darklight03/StackMIAsub huggingface dataset:
Once again, y'all can blame my boss. Well, him or Captain Picard. He (my boss, not Picard) has the annoying habit of saying "Make it sure that", instead of "Make sure that". No matter how many times I correct him (usually via a post-it note thrust in his face while he's on the phone), he keeps making this mistake. Today, he clarified the root of his confusion: if there's an it in "Make it so" (he's a big ST:TNG fan), then why shouldn't there be an it in "make sure that", also? As a native speaker, the best I can come up with is "because it sounds wrong", and that's never enough to appease my boss. Help? How can I explain the difference to him? Is there logic behind it, or is it merely idiom?
everyone. When referring to a person, are there any firm guidelines when it comes to the use of "a" or "the" after the comma that follows their name? To clarify: Recently, I was writing an article about Amy Winehouse, and I referred to her like this: "Amy Winehouse, the troubled singer-songwriter who..." A few weeks later, however, I was writing an article about a celebrated photographer, and it felt wrong to use "the" after the comma, so I wrote: "Sebastiao Salgado, a celebrated Brazilian photographer who..." As a result, I am now wondering if there are any solid guidelines? I realise that "a" is used when the subject is one of many, and that "the" is used when there is only one, but there have been times when I have followed these guidelines and the sentence has looked / felt wrong. Can anyone offer some guidance?
In order for a body to move with uniform velocity in a circular path, there must exist some force towards the centre of curvature of the circular path. This is centripetal force. By Newton's Third Law, there must exist a reactive force that is equal in magnitude and opposite in direction. This is the reactive centrifugal force. My question is simple, and it is probably the result of lack of common sense but here it goes: In uniform circular motion, why don't these forces simply cancel each other out? If they did, how would we know they exist in that situation? When I swing a rock tied to a rope, I feel the centrifugal force, but not the centripetal force. In this situation how can the reactive force be greater than the force itself?
This question refers to the paper Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures by Altland and Zirnbauer. In the paper the authors give a classification of Bogoliubov de Gennes Hamiltonians. More precisely the authors state that The aim of the current section is to classify systems according to their symmetries. Using the BdG formalism we will show that the presence or absence of time-reversal and/or spin-rotation invariance leads to four distinct symmetry classes. While I do understand their classifications I am wondering if it is sufficient to restrict oneself to time-reversal and spin-rotation invariance only? I am wondering why the authors seem to disregard important symmetries such as inversion symmetry of the underlying lattice or other point group symmetries? Hence I am wondering if the classification given in the paper is in fact complete? In particular the presence and absence of inversion symmetry plays a key role in the theoy of superconductivity (centrosymmetric vs. non-centrosymmetric superconductors) I would be very happy to hear thoughts and opinions on that.
The number of points on a line is uncountably infinite. The number of lines on a plane is uncountably infinite. It seems like it follows that there would be an uncountably infinite number of points on a plane, too. But it seems unsatisfying to believe that these are both the same thing. Surely adding an entirely new dimension must in some way increase the cardinality of what we're talking about, right? Or if not, is there a convincing demonstration that it doesn't change anything? If they aren't, is there a way to show that they aren't? Are there mathematical ways of describing the distinction between the sizes of these sets, and if so, what are they called? (I'm having a lot of trouble searching for an answer because I'm not sure what words to use.)
I'm looking for a good introductory text to analysis, or, more specifically, a text that puts calculus on a much more rigorous ground. I've just finished a year of calculus at my local university, and I feel a bit cheated by the course I took. In addition to having a poor teacher who focused on rote memorization, our text was abysmal. I ended up resorting to self study, which was a blessing in disguise because it led me to discover a love of logic, set theory, abstract algebra, and topology. I'm interested in becoming a math major when I graduate hs, and I'm comfortable with studying dense, more sophisticated texts as long as they are well written, comprehensive, and build the subject on the ground up. Online texts would be appreciated, as I'm spending the next few months travelling and wont be able to receive packages.
Suppose we have a circular table. We have made a straight line groove in the table extending from the center to the circumference. Now we place a block at some distance from the center in the groove and start rotating the table. Suppose there is no friction between the walls of groove and the block. Result: The block finally moves out of the groove. If we consider the rotating frame of reference of the table, this motion can be easily explained with the help of centrifugal force which acts radially outward on the block. But when we consider the frame of reference of earth, I was not able to explain it. There are no radially outward forces on the block, just the normal reaction from the walls of the groove(which acts in a direction perpendicular to the groove) and the weight of the block(which acts downward). So how does the block eventually move out of the groove?
I have just recently started learning some very basic thermodynamics and there is one question that has been driving me crazy: Why do we even need the Zeroth law of thermodynamics? The law states: If a body A, be in thermal equilibrium with two other bodies, B and C, then B and C are in thermal equilibrium with one another. (Wikipedia) This seems like the most obvious statement ever. How could B and C not be in thermal equilibrium? While looking for an answer I came across a Khan Academy video that deals with this exact question. The lecturer in the video says: "...yeah our universe is like that but think about it a little harder, you could problably think of a universe where it might not be like that." (Video) This just confused me even more. If we follow that logic wouldn't we have to formulate something like Newtons Zeroth Law or Keplers Zeroth law too?
I keep all my references in one huge BibTeX file, which happens to include the full journal name for each one. I'm currently preparing a manuscript that needs the journal names to be abbreviated. From the research I've done (including reading related questions on this site), it seems that (i) there is no standard automatic way to do this, but (ii) there are various tools such as biber and jabref that will allow me to pre-process my .bib file with a sort of global seach-and-replace for the journal names. However, since my manuscript only has a few references it would be easier to just manually type in the new journal name for each entry. Is there a way to do this? I'm looking for a quick-and-dirty LaTeX-only solution that won't require me to install anything that isn't already part of TeX Live, since I'm on a tight schedule. I know I could just edit the entries in my .bib file, but I don't want to do that, because I like to keep all my references in the same place. In case it's relevant, I maintain my .bib file using BibDesk on a Mac, I'm using the natbib package, and the bibliography style is apalike.
This question related to the Grandfather Paradox. Assume that time travel to the past is a reality. What experiment/test could the time traveler perform in order to determine if he is in his own timeline or an alternate timeline/universe? If the time traveler was in his own timeline and kills his grandfather, that means he would have never been born -- and thus cannot travel back in time to kill his grandfather. If his grandfather was not killed, that means he would have been born -- and thus could travel back in time to kill his grandfather. And so on ... At the moment the time traveler kills his grandfather, what would happen if the time traveler was in his own timeline/universe? Would it be any different if the time traveler was in a different timeline/universe? How could the time traveler know for sure if he is in his own timeline/universe or not?
English is not my native-tongue, so I always find it hard to grasp the concept of "question tags" and more importantly the way to answer to them. Let me explain with the help of this situation - I am supposed to complete my homework and I haven't. My mom suspects that I haven't and asks me the below question. I want to confess that I haven't. What should I answer? Mom : You didn't finish your homework, did you? Me : Yes, I haven't [OR] No, I haven't? I've always thought that it is "Yes, I haven't" because the questioner has already found out that I haven't and I should just assert it by saying 'Yes'. But a friend of mine says that it is "No, I haven't" because I am effectively answering the question "did you?". Which of us is correct?
The latest Stack Exchange blog post contains the following section header: In which we stop being dumb I have never really understood what is going on in these "in which..." constructions at a grammatical level. Is it just an elision of something like "this is a section in which..."? Or, perhaps, is it an imitation of a famous quotation/title/etc. that has the same structure? I feel like I've only seen this construction on the internet, which suggests to me that it is either a piece of internet lingo that I've somehow missed or a very new construction that hasn't caught up to me yet. I am a native speaker of American English, but am relatively ignorant of other varieties, so perhaps this is just a feature of BrE that I'm unaware of or something. Note that I am not asking about constructions like: In which of these two fields should I write my name? These constructions are full sentences in which the preposition "in" has been hoisted to the beginning of the sentence, and I understand them perfectly well.
I've been reading Lois Lowry's The Giver recently, and have questions regarding a sentence from her book. I know that some sentences in literature, like The Giver, do not always follow strict grammar rules and do not need to follow them, but I still can't understand the exact meaning of the sentence: They(Jonas and Gabriel) saw deer; and once, beside the road, looking at them curious and unafraid, a small reddish-brown creature with a thick tail, whose name Jonas did not know. In this excerpt, How does the adjective phrase, "curious and unafraid," work in the sentence? Does it modify the verb "looking at"? To be grammatically correct, should it be changed to "curiously and unafraidly"? Where does "a small reddish-brown creature with a thick tail, whose name Jonas did not know" belong to? Why is the noun phrase placed at the end if it modifies the "deer" in the first clause? I absolutely don't consider it is wrong and this is not necessary to understand the whole story, but I can't help myself wondering how this sentence works. Could you help me parse this sentence?
I am working on a document (using the scrbook class, if it is relevant) which will end up consisting of lots of text and a large number of tikz figures. Even when writing the very first chapter, I notice that running pdflatex, bibtex and makeindex takes a considerable amount of time. I expect this to become worse (i.e., even longer) when the amount of text and figures increases. I already structured my document into a number of files, since, during writing, I often make changes to only one part of the whole document (e.g., one chapter or one part of the appendix). Is there any way to reuse the files generated by pdflatex during the last run to get a preview of the updated document (without having to wait for the document to be rebuilt completely)? I would be fine with things like the TOC not being updated. My current toolchain and editor are set up on both, Windows (MiKTeX) and Linux (TeX Live), but I could live with being limited to one of the two platforms. My highest priority is to reduce the build times required for previewing.
I'm very confused about how I should be using TexWorks on Ubuntu, and what the difference is between TexWorks, TexLive, and MikTex. So, I installed the TexLive package with sudo apt-get install texlive, because according to the website, this also installs TexWorks. However, after this installation, I could not find any reference to TexWorks on my machine. So, I then installed the TexWorks package with sudo apt-get install texworks. Now, I can open a .text file with TexWorks. But I am confused as to whether I am now using TexWorks, or TexLive (and what about MikTex?). Also, I am getting errors such as LaTeX Error: Filebbm.sty' not found.` This means I need to install this package. How can I do this? I am used to running TexWorks and MikTex in Windows, where packages were automatically installed on-the-fly as they were required, and ideally I would like something like this. Thanks!
I'm not sure if my problem was asked before, but if so, a simple link to the answer would be appreciated. Basically I've recently seen videos about spud cannons that use compressed air and it got me thinking about the math behind it. Obviously for targeting purposes, one needs the final velocity at the end of the cannon barrel to substitute in newton's projectile motion equations and get the distance which is cool. Now to find the velocity at that point is where it gets really messy. Since the pressure of compressed air changes as it expands throughout the cannon barrel, the force it exerts on the projectile decreases and so does the acceleration. With the assumption of an isothermal expansion of the air in the barrel, how do you find the end velocity of the projectile at the end of the cannon barrel?
I cannot understand why we cannot use "even though" instead of "even so" or vice versa. For example : I know her English isn't very good, but even so I can understand her. ( original sentence) If we can rewrite it with "even though", does it mean different thing? Even though her English isn't very good, I can understand her. (my sentence) Some other examples: The evidence was only circumstantial. Even so, he was convicted and spent ten years in prison for a crime that he perhaps did not commit. (original) Even though the evidence was only circumstantial, he was convicted and spent ten years in prison for a crime that he perhaps did not commit. She is loud and unfriendly. Even so, I like her. (original) Even though she is loud and unfriendly, I like her.
One implication of general relativity is the concept of gravitational waves or gravitational radiation, ripples in spacetime thought to travel at speeds close to the speed of light. As far as I have researched, there is no direct evidence supporting their existence, but I have read many examples of indirect evidence. My question is regarding the nature of these proposed waves. I understand the motivation behind the idea of a gravitational wave, but I do not understand the reasoning behind how said wave is created. For instance, how is it possible for a wave to be created in spacetime, unless we make the assumption that spacetime (like a fabric) has some form of internal tension? When I attempt to visualize waves I tend to think back to sound waves and ocean waves...but these waves rely on internal forces between molecules in the medium to create the ripples. Do similar mechanics take place in a gravitational wave or is there some other explanation? Thank you for any help with this question.
Let us define an inertial frame as a frame of reference where the laws of physics take their usual form, as opposed to non intertial frames where one has to introduce pseudo-forces. We can further define an equivalence class which contains other inertial frames as the class of frames of reference moving of constant velocity with respect to an initial inertial frame. Is it possible to show formally that there do not exist two inertial frames which cannot be put in the same equivalence class -- namely two inertial frames which are not moving at constant relative velocity one with respect to the other? I am aware of the fact that in a frame accelerated with respect to an inertial one there are pseudo forces, but I am concerned in particular in showing that there is no possible configuration in which they would all cancel out.
Different authors seem to have different conventions when they define the term affine variety (similarly projective variety). For the purposes of this question let us stick with the affine case, and let us work over an algebraically closed field. For example: In Harris's Algebraic Geometry: A First Course, an affine variety is the zero set in the affine space, of a collection of polynomials. So, it is just a closed subset of the affine space under the Zariski topology. He calls an irreducible closed subset, an irreducible affine variety. (A similar convention is used in the book by Cox, Little and O'Shea) In Hartshorne's Algebraic Geometry, a closed subset of the affine space is called an affine algebraic set, and an irreducible closed subset is called an affine variety. In the recent book Algebraic Geometry I: Schemes With Examples by Goertz and Wedhorn, the authors use the terms affine algebraic set, and irreducible affine algebraic set for closed and irreducible closed subsets of the affine space respectively. They reserve the term affine variety for a space with functions that is isomorphic to a space with functions associated to an irreducible affine algebraic set (so, this is more in the spirit of Hartshorne). While it is usually clear from the context, what the authors of a particular book mean, when they use the terms above in bold, why are there different terminologies? Is there a consensus among mathematicians today, as to what they mean when they use the term affine algebraic variety?
The five postulates (axioms) are: "To draw a straight line from any point to any point." "To produce [extend] a finite straight line continuously in a straight line." "To describe a circle with any centre and distance [radius]." "That all right angles are equal to one another." "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles." What's wrong with them? Which axiomatic system is being used nowadays? Hilbert's or SMSG (School Mathematics Study Group)? I believe in the case of SMSG the list of axioms contains some redundancy. Why do people say Euclid's axioms are 'far from being sound', even if they are all still (I guess) believed to be true? If there's something wrong with them, then maybe our better (Hilbert's or whatever) axiomatic system contains some false statements?
I'm looking for a succinct way to describe what I believe is a semi-common situation, both in online discussions and sometimes in real life (e.g. with siblings during long car trips): when a discussion between two or more people turns sour, such that rather than discussing or debating the subject at hand, the people involved get sufficiently irritated with each other that they instead get drawn into a back-and-forth series of pointless/petty/passive-aggressive criticisms of each others' style, grammar, minor logical ambiguities, etc. I might call this "hen-pecking" (in reference to possibly-apocryphal reports that chickens packed into too-close proximity with each other will eventually start pecking each other to death, and must therefore either be given more space, or fitted with red contact lenses to calm them down), but I think there might be a better, more well-known phrase that describes the phenomenon. Can anyone supply such a phrase?
In logic and computer programming, a conjunction of two logical statements is said to be true if and only if both statements are themselves true. For instance: "The sky is blue" and "the grass is green" is a conjunction of two logical statements. Note that a conjunction in this context is not the same as a grammatical conjunction. In product manuals, one often sees things like: "These values are anded together". However, "anded" doesn't seem like a proper English term, and it seems like there should be a verb for the act of combining two logical statements with a conjunction. Other logical operators like "xor" certainly use "xored" or "xor'd", but "anded" seems less acceptable somehow. Is there a nice English word for this operation? Some thoughts: "conjoined" doesn't seem sufficiently precise, because we're not just sticking the logical statements together, we're combining them with a particular operator (i.e. the clauses could still be conjoined with a disjunction operator instead). "conjuncted" might be appropriate, but I can't find anyone using it on the net, and I've never seen it used before in manuals and the like.
The Poincare group has ten generators, which have the physical interpretation of energy, momentum, angular momentum, and the system center of mass, and which are of course conserved in any Poincare invariant system. Adding five more generators (of dilitation and the four special conformal transformations) extends the Poincare group to the conformal group. Do these five new quantities, which are conserved in any conformally invariant system, have any natural physical interpretation (something I can picture in my head)? Edit: To reiterate, I am familiar with the physical interpretation of the comformal symmetries. I am looking for a physical interpretation for the generators of the conformal symmetries. I'm not looking for the analog of "momentum is the generator of spatial translations," I'm looking for the analog of "conservation of momentum tells you that something moving in a straight line will continue to move in a straight line."
I know there are a lot of reference requests for differential equations textbooks but none seem to be what I need. I'm looking for a book I can use for self study that isn't overly complicated and explains a lot (meaning it doesn't often say "left as an exercise for the reader" but instead proves all major results). I have taken mutlivariable calculus and am currently taking linear algebra so I also need a book that assumes no prior knowledge/experience with differential equations. If possible I'd prefer a book that explains the reasons for doing things and not just the methods. Thanks in advance. (If there is another question that I missed that asks for all these criteria please let me know and I'll see if those are what I'm looking for.)
When someone says something unpleasant or rude, often the reply is "Bite your tongue!". But where did this come from? I can find a number of sources explaining that to bite one's tongue is to hold it between the teeth, preventing speech, and thus is a metaphor for not speaking; this makes sense, as I've seen "I bit my tongue" to mean "I didn't say anything". However, I can't find much about the usage as a response to something already said. Is it along the lines of "You should have bit your tongue instead of saying that"? Are the two usages actually related or just similar? For clarification: usage A of the phrase "bite your tongue" is a synonym for "hold your tongue", whereas the usage I'm interested in is used similarly to "Wash out your mouth with soap" (though that's usually used for swear words, whereas this can be used for any negatively-perceived statement, like saying something bad about a public figure who is well respected, or implying that a woman is over a certain age)