"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way--in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only." -- Charles Dickens, A Tale of Two Cities. From Wikipedia. A comma splice is the use of a comma to join two independent clauses. For example: It is nearly half past five, we cannot reach town before dark. Although acceptable in some languages and compulsory in others (e.g., Bulgarian or French), comma splices are usually considered style errors in English. Would the sentence above be an example of an author making stylistic error on purpose? Thanks


Normally Latex puts hyphens inside the text: ------------------------------------ Lorem ipsum dolor sit amet, consec- tetuer adipiscing elit. Aenean com- modo ligula eget dolor. Aenean mas- sa. Cum sociis natoque penatibus et magnis dis parturient montes, nasce- tur ridiculus mus. Donec quam felis, ultricies nec, pellentesque eu, pre- tium quis, sem. Nulla consequat mas- sa quis enim. Donec pede justo, fringilla vel, aliquet nec, vulputa- te eget, arcu. ------------------------------------ But I want to put it beside the text, because it is easier on the eyes and better for the reading flow: ------------------------------------ Lorem ipsum dolor sit amet, consecte- tuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridi- culus mus. Donec quam felis, ultrici- es nec, pellentesque eu, pretium quis, sem. Nulla consequat massa quis enim. Donec pede justo, fringil- la vel, aliquet nec, vulputate eget, arcu. ------------------------------------ I know that it is possible because I have seen it in some PDFs which were most likely created using Latex, but I did not find out how it is done.


I am not a native English speaker, and I have just started to study physics in English. However, I came across the term heralded photon while I was reading a review article about optical quantum memory. I don't understand what it means. A dictionary explains herald as, "to be a sign that something is going to happen," but it does not make any sense. Below is the excerpt from the article: If a single-photon detector is placed in one of the emission channels of non-degenerate spontaneous parametric down-conversion, a detection event indicates emission of a photon pair, and thus the presence of a single photon in the other channel. Such a heralded photon is emitted at an arbitrary time, however, making it unsuitable for many application. Would you help me understand this term?


In the Cambridge Grammar of the English Language, Huddleston and Pullum use the term "determinative" for the lexical category of words like the, etc. And they use "determiner" for the grammatical function that is characteristically filled by determinatives (but which can also be filled by things such as genitive noun phrases). In an older generation of reference grammars, however, notably Quirk, et alia's Comprehensive Grammar of the English Language, the use of these terms is exactly reversed. That is, "determiner" is the lexical category and "determinative" is the grammatical function. The difference has been bugging me for a long time. Can anyone provide a principled explanation as to why we should prefer one over the other? I'm sure Huddleston and Pullum had a motivation to alter terminology that's been in use since Bloomfield's day, but I can't find any discussion in their work.


I've been trying to determine an explanation for the falsity of a logical statement for some time now and I've had no luck in figuring out exactly how to go about it. The two part question goes as follows: Consider the arguments below. If the argument is valid, identify the rule of inference that establishes its validity. If not, explain why. a. If Robert understands the concepts correctly, he will be able to finish his assignment in two hours. Robert finished his assignment in more than two hours. Therefore, Robert did not understand the concepts correctly. b. If taxes increase, the housing market will decrease. Taxes are not increasing. Therefore, the housing market will not decrease. Perhaps I'm misunderstanding the way to determine the falsity of a logical statement? Any help is appreciated.


I seem to remember hearing a medical term for the act of causing pain to one part of your body to relieve a chronic pain elsewhere in the body. For instance, someone who suffers from chronic back pain might break their finger so that they can stop focusing on their back pain. Or someone with a broken arm might intentionally drop something on their foot so the focus of pain transfers to their foot for a while. Is there such a term for this type of pain management technique? I was thinking this was called "deferred pain", but I cannot find anything on Google for that. Most of the search terms I've come up with lead me to "referred pain," but that's not the term I'm looking for. That's completely different than what I'm talking about.


I am trying to prove if f is continuous and closed ("closed" means the image of any closed subset of the domain is closed) then f(closure of X) equals the closure of f(X). I was able to prove that if f is continuous then f(closure of X) is a subset of closure of f(X). Now, I am trying to prove the other way around: closure of f(X) is a subset of f(closure of X). So here is my attempt: Let y be a point of the closure of f(X). Then y is either a point of f(X) or a limit point of f(X). I am wondering if f(X) is a subset of f(closure of X)? If this is true then in the former case, it is easy to conclude that y is also a point of f(closure of X) and in the latter case, I can show that y is also a limit point of f(closure of X). Since f is a closed mapping and the closure of X is closed, f(closure of X) is also closed, which implies y is a point of f(closure of X). Also, if you know how to prove that if f(closure of X) equals closure of f(X) then f is a continuous and closed mapping I would really appreciate it if you could give me some hints. Thanks a lot.


I have a question regarding the usage of the words to and with in the sentence "He lodged a complaint to/with the Authorities". Which is correct? Note: Lodge in this context is "to present (a complaint, appeal, claim, etc.) formally to the proper authorities". I have been told that, in the said sentence, with is correct and not to. But, I am confused as to why with is correct and used more often than to, especially since the definition of with is "accompanied by (another person or thing)", while to is defined as "identifying the recipient or intended recipient of something". How could someone lodge a complaint with the Authorities? In my mind, with denotes that a person is lodging a complaint together with the Authorities. Could someone explain this to me?


I am trying to prove the following statement regarding nowhere dense sets: "In a metric space X, the frontier of an open set is the set of accumulation points of a discrete set." As far as my attempts go, I have gone back and looked at an earlier proof of Baire's Category Theorem and worked out the details (as to my understanding, it should be similar). However, I am still not seeing how to prove the above using said theorem. Does anyone have any hints or suggestions as to how to proceed? Note: I have already proven (as part of the above) that: a)In a metric space X without isolated points, the closure of a discrete set in X is nowhere dense in X. b) In any space X, the frontier of an open set is closed and nowhere dense. c) Every closed nowhere dense set is the frontier of an open set.


My question concerns the usage of "as if" as an idiomatic interjection. The references I have consulted (etymonline, online dictionaries, etc.) seem to agree that "as if" is used in this context to convey incredulity or doubt. This is how I have always thought of it. The other day, I was with friends who used "as if" to express their surprise and joy about a wedding proposal. They weren't being sarcastic or incredulous; they were genuinely happy about the proposal. Here is a loosely paraphrased version of what they said: "As if they're getting married!" Is my friends' usage of "as if" standard? Is it a primarily regional distinction? (I am in Ontario, Canada right now.) The closest example we could come up with is someone says "I can't believe that you won first prize!" Of course, the person can and does believe it, so their words ought not to be taken literally. Is it the same idea with "as if"?


A year ago, I took a statistics course at my university. The course was based on Rice's "Mathematical Statistics and Data Analysis". Apart from the fact that I did not find the book terribly good, I found that the lectures did not aid me a lot in understanding the material either. I did pass the course, but I didn't feel I really understood the material. Fast forward a year. I have now come to realise that statistics can be a very interesting and useful subject, but I haven't done any statistics ever since the course I just mentioned. I'm thinking of doing some statistics courses for my Master's degree, though. Question: do you know any good resources (video lectures, books, solved problems) which I can use to brush up my statistics knowledge? I like books that have a large number of solved problems and worked examples, so I can check whether I actually solved the problems correctly.


I am fairly certain that there's an idiomatic phrase for this, referring to either the situation or the person. It's on the tip of my tongue. Scenario: Alice tells Bob to stop making a such a noise with his power tools. Bob replies that he had already stopped an hour ago and was anyway done for the day. How would you describe Alice, who instructed Bob to do something which he already did or was going to do? In other words, she gave him a redundant order that serves no purpose other than to reaffirm authority and stroke her own ego. Alternatively, she's making a show of strength by demanding that something that's already been done, be done. It's similar in concept to the French phrase "faire la mouche du coche" but not quite. It's along the lines of gadfly, backseat driver, busybody, or tooting one's own horn. EDIT: The closest matches so far are control freak and megalomaniac, but those still don't describe the post-facto aspect.


The figure shows a circuit consisting of a battery, a switch, two identical lightbulbs, and a capacitor that is initially uncharged. a. Immediately after the switch is closed, are either or both bulbs glowing? Explain. b. If both bulbs are glowing, which is brighter? Or are they equally bright? Explain. c. For any bulb (A or B or both) that lights up immediately after the switch is closed, does its brightness increase with time, decrease with time, or remain unchanged? Explain. I really don't understand the concept of how a capacitor affects the flow of current in a circuit, and am having an incredibly hard time figuring out this question. At least an idea of where to start would be great. I had thought that for part A both light bulbs would begin glowing since the capacitor isn't charged, but i have no idea how to tell which one is brighter. I also think that for part C, the brightness of the bulbs would decrease over time after the capacitor is charged because once it's charged the voltage of the capacitor equals the voltage of the battery, hence there is no voltage potential and no current. Am I on the right track at all for this???


Consider the following scenario: I get in a spaceship, and travel really close to the speed of light for a while, and then come back. A lot of time has passed on the Earth, but since I was traveling so fast, I only experienced a few years passing. So, my friends on Earth are dead, whereas I'm only a few years older. But what I'm having trouble wrapping my head around, is why is it them that's dead, and not me? After all, given what I understand about relativity, it's just as fair to say that my spaceship stayed still, and it was actually the Earth that traveled really fast and then came back to my ship. In that scenario though, the Earth being the fast-moving ship, and my ship being the stationary body, wouldn't it be that I am dead, and everyone on the Earth is just a few years older? If there really is no preferred frame of reference, then why does the ship-traveler live while the people on the Earth die?


I often find myself putting excess commas and brackets (parentheses for all you US English speakers out there) into sentences, in hopes of rendering it more 'readable'. The trouble is, I am never sure just how much is too much and often need to seek the services of an adjudicator. However, this time no one could decide: how should the following phrase be punctuated? Like this, without commas? During the Great Depression the Nazi Party gained a lot of popularity because they promised to make Germany great again and there was nothing the German people as a whole wanted more. Or like this, with only one comma? During the Great Depression the Nazi Party gained a lot of popularity because they promised to make Germany great again, and there was nothing the German people as a whole wanted more. Or like this, with two commas? During the Great Depression, the Nazi Party gained a lot of popularity because they promised to make Germany great again, and there was nothing the German people as a whole wanted more. What option is the most grammatical and readable?


I need someone to help me to define the meaning of the word "en masse" in the following context: the initial aim of internment during the later conflict was to identify and intern those who posed a particular threat to the safety or defence of the country. As the war progressed, however, this policy changed and Japanese residents were interned en masse " Which of the following interpretations is correct? the initial aim of internment during the later conflict was to identify and intern those who posed a particular threat to the safety or defence of the country. As the war progressed, however, this policy changed and Japanese residents were interned together the initial aim of internment during the later conflict was to identify and intern those who posed a particular threat to the safety or defence of the country. As the war progressed, however, this policy changed and all Japanese residents were interned


I came across the following thought experiment, and I would like to understand whether the controversy around it is justified. Imagine an experiment in which a mathematician is put to sleep with some kind of drug. He is located in a room that is designed in such a way as to keep him completely isolated from any kind of external information. The researchers have a sleep inducing drug that is able to put you to sleep and make you forget it was even administered. After the researchers have put the mathematician to sleep with this drug, they toss a fair coin. If it comes up heads they will wake the mathematician up once and administer the drug again. If it comes up tail they will wake him up twice, each time administering the drug again. Whenever the mathematician is awoken during the experiment, they will ask him for his best guess regarding the result of the coin toss. Eventually the experiment ends, and the researchers will awaken the mathematician a final time and tell him the experiment has ended. During the experiment, what answer should the mathematician give as his best guess for the result of the coin toss ? I think he should say that odds are the coin came up tail, but I am very curious what other people make of it, and whether there are any grounds for dissent at all.


I'm looking for good book recommendations for preparing for the International Physics Olympiad. As stated on the IPhO syllabus, the topics covered are about the same as those in the first year or two of a physics degree: Mechanics: kinematics, dynamics, celestial mechanics, hydrodynamics Electromagnetism: Maxwell's equations, circuits, matter in EM fields Waves: damped/driven harmonic oscillators, waves, interference and diffraction, geometrical optics Modern: special relativity, matter waves, particle and nuclear physics Thermodynamics: laws of thermodynamics, heat engines, phase transitions However, there's less of an emphasis on complicated calculations, and more of an emphasis on problem solving and insight. For example, multivariable calculus is almost never used; instead many questions can be elegantly solved by symmetry. I'm looking for textbooks or problem books to bring me to this level, starting from the level of high school physics.


I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay in "orbit" around a positively charged nucleus. Even if the electron actually orbits the nucleus, wouldn't that orbit eventually decay? I can't reconcile the rapidly moving electrons required by the planetary model with the way atoms are described as forming bonds. If electrons are zooming around in orbits, how do they suddenly "stop" to form bonds. I understand that certain aspects of quantum mechanics were created to address these problems, and that there are other models of atoms. My question here is whether the planetary model itself addresses these concerns in some way (that I'm missing) and whether I'm right to be uncomfortable with it.


I am interested in self-studying real analysis, and I was wondering which textbook I should pick up. I know all high school mathematics, I have read How to Prove It by Daniel J. Velleman (I did most of the exercises). I have completed a computational calculus course which covered everything up to and including integration by parts (including the substitution method and Riemann sums) I am currently considering: Principles of Mathematical Analysis by Walter Rudin From what I have heard this is not very well suited for self-study and that while the exercises are extremely difficult, if you take the time they are worth the effort. Calculus by Michael Spivak I have heard that while Spivak explains proofs in much more detail than Principles, it doesn't cover all of the material in the latter. Understanding Analysis by Stephen Abbott I don't know much about this. I have only seen some comments saying that it is an excellent introduction to analysis. Mathematical Analysis by Tom M. Apostol Extra clarification edit: I would prefer a book not to ''dumb down'' the material, something that would not hold my hand through every step, something that would force me to fill in the gaps myself instead of explaining every single step. That is why I am currently leaning towards Rudin, but before I decide I would still like some information on the book by Apostol.


The answers to this related question suggest that to and in order to are pretty much interchangeable, the former being preferred in informal contexts. My question is about negative clauses. According to the answers to the linked questions, the following two sentences are fine and mean the same thing: We were speaking loudly to wake up Mr.Smith. We were speaking loudly in order to wake up Mr.Smith. Can the same be said about the following sentences? We were speaking quietly not to wake up Mr. Smith. We were speaking quietly in order not to wake up Mr. Smith. I am asking because when I used the first variant a friend of mine corrected me and said that I must use either in order or so as to make the sentence grammatical.


I have taken a course in abstract algebra, which used Fraleigh's book. This semester I'm taking a course called Rings and Modules, which uses Bhattacharya's book, which is fine for the most part, but sometimes I can't understand the material. Today after the lecture I spoke to my professor, and he told me he thought some explanations and constructions in the book aren't very good. So I have Fraleigh, which is insufficient for the material I'm studying now, and I have Bhattacharya which sometimes confuses me. I've heard so much about Dummit and Foote, so I'm wondering if it's worth the cost of buying it now only to improve my understanding of certain topics? I'm also planning on taking Galois theory next semester, and if Dummit and Foote covers that as well, I suppose that's another reason to buy it because the Galois course at my university also uses Bhattacharya.


I am wondering whether to use a restrictive relative clause such as: "Multicopters belong to a family of aircraft called rotorcraft , which also includes helicopters, and although they appear to be similar, a multicopter's design is mechanically much simpler." or non-restrictive relative clause: "Multicopters belong to a family of aircraft called rotorcraft that also includes helicopters, and although they appear to be similar, a multicopter's design is mechanically much simpler." I am leaning toward the latter because the second half of the complete sentence relies on the inclusion of the statement "also includes helicopters" for its meaning. However, the first part of the sentence ("multicopters belong to a family of rotorcraft") makes sense by itself (i.e. it could be a complete sentence), and the second part of the sentence is really another statement attached with "and". So I'm not sure. Would it be better as two separate sentences: "Multicopters belong to a family of aircraft called rotorcraft, which also includes helicopters; although they appear to be similar, a multicopter's design is mechanically much simpler." Side-note: Now I'm going crazy, wondering whether it should be "include" or "includes". This is why it takes me so long to write anything. sigh


There is a related question on this site here: Why glass is transparent? Which explains that glass is transparent because the atoms in glass have very large energy differences between energy levels and photons of visible light do not have enough energy to excite electrons from one energy level to another. Whereas, electrons in atoms of most other substances can be excited so the photon is absorbed. But my question is, why don't these excited electrons return to their original energy level and release a photon in the direction the original photon was travelling, hence allowing the light to pass through the object? Edit: I had not realised earlier that this exact same question had been asked before on this site here: Why aren't all objects transparent? So, I shall clarify my question a bit more. The answers to the linked question say that the energy of the excited electron is lost so the light is re emitted as waves with longer wavelengths which we cannot see. I'd like to know how exactly the electron loses this energy. One answer to the linked question states that the energy is lost to lattice vibrations, but I'd like to know how exactly an excited electron still bound to the atom can transfer its energy to lattice vibrations.


I often hear the following, particularly during announcements when travelling by rail or air: On behalf of myself and the rest of the team, I would like to wish you a pleasant journey. I've always wondered whether this is grammatical. I found this question, which discusses how to form such a sentence, but it still seems unusual to me even if it is correct. Something closer to the following would seem more rational: On behalf of the whole team, I would like to wish you a pleasant journey. This is because the whole team is not speaking. Contrast this to the first example in which the speaker claims to be speaking on behalf of himself. Can either of these sentences be used to mean the same thing? Is one preferred over the other?


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)


You often hear it on the news. Some embarrassing nonsense goes down, and then some honcho steps in front of the cameras looking concerned and goes, "I take full responsibility for what happened." What do they mean by that, exactly? Are they willing to be put on trial? Ready to pay a fine? Eager to resign? Do some community work for free? What? I believe I've heard the President, and some others in high positions, say it on a few occasions. What do they mean when they say it? Today I want to say this, as president and as Commander in Chief I take full responsibility for all of our counter terrorism operations including the one that inadvertently took the lives of Warren and Giovanni. President Obama from the White House (Here's the link)


In this answer on Stack Overflow, the term "several" is used as an indeterminate number, the actual value of which is literally in the quintillions: Zero is one of several values that can be represented exactly. To my ear, this is an exceedingly strange use of "several", which led me to believe that the writer was confused. I realize that trying to truly pin down "several" is probably a hopeless task, but I'm curious if anyone else would use it for such an immensely vast quantity, and if there's regional variation in the usage. So: How many is "several"? Would anyone else use "several" for "quintillions"? This question addresses similar issues, but doesn't seem to have the answer I'm interested in (much of the discussion mentions lower bounds for "several", but not upper bounds).


I'm relatively new to PDEs and ODEs. It seems that PDEs are generally more difficult to solve than ODEs, and so I intuitively have the feeling that one needs more information/knowledge/theorems in order to solve PDEs. I've seen many examples of going from from the ODE domain to the PDE domain, and vice versa. For example, I could set up an infinite series of ODEs that model an infinite line of masses connected by springs. Then one could, loosely speaking, get the wave equation (a PDE) when letting the mass go to density. Or, FEM approximates a PDE as a finite set of ODEs, but by letting each element go to zero size, one could regain the original PDE. Vice versa, the method of characteristics, or the method of separation of variables, allows one to rewrite a PDE as a (finite) set of ODEs. I'm wondering if there are general, perhaps hand-wavy, arguments for when it is possible to do such transformations? I feel that the PDE has to be sufficiently simple, or we need to know some additional information about the solution, in order to rewrite it to ODEs. Likewise I am guessing that only infinite sets of ODEs can be written as PDEs, but I am not sure if all infinite sets of ODEs are equivalent to a PDE.


I'm a software developer, and as such I often use an IDE to fulfill my goals. For those who don't know: An integrated development environment (IDE) is a software application that provides comprehensive facilities to computer programmers for software development. Sometimes while programming I find myself making certain errors. One of them is creating a variable (A name that holds a certain value) that is never used. An IDE can show a certain message and underline the error for me so that I notice it quickly and fix it. I have been using multiple IDE's that have shown me the error shown above, but I just noticed something. In one IDE, the message is shown as "Unused expression", while the other says "Useless expression". Which IDE is saying it right? Is it supposed to be "Useless" or "Unused"?


Can any noun ending in -ism describing some system or belief be changed for -ist to describe a member of that system? My question might be confusing, so I will run through a few examples: Nihilism => nihilist Feminism => feminist Racism => racist This seems to follow a pretty predictable pattern. So, when I learned a new word a while ago - misoneism (having a fear or hatred of innovation or change) - I was expecting to be able to call someone a misoneist, if it ever came to that. Unfortunately, while most dictionaries (online and paper) I have checked so far contain the word misoneism they do not contain the word misoneist. Were my assumptions correct that you can create any -ist noun from a root of -ism, or is this word in the dictionary because it really doesn't exist?


I want to study Mumford's Abelian Varieties in the coming winter break. I tried to study it before, but I didn't find my self really understanding(or memorizing) too much. I guess a better and more solid way to learn something is to go over many exercises. So I'm asking for some exercises(or problems?) on abelian varieties, it would be nice if I can get them online. Thanks in advance. And about the exercises: I wish it would be kind of like the ones in Hartshorne, so that I can solve them if I understand the material well. And not too hard, I guess I'm not looking for some research level questions... Also I wish those exercises may focus more on the algebraic/arithmetic side. I know the description above might seem a little picky, I'd be very appreciated if anyone has any idea or source about this, thanks again in advance...


I've been reading about how the conical shape of train wheels helps trains round turns without a differential. For those who are unfamiliar with the idea, the conical shape allows the wheels to shift and slide across the tracks, thus effectively varying their radii and allowing them to cover different distances while rotating at the same angular velocity. A cross-sectional view of the tracks and wheels generally looks something like: But what about a configuration like the following? I read in an online article that wheels in the second configuration may more easily slip and derail from the tracks (assuming there are no flanges to prevent them from doing so). But I can't convince myself using physics why that might be. Is one of these two configurations actually more reliable than the other?


The following binary relation of the set {a, b, c, d, e} is given: R = { (a,b), (a,c), (b,c) } What I have to do is to find the smallest reflexive / symmetric / transitive / antisymmetric relation including R. I know what these relations are all about, but what I have trouble with is how to find them. For example, I see no reflexive relation in the set. Does "including R" mean that i can extend R with any element from the given set? So for example, if I am looking for a reflexion can I just add (a, a)? If I can extend the set, my solution would be: Reflexive: Add (a,a) Symmetric: Add (b,a) Transitive: Already satisfied Antisymmetric: Already satisfied? I am not sure about this one


In the Wiki page A permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. ..... A formal language is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. The transition monoid of an automaton is the set of all functions on the set of states induced by input strings. See the page for more details. The transition monoid can be regarded as a monoid acting on the set of states. See this Wiki page for more details. In many literatures, an automaton is called strongly connected when the monoid action is transitive, i.e. there is always at least one transition (input string) from one state to another state. The transition monoid of a permutation automaton can be regarded as a permutation group acting on the set of states. If the action is transitive, then the transition monoid is a transitive permutation group. My question is What is the class of the languages accepted by DFAs whose transition monoids are transitive permutation groups? Is this class a proper subclass of p-regular language? Any literatures discussing this class of languages in details? I have searched many books and articles and found nothing helpful so far. I believe I don't have the appropriate key words yet. Thus I am seeking help. Any pointers/references will be appreciated very much. P.S. I asked a related question on CS.SE with more technical details toward computer science.


Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit using "color code": Quantum computations on a topologically encoded qubit (arxiv). The other one was John Martinis' group, who used superconducting qubits and performed a simplified version of a "surface code": State preservation by repetitive error detection in a superconducting quantum circuit (arxiv). Can anybody please explain to me, what is the difference between "color code" and "surface code"? What are the advantages and disadvantages of those? Why aren't the trapped-ion guys using the "surface code" or vice versa? The Martinis group has shown recently that they are above the threshold for surface-code QEC arxiv. Has any ion group (maybe by Blatt) shown similar quality of single- and two-qubit gates? Are there other groups who have the same level of control over their systems to perform multi-qubits quantum error-correction codes?


Is there any easy (scriptable) way to convert a PDF with vector images into a PDF with raster images? In other words, I want to generate a PDF with the exact same text but with each vector image replaced with a rasterized version. I occasionally read PDFs of technical articles on my Kindle, and have found that reading a PDF directly is frustrating. Thankfully, Amazon's automatic conversion of PDFs to the Kindle format does a good job of reflowing the text portions of most of PDFs I have tried. However, while raster images seem to make it through the conversion process fine, vector images get horribly mangled. It would be great if I could easily convert a PDF so that all of its vector images were rasterized. I am interested in any possible solutions, but a Linux- or Windows-based one would be preferable. I can also get access to Adobe Acrobat if necessary.


Looking at the nCatLab page on chain complexes, it is implicitly assumed at the start of the page that one is working in an additive category. However, the only structure required to define chain complexes is that one be working in a pointed category, so that the notion of a zero morphism makes sense. However, I have not been able to find any papers which consider chain complexes even in categories such as preadditive or semiadditive categories, much less arbitrary pointed categories. I understand that many of the results of homological algebra rely on an Abelian structure to work. Is it simply the case that non-additive categories don't have enough structure to yield any interesting results about these complexes? Or is there a concrete issue that prevents chain complexes from making sense at all in more general pointed categories? Do these issues still arise even when working in preadditive or semiadditive categories?


Can someone please explain extraordinary optical transmission (EOT)? I'm hoping someone can describe the physical process by which light is transmitted through a periodic metal hole array which is optically thick (i.e. thickness > skin depth), for which the holes are sub-wavelength vs the incident light. I'm trying to visualise how this process works but I'm not having much luck. From what I understand, EOT is a mixture of surface plasmon polaritons (SPPs) being excited on the surface of the hole array and wave guided modes for the SPPs(?) to travel through to the opposite side of the array where they are decoupled into transmitted light. I guess it's the wave guided SPPs I'm having trouble with...i.e. why would there be a cut-off frequency due to the wave guide mode if SPPs travel along the metal surface? (Also, the position at which the SPPs would decouple has also been bugging me.) Any help would be great!


I can't quite figure out which of the following expressions is more correct: He is the devil's advocate. He is a devil's advocate. He is playing devil's advocate. The combination of an article with the possessive is what confuses me. Exactly which word(s) does the article apply to? The first form seems to suggest either that he is an advocate of The Devil -- namely, Satan himself -- or even worse, that he is The Advocate of The Devil. (Kill him with fire!) The second form seems to suggest that he is an advocate of a devil (but not necessarily of The Devil, nor the only advocate out there.) This seems to fit better with the way this idiom is commonly used, but I haven't seen this idiom used very often with the indefinite article. It's usually used with the definite article. The third form suggests that he is playing a role named "devil's advocate", with no article attached to it. Similar examples: The King's speech, the Indian's prayer, the mother's room, etc.


I've compiled a LaTeX document successfully by typing latex documentname.tex into terminal when in the correct working directory. The document successfully compiles. I'm using TexLive. I then make changes to the document. For some reason, when I type latex documentname.tex again, it compiles very quickly and gives me the previous version of the document out. I've tried deleting the output file and log file and typing latex documentname.tex yet again, but it still somehow outputs the old version of the document. Same for the pdflatex command - what is going wrong here? Is there some other command I should be using or extra arguments I can pass in? Even changing the filename of the document does not cause the new version to be compiled - I still get the old one out.


Addiction is defined as "the state of being enslaved to a habit or practice or to something that is psychologically or physically habit-forming, as narcotics, to such an extent that its cessation causes severe trauma." But sometimes a person will find something which they do not suffer any withdrawal from when the y stop doing it for a while, and they do not feel any great need to seek out on your own. Yet when they are actively engaged with it, they just do not want to stop and can find it very difficult to pull themselves away from. As an example, "My son is addicted to MineCraft. Once he sits down at it he will play for hours, not even wanting to stop to eat or sleep even when all his friends have gone home. Yet unless one of his friends wants to play it with him to begin with he never touches it." I feel like "addicted" is the wrong word, because while the "psychological enslavement" part is correct, it does not seem to form a habit or exhibit withdrawal symptoms. It's almost like a temporary addiction that goes away whenever the stimuli is removed. Is there a word for this?


As explained in the answers to this post, photons apparently exert a gravitational pull on other objects. It has also been explained on this site, that gravity propagates at the speed of light. I'm wondering, though, how do you reconcile these two facts? I'm trying to imagine the gravitational field made by a photon and it seems like there are some paradoxes. For example, how can gravity propagate ahead of the photon at the speed of light, if the photon is also travelling at the speed of light? My guess is the solution is probably found in relativity, but I certainly can't figure it out. Right now, the best I can do is to think about gravity as sound, and a photon as an object travelling at the speed of sound. Can anyone help me out?


I would like to teach a little nonlinear PDE to an undergraduate who is taking a course in second-order linear boundary value problems. I have never taught nonlinear PDE before, although it is my research specialty. I have a decent book on solitons, but my research specialty is critical point theory in elliptic PDE. Several of my colleagues are experts on solitons. The critical point theory would probably require some Sobolev spaces, which I would like to avoid. I have Evans's great book on PDE, but I think it is too advanced for him. I would like to know if there are any free resources on the Web which I can use, to get readings for myself and the student, and exercises for the student. One more thing: I am interested in PDE that have explicit analytical solutions, or at least can be written as infinite sums of specific functions (I don't want to get into numerical methods for this project).


I am not a physicist but I would really like to know what trained physicists think about this problem that came up in conversation the other day. I have been reading about the search for habitable planets for a little while and about the conditions it takes for a planet to be habitable. I understand that the right amount of heat is important for ideal conditions. Then I caught an interesting documentary on Oppenheimer, Heisenberg and the race for the atomic bomb in world war II. The documentary said something to the effect that a nuclear detonation or any nuclear reaction is very much like a small, very temporary star on earth. It got me thinking that nuclear reactors must also be analogous to mini-stars or suns so I started wondering what it would take to create a nuclear reactor that could make a planet (or moon) more habitable by allowing the heat produced to escape the reactor and warm the planet's surface. As an example, once the technology exists for a nuclear fusion reactor, could it possible to assemble one outside our atmosphere, send it into orbit around, for example, Jupiter's icy moon Europa in order to heat the surface and create more habitable conditions for life?


We are going to establish a company in order to commercialize a stuttering treatment/therapy program. The treatment/therapy is really effective and backed by a lot of scientific research. In our recent discussions, some disagreement has come up whether to market it as the "XYZ stuttering treatment" or the "XYZ stuttering therapy". On one hand, calling our product the "XYZ stuttering treatment" might be advantageous, because in all the research literature it is referred to as such. On the other hand, calling it the "XYZ stuttering therapy" could be better, because all the competition markets/offers their programs as "therapies", and having the term "therapy" appears to be more serious and seems to imply effectiveness. Also, the word "therapy" appears to be more international, which could help if we offer the program abroad. I'm not a native speaker though, so I wanted to hear your opinion and feedback. What's really the difference between "treatment" and "therapy"? Would you rather recommend calling it the "XYZ stuttering treatment" or the "XYZ stuttering therapy"? Why?


I don't understand how a vacuum, the absence of matter, can hold energy. How can it hold energy when Einstein proved that matter is energy? And a second related question; how does the energy in a vacuum allow the Universe to produce itself? And how does that account for why the Universe is expanding? I saw Krauss' lecture on YouTube called Universe from Nothing and only understood some of it, even though he was fantastic at putting things in layman's terms and making these concepts easy to visualize. However, he had a bunch of "asides", so it was a bit confusing. He mentioned that the curvature of the Universe was flat, but then also went on to say how that was the worst possible scenario. Why is a flat Universe such a bad thing?


Often in my studies (economics) the assumption of a "well-behaved" function will be invoked. I don't exactly know what that entails (I think twice continuously differentiability is one of the requirements), nor do I know why this is necessary (though I imagine the why will depend on each case). Can someone explain it to me, and if there is an explanation of the why as well, I would be grateful. Thanks! EDIT: To give one example where the term appears, see this Wikipedia entry for utility functions, which says at one point: In order to simplify calculations, various assumptions have been made of utility functions. CES (constant elasticity of substitution, or isoelastic) utility Exponential utility Quasilinear utility Homothetic preferences Most utility functions used in modeling or theory are well-behaved. They are usually monotonic, quasi-concave, continuous and globally non-satiated. I might be wrong, but I don't think "well-behaved" means monotonic, quasi-concave, continuous and globally non-satiated. What about twice differentiable?


I have always believed in keeping magnets and data storage devices far away from each other. Friends say I'm excessively cautious about it, but I seem to have a lot less data loss than they do! As cell phones have gained popularity, so have cell phone cases with magnetic clasps. Often these clasps are positioned near the center of the phone, in close proximity to where the microSD card is located in the phone. A friend has had two genuine Sandisk microSD cards (purchased at large brick and mortar retail stores) fail in their phone. They keep their phone in one of those cases with a magnetic clasp. Is it likely that the magnet is causing the loss of data, or are such magnets much too weak to result in affecting the data on a microSD card?


I'll start with a disclaimer -- this is not a question about astrology itself, I'm neither trying to refute nor to defend astrology. I'm interested in purely technical things, which are mostly related to astronomy. Given a time and a place (usually related to the moment of birth of a person) one can create a horoscope -- kinda diagram, which represents the positions of planets, Sun and Moon, usually projected on ecliptic. The information about position is usually represented in a form of astrological "houses", which are related to the horizon position. I'm interested in a "reverse" process: given the horoscope with ecliptic coordinates of Sun and Moon and planets, and given those "houses" -- can one find the place and time for which the horoscope was constructed? I'm pretty sure that such kind of problems would be interesting for, say, historians -- maybe there are some research papers or literature describing techniques that allows one to do such things?


First question: I have been reading English: An Essential Grammar by Gerald Nelson and it gives an example of the words 'hard' and 'fast' being used as both adjectives and adverbs: Adverb: John works hard. Peter drives fast. Adjective: John is used to hard work. Peter drives a fast car. I was wondering, can all adjectives be used as adverbs in this manner? E.g. Adjective: Small girl. Are these adverbs??? She is small. She was small. She looked small. Second question: Can present participle verbs be considered as adjectives? E.g. Are these adjectives or are they still considered as verbs? The singing lady. The growing crowd. The advancing army. Third question: Can all past participle verbs be considered adjectives? E.g. The written book. The cooked fish. The bitten apple. And lastly: Can all past participle verbs be considered as adverbs? E.g. The book was written in black ink. The fish seemed to be cooked.


I'm trying to find out whether I should use a singular or plural verb when there are multiple gerunds as the subject of the sentence. For example: Running the correct course and keeping a steady pace are/is necessary in order to win. With either one of these by itself, "is" would be correct: Running the correct course is necessary in order to win. Keeping a steady pace is necessary in order to win. With both gerunds combined, I can't seem to figure out whether the verb should stay singular since each phrase is singular, or if it should become plural since there are two connected by "and". If we just treat the gerunds as regular nouns, then obviously it would become "are", but I'm not sure if gerunds have the exact same rules as regular nouns. I know that if the sentence was: Running the correct course and keeping a steady pace are both necessary. That "are" would be correct, but without the "both" it sounds incorrect to me. Does anyone know the official rule here?


I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances. I have been trying to solve these equations using Orthogonal collocation (rather than using those algorithms used by NDSolve in Mathematica - my hope is to speed up the computation). I have found a lot of examples and lectures on using Orthogonal collocation to solve a single ordinary differential equation, however, I have not come across anything in the literature, as how to solve these equations when they are coupled. I therefore wanted to ask if anyone has experience with this, and could possibly point me toward some literature, and/or worked examples, or explain the twist on how to migrate from a single ODE to coupled ODE's. Best Regards


So here's what I'm trying to do: Given a collection of lat/long coordinates that form a polygon like below, I want to be able to select a point inside the polygon and determine which side of the polygon it is closest to, and determine its distance to this closest edge. My problem is that I need to somehow get rid of the extra coordinates so I can do computation on them -- if, for instance, I only had four points that formed a four sided polygon (i.e. the west-most and east-most points on O'Farrell, and the west-most and east-most points on Ellis), I could do this computation. For instance, putting in the point for 'JINS' as input would return the edge that runs along O'Farrell St. We can assume that the polygon will not be smooth, and that each polygon represents a city square block, so they're relatively simple polygons. Can anyone think of a solution to this problem (whether that be getting rid of extra points or finding some other way to do this computation)? Thanks.


I'm a student of Physics, however I usually study mathematics on texts aimed at mathematicians to gain a deeper understanding. Currently I'm studying differential geometry on Spivak's book and one of the main results I need is the relationship between vector fields and infinitesimal transformations, i.e.: the idea of infinitesimal generators. The only problem is that Spivak's way to get into this is a little more complex than what I need. Indeed he spends time with differential equations and topological properties of manifolds that are related to differential equations. These are interesting topics, but for now what I was really needing was this relationship of vectors and infinitesimal transformations and the understanding of where Lie Groups come into play. Is there a shorter path into these results without needing to go through all of that stuff on differential equations? Is there a more direct way to get into these topics? I ask that because perhaps Spivak just presented that way because he wanted to show how vector fields relates to differential equations in a more concrete way. Thanks very much in advance.


I am having a discussion/conversation with a very close friend, and this conversation concerns me personally (you might even go as far as saying this is my best friend). At one point in our conversation he starts to "spam" (not literally, the messages have meaning and are well-formulated) me with many messages, but I really have nothing to say back (or anything useful to say back). I should clarify by saying that I completely understand what he is saying, and I somewhat agree with the things he said. He then proceeds to send me another text saying: "Don't you have anything to comment?.." How could I respond nicely with a proverb/saying of any kind that means "silence is sometimes better than speaking when one doesn't have anything useful to say"... I know some sayings like "silence is gold" or "better to remain silent and be thought a fool than to speak and to remove all doubt", but they don't really work for me in this scenario. I hope I was clear enough. Thanks


I have been trying to find out what the definition of a noncommutative regular local ring is, but to no avail. In fact, how does one even begin to define Krull dimension for a noncommutative ring? Hence, I would appreciate it if someone could kindly provide definitions for the following, in the case when the ring under study is noncommutative: Regular. In the commutative case, the definition of regular involves localizing at prime ideals. However, in the noncommutative case, how do we do localization? Is Ore's Condition invoked somewhere? Regular local. In the commutative case, the definition of regular local involves Krull dimension. However, in the noncommutative case, do we have an analogue of Krull dimension? On a different note, in the commutative case, is it true that a local ring that is regular the same as a regular local ring? (This might seem to be a stupid question.)


The use of the term sir as a form of address for men, especially those of higher rank or status, is discussed in several prior questions including this one. They all indicate that the term is reserved to males, and that there are a number of related terms for females, such as ma'am. A review of the first dozen online dictionaries at onelook.com confirms that sir is strictly reserved for male addressees. For example ODO defines it as used as a polite or respectful way of addressing a man, especially one in a position of authority: excuse me, sir On several recent television shows in the US, the term sir has been used by a police officer to address his or her supervisor who was female. In the context, the use was sincere and was not objected to by the superior. Has the use of sir when addressing a superior female in a military or quasi-military setting become acceptable, or is this merely literary license?


Could you please recommend any good texts on algebraic geometry (just over the complex numbers rather than arbitrary fields) and on complex geometry including Kahler manifolds that could serve as an informal introduction to the subject for a theoretical physicist (having in mind the applications in physics, e.g. in the string theory)? What I want for a moment is to get some informal picture of the subject rather than being dug up into the gory details of the proofs and lost in higher and higher layers of abstraction of commutative algebra and category theory. The texts I have found so far are all rather dry and almost completely lack this informal streak, and all of them are geared towards pure mathematicians, so if there exists something like "Algebraic geometry for physicists" and "Kahler manifolds for physicists" (of course, they would probably have different titles :)), I would greatly appreciate the relevant references.


How would I say that a phrase or word has "lost it's meaning due to constant repetition." Take the word "awesome": "Awesome" used to denote a situation in which the speaker (or writer) was overwhelmed with "awe." "Awesome" is now used as a measure of how "interesting" something is and isn't terribly high on that rating scale. How would I describe the loss of meaning due to the constant repetition of the word "Awesome"? Take George Santaya's words "Those who cannot remember the past are condemned to repeat it": People often say this phrase to try and instigate action but because of it's overuse, it no longer has any meaning. It's just something people say when they talk about The Holocaust, or the bad grades they got last semester in college. How would I describe the loss of meaning due to the constant repetition of the phrase "Those who cannot remember the past are condemned to repeat it"?


Fat lot of good is a phrase that I grew up with and continue to use occasionally as in the following: He is working hard to fix the problem, but a fat lot of good it will do him without the proper tools. Which means that despite his best efforts, he is not likely to fix the problem until he starts using the proper tools. I've only heard the phrase used with a sarcastic tone as if the phrase is supposed to mean that it will do a lot of good. (Similar in tone to when someone says I could care less when they really mean I could not care less.) What is the origin of fat lot of good and was it ever in common usage with a positive meaning?


I would not be able to put this into symbols, but I ask here because I think it's the correct place to ask. Would the chance of my parked car getting damaged (bumped or scraped) by other cars parking nearby increase over time? Gambler's fallacy says: if something happens less frequently than normal during some period, it will happen more frequently in the future. (wikipedia) For every time I leave my car parked, there is a chance it will get damaged. If I don't want to commit the gambler's fallacy, I should consider the chance of damage the same every time I park. But if I park at the same spot every day for many years, the chance that my car would have been damaged after all those years, would surely be greater than if I just parked there one day, right? How does this not contradict the gambler's fallacy? My insurance company asks a higher premium if I park on the street all year round, than in a garage, so somehow they must figure that the chance is higher than if I just park on the street one day. How does this not contradict the gambler's fallacy?


The three laws are: First law: The velocity of a body remains constant unless the body is acted upon by an external force. Second law: The acceleration a of a body is parallel[disambiguation needed ] and directly proportional to the net force F and inversely proportional to the mass m, i.e., F = ma. Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. The first law had already been formulated by some philosophers prior to Newton, Hobbes said in the Leviathan '...[the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it, though the reason be the same (namely that nothing can change itself)...', given his reasoning, I think it safe to mean constant speed and direction, otherwise change is occuring and he explicitly rules that out. I think the same proposition is mentioned in Lucretious's De Rerum Natura. Are there any antecedents for the second and third law?


I was listening to The Infinite Monkey Cage on the BBC and they were talking about general relativity and gravity. They were saying that gravity is not a force as Newtonian laws describe and is at odds with your real world experience. They said that if you are sitting on a chair, you don't feel a force pulling you down onto the chair. You feel the chair pushing up onto your bottom - at least that's what it feels like when you sit down and try it. They seem to be saying that gravity is not a force pulling from the center of the Earth, it's me that's still and the chair pushing up against me due to acceleration. My question is if this description is accurate or have I misunderstood this? If you are sitting on a chair, is what we call gravity actually the chair accelerating up onto me due to the geometry of Space Time? Is there a better analogy for this?


I'm having trouble completing a proof that for positive integers a and b, that the least common multiple of a and b is ab/gcd(a,b).This is how I've approached it so far: For s = lcm(a,b) we have the following definition: i) a|s and b|s ii) for any integer k where a|k and b|k, s|k Thus the proof comes down to proving that s satisfies these two properties. For i) let gcd(a,b) = d. Thus s = ab/d. Since gcd(a,b) = d, it follows that b/d is an integer so a|ab/d since ab/d = ta for t = b/d. The same conclusion can be made for b so i) is satisfied. Now comes the confusion. I'm not not sure how to prove that if a|k and b|k then ab/d|k. I tried using am = k and bn = k for integers m and n but it lead to no avail. Should I approach the problem som other way?


I am teaching my students about the fairness criteria for voting system, working up towards arrow's impossibility theorem. One of the voting methods is called the pairwise comparison method: voters rank each of the candidates from most to least favourite. To tally the votes, talliers compare each pair of candidates. If candidate X is more often preferred than candidate Y, then X receives a point. (If they tie, they each get half a point.) At the end of the comparisons, the candidate with the most points is selected. We discuss criteria for a voting system to be fair. One criterion in particular is the "irrelevant alternative criteria" which states: If an election is held and a winner is declared, this winning candidate should remain the winner in any recalculation of votes as a result of one or more of the losing candidates dropping out. Can anyone think of an example of when the pairwise comparison method violates the irrelevant alternative criterion?


I am trying to grasp some aspects of the quantum entanglement, but the existing resources (including some of the links here) seem a bit confusing. I am trying to find an answer to the following questions. If two particles are entangled and then separated, will affecting one of them affect the other (for example, the particle is placed in a field that would set some property of it in a specific direction), or will it disentangle the system? If affecting one particle affects the other, then how is it not possible to use this effect to transfer information (once; for example by affecting the spin of the first particle to be up the other particle would have its spin down)? Is affecting the particle equivalent to measuring the property affected (for example the spin)? When a property of the particle is measured, does the particle get entangled with the measuring apparatus? More precisely, does interaction imply entanglement of a sort? I apologize if the questions are trivial or nonsensical, but I am asking as a layman in the field.


Here's what happens. I get stuck on some proof or some mathematical construction and I end up staring at the problem for hours, sometimes not making any progress. I do this because sometimes I think that I'm being lazy, I'm not thinking things through, or I'm just not thinking clearly. This approach is not practical because I only end up falling behind on other work. I don't like to look up solutions because I feel like, given enough time, I would be able to come up with the answer (or some good reasoning). But maybe I should start looking for answers after a shorter period of time. I don't know what the right thing to do is. Do you guys have similar problems? Should I feel bad because I have to look at solutions? Or is this just part of learning?


I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long as it gives a good review of the status of the field, the interesting results and applications, I would be happy. Also, if anything related to multifractal analysis and statistics or time series comes up, I'll take it as well. Books, papers, internetpages, videos, etc... accepted! EDIT: Since the question has been bumped, I decided to put a bounty on it. But I also want to make a bit more precise what I'm looking for. I have always had the impression when encountering the multifractal techniques that people are able to compute a whole bunch of numbers with some nice and fancy formulas. But I have always missed an "understanding" of what the numbers mean. Why is it useful to do a mutlifractal analysis of fluid flow? Of species abundance distributions? Etc... I feel like the technique is purely descriptive with little theory backing up the connection with some deeper underlying structures. But that may just be due to my limited understanding of the field and that is precisely why I ask for pointers to where I can look for this.


Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical formulation of the theory, but also in the physical applications. I am familiar with differential/algebraic topology/particle physics and some basic notions of homological algebra, but am fairly weak in functional analysis. What books/references/review articles would one recommend as the best or easiest starting point to learning this subject? A book that is the most self-contained/pedagogical? (I am currently starting to read Basic Noncommutative Geometry by Khalkal, but was wondering if there were any books even more suitable for a beginner). As I want to get started with learning NCG as quickly as possible, are there any short review papers, notes, or specific chapters of texts where I can gain a bare minimum of prerequisites such as functional analysis to start reading a book on NCG instead of having to read an entire book on operator algebras before starting my study? Or some books that would be helpful that I could read concurrently? Thanks!


Everyone knows how Schrodinger's Cat is set up, so the question becomes whether there's a quantum/classical boundary and what that boundary is. Some people say everything is quantum while some may think there's a line that separates quantum/classical. So the cat in the box would have to be a mixture of live/dead cat until one of two things happened. Decay occurred and poison gas is released that kills the cat or it doesn't occur and the experimenter opens the box and sees a live cat. Wouldn't the wave function be a quantum ensemble of these two states described in Hilbert space until one of these measurements occurred? What state is the cat in before one of these measurements occur? Doesn't it have to be in a quantum ensemble of both states until one of these measurements occur?


Often it is said that Bell's theorem (and the observed violations thereof) rules out local hidden variable theories as the explanation for the seeming non-determinism found in quantum mechanics. I'm wondering if this extends also specifically to radioactive decay processes. So I guess this is really a question of whether the radioactive decay processes are currently understood to a level so that one can say that the seeming randomness boils down to some well-known quantum phenomena that would be covered by Bell's Theorem. Or, alternatively, that the decay processes are not understood to the extent that they are reducible to quantum phenomena and hence could have a different explanation. For example, one could imagine radioactive nuclei being a deterministic but chaotic system of interactions going through states, where sooner or later a state is reached where the decay occurs etc. The question is if such a view, where the individual decay is actually a deterministic phenomena (but appears as random since we dont know the current state of a particular atom) is compatible with current knowledge of radioactivity and quantum mechanics. The section https://en.wikipedia.org/wiki/Radioactive_decay#Theoretical_basis_of_decay_phenomena seems to leave the impression that the underlying mechanism of decay is not understood.


Sometimes people make insincere arguments to justify an action (or inaction), based upon the impact to a particular group. For example, a person might say "Building that sports arena near my house is irresponsible! Think of how many homeless people we could house with that money!" In truth, the person does not want the arena near his or her house, and does not really care about whether homeless people are housed or not. What is the term used to describe the homeless people in this situation? Another example might be large industrial agriculture organizations defending government policies "to protect the family farm" when these organizations are not family farms and do not care about protecting family farms. What is the term used to describe family farms here? The best term I can think of is "smokescreen", as in "Homeless people are being used as a smokescreen to hide other concerns about the sports arena" but this seems informal, and there are probably better phrases (formal or informal). What are they?


I'm building a website for a client in which customers can customise the shape of their board (curvature, length, width, thickness, and so forth) and the client has asked if we can calculate the volume of the board and display it in response to the user's customisations. This sounds like scary advanced calculus and/or differential geometry territory, but I said I'd try to find out the feasibility of doing so nonetheless. I'll mainly be using a set of bezier curves as a baseline to define the board shape and there will of course be curves in all dimensions. The nose will sometimes come to a point and other times be rounded off. The tail will come in a variety of shapes, including being rounded, coming to a point, or even having an inverted "fish tail" shape. Where would I even start with calculating the volume of a surfboard like this? I'd be looking to represent the volume in litres. Edit: I'm guessing I'd need to break the board down into chunks that minimise the number of simultaneous curves and calculate them individually. I'm thinking maybe it's also easier to calculate the volumes of each chunk relative to a uniform enclosing box and subtract each value from the total box volume to get the final volume...


I'm trying to write a database schema for measurements in a variety of categories, and am having trouble coming up with names for some basic elements. Let's assume we are gathering heart rate and blood pressure measurements from a group of people. Each observation is composed of the individual being measured, the time the measurement was taken, and the amount of the measurement. What are each of these called? What is the name for the type of measurement being taken (heart rate or blood pressure in this example)? The collection of individuals is the sample, correct? If so, what is the term for the collection of observations? Please feel free to revise the question, as my lack of knowledge makes it hard to ask accurately. I can come up with names myself, but after failing to find anything in some statistical glossaries, I'm curious if there are canonical names for these basic elements.


So this is my second query about the photovoltaic effect. I've looked into it more and understood it for the most part, but there's still something I don't completely get. After the electrons are excited into the conduction band, some sources say that they can't cross into the opposite material due to an electric field blocking their path and would need an external circuit, others say that some electrons do cross into the other material but their flow gets halted gradually into nothing by the formation of a depletion region, and would then need an external circuit to maintain a consistent flow. So which one is it? Another question is, what exactly causes the electrons to move in the first place? Their attraction to the holes in the opposite material? Simple as that? Much obliged, and thank you for your time. Bonus: If you could explain in a general context, rather than in relation to P-N junctions, you get extra brownie points.


I've been reading up on nuclear reactors, and understand explanations of how it works, how water is heated to steam, which turns the turbines, etc.. I understand all of the safety features, and how control rods are used, and what they do with spent fuel. However, what I can't figure out (after lookin at many websites and videos) is where the reaction actually starts. The fuel rods contain Uranium pellets, and then they're put in the reactor, where the reaction starts and neutrons start hitting each other to create heat? So is this happening all over the reactor, or just in each fuel rod assembly? Also, you can hold a Uranium pellet in your hand (ideally wearing a glove) and it's not dangerous, so what starts a reaction? A lot of people say the reaction can start by itself, so why do uranium pellets not suddenly heat up and start spreading radiation by themselves? Is it because they haven't been enriched? What if you dropped a Uranium pellet on the floor?


I'm not much informed about manifold but I should answer some questions about it. Based on the definition I have written an answer for the following question but I feel there is something wrong with it! Could you please help me? Q: Let M be a smooth manifold and suppose that we have an open cover for that. If S is a subset of M such that the intersection of each element of that cover and S is a submanifold, then S itself is a submanifold. A: Fix an arbitrary point p in M. This point belongs to an element of that cover and as we know the intersection of that element with S is a submanifold, so there exists a map around p such that satisfies the condition, so we are done!


I hope it is appropriate to ask this type of question. I'm in my second year as an undergraduate right now. While my problem solving skills have improved tremendously, I almost never tried to actually remember what I learned. I always had the attitude: "If I don't remember it, I will simply look it up." While this might be legitimate to a certain extent (especially when it comes down to definitions), I'm not sure where this leads to in terms of being able to see various connections much faster. Would you say that it is necessary to remember most of the things that you learnt so far? Of course it wouldn't do any damage at all, but one has always think about it in terms of efficiency, I guess. I mean, it's hard enough to learn mathematics itself - but remembering all of those things just to gain the ability of solving some problems faster? I'm not sure about that and would like to hear your opinion on it.


Timothy Gowers asks What is so wrong with thinking of real numbers as infinite decimals? One of the early objectives of almost any university mathematics course is to teach people to stop thinking of the real numbers as infinite decimals and to regard them instead as elements of the unique complete ordered field, which can be shown to exist by means of Dedekind cuts, or Cauchy sequences of rationals. I would like to argue here that there is nothing wrong with thinking of them as infinite decimals: indeed, many of the traditional arguments of analysis become more intuitive when one does, even if they are less neat. Neatness is of course a great advantage, and I do not wish to suggest that universities should change the way they teach the real numbers. However, it is good to see how the conventional treatment is connected to, and grows out of, more `naive' ideas. and gives a short construction of the real numbers as infinite decimals, then using that to demonstrate the existence of square roots, and the intermediate value theorem. What are other reasons for or against thinking of real numbers as infinite decimals?