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My question is whether there are some books on chess mathematics with theorems and their proofs concerning winning strategies for classes of initial positions. Despite there being a lot of books on chess theory and surveys on the use of AI in chess, it seems there is no purely mathematic chess theory that may use the results of game or group theory. If this is the case, then someone has to start it (despite obvious combinatorial difficulties). | 0 |
What is the best way (as in most efficient) way of writing pseudocode like below? In particular I like that it is well-structured but gives enough freedom in writing (in reality it it is just standard inline text aligned in a specific way). If a library was used I would be grateful if anyone can spot if. In case there isn't such library, how can I achieve the result? | 0 |
The following graph is a sensor measurement. Scatter plot The data points are also available in this excel file. I want to do some offset correction/scaling to make the measured points match the actual points. What is the simplest algorithm to do computationally by programming language like Python or MATLAB. These data are acquired in MATLAB continuously point by point, and I have to apply these offset to each point. Will something like finding a linear fit for all possible points and multiplying it with a polynomial work? or if there are any better methods, please suggest. | 0 |
I am wondering if a vertex can lie on an edge in a planar graph- I am not sure if an edge of this vertex is regarded as crossing the edge on which the vertex lies. I have two questions here: Is the actual edge from the vertex tangent to the edge on which the vertex lies? Even if it only is tangent, does it still fit the definition of a planar graph that edges don't cross- as crossing would mean it would have to go through the edge and out of the edge, rather than just touching it at a single point? Is a vertex simply a point and an edge a line segment in the sense in which these terms are defined in plane geometry? | 0 |
I'm not scientifically adept, so bear with me. Would it be feasible to retain enough fuel on new satellites/space stations, etc., that we could dispose of them when obsolete by sending them to the sun where they would likely incinerate before they came close to the "surface." How would we ensure burn up rather orbiting the sun? Already in earth orbit, how much speed would be needed to "hit" the sun? Impractical because of fuel needs? We could use the space station as an example. It would seem to me that eventually the gravity of the Sun would pull it lessening the need for fuel, it's getting way from the rest of solar system's gravities that would require fuel. | 0 |
according to my book the perpendicular component of reaction force is called normal force when there is contact between two bodies. I can not understand that how for example when we jump we pushes the ground downward(action) and the ground pushes us upward(reaction) how this reaction is normal force? or for example if someone jumps to the shore from a boat, the boat moves in the opposite direction we push boat in backward direction and boat pushes us in forward direction(reaction) is this also normal force or friction force plz someone explain i dont understand. | 0 |
Countable atomic structures are homogeneous, i.e., all finite tuple of the same first-order type are conjugate under automorphisms. While this is classical, I can't think of an example of a countable structure whose homogeneity is best proved via atomicity. Competing proof strategies include construction of that structure as a Fraisse limit possibly in an expanded language. Is there a countable structure whose homogeneity is proved via atomicity in a manner at least as good (whatever that means) as via Fraisse theory? | 0 |
here is a vague question: I recognized that adjoints of operators and commutants of non-degenerate self-adjoint algebras share similar features, e.g. the double adjoint of a closable, densely defined operator is the closure of this operator. The double commutant of an non-degenerate self-adjoint algebra is the strong/weak closure of it (double commutant theorem). It seems to me, that this property of double(something) implies closure is a recurring feature and I was wondering whether they are somehow related in a maybe category-theory kind of sense? Thanks | 0 |
When is a category of sets and spans just a category of sets and kleisli morphisms? There is a link between spans and kleisli morphisms, but I feel like they are the same things. I guess I am assuming that the base category for the monad is Set. Is this only true for the multiset monad? To see how we can have a category of sets and spans, just see the nlab article here: | 0 |
We know that a pair of scissors is hard to use at maximum opening angle, because the force from the blades pushes the object away from the scissors and the actual cutting force is reduced. If we would design a pair of (simple, two-piece, with one point of rotation) scissors whose blades have a limited maximum incident angle, or even better, a constant incident angle, then what shape does it look like? Does it have a mathematical form? image source amazon.com | 0 |
If the large space voids between galaxies had uniformly-distributed "negative" gravitational lensing, would its presence be obvious from photos in the same way that the presence of Einstein crosses and Einstein rings make clear the existence of positive gravitational lensing? Or would it only cause subtle distortions, such as reducing the angular diameters of distant galaxies as a function of their distance from us or by distorting how light transitions into and out of a positive gravitational lens? If it would only cause the subtle effects (not obvious ones involving the inversion of images), is it possible for this effect to exist given what Hubble, Planck, etc. has received? | 0 |
I have a question about article usage. I have two sentences and I'm struggling with the articles in the second sentence: There may be invoices on each table. When (?) invoices lying on (?) table disappear, it's a problem. I would guess the invoices and a table. My reasoning is that I'm not talking about specific table so it should be indefinite article. But definite article for invoices because we talk about specific invoices on that table. | 0 |
If we get magnetic field lines on a piece of cardboard, shouldn't it form a gradient of metal pieces across the board (thick layer of metal pieces near the magnet and thin layer of metal away from magnet) rather than forming lines of metal pieces leaving crevices between them. Like in the red areas it is somewhat evenly distributed on board. But in the blue area they forms pattern of lines. Why do they forms lines? Why don't they form a gradient of metal pieces? According to me there are infinite field lines, and only the magnitude of magnetic field decreases as we go away from the magnet. | 0 |
Lately I've encountered a few situations in discussions where I feel like there may be a word that is either more succinct and/or perhaps more wry than just 'ethically convenient'. An example sentence would be: You can only say you wont be involved in unethical thing because it so happens that you cant be because reasons unrelated to your ethics. You are being/You are _______. Basically something just fell on your lap with no personal effort, but you then take advantage of that to further your moral standing. Often it is done willingly, but it could be done with less awareness, perhaps through a form of delusion. 'Casuistic' from the answer here is interesting, but not quite right. | 0 |
A dude has the power to split a nucleus. But this nucleus doesn't hit anything, it just explodes, and that's that. He explodes the atom. He can let the nucleus explode, or he can absorb it. I was making this character thinking he could just split an nucleus, and it would make a nuke-level explosion, and then he could absorb the power of a nuke. But is ONE SINGULAR nucleus splitting, with NO help whatsoever, would that ONE singular nucleus explode with the force of a nuke? | 0 |
What bugs me the most is that since there is net charge, i dont know two things, how would that charge distribute across the surface (even though my intuition says that one of the sides will have more charge than the other) and how would one calculate the dipole moment since the distribution wouldn't be symmetrical about the X-axis (in this problem the equator of the sphere), i've found the potential around it via legendre polynomials which i guess could help, but i just... dont really have a good idea of what to do neither the confidence | 0 |
To clarify with a made-up example: When you address the nation state ... Above, 'state' could be taken as either a part of an open compound noun ('nation state', see footnote), or a verb ('to state'). As a non-native speaker I notice that such ambiguous interpretations do briefly hinder my reading flow, as I have to retract a bit. Also, similar ambiguous cases don't seem that rare. Hence, must, or at least may, one use a comma to disambiguate such cases? In the running example, is this allowed (or even required)? When you address the nation, state .... | 0 |
In piezoelectricity, the piezoelectric tensor is of rank three and its a reason why piezoelectricity is not present in all materials whereas for electrostriction, it is present for all crystal symmetries because the electrostriction tensor is of rank four. So, I think the presence of the electromechanical phenomenon is related to the rank of the related tensor because the rank is related to the crystal structure ? | 0 |
I've always curious about one interesting fact. I will explain it with example. Currently, I'm watching an example which shows the following picture and says that box at the left is the speaker and it produces a sound wave. I wonder why it's being drawn like the above. since it's a longitudinal wave, which actually doesn't have the shape like that. Since particles move in the same direction as wave, their motion is right and left back-and-forth. On the graph though, I get why they end up drawing sin/cos functions, but in the real motion, they don't have the shape as on the above picture. Transverse waves do though which I get why. Thoughts? | 0 |
I am learning multivariate regression, with matrix equations and heavy use of: Transposes Inverses Identity, idempotent matrices Can anyone refer some books where I can learn the properties of matrix equations. Practice problems would be a great help. (I looked up some standard books on Linear Algebra - for example, Anton - but the topics are different from what I need. For example, Anton has Vector spaces, subspaces, eigenvectors, which is not really what I need). | 0 |
I have a question about the potential and wave functions of discrete energy levels of quantum point contacts. Assuming one has a rectengular potential well: Can the potential of the QPC be assumed to be infinite or is it finite and the charge carriers also have a probability of being outside the potential well? Is it also necessary for the wave functions to drop to zero at the edges so that the quantized conductance can be observed? | 0 |
On looking upon the process of penetration of radiation. I came upon this: "If the particle has enough energy, it can deposit its energy to break the molecular bonds displacing the electrons, hence it can penetrate the object. So, if the same thing is done in a large scale with higher concentration of radioactive particle hitting an object per unit area, would it be possible to break nearly every single molecular bonds, and resulting into the object breaking apart in dust? | 0 |
I'd just like to enquire on how this sort of chapter style is done. I am aware it is some permutation of the memoir class with hansen style chapter headings, however the number seems to be in sans-serif, the text in CMU serif, and the document to be in a different font to what I typically find on hansen templates. If anyone could replicate this for me, it would be greatly appreciated. | 0 |
Is the wire in the figure below homotopic to a wire between the two points that just go straight above the pipe? My knowledge of topology is very basic, and it seems to me that the pipe can be seen as some kind of hole, so the wire seems to really be impossible to untie. However, there is a youtube video that seems to untie it. Is it a trick or is my intuition wrong, and if so is it easy and evident to tell why they are homotopic without having to watch the video? Or something else that I am misunderstanding? enter image description here | 0 |
In the Wikipedia entry associated with the Kahn-Kalai conjecture, there is the following assertion This conjecture concerns the general problem of estimating when phase transitions occur in systems. As this entry notes, the conjecture (technically "theorem", as is recently proved) is in the field of graph theory and statistical mechanics I am particularly interested in the consequences of this conjecture in view of statistical mechanics and (even if possible) its implications and applications to formation of complex networks in engineering fields. The main article, as far as I can see, heavily focuses on graph-theoretic facets of the conjecture. So, is there any applied exposition of this conjecture? | 0 |
For example: Should the free market then only capture that which is beyond necessity? I'm not sure if "then" is accomplishing anything, or if it is even correct in this sentence. Perhaps it should be written more like Should the free market only capture that which is beyond necessity? But this sentence doesn't sound like it is referencing any contextual information. Perhaps this Then should the free market only capture that which is beyond necessity? | 0 |
So some authors consider (sigma additive) signed measures on algebras (that are closed only under finite unions) instead of on sigma algebras. This happens for instance when considering the subset of finitely additive signed measures that are sigma additive. So my questions is what can I do with these a sigma additive measure on an algebra? I.e., do the usual convergence theorems hold? What kind of restrictions arise? | 0 |
When firing single photons and letting and interference pattern occur. If you were to draw a straight line from one of the slits to a particular interference gap on the screen, and continued this line through the screen, when you moved the screen to different distances from the slits, would an interference gap be present along the lines trajectory at all screen distances? Or would the interference alternative between gap/no gap along the lines trajectory at different screen distances? | 0 |
I'm using the FrontiersinHavard Latex class provided by the author guidelines of the Frontiers Media. Strangely enough, even though their guidelines specifically state table captions should be placed above the table, the class forces the captions under the tables. There is also little to no documentation on that document class itself. Are there any options to disable this behavior when declaring the document class, or does one need some other workaround to override the document class? | 0 |
When water molecule is cooled, it is well known that it expands: That's the reason the rocks in the desert explode in the cold of the night: the rocks have water inside that expands with cold and breaks the rock. Other molecules compress when cooled. Could this effect (expansion/contraction when heated) be used to moved an electron as a POC of doing work? For example, water is a polar molecule, so it's mere expansion/contraction seems to point that it can move electrons. Given there are random temperature fluctuations everywhere, it seems possible to use these micro contractions/expansions. Does this break any known rules? If we manage to use a diode equivalent, it would move electrons in only one direction. | 0 |
We consider an electron "Bob" trying to escape from a metal surface as shown (blue circles represent electrons, red circles represent ions). I know that Bob can't leave the metal surface is because the attraction due to the ions is greater than the repulsion due to the electrons below. My question is: why F(attraction, by ions near the surface) is greater than F(repulse, by electrons)? Thank you! | 0 |
Suppose I have N unique objects, where N is known, but I have a subsample of only M of them in a bag, where M is unknown. I draw X from the bag with replacement (where X is known) and observe A unique objects (where A is known). If I next draw Y from the bag with replacement (where Y is known) what is the distribution for B, where B is the number of unique objects I will observe? | 0 |
In one of our class discussions about the origins of the word Bank (Money), a guy guessed that maybe it comes from the Bank (the land alongside a river) since the sand gets deposited there, as an equivalent to Bank being a money depositing place. It felt right, except Bank comes from Banque, a Latin word for table, as that's how the financial transactions used to happen, over a table. Now, what I want to know is could it be that Bank and Bank are related? One coming from the other? If so, which one came first? | 0 |
Is there any difference between an axiom and a postulate? I would say that while an axiom is any proposition fixed as true without premises in a theory, a postulate is (also according with its etymology postulatum = something that is requested) something that is necessary to assume to make a theory fit (also in a consequential way) with some kind of experimental measurement. Is there any convention about it? | 0 |
Although inertial forces are just our mathematical creation to help apply Newton's law even in non-inertial frames, can we assume or is it (mathematical proof) that inertial forces also create its field. I think it does so, because when we say that we cannot distinguish between gravity and accelerated motion, we assume them to be same. Is it just as assumption or a correct assumption? | 0 |
Im currently a math masters student. Im doing good and i obtain good grades. Im interested to pursue PHD. At a masters level course i have never been able to solve all exercises which a lecturer has given. This really bothers me and i feel like i need to solve every single exercise problem easily if i want to pursue PHD since these problems in most cases have known solution, hence how i should be able to do research in mathematics if im not able to solve these known problem? My way of thinking might be too black and white in this sense. So my question: people who have completed a phd or a fellow masters student; were you able to solve every single exercise at classes? | 0 |
I know that if a wire is carrying current, the force is F= iBl sinc But what if the wire does not have current, and rather the magnetic field around it varies. Will there still be a force? If so, what will be it's magnitude. You may consider magnetic field direction as required to get a value of force if possible. Note: This is not repeated question. Other similar questions are regarding wires carrying current. Mine is for wires with no current. | 0 |
Why are terrestrial planets like the Earth so much smaller in size than the gas giants? Why can't they be the larger ones? Why are there no stars made up of something solid(/rocky)?(To generate energy, it could maybe use fission in place of fusion)But anyways, Is it because that would violate some laws of physics or mathematics or is it just the way the universe formed? If it is due to the former then what fundamental laws does it break? | 0 |
Is there a general book of mathematics which starts from first order logic, treats set theory (in ZF setting) in which first order logic is used, then abstract algebra (in which set theory is heavily used), topology (at least point set topology) and finally mathematical analysis (in which all the previous concepts are used). In all these parts most important results should be covered. In this way one can study mathematical analysis having solid foundations of mathematics? Am I dreaming or a book of this kind exists? | 0 |
I know from calculus that Riemann Integrals are Riemann sums. We use such integrals to calculate areas under curves. But why does adding an infinite amount of small terms give a finite result for non divergent curves? I know the obvious answer would be to just look at the graph of the function and we can see there is a finite area. But I keep thinking of the Harmonic series and how adding an infinite amount of smaller and smaller terms has as a result infinity. How can we be sure the small terms if the Riemann sum also don't add up to infinity? | 0 |
I have read yesterday the following statement: An initial object when it exists is the colimit of the empty diagram. A terminal object when it exists is the limit of the empty diagram. And I found some justification of the second statement here: What means an empty diagram? but still the justification is not very clear to me, I am wondering if someone can explain this to me in a simpler way please? | 0 |
Using a magnifying lens with the sun as the source, one can focus the light in a single point. Is it possible to use just lenses, or any number of transparent materials of any particular shapes, to focus sunlight into a line and not just a point, and turning it into what I think is called a "focused beam of light"? Is it possible to do with just transparent materials? | 0 |
In a recent chat conversation, I asked someone quite high up in my global organization but not belonging to my regional org setup - "Shall I send an email copying my supervisor", and he replied in the chat window with a "I am good". What does it mean? I wanted an opportunity to introduce my supervisor to him through email, but what should I make of his response? Is he asking me to send the email (OR) is he asking me not to send the email? | 0 |
According to several dictionaries I have, "validate" is a transitive verb. But both Grammarly and ChatGPT judge the following (imperative) sentence as correct: Ensure feature quality by validating with the UI team before release. I would use: Ensure feature quality by validating it with the UI team before release. Is the sentence without it correct? If yes, is it because the verb can be intransitive or because of something else? Edit: corrected them to it. | 0 |
It is well known that the electric field by a ring on a point charge can be easily calculated by integrating the each infinitesimal electric field by each infinitesimal charge. However if one were to attempt to calculate the contrary, that is, electric field exerted by a point charge on a ring, how can one integrate each infinitesimal electric field by the point charge on the ring, since unlike the former, the electric field in the latter case is not generated by an infinitesimal charge, rather by a well defined, let's consider, Q charge? | 0 |
After learning about progressive waves, I struggle to understand what physically causes particles to move up and down in such a wave. What mechanism is actually transferring energy as these particles move up and down? Only longitudinal waves seem intuitive to me. Furthermore, consider water waves. Do we still consider this transverse, even though the particles move in circles rather than up and down. What causes this movement? Is it true water can only be transversal due to the attraction and interactions between water molecules? | 0 |
In all the textbooks that I've seen complex numbers were presented as a given (from history - Cardano's formula etc.). Fundamental theorem of algebra, Frobenius theorem and others use complex numbers as some answer. But is there a way to deduce complex numbers constructively from some (algebraic) reasons without any knowledge about its existence? I'm looking for questions where the only best answer would be complex numbers. Something like "what is algebraic closure of the field of real numbers?", but without any a priory reference to complex numbers. Maybe someone can tell me where I can read about this? | 0 |
I'm currently learning Latex and using Overleaf plus documentation. Sometimes I want to quickly see what other options a package has to offer. Since Overleaf shows a PDF preview, I would like to know if there is a way to quickly list that package's options. Basically what I'm looking for is a page like TeX_primitives_listed_by_TeX_engine that shows each primitive but with a link that explains watch each one does. Like the docs for any programming language, for example. | 0 |
Imagine if you have a molecule with a large size, e.g. proteins. Anything that rotates experiences pseudoforces if my understanding is correct (e.g. coriolis, centrifugal etc). Since every molecule rotates, does this have any effect on these molecules that we could measure? Or properties that arise because of these pseudoforces? My guess would be more smeared out electron clouds, or weaker covalent bonds or something. Or a clustering of more heavy atoms in the centre point since farther from the centre would mean weaker bonds. My guess could also be that the effect is so small that it is negligble. Probably only really big molecules that spin very fast could have an effect (if any). | 0 |
I hope I can ask this question here. I have downloaded Asymptote from windows-binaries and want to run an asy-program that contains the row (it has worked a long time ago) import gsl; But that seems not to be included in the distribution. The manual says something about If asymptote is compiled with... you have access to the gsl-library. Obviously the version I downloaded from the webpage is not compiled with gsl. How do I find a version that is, och how do I add it to the version I have? -anders | 0 |
I'd like to achieve the following using Latex: I'm open to still-better ways of formatting such block matrices. But the above is what I'm thinking towards, right now. I'll be doing a lot of these and I'd like to beautify the stuff I've been posting before. Especially since directed graphs, column and row spaces, the left and right nullspaces, modified network analysis, and the Schur complement method can figure prominently in analysis. I'm not very familiar with using tikz packages. But I'll learn more, if needed. The following is an example of the above that I do not want to produce: It's sad-looking and I'm hoping for something significantly better, more in the direction of the first image above. | 0 |
We know that inside solenoid the magnetic field are same at all point's and are parallel to each other My question is why they are parallel as my teacher explained it as solenoid is set of multiple circular loops and one face coil form North pole while other will form South pole and magnetic field lines from both poles will join in parallel I think this explanation is not correct Any response would be appreciated | 0 |
A long rectangular cardboard thrown in air starts spinning automatically on its way down. Few observations in this experiment: Long rectangular cardboard pieces spin well Doesn't work well with square / circular pieces Long ellipsoid pieces seems to spins the most Also note the spin axis on the way down. Even if you give a little torque to it spin it vertically upwards, eventually on way down the spin stabilizes so the body starts spinning around the horizontal axis This doesn't work with paper / foam as they start floating. Higher density materials like iron / glass of the same size/shape also don't spin A small demonstration can be seen in this video. Can someone explain the exact physics/aerodynamics behind this? | 0 |
In a system, the total energy is composed of Electronic >> Vibrational > Rotational >> Translational. As far as I understand, temperature is only related to the average kinetic energy, which includes Vibrational, Rotational, and Translational components and not electronic energy (excitement states)?? If theoretically, so much energy is added to the system that initially, the temperature increases due to these first three degrees of freedom, but then more and more electronic excited states are populated because the molecules kinetic energy provides enough that electronic excitation occurs, which, of course, takes up that kinetic energy, wouldn't this lead to brief drops in temperature with energy input? | 0 |
I wonder about the Hmiltonian form fo the Potts model and would like to know about its matrix form using the generalized Pauli matrix. I believe it might be possible in a smiliar way applied to the Ising model, as you can see in the website below: How can I explicitly express the Ising Hamiltonian in matrix form? I'm not sure if it's just changing the Pauli matrix into generalized form from the Ising model. | 0 |
I try to apply the replica trick in a two-dimensional gravitational model. I interesting for the case where the semiclassical geometry is an evaporating black hole. These geometries have no time-reflection symmetry. In many related articles they say that the geometries must have time-reflection symmetry, but I can't find why. It seems to me that the method can generalize to geometries with no time-reflection symmetry. | 0 |
I am organizing an algorithmic lecture at my university, which is more theoretical. Regarding Landau-notation and runtime analysis, using algorithms that implement mathematical formulas is great. In my opinion, it helps the students see the connection. Of course, I also want some difficult exercises, and I am searching for mathematical functions that have a very algorithimal touch, if you know what I mean. Because it is hard to describe, here are two examples of such functions: nth prime number and nth Dedekind number. Can you provide me with similar formulas? | 0 |
Force acting on person when jumping from boat is denoted by red colour and force acting on boat is denoted by yellow colour. I have not included the buoyant force and boat weight force on the boat. Coming back to my question:- The force applied by the person on the boat(F)can I Say it friction force which moves the boat in backwards direction and in reaction force acts on person feet can also be called friction force?? Or it some other kind of force like muscular force which moves the boat in backwards and person in forward?? | 0 |
The force repulsing two protons never goes away, meaning that there is a constant force pushing the protons apart forever. Firstly, where are these protons getting the energy to constant apply this force, and where is the nucleus getting the energy to continue to hold them together? Is it the binding energy? If so does it eventually run out of energy to hold them together? | 0 |
I'm writing an academic article title, and, for matter of capitalizations, I would like to know: if "-based" is appended to a word, is "-based" treated as another word and should be written with capitalized "B", or is "-based" treated like a suffix that became one with the word, and thus is written with a non-capitalized "b"? Title example: "Computer-Based Strategies For Asking About Title Capitalization On Stack Exchange"; "Computer-based Strategies For Asking About Title Capitalization On Stack Exchange". | 0 |
I need a reference for this elementary result which I assume to be true and known. Adding a citation in the paper I'm writing (even to a problem in a textbook) would be faster and more elegant than adding the proof itself (which may elude my decaying brain): Given a finite set S of real closed intervals, if each pair of intervals has an overlap (intersection) of length at least k, then the intersection of all the intervals in S has length at least k. Thanks. | 0 |
Which could exhume a response like, "Lul, nice term for this type of pun subgenre." A pun is the humorous use of a word or phrase so as to emphasize or suggest its different meanings or applications, or the use of words that are alike or nearly alike in sound but different in meaning; a play on words. But I'm not sure of this type of subgenre. Edit: If it's not a pun (the jury seems out on whether it counts, I didn't think it was myself until I saw it included any play on words), an answer on what type of joke it is would then suffice. | 0 |
How do we define radius in quantum mechanics. A particle has wave-particle duality, so do we define the radius as Compton wavelength or Bohr radius or some sort of superposition of both? I don't think that either of it works, because of the Heisenberg uncertainity principle, the Bohr radius would vary because the electron shell is probabilistic and requires a wave function. Also we have defined classical electron radius, but as the name says it is classical rather than quantum mechanical. I was curious about this because as I was estimating the Kugilblitz Swarzchild Radius that is required to produce a Micro Kugilblitz with LHC at it's maximum energy, I got the result but I was unable to find the particle at the same or below size Thanks! | 0 |
I've been having a little bit of a debate with one of my friends about the correct use of a word. I hope the native English speakers can help me put an end to this :) I know the word "bold" is mostly used as in brave and courageous, but is it right to use it as prominent, too? This aspect of this issue seems bolder than the rest. Can it be used like this or is it meaningless? | 0 |
I have seen in this link that there is a way to calculate the rolled material length and the number of turns based on: the material thickness inner diameter of the roll external diameter of the roll Is there a way to calculate the length of a material roll (in my case fabric) without knowing its thickness but with knowing its number of turns? So calculate the length by knowing: the number of roll turns inner diameter of the roll external diameter of the roll | 0 |
"Norton's Dome is a thought experiment that exhibits a non-deterministic system within the bounds of Newtonian mechanics. " A ball rolled to the top can reach it in finite time with zero energy at the end, which means if you time reverse it the ball appears to star moving for no reason. By don't use just use an inverted cone with a point at the top? Whouldn't this be much simpler? | 0 |
We see only stars whose light is not older than the age of universe. This is understood. If a star is too far away that currently we don't see it then possibly we will see it later, then the age of the universe will grow. What I don't understand is how a star that we see now can move away out of visible universe in future. | 0 |
I have created some otf files of fonts for symbols and I'd like to write a package from them and then upload it to CTAN. But I have no experience in writing a package. So is there any reference to write a package from otf files? Please give some advice on the references which should be very basic. Specifically, with otf files of some fonts for symbols in hand, how to write a package like MnSymbol? | 0 |
I'm a beginner in the subject & my question can be meaningless, so I'm sorry from start if that's the case. I just don't understand why all of the image f(L) can be a sublattice of L' when f is a homomorphism from L to L'. I learned that all subsets of a lattice don't have to be a sublattice at all. If I don't understand wrong, it's not about the elements of the lattices actually but about the operator differences between them. So why there is not a possibility of a non-inherited operator of f(L), or a non-sublattice lattice of the L' as f(L)? | 0 |
Like the multiple pronunciations of "ough" or different spellings for the same sounds in English I've read come from mixing different dialects into one language. Whereas with French, they imposed on centralized set of rules. Or in Spanish, there are multiple languages/dialects in Spain (though I think at least Franco did try to impose Castellano for all). And other countries have their own histories of language homo/heterogeneity routes taken. What made English turn out the way it did, as opposed to others? In other words, did England ever try to impose one set of rules on how to say written letter combinations (e.g. 'ough'), like other languages have done, one way or another? | 0 |
Suppose a square table. You are shooting from a corner. A ball ends its path upon landing in a corner. At what angles can you shoot a ball from your corner such that the ball will never come back to your corner? Edit: seemingly my question would be how can you prove that if the trajectory is periodic, how can you prove that it will encounter another "corner" point before it returns to itself? | 0 |
I have a matrix, if I apply inverse function from existing softwares, I get an inverse matrix for every non singular matrix. I would like to know if there is a measure that tells that how close the approximation to check weather to consider the inverse matrix not. In my application, there is a possibility to discard an inverse matrix that's not well approximated. I am looking for few hints, keywords to look for or an advice in calculating the measure. I really appreciate any kind of help. | 0 |
I know that particles don't go from one end to the other, they just vibrate and transfer sound energy to next particle. How do they return to equilibrium again? Do they return just after collision with next particle in the medium or do they return as a consequence of reflecting off objects like a slinky? And if they return after reaching objects and reflecting back, is that how we hear our own sound. What will happen if you levitate in the atmosphere arbitrarily at one place (assumption), will you be able to hear your sound provided there are no objects around? | 0 |
Is it important to understand the concept of a universal 'now', to explain that time is a local phenomenon, and the rate of time varies throughout the universe, always dependent on the local distribution of mass, and within passing particles dependent on their relative velocity? I currently think that there is a universal now, but each point in space 'thinks' that it is a different age. I understand that photons don't age (relative to us) because of their relative speed, and they see their entire path since they were formed, (perhaps in a primordial star) as all squished into a single instant, including my retina as I see it. | 0 |
Couldn't we just assume that waves have mass and momentum and can become localized? Dirac Deltas can be given a rigorous mathematical foundation but physicist do not use the Gelfand triple. Why not just assume that electrons, photons, etc., have the same dimension as space? I know string theory does this but are there reformulations of QFT that use this idea that together with the insight that renormalization has a connection with scale invariance gets rid of all the problems that plague QFT? It just seems to me that the concept of a particle is a very unphysical idea. | 0 |
This is the answer. My question is why the integral of E is not zero if there is positive charge on the inner surface when the field lines end on the shell. And why the integral of E is zero when all charges is negative on the inner surface, the field lines also ends on the shell. What is the difference between these two situations? | 0 |
Molecules in solids get polarized and the resulting dipoles align with the external bias field. Can this be done with lightweight spheres that are oppositely charge on their surfaces? Like surfaces that are contact electrified. If a powder made of such oppositely charged fused spheres is placed in a bias field, will each individual particle (two oppositely charged fused spheres) align themselves? If clumping becomes an issue, I guess we could vibrate them lightly while in the bias field. | 0 |
How do they calculate the line of sight of a galaxy or binary star system from an observer's point of view. the velocity of a star in a binary star system depends on the line of sight so how do they measure that crucial parameter with precise values? but in case of unresolvable binary star system like spectrometric and astrometric binaries how do they take the (sin i) parameter | 0 |
I know this may sound very weird, but I'm curious on what makes the water be like water? Like why, when we get into a pool, we are like in a "lower gravity" pull? All our movements are slowed down in water in comparison to air? I very much know it is a strange question, but I've really never thought of it this way, I've always assumed water is like that, but never actually started to think why we move like that underwater. I'm guessing, it has to do with the properties of the water, but if someone can shed some more light on this, I'd appreciate it? | 0 |
Apparently, the special relativity theory is based on analyzing the motion of a point particle with relative speed near the speed of light. However, if I apply and combine this theory with a collection of particles with Newton's third law acting, is it correct to analyze the mass as a whole, whose dynamics equation is still modeled by F(net)=dmv/dt, where F(net) is the sum of all forces experienced by sub-particles within the system, and that m is modeled by Is this correct? If so, please provide reasonable reasons. | 0 |
Suppose a bunch of micron sized particles are charged positively on one half of their surface, and negative on the other. If they are arranged randomly, I understand they will have high entropy, as the system is in disorder. If under the influence of an electric field, we shake these particles such that they align themselves (they will, right?), the dipoles are now in the state of least energy and the system is more ordered, so I understand the entropy must have decreased? Yes, not the total entropy, just the particles themselves. Is my understanding correct, and if yes, will this bring a decrease in temperature of the particles? Before: After applying electric field and shaking: | 0 |
The white line is a flexible conducting foil suspended on the metal wire. I think the external DC circuit will induce a charge on the flexible part and the other charges move to ground. The charged flexible part will incline towards the oppositely charged electrode from the AC circuit and once the voltage reaches peak, the air breaks down and the charge is transferred. When the current switches, the flexible part moves towards the other electrode and a spark transfers the charge in the same direction as before. Am I hideously mistaken? | 0 |
In Arabic, this idiom is used to refer to the fact that when your survival, basic, or primitive needs are not met, you can't think of arts, music, your ambitions, or luxury. e.g. A: "Why is he not planning with us for the vacation? It will be a once in a life time tour around the world!" - "He has a trial next month and could lose half of his savings to his wife, a hungry man can't enjoy the sunset" In the example, the primitive need for the feeling of safety blocks the way of planning for luxarious vacation. | 0 |
I am doing competetive programming task called "Ptaszki" Its easy dfs with some observations. But i came across the following problem: I have two sequances of size n and m respectively and i want to count the number of ways to insert x different elements into this sequances You can choose for every element to which sequance it will go. You can also insert every element to the start or the end of the sequance. I dont have any idea how to solve it. Could you please help me? | 0 |
I see some textbooks showing how Hubbard model with Mean field approximation can explain ferromagnetism of band electrons(stoner theory), but intuitively I can't understand why an on-site Hubbard repulsion term (rather than say Heisenberg term which correlate neighboring sites) can lead to a long-range ferromagnetic correlation. Although hubbard U seems to prefer non-zero spin at a certain site, whether one site's spin is up or down will not have any influence on another site's spin direction, so by what means are different sites correlated? | 0 |
Now (hypothesis) -- And the Physics of Time In this page the author talks about (find in page) (in the context of LIGO Observatories-->) "In their most powerful event, reported just this past February, the combination of two massive black holes should, according to general relativity theory, have resulted in a massive amount of new space in the vicinity of the final star" Please explain my question. I don't get this!!! | 0 |
I came across this sentence: But I craved it so hard at the time, didn't I just? The author appears to be a native speaker. The part that confuses me is the "just" at the end of the question. Is it meant to lessen the guilt of "craving it"? If so, can question tags be ended with other words than "just" to slightly alter the meaning of the question? | 0 |
Dark matter is believed to be a substance of unknown origin with mass that is distributed in space. Can the same observed effects be explained by an intrinsic curvature of regions of space without presence of any mass energy in them? Say during big ban the space got randomly curved such that there are areas with curvature that is just the property of space, like valleys and hills in a landscape. If so, it might be that there are no dark matter particles or any baryonic matter to explain visible effects. | 0 |
What is the correct way to describe people inheriting a castle? (American and British English) Castle heirs or Heirs of the castle or Heirs to the castle It's just a phrase I've heard, but I've seen it written in various ways and I want to know which is the correct way. "heirs to the kingdom, heirs to the castle, heirs to blah blah". Sometimes they put, example, "heirs of the crown" or "crown heirs". | 0 |
I have three doubts regarding the magnetic field due to the charge:- Is a magnetic field generated when a charged particle moves with constant velocity or it only generated when the charge particle is accelerated or both? Why and how does movement of charge result in the creation of a magnetic field around the particle? We also know that motion is relative so if we observe in frame of moving charged particle then its magnetic field should not be there, then what we do in this case? Note (related to third question): as we use pseudo force in non-inertial frame then what do we use in this case? | 0 |
I was studying various cryptographic encryption schemes and why modular arithmetic is being used so much while encrypting messages. Why don't we use simple multiplication with a large known prime with the message, as factorizing large numbers takes exponential time complexity, so it would be hard for an intruder to decrypt the message? So, simply using an encryption scheme that multiplies a large prime on the message to be encrypted is also hard to decrypt for an intruder without knowledge of the prime number multiplied. Why was there a need felt for modular arithmetic-based encryption schemes? wanted just a motivation why we should study modular arithmetic... | 0 |
Can modular exponentiation be used to shuffle a list? I have noticed that modular exponentiation sometimes repeats every number only once, and therefore works like a shuffle mechanism for a list. I do not exactly know within what constraints it does this. I am interested in modular exponentiation for shuffling lists to reduce the computation needed to know the new position of any given object (that each object can know its new position, without knowing the position of every other object or the list as a whole). | 0 |
A transgender colleague requires being referred to as "they" and not "he /she" In what number do I use verbs with this pronoun when it refers to a single person: they is/ are(?) a transgender ? Anther example: When a person is elected the chair of the committee, they give(s?) an inaugural speech. I know I could say "he or she" gives, but this sounds to me too formal or too long. With a transgender, this option does not work; So, back to the transgender example: Do(es ?) they require being referred to as "they" ? | 0 |
Here contains a template for a thesis. In style_sheets there's a template.tex file. The template works by editing that file and compiling. When one does so there is an appendix A and appendix B at the end of the pdf. I have used this write my thesis, but still am not able to remove appendix A and B. Erasing the appendix code in template.tex makes it where the file won't compile. How can I remove the appendix chapters? | 0 |
The above is one of the four two-dimensional lattice systems. See this article for some info. The parallelogram is the primitive unit cell, because it can be translated in order to recreate the entire lattice. So, what is the hexagon then? The conventional unit cell, whatever that means? Is it shown because the symmetry operations that can be performed spans a greater part of the lattice than that which is provided by the primitive unit cell? | 0 |
In very long wires, such as hundreds of kilometers, when we flip a switch and turn on the electricity, does the magnetic field (that iron filings organize around) start to form in one direction and then move through the conductor to the other end? Such that iron filings around the whole wire, would start to react to the magnetic field at different times, with delay the further from the start we get? If yes, does the magnetic field forming propagate in the opposite direction to conventional current, the direction that the electrons travel in? | 0 |
Assuming that light travels as photons that can interfere with themselves while also only being detected as specific localized points, the results of the Elitzur-Vaidman quantum bomb tester experiment demonstrate that the interference of a photon can be affected without the photon itself being absorbed/affected by the object which affects the photon's interference. Does this mean that events that could have happened but did not ("counterfactual"), e.g. the photon being absorbed by the "bomb", are what determine what actually is observed, e.g. the photon being detected at Ddark? If so, how can this occur -- is the explanation for this, for now, strictly dependent on interpretation? | 0 |
In the above question , there will be induction of charge on inner sphere , hence on its surface there must be non zero value of electric potential . But in the solution , the electric potential on the surface of inner sphere has been taken as zero. Inner sphere is connected to earth does it mean that electric potential on its surface is zero despite of charge on the sphere ? Does it mean that any conductor even if it has charge is connected to earth will have zero electric potential? I can't digest this , pls provide some useful insights | 0 |
Suppose event H is a subset of G, where everything in the event H is contained in G but not vise-versa, the probability that H occurs is r and the probability G occurs is s, what's the probability that either G or H will occur, but not both occurring? The probability that G will occur but H will not occur is (s-r). The probability that H will occur while G not occurring is zero. | 0 |
I am curious to know if the relatively newly developed melanin-based semiconductor materials made with polydopachrome have been able to create films or crystals which visually reflect blue, purple or green hues (translated in to nm). If so, was the form of synthesized polydopachrome utilized in creating those outcomes more resembling that found in in the plant/fungi or more represententative of those found in the animal/insect kingdoms? If blues, greens and purple light reflecting melanin based semiconductors exist, are the structures associated with concentrated or unusual copper bonds? Zinc? Manganese? | 0 |
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