darklight03/StackMIAsub huggingface dataset:
I was considering honorifics and I realized that sometimes we include and sometimes we omit a possessive in front of them. I was wondering if there was a formal rule for such? For example: Your highness, the French delegation has arrived. vs. Highness, the French delegation has arrived. Obviously, the your has been omitted here (or perhaps elided). But, there are other honorifics where this is never done. For example: when addressing the mayor or a judge (in AmE), you might say "Your Honor", but you'd never say, "Honor". Rather, you'd say Mr. Mayor or Judge in those cases. Is there a rule to this, or is merely that your has been elided in the above example, and it should have been written with an apostrophe: 'Highness, the French delegation has arrived. Note: I'm deliberately ignoring the honorifics that never carry a possessive: Mr., Mrs., Dr., etc.
It is uncanny how many books will insist that neither 'many' nor 'much' can be used in positive sentences. Have you got many pens? / Have you got much money? --> correct I haven't got many pens. / I haven't got much money. --> correct I have got many pens. / I have got much money. --> INCORRECT And yet, those same books will invariably have a text where - lo and behold - 'many' is used in a positive sentence! I can only guess that proper grammar rules are as dictated, but every day use has drifted considerably from the said rule. So I ask you: what is the real usage of 'many'. Has it become common in any type of sentence? Or are there situations when 'many' can be used in positive sentences and situations when it can't? Because I really don't know what to say when the students point at a text and say it isn't following the rule they are supposed to follow.
I'm interested in others' suggestions/recommendations for resources to help me acquire reading proficiency (of current math literature, as well as classic math texts) in German. I realize that German has evolved as a language, so ideally, the resource(s) I'm looking for take that into account, or else perhaps I'll need a number of resources to accomplish such proficiency. I suspect I'll need to include multiple resources (in multiple forms) in my efforts to acquire the level of reading proficiency I'd like to have. I do like "hard copy" material, at least in part, from which to study. But I'm also very open to suggested websites, multimedia packages, etc. In part, I'd like to acquire reading proficiency in German to meet a degree requirement, but as a native English speaker, I would also like to be able to study directly from significant original German sources. Finally, there's no doubt that a sound/solid reference/translation dictionary (or two or three!) will be indispensable, as well. Any recommendations for such will be greatly appreciated, keeping in mind that my aim is to be proficient in reading mathematically-oriented German literature (though I've no objections to expanding from this base!).
My current background in analysis is approximately the material in Folland's Real Analysis. I've also read the Analysis text by Lieb and Loss and I also took a graduate level class on complex analysis, which went up to Big Picard and some Nevanlinna theory. For my own amusement I've thought about furthering my knowledge of general analysis. I've heard wonderful things about Stein's book on Singular integrals and his Fourier analysis on Euclidean spaces. Would these be an interesting next step? I'm especially interested in learning more about harmonic analysis and especially learning enough to understand the modern language of these fields. EDIT: Here's maybe a more concise way of phrasing this questions: What's the core knowledge that every graduate student in analysis, regardless of specialization, at a top school is expected to know? What would be a reading list?
When you're taking a mathematics class, you usually know exactly what sections of a book you need to know, and you can focus your time on these important sections. However, when studying by myself, even when I'm trying to study the book as thoroughly as possible, I often feel tempted to skip sections of material (maybe a subsection of a chapter, a proof, or an exercise set). Yet at the same time, I don't want to skip it, fearing that what I want to skip might be something really important. Some reasons you might want to skip are: You might feel that you already know it well enough The proof or the exercises might be too difficult or boring The section might seem not very important For instance, when self-studying from Apostol's Calculus, I felt the need to skip the section on calculating errors of the taylor series for the log function because it seemed unimportant, and the 'rigorous' proof of the FTC which seemed completely unmotivated. What are your strategies for studying material in a thorough, complete way? When is it best to skip -- and how should you determine if the material you're skipping is important or not?
I want to refer to parties that are hosted for players. Which of the following phrases is grammatically correct? "Player Parties" "Players Parties" "Players' Parties" "Player's Parties" A sentence where I might use this phrase is as follows: "We host [...]" Intended usage: I want to use the phrase in a promotional clip alongside a party that is taking place. The clip will show the party happening, and the phrase will appear over the video to describe the event taking place in the clip. The parties are put on for players to provide an opportunity for them to socialize, meet other players and relax. This reference cites the two main uses of the apostrophe that we are all familiar with (the possessive and to indicate omitted letters). In the context I have used the phrase, do the parties belong to the players? Which of the four above phrases would best match my intended meaning? This is most certainly not a duplicate of the question related by Edwin, I am referring to the specific case I have outlined above, which is dependent on the correct meaning to be ascribed to this phrase, as per my intended usage.
First of all, I want to make clear what I'm NOT asking. I'm not hoping to do a rehash of the implications of nonstandard analysis on calculus. Rather, I'm interested in its use in "harder" math. I'm currently reading through Goldblatt's Lectures on the Hyperreals and working on the later sections, wherein he discusses ways of rephrasing other areas of math in nonstandard language (e.g. Loeb measures). I'm trying to understand what the purpose of this is. I understand that nonstandard doesn't get us new results, that is there's nothing we can prove in a nonstandard framework that we can't prove over old-fashioned ZFC. I also understand that generally nonstandard allows us to see the spaces we work in "more intuitively", e.g. Loeb measures allow us to see Lebesgue measure in a more finitary light, but I don't have much of a sense for what this more intuition looks like when we're actually trying to prove statements. So what is the use of nonstandard analysis in its broadest sense? To those of y'all who study/use/teach it, what do you see it as buying you over "standard" analysis?
First time I've asked on this Stack; I hope this is on-topic. I'm laying out a control panel. One of its functions involves an alarm, but under certain circumstances the alarm might be triggered repeatedly, which is annoying. So there's a button which prevents the alarm happening for a while, which is labelled "[problem] Alarm Silence" - not entirely grammatical, but I'm happy with it in context. The alarm warns of a potentially expensive mistake, so you don't want to accidentally leave it silenced. So you should manually press this button again when silencing is no longer really necessary, and the control system will also do that for you if it notices you leaving the specific situation that causes multiple alarms. And in any case after a certain length of time. Underneath the button is an explanatory note which currently says: Silenced when lit. Press to re-enable. Also re-enables automatically. I think that's clear, but I don't really like the word "re-enable". Can anyone suggest a good alternative, bearing in mind the limited space available on the physical panel? All the replacements I can think of - "activate", for example - imply that they will immediately sound the alarm. That's not what happens; re-enabling just allows the alarm to go off if it wants to, it doesn't actively cause it to sound.
I recently started to study problems with prolate spheroidal geometries, for which prolate spheroidal coordinates are most suited. In particular I have the advantage that the problem is axisymmetric around the spheroid major axis. While I'm used to Spherical Harmonics expansions and also to solutions of Laplace equation in terms of Spherical Harmonics I'm not used to spheroidal coordinates and spheroidal harmonics. Specifically i'm looking for some reference on spheroidal harmonics, and how to expand scalar functions in terms of spheroidal harmonics. Do you have any reading to suggest me? Perhaps a book? I couldn't find anything useful with a (rather) quick search on google. PS I am an engineer so I don't want to go deep into the geometry and mathematical details of spheroidal coordinates and harmonics, i only need a way to solve a biharmonic scalar equation in these coordinates Thanks in advance.
In my physics lessons, my teachers have always been keen to tell my class that Jupiter is considered a 'failed star' by scientists. Is this true? In my own effort I wondered if maybe this could just be being regurgitated from an outdated physics syllabus that still considers the Solar System to have nine planets. From that thought onward, through my research on the Internet, I haven't found people referring to Jupiter as such and people always call it a planet rather than a brown dwarf. Furthermore, it's my understanding that brown dwarfs possess more mass than Jupiter suggesting to me that Jupiter possesses too little mass for fusion to even be plausible. So am I correct in thinking that Jupiter is 'only' a planet, or are my physics teachers correct in saying it is a failed star (and if so, why)?
I have read this text about a man who has spent a terrible holiday (in the island of Thassos) due to the disorganisation of the travel company. In fact the text consists in the complaint letter that he wrote to the bloke of the company... I report the passage that I can't understand: Over the years I have been on many holidays to Greece and I can safely say that, until this year, all of those holidays were wonderful. For example, I once spent six weeks on Crete. I loved that holiday so much that I have returned every spring for the last four years. Could you please tell me based on which rule is it necessary to use the present perfect (that I have put in bold) instead of the simple past?
I remember sitting in on a conference talk by a person (possibly Rainer Blatt) doing research with trapped ions (or single atoms strongly coupled to light in an optical cavity), and the person showed a photo of the trap with dots of light from the fluorescence of the single atoms/ions. I thought the person mentioned you could see this with the naked eye b/c the optical coupling to the ion in the trap was so strong, but thinking about it now I'm not sure if this can be true and I can't seem to find any (obvious) reference to this in the literature. So my question: Is it possible to see light from a strongly coupled single atom or ion with the naked eye? If so can you point me to a reference (and hopefully an image of this as well)? Note: The best I can find is the image below from the Blatt research group taken with a CCD (details here). However it is not at all obvious that this would be visible to the naked eye, or if the exposure was just set very high on the camera.
I am standing on the surface of some planet. Gravity is described via General Relativity with some static metric (e.g. the Schwarzschild metric, so static means no time dependence, but the metric may vary from place to place). I send a blue photon up to my friend, who is x meters above me in some tower (we are both at rest relative to each other). He measures the photon and finds out it is red. We both conclude that a gravitational redshift occured. However, where did the energy go? In GR there is no gravitational energy so the photon did not trade "light energy" with potential energy. I found several threads about this, but often they viewed this topic from a cosmological point of view where the metric does depend on time and thus Noether does not work to argue for a conservation of energy. Arguments without cosmology used the explanation via potential energy (which is not a thing in GR, as far as I know). So, since the metric is still time independent the energy should be conserved according to Noether. What is going on? Edit: On the Einstein thought-experiment in the linked question: This does not explain why energy is not conserved from a mathematical or physical point of view. This could also be viewed as a reason why you can not turn photons into matter (and vice versa) without losing energy.
Trying to name things in a computer data model. People have a variety of name roles, such as legal name, maiden name, etc. "The Sultan of Swat" is a nickname or pseudonym of George Ruth. It seems to stand alone. You don't often see him called "The Sultan of Swat" Ruth. "Babe" is also his nickname, but is often used together with other parts of his name, as in "Babe Ruth". It's more like the "Bobby" in Robert "Bobby" Kennedy. I've seen "diminutive" as well as "appellation" used. Are the two kinds of nicknames actually different? And if so, what terms to use? Update. A few more examples for clarification: Is Malcolm X a sobriquet, pseudonym, or just his preferred name? If an Asian student at a western college takes a more western name is that a sobriquet or preferred name?
I find it hard to comprehend the law of conservation of energy. Allow me to explain my confusion. I understand that the law of conservation of energy states that energy is neither created nor destroyed. However, it has to come to a point in time where the origin of that energy is magically 'created'. How do we explain that? For example, you can say that the energy in a falling ball comes from a human lifting and dropping it. Of course, that energy comes from food that we eat, and so on, all the way to the Sun. I know that some of you may be able to explain how the sun gets the energy, etc., but you get my point. I can go all the way back until a single point where you can no long go back.
I was copy-editing a report at work and came across the following sentence: While sustainability in the transport sector was rated relatively high, the sustainability of the power sector was found to be weak. The grammar nerd in me says this should be: While sustainability in the financial and transport sector projects was rated relatively highly, the sustainability of the power sector was found to be weak. Because after all, it feels more natural to say "The project was rated highly", rather than "The project was rated high." But for some reason, I would feel more at ease saying "The project was rated relatively high." and not "The project was rated relatively highly.". What is it about adding a "relatively" to this sentence that makes it different, when the fundamental syntax structure does not change? Adding one adverb in front of another doesn't automatically turn the former into an adjective does it? So why do I feel like it does here? Is "relatively" somehow unique relative to other adverbs? (see what I did there!)
To be clear on this, I know what is the definition of an inner product space and some properties and theorems about them. What I am asking for is an intuition for this definition in the complex case. In the real case, the intuition (or at least one of them) is geometric: The inner product of two vectors is the length of the projection of the first to the second scaled by the norms of both vectors so that it is symmetric (modulo some details). In particular I (and everybody else) think of "inner product zero" as geometric orthogonality and of orthonormal bases as, well, orthonormal bases and so on. The question is, what should I think about when working with complex (or should I say hermitian?) inner product spaces? what is the "meaning" of the complex number associated to two vectors called their inner product? I will be happy to hear all kinds of answers. For example, what physical phenomena does it model or in what mathematical situations does in "naturally" appear. Answers that stress the "nice structure" resulting are also welcome, yet I feel that by itself it is a bit unsatisfying.
Sometimes, I got really confused by the use of the Present Perfect tense. Given the fact, that we don't have this structure in Russian, all we can is to base our knowledge on grammar rules. The rules are quite simple: Experience: I have been to London twice. Unfinished actions: I have lived in Moscow since I was born. Close connection to the present situation: I have just cooked dinner. However, when it comes to simple questions, all that grammar rules are not so obvious. For example, if I am not sure and want to re-ask, could I say something like Have you meant? or Did you mean? Another case: I've sent you the letter and I sent you the letter. Does the first mean that I have just done it and the second that it was some time ago? How do you use it?
I am modeling a closed natural circulation loop, filled with water. Some parts of the loop are heated, some are cooled and other are assumed adiabatic. As an effect of heating and cooling the density of water changes and so does the total pressure in the loop. My question is as follows: Is there a way to calculate the total pressure of the system in terms of, for example, mean density, mean temperature and total volume of the system? For air, the ideal gas equation should be a nice approximation, but it is not applicable for liquids. The problem becomes more complex when the water starts to boil at some point, then it is a two-phase fluid. I have seen answer to this question What equation of state is needed for liquid states? but it does not help in my case.
I am trying to the calculate the link budget for link between a ground station on Earth (with a particular latitude and longitude) and a rover at a particular location on the surface of Mars, either directly or through a satellite on Mars. Now, if I need to determine the link availability between the rover and the ground station, the first step is to determine weather I have a line of sight between the ground station and the rover. For this, the first step is to determine whether Mars is above our horizon or not and if so, for how long. This can be easily done using packages such as PyEphem or Novas. The next step would be to determine if the rover is actually facing Earth or is on the other side of Mars. It is this second step that I need to determine with reasonable accuracy, but have not been able to figure out how to so far. Later on I would need to include the satellites in the link path as well, but for now, I need to determine if I can get a straight line of sight communication between the rover on Mars and ground station on Earth. Any sort of help will be appreciated.
I can find good explanations of how the disjoint union topology is constructed, but I am confused about how things such as complements, boundaries, limit points, etc. are to be understood in this context. For example, suppose we have two spaces, P and M and create their disjoint Union X with the disjoint union topology. It would seem that subsets of P and M must then be subsets of X that are disjoint. However, do they need to be separate as well or could a subset of P have limit points in a subset of M? With what open sets would the limit points be defined? How about the closure or boundary of unions of subsets of P and M? It seems from what I have been able to find that you could not define an open set in X that did not already exist in P or M, so I am confused. Any clarification or a pointer to a relevant treatment would be greatly appreciated. Ernie
A nice little oddity which I thought I'd ask about. I stumbled across the delightful word 'Boustrophedon' in relation to the scanning actions of some printers (inkjet/dot matrix). I believe that this roughly derives from the notion of 'As the ox ploughs the field'. I mentioned this to a colleague who had a farming background. He stated that in older times, this isn't actually how an ox would have ploughed the field, owing to the direction the plough would have turned the earth. Apparently, the field would have been ploughed in spiral pattern to ensure that meeting edges of the plough lines would have their earth turned in the same direction, or 'like the spider builds its web'. Which got me thinking. Is there a colourful noun of some sort that describes this sort of pattern/action?
I just graduated and a mate moved into a flat (none of us are physicists by the way). So, were graduates, we got a new flat, and were broke. So, were now having a debate on how to keep a fridge cool... well, cooler. I suggest that a fridge full of water will keep the food colder, as objects get cooler when water evaporates, (like when we sweat). He says that the fridge just has to do extra work to keep the water cool, but I said it doesn't matter as it's already colder when it enters the fridge, and it's properties should mean that the overall effect, is a colder fridge. Another conundrum, if I AM right, is it more effective to store the water at the bottom, middle, or top shelves? Also, what size/shape should the water be in, should it be stored in glasses, bowls, or in the form of cloths, where the surface area can be distributed, a lot more widely.
Let's imagine standing on a shore, and dropping rocks into a lake. Each rock causes ripples to travel outwards. Now let's imagine there is a monstrous whirl pool somewhere out there in the lake gobbling up waves.. It's quite complex to picture, but In my imagination I could envision a clever enough person analyzing the waves coming back to the shore and deducing things about waves that "got lost" so to speak. Now I understand there was some great debate between Stephen Hawking and Leonard Susskind about information theory and black holes. I don't remember who won that debate, but my understanding is that either way black holes are supposed to do a pretty bang up job of destroying information. So either my simplistic universe is flawed, or maybe I'm over estimating how clever the rock guy could be.. but I don't think so. Let's picture one single rock throw. The outgoing waves at some point get destroyed and you have something like this: and then at some point the wave pieces that didn't get destroyed reflect back and I can't draw that good and it get's all messy, but surely a lot of information comes back to the shore guy right?
A hollow metal sphere is electrically neutral (no excess charge). A small amount of negative charge is suddenly placed at one point P on this metal sphere. If we check on this excess negative charge a few seconds later we will find one of the following possibilities: (a) All of the excess charge remains right around P. (b) The excess charge has distributed itself evenly over the outside surface of the sphere. (c) The excess charge is evenly distributed over the inside and outside surface. (d) Most of the charge is still at point P, but some will have spread over the sphere. (e) There will be no excess charge left. Which one is correct and why? I guess it is some kind of electrostatic induction - phenomena going on. Am I right? I understand that excess charge is distributed over hollow sphere and that negative and positive charges are distributed opposite sides, but don't know which one positive or negative go to inside surface.