darklight03/StackMIAsub huggingface dataset:
A video shows two spherical objects (made up of particles) collide. The title refers to them as two planets colliding. When the objects are indeed as large is planets (however large that might be), the video seems sped up. What if the objects are smaller than that, like the size of marbles? Would they still move as slowly (relatively to each other) as if they were planets? So, to put it differently, when scaling such a situation down, would they move faster relative to each other? Could the video be showing 'real-time' progression when they would be marbles? Updated question If there are two situations that both have two spherical objects in them that have the exact shape etc. (so both situations only differ in proportion), and you would look at both situations at the same time, would one be progressing quicker than the other? Disclaimer: I have limited physics knowledge. Please help me improve this question if it is unclear or hard to understand.
I'm spending too much time thinking about this problem : I need to show that the shrinking wedge of circles which is path connected, locally path connected ,doesn't have a simply connected covering space . hatcher gives a condition for a space to be semi locally connected it's about the induced injection between the fundamental group of a neighborhood U and the fundamental group of our space (here we need the opposite of that) . I've asked my doctor about it and he told me that I can't use it since our space is "locally path connected " and not semi locally ..Can anyone help me prove that this X : shrinking wedge of circles does't have a simply connected covering space ? I supposed it had , then i took a loop in my space X ,I lifted it up to a loop in the simply connected covering space , this loop would be homotopic to the constant loop, my intuition is to project it down , and prove that since my space is not simply connected this loop can't be trivial but I'm feeling there's something missing or wrong .. Any help is appreciated.
This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at hand where the chemical potential is negative. (why?) For fermions, isn't the sign of the chemical potential a matter of definition? The way we normally write our equations for the Fermi-Dirac distribution the chemical potential happens to that value of energy at which the corresponding state has a occupation probability of half. And within this definition the holes in a semiconductor have a negative chemical potential. It would be helpful if someone can help make a statement about the chemical potential which is independent of any convention. {Like one argues that negative temperature is a sign of instability of the system.} Also isn't it possible for fermions in an interacting theory to have a negative chemical potential? Also if there is a "physical argument" as to why bosons can't have a positive chemical potential? (Again, can an interacting theory of bosons make a difference to the scenario?) And how do these issues change when thinking in the framework of QFT? (No one draws the QCD phase diagram with the chemical potential on the negative X-axis!) In QFT does the chemical potential get some intrinsic meaning since relativistically there is a finite lower bound of the energy of any particle given by its rest mass?
Is there a way to selectively disable a specific ligature in XeLaTex? I cannot see how. The selnolig package seems to do what I need but I don't even know how to use Lualatex with my Texshop setup on Mac. Specifics: I am using XeLaTex, new to it and trying to figure my way around and set up some standard templates for my own use, e.g. academic papers. I am mostly using Linux Libertine O. I have the same issue with Adobe Caslon Pro. Why: The "Th" ligature bothers me, particularly in titles. I never see it used in print. See, for example, the New Yorker magazine which uses Caslon, most ligatures are set but never Th. I never see it in books either. (I know this is picky).
If a body becomes charged by losing electrons for example, it will experience a braking force when it is accelerated due to radiation called Bremsstrahlung radiation. Part of the energy used to accelerate the charged body will be emitted as radiation. It should therefore take more energy to accelerate the charged mass than the energy required to accelerate the body without the charge. The Larmor formula calculates the non-relativistic power radiated by the acceleration. There is also a relativistic derivation. The charged body will appear to be more massive due to this effect. It can be explained by the fact that part of the energy is going to kinetic energy and part to radiation. Nevertheless, F=ma should imply a higher mass so are we dealing with a more massive body?
Why can't you create energy out of nowhere For me it's not enough that a smart guy for hundreds of years said so. Some scientists and religious people said that the earth was flat - untill someone said it wasn't. And we know that it isn't flat, we can prove it. I can prove it. Do we just say we can't create energy out of nowhere because Newton said so? Is that our argument - and that no one has proven wrong yet? I think you know some kind of mathemagic that proof that Newton is correct; could you please explain it to me? What about Vacuum Quantum Fluctuations and the Casimir Effect? Is that just a mathematical estimation? Or where do the energy come from? In my (non scientist) eyes it comes like - from nowhere. Is a Zero Point Energy Module possible? I have found this article. Actually all my questions are based on this article. It would be nice if you take a look on the article and try to explain against it. In this article on a no-name-blog there is the claim, that a lot of scientists (phds, professors and so on from well known universities) say that such a "free energy generator" is possible, and that it was build. But because companies would lose money, it will never come to society. There is a lot of fancy words in it, a lot of PhD and other titles and sources on like Nature.
Below is a review by music critic Robert Christgau of a Flaming Lips album. I've pasted the entire review, but my focus is on the first two sentences. Primarily, is it idiomatic to use "couldn't" here? Because unless I'm wrong, isn't the point of what he's saying that you don't have to hate Sgt. Pepper to think it "could" do with a little ribbing, etc.? You don't have to hate Sgt. Pepper to think it couldn't do with a little ribbing, travesty, desecration. In fact, you could love it as much as I do and think that. As hilarious sobersides from multiple generations charge indignantly that the Lips and their various beards fail to "interpret" the songs, all three modes of deconstruction are in play on this grand hoot of a fore-to-aft remake. Highlights for me include a theme statement that gains meanings it never had from its attendant distortions, a creaky "When I'm Sixty-Four," Miley Cyrus so sweet on "Lucy in the Sky," and Julianna Barwick adding just what "She's Leaving Home" cries out for--a female voice. Only "Fixing a Hole" truly fizzles. As for "A Day in the Life," yeah--the original rocks. A-
M-W has the following definition for mixed metaphor: a figure of speech combining inconsistent or incongruous metaphors Hence a requirement is that a 'mixed metaphor' contains more than one metaphor. Eric Lippert comments in another thread: "mixed metaphor" is more commonly used to describe the result of accidentally combining two metaphors in a way that does not make sense as a whole. "For me it was stormy in the great sea of life, but then I came to a crossroads." He does not claim that this is a necessary condition, and I'd agree. I've just written in another thread: ' "John is a real tiger" works, but "That lion is a real tiger" is best avoided.' Each of these two statements contains a single metaphor. Does any definition of 'mixed metaphor' apply to the inappropriate (incongruous juxtaposing of tenor and obviously related vehicle) metaphor in the second sentence?
Else-site, I got into a discussion with a member where the thread turned accusatory and defensive because I said a programming language had tricky details that you learned over time. I did not mean that it was a bad thing, only that there were features less traveled that really enhance the effectiveness of code. One of the Definitions of 'tricky' given by M-W is "requiring skill or caution" and the other two are even more negative. Even "difficult to do or deal with" leans negative into the "It shouldn't be that difficult" realm. Yet difficult is not always bad. Sometimes it just is, mastery of any topic is difficult, and sometimes just knowing the subtle features is enough, it's a sign of a skilled practitioner to leverage these subtleties, and it's those I call tricky. Am I off on my usage, and what resources exist to try to divine these usage subtleties? I'm a native speaker, yet I can't always explain why I shade word meaning a certain direction that is not supported by a dictionary.
I came across a question where i was asked to find the force exerted by the walls of a frustum shaped bucket on a liquid inside it . I found the force exerted by the liquid on the walls of the bucket by concepts of hydrostatic force and thought that by newton's third law both the forces will be equal and opposite . But the answer was totally different . I checked the solution in that simple force dynamics (newton's second law) was used considering the weight of the liquid , the normal force by the floor of the bucket, the atmospheric pressure and the force by the walls. Then since the liquid was at equilibrium all the forces were vetorially equated with each other . I am convinced with this solution but i also don't see any problem with my approach . So how should it be ?
How do you see non-academic mathematics? I have an impression that the academy has still a quite significant prestige and is thought to be the safe-guard for "real science". That is, to verify that those that have the most experience in science, can produce science and have the "blessing" of the academy, in order to deviate from informal publications made outside of academia, whose content cannot be guaranteed and that do not necessarily go through peer-review. However, esp. in mathematics, there's no real reason why mathematics cannot be produced anywhere. I.e. academy does not add much to the process of doing mathematics. Social connections to like-minded people perhaps. Then there's the internet, which makes all information pretty accessible. So do you think there's a place for "open source, non-academic mathematics"?
So basically, I was trying to find a good answer to the question of how light interacts matter. Namely on the quantum level what causes matter to appear transparent, reflective, opaque, etc I came upon the answer with respect to transparency here, but I feel that the concept isn't fully explored here and that something is missing (particularly in the coloured light talk). The jist is that light passes through some matter because the energy gap between the matter's electron's low and excited state exceeds the energy of the photon, and thus the light is not absorbed and the photon passes through the matter. Could someone provide more detailed information about transparency, and information about reflection etc. So I guess for the purposes of forming this into a question I'll simply ask why some materials reflect light and look like mirrors while other materials reflect light with less precision? (thought I get the feeling it has similarly to do with basic mechanics and the regularity of the electron distribution)
I live by Internet, as both a user and a developer. This dual role gives me a chance to observe. Every time I try to ask something in communities like StackOverflow, I always pick words carefully and provide sufficient information, hoping that my questions will be answered in a short time. But even so, sometimes my questions still get ignored. Maybe StackOverflow, or even the whole Internet, is too big a world, filled by floods of information. Small people try to fit in, but end up being swallowed by Twitter and Facebook, without even a sound. So, enough of complaining, I just want to know: Is there a word or a phrase to describe this phenomenon where people find themselves lost in the the great Information Age, ignored by others?
I've been reading the book "Geometric Mechancis" by Darryl Holm and the in the first chapter he treats geometric optics. There the author talks about light rays and those light rays looks like trajectories as of particles as we consider in Classical Mechanics. The first thing that the author state is Fermat's principle that seems to define one action and then determine the path that light follows (i.e. the light ray) being the one which extremizes the action. In all of that discussion, it seemed to me that geometric optics is then all about treating light not as a wave, but rather as a collection of particles. Is that it? In geometric optics we should think of light as a collection of particles? In that setting, a light ray is just the path followed by one such particle, or is it composed by many particles?
This question stems from a disagreement between me and my girlfriend. During the hot summer months, we like to open up the windows during the early morning to cool down our flat a bit. One of us thinks that every window should be opened fully, since that will ensure maximum airflow, the oter swears that the actual area of open window is not a huge factor. We both agree though, that at least in most situations, opening the windows fully is the best option; the question is rather. All other things being equal, how will doubling the area of one open window affect the airflow in a flat? If it helps at all, we typically also have a fan or two running in the flat and we have windows at opposite ends of the flat, which are all open.
Let imagine a tunnel that connect two distant places at the globe (eastern-western or north-south) There are a lot of posible "distances" or metrics, defined by maps, routes, "as the crow flies", etc.. but none of those distance can be shorter than the distance of the tunel. So if two trains travels at same speed, one inside the tunnel and other above in the surface, the one on the tunnel will reach first. If this is possible, then perhaps it's possible to have differents coexisting metrics with differents dispositions or topologies, within the same system. Of course that if we describe a space-time metric surrounding a sphere, then "holes" in it would change the metric (just because it's not a sphere anymore). But it's strange for me that making a hole we could change in some way the space-time shape. In an extreme case. Could be an euclidian space of same dimension be build within a non-euclidian space? I would like to have a view from people familiar with general theory of relativity, thanks
The hippopede is historically famous because Eudoxus used its properties in the first mathematical model of planetary motion. He nested concentric spheres rotating at different inclinations to each other, and had the motion transfer from outer ones inward, the planet was attached to the equator of the innermost sphere. With three or more spheres he achieved trajectories with backward loops ("retrogradations") similar to those observed for the planets. But with just two (see animations here and here) the trajectory is the figure eight shaped curve obtained by intersecting a sphere with a cylinder touching it from the inside (see interactive graphic illustrating that it really is the same curve). Clearly, under any composition of rotations a moving point has to stay on a sphere, but why is it also confined to an off-centered cylinder?
I was reading G.I.Taylor's Single - Photon Double Slit experiment. Now, at a time only a single photon gets emitted. What is the probability of it at a certain point of the screen to hit? The answer is written rather abruptly: Although the photon can hit anywhere, the probability is more, where the brightness(bright fringes) i.e. Intensity is more. Now, this means intensity existed before photon actually hit the wall? How can it be possible? When photon hits the screen, the energy gets transferred to the screen. So, after photon collides, intensity does come in discussion. But if we accept the answer, it is like saying that energy came somehow on the screen before the photon; after that photons would strike there where the intensity of the energy is more. So, who is actually transferring the energy: photon or the waves? If it is wave that transfers energy as being evident from the above quoted argument, then what photons are doing actually ?? What are they meant for if they are not responsible for transferring energy??
Let's define a "hand-incalculable problem" as a mathematical problem that can not be solved by available human calculation power (using only writing materials and utensils) at a specific date and geography, during lifetime of the person who posed the problem. Given a specific date and problem can we strictly label the problem as "hand-incalculable"? Edit: We assume that algorithm to verify the solution is known. Edit: I am looking for a general classification similar to P/NP/NP-Complete which is used in computation theory. I wonder if we could define such classes for mathematical problems as HC(hand-calculable)/HI(hand-incalculable)/HI-Complete at any specific date. Even an absolute classification based on available human FLOPS and not related to a specific date, would be nice. Edit: HC: Hand-calculable at a specific date. HI: Hand-Incalculable at a specific date. HI-Complete: Hand-incalculable no matter how far mathematics will advance in future; consider a dynamic programming problem that needs millions of FLOPS of calculation power to be solved in reasonable time (during lifetime of the person who posed the problem).
I'd like to know if there have been attempts in solving the full problem of the dynamics of a classical hydrogen atom. Taking into account Newton equations for the electron and the proton and Maxwell equations for the electromagnetic field produced by these charges one obtains a higly non-linear set of coupled equations. In such a nonlinear system could some feedback effects between proton and electron take place so to make possible a stable dynamics (or at least a dynamics unstable on such long time scales longer that we can consider hydrogen to be stable)? In this way the system's stability already obtained through quantum mechanics could be reproduced by a full classical approach! P.s.: Please, as I know of the great successes that quantum theory has had since its birth, try not to answer the question telling how quantum mechanics wonderfully solves the problem. P.p.s.: I'm also aware of the fact that electron should lose energy and that this should cause it to fall on the proton in a very short time, so please try to avoid also this argument. I asked this question to understand if the oversymplifing hypothesis', which are fundamental in solving this problem (neglect proton's motion and, as a consequence, magnetic effects) and are quiet ubiquitous in physics, wouldn't mask the potential richness that could arise from mathematical complexity.
He was born and brought up in this village, but after staying and studying abroad his childhood friends seem backwards to him; he _ this place now. Or He had lived in this city all his life but whenever he gets a chance he starts counting the flaws. He thanklessly _ his homeland. It might even apply to a situation like say you party every weekend but if somebody else does the same you criticize them. Note: Read title: act of crticizing one's own homeland/city/country I can use words like criticize, betray or badmouth in my sentences, but I am looking for more like an idiom or phrase or even a proverb, that may or may not fit into my sentences but explains the intent. The intent here is being a hypocrite to an extent, yes but there's an addition of viewing one's own homeland or people as backwards(where I don't think that person has changed, they are just trying to show off). In hindi there's a saying "jis thali me khaya usme ched kiya" which means destroying the plate in which you are served. I'm kinda looking for an english analog for this proverb. I thought "don't shit where you eat" would be the close but it was hilarious to find out it's meaning and of course that it's nowhere close.
Whenever I write TeX/LaTeX documents, I always find that annoying because I can't really focus on the content, It's not that I don't like TeX or what it does for me, it's just the fact that the document quickly becomes something way too verbose. I was thinking about adopting an intermediate syntax, something more "dry", that can help me focusing on the content and only use LaTeX later on in the process to create the last pieces of the layout and the paging. So far I was able to identify rst ( reStructuredText ) and docbook, needless to say I have no experience with neither of the two, but I have a few requirements while asking for your help: support for math formulas support for include external resources like snippets of code or images (vector images for the most part) The kind of documents that I would like to write while adopting this "dry" solution are small books and articles for the most part, so often times I need to separate things into chapters or paragraphs and I would like to have a solution that is modular and flexible.
First and foremost I want to say that by no means am I a physics guru, but I still ponder this question. While I can understand from my current understanding of physics that a perpetual machine is yet,by current understanding, unattainable, does that mean that there is no hope for a free source of energy? Confined to the forces of the Earth we are bound by gravity, a constant form of energy acting on all, but what is the reasoning for not attempting such a feat in the midst of space where the levels of interference with the generation of energy(again from my current understanding) is so minimal? I understand that there would technically be friction on a molecular scale with particles bouncing and colliding with each other, and other potential space debris. However, other than that what is stopping us from achieving the goal of this, or am I simply missing information?
So I decide to self-study the real analysis (measure theory, Banach space, etc.). Surprisingly, I found that Rudin-RCA is quite readable; it is less terse than his PMA. Although the required text for my introductory analysis course was PMA, I mostly studied from Hairer/Wanner's Analysis by Its History (I did not like PMA at all). Although I said readable, I do not know if I actually understand whole materials as I am middle of first chapter, and I already have topology background from Singer/Thorpe and Engelking. I actually like Rudin-RCA, but I am not sure if I am taking great risk as many experience people seem to not liking Rudin for learning... Is Rudin-RCA suitable for a first introduction to the real analysis? Is it outdated? What should I know if I decide to study Rudin-RCA. I am not planning to read the chapters in complex analysis as I am reading Barry Simon's excellent books in the complex analysis.
I have the following sentence: Increase your rating as you develop your coding skills while you evaluate the skills of other developers. However, I now realize that this sentence is a bit off since it doesn't communicate properly. Some feel that this sentence sounds challenging since some imply that you're competing and working with other programmers. I am trying to make it feel more inviting and feel less like a challenge but an opportunity to not only give back to the community but also improve your own skills. I am trying to remove the potential stress that goes into evaluating someone or letting x number of people evaluate you since you're already judged by your manager. I was thinking that maybe changing the tone of this sentence to be less a declaration but more of an open suggestion. Any help would be greatly appreciated.