darklight03/StackMIAsub huggingface dataset:
At the end my document, I get a new page that contains, Temporary page! LATEX was unable to guess the total number of pages correctly. As there was some unprocessed data that should have been added to the final page this extra page has been added to receive it. If you rerun the document (without altering it) this surplus page will go away, because LATEX now knows how many pages to expect for this document. I know that by just recompiling the document, I can get rid of this error, but I was wondering why does this occur and what unprocessed data that LaTeX couldn't process. For citations, table of contents, table and figure references, LaTeX needs to be run twice, but I have never ever seen this "Temporary page!" page before.
As we know, in EM wave, with the oscilation charge (for simplicity, charge was moving at constant speed, then accelerated and then continued moving with constant speed again), kinks are produced. The funny thing is as the kink moves outward, its length actually increase(the joint vector between the new field line and old field line) due to the fact that new field lines move at a higher speed then old ones. I wonder what we exactly call a wavelength of wave then. Is it the kink's size ? but if it's kink's size, then it means with just one acceleration, kinks size increase and wavelength increases as well which seems to me wrong. one acceleration only should produce one wavelength. So what's the connection between kink and wavelength? If there's no correlation between kink and wavelength, then wondering what's the wavelength truly is in terms of EM wave?
I want to simulate typewriter style typesetted math articles. There are a few major requirements: All characters in all environments be tt style and of the same size and width (including super and sub scripts in math mode). In math mode, sub and super scripts should be one character higher than the base. All emphasizing should be replaced by underline. Spacing between all kinds of lines, including spacing between lists or figures and texts, should be always integral multiples of character height. The multiple can vary according to the height of inline equations (e.g., when too many levels of superscripts, should leave space for superscripts to avoid overlapping). All spaces being the same width as characters, no adjustments to fit line breaking. If a word cannot fit in one line, leave it to the next line. To conclude, all elements should be arranged as if the page is separated into "grids", each grid of the size of a tt character. All elements should be placed exactly fitting one or multiple grids in both vertical and horizontal directions, there is no "half" space or something like that. Is it possible to fulfill these requirements in LaTeX?
We know that when the wave model of light was being used in physics there was Thomson Scattering Model to explain the interaction between a free electron and a light. The Thomson Scattering was explaining the force that acts on an electron when a light hits it, with the force that the electrical field component of that light possesses. (Rather than billard ball explanation) However, I do not understand Thomson Scatter in relation to Doppler Effect and Low-Intensity waves. For the wave model of the Photoelectric effect, it was clear for me to understand where was the wave model wrong when explaining the necessity of the quanta of energies. But, How was Thomson wrong when talking about Doppler shift and low-intensity waves not being able to explain the movement of electrons? I know for a fact that low-intensity waves were insufficient to supply energy for an electron to have the speed and kinetic energy it is supposed to have. I am not sure how built-up energy by low-intensity waves have been thought to be a supply of energy for the acceleration of electron in the first place and how is this related to the Doppler shift by Thomson.
I am trying to have better understanding of localized wave functions. Apparently free particle de Broglie waves are NOT normalizable and act as delocalized functions which was the original rationale behind their use for explanation of electrons in double slit experiment. so far so good ! But then we use Fourier transform to make them localized that they can represent a particle and behave normalizable . Here is what I can not understand: if wave function gets localized ( say to the size of an electron - which actually is supposed to be point-like ) , then such wave can not cover the distance between both slits to be able to make interference patterns in the double slit experiment, .... and if wave function remains delocalized , then it will not be able to get normalized and consequently its wave function will not present accurate probability amplitude . The only way I can think of this is to have a localized wave function that is substantially larger than the slits distance but vanishes at the infinity, but it will be much much larger than a particle - let alone a theoretically point-like particle. My question is: when making a localized wave function, how big the particle size or wave area should be to make interference patterns and be normalizable at the same time? are there known limits for that Fourier section?
I want a tool to easily make geometry diagrams. For example, say I wish to overlay two circles, and then fill their overlap with the color red, whilst coloring other areas with other colors? Let's say I want to make a triangle with curved sides and a flat bottom side; that could be done in no time with the right tool. I could insert a square and then delete circles from its upper two quadrants. To be more clear, here are the list of features I'd like: A gallery of shapes that can be sized and colored as one wishes. The ability to fill any area enclosed by lines with a color. The ability to draw lines between highlighted points on shapes, like the centers of their sides, their corners, points between the quadrants of the circumference of a circle (allowing the drawing of diameters), etc. The ability to insert text into the diagrams. Is free to use. To give examples of close contenders: Draw.io has all features except number two. Microsoft paint and sketchpad has all features except number three. Does an app that has all features exist?
Much of physics education focuses on equations of known possible reactions, how to balance them, how to predict the result if certain elements happen to react with each other. What I don't see a lot of is an explanation of what chemical reactions are likely to happen in a complex system. Assume I was building a physical simulation where I know the position/velocity of any number of elements or compounds. What would the process be to determine which chemical reactions are most likely to occur? Given my assumption: Treat the collision of each atom as a sphere of varying size depending on the size of the type of atom's valence field (sphere collision is to reduce computational complexity). Calculate magnetic attraction/repulsion between local atoms and manipulate the velocities accordingly. If the valence fields of two atoms overlap (or are near each other?) due to attraction, electrons are exchanged, and other atoms that are the least magnetically attracted are either re-positioned or rejected from the compound depending on the magnetic forces and electron availability. I assume "heat" based reactions can be derived from velocity of a collision? Would this be a sufficient model to predict an arbitrary chemical reaction or non-reaction?
I am studying the Newton's Law's of Motion, and really confused about one thing. I know that bodies of very small mass get attracted to our earth due to a force it exerts, due to its huge mass. So that, according to the Newton gravitational equation, a given small mass on earth will be attract by a certain force and depends on the distance of separation from earth's core. Right now I am dropping a pen on a table and observing the sound. Higher the height from which I drop it more the sound it makes, showing that (I believe) more force is being exerted. Although from Gravitational equation of Newton, we can observe that the same force is being exerted on the pen because I am dropping the same pen from heights not so far away from each previous drop. My question is that from second law of Newton, change in momentum causes force. But from gravitation law of Newton, the same force pulls the pen down. But the change in momentum is happening due to gravity, but the gravitational force is constant so that, the pulling force is constant, thus, why every different drop do I hear a different sound. What is the right thing here? I am really confused...
This question is perhaps more on the use of certain parameters in BibTEX than on the use of TEX/LaTEX itself: nevertheless I think it could be of some help to other persons who, like myself, need to redact large bibliographies. In order to list information on the existence of a review in the ZBmath database on a bibliographic item, I am aware of the existence of the following three parameters: ... zbl = {}, zbmath = {}, zblnumber = {}, ... Until a few years ago, only the last one seems to have been used (possibly my opinion is biased by the heavy use of Jabref I do), therefore I'd like to ask why the other ones have been introduced, if there's one of them which is preferable to use. P. S. Finally, let me point out that the American Mathematical Society always codes the analogous information in the univocal parameter mrnumber = {}, which works perfectly in many bibliography styles.
We know from molecular spectroscopy that incoming light on a molecule can change a molecule's rotational, vibrational and electronic energy levels. If the incoming light is, on the far-infrared and microwave region the molecule gets rotational energy.(microwave spectra) on the near-infrared region the molecule gets both rotational and vibrational energy.(infrared spectra) on the ultraviolet & visible light region, the molecule gets all energy levels rotational, vibrational, and electronic energy (electronic band spectra) We also know that, Rayleigh Scatter does not excite electrons of atoms to another electronic level but only causes them to oscillate. Thomson Scatter happens when an electron is free or quasi-free and it also makes the electron oscillate and more, accelerate. Taking into account that both Rayleigh and Thomson most probably happen at low energies and vibrational and rotational energy changes of molecules happen at microwave and infrared spectra: QUESTION: It is clear that, Thomson Scattering can not cause rotational spectra or energy build-up, which requires the whole molecule to rotate since Thomson Scattering is about free and quasi-free electrons. But what about vibrational energy spectra, or energy build-up on such a free electron? Rayleigh Scattering happens on the atomic level so it begs the question, "can it cause both rotational and vibrational energy level changes in atoms or molecules?"
For a given n dimensional chaotic system such as a chaotic attractor or really a time dependent chaotic dynamic system does there exist a higher dimensional representation where the behavior is in fact deterministic? This question comes from a data science problem in multivariate time series forecasting. Most real world behavior is chaotic in nature, such as the stock market or Earth climate cycles (milankovitch cycles etc.). Lets say I could build a really big model that takes into account everything that might impact the system of interest, would there be some set where all the chaos would just go away? Take the TV show foundation based on the books by Isaac Asimov. In there they postulate the Abraxis conjecture which is solved by folding space and is critical to the success of psyco-history (which is really just data science). One of the steepest challenges with time series forecasting is the ease at which it is possible to leave conditions where your inital state no longer applies. If chaos could be eliminated then this problem could be pushed out. Effectively with infinite information we could forecast for infinite time (in the theoretical limit only).
While playing with GeoGebra a few days ago I came up with an initial property of my Cardioid curve, I heard this curve is well studied so I'm not sure on my guess if it's already discovered or new, adding references would be appreciated You have a Cardioid and its circle of perpendicular tangents The red point is an arbitrary point of the circle of perpendicular tangents The violet line is a right angle bisector The blue line is the hypotenuse of a right triangle The green line is the reflection of violet with respect to blue The brown line is the reflection of blue with respect to green The brown line is tangent For giving me Cardioid. I don't have progress on it yet, but I do have other cardioid guesses that I can include in a follow-up question on the site.
I tried lots of research, but still couldn't wrap my head around the difference between free and mobile electrons. Free electrons, from wikipediaLink(I mean free particle bullet point, because other bullet points are not really free electron - as an example valence electron is not free, but mobile) are electrons that don't experience any external force, hence it experiences zero "electric field" from others. as for the mobile electrons, they are loosely bound to the atom (valence electrons). Though, even if these electrons are ejected from the atom, they still experience some electric field from other atoms and could jump into their orbitals. If the above is correct, how can both of these cases exist? how can free electrons not experience any electric field, while mobile electrons do? I know that in sun's core, there're free electrons moving through material. Why don't they then experience the electric field of other atoms?
For some extended context, this is how Heads Up Displays (HUDs) and Reflector Sights work: However, as far as a I know, a lens will take collimated light and focus it to a very small point called the focal point. And since the reverse is also true, only the focal point can be collimated and "focused to infinity" to create the virtual image in a HUD. The reflector sight diagrams clearly show a source reticle that is larger than a focal point, and HUDs in general usually use an LCD display to create the initial image. Although modern HUDs use several optical elements to correct for aberrations and other distortions, most early HUDs and all reflector sights used a single large convex lens to collimate the image. Is this merely an issue of lens diameter? Would using a larger lens allow for the focal point to be larger in diameter too which would allow for a small display to be completely collimated?
If we bring a separable dipole (say a single ammonium chloride molecule) from infinity to the center of a capacitor, once the dipole stabilizes and the rotational energy is lost to electromagnetic radiation, the net work done is negative. If the capacitor plates be perforated and the field be strong enough to separate the dipole and the ions pass through without collisions, they then may be accelerated in the same direction by two other capacitors with perforations, in the same direction and then may recombine after exiting because of their electromagnetic attraction. Once they combine, they still have the velocity gained by the two additional capacitors but none of the three capacitors lose their charge. The dipole gains some kinetic energy so where does the energy come from? The capacitors are not connected to batteries and are pre-charged, the entire setup is in vacuum and gravity is non existent
Recently, I play a game of Turing completeness where I utilize various gate circuits such as NAND, AND, and NOT to construct a circuit that satisfies the given truth table. I didn't learn digital circuits or relevant content. When I play this game, I want to know whether there are any theory to deal it. For example, given a truth table, is there any theory to get the circuit with least basic gate (or only Nand gate). It seems to be a bit like graph theory (but the vertices are special). On the other hand, I know a little about retina from From Neuron to Brain. The retina responds to certain shapes of light, such as a ring of light. I've always wondered how build a neural network with neurons that respond to ring of light but not solid circle light. Of course, I'm not really asking for the details of these questions. I just feel they may are the thing not liking analysis and algebra. If I want to deal these questions, what book I should begin from ?
A parabola is supposed to be a conic section, obtained by slicing through a cone with a plane, like this from Wikipedia: But if you do this, what you get is just part of an elipse, since if the cone and the plane were bigger, eventually you'd end up with an elipse. And a section of an elipse is not a parabola - there is no possible focal point that satisfies the condition that all points on the curve are equidistant from the focal point and the directrix - at least not when I try to construct this in my CAD software Answered by JonathanZ, the key thing was the parabola needs the slicing plane parallel to the slope of the cone (not illustrated or explained clearly in either Wikipedia or Wolfram IMHO). Here's what it looks like in my construction:
I've attached an image that describes the light-rays refracted through a thin lens. P' represents the first real image that is created when light is refracted through the first convex mirror. But how does this translate to the second image point P'' through refraction? I understand the convex mirror formula and how if you plug in the numbers it just works out that Q'' is where it is, but intuitively, this does not make sense. If the image P' is what P'' "sees", as it is the image, how can the refracted image (P'') be on the same side as the object image (in this case P')? As far as I understand, P' acts as a real object for the second surface (the right side of the lens), and the rays that diverge from P' are what get refracted onto P''. But how is this possible, if they are both on the same side? As far as I understand, the model above depicts virtual object through refraction. How is this shown in our case?
The reason we can see the color of objects is light rays undergo scattering in the subsurface of a material, and in their walk in the material lose some wavelengths, and finally exit at a random direction (link) However, aside from this, you see white highlights on an object from the light source. These can be diffuse or specular depending on surface roughness (I'm assuming they're both from surface interactions) Look at the highlights on the shoulder here for what I mean. Not where the arrow is pointing. However, I just found that that aside from metal, most common surfaces, even when highly polished, specularly reflect only a few percent of the incident radiation. How are these highlights then so pronounced, especially for the diffuse highlight case where the light is distributed in all directions.
(Edit: This was closed because it was marked as "opinion based" and I was asked to edit the question so that it could be answered by facts and citations. @Fumblefingers gave citations, thank you. On re-reading several times, I think yours is the correct interpretation, rather than assuming the existence of some actual physical flag. It's like as if we referred to captains & sailors dying in the line of duty as a "badge of honour", there's no physical badge. In my opinion, expecting facts about poetic allusion is a bit unrealistic. Thank you @KillingTime, I hadn't known about the literature forum. I can ask such questions there, and keep this forum to linguistic questions. ) ORIGINAL QUESTION: Does any English literature expert know what kind of pennant Walt Whitman was referring to by "a pennant universal" in the poem "Today a rude brief recitative of ships" in "Leaves of Grass" ? Flaunt out O sea your separate flags of nations! Flaunt out visible as ever the various ship-signals! But do you reserve especially for yourself and for the soul of man one flag above all the rest, A spiritual woven signal for all nations, emblem of man elate above death, Token of all brave captains and all intrepid sailors and mates, And all that went down doing their duty, Reminiscent of them, twined from all intrepid captains young or old, A pennant universal, subtly waving all time, o'er all brave sailors, All seas, all ships.
I am aware that in the theory of classical infinite sums , one can not generally interchange the order of a double sum or do other infinite sum manipulations. However, these infinite sum manipulations can be valid if absolute convergence is available. I am working on a problem , where I would like to manipulate a double infinite sum but absolute convergence need be satisfied in my context. I am under the impression that these classically illegal infinite sum manipulations can hold under less strict conditions in the context of non classical summation methods. I would be glad if someone can write an answer that discusses when interchanging the order of a double sum is allowed in the non classical setting and direct me to a place where I should read about this. Thank you a lot.
After verifying that it was a real word, I just posted a chapter named "Processioning". I have begun to wonder what kind of thing that is. As far as I know there has never been a verb, "to procession", and "to process" is something else entirely. Yet, "they were processioning through town" makes perfect sense. I am thinking that there may be a class of such words, apparent verb forms made from nouns. Am I misguided, or simply ignorant of what the heck that is? It is also weird that processioning would not be used as a gerund, because the noun form is procession. I guess it could be an adjective though, "the processioning group". edit: talented musicians an unconvincing argument an enterprising foreign policy a fun-loving guy are sound examples with no corresponding verbs [EA].
Suppose there is a ridiculously large bridge, fixed at either end (light seconds long at least). The bridge is constantly under the influence of gravity. If the ends are severed simultaneously, the whole bridge will fall. I assume simultaneity isn't a problem as the bridge is all in one reference frame? Will an observer in the middle register the change of inertia, but be unable to see or detect any damage to the ends of the bridge until the light from each end or the signal from electronic sensors has caught up at light speed? If so, does this mean that they can infer from the fall that the ends must be severed I.e. have they recieved information about the state of the ends faster than lightspeed? Or will they not begin to fall until the information about the severed ends has caught up?
Usually in a Cartesian form of derivation in math and physics, I have seen that a particular formula is derived for simplicity by taking concerned points say in the first quadrant. Few examples are the derivation of mirror formula, lens formula, lens maker formula, distance between two points. Later, they extend the formula to all cases and say : "The formula is valid for all cases independent of quadrant and position because we have taken proper care of signs". For example, see the case of mirror formula derivation in the book (especially the pointed last paragraph): Similarly here for distance formula in SL loney. I do not understand deeply that why do this happen ? I know that it can be proved in the above cases by actually deriving for all cases and observing that it is confirming, but how can we say it generally? So the question is : Why do the sign convention in coordinate geometry work the way it does ?