon. The lemon doesn't touch either the bottom nor the edges of the jug. The challenge is to successfully balance a coin on the lemon. Modifying, moving, or more generally touching the lemon are not allowed. Any attempt to balance a coin on the lemon seems to result in the lemon flipping over, and the coin to sink in the water. Why is it so hard to balance the coin while it's extremely easy to balance a coin on a lemon set on a table? How do you beat the lemon challenge?
I've been using OpenOffice and/or MS Word to do my college assignments, but since I started this new discrete math course, I'm finding myself very annoyed with the math formula options in those programs. I learned about LaTeX and figured it would be my best option. Since I really just want to get my college assignments done with it and not use it for printing books I've written or anything, I decided to go with LyX. It has a quick and easy preview option, and isn't so different from what I'm used to. I still can't find a way to make the fancy, cursive script "U" that represents universe or universe of discourse that is used in set theory. Is there a specific package I need, or did I just miss it somehow. Also, if I do need a new package, how is that even done with LyX. Anyone with assistance has my gratitude.
My wife was discussing pudding consistency this morning and used a sentence along the lines of, "I only like the pudding you make". I blinked and asked if she really liked the pudding I make and she replied, "No, I mean the pudding you make, you know, like if I were to make some pudding". She was using the "you" in a sense of a hypothetical person, I guess, like saying, "That's what you do in a crisis" when commenting on a riot scene in the news. You're not using "you" to refer to the person you're speaking to, but rather a form of general humanity. Anyhow, is there a term for such a usage such that you might be able to answer, "Oh, sorry, I was using 'you' in the [term] context, not referring to you specifically"?
I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the lecturer just drew a picture of a solid wall with two slits and then showed pictures of the interference patterns generated by shooting a single electron at the slits. Fine enough, the electron interferes itself, which is beautifully explained by the wave function. However, aren't the atoms in the wall with the slits also described by a wave function? I mean, can we even meaningfully draw a picture of a 'slit' if it is roughly at the scale of an electron? Aren't we supposed to be dealing with a wave function there too? Looks to me the wall with the slits is treated as a 'classical' object (you can touch it, feel it, smell it) while electron is treated as a quantum object. But that simply cannot be the case. Question: how does the wave function that describes the atoms around the slit 'know' to interact with the wave function of the electron? Does it collapse? The reason I ask this is because when the electron does not make it through the slit, it must have collided with one of the atoms: but wouldn't collision imply that two particles were at the same place at the same time? Doesn't that require wave function collapse? I'm confused ...
I'm trying to understand the connection between the wave model and the particle model for light. It's understood that the energy of a photon is given by E=hf, but from my understanding of fourier analysis, the only kind of wave that has a precise frequency is a plane wave. The plane wave is an idealization, since no real wave permeates all of space and time. So imagining a more realistic EM pulse, the frequency spectrum will have some kind of spread depending on the shape of the pulse. Is the pulse a single photon? Or is it a collection of photons, each with different frequencies? In the photoelectric effect, it's usually described as a single photon with sufficient energy being absorbed, kicking the electron out of its orbit. Let's imagine the pulse is symmetrically centred around the frequency with energy exactly equal to the metal's work function. What exactly happens to such a pulse? Will the whole pulse be absorbed, since its average frequency has energy of the work function? Or will the half of the pulse that has the higher frequency be absorbed, leaving the rest to reflect or what-not?
Whenever I add milk to my morning coffee I often enjoy watching the patterns which are created. These patterns have a striking resemblance to certain fractals and my question is, "Why?" Oh dear, that is never a good question, so let's try "Why shouldn't they?" The obvious observations are that the water is very hot when the milk is added, so we expect the "coffee particles" (non-milk part) to have a higher velocity relative to the "milk particles". Secondly, the coffee part, having been recently stirred, is often still rotating (clockwise in my case). Finally, the image we observe is a projection of some distinct portion of a "top layer" of the milk and coffee mixture. Add diffusion into the mix and it really seems like some crazy stuff should go down! But I'm afraid I'm not satisfied. Why physics.SE... why?
I read about this law / property a couple of months back, but I've forgotten what it's name was and I can't seem to find it by Googling. I was hoping someone could give me the name for this property. If I recall correctly, it was named after same famous mathematician like Gauss or something... More detail: This site was basically describing how you can make a long piece of metal, paper, etc. stronger by bending it along its long axis. This way, it is less likely to collapse along its length when upright. An example of this property was grass blades, which are able to stay upright due to the fold / bend along their long axis. If someone knows the exact name of this property, please do tell me!!
I am familiar with basic quantum mechanics and I know that there is no concept of 'force' in quantum mechanics, unlike in classical mechanics. Problems in quantum mechanics are solved by writing down the Hamiltonian for a system, and trying to solve for the various eigenvalues. Some of the first problems that are taught to students learning Quantum Mechanics are the harmonic oscillator problem, and the Hydrogen atom problem, where the Hamiltonian takes the same form as a classical system. Since moving over to quantum mechanics requires one to lose several ideas that have been built up while learning classical mechanics, why is the potential found in quantum mechanics problem of the same form as classical mechanics? The potential for the hydrogen atom, for example, is classical in origin and is derived from the Coulomb force. How is this direct usage of the potential, which is purely classical in origin, justified by the theory?
I'm in doubt in the application of Gauss' Law to find electric fields when the charge distribution is symmetric. Well, first of all: I know how to find the magnitude of the field - we just enclose the charge distribution with a gaussian surface on which the electric field will not change it's magnitude, and then using Gauss's Law we can write it in terms of the total charge inside and the area of the gaussian surface. My problem is: how do I find the direction of the field? I mean, in a spherical symmetric distribution it's easy, because we know what's the vector that points radially outwards (it's simply one of the unit vectors from spherical coordinates). But what about a cylindrical symmetric distribution ? Would I need to use the unit position vector of cylindric coordinates ? In the general case I would need to switch to more appropriate coordinates to write the field ? Is there a general way of treating this ? Sorry if this question is to silly or too basic. I'm just trying to understand how to use properly this law.
Good afternoon, I'm trying to learn about Fuzzy alone, I was using some texts on the Internet about it, but it was very difficult to learn. I want to learn about Fuzzy set as shaper of uncertainty. Operations with fuzzy sets. Characterization and properties of fuzzy sets. The Zadeh extension principle. Fuzzy numbers. Fuzzy relationships. Fuzzy relational equations. Systems based on fuzzy rules and the Mamdani inference method. Fuzzy controller and an application. Compositional rule of inference. Inference method of Takagi-Sugeno-Kang. Approximation properties of fuzzy systems. Measures and fuzzy integrals. Introduction to fuzzy dynamic systems. I found these books on web -Fuzzy Mathematics: An Introduction for Engineers and Scientists, John N. Mordeson, Premchand S. Nair -Fuzzy logic with engineering applications, Timothy J Ross -Fuzzy sets and fuzzy logic, George J Klir Does anyone know any of these books? I am totally beginner in this matter, and unfortunately none of these books has available solutions. If anyone knows of any video material on this topic I'm grateful too.
After spending almost one year on this site, I've realized that my knowledge of mathematics is not deep enough. I love mathematics, i mean I am obsessed with it. I have a masters degree in mathematics from a reputed university in India and now I want to pursue PhD in this subject. It's been one year since completion of masters degree and I am unable to find a place in any university for PhD (I failed at couple of entrances). So my question is, is my love and passion for this subject will help me to do research or to do research in mathematics one need an unusual brain? By unusual I mean who can instantly catch the logic and solves a problem, which I can't. I am slow. So I need some advice on this? How should I prepare myself? Thanks. Edit: By this question, I am not asking about which career I should choose. I know I want to do PhD. What I am asking is, "How one should prepare before starting a PhD?" What are the basic points I should be working on? Simply just reading many things would not help I guess. So if this question can be reopened and some one give me a pointer then it would be helpful.
I'm writing a paper about classes of formal languages, and I'd like to have a diagram showing their heirarchy. Something similar to this (from Wikipedia:) Is there a LaTeX package which, I can give the relationship between the classes to, and have automatically generate and lay-out a venn-diagram for me? The idea is that I would give it the list of classes, and some relations between them, i.e. which were contained in each other, which were disjoint, which were incomparable but not disjoint. Containment is assumed to be transitive (i.e. if A is in B, B is in C, then A is in C). Is there a way to do this programatically, or a package to do it automatically? The idea is that I'm continually adding new classes to the diagram, and would love if it would automatically update itself every time I discovered a new relation.
This sounds like a daft question, but I'm serious. Translation and rotation are clearly different -- the symmetry between them is broken by Newton's Laws. But in the Lagrangian/Hamiltonian frameworks, they look extremely similar! The Lagrangians for free rotation and free translation are exactly the same, up to the replacement of some letters. Working entirely with the Lagrangian framework, it's unclear when and where the symmetry breaking happens. Despite this, there are many clear asymmetries between translation and rotation: There is absolute rotation, but not absolute translation. (At least, I believe this is the orthodox position.) In space, starting with zero linear and angular momentum, it's possible to change your angular position but not your translational position (you can turn yourself around, but can't move your center of mass). In quantum mechanics, free particles can have continuous values of linear momentum but have quantized angular momentum. I know why the third point holds: localization causes quantization, and the set of possible angular positions is compact, while the set of possible positions is not. In fact, I feel like this is the only difference, a priori, between translation and rotation. In layman's terms, if you keep rotating, you'll get back to where you started, but if you keep translating, you won't. Is it possible to use this reasoning to extract the first and second bullet points above? If not, what exactly is the difference between translation and rotation?
It's my first time to write latex with Mac os (or in fact, using Mac os in general) and unlike with Windows I'm having some trouble viewing my output files. I'm using texmaker. I would like to have either dvi or pdf viewer constantly open and auto-refreshing when I save changes or convert them to latex. I was told that Skim application should do the job, but I always have to close the dvi/pdf and re-open it for Skim to refresh my changes. Any suggestions or advices how to handle this properly? This might seem like a small problem, but when I save and view my changes constantly it is really painful (and time consuming) to always close the pdf/dvi viewer, re-open it and then scroll to the correct location. Thanks for all the help in advance.
Basic books dealing with the interaction of X-rays with matter ussually don't mention anything about the polarisation, but I read somewhere that X-rays scattered in matter are linearly polarized, specially those scattered at right angles of the incident rays. If I remember well, the reason was discussed considering the unpolarized X-rays as a mix of classical electromagnetic waves polarized in all the possible directions: each polarized wave produces electrons oscillations in the direction of the polarization, and this oscillation leads to the emission of (scattered) waves with the same polarization but with maximum intensity in the plane perpendicular to the polarization. But we know that X-rays are not classical waves but quantum entities and they can be scattered by different mechanism: Rayleigh scattering, Compton efect...so, is the statement about the polarisation of the X-rays true? Is it valid for both types of interaction (Rayleigh and Compton)?
This was explained to me many years ago, by a physics teacher, with the following analogy: "If someone on the beach wants to reach someone else that is in the water, they will try to travel as much as they can on the beach and as little as possible on the water, because this way they will get there faster." I'm paraphrasing of course, but this is as accurate as I recall it. This explanation makes no sense to me. Was he telling me the light knows where it is going? It wants to get there faster? It chooses a different direction? (No need to answer these questions, this was just me trying to understand the analogy.) My attempts to clarify the issue were without success and many years later I still don't know. Why does light change direction when it travels through glass?
I am attempting to write a program that will compute the average amount of a particular product produced when randomness is involved. Let's say that I am trying to produce some widget. Whenever the production process for this widget is started, it is not guaranteed that the process will be successful. So let's say that the probability of successfully producing a widget is P(s). However, you only start with M number of materials, and whenever a widget is successfully created, then C materials are used up. Similarly, whenever a widget fails to be prodeced L materials are used up. So we know the following: P(s) = probability that production process will yield a widget. M = Amount of starting materials C = Amount of materials used if widget successfully created. L = Amount of materials lost if failure to make widget.</code> The problem I am having is in trying to compute the average number of widgets created (and similarly, the average number of failed widgets) given different values for P(s), M, C, and L. How can I come up with an equation that gives me the average successes and failures to create widgets?