Ignoring non-trivial solutions with repeating primes, so let's say the sequence is strictly increasing. Then could such a recurrence relation exist?
If so, could one exist which defines each and every prime?
And how would you go about proving the non-existence of such recurrence relations?
I am trying to solve a hyperbolic equation using finite difference as shown below.
My main confusion is that to calculate for U_i,2 (i.e. the first iteration), where do I get U_i,1 from? Because the only given initial condition is U_i,0.
Note: I did try assuming that U_i,1 = U_i,0 and the solution does seem right, but I just would like to see if there is a better approach.
https://preview.redd.it/gizjjpmqncc81.png?width=613&format=png&auto=webp&s=ad33dee5a12cf9b241bfb2ce5c96068c4adbf9d3
I'm watching a video on finite Calculus right now, i.e. Calculus on discrete sets. The analogue of derivation in this method of Calculus is differences, and so ∆ f(x) = f(x + 1) - f(x). The video, though, doesn't explain why exactly ∆ f(x) is taken as the difference between f(x + 1) - f(x), and not f(x) - f(x - 1). My question, then, is why is that? What justification is there for describing the difference as the former and not the latter?
Can I know if there is any website/resource that explains how to solve fin numericals using Gauss-Seidel iteration method to obtain temperature distribution curve? I searched the web and couldn't find any. It'll be useful if the source contains how to solve the problem in MATLAB to obtain the TD curve
Hello there, I am looking for software or scripts for waveform propagation scripts or software (either finite element or finite differences) that allows for viscoelasticity (and, ideally, for anisotropy as well). Currently, I am testing SOFI2D, SOFI3D, and Comsol.
Any suggestions?
Thanks!
In this question, it is asked to calculate the lift to drag ratio for the airfoil at a given angle of attack. However, the mark scheme indicated that the correct way to do this is just use the CL value for the wing at that angle of attack when finding the ratio for the airfoil. I thought that at a given angle of attack the wing and airfoil have a different lift coefficient due to the affect on induced drag? So wouldn't it be correct to first calculate the lift coefficient for the airfoil (not the wing) at that angle of attack, and then divide that by the Cd value?
Thanks
sparsity structure of coefficient matrix
I have a coefficient matrix which is obtained through finite difference discretization of a 4d dirac equation in terms of the 12 unknown(4 spins and three colours) with 4 points in each dimension of the space time.Overall this sparse matrix has a size of 3072 x 3072 and its sparsity pattern is shown in the image "sparsity structure of coefficient matrix".I am interested to obtain some specific mass dependent blocks in the matrics(these blocks are obtained when one fixes each of the four spins and write the equation of the three colours for each spin.)
If I dig deep into the structure of the matrics ,then I observe the following pattern repeated every 48 diagonal points as shown in thr imagestructure.I can not deduce any equation ordering from this structure.
My question is how can i find out how the 12 equations for each grid point is ordered and which permutation can help me to achieve the desired structure where colours are arranged per spin.Has anyone worked with a 4d finite difference ?
The explanation I got was "Whereas correlation explains the strength of the relationship between an independent and dependent variable, R-squared explains to what extent the variance of one variable explains the variance of the second variable". That just doesn't help me understand the difference, even if that's the difference.
Could one a y'all help me?
Background: I work in a thermal analysis/characterization lab and was just asked if my instruments could measure CME. Doing some research I found that one instrument (DMA) could measure CHE if we bought a humidity accessory for it. They seem to measure the same thing (expansion with moisture absorption), but the CME measurement method I read used a dilatometer and the moisture absorbed was measured by mass change rather than the relative humidity of the test chamber (after the sample is given plenty of time to equalibrate). Is there any difference in CME and CHE? If so what specifically?
ǥͤ͑̉̋̊ͨ̋͋͑̊͂͐̿ͧ̃̿̾͐̇̔ͨͦ̆͋́͗ͨ̀̿̒̌̓ͤ̈́̈́͛̇̑́̏̍͋̍̉̌̂̈̀ͫ̊̑ͬ̅̄̒͌ͬ̏ͮ̓͂͆ͯ̏ͭ̀͑̒ͩ̈̍̋ͯ͋ͪ̉ͤ͊͂̽̎̐̉̑̊ͭ͑ͥ͛ͧ̃̑͐̅̃̉ͬ̅̌̑͊̒̄̔̑̊̑̿͐̀̍͐ͧ̏̐ͬ͊́̉̓ͨ̒́ͪ̿͐̅̑͒́̇͗ͥ̌ͤ̊̿̒̊ͬ͂̍ͭ̊̂ͥ̄͋̓̇́͐̄̅̉̅̌ͩ̍̋̆̒͌͑̓ͥͥ̎̌͑̃ͩ͗ͦ̿͋̎ͤ̐̎̎̓ͦ̄͊́ͪ̐͂ͯ̍̏͋ͩ̉̔̃̑ͩͥ͗ͣ̑̆ͧͤ͗͊ͬ̄ͨ̂̀̋ͤ̐ͦ̐̊ͪͦ̓͐ͭ̑ͧͬ͌̽͗̉ͨͭ͗͋̾̍͐͛̿ͨ̋͐̿̔ͦͯ̎́͐ͧ̔͗͋̀͊̇͑̈ͪͥ͆̈̍̾ͮ̈́̀ͪ͛ͦͨ̓̾̆̔̔́̿̈́̈̄͗ͮ́̒̔̄͑͐̎̀ͨͥ̑ͯ̄̔͐̌̇̚̚̚̚̚̚̚ｔ̥͓̳̟̘̓͊̂͂̋ͥͨͤ̍͂͂ͥ̏̓ͫͣͥͥ͗͂̈́͗͆͋̾͆̔̂̂ͫ̉ͧ͛ͣ̋̽̓̊͆̇̔̓͋̓ͪ́̌̄̅̅̆ͮ͂ͣͨ͒̐̋̾͂ͣͪ͗̿ͭ̒ͧ̇̔ͮ̀͋͐̏ͬ̂̾̑̎̂̎ͩͤ̆ͮ̔̓̆ͫ̍ͫ̈̿̿͑̄ͣ̈́ͨͦ̈̄ͬͤ͑ͮͮ͋̂̉̐̍̊͋́̾ͭ̌̈́̽͂̈́̍͗̊̄͗ͨ̓͑̇̿ͭ̄̈̊̍̑ͨͩ̐̋ͦ͌͂̾ͫ̄ͧ͊̅̽͗͆̅ͧͨͦ̚̚̚̚ｇ̬͙̩̺ͤͧ̽̎̽ͥ̐̔́̔̿͒ͦ̍̓͛̂ͫͥ̇̇ͬ̉̎̏͛̅͌ͮ̎̽ͪ̆ͦ̑͒ͬ̅͋̍͊̉̐ͨͦ͆ͭ̅̐̌ͦ̂̿̽͑̄̽̒̑ͫ̊̊̐̈́ͫ̌ͧ͑̓ͫ͗̌͒̐̉̂̽̑̆̽̌̒̅ͭ͗̿̅͂́̄͋̇̄ͤ̏̀̊̀̍͆ͣͯ̃̇̽ͪ͋̊ͭ̒͒̾ͦ̐̈́͑ͦ̏͐͑͆́̅̍̽̿ͥͩ̃̓̂̿̄̈̊̐͂ͪͣ̌͊͗ͥͮ͂͛ͣ̋ͩͬ̏̌̃̒̅ͮ͛͋ͩ̋̔̆̑̓̾ͦ̏ͧ͗ͤͪ̄̋ͮ̑ͪ̃́̽̒ͦ͆́̀̈͆̑͒̀̾ͨ̋̿̽ͣ̀̃͗ͨ͐̀ͧ͒ͩ͂̓ͫ̋͐̈́̓̉ͥ͑͛̎̑͒͒̽̆̽ͧ͗ͨ̂ͬ͆̊̄ͤͨ̔ͮͭͫͭ̒͆̀̈́̎͂ͬͮ͂ͯ̋̒ͤͭͬ̔̐ͫͦͧ̊̈̓̓ͦͫͦ̌̐̋̅̌͊ͣ͊̓̽ͧ̿ͨ̒ͫͥ͋ͧͬ̓̑̍ͩͦͥͯ̾̔ͫ͗͆̏͊̚̚̚̚̚ͅǥ͍̹̒ͫ̐ͨ͒͊ͤ̓̉ͫ̒̌ͬͧ̑̔ͩ̾ͩ̆͒͗͌ͤ͋̈͋ͪ̌ͭ̽͌ͥͭ̊̓̿͗͛̿̎̀̀͑͐ͫ̓̄̂̉͋̔͂̉̍̿̒ͬ̌ͣͦ͂ͥͧ̓ͫ̈͂̃̎̾̉̓́͐̄̋̄͋̾̅̀ͪ̌̍ͬ͐ͪ̌̓ͩ̏ͫ̒̋ͫ̐̃̆ͩ̔̌ͬ̑̌ͥ͆̋ͮͤ͌̎̐̇̃ͪ̉ͥ̏͂͆̉̈̀̃̔ͤͧ̈̏ͮͫ͑̉̎͒̓̾̋̓̏̊̑́̎ͤͯͫ͒̾̋͆̉ͬ̓ͤͥ̏̉͂͑̊́͗͒̆͐ͮ̀͑̈́͆ͤͪ̾̊͂̅̽ͨ̌̌ͦ̽ͮ͂͋̍ͣͫ̓̀͆͆ͬ͆̓̃ͦ͂̊͋̔͐̊ͦ̉ͫͩͭ͐ͩͩ̐͐̽̑̉̍ͪͧͦ̀̍ͬ̌͛̃ͫ͂ͦ̂͋̈ͦ̈͋͋͒ͨ̀̎ͦ̆̈ͬͭ͑͌̋ͩͣ̅̋ͬ͛̀͋̌̏̇̎̉̄̃̌̎͑́̋ͭ̃̍ͨ͒ͧ̎͑̒͆͐̃ͦ͂̂̿ͮ̍̂̈́ͩ́ͯ̓̒̾̎̽̚̚̚̚̚̚̚̚̚̚ｆ̬̼͙͌̅̌̐͑̏͗ͭ̓̾ͣ̾̊ͣ͐ͭͤͥͪ͗ͪ͊ͥͥ́̄̔͂ͪͤͮ̔͗̃̔͑̂ͨͧ͑̅͑̀̇͛͑ͤ̓̋͊̀̿̋̆̂ͨ̆͆ͨͥ͑͂ͭ̑ͥ̈̓̋̒̾̑͐́͗̍͋̃͐̈́ͯ́ͮ̓̔͆͗͌̐̋ͦ͌͆̊̾ͣ̈̿͒́̓̍̈̏̐̐͆̐͗͐͌͂ͫ̓̍̔̔̔̇̈ͮͭ̍̎͋͒͊͊̾͐͌͂ͭ͆̈́ͭͬ͌ͯ̓̃ͤͤ̊ͩ̎̐ͪ̍ͨ̅ͦ̉̎ͦ̒̈͒̂̈́ͭͮ͂̽͊̿ͭͬ̈͛ͦͯ̅̎ͤͭ̾ͧ̈́͋̔̂ͮ͂ͤͧ͋͒̑ͯ̓͊́̊̉ͫͬ͒̈̊̋̓͆ͧ̾ͥ̊͋̽ͪ̽̔͗̽ͭ̓̓̉̈ͦͦͦ̈́ͬ̉͛ͥ̔ͮ̄̆ͪ̀ͭ̍ͯ́̆̈́ͦͥ̈́̊ͮ͆̒͌͛ͭ͒͐ͣ͒̍ͧ̅̇̈̋̊̾͊ͦ͒͒̃̐͂ͫ͋̔̇ͨ̚̚̚̚̚̚̚̚Ꮷ̗ ̯ͪ̐̎̈̃ͦ̇̒ͭͯͦ͒̀ͤ̔ͥͥ̐̆ͤ̔ͯͩ̊̌̃͆ͥ̀̾̃ͣͨͦ͗͗̑̎̔ͤͤͫ̑͐̿ͪ̓ͣͯ̇͒͗̐ͮ̒ͯ̅͗ͤ͂̈̌͒͂͊ͤͪ̀ͮͭͦ̈͑̈̎ͭ̂̈̾͐͒̽̈́ͩ̈́̆͛͋̽ͥ͗̍̊̔̎̊̓̓̈̀ͧͧͥ͊̓ͪ̍ͬ͛́͗̃ͨ̎͆̾̈̎ͤ̐̐̋͛̈́̆̓̈́ͥ͋̌̂ͥ̉́́͆̐̃̉ͣͬͬ͂ͣ̌̎̉͒͑̔̏̆̓̎̽ͪͭͮ̔͑̓̈́̾̀ͨ͆ͨ̔ͦ̾̉̔ͭͤ́̉̾̓̿̿͑ͭͦ̿̒̆ͧͣ̉̐̃̎ͣ͐ͮ̉͗͊̊̓ͨ́̒̒̃̏ͭ̈́ͦͧ̿̾̽ͥ̒̇̋̀̽̇͐́ͮ̅̓ͧͩ̽̃̒ͨͪ̔͛ͥ̆ͧ͆̾̈ͯͧ̋͆ͦͦ̊̀͒̉͒̌̿̀͛̚̚̚̚̚̚̚ｖ̖̠̖͉̍ͦ̌̀̂̅̉ͧ̿ͯ̃̿̓́ͥ̅͐̌̔͆ͯͫ̾̓͋̓ͦ͛̒ͮ̾ͭ̔̂͛̄̓̎̔ͥͩͫͫ͌̾̓ͯ͋̆̆̃̽ͤ̃̓ͯ̔ͬͥͩ͆̈́͆̎ͥ̍ͮ͆̇̂͒̿͛̓ͯͫ͑̈̿̎ͥͯ̆̐̄ͣͣ͊̾̊ͪ́́ͪͬͪ̔̑͋͌̑ͮ͐̄̓̚̚ ͍̗̗̰̼̌̊̉͊̇̿͑ͤ̎̉ͧ̏͗̒̃̽͑ͨ͒͛ͭ̍͌̄̄̃ͬͤ̋ͪ̓̈͂̾̋̾̽̂͒ͭ̃ͮ͌̄͆̃̌͐ͧ̊͒̽ͣ͗̒ͧ͐̌̈́̎ͨͣ̏͆́ͤ͆̽̃̀̈́ͭͭ͒ͦͨ͑̎ͦͤ̇͊ͯͯ̍ͤ̍ͭ͒̅̄̇̍̉̆͗ͮ̆̍̿̓̇̍ͬ̽ͤͩ̊̒̌̏̃̌̓͗̽̌̃̒ͯ͑ͭ̄ͬ͂̋͊̿ͭͧ͑̍ͦ̅ͤ͗ͥ͋̈̈͆̓ͭͪͧ̉ͫ̏̾͆͆͗ͣͣ̆ͩ̊̃̑ͧ͂̎̀̾͋ͭͤͧ͆ͪ͌̊̇̂ͫ̅̎̈́ͮ̿ͯͪ́̈́͊̍̾ͦ́ͯͦ̌ͥ͌ͭͥ́̃̓͒͌̌̐ͮͮ͒ͯ̀̋ͩ͋ͮ̐̆ͫͣ̇̔̈ͥ̓̋ͣͧ̀ͨͪ̔̊͗̑͂͗͋̑ͨ͑ͤ̎ͣͧ́̊̈̒̽͗͂̊͆̏̋ͫ̌͗͋̾ͧ̽̆ͣͤ͐̏ͤͯͤͬ̆̿̽̍ͩ͂ͮ̍̾̽̿͋͐͒̆̓ͫͨ͒ͦ̉ͯ̉ͭ̔ͯ͗̅̄̇̎ͦ͑͗͐͊̓͌̽͛ͪ͒̎ͫͣͭͨͤͨ́ͥ͑̿ͥ̏̈͗͂̀͗̂̏̈̓̂̓͒ͩ̔̈́̏͂͛͛̄̈ͥ̈́͗̍̓ͯͨ̑ͦ̏́̏̓̅̀̀͛̌̾͆͆̀̄̏̓͑̐͆̋̏́ͥ̒ͮ̑ͥ̂̆͆̿̌ͯ̅̋̑ͬͣ͛̅͆͂̓̒̎ͧ́̓͐̆̾ͯͪ̆̈͋͆̄͗̏̈́̓̅̅̓̆̃ͫ̏̑̏ͫ̄̔ͨͯ̈́͋͊ͣͯ͋̽͛͊͊ͦ͌̏̏ͨ̔ͤ̎̓̓̚̚̚̚̚̚̚̚̚̚̚̚̚ǥ̣͎̘̞͖̅̐͑͛̋͗͊̉͐̎̋ͣͧ͛̓ͩ͛ͣ̂ͥ͊̊͊̃̍̓ͭ̍̑̀͂̽̐̃ͭ̏ͦͧͪͩͧ̑͒̇̇͆̂̅͋̌̉̎̇ͥ̆ͩ̋ͩ̂ͪͥ̄ͤͥ̓̄̏͂̾ͬ͊ͣͣ̎̽̅̊̓ͫ͊͑ͯ͆̎͋͂̇̒͆ͨ̏̑̒͊̾̃̏ͯ̉ͦͣ̾̐ͬ̒ͤ͌̿̃̒ͭ̍̍̽̎̍̋̔ͤ͐͗ͭ̆ͩ̅̌́ͣ̆̔ͮ́̄ͣ̌ͫ̋̍ͧ̉̏ͪͩͩ̃́ͯ̊̇̇͂̏ͩ̓ͨ̎͂ͭ͛̇͋͌͂̏̏̒͑̌̂̒̎̋̓ͣͤͫ̚̚ѵ̿ͣ͑̌ͤͭ̍͑͋̐ͤͯͧ͗͐ͣ́̂̿ͮ̾͗̔̌̈̆̔ͯͯͧ̅̈̇͗͂̓̋̂̅͑̅̄ͮ̓ͬͮ̒̿ͬͣ̑ͥ̈̿̂͒ͭ̏̊͆̌̈͐͋̾ͫͥ̽͋̊͐ͧ̓̎̆̈ͥ͒̓̄̿ͣͫ̾ͮ͋̚̚
... keep reading on reddit ➡Gini is the highest among black Americans and lowest among Hispanics, even though the two groups are a lot closer in median wealth. What are some possible explanations of this disparity?
I don’t even know what these words mean😅
I searched a lot and found methods such as Gelerkin and collocation methods and can anyone confirm if these are similar to finite difference analysis ? My condition is they have to be discretization methods.
That pretty much it. I want to apply a wald test between the treatment coefficients of two separate triple difference regressions to check if they have no significance between each other.
Actually I want to do it between four coefficients, but being able to do it between two would be amazing already.
Apparently I mixed these two up in my FEA class. We were solving a problem for homework where we had to calculate the stresses and deflections in an I-beam, and divide it into 3 sections (the two flanges and the web). The question explicitly asked to use the direct method of solving, and I got the correct answers, but my prof told me that the direct method is the same as the finite element method...
To be clear, he wanted me to solve it this way:
{stiffness matrix}*{deflections} = {reaction forces}
As opposed to what I thought was the "direct method":
deflection = (PL)/(AE)
Any clarification is greatly appreciated
I'm a PhD physicist, working in the field of optics and photonics.
Many of our problems and simulations are hugely complex, run on background servers which are expensive to maintain, and which aren't running 100% of the time. Upgrading these servers in the lab happens every few years, but again - at a huge cost.
Id be interested in offloading these tasks onto a decentralized computational engine which is "pay to play" - in that I pay small amounts of ADA tokens for people to solve a set of paralleled equations.
In particular, I'd be interested in solving the finite difference time domain problem as per Maxwell's equations.
There already exists a fairly substantial set of code for these solvers - such as lumerical, etc... I really just want to know if I can produce a dApp which solves the problem instead of doing it on my own machine.
for a better idea of exactly what type of problem I'm trying to solve, read this comment I posted : https://www.reddit.com/r/CardanoDevelopers/comments/lpuytp/limits_of_cardano_decentralized_physics_computing/godyk8x?utm_source=share&utm_medium=web2x&context=3 .
Here's the next 2 lectures, problem set, and solution set.
In RT8.1, we repeat the story for finite abelian groups for general finite groups. Now, instead of a character basis for L^2 (G), we use matrix coefficient functions for irreducible representations. The key result is the Schur Orthogonality Relations.
in RT8.2, we give orthonormal bases for both L^2 (G) and Class(G). In turn, we obtain important numeric results for representation theory: the sum of squares of dimensions formula, a counting formula for irreducible classes, and a counting formula for irreducible types in a given representation.
Video - RT8.1. Finite Groups: Schur Orthogonality Relations
Video - RT8.2. Finite Groups: Classification of Irreducibles
I am performing analysis for my master thesis and found a paper that gave me a good idea on how to analyze my data. In this, I am performing an FF3 regression in order to check whether the 2 portfolios are significantly different from each other. In this, I've got excess returns for 2 portfolios for the same time frame, the thing I would like to create now looks like this:
Alpha RMRF SMB HML
High ESG Portfolio 0,0029* 1,1882*** -0,0069 -0,2420***
(0,0015) (0,0376) (0,0698) (0,0582)
Low ESG Portfolio 0,0013 1,086*** 0,0725 -0,1324**
(0,0016) (0,0392) (0,0728) (0,0607)
Difference 0,0016 0,1017 -0,0795 -0,1096
What I am looking for now is how to calculate the standard error of the differences between these coefficients based on the regressions outputs. How would one go about this to see whether the difference in returns and risk factors is significant?
Pretty much the question. Our teacher's slides have dGi°= RT lnfi°, which he later mentions as fi°= yiP= Pi, which is same as ideal gas. Then what is the difference between them?
Hello, I am in the midst of writing my dis, and I need help with deriving the finite difference method, for time.
I understand how to derive the finite difference approx (forward, backward, central and symmetric) is formed by manipulating the Taylor series -
however I would like to know how the finite difference method is derived via a similar method to above, for time. (for forward, backward, central and symmetric)
Any explanations, links to videos or textbooks would be greatly appreciated
thank you !
Hello Everyone,
I hope you are well! I am carrying out mediation analysis. When I select "standardized coefficients" the results are significant. When I don't, the results are not significant. What does it mean?
The variables I am using in the mediation analysis model are not standardized. I am only adjusting for age and sex as confounders.
Thank you!!
Just a simple question for a confused medical graduate without proper statistical background. I am interested in the difference between time varying covariates, coefficients and time dependent covariates, and how to apply it in survival analysis in actual study
Any help would be appreciated
Why once a body start moving the friction coefficient decreases? I guess it has to do with some phenomena at an atomic level but I don´t know much more. Is there some standard explanation of this phenomena?
What is the drag coefficient difference between RWD and AWD models?
