In the rational sequence topology, rationals are discrete and irrationals have a local base defined by choosing a Euclidean-converging sequence of rationals and declaring any cofinite subset of this sequence along with the irrational to be open. Do these choices of sequences matter? Or does there exist a homeomorphism for any pair of sequence assignments?


What is the linkage between Loop Quantum Gravity and the approach of the Polymer Quantization? I know you get a lattice using the correct polymer representation, so that's a good toy model for the full theory of LQG, but what are the assumptions to justify this as toy model? What is that we are neglecting/suppressing of the full LQG?


I am working with some textbook trigonometry. Its proofs always take the LHS and show that it is equal to the RHS, but I find cross multiplication easier and faster. Can we indeed do it my way? For example:


A Euclidean space is an affine space over the reals such that the associated vector space is a finite-dimensional inner product over the real numbers. https://en.m.wikipedia.org/wiki/Euclidean_space#Technical_definition Is the theory of Euclidean space Euclidean geometry?


I want to use different calligraphic versions, mathcal and pazocal, of some letters in the same project. However, when I add the pazocal package, even mathcal letters show up in the pazocal format. Is there a way to use both styles for different letters in the same document? -RD


Was playing around on desmos and discovered that the graph of x! = y does not interact with zero at any point. Was wondering if any maybe complex number or number that desmos didn't properly compute who's factorial equals zero. Keep in mind I am just a highschool student so I might not understand some terminology


I understand it requires Newton's third law but how to prove it. Is it like an axiom in physics like in mathematics. in mathematics you cannot prove it, in physics you cannot explain it elementarly (if that's a word).


I have a question about hyphenating compound nouns when they function as object complements. For instance, should entertainment oriented be hyphenated in below sentence? Much of the radio programming was entertainment oriented. Likewise, well-acknowledged This issue is well acknowledged.


What can I call a thing that is one-of-a-kind? This restaurant's Loganberry Duck is one-of-a-kind, and the Crystal Brush Pulpo is another _______. I want to use it to compliment a dish, to express the "you can only get this here" kind of meaning.


I am basically confused as why can't larger nuclei undergo fushion and release energy. One reason I know is because of too much protons than neutrons which generates stronger electrostatic repulsive forces.But another reason is something related to binding energy per nucleon which is making it difficult for me to understand.


So a type of measurement, in units, is length, position, mass, etc, and a unit is meters, kilograms, etc. Is it accurate to say that "an hour" is a time measurement, but also a form of length, especially if we're talking about time "passing"?


Is it possible to increase the dielectric strength of any or some materials by adding a certain layer on its surface? And do you know any? The purpose is lastly to improve the electrical breakdown.


Frictional electricity makes the charges get separated so when the airplanes are running in air at very high speeds, resistance will be created by the air so due to this frictional electricity will be developed on the surface of the plane, so by this method can we generate electricity?


Is 'clinch' used not for embrace but the romantic relationship itself? I think I've heard it used, though I may be imagining it/misunderstanding. Is it idiomatic enough to be something other than a metonym?


How can I typeset a proof in this style? That is, how can I write proofs with three columns, the first numbering the premise or assertion, the second containing the premise or assertion itself, and the third containing the justification of the assertion (if the second column of that row contains an assertion)?


So lets assume for this question that negative mass exists then will a theoretical planet made of negative mass create an outward bulge in spacetime to create antigravity (repulsive). Also for this question use this image to represent spacetime curvature created by positive mass (Basically regular attractive gravity). I thought that negative mass would make spacetime bulge in the opposite outward direction.


Covariant derivatives take into account for both component and basis changes, thereby applicable for curved spaces - where partial derivatives only take component changes into account - is this statement correct? In a polar coordinate system basis changes, even though the space is flat. Will that be considered in partial derivatives? Or we need covariant derivative for that?


If spacetime is a single enitity, and the Big Bounce is the idea that space itself will collapse back in on itself, does that mean that time will collapse back in on itself? And... what does that look like?


Metric space d(z,w)=|z-w| is complete metric space .i have idea that any sequence in C is Cauchy iff its it's real and imaginary part are Cauchy sequence in thus by using completeness of R can I prove this statement please verify it.


Many physicists use thermodynamics to understand what is happening at a cosmic scale. It feels a bit off. Will most concepts directly apply, or do we need to be cautious while using some formulae?


There is a point (x,y) in the elliptical orbit inclined at theta angle. I know the x, y coordinates and the center coordinates and Major Minor. In this case, is there an equation to find the tangent line?


I can't find the definition of this terminology. Actually, there is a similar question 'what is the split k-algebra?'. But the notes in the answer is unavailable and I can't add comments somehow. So I ask a new question.


Problem Hello, I am studying modeling and control course and I'm struggling with drawing neat figure describing the reactor system and to write the differential equations in detail describing the evolution of the variables of the system. My scratch This is the way I approached. Is there any mistakes or wrong approach/assumptions that I made? Fill free to give me any advice.


This comes straight up from a certain text that I was going through, which of course is in the form of a question which asks 'A solid cylinder is rolling without slipping and how many generalized co-ordinates are required. Are there any quasi-generalised co-ordinates?' Any help is appreciated.


The harmonic series symbol is often denoted by H in LaTeX, that looks like this: On Knuth's Concrete Mathematics book, the symbol looks like this: The book used AMS Euler as the typesetting font, where the normal "H" and the harmonic "H" were different. Is there any dedicated symbol for the harmonic series in LaTeX?


I know that for a linear vertical spring, the governing equation of motion written in the presence of gravity is the same as the one written in the absence of gravity. We can either undergo a transformation or cancel the terms while balancing the laws using the free-body diagram. What about nonlinear springs? Please let me know the possible explanations.


Why doesn't light simply go more slowly without bending? Is there a macro phenomenon, say a stream of bullets, that will also bend as it changes from one medium to another or is light somehow unique?


As per my knowledge, the node which having the least cost is branched in branch and bound approach to solve n puzzle problem. What happens if there are multiple nodes with minimal cost ?? Any of the node is taken or every node must be branched ?


Since ALL operating systems have a 'Desktop' - The area of the screen that contains your regularly used shortcuts, taskbar, menu and notification areas. It would be more accurate to be 'Workstation' that shows a 'Desktop' for user interaction. Equally, a 'Laptop' or 'Portable' that shows a 'Desktop' for user interaction. ... All PC's have a 'Desktop'


I would like to tie my new connector to my cable tightly using the provided string. This is what the untied knot and the the tied knot look like; unfortunately, the adaptor can still slip and slide around the cable since the knot is loose. What type of topological problem is this? And how would it be asked mathematically?


reflectivity of a mirror is very high but on a microscopic level no mirror is perfectly smooth so all the reflections must be diffused and we should not see any perfect reflection so how do we see such perfect reflections


The question hung in the room we were in, trembling in the cold. Is the antecedent (in the broader sense) of the dependent clause 'we' or 'the question' here? How would you improve the sentence, given that it needs to start with 'The question..."?


A basis for the density matrix operators is the Pauli Matrices set, but if i'm understanding correctly all Pauli matrices are square and even dimensional, since they are kronecker products of the basic pauli matrices, then maybe they're a base for just even dimensional density operators? if yes there's a way to write odd density operator only as Pauli matrices?


I want to produce a beamer presentation exactly as the one attached, it is like the Antibes theme but not exactly. I need to know which theme it is or if is it a customized theme. Antibes theme does not include the Author or the title at the footer, which is exactly what I need to add.


Dears, I have a sum of two polynomials, and I want the roots of this sum in the left half plane, meaning negative roots. I am looking for some useful theories, but I have not found good things yet. I want to find some condition on each of these polynomials so that their sum has negative roots.


I want to see the page corresponding to edited Tex page when I compile the file on Overleaf, but it always return to the first page in PDF file. How can I fix this?


Sean wasn't as keen about maintaining his gun as a proper soldier should be, and that led to his rifle jam/jamming during the battle. Is there only one right option here, or are both variants valid but have different meaning?


There is a voltage drop between the start and end point of a resistor. How does it achieve this difference in potential? For there to be a difference in potential there must be difference in charges. So do electrons build up at the entrance which in turn creates a difference in potential?


So a dipole antenna is supposed to work with AC supplies. But would it still produce propagating EM waves if pulses of DC are supplied instead of AC current? show in the image:


How can you succinctly say that something is likely to draw the jealousy of others? That would be ____ Especially if it's slightly negative too, attracting not only jealousy but also hate or dislike because of how jealous they are


I understand what reflexive relation on a set is, but I struggle to come up with a practical use of it - why would you even bother defining it? I would really appreciate a couple examples, where reflexions are used, so it would be a little easier to understand - why they are needed?


It seems like most phones, tablets and computers have features when charging to prevent battery degradation. When this feature is activated, it seems the battery does not charge constantly, the best way I can describe it is the battery charge percentage has a similar feature to the enzyme, kinetics reaction. Would a logistical or exponential equation best approximate the charge time.


My professor told me torque can be calculated about any point in space, but would such a torque ever make sense even if the particle is rotating about some other axis, on which the point does not lie?


such as IEEE Transactions on Affective Computing format is shown below, The PDF generated by the template obtained through IEEE Template Selector is not in this format. How do I get the right template? Thanks in advance.


I realize that this editing won't make the question open (since this is against the guidelines to share results and ask to check them). Meanwhile, I'd like to replace a lot of text with a link so those who can see it won't have problems with rendering.


assume a perfectly vertical plane, smooth surface with no deflection and an elastic ball. the moment the ball reaches the lower surface, kinetic energy is at maximum when the ball strikes the lower surface, it then compresses, and some (or all) kinetic energy becomes elastic energy. when the ball has reached maximum elastic compression, does it momentarily stop?


I was wondering if there is some theoretical result (different from the connectedness definition) that characterises the connected subspaces of a connected space. I have looked over my General topology but I do not find anything and I do not see any way to prove something like that. Moreover, if the space is a topological manifold, is there such a result?


I've found this diagram about the conduction band (https://energyeducation.ca/encyclopedia/Conduction_band): But are there other energy bands over the conduction band? Or is the electron simply kicked out of the solid (and so its energy becomes continuous, not in discountinous band).


I would like to draw the following graphs in tkz-graph package. These are the unit-distance colored Golomb graph and Moser spindle respectively. when i try using the regular polygon operation it misaligns the edges and the second graph isnt regular so idk how to draw it


A Smooth Disc with a grove is rotated with constant angular velocity, about its center A block is placed in the grove. What force is acting on the block here to "throw" the block outside the grove, if we look at it from the ground frame?


Please can you explain me this notation (B)^I ,where B is basis of topology and I us interval and U belong to topology generated by B and Ui belong to (B)^I and U = union of Ui Thank you


Used be, one gave a gift. It was called gifting, the gift was given. When, why and how did "gift" replace "give" as in "I gifted her a bouquet"? "Gifted" used mean talented eg "a gifted musician".


In other words, I want to prove that angle is at its maximum when it lands at A. Each of these angles goes through a third of the diameter. That is, if we set O as the center of the circle, Angle A reaches its maximum when AO is perpendicular to the diameter in the figure.


Is there any chance, that you can help me with my problem? I've already used answers from topic: Circle and arrow on a single term of a math equation It works very well. But is it possible to have an arrow going down, when expression is in a denominator? I would like to have something like this:


I have added the image of the part of page (the specific statement is highlighted), why does the text says that the capacitors are not connected in series ? And why the text says that they are not in parallel connection ?


Can proton convert into neutron and another neutron simultaneously into proton in nucleus of a stable element? Which conditions are needed for this? Is this question make sense at current stage of science and technology?


I want to increase the length of the legend symbol (like solid lines, dashed lines, dot dashed lines, dotted lines etc) in the legend box since for dot-dashed lines the length of the symbol is too small to be differentiated by other symbols in the legend box that I use.


I understand some parts of the theory, I've read from here https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Carlip/Hawking_Radiation What exactly is negative energy and how is it different from the "negative" or "positive" we use when talking about an electron or a proton? Why can negative energy only exist inside the blackhole?


I understand that there are different definitions of finite. They are all equivalent over ZFC, and some of them are even equivalent over ZF, but not over weaker theories than ZF(C). I would like some texts that define various notions of finite, and develop the theory quite a bit.


If everything in the universe happens according to rules, thermodynamic or otherwise, then how would anything (or any choice) ever be stochastic? Multiple choices might be probable, but in any instant the ones that get chosen are based off of those rules. Doesn't that rule out stochasticity?


This problem came in my mocks. I tried writing the sum down and sandwiching it but I could not find appropriate "sandwiches" to this. Please help me with this. I nearly spent an hour on it and could not find a solution.


I'm struggling with the correct way to use barrier to entry in the following sentence: Technical interviews are an ever present barrier to entry in the software industry or Technical interviews are an ever present barrier to entry into the software industry Does using 'in' versus 'into' dramatically change the meaning of the sentence and is one more correct in this context?


Usually optimisation problems consist in maximizing a function given some linear constraints. What if one simply has a system of linear equations with some constraints on the variables that come in the form of linear inequalities. Can this be cast as a linear programming problem? If so, how is it classified/where can I read more about it?


Can all verbs with to infinitives in the place of the object complement use both the past participle and to be p.p. form when the relationship between the object and the object complement is passive? I expected my car (to be) repaired soon. Is it okay to use either form?


Is the intersection of two connected set is connected?? I think it is connected, I can't find any counter example to prove it disconnected. My approach is-> A,B connected. Let A meet B disconnected,A meet B =PUQ where P,Q are separated set What next??


Force is defined by acceleration , and acceleration requires the determination of" inertial frames". But an inertial frames also requires the knowledge of forces which requires measuring acceleration, but with respect to what ?


Hi could you please let me know if the "that modifer" modifies the closest noun (i.e exercises) or further away head noun (i.e. vocabulary), in the following passage. Let's review some vocabulary from the last few reading exercises that I've published here on the blog.


If we place different materials in the microwave owen, they will get hot at different speeds. For instance meals get hot really fast. What material property decides on the strength of the coupling? Resistance? Permeability?


Can't we make a face with just two edges(sides) and two vertices? We just connect those two vertices twice each with different edges and we can make a face between the two edges with only two vertices and edges like the image.


If all matter began from one infinitesimally small point, and flew outward from there. How can we have galaxies colliding? Did they make left hand turns or something? Or it is possible multiple galaxies were created by secondary coalescing and re-exploding of galactic material, flinging them in new directions? Wouldn't that increase the time-frame of the Universe's age?


Is it practically possible to detect big and solid amounts of steel on the ground at long distances? (e.g. vehicles on line of sight) Metal detectors do it but at short distances and suffer of parasitic detections from minerals in the soil and etc. Radars detect it well but can't distinguish from other non metal but big objects.


I know that such correspondence exists when the group is finite. I'm trying to take the basic linear representation theory of finite groups to compact groups. Specifically I'm trying to see if the concept of F[G]-module is well defined.


I have been looking for examples of essential discontinuity but have been confused, as different sources cite different things. I know that it might be non-removable discontinuity and infinite and oscillatory are its types. Am I correct? Can somebody explain with examples?


For example, if you have a battery and you connect both ends with a short circuit with zero or low resistance, why does it short circuit? What causes this internally? What are really happening with the charges that cause this "explosion"? edit: I specifically want to know why connecting two ends of the battery with a wire with (hypothetically) no resistance would short it.


Light always moves in a straight line unless gravity acts on it strongly, but since it is made of electric and magnetic waves, shouldn't it be pulled towards different charges and magnetic, or is light neutral?


Can you link action verbs with verbs of being in a sentence? As in say These are people who think critically, solve problems collaboratively, and are prepared to thrive in a global society.


Are there words that describe the directionality of languages? I only see compound words, such as left- to- right or top-to-bottom. I would have thought a human practice so ancient as language would have established words to this effect!!


Im a mathematician which also learn physics, Ive read several papers on sigma models, and it was quite interesting . So my question is where can I read about open problems of sigma models?


When I say 'Been around for a while' I mean like someone who has been somewhere, or been a member for a while. I'm trying to make a role for the people in my discord server for some of the oldest members, you see.


I found that it is a normal concept appearing in condensed matter physics and especially topological order field. I have been aware of the topological defect. But what is a symmetry defect? Could someone explain or give a simple concrete example?


A person who is especially proud to be from a particular city, and puts down others from opposing cities. They rep their city as if it's a sports team. This is especially true in the US. Could you please suggest a single word one could use to describe such a person well (not a gross hypernym like 'supporter')?


If causality is an axiom or a fundamental law in physics, would the existence of causality be a reason which forbids time travel? Because time travel could break causality so we see first the effect and then the cause.


In a opening of the news about several drugs for Alzheimer's disease, the news broadcaster said, He(the reporter) has "our" look at the breakthroughs and what they could mean. Why is not just simply "has a look" instead of "has our look"? What implies "our" in that sentence? Thanks.


I come from symplectic/poisson geometry and I am curious about shifted symplectic/poisson structure on stacks. From what I've saw, the general context there is derived schemes/stacks, so, Algebraic Geometry. What would be the shortest (and most useful) reference for learning AG for that? Hartshorne?


Please help me with my query regarding rainbow formation. Many Books gave formation of only red and violet colour whereas middlemost colours are rising doubt.please check the following picture .My Questions are also marked there..


I just came across a snipet of codes where a long vertical bracket is used to mark a loop. I really like that. I wonder what is the best way to implement this in latex? Thanks


If a stone was tied To a string and then we made it undergo uniform circular motion. Is the centripetal force provided by both the weight and tension or the tension only? What force balances the weight if this is not the case?


I'm having a hard time to understand the unification algorithm properly. Why are these two problems: P(x , h(b), h(x)) and P(f(g(y)), y, h(f(g(h(a))))) P(f(g(x)), g(b), h(x)) and P(f(y), y, h(c)) don't have a MGU, although I cannot see any circular dependency or function mismatch here.


Beyond a formal preference for background independence, what is stopping us from setting cosmological time as a de facto universal timeline, analogous to newtonian absolute time? General relativity doesn't entail it on its own, but neither does it forbid us if certain conditions hold (for a given model.)


In nuclear physics literature, both appear very often. HF is easy. It refers to a variational method with a Slater determinant variational wave function. What is HFB? Does it refer to a similar variational wave function which is annihilated by some quasi-particle annihilation operator? The quasi-particle annihilation operator is a mix of some common annihilation and creation operators.


The context that I intended to use the phrase was along the lines of: The registration page no longer works because the workshop is [insert the phrase or word here]. The workshop was free so I was not sure if "sold out" was correct. Is there something else I can use?


Im trying to find the Integral over the real Numbers of a constant Number (j-i) with respect to a probability measure P. Im new to lebesgue Integration and would appreciate any help :).


Can anyone can help me why when we rotate a object on oxy ,that is a linear transformation but not nonlinear transform . I can't imagine the relation between when we rotate a point in oxy and matrix ?


Could anyone please point me out in the direction of a book or a paper on Skorokhod topology on caglad functions? Or any other topology on that same space if this one fails. I expect that there is no magic hidden there, but maybe I am wrong.


I cannot comprehend how can we break a seemingly non-ideal choke coil into just a pure resistor and inductor in series according to the following solution of a question. Considering the data in the question (all given values are R.M.S values),krichoff's voltage law is seemingly violated,is the question or solution incorrect or am i missing something.


The pancake theorem guarantees that there is a line that can bisect a rectangle and a triangle simultaneously. The Borsuk Ulam Theorem can be used to prove that theorem. Show that any line through the center of a rectangle bisects the area of triangle simultaneously (the position of the center triangle can be the same as position the center of a rectangle or not)?


When proving the statement above, I completely understand the textbook proof with convergent subsequences and contradiction, but I wonder: when function is continuous by classic epsilon-delta continuity,for all possible points in the closed interval, there is a delta that satisfy epsilon-delta definition, so if we take the smallest delta, will that exact delta satisfy uniform continuity?


I was wondering why is it that I can replace heat going into a carnot engine with the temperature of the "hot place" and vice versa, i.e , why can the temperatures of the places replace the heat going in and out of the engine


I see that electrons are quite small in size, moreover it is moving fast but I have a question why do free electrons not leave a conductor (like a wire) ? but they can only move at the edge of the conductor?


What is the equation for the reverse bias current in terms of voltage applied? And this even be analytically derived? If so, how to derive it. I can't seem to find good resources on this topic.


I am trying to change the color of the title block in template GeoURV Poster template. I know that i may change color in the beamerthemeGeoURV.sty. But I would like it to change in the gradient style, let's say from black to orange.


This is the integral I want to calculate. I want to integrate over this range: So I set up this integral: However this gives me the wrong answer. Correct answer is: Why is that?


If salt water is a good conductor of electricity so does it mean if we put a very large voltage somewhere in the sea then person all across the world will experience some current and are there any physical parameters to quantify this.


Please see diagram below showing a rigid rod mass 'm' connected at one end to a fixed frictionless pivot. The rod swings from position A to B changing its orientation around its centre of mass. Can anyone advise how an external torque can be formed that causes the rod to spin about its centre of mass?


I understand that the Coriolis effect is not responsible for the spin effect in the bathroom, but I have never seen a rigorous math prof of this. Where could I find a proof of this? What references could I read to try to proof it? is it very long?


how does an electromagnetic wave detach itself from something rather than fluxing? electromagnetic radiaton. I need the info for a project and simply couldn't find any useable information on YouTube. other than that all the info I saw on other websites where different/didn't answer the question I had.


I was told and convinced that gravity is not a force, and in free fall you're an inertial frame and experience no force, and when on the surface of Earth you would be accelerating upwards. What I admit I can't understand is Earth accelerating, why so? what property of mass explains this? Is there a relationship between an object's mass and its acceleration?


In Special Relativity, the diagram we most commonly see is the Minkowski coordinization of Rindler Spacetime (the accelerating observer's coordinates as seen in the inertial frame). Are there any visualizations of the inverse/ how motion in an inertial frame would appear to an accelerating observer?


I downloaded Mathpix snip but when I was convet to .tex file it just put an includgraphics. I'd like the commands in Latex in order I can edit the formulas. Is this because I'm trying a free version? Could you give more options?


I'm sure this implication is correct. However, are there rules on how one can manipulate with quantifiers? It might somehow be related to whether no free variables are becoming bounded after the operation.


Can't find this after googling thirty minutes. In the following sentence, should I use quotation marks or not? James used the words stupid, dumb, and fidiotic in his briefing. James used the words 'stupid,' 'dumb,' and 'fidiotic' his briefing.


For example, people that are ostensibly unaware but in reality behaving in a methodical way. Playing dumb but also ingratiating yourself in a savvy way. A word to describe politicians, influencers, and the like.


Does "for all the" mean a contrast or a cause and effect? "For all the work he put in, the project was sure a disaster. " Does this mean because of all the work he put in, the project was bad? May you infer if he the project was good, then he didn't work hard?


I have searched and I know that it is used in mathematics, but can it be used in the context of a sentence? Like the way we do simplification of a sentence, so for this usage, can we say that we perform complexification of a sentence?


My task is to summarize a book and in that summarized version I need to keep both references to page number in the summary and also add manually the page number from the book something like this: I've tried with redefining some of the tocloft commands but it is not working... Thanks!


Some people who try to deny the Cavendish Experiment say that the masses attract each other because of the atoms, not gravity. Doesn't an atom have a null electric field by nature? Is there any other way they could attract each other?


Suppose I blow dry a region with some water on it. Would it dry it faster than otherwise? If yes, why? I can give one qualitative reason against it, since the blow dryer is blowing room temperature air, no real heating is done on the hair. But perhaps there are some effects I'm not considering, so some more authortative answers would be appreciated. Related


After a linear transformation, some vectors may not change direction, they only scale by a number. The scaling factor of those vectors is called eigenvalue. Can we think of singular values in this manner? Since eigenvalues are related to only square matrices, Are singular values the generalized "scaling factors" of a linear transformation (matrix)? Thank you.


There's the word luthier for a string instrument maker, but with winds, the only option seem to be more like naming something in modern English, like "reedmaker" which would more apply to double reed instrument players who make their own reeds or something like "wind luthier" even though that's the best option as far as I can tell.


A colleague who is a ELL used the word "cork" to signify a mistake/error/typo on a schedule. I thought that the four-day schedule was a cork. She says she thinks her English teacher was a Kiwi. I can't find any such usage.


To describe transformations from certain programming constructs into e.g. assembler I need a horizontal line with a downward pointing arrow in the center of the line. Is there also a way to achieve this without tikz?


I am looking for a way to determine the rotation of an electric motor externally as i can not see the shaft the outside of the motor is smooth all the way around. is there sufficient magnetic field to have a pull on a magnetic ball?


I wonder if all interrogative pronouns can be used in structures like Where better to learn about the resilience of life? For example, Who better to repair my car? How better to cook potatoes than by baking?


I have seen the doppler effect derived quite a few times when the observer is moving. What is the source is also moving at some random velocity in some angle? How would one go about thinking about this?


I am trying to draw a bold diameter symbol. I imported the diameter symbol by the package wasysymas shown in this answer and looked at several ways how to use bold math symbols as shown here and here, yet none of them seemed to work for me. How can I achieve this?


In a solenoid, when current changes with time an EMF is induced, but it should not be like this, because the wire which is bend to make solenoid is isolated (usually painted to give it an insulation) so each turn of solenoid is not completely a closed loop because the ends of the wire forming the turn are not joined, the coating is joined.


i was trying to show it with polar coordinates but it showed that the limit exist however wolfram alpha stated that the limit does not exist so im confused does not polar coordinates proof is enough


I am a total newbie so I appreciate all your answers as simple as possible. I want to have in my entire document all examples to be "non-floating", it means when I write: The following example shows this: IMAGE ...so I want it to be fixed there, below, centred. Is there any way to make that setting permanent in the header of the document?


Quantum fidelity estimation is to estimate the similarity between two quantum states or process. Could quantum fidelity be viewd as a parameter? And what are the similarity and difference between quantum fidelity estimation and parameter estimation problem? Cross-posted on qc.SE


It is clear that the Zorn lemma guarantees the existence. I prove that the minimal element is unique, and obviously the set is totally ordered. So because the uniqueness of the successor of all elements of the set, in same sense it seems reasonable to me that we will find the uniqueness of the maximal element, but i don't know how to prove it


If denser medium tend to decrease the speed of light (that is why the light rays get refracted to travel a shorter distance to maintain the highest speed possible) Then why total internal reflection happen? if light escapes the denser medium then it will be at more speed - right? then why do the opposite of what is intended?


With reference to this article, I'm curious about how the modular inverse of a polynomial is computed. Moudluar inverse of a number with respect to a modulus exists when the two numbers are relatively prime. I was initially expecting this to hold for coefficients of a polynomial function.


My question is what is the name for words that intensifiers cannot be used with. Words like unique or impossible. Something cannot be more unique or more impossible than another thing. I forgot the name for these and am very curious.


In theory, since the stone acquires the velocity of the balloon, it should go upwards slightly before coming down since it's velocity is equal to that of the balloon (in upward direction). But realistically, does it so the same? Asking from the perspective of an observer on the ground.


For a sentence I got this book from Tom, if we simply rewrite it with passive voice, it would seem to be like This book was gotten from Tom. But I haven't quite met such expressions as Something is gotten from somebody. Is it idiomatic to say so?


I am going to help you. What is the grammatical function of to help you here? Reopen note Please note that I did not ask about going to (and that the to belongs with the following verb as shown above, not with going). The question is about the grammatical relations of to help you, not about going.


In the context of a section in a technical document that describes several topics, one of which is essential and others can be skipped, which of the following is better? You can skip the others on first reading. vs You can skip the others at first reading.


A chapter title appears on bottom of page in toc with section titles beginning on the next page of toc. Is there some way to force the chapter title onto the next page?


My actual question is that i want to know the molecular interaction can all takes place between non polar solvents and non polar solutes and also i want to know that why does some non polar substance dissolve in water like sugar??


Forced fun would be the dreaded company outing with icebreakers and other group activities meant for enjoyment but often achieve the opposite. But, what is a single word that defines this? The major drawback in working for ElboniaCo was the unavoidable requirement to participate in the company's ill-conceived ______ activities.


Could someone please help me in downloading the paper 'On the distribution of almost primes in an interval' by Jingrun Chen (journal: scientia sinica)? I was not able to find it on internet? Any hel would be appreciated. Thanks in advance


The title sums it up; are there any practical examples of not uniformly charged line charges and ring of charge? Line chargers: I know they are used in wire chambers for high-energy physics experiments, but usually, they are uniformly charged from what I've read. Connected wire to the battery are chargeless, so I'm kind of clueless now. Thank you:)


Let's say that an AI was created to toast bread. That is its only function, and only use. How would I describe such a thing in one word? For instance: Like a _____, it executed its task.


He made no comment and there was a long and unhappy pause during which the cab leapt forward a foot or so, only to pause and pant again, frustrated. I thought 'frustrated' explained the atmosphere of the whole part of the sentence before it. Then, can I assume it is a kind of appositive?


draw a circuit graph; check the fulfillment of the ergodicity criterion; calculate the marginal probabilities; write down the limit transition matrix; carry out simulation modeling of the system corresponding to the one under consideration


I was using Ipe to draw "Venn regions" (not really the classical ones) as this one, However, I have the impression TikZ has better renderings in latex work. How can I produce such diagram in TikZ?


I am using integration by part concept in my proofs in which I will use it recursively infinite times. In this regard, I am wondering, what will be the last term of the resulting series which will have infinite order derivative of the first function. Can anybody give me abstract mathematical form or the resulting infinite sum?


A rod with a fixed pivot is rotated by torque T so that its free end pushes on different masses (see images A, B and C). Let's assume there is no force of gravity involved. Will the combined MOI of the rod/mass affect the contact force value?


I struggle with commas. Not sure if it's because I never learnt any grammar, I have unusual breathing habits, am oddly polemical in speech, or what exactly. Anyway Should you include (the) commas in sentences such as I am, if not stupid, then dim. And why (be as technical as you want)? In general: any help with commas?


I have measured the rotational speed of a bicycle wheel in free rotation up to stop and i would like to have the physical equation (it is not linear). I would like to compute the frictional losses in the bearing.


This is similar to another question on my page but this one is more conceptual: If you have a saddle point, is this always classified as unstable if you're doing a stability analysis? What do they mean?


Does the following sentence sound grammatical to you? There danced a man in the hall With the meaning: A man danced in the hall. And compare it with There died a man in the hall Which one sounds more grammatical? Focus on the verb distinction between dance and die please.


Maybe something like, "loser loser drunken boozer"? I couldn't find examples online, other things come up in a search. A scenario to be used in would be when someone loses a competition and they are mocking the loser. Answers should be something that has been used before, in contrast to the original phrase.


When talking about the growth of a production plant, which of the following is correct, and why? We are growing in area and number of employees. Or: We are growing in area size and number of employees.


Simply what is our best estimation of what came first in the the first fraction of time of the BB? Was it the vacuum and then matter popped out from violent quantum vacuum fluctuations or matter then after matter diluted making vacuum?


I am wondering if vertices of a planar graph can lie on top of each other in an embedding of the graph. Also, when drawing a picture/representation of the graph, is drawing vertices on top of vertices precluded? thanks


So I want to start self-studying topology. What do I have to necessarily have some base knowledge in? So which specific mathematical areas should i be decent/good in? Also I'd happily take any suggestions on where to start. Thanks in advance.


I'm searching for a synonym of word like savvy or veteran but I need another expression , which would have the exact meaning of someone reaches very high level of mastery of skill or technique and appears with much respect from other people,and I would thank you all for answering!


why does the sum disapear in this derivation: derivation of loss Mean Squared Error. It comes from the following wikipedia page: https://en.wikipedia.org/wiki/Gradient_boosting. It is the last equation of the informal introduction section. Thank you very much !


Found this formula being used in a polytropic process where pressure was not even constant. So how are we finding specific heat for constant pressure? k in this example was the power in the polytropic equation. What is the derivation and actual use of this formula?


An aperiodic tiling shape, "the hat" was discovered recently. If you split a tiled planed into hexagons, containing the borders of the hat, would there be a finite number of unique hexagons. If so, would there be a simple rule to use said hexagons to recreate the tiled hats?


If comets are thought to brought water on Earth could there be water in form of ice on the neighbouring Moon's poles? As water can easly evaporate if there is no atmosphere as in the case of Moon's equator can it 'survive' on cold places like the poles of the Moon?


I am studying about tomographic interferometric sar polarimetry and i don't have enough knowledge about complex hermitian matrix , special unitary groups, their quadratic forms and numerical optimization based on these kind of matrices and forms in linear algebra. Is there some book or books to start learning these topics for my lecture??? Thanks


I want to put multiple figures (with partial regular name) into Latex with section ranking number and picture name, could you teach me how to do that? The picture's format is .jpg, please find the detailed name in the picture below, thanks.


I have no clue on how to solve this problem. Please help me as I do not understand the solution on my book. Edit: Sorry for not sending the solution: The issue is in the fourth line I understand how the process should work but I wonder if there are other ways to solve the problem


Matter is something which has mass and occupy space . So it's indivisible particle must also occupy space . If it occupy space then it must have some boundary surface which encloses its volume . If realy those particles have volume , then what is the charisteristics of the boundary surface? And how do one particles interact with the boundary surface of other wall?


Is it possible to have light refract in one direction, then reflect off a mirror but come back as a straight line like the picture below? The context of this problem is in lens optics when a microdisplay is on the frame of the glasses and light is shining into the lens to project into the eye


I am reading up on finite approximation recentlyenter link description here, can someone help me explain why the author expressed the interval h as a sinusoidal function in this paper? And how did that come about? Or I just don't understand this way of writing, for example, why the symbols s and k are associated with the interval h.


When creating LaTeX language packages for use in by French mathematicians, German , chinese mathematicians and other mathematicians, it is helpful to know what English words various LaTeX commands were derived from. For example, a Chinese mathematician might have difficulty translating dfrac from English into Chinese (or Putonghua). What is dfrac when spelled out in full English words?


Suppose we have a bulk theory that has some holographic CFT dual at the boundary. Suppose we construct an operator that 'looks like' (whatever that needs to mean) a Fourier mode in the bulk perspective. If we consider this as operator purely from the perspective of the boundary theory, what sort of data is this picking up about our CFT?


Dyes and different colorings are often mixed into materials. These are usually a small fraction of the total material volume/mass and aren't painted on so don't have a uniform surface coat but some manage to block all light or all light from a certain wavelength. How does this work? Why can widely/randomly spaces molecules block light?


what we have to see if we replace the electron from proton and proton in nucleus is replaced by electron ? Will it change the atomic structure of every substance or it changes only in calculating reydberg constant?


This is an image representing a part of a page of a book and this are two screenshots showing the fonts used in the PDF of the book Someone know if and how is it possible to use these or similar fonts in latex? Thank you


calculate the angles I am strugling with this one, wouldnt i need to know what triangle it is or can it be done with just these informations? greatfull for any help. If it has a right angle i can just use trigonometry and do it but if im not sure it has a right angle what can i do?


I typically end sentences with the phrase: ...annexed hereto is Exhibit "A". In such a case is grammatically acceptable that the period is outside the ending quotation mark? Inside the ending quotation mark just doesn't look right.


Coming from Don't number first frame with allowframebreaks, I wondered, whether it is also possible to not display a number for frame breaks only when there are no frame breaks required. That way, the frame behaves like a normal frame when no frame break is needed and numbering will be used only when frame breaks occur.


In a book I am writing, a girl wants to have PTSD or abuse so her life is exciting. Like, she wants to live in a book or TV show trope. What is the word for wanting a little kink in a boring life to throw you off-course?


In a comment I found online you can see, I assume this answer is sarcasm, because you are not feeding the trolls, are you However, I don't understand this comment. Clearly trolls are bad and online, but why would feeding them be a bad thing? Is the intent for them to starve? And what is troll food historically?


If a body is kept on the surface then it applies its weight on the surface and the surface applies the normal force on the body. Both are being applied to different bodies, then how do they cancel each other out? And what about other forces like reaction to weight and reaction to normal, how do they affect the body?


I marked the red region why the person pushes the boat at that point? What I think is they push the boat at that point to avoid friction between his leg and boat surface. If I am wrong then please correct me.


Look at the picture that this question shows The direction of induced electric field around a changing current wire Will the induced magnetic field (red circle) induce another electric field (blue circles) that circulating around the magnetic field like the picture below?


In my class, we write dot products like <v, w>, but the < and > on LaTeX are too stretched out and become too close to the adjacent elements. The symbol is used in the cover of this youtube video


Consider a damped system with only acceleration - time data is available, how to determine the structure stiffness (k)? Mass of the structure is also known. It moves in a horizontal direction, like a horizontal mass-spring-damper model. The y-axis should be acceleration instead of displacement for the image.


What is the passive form of "Who knows you?", is it "to whom are you known?" or "by whom are you known?"? Some people are saying 'to', some are saying 'by'. I'm confused. If it is one, then why not other?


A normal way to refer to the next president is to call him/her future/next president or president-elect (in case of selecting through an election). However, I'm looking for a pattern to refer to that situation similar to ex- style, e.g. ex-president.


In quantum optics, there are squeezed states that are very precise in one quadrature. You can analoguously have state squeezed in position instead of one quadrature. Can I perhaps make a slightly more bold bet, where the electron is going to be after the third short time interval measurement, than just the quantum mechanical "It could be anywhere. Momentum is maximally undefined"?


Can every proper subset of uncountable set be countable? If yes, is there any example of it? If every proper subset of uncountable set is countable, could then there be no injection from the uncountable set to any of its proper subset? Then would that uncountable set be not infinite and not finite?


Im having hard time understading one of the derivation steps in histogram equalization, Wikipedia (added picture). derivation In the last sentence it seems to me like they are suggesting that the CDF of the original CDF is linear, is that true? If so, why?


The context is a path being eroded with use, except it's more like the path is being crafted with love by use. Are there any better words or phrases to fit this use?


I think in very thin air, high average kinetic energy of air molecules might still be perceived as cold because the number of impacts per unit time would be fewer. Is this a measure that combines density and kinetic energy? This measurement might be "perceived temperature" or something.


Recently, I've been trying to read up a lot on active matter, and I realize most of what I read are papers that are relatively new. But to dive into the topic as well, I am unable to find much backing with the theory taught to us in classes. Can anybody give me some solid references to start properly in this field?


Is there an converse phrase to "in writing", in the sense of completing a task or a calculation in-writing? This should have the sense of "in explicit thought, but not in physical writing". PS - Not sure whether this is a phrase-request or an idiom-request, please retag as appropriate.


In Proving the Inverse function theorem in Mathematical Analysis Book of Rudin, when he want to show that V is open, Why he simply does not use that under continuous function (Mapping), the open set U mapped to the open set V. He used this:


I'm establishing standards for my code projects. Among those, is that I want contributors attribute their notes to their GitHub username, in forms similar to: "@username". I'll need to document this, but I'm not sure what it's called, maybe "at-handle" or something?


The question is this: I believe the answer is A as the gravitational field strength becomes lower for larger distances of the object from the earth, but the model answer as as below: Are they completely disregarding that the weight changes?


From noises/acoustic emissions monitored and data collected by US Coast Guard (or other agencies) was it possible to determine at what depth the fatal implosion occurred? If time differences from three deep stations (in a vertical plane of the Atlantic) are known, Hyperbolic Navigation helps to determine the depth of implosion from sea level.


When it comes to proofs there is no way to tell whether I have done correct or not. In the solution they did in another way which makes me wonder if this correct? For future question, how can I verify whether it is correct or not? I have heard of websites that can check but can't find any that works.


When air molecules are given energy they compress the layer of air molecules next to them and so on which causes a high pressure wave to move forward so does this make any change in the average kinetic energy per molecule/atom of air and change its state like increasing temperature or internal energy and enthalpy


I have doubt regarding how can COP of a refrigerator can be one! It can happen only when heat is more extracted when work inputed or rate of heat absorbed is more than power? Can any one of the reason is correct? Explain!


I am watching Tensor for beginners by Eigenchris, and I was confused when he said that, not all vectors are Euclidean. So, can someone explain me the meaning behind this by an example or visualisation


Instead of giving the past tense form bended, the verb bend fuses together bend and -ed and removes voice, producing bent. Lent and sent are produced in similar fashion. What's the word for the fusion here?


One can certainly create a digital circuit the achieves this - is it possible to do it in a purely "optical" manner? If not with light waves, would it be possible with any other type of wave? Low amplitude wave remains unaffected High amplitude wave gets its amplitude lowered


enter image description hereI am stuck on this graph. Not sure how to map this I have research everywhere but can't find satisfying answer. I am asking this question on someone's behalf I do not know how to ask this question properly or what i formation is missing but I do my best to give all information i have. Below is the picture


Is there a way to compare two LaTeX outputs such as DVI compare or PS compare from the LaTeX utilities? P.S: Please do not mention the PDF compared with Adobe Acrobat or other PDF tools or with LaTeXDiff TeX file comparison.


If we have a physical wave, say a waves in ocean, then we can observe still ocean and also disturbed waves on it with sight. But, why can't we do observe still eletromagnetic field with sight?


Mr. smith and Mr. Jones can be expressed as Messrs. Smith and Jones. How can Ms. Smith and Ms. Jones, or Miss Smith and Miss Jones, or Mrs. Smith and Mrs. Jones respectively be so consolidated?


In the following diagram, The human will see the real image, P', standing where they are. But, what if the human is closer to the mirror? Then P' is behind them so they clearly can't see P'. Do they see a blurred image?


ANS GIVEN IS "B" I did understand that as the particle on the left oscillates, the tension in the string also oscillates and hence the particle on the left string too starts oscillating up and down as there is no torque on it, but I don't seem to understand why a net upward motion is there. What is the correct reason?


We understand electrons move in the opposite direction of the electric field because of its negative charge. It was said magnetic fields are generated by current flows. What exactly are current flows? Is it the electrons or the electric fields?


The simple definition of optical center for a convex or concave lens was given as point through which a ray passing suffers no deviation from its path, but is there any geometrical location of this point? (i.e. the point of intersection of principal axis and radical plane of two spheres containing centers of curvature or something along the lines of this?)


When we type good in most online dictionaries including Oxford, Collins, Webster etc, various meanings come out. However, when it comes to standard, quality or performance both senses are given: satisfactory or acceptable excellent; high quality How can good mean both of these levels or does the context vary? The example sentences they provide do not really make it any clearer.


It is of course overkill to use string theory for this, but I am still interested in how, for example, the trajectory of a horizontal throw of a mass point could be derived from string theory, after all, everything should be available in this theoretical framework to derive something like this.


If one encodes the real numbers as the surreal numbers with countable birthdays, it seems that the tree representation can be mapped to the naturals by a simple breadth first traversal. What am I missing?


Bakoma Tex software has stopped its services. I purchased the latest version, but now I am unable to install a new system. How to transfer the existing BaKoMa files to a new system?


English doesn't really allow word contractions the way German and Dutch allow or even require. What rules, if any, are there when two nouns should contract to one or not? e.g. Why toolchain and keychain, but then supply chain and not supplychain?


With the Gravitational perturbations among Neptune, Uranus & pluto, Is there anyway to know conclusively that there is no rogue Blackhole roaming the solar system? The Event Horizon may be very small, so no Mass falling in right now or for millions of years to increase the Surface Area, thereby, the Event Horizon...Thanks!


Because if drift velocity of electrons is so slow than the actual speed of electricity which is near the speed of light. Then it might be possible that only electrons at the surface of metallic wire move at the speed of light .


Despite quantum mechanics being in deterministic, is an event such as when the next eclipse will happen on earth be exactly determined since the beginning of the universe? Or the rough shape of and direction of a particular rock formation ? If one knew everything there is to know about the initial conditions of the universe, could one know this with certainty?


While I was reading a book on basic vectors I struck a question that when we define resultant vector of sum of vectors is the vector joining the tail of one vector to head of other vector. But why do we join it? because how do we prove that it is the resultant vector? And sorry for that silly doubt


My English grammar teacher said that English has following rules: A variety/number of something are... The variety/number of something is... We had the examples: A number of my colleagues are from Spain. The variety of monuments in Central Rome is shocking. Is it the only right answer?


A TV presenter of "Who Wants to Be a Millionaire" lamented it would be a "jolly weezer" if the man made less than his wife on a game show. What did he mean?


Is there any slight difference between these two? She bought two dozens of eggs. She bought two dozen eggs. In an online course a tutor told that second one is more appropriate if both options come in exam. They both appear same to me.


How can I have an option to require some packages in a style file I am writing ? For instance, I can have a Science and Technology Option that makes available certain symbols. And another option to allow use of different fonts.


Can a scenario be considered free fall in physics if the work done by forces other than gravity is zero, but those forces are still present? Or is it necessary for gravity to be the only force present for an object to be considered in free fall?


I know this is out of convention and norm but I am typesetting an exam and using points for each question part and subparts seem to consume a lot of space. How do customize it to pts instead of points? Thanks for your help.


Is Fock state a squeezed state? I assume that 'yes', that is how it beats shot-noise limit the next question is that what is its complementary variable? Basically is delta N -> delta p what is its delta x?


I have a background in fiction writing and creative event planning as well as in business operations in international shipping. I want a word that could help me describe my background. With my ____ background, I possess a unique skillset that lies at the intersection of business development and creativity. Something like cross-industrial? but hoping for another word


In reference frame moving with rocket exhaust speed is constant, so what is with power as speed increase? If power is const. in this frame, how is possible that at frame at rest power rise? Shouldn't any frame you choose must produce same results in physics?


I would assume that complex polytopes (according to Shephard and Coxeter) too could be alternated (snubbed), rectified, truncated, etc. - possibly given some further restrictions. However I have currently no plan on how that might work in details. Could someone explain such operation actions, when being applied to those?


Most sites that had a copy are now blank. I am looking for the version that was based on JRE. There used to be a DField and a PPlane. I am aware of new versions that are tied to MatLab but I am looking for the one that ran without having MatLab.


So, simple question, are the bouyant force applied to an object by a fluid and normal force (Is it even there?) related? If no where is the normal force and why does bouyancy even happen?


Given the spatial overlap of nucleon wave functions within the nucleus, why is the bonding of nucleons only the result of pion exchange and not of gluon interactions between quarks in different nucleons?


In this diagram, as well as our universe, you have a parallel universe. Where does this come from? Is this just a artifact of the diagram, or is it predicted by the maths in some sort.


I'm struggling to understand the statistic relation referring the observations of an HMM. That's clear for me: Output Independence My problem is how this equation can be derived: probability of an observation given the state sequence Thanks


Figure captions stagger out of margin in the Chapter List of Figure created using the package titletoc. How to fix and make sure captions stay within the margin? Using package tocloft changes the heading title from the other chapters.


The kinetic energy of rotation of a rigid body is given by: Write T in generalized coordinates in the form: Determine the explicit form of I opened the cross product with the civita levi symbol and the dot product with the product of the levi symbols, but I can't get the requested answer


The title says it all. This is the polar opposite of this question. Whereas lexxie there was dissatisfied with the default behavior of longtable, I need to achieve this very behavior with tabularray.


Simplified the question. Now if anybody can kindly explain the FBD for direction of normal force. PS: do not need the solution to problem of roller curb at a step but how the Normal force at A is pointed toward the point of application of force and not toward the center of roller


Why the tangent line has two equivalent definitions, one is according to the Angle, the other is according to the limit position of the cut line, how the two definitions are equivalent, please give proof, looking for a long time can not find


The range of electromagnetic waves and gravitational force is infinity and the particles exchanged during these interactions are photons and gravitons respectively. Both are massless following the relation: the range is inversely proportional to why. Then why are the intermediating particle (gluons) massless in strong interactions (as their range is in fermi)?


This is similar to the totient function, but obviously somewhat different. I would be interested to know if formulae exist for counting the positive odd integers and the positive even integers up to a given integer N that are relatively prime to N.


Especially for digital (modern) radar? Also is it possible (in the same configuration to integrate multiple pulses with the same carrier frequency with intrapulse modulation (each pulse has a different modulation pattern between each other ( frequency modulation for example or phase modulation))?


Using pstricks and psaxes I'd like to create the axes just like in the attached figure. I tryed to change Oy, dy and Dy as well as the origin of the axis but I'm not getting the same as the figure. I suppose that it is very simple, but how? Thanks!


So uhhh lets say there is some air, you've just put it onto the surface of the moon. Question being, if you are present within the mass of the air, can you listen to others and talk to them within the space that the air occupies?


What is the difference between linear map, linear transformation and operator? Is linear map a definition requiring the domain and the range have same dimension and the latter two for domain and codomian with the same dimension?


The answer to this question is gonna to be very short: what is the proper command to format the names of big mathematical theories like ZFC/PA/RCA etc. I.e. set theory and Peano arithmetic. I believe that they might be something like sanserif, but I'm not sure. Can someone help to me ?


Anyone knows how to elegantly improve the following wikipedia (wikimedia) image quality from a Lipschitz continuity function to make it vectorial in Tikz or Pgfplots? Wikimedia Lipschitz continuit Visible here below: Thanks for your contribution!


What is another way to say "the problems that led to it"? As in, Provides overview of the case, participants, background, and problems that led to it. Arguments for the plaintiff and defendant are thoroughly covered.


I once saw a word for a hole carved out in a wall on purpose to accept a wooden crossbeam that fits into the hole. I think it had a "p" in it, something like "pit hole" ?...


Why does increasing the magnetic field strength increase the force on a current carrying wire?- as outlined in the equation F= BIL where B is equal to the magnetic flux density around the wire Thanks


People commonly see the insides of their eyelids and see a little amount of light and no amount of light of the insides of their eyelids depending on what environment they're in, What's the difference of seeing the amount of light of the insides of their eyelids?


I am trying to type Python code by using LaTeX. The code is not being formatted properly Example: #PDF var = function(data, parameter= 'compile') #Copy it on my terminal var = function(data, parameter= ' compile ') Does someone has some suggestion how to fix it?


For instance, there are the sentences "Reading books is good" and "To be a hero is your duty." Could I say that books and "hero" are objects of the verbs reading and To be, and that together( verb and object) act as a noun, more specifically, as the subject of both sentences?


What is the physical significance of electric potential? I know that over dx length of an electric field it varies but let us assume the field to be uniform, how exactly does the potential still change?


I have a prism spectrometer which has two entry slits, two collimating mirrors and a rotating prism. I need to to find the the spectral resolution in respect to the changing width of entry end exit slits. What formula describes this dependency?


My question is very simple I want to use the the LaTeX Math Black Board Font for a commercial design in Inkscape (does no matter file format), but don't know font name, nor download link.


the plot is potential vs deformation, I want to know why there is difference between two potential vs deformation curves for the same and different compound nucleus and why the shape is like that.


I am trying to create a compact database schema similar to the one presented Here and here is a screenshot for that : I am on two column setting too and I looked at this post but it is not as compact as the one in the picture.


If that was the diagonal of a square grid Then, is there a common mathematical termonology of this diagonal ? And what about this Zig-Zag digonal-like shape, is there a common mathematical termonology for it ? By terminology, I mean a common name used in books and references to refer to these aspects.


I know when mass becomes massive we need general relativity. My question is why do we need to incorporate special relativity since the mass is not in high speed .Cant we have Newtons law of gravitation for massive objects(curvature of spacetime without special relativity) Or we can say Curvature of spacetime without special relativity Or lets say curvature of Space, not time


I have a default page header for all pages of my document. And the longtable headers which continue to the new pages overlap the default page header. Is there a way to make the continued longtable to leave enough vertical space to avoid overlap with the default page header? Thanks! Reshmi


i have problem in my preamble, i observed that as the page number for the "List of Tables" is taking the page number of the last page of your document for example Tile page (i), Declaration (ii), Certification (iii), Dedication (iv), Acknowledgements (v), List of Tables (xiv) instead of (vi) . what can i do


Two BML models M, w and N, w' are given: in M, w has with infinitely many R-transitions of finite length, and in N, w' has infinitely many R-transitions and also includes an infinite-length R-transition. How can one use bisimulation games to prove that M, w and N, w' are equivalent but not bisimilar?


In a standard jet engine on a standard aeroplane, is the majority of forward force received by the aeroplane (which causes it to be propelled forwards) applied on the compressor blades, the rotor blades, the internal body of the blade surrounds, a combination of these, or somewhere else?


Imagine I bought something, but instead of giving me worse product for what I'm paying, the seller gives me a far better product for my price, without my knowledge. Is there any term for this?


Commands can autocomplete, but ideally, I would have an extension that can also autocomplete main body text. I have this in VS Code, but I like the overleaf editor more. Does anyone know if such a tool or (chrome) extension exists?


As a naive person I thought annihilate meant destroy. Matter and antimatter destroy each other, cancel each other, nothing left over. This pure energy idea is a big surprise also it fits no category of energy as we know it, kinetic etc Can someone bring me to understanding with simplest possible maths, please?


For a symmetric matrix we have: That is comparable to what we do, to what you learn in the first analysis course with one variable. And that was already clear to me, also in linear algebra. But the reason behind it is the following: Can anyone explain the intution behind the second equation? It's a definition in the book I currently read.


Is it true that electron wavefunction can be conceptualized as different periods the electron spends in all possible states, so when we interact with it it's more probable to find it in states in which it spends more time compared to states in which it spends less time just like unfair coin when it lands.


I have a table in .png format and want to place it in half a column, the other half of the column will have text as in this example figure. How do I do that?


Mass(-energy-momentum) curves space(-time). However - what is space-time? Is it (the background) necessarily flat(without something in it) ? If there were an empty universe - is there still spacetime in it - or not?


I am working on a presentation on beamer and i used the theme Madrid but i am obliged to use the title page ppt template given by my institution, how do i have the first page as the template and the rest of the presentation following the theme ?


In the introduction of the book lambda calculus with types by Barendregt, there are examples of typed functions like And I wonder what operation the underlined type expression is for. Although we can surely make an operation of the type, I want to find the real example in functional analysis that the author was thinking about. The cited book is Lax, Functional Analysis.


When one has lost both parents due to death the word orphan is used. This word is generally but not always used for children. It can in spoken English also be used for adults. My question is what about the loss of one parent? Is there a word for this?


Given the following question - I'm required to find all the Perfect Bayesian Equilibrium and specifically state whether they are pooling / separating. Struggling to understand what would be the types (beliefs) in that game, is it <D, D'> are the pooling, and <C' D> , <C' D'> are the separating?


If as water evaporates it carries energy with it and therefore there is a reduction in temperature, why does the temperature remain constant in the phase transition between liquid water and gas water?


Can we define an average time for the entire universe relative to the Big Bang and call this the universal time since the beginning of the universe? (time, averaged relative to all possible reference frames)


I'm using pst-barcode to generate rectangular datamatrix. Although I have problem with the fact "that the barcode is printed in a TEX box of zero dimension". The manual suggest using fbox and pspicture environment, but it require to know the both sizes of the code apriori. Specyfying only width results in deformed code.


Consider the attached Toroidal wind Tunnel. The Wind tunnel is in Vacuum and the moving air and the attached wing are only inside the toroidal tunnel. Will the mounted wing on the walls of the tunnel experience force and move the Toroidal tunnel as shown in the picture. Thank you.


I could come up with examples for rings;say for example defining the homomorphism to be a left shift of elements which are taken to be of the form of a countably infinite tuple.Can someone help me out by giving an example for Integral Domains


Do you know any reference where this result is proved? We have already proved it but since we know that this is a known result, we want to omit the proof and cite a proper reference. Here you have a caption of the result, which involves the roots of a monic polynomial and the gamma function Result


I have got a lecture and there were the following frames used in the presentation. Can anyone please tell me which style this is, because I really would like to use this as well.


Does the event when two BH without polar jets merge, cause a short living polar jet on the newly formed BH? As BH need infalling material to activate their polar bursts does the BH falling into another one as it brings the needed material provoke the polar jet?? (Thanks for answering...)


English is a foreign language for me, so I have to use a Google Translate or similar services. They give same translation to my first language, and I feel some nuances are being lost. Examples: Confession with the venerated minister. vs A highly revered missionary from Africa.


Hi I am doing a presentations, and to all of them I use the same tex file with document settings. I'd like to have one folder on desktop with file with settings, and in each presentation a path to this tex file. Is it possible? If so, how can I do this?


I think it is impossible for a group to contain just a left or a right zero, because it would violate the identity property, but I am unable to put it into words. Could someone help out?


What I'm looking for... Do it exist tools "tracking" or reporting macros and environments used when compiling one TEX file? Why? To build my unit tests, I need to verify if my package is fully tested.


Talking of memory, which is correct? To my heart Or In my heart If talking of belonging, which one is correct? She always belong to my heart Or She's always in my heart Can I use "always to my heart" without indicating "belong"?


I need to know if what I said here is true or false. "can a Bayesian model give a probability distribution over potential diagnoses"? (HS student) if this statement is not factually correct is using Bayesian analysis for the same use factually correct


click here for image Could I please have confirmation this is the correct way to solve this question using the given information? Note: I could not directly upload the image since it was apparently too large.


Hello there is a problem and a solution to it ,which shows how to find the resonance. There is a solution to the problem which basicly looks at a periodisity of an exponent. but how they got to this conclusion that periodisity of exponent is linked to resonanse? Thanks.


Do only gas planets have discs or even rocky planets may have them orbiting around? If rocky planets are great in volume is then a higher chance for an orbiting disc to exist in the planetary orbit?


The two Spanish prevailing explanations that get repeated are the Spanish vamos and the British dialectical mose about. These explanations are at least two decades old and predate the internet digitization of substantial material. And, from an American perspective, not very convincing.


enter image description here By introspection I think i will have to somehow use a difference of two numbers in the numerator to cancel our excess terms. The main problem I am facing however, is with a clean approach to the min function, namely finding the coefficient of the x-squared term.


These two possible combinations confuse me: The energy required to heat the water is... The required energy to heat the water is... I have always used the first combination, but the AI grammar check generally prefer the second option. Which combination is in your opinion the correct/better one? Why?


Do the running with energy of the electron charge and of the W boson electric charge differ or are they the same? Is there any theoretical or experimental evidence that allows the comparison?


Suppose you specify that the sea must be a royal blue, and no land territory is allowed to be. Does the map then need five colors? Or can the island necessarily be colored with three (non-royal blue) colors?


This is the equation: It's from mynt.T.U book for Advanced engineering mathematics. I just want some hints. Edit: how can I reach to right side of the equation, using the left side and fourie transform. I don't know what to do with (ax-b)


When you charge a lithium battery for instance the electron momentum that coming out of the source is stored in the battery. The problem is that the direction of the electron might change when connecting the battery to consumer


I want to create a solution environment that works somehow like this: If at the beginning of the document, solutions are TRUE I want to show the text in the environment and be highlithed. If it is FALSE, the environment should pretend as if there is no text at all. Is there any possibility to create such an environment?


When a particle leaves vertical circular motion after slacking. Is it possible the body at the end of string will move to the centre and can we calculate that intial velocity in a parabolic motion as well as intial velocity in which the ball is thrown at the starting? Given centre coordinates (a, b)


Consider a circle inscribed into a regular pentagon. (a) How to prove amount of straight lines which can dividing into two parts with equal area the disk and the regular pentagon as much as amount of vertex pentagon. Also (b) amount of straight lines will be same if regular polygon inscribed into a circle.


In the logic context, both the terms operator and connective is used. I wish to know what their differences are. Do we use an operator when we have something that effect only one formula and connective when it some sort of connect two formulae and effect both?


I was doing a test in which it involved the change of variables theorem, but the answer he had was negative. I found out that my professor used the determinant of the u and v, but ignored the absolute value? Is there a reason why that may be the case?


I am currently studying categories without products. I have found that the category of fields has no products Examples of a categories without products, in the proof an endomorphism appears and while I was trying to understand it, I came up with the question Are all endomorphisms identities in a category? I have no idea how to answer that question. Can someone help me?


I want to have a book name Solution manual: Steps in commutative algebra R.Y Sharp I don't have so much experimence about commutative algebra. So someone here have a file or link about this Solution manual book Please help me


since the rotating coil which produces the induced emf that varies sinusoidally the emf produced for one complete revolution of the coil is zero. then for any number of rotation the induced emf should be zero only no then why they are calculating the emf induced


I am unable to find a representation online about the Dirac three polarizers experiment with a time development operator and Griffith's Consistent Histories treatment of the set up. Would anyone like to present it here?


I heard the royals used 'we' instead of 'I'. The royals makes impressed food. So we are gonna roll out the red carpet and spare no expense. Word 'We' means 'I' in this sentence?


. . . and is one preferred over the other? I believe he sent these contacts an email earlier this week. I believe he sent an email to these contacts earlier this week. I feel the second is preferred because "an email" is the true object of "sent". But I'd like to know why.


Sometimes it is described as a state of disorder and sometimes it is called the inavalability of the thermal of energy of the system to do mechanical work. So How exactly is entropy defined? Also, how does it explain why time flows in one direction.


My university is asking for a specification of an algorithm and provided this block scheme as an example. I an not very good at latex so I googled how to do this with tikz, but did not found something useful.


Two points are moving on Euclidean plane (absolute space) smoothly and in every instance velocity vector of each of them is in the direction of the position of the other one. Is it true that they are both on a fixed line?


What is the analogue of the Malus law for polarized electromagnetic waves to the cause of plus and cross polarized gravitational waves? Bonus: What if gravitational waves have further degrees of polarization like those in modified gravitational theories?


Let say that there is no air drag. A ball is thrown towards me and I hit it with a bat. Here of course I apply some force in hitting it. Then can someone help me out by explaining how does the ball obey first law over the course of its motion.


I do found lots of introductions about the definition some other characters of Half-Plane model. But now I need to study characters of the curves above it, like curvature, evolute. While I fail to find relevant theses or textbooks. I hope someone could give me some suggestions.


I am looking for self study inner functions and Blaschke product from the scratch, yet I could not find any beginner friendly resource out there. It would be much appreciated if you could recommend me a source.


I a book the "Upper closure operator" definition is given by: I do understand the concept of the Upper closure operator. But I cannot figure out how to read the last line. Could someone explain it? Thank you.


According to the readme of the ebgaramond package it adds font styles: What do I have to do to set a certain part of the text to semibold? What do I have to do with the sb?


I understand what a taylor series mean and how does it work but I don't understand what it means for it to be about a point or does that point have any outcome on the result of the series.


In figure (A), book shows electric field lines just coming out of each face of the infinite sheet having charge perpendicular to area vector but I thought that the electric field lines which are anti parallel to area vector of both surfaces must also be there, which I tried to show in figure (B).


I want to write some research paper in number theory and graph theory , but dont know where to start , which topics to learn . PLS suggest some topics and new fields under these subject which are under development and research.


I want to determine a suitable range for the efficiency energy conversion of magnetic energy to thermal energy in usual magnetic reconnection because usually it is said that this process is highly efficient but I want to put some numbers there and of course try to compare with other processes to explain why it is an efficient process.


The number dimensions defined by new theories keep going up. Is there a limit as to how many dimensions the universe can have? Weird question. The curse of dimensionality in computer science illustrates how two data points get further apart as more dimensions are added to its analysis. Could a similar analogy be applied to the dimensions of the physical world?


I use Charpit Method to solve the problem but calculation is so big. Is there any another method to solve the problem.I think I need some variable transformation which gives me a standard form then I easily solve the problem.


when I using the kpsewhich to find the system font like this: /app # kpsewhich --format="ttf" Kaiti.ttf warning: kpsewhich: Ignoring unknown file type `ttf'. is it possible to use kpsewhich to search the ttf/otf fonts?


enter image description here It is claimed that an intersection touching the base details of a square prism of this shape must be rectangular, what is the reason for this, can you help?


I am new to LaTeX and I have received instructions from the journal to change my LaTeX references to conform to (journal is Cell iScience). whatever I do I cannot fix this issue, please help me.


Except for the well known one , using the auxiliary quadratic equation, is there another formula, either using only elementary math or not? This is a nice elementary alternative which is nearly a formula.


If a craft is positioned at the strongest point of the earth's electromagnetic field being either positive or negative and the craft activates the same field it would repel each other would it create trust and what speed would the repel be


This is not technically a question but more of a help , I need some books to help me go into the theory of two scales and their applications in Partial differential equations.


like charge is fundamental property of matter which exist in both negative and positive aspect and help us to understand the electro-magnetism ,in the same ways would mass be negative ? in that scenario gravity could be repulsive too?


Is one of you near my office? Are one of you near my office? ChatGPT says that they are both grammatically correct which means people use both (i.e., there exits mass confusion). The subject is "one" which would imply the first but that option still sounds weird. I thought it was time to move from AI to RI - that's where you come in!


It was supported by stating that a reliable fabric supplier has been found and that a major competitor is no longer making alpaca overcoats, because of which demand will be high. Why is there a comma in this sentence?


If the JWST has just discovered the furthest away galaxies in one place we can now triangulate to where the centre of what we can see This is observable and appears not symmetric with everything expanding symetrically.


Here we get two energy levels uB and -uB which are discrete, but particles follow MB stats, it means there energy is continuous. I am getting confused, what is the role of the MB stats in such a case?


Current flow from positive to negative terminal in a circuit. But the charges which are moving in the circuit are the electron that is moving from the negative terminal to the positive terminal. Why we chose the opposite direction as electric current, not the real one?


I wanted to align a table of equations all left, no numbering needed. A similar question was asked before, but not answered in a way useful to me: Align equation left The page urged me to ask my own question since I do not have enough reputation. But I have figured it out, so the answer is below.


The lthooks documentation says: But how should one know in advance if the hook with this given label exists or not? In my package I wish to clear the code with a given label in a hook before adding new code with that label to ensure that the code added is not duplicate. How should I do this without triggering the warning?


Those hydrogen or mercury tubes should not be coherent, but when looking at them through a grating without using a small aperture in front of the tube, you still see the discrete lines. Or just any random ceiling light really, without using any aperture you still see rainbow through a grating. How could that be?


With regard to the answer of this question, Full proof of Black Scholes may I know how does the dz was changed to dy in the first few steps and later on switch back to dz?


In a comment of Fractal of the topologist's sine curve is connected and totally path-disconnected? M W asserts that the existence of a dispersion point, a point for which the removal of results in a totally disconnected space, implies that the space is totally path disconnected (even before the removal). Why must this be the case?


is the viscosity of a fluid maximum at the layers adjacent to the surface? I think this because the molecules of liquid now experience a greater friction force because the adhesive forces also resist their ability to flow.


Each of the spectacle lenses in this image cause two separate refraction patterns: The patterns are different between the lenses because each eye is different, obviously, but why are there two different patterns within each lens?


Which exactly is the difference in meaning and usage between choosing whose versus choosing which in this first sentence? He chose to live in the room [ which / whose ] door was broken. How do these compare with this second sentence? He chose to live in the room, the door of which was broken.


As we can see below. The theory says that A,B coeffietionts are depending on excitation. I have simulated a circular waveguide, How do i need to excite my waveguide so i will see the A and B coeffiencts of the field change?


Here are two boy's cars. But. Here are two solutions key points. Why in first example is "'s" used and in second one it's not? I checked with LanguageTool and GoogleTranslate. I want to explain to key point for the solution of a problem, then used a tools and get confused. https://www.britannica.com/dictionary/eb/qa/How-to-Make-Possessives-in-English Or is this correct? Here are two solution's key points.


How I do create an index of a text with all words of the text. Words in the index must have the reference of the section, the page and the line where is the word. thanks


I am making a academic presentation. I want to put the reference in the block. But I want to put the reference number directly after word "Theorem". so I tried The reference showed up right in the block which is really terrible. It seems that the block affects the footcite. How do I solve it?


I want to find a formula for the nth dose derivative of the function I have tried to use the first line as my start point but am getting confused. I want a set of coordinates that can depict the local maximum of the nth value. the equations above are surge functions.


While obviously not optimal, I've usually found that such an "algorithm" is pretty close to the true shortest possible path, and is obviously runnable in polynomial time, with an O equal to your sorting algorithm


I am using a document class report and I need the first page after the title page to have some text on it (it is my layperson summary) and after that the abstract and the main part of the file. Is there a way to do it? I am inputting both that piece of text and the abstract from separate .tex files.


My professor explained me in the best manner possible about the electric potential energy and why it is NOT defined for a single charge, BUT my question is as Electric potential is just electric potential energy with one charge being a unit positive charge, therefore is electric potential also defined for a system of charges?


when I worked with idea of something being homogeneous. I always felt I reverse engineering what we are doing in linear algebra to find the eigenvectors and eigenvalues. could someone explain it simply


I am reading the synctex source code, now I found he comment mentioned two type of coordinates, page coordinates and TeX coordinates. anyone know about the two type of coordinate system? The docs only mention that page coordinate The origin is at the top left corner of the page.


Inside negatively charged ball there is constant electric potential. If electron will be placed inside ball with constants potential will it give mass from electric potential as same as higgs field give mass?


I'm trying to determine electric motor power sizing with requirements given for covering a particular distance within a certain time. The knowns are the vehicle mass, the allotted time, the target distance to cover, and the vehicles initial velocity. The result would be used as the absolute minimum possible motor output power rating that would satisfy the requirement.


Do Solar Eruption occupy more than one rotational layers? Is it possible to confirm this just for most outer layers? Does the number of layers occupied by those eruptions when they happen tell us anything about the relationship between Gravity and Entropy? #Update This is how i imagine Sun's Differential Rotation Each speed on the image has a different value


So it just hit me, "When is just before"? Cos just before could be a second ago or half a second ago or a tenth of a second ago and so on. So when? And do the final velocity formulas put this into consideration?


if we are able to create plasma in isolated environment possessing temperature much more than temperature of sun then why are we not able to create something that can go to the sun?


It is always confusing to me what to call the network with which we make phone calls. If mobile network regards to accessing internet with cellular data, then what network it is called to make phone calls?


Just curious how these two magnets are spatially related to? And in case there is no any special preferred particular orientation, what is anyway their spatial orientation relation (relative angles)? Possible varying with seasons or year cycles. There must be a record of these measurements? I cannot find anything about this on the internet?


In mathematics different integer also that mean different rule to for divisibility of integer, But this is not flexible way to learn divisibility of Integer then Is there another way, maybe some kind of formula to learn it? And also if there is, please provide the source, I would really appreciate it


I understand the kernel is the map of everything to zero, but does that mean that the only way for a kernel who is just made up of the zero from the previous area is for the range to equal the codomain.


When I was under the shower I experienced when I look quickly at a single line of water falling from one pore (from top to the bottom) it looks "drop drop" instead of continuous. Why is it like that?


Pretty coincidental that time happens to be like the three spatial dimensions.. or is it? Time is one dimensional with past and future, similar to left and right, up and down, back and forward of the other dimensions.


We are currently using the term circularizing (I made it up) as the technique of using artificial intelligence to check something, have devs check what artificial intelligence suggestions, which allow artificial intelligence to spit out new data, that devs have to check, and on and on. Is there a word to describe this process or can I just use what I made up?


If we change slits' width in ydse, what changes will be seen in the fringe pattern and it's density I found a source from a book saying but how could the pattern gets less sharp on increasing the width, if we increase the width less waves will be diffracted thus more sharp please someone help me with question


What maths notation to give to the set of elements composing leaves of a tree structure? Suppose the tree T is n-ary, I want to notate the set {n / n in Leaves(T) } How to do that?


If gamma ray burst contain energy equivalent to the mass of the sun, then it would be bent by its own gravity and refocus periodically, right? It could possibly go on forever without dispersion, enabling it to travel across the universe?


In LMFDB, equation of some curves are given however there are also those are not. My question is "Is it possible to find explicit equation of curves by using its generating vector?" I add link for you to see example. The curve that we have its generating vector


We know in pure translation force distributed evenly in each particle on rigid body, so in effect every particle of body moves with same velocity or acceleration in pure translation. What happened in pure rotation, how force is distributed in pure rotation particle by particle to moves a body in pure rotation?


The question is as simple as that. This is the kind of thing I want to achieve: The idea is to make a symbol used for divided differences. It needs to be a true delta letter rather than a triangle, but actually it is not that easy.


the graph of the function[The graph of the functionthe graph of the first derivative of the functionThe attached graph shows the existence of turning point but the first derivative of the graphed function is never zero anywhere within the domain of the function. What does this mean?


In general spectral analysis, we have examples of unbounded from below hamiltonians with discrete spectrum. Is it okay to say that they have no sense in physical context, because for me it looks like particle can emmit infinite energy in some weird sense.


I want to mark a fraction, which I shorten, with an arc. Haver anybody an idea how to start? I wish that it looks like the text in the picture. Is there a way to do it?


i Know elementary and their applications and there is a theorem: "The inverse operation (function) of an elementary row operation exists and is a elementary row operation of the same type." i want to know the proof of this theorem! thanks :)