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I want to fill the holes in my knowledge and get to a masterful level at undergraduate material, so I am looking for books to help me with that. I recently took the GRE Math Subject test and I focused on calculus problems. I am not sure how I did and I will be happy getting into just one graduate school, but what I rea... | 1 |
Tchrist's comment here on my answer to an etymology question brought the following to mind: Ox (from Old English oxa) maintains the same vowel in the plural oxen that it has in the singular. But child has a different vowel (an English short vowel) in the plural. Brethren, an archaic or specialized form of the plural of... | 1 |
I just had a conversation where the sentence 'The system is broken because it's fixed!' was correctly spoken under the pretense where fixed means that it's rigged. Assuming that context of rigged matches as a weak synonym for broken, the question came up - what's the word for a pair of words that are simultaneously syn... | 1 |
In the Hindi language there is an equivalent phrase which is widely used when a common man who is trying to suggest an idea to a person in power or some higher authority respectfully without challenging the latter's incompetency to 'not see the flaw' in the system. Example: A head of the police department being address... | 1 |
I am a physics undergrad, wishing to pursue a PhD in Math. I am mostly self taught in the typical math undergrad curriculum. I am looking for more input, in ways I can improve my mathematical thinking. So, my question is once you read a proof of a particular theorem, what should be the important things that you are loo... | 1 |
I've learned that there is no authoritative dictionary for English. I wonder on what juristic basis students are corrected when making mistakes in an English class. How can someone say that whatever the student did wrong is not considered correct English by other people. In German schools, students may only be "punishe... | 1 |
On our sister site a user recently used the term "tags" in relation to taxis in China. I thought it might mean some kind of official authorization to operate a taxi. But upon clarification I was told "tags" actually means "License plates and stickers that show the registration is currently valid". I'm a native speaker ... | 1 |
I am working on a Project and one of the major part of it is a GAS Detector, The GAS Detector detects the large number of flammable gases, but in order to test the Detector I am required to release certain gases in a room from the GAS cylinder with different flammable gases. There is no such thing in a room which could... | 1 |
Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B. Therefore electron B must be on the forward lightcone of electron A. In the normal forwards in time description a virtual photon propagates from A to B depositing a certain amount of energy and momentu... | 1 |
Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be interpreted as the distribution of momenta? I know this is the case in QM but what happens in the Classical case? For insta... | 1 |
Complex analysis, and in particular contour integrals and the residue theory have proved a very powerful tool in computing a large class of real function integrals which would be quite troublesome to compute if only within the scope of real calculus. There are a great many techniques designed for this purpose, for inst... | 1 |
S.E friends, Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of mathematics, I decided to self-study "introductory" number theory as I never took a number-theory course in past. While brows... | 1 |
I hope this is the right word to use. To me, these forces seem kind of fanciful (except for General Relativity and Gravity, which have a geometric interpretation). For example, how do two charged particles know that they are to move apart from each other? Do they communicate with each other somehow through some means? ... | 1 |
Is it possible to let LaTeX manage minipage placement similar to how LaTeX manages figures and tables to be placed? This question comes from my previous question. I could move the minipages around manual for the best use of space but this becomes a hassle as the number of minipages increases. If possible, it would conv... | 1 |
In case of a charged particle which is travelling at a uniform velocity, the electric field due to it at a given point doesn't change instantaneously . The reason for this delay in change of electric field , physically , can be explained as the time the electric field needs to propagate to that point, or, let's say, th... | 1 |
Mass and energy are interchangeable. Does that mean time and space are interchangeable too? Reason for question: The only difference I can comprehend between matter and energy is that energy has no duration; a photon does not age (even if the universe does). Matter has endurance, and travels through time. Close to a bl... | 1 |
I've asked a question about olfactory's relation to observational and it got me thinking about other senses as well. There are five (or six if you're supernaturally believing), so, what are the exact term to fill out the blanks in the following? It's the bold parts that are interesting and I wonder if the already fille... | 1 |
Take a look at the image below. At the point B a motor is spinning really fast in anticlockwise direction. The motor should be connected to a propeller (I didnt draw it) that will pull the bar upwards but let's suppose the propeller is not connected and the motor is just spinning really fast at X rpm. A person is holdi... | 1 |
This part of the book says that, because the two liquids have the same pressure at the same height (that's true), then if a liquid has a higher height, the liquid would have more pressure at a horizontal line, and then the liquid would tend to flow to the weaker side. However, it isn't really pressure that drives the l... | 1 |
So I have often read that, at least in e.g. northern Europe, in the colder seasons, there is not enough UV (-B) light arriving from the sun, so many people have not enough vitamin-D from that. At first I thought it was simply due to the sun "shining" for only a much shorter period of time in winter compared to summer a... | 1 |
Background: In the SG experiment, an inhomogenous magnetic field affects a force on particles passing between two magnets. "Measurement" takes place when a screen is placed on one end, blocking one of the states. The final measurement we perform (spin state of particles exiting) is heavily dependent on whether we perfo... | 1 |
How are Superposition and Entanglement related? I don't know much of Quantum Mechanics. I am CSE student and got started with this Quantum Computing. It is interesting! If anybody can help me on this, without digging deep into mathematical details. "The principle of quantum superposition refers to pure states of a quan... | 1 |
There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to describe the mean behavior of spin-spin interaction. But, in the antiferromagnetic Ising model, the ground state is an anti... | 1 |
My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation, but that's about it. Similarly, I can follow arguments that pseudovectors behave differently in "mirrors" than vectors... | 1 |
We are two partners about to launch a product that is currently called "Coralline". We are inspired from the animal and its habitat in underwater. Since this will be an international product I am having second thoughts about this word because it is hard to pronounce and transcribe for non-native English speakers. Also ... | 1 |
I can understand the causative form (quite less frequently, we simply say causal verb) with make and get but when used with have/has, it sometimes makes me think differently. Of course, I can understand the construction like the following. I had a barber cut my hair yesterday. In its passive form, it can be written as ... | 1 |
Referencing Stephen Hawking's recent paper Information Preservation and Weather Forecasting for Black Holes and this question. I understand concept of holding the information on the apparent horizon of a black hole for later release in the form of garbled radiation, but how is it that this differs ( if at all ) from th... | 1 |
I'd like to know why in a parallel loop, the voltage, along with the current, isn't divided. e.g. in this image from a youtube video the voltage in parallel loop is the same across both resistors, for some reason this seems counter-intuitive to me. Also later on in the video, the resistance was proportional to the volt... | 1 |
I have joined a grammar MOOC starting with an introduction to English tenses. One of the practice questions left me confused. The question is as follows: Do these two sentences have similar meaning or different meaning? Julie has studied French for two years. Julie has been studying French for two years. I'm not sure h... | 1 |
(Too) Long ago, I had some problems with some equation. I wanted them to look like this (this is how they looked in LyX), but when compiled they looked like this: . What botheres me compared to how it looks in LyX is that way too much spacing between the columns is used in the compiled version. there isn't a space afte... | 1 |
Personally I learned Physics in high-school and found it very interesting, I read up a lot about physics in my free time. Personally I am also a programmer which I think is also good when it comes to Physics. Now I want to start studying in a university and my dilemma right is mainly between Math/Computer Science/Physi... | 1 |
Why does the definition of an irreducible element require us to be in an integral domain? Why can we not define an irreducible element exactly the same in a commutative ring that is not an integral domain? We have that an element is irreducible if it cannot be written as a product of two non-unit elements. Unit element... | 1 |
I am not sure whether the sun originally emits everything in the electromagnetic spectrum, (whatever the relative strengths of each portion might be), but I do read that many waves, including gamma / x-ray, and UVC, are filtered or 'converted' to heat after travelling through solar plasma and atmospheric layers like oz... | 1 |
When a nuclear device is detonated at ground level, we see the familiar mushroom cloud, which is undoubtedly caused by the weight of the atmosphere suppressing the upward thrust, causing the debris and dust to be curved down back towards the Earth. The horizontally propelled mass again does not travel very far from the... | 1 |
While googling about whether "atheist" should be capitalized, and skimming past posts by people blogging about atheism rather than about English grammar, I came across http://uwf.edu/writelab/reviews/capitalization/ It says [Capitalize] Religions and religious terms Examples: Catholicism, Hinduism, Buddha, the Bible, C... | 1 |
Say you have an author who has a lot of random personal stories from their life, all interesting, but don't stand on their own to be an interesting, single story. The author decides, "why not combine them all into one story?" Well, that sort of becomes an autobiography, I guess, if you actually tell the story in a more... | 1 |
I am looking for a figurative or graphic expression to describe the minimal luggage content, fast to pack, or that you always have with you, without which you would feel less safe when travelling. The expression should be concise too. When I take a plane, and since luggage in the cargo area can get lost, I generally ha... | 1 |
I'm taking the curl of the deviatoric stress tensor in index notation, and I've ran across something that I can't seem to be able to simplify. The issue is shown in the following portion of the curl operation: The first two terms on the right hand side should be zero because the curl of a scalar and the curl of a gradi... | 1 |
The setting: Imagine the scenario where I am searching for something and once I find it I identify it, then afterwards when I no longer need it I discard it. If at some point I need to identify it again I perform the search again and will succeed since it's still there. The problem: The noun for the process of identify... | 1 |
Although I know the clear meaning of commonly used prepositions in English, sometimes, I'm a little confused with them and cannot understand the difference between them. A week or so ago, I asked a question on StackOverflow which was titled by me as follows. Varargs in method overloading in Java. In this simple questio... | 1 |
Many of the books I use are parts of series. biblatex gives you more fields to add bibliographic information to than BibTeX does, but it has no fields appropriate for the editor of a series. If I use the EDITOR field, the bibliography will (by default) print edited by, which doesn't give the right impression of what th... | 1 |
Pardon my ignorance, but I am really interested in understanding the quantum mechanics and it's interesting implications, but clearly I don't, since I keep coming up with violations to many physics theorems. In particular, the delayed choice quantum eraser experiment is of interest. Consider the wikipedia diagram, In t... | 1 |
On this site, people ask questions and then answers and proofs for those answers come from readers. Readers mark the best answer and then people focus on the next interesting topic. Sometimes, a question will have many answers with proofs from different points of view and people commenting on whether the proofs are val... | 1 |
I would like to make the bubbles in my soda drink last longer. For example, one good thing to do is to keep the bottle shut when you don't drink. But what else I can do? Should I try to minimize the surface between the drink and the air from the bottle? How about the surface of contact with the bottle? The bottle shoul... | 1 |
I'm trying to understand where energy is located in a quantum field world. For force fields, there are conserved properties that (in my mind's eye) are always stuck in that field. These arise from symmetries in the fields, by Noether's Theorem. As such, I imagine that properties such as charge can move around in the fi... | 1 |
Theoretically, a change in either electric or magnetic field will cause a current to flow , I am already familiar to Faraday's law of electromagnetic induction, so I tried to search about producing a current using a varying electric field, didn't find anything, I found an interesting apparatus though: Tesla's electrost... | 1 |
I just met with a very basic question. (Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of matter just because they flow! So there must be some significance to 'flowing'. That further led me to ask why in the first... | 1 |
I have a hard time understand the statement that When you only look at the classical limit or classical physics, string theory exactly agrees with general relativity Because from what I know, String Theory assumes a fixed space time background (ie, all the strings and membranes interact in a fix background, and their i... | 1 |
What are the rules for typesetting superscript, subscript and fractions (as in a/b but with an horizontal fraction bar)? I am centring the subscript on the baseline, the superscript on the cap height and the fraction bar on the x height. Latex appears to be doing that as well. What I haven't figured out is how to posit... | 1 |
The idea is that the difficulty of the game of chess is derived primarily from the asymmetry between the king and queen. all other chess pieces are arranged symmetrically and can move symmetrically, then, if there were two queens (or two kings) instead of a king and queen for each player, the game would be exactly symm... | 1 |
I have gone through a lot of seemingly similar questions/issue but have not find a solution. Since we are working as a group there are some that prefer to write using MS Word-EndNote. I have all references in BibTeX and these are updated from time to time (when something moves from pre-print to actual publication with ... | 1 |
I am writing a technical research article. I have an experiment where precision can be easily determined (bid-ask spreads for the economists). Calculating some formula twice based on the precise observation of the upper bound and the lower bound does change the results (obviously) and is not negligible, but it does not... | 1 |
John Rennie's answer to this question got me thinking about the water supply in a house. I know that water supplies are normally operated at an over-pressure with respect to atmospheric pressure to make sure that if you open the tap the water will flow out due to the lower pressure at the exit of the tap (including a c... | 1 |
Wikipedia mentions that: Some languages flexibly integrate onomatopoeic words into their structure. This may evolve into a new word, up to the point that it is no longer recognized as onomatopoeia. One example is English "bleat" for the sheep noise: in medieval times it was pronounced approximately as "blairt" (but wit... | 1 |
When using the method of action variation to establish GR field equation in one of the steps we use Stock's theorem on an arbitrary manifold to show that one of the terms contributes nothing to the variation wrt the inverse metric. See for example the Wikipedia entry on Einstein-Hilbert action. Most texts that I read, ... | 1 |
In this question the issue came up as to whether there's any difference in the level of politeness/correctness involved in I'd rather not say as opposed to I'd prefer not to say. My own gut feeling is the prefer form is a bit more "formal" (and thus arguably more correct/polite). This NGram shows that I'd rather occurs... | 1 |
I'm about to dive into LaTeX in preparation for writing a (technical) Master's Thesis. Since I'm kind of disappointed with the disregard to typography that is sometimes shown in such works I want to do it better, and just picked up The Elements of Typographic Style by Robert Bringhurst. Thanks to LaTeX and clever templ... | 1 |
This is a soft question. It's extremely commonplace for mathematician's to refer to work as "elegant," "beautiful," and I've seen many compare the process of doing mathematics to painting, or playing music. I think that for the most part, I can understand how certain theorems, formula, or general theory can be evocativ... | 1 |
I think this is a genuine math problem. And it's somehow related to knot energy but not directly solved by the latter. Why can't I tie a hard knot on a rope of infinite length? By infinity I mean you never pull back either ends of the rope. And I attentively add a constraint to the rope that the rope is smooth thus no ... | 1 |
I was soldering an LED when accidentally the soldering wire touched the LED's other Pin while the soldering iron was touching the other and the LED lit up, not bright but bright enough to be seen. I did it again to see did it actually light up, and it did. I noticed my bare feet were touching the ground so I raised it ... | 1 |
Sometimes I hate classes for mathematicians. It is not their precision and formality in building the concepts, but they never give a motivation. So in the course my professor started right with the definition of vector space, assuming I suppose that everybody knows what he is talking about. Well, reading some books for... | 1 |
I had an interesting conversation with CuriousOne the other day about the question Experiment that demonstrates the wave-particle duality of electrons. I thought that wave-particle duality existed, CuriousOne thought it didn't (whether CuriousOne thought this wasn't true for both light and matter, or just matter I'm no... | 1 |
In elementary school, I was taught the rhyme: "i" before "e" except after "c", and in words like "neighbor" and "weigh" Obviously this means that "ei" is used in "deceive" (it comes after "c") and "sleigh" ("gh" follows it). The word "weird" does not follow this rule, and I have always thought that to be weird (please ... | 1 |
To start with, I have almost no any experience in the theory of finitely additive (f.a.) measures, but I work a bit with countably additive (c.a.) ones and find the theory in the latter case amazingly beautiful. My concern is that at the moment measures have been introduced as an extension of such notions as area and v... | 1 |
I recently started reading the book Multiple View Geometry by Hartley and Zisserman. In the first chapter, I came across the following concepts. Projective geometry is an extension of Euclidean geometry with two lines always meeting at a point. In perspective, geometry parallelism does not exist. Then he goes on to exp... | 1 |
I've landed in a physics debate amongst bike mechanics. In a typical bicycle hub you have a simple bearing; the cups are set in the hub, the race (cone) threads onto the axel and there are just loose ball bearings in between (no ball retainer). When properly adjusted, there is no play in the system, and the axel turns ... | 1 |
Is it correct, and safe to say, that -- generally speaking -- verbal constructions with "with' are to a certain extent more widely and commonly used in AE than in BE and other varieties of English ? E. g. Speak/talk with (as opposed to the shared speak/talk to); visit with (=chat/converse with); meet (up) with (origina... | 1 |
Before starting algebraic geometry, I got some understanding of Compact Riemann Surfaces which is more or less rigorous; and then I attended a couple of lectures on analytic geometry. I did not quite fully grasp the analytic geometry rigorously; but it stuck in my mind and this previous experiences helped me greatly wh... | 1 |
I have been trying to read about the energetics of observed supernovae for some time. And while the observed core-collapse supernovae have many scientific papers about them trying to estimate the energy released in different evemts like this one, I couldn't find similar reports for Type Ia SNe telling how much energy w... | 1 |
I was wondering if there has been any category theoretic advancements in the study of the Riemann Hypothesis and the theory surrounding it? This question is meant in the same vein as these questions, but specifically for category theory. These other two questions do not have any answers related specifically to category... | 1 |
One of my friend who stopped studying maths in high school told me once You study maths, can you help me fill my tax forms? In her mind, advancing in maths studies implied manipulating an increasing amount of numbers. The reality I faced was the contrary: I dropped numbers for some more abstract notions (i.e. letters a... | 1 |
I have a ... pdf file, which contains figures of plots such as the following: Now the second plot isn't too hard to draw on TikZ (I assume... I hope? I don't have any experience apart from drawing circuits!), but it's figures like the first picture that I'm more worried about. I want to re-draw them in code (like in Ti... | 1 |
I'm reading a Mathematical Logic book (A course in mathematical logic, Bell.M ) and the author is saying that the symbols of a formal language don't have a well-defined shape, he's claiming that they are abstract entities. I think he is saying that even though symbols are usually defined by its shape, the symbols of a ... | 1 |
The thought experiment goes like this: Say there is some circuit which turns a lamp on/off with just a flick of a switch. Say its off; you flick it, it turns on; flick it again it turns off, and so on. So say you are conducting the experiment for two minutes. When the remaining time halves, you flick the switch; and wh... | 1 |
Imagine the following gedankenexperiment. Observer Alice is right here on Earth. Observer Bob is at say Alpha Centauri. A pair of maximally entangled qubits is formed with one qubit handed over to Observer Alice and the other sealed in a box on Pluto shielded from decoherence. It takes a few years for any signal to rea... | 1 |
Many dictionaries use a semicolon in a meaning for a word. For instance for the word impertinent I have seen: "outside the bounds of proper speech or behaviour; impudent; insolent; saucy" Then there is a synonym explanation of connotations for impertinent, impudent, insolent, and saucy. My question is: Does the semicol... | 1 |
A question that has been bugging me for quite a while was raised by some communication between my employer and a partner organisation based in Dubai. It turned out that more than once, it's been noticed that this other party tend to use a particular tone of address in letters and emails. Whereas they will address male ... | 1 |
I'm reading Yelizaveta Bam of Daniil Kharms (tr. Neil Cornwell) and stumbled upon the following dialogue: Ivan I.: But who then lights the lamp? Pyotr N.: No one, it burns by itself. Ivan I.:But that surely cannot be! Pyotr N.: Empty, stupid words! There is an infinite movement, the breathing of the lighter elements, p... | 1 |
First of all: I was not able to compile a MWE, since the error seems to be connected to one of my documents, all of which are classified. I'm experiencing (for the first time) the following error: When opening a file in Acrobat Reader and then trying to print, I receive the errors The document could not be printed Ther... | 1 |
I am looking for a method to save the lecture materials, and examples without hand copying from the boards during the lectures. Unfortunately some courses don't have the material available, and sometimes you want to copy a specific example. EDIT: The reason I would like to avoid copying by hand is that it is sometimes ... | 1 |
I was writing a market research report the other day and listed the challenges my company faced in the market in question, then I created a new section header for the... uhh... easy bits? That's when I realized I could think of no reasonable antonym for challenge in the noun form. I can certainly describe it -- charact... | 1 |
When speaking with my mother a couple of days ago, I read to her a message I was sending to my cousin on her behalf ending with: "... the birthday of your youngest." [implying her child] She immediately leapt on this and said that as my cousin only had two children, the use of the superlative was not permitted and the ... | 1 |
English or any other language could be written or spoken in both the forms, either the user could use simple words or he could use some technical words, my question regarding English is which has more impact on listener, Simplicity in language? or Complexity by using technical words? and is it dependent of whether you ... | 1 |
Unlike the use of "no problem" as an alternative to "you're welcome" or "my pleasure," neither of which bothers me much in common speech, its use as a reply to an instruction or directive to put right what the respondent has done wrong, particularly if at great expense or at substantial loss of available time, tests my... | 1 |
Here is a sentence from Chapter Seventeen of Huckleberry Finn. The sentence appears in a grammar worksheet: When I got to the three log doorsteps I heard them unlocking and unbarring and unbolting. My English teacher stated that "them" was an indirect object, and unlocking and unbolting was a direct object, as that is ... | 1 |
I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to manipulate the equation into the ideal form - I find myself easily making mistakes. The obvious solution is more practice. But I ... | 1 |
I am currently an undergraduate and thinking about applying to graduate school for math. The problem is that I don't know what field I want to go. Taking graduate classes even more confuse me because the more I learn the less I know what specifically I want to do. My question is to where to find an information about di... | 1 |
I have searched for some time for the "insider scoop" on how academics operate when it comes to mathematical research (theoretical physics research would also be interesting, but mostly interested about math research).I read "Letters to a young mathematician" which was a nice book but didn't talk much about the researc... | 1 |
TikZ provides the two keys execute at end picture={<code>} and execute at end scope={<code>} which can be used to execute any code at the end of the picture and of the current scope, respectively. I now like to execute some code at the end of the picture if a TikZ key defined by me is used outside a scope environment, ... | 1 |
I'm trying to submit a journal paper through ScholarOne Manuscript (an outdated automatic build system some scientific journals use). The issue is that I'm using biblatex. I tried with both backends, biber and bibtex, and I couldn't get it through. Has any of you managed to make a successful submission to ScholarOne wi... | 1 |
Frequently I hear Americans (admittedly mainly in TV/movies) say "personal" and "regular" in the following contexts: "Don't take it personal." "I like that he treats me regular." Both of these are horribly incorrect to my British ear - I have never heard either here, it would be "personally" and "regularly", ignoring t... | 1 |
I think I kind of understand this process but I would like someone to explain it more completely. For those who aren't aware here is the scenario I'm talking about: As terrain maintenance at my local ski slope we often use salt to firm the snow around jumps on warm slushy days. Throwing down a even layer of salt causes... | 1 |
I am a native German speaker and in German it is considered very bad style to use a word more than once in a sentence or even in close proximity. So you usually have a big list of synonyms in your head and you always cycle though these words while writing or even change complete sentences so you will not have to use th... | 1 |
I want to tell that something reminds/hint us of another thing. For example, in an application, a sorting method used in it has similarities to bubble sort but not completely the same. In this case, when reading about the sorting method used in the application reminds or hints me of, or brings to mind the idea of bubbl... | 1 |
With the following definition: To lower in quality or character. Synonyms found: corrupt, pervert, subvert, demoralize, demoralise, debauch, debase, profane, vitiate, deprave, misdirect However all of those have a very "intentionally evil" connotation. I would say more along the lines of "messed up", but it needs to po... | 1 |
What is the formal definition of an event? According to Wikipedia, "an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it." This definition seems too large because it includes even points where no identifiable process is happening. On the other... | 1 |
There's an experiment demonstrating the properties of super-fluid Helium compared to normal fluid Helium, in which the Helium is put in a jar who's bottom is porous. The super-fluid can pass through the small capillaries, while the normal fluid can not. Another experiment uses a fine grained powder (implying the same h... | 1 |
In some posts in this forum I've read that sign convention in optics is useful for making formula memorizing easier, and that we have to use sign convention again while applying the formulae to neutralize the effect of taking sign convention... I tried to use geometry and saw that indeed without sign convention we get ... | 1 |
From Planetmath A meager or Baire first category set in a topological space is one which is a countable union of nowhere dense sets. A Baire second category set is one which contains a countable union of open and dense sets. From Wikipedia: A subset of a topological space X is called nowhere dense in X if the interior ... | 1 |
This is the law of stable equilibrium, according to Hatsopoulos and Keenan: A system having specified allowed states and an upper bound in volume can reach from any given state one and only one stable state and leave no net effect on its environment. Consider the following system: two sealed containers of gas. Containe... | 1 |
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