I am looking for a bell-shaped periodic function f(x) with parameters a and b, with following characteristics: ( not sure if such function already exists or one can formulate one ) : oscillating between zero and a constant non-negative number A. Width of bell can be modified through parameter b. customizable period of c. Preferably easy to calculate its integral Obviously such function should look like a spike with lower b numbers and conversely turn into square-like with larger b. I tried playing with Gaussian and normal distribution, it satisfies the first two requirements but fails to drop to zero at periodicals of x = c. something like the picture below any suggestions highly appreciated !


Is there a way to avoid division through size n in ift (ifft) ? Performing the Inverse (Fast) Fourier Transform on the complexnumbers, you go with a for loop through every element dividing it through the sizeof (dimension) of the array, to complete the last step of the inverse fourier transform. Is there a (more efficient) way to go without it ? Division is computationally expensive.


If you take empty space right next to a black hole once in awhile, you will get a positive particle being admitted in the opposite direction of the black hole. In the creation of the photon this demands that a negative energy is supplied in the opposite direction of the positive particle which would be into the black hole. But why can this not happen the other way around?


is there already a technology that provides one-way viewing glass with no regard to whether the back side is lit or not? the case is: two rooms (A and B) side by side, people in room A want to see directly into room b without room b knowing, all the while room A must be lit all the time of viewing is there such a glazing solution for this problem?


I've been reading various papers relating bounded gaps between Primes, sieve theory, Carmichael numbers and the like and Thomas wright's papers stood out to me as being very well written and yet proving non trivial results. I found his papers to be a good way to also get interested in a topic such as his paper on siegel zeroes and K tuples Conjecture. It like seeing math tools in action before finding out what they are. Are their any other authors who struck you as such? Maybe their papers taught you a lot or felt very deep in ideas or just very well written?


enter image description here I calcultaed this integral in three different ways. contour integral, fourier TF and obvious way. I've seen this integral depends on distribution. if we just calculate this with normal way, apprently it diverges, but given (Schwartz) distribution, it's gonna be dirac-delta distribution. I also solved this integral with complex contour integral. but in this way, it concludes -i which contradicts above conclusions. so here are my questions I assumed that this integral just depends on how we tackle. Am I correct? Is the last way with complex integral correct? Thank you.


The chorus of False Disposition begins with this line: When a boyish constitution gets to lead the revolution, everything about this seems a bad idea The definitions I have found for 'constitution' mean either: some sort of document or rules, or an attribute possessed by a person or thing. Neither makes much sense in the given context Is there another definition which fits this line better?


If we think about inertial mass and gravitational mass as independent concepts and develop physics then we would know after a while they are only propotional (by precision we have by now). but it seem physicist say they are equal. when in history they became equal? two guesses: Newton himself says gravitional force is propotional to product of inertial masses and doesn't bring to play another thing such as gravitational mass. then this gravitional force itself acts on inertial masses and produces acceleration. this two masses were propotional and somewhere in history physicist changed units to coefficient of proportionality became one.


The theory only deals with the local curvatures, not the global topology. Hence any manifold with an allowed metric is allowed. These can be infinitely many, especially for negative curvature space-times. From So I suppose for the same physical situation, there would be many manifolds from which it can be studied, then, how do we choose on which manifold that we actually do the calculations?/ find the manifold that fits for that scenario?


When charge moves at a constant speed, it is said that it produces static magnetic and electric field. Why static ? If it moves, at every points, electric field and magnetic field change as they are dependent on a distance to the point. So even if charge moves at constant speed, we still should have electric and magnetic fields changing in every point in space.


Assume that you are using the FAST algoritm for corner/feature detection. You pick an image and run the FAST algorithm. Question: All these green dots are actully coordinates in x and y direction. What type of rotational invariance information can I get from only knowing the coordinates that are created by the geometical shapes inside the image? For example: If we measure the angles between every point, the angles are going to be the same, no matter how we rotates the image. NOTE This is a feature detection algorithm, sometimes one or more coordinates can flicker e.g some green dots disapear and appears few milliseconds after.


When a perturbation makes open and closed channels coupled and A closed channel's bound state energy is lower than an open channel's contiunum enrgy, a coupled state energy (e.g. spin triplet and singlet) is higher than the open one by Secondary perturbation. I think it is described as a repulsive interaction and it prevents atoms from creating a molecule. But moleculu is stable because of having lower energy. It confuses me. The open channnel is coupled with the state which has lower energy. Intuitively I feel like the energy is going down and the Molecule is easily formed.


I am self reading textbook "Visual Complex Analysis" by Needham And I am unable to "solve" this part . Like in terms of understanding I have a good image of how these translations and rotations happen but I don't know how to actually like write it in mathematical form I got where this k come from but I have no idea where c comes out Similarly i am trying but i cannot figure out what p should be ? Similarly this v here makes no sense to me and i cannot interpret what this means ? So plz help?!


Just a thought from a dream Since water expands so greatly when frozen could it be possible to freeze the water in a metal cylinder but one side is like a car piston with a very high gear ratio which would be no problem to turn because the pressure the ice builds up which generates electricity to freeze the water again and repeat (Would doing this test in a vacuum help or?) Please someone debunk me


I'm writing a game theory book, and I've wrote something like this: As it can be seen, that mathematical expression has been splited into two lines. It surely can be fixed, by making some spaces' width more, and if needed, leaving a little space for the expression to appear in the next line, as latex sometimes does. How can I force it automatically do it when needed?


So we know that EMF of the battery provides an electric field in the circuit and thus accelerating the electrons inside them, so my question is that lets say if there is a perfectly conducting wire, so there the electric field will continuously accelerate the electrons(as no resistance if there for them to collide and make them lose energy) and we know that nothing can go beyond speed of light, so will there be a current in the circuit or will the current be just too high? I looked for the explanation at many places, but everywhere people just say that such a wire is not possible, but what if it is?


Can then resultant vector pass through the vectors being added? Does the order in which place vectors according to head to tail rule matter? let's suppose that vectors A and B are pointing east while C is pointing south. is it necessary that we place A and B first according to head to tail rule? because if place A first then C, then it gives a resultant vector that is passing through the vectors being added


Can English have words that are both alliterations and also rhyme? is looking for the sets of words that I want to put a specific term to. Sets of words such as: divide, deride, decide alliance, appliance dusty, dirty I'm wanting the missing word in These words X with each other where 'X' is something more comprehensive than "alliterate" or "rhyme" because they don't encompass that the other pattern is occurring too. Minimal pair is close, but that allows single phoneme variation in any location, not just the middle, and wouldn't allow a hypothetical set of four-phoneme words that vary in their middle two.


i have a question about numeral systems that use the place value concept , in the decimal system the position is a power of ten and it has set of ten unique digits, the binary system its position is a power of two and it has a set of two unique digits and so on for all systems that use the place value concept my question is why the position value depends in the number of digits ? why cant we have a system that has n unique digits and use a position value different than n let's say m for example ?


if there is a block on top of an unfixed inline. and if the system is released from rest what is the acceleration of the block and the incline? can someone draw fbd and show? the difficulty in this problem is that you can't figure out the normal force and stuff like that. This is not an a= homework question, I'm genuinely curious about how to draw the fbd.


Imagine we have a double walled sphere from an insulating material.(So like an outer shere with smaller sphere inside it) If we insert a fully ionized gas inside the space of the double wall could we theoretically "trap" inside the sphere protons for example? Will the electrostatic forces the electrons feel from the gas when near the wall of the sphere be enough to stop them or they need a classic electric or magnetic field to be contained?


I would like to have a list of documents to read so that a newcomer can start working on Latex Programming. What would be a good material sequence to read (e.g. described by documentation section names) and study ? Naturally, on things that are freely available, no books to purchase. Some have suggested the question What is the best way to learn TeX? But I want to focus on the latest way to program; for LATEX.


I need a reference for the proof of the bordered Hessian test. I know how to use it, but I kinda learned it "in the wild" and need a standard good reference for its proof to add to my references section. I tried to google for it, but I only found tons and tons of manuscripts teaching how to use it via computation examples, with no proofs/books.


As we know there are two way test a hypothesis. One is critical value method and the other is p value method. I've discovered that its very difficult to calculate p value in hand besides there are some statistical tools to calculate p value instead. But my professor will not let me use statistical tool. If I follow critical value method instead to solve problems more efficiently and easily will it be wrong? As there are two methods available. And is there any shortcut way to calculate the p value in both t and z test please help me to find out. Thank you and apologize for making the this long.


I'm working with ascelike-new journal template (located here). The editor asked me to remove figures from the submitted pdf. Since the journal uses an online system to compile the uploaded tex files, and I cannot manually delete the pages with the figures. I tried many existing solutions (examples here and here) and was unsuccessful (the tried solutions either put a frame or hide the figure and its text references). Is there any way I can remove the figures and list of figures and keep references in the text?


I have read other threads. However they cannot solve my problem. Anyone has any firm knowledge about how could we do that? I have a limited time and I dont know why my supervisor insists on word file. Actually does anybody have any idea whether wiley accepts latex original file for the revision process? The editor asked for word file but I believe he forgot to mention latex. How come for initial submission they accept latex but for revision they mentioned just word? I might get answer here g ask editor. Please do not answer like that since we could not ask directly from editor for many reasons.


Using an unnumbered ruler and a caliper you should Construction of two Focus for conic section with five points. The difficulty is that the conic is not drawn, only the five points must be used I was interested in this question in the past and I am asking it now for the sake of knowledge sharing because I think there are a lot of people who are interested in getting the build steps, I will not put the full details of the solutions because it will be too long but I will put simple signs and graphics, you can add more details in the other answers...


If mass does not interact with charge, why does the mass of an electron move (means by which mechanism it moves) in an electromagnetic field? It is same like we stick ball on magnet with fevistic and than that magnet move due to magnetic force towards other magnet also that ball moved with that magnet it moves because of sticky force not magnetic force right ?? So there is some force in first place that bound charge with mass right?? so mass moves with charge in electromagnetic field due to that mustric force that bound charge with mass and not moving under electromagnetic field interaction .sir please tell am I right or wrong ??


I have walked. I will walk. I walk. All of these immediate verbs have infinitive forms in to walk, to will, to have. Thus one can naturally say you seem to walk, you seem to will to walk, you seem to have walked. But what of the case of I would walk? The closest grammatically proper construction that I can think of would have to be you seem LIKE you would walk. See titular question


Light exists with energy E = hf. That is supposed to be quantized and discrete but maybe "f" in the equation is continuous when not emitted specifically from an electron (moving through the g well). But light exiting a gravity well loses energy and is red shifted. What about light at the frequency of one in a decent gravity well? As it tries to exit, it would lose energy, but it may get to a point when that energy is zero. Is it reflected back into the well? Does it kick around within the energy well that it can exist in because it can't leave?


In this Youtube Short it was mentioned a way of constructing a shape that followings any curve one could draw. Apparently the motivation to construct it is to do the following, roll a sphere of clay as it rolls on the curve (on a paper). The identations would cause it to exactly follow the curve. ...but...why? Why does the intendations cause it to follow exactly the curve that caused it's indentations?


Suppose we work in GR, then space time is four dimensions, but, if we have a mechanical system with a high number of degree of freedoms, say five then how would we fit it into a four dimensional space time. Now that'd obviously be impossible, it'd suggest that the sense we talk about dimensions of physical system is different from that of the arena. But, how exactly?


in our physics lessons we often learn how to calculate the time that sound of a plane that travels faster than sound takes to reach us using the Mach cone. But can we use the same method to calculate the same value for a plane that travels as fast as sound? Does it make a cone? I would be really grateful I f you could explain this with some examples.


I would like to create a pack of graphics to highlight the simple interest rate gain like below. The blue, or any color available, would be the initial capital and the green the gain month by month. Hopefully coming from a math formula but not required to be, it can be static also. How can it be done? The pie chart is not big deal but the histogram with two colors is the hard one to me.


I'm asking myself a question related to temperature integration. First is possible to integrate a temperature distribution over the time and over a certain volume? If yes, these resulting integrals which physical quantity are representing? For example, the integral of the temperature over a volume can represent the Internal heat energy divided by the specific heat and the density of the volume (assumed both constant)? While the temperature integral over time can be assumed as the opposite of the heat flux density?


Say you have rising steam forming water on some surface and when the water accumulates, it forms a drop that falls because of (I suppose? Not sure) Mass exceeding the force of surface tension. Does the material on which the steam gathers influence the size of the drop when its mass is heavy enough to make it fall ? If yes (pretty sure it does), what criteria allows to calculate that specific point where a drop is too heavy to hold onto a surface ?


I can understand, how it is constant after awhile, that due to the range of strong nuclear force the force is increasing linearly with the linear increase of the nucleon number, making it a constant. But At the beginning, shouldn't the same would have been take place, the energy required to bind the nucleons per nucleon be constant as it is still inside the range of nuclear force, only in the heavy elements the range is exceeded and the nucleons does not possess enough binding energy as before contributing to the decrease in binding energy per nucleon. Why is it in the start increasing?


When building electronics to measure usually it is asked what the bandwidth of the signal is and what is the frequency range usually done to limit noise bandwidth and thus have more SNR. To me it seems like measurements are preconditioned, I know what I want to measure and I limit my equipment to that expectation. Why there is no paradox in the sense that I prepared the measurement to measure what I expected and then I measured what I expected?


I am asking this question only because I want to figure out does space move in this case similarly to a fluid like water or oil are or even more better as speeds o planets around a star.. or this phenomena has a different formula describing a complex effect caused by the gravity as a force deriving from S-T curvature? Thanks in advance for an 'easy to understand' answer....


This site has lots of similar questions like mine, there is force just instant strike after that object moves freely, so my question is not like these. Rocket engine produce continuous force at one end of rod in free space. Initial condition: rod is at rest, not rotate, not translate in relation to space station that is near him.(Neglect tiny gravitation due to mass of station and neglect rocket fuel mass loss) Will rod when RPM increase enough end up in pure rotation around CoM or CoM will orbit aorund center of smallest circle? Is this left trajectory of Euler spiral, path of rod CoM? Fersnel integral Like this?


I want to illustrate overlaps in three sets, similar to how one of these standard color plots [do they have a name?] look like except that I want to choose my own colors and different text [not C, M, and Y]. (I want the inside most quasi-triangle to be a red, the area outside of the plot to be a green, and the partials [both three inner and three outers, though different] have some sort of mix colors. presumably a little bit lighter, because I need text in each intersection, too, that needs to be readable.). the idea is to show that when all three things come together, it's bad. a trifecta. maybe I need a graphical artist rather than latex...or is this somehow built in?


If we draw a curve of a function without drop the pen then the function must be continuous or not?I am confused with it. If there is curve for which some portion of the curve parallel to y axis at any any x then there have many value for single x and we can draw this curve without drop the pen then the curve is continuous or not?


If simple CFD softwear like XFoil and OpenVSP use the panel method to find an estimate of the drags and lifts/pressure distributions. How do they find drag and lift if the panel method works based on invicid flow? I thought that there can be no drag or lift created in a complete invicid flow which i think i do understand. (I am awear its obvious the panel method cant calculate purley from itself the skin friction) But it is not at all obvious to me regading any form/induced drag Im at university but we mostly just use the softwear/equations, but i recetly take the time to actually try understand the working/derivations so apologies theres something obvious missed.


before I write the an article, I would like to roughly partition the text. The sections and images should be where they are in the final article, with white space where the text is supposed to be. For that, I would need placeholders that consists of a certain number of white spaces, which automatically reduce as soon as I add real text. (I load the single chapters as single files into the main file and maybe here "filling up the text with white spaces" is possible) One could hence compare it to a "Latex-form" for the text. Does a package or a method like this exists?


Suppose we look at the surface of a lake and see a reflected image of high-altitude clouds in the sky. The distance of a cloud from the lake is far more than the depth of lake. So then how can an image be formed? I know that we see an image formed into the lake because still water surface of lake can be treated as a plane mirror. But in this case, how can object distance be equal to image distance that happens in a plane mirror? The height of cloud will be kilometres, but the depth of cloud will be a few metres.


forward implication f is continuous therefore it is bounded hence u is bounded hence u is a continuous. Reverse implication: f is expressed as function of u(x) - i((uix)) u is continuous and hence real part is continuous imaginary part contains scalar I therefore it is also continuous. and hence f is continuous. f(x)=u(x)-iu(ix) u(x)=Re(f(x)) <= |f(x)| ||u(x)|| <= ||f(x)|| now define k(x)= bar of f(x) / mod of f(x) |F(x)|=k(x)f(x)= f(k(x)x) = Ref(k(x)x) = u(k(x)x) and ||kx|| <= ||x|| and I don't understand how to proceed ahead


If we take two balls that change colours white and black, if we set that change in colours is always opposite one from another, for sure if we take one ball to the end of universe, if that ball will have black colour and second will have white colour.. How we know that spin (black and white balls) are not set from start when two entangled photos are made?


I have been thinking about this situation, I have no idea how the normal force act of such a body. Here I have taken the point mass and ring of same mass m but please provide a general solution. So I will state it as a question: How will normal force of the floor act on the ring of mass m and radius R, with a point mass on it when released is the same position as I have given in the picture. And ofcourse gravity is acting on it, take it g.


P= Pulling Any reference for the gradient of Normal Reaction. Will pushing the weight lead to reversal of gradient? Does this mean there is gradient of friction force (as it depends on normal reaction)? While it seems that based on irregularities the reaction developed should be different at each point of contact between surfaces which would lead to different friction & normal force magnitudes at each point as illustrated in which supports intuition.


I am reading measure theory in Rudin Book and in one of the its proofs, it is derived from an equality which exists between four sequences that this equality should also exist on four Limits. I think it is resulted from this fact that sum (and so difference) of two convergent sequences converges to sum of limits But I feel somehow unsure in this case. Can some one describe equality on limit more for me? Thanks in advance This is the sequences and the limits:


If we have any simple object like sheet,rod or sphere with uniform charge at them, is electric field at surface always finite? For sphere I read that it is finite because as test approaches the surface the area patch which can cause infinite field at a point is also getting smaller hence charge on patch is also getting smaller. So it is applicable for all case and if not why not?


And what if the line that being fitted has an additional constraint of avoiding certain points while making the polygon? Is there some specific fields I need to be exploring? For instance, set theory. The points that forming a polygon can be a set, and points under constraint condition can be another set. Another thinking direction was convex optimization of set points with constraints. PS: I do not mean fitting of line as in machine learning.


I think that would be a very helpful website where you could search for a theorem or topic and get instantly a list of proofs published by the users no matter where they come from books or made made by themselves and were each proof of the list will by ranked by votes so each user will ideally vote by the most accurate or easy to understand proof