Finite Definition and 1000 Threads

I am computing magnetic field around a thick conductor to do railgun force modeling. I am currently re-examining my magnetic field computation, and I have found some confusing results stemming from a fairly simple use of the Biot-Savart Law. The main issue is that the more nuanced application of...

Homework Statement Let ##({a, b, c}, *,+)## be a finite field. Complete the field table for the operations ##*## and ##+## ##\begin{array}{|c|c|c|c|} \hline * & a & b & c \\ \hline a & ? & ? & ? \\ \hline b & ? & ? & ? \\ \hline c & ? & ? & b \\ \hline \end{array}## ##\begin{array}{|c|c|c|c|}...

Homework Statement A charged wire of negligible thickness has length 2L units and has a linear charge density λ. Consider the electric field E⃗ at the point P, a distance d above the midpoint of the wire. What is the magnitude E of the electric field at point P? Throughout this part, express...

I am reading David S. Dummit and Richard M. Foote : Abstract Algebra ... I am trying to understand the example on Finite Fields in Section 13.5 Separable and Inseparable Extensions ...The example reads as follows: My questions are as follows: Question 1In the above text from D&F we read the...

I am reading David S. Dummit and Richard M. Foote : Abstract Algebra ... I am trying to understand the example on Finite Fields in Section 13.5 Separable and Inseparable Extensions ...The example reads as follows: My questions are as follows: Question 1In the above text from D&F we read the...

Hello all, I have another question about partial order relations, again, a few statements which are either true or false. R is a partial order relation on a set A which is not necessarily finite. 1) With this order, A has at least one maximal and one minimal elements. 2) If with this order...

Homework Statement Prove in any finite group G, the number of elements not equal to their own inverse is an even number. Homework Equations if ab = ba = e, then a = b-1 and b = a-1 The Attempt at a Solution Let S, A, B, be subsets of G where S = A + B. Let a ∈ A s.t. there exists a unique b...

Homework Statement In the third picture , I don't understand the circled part , add up the values in the diagonal .. How to do that ? I don't understand how to get k13 , k14 , k21 , k22 , k33, k41 and k42 . Homework EquationsThe Attempt at a Solution As we see in the second picture , the k21...

I am unsure of my approach to Exercise 2 Dummit and Foote, Section 13.2 : Algebraic Extensions .. I am therefore posting my solution to the part of the exercise dealing with the polynomial g(x) = x^2 + x + 1 and the field F = \mathbb{F}_2 ... ... Can someone please confirm my solution is...

Homework Statement I need help with Exercise 1 of Dummit and Foote, Section 13.2 : Algebraic Extensions .. I have been unable to make a meaningful start on the problem ... ... Exercise 1 of Dummit and Foote, Section 13.2 reads as follows: Homework Equations A relevant definition is the...

I need help with Exercise 1 of Dummit and Foote, Section 13.2 : Algebraic Extensions .. I have been unable to make a meaningful start on the problem ... ... Exercise 1 of Dummit and Foote, Section 13.2 reads as follows: I have been unable to make a meaningful start on this problem ...BUT ...

Homework Statement I'm trying to understand the intuition behind path-connectedness and simple-connectedness in finite topological spaces. Is there a general methodology or algorithm for finding out whether a given finite topological space is path-connected? Homework Equations how can I...

Hi. I am trying to simulate this paper since apparently I have a lot of time. Scrolling down to the last page, he simulated a transient 2D heat conduction plate with composite slabs on it. Darkest one is copper, lighter one is steel, lightest one is glass. If you look closely, the authors said...

So I have this PDE: d2T/dr2 + 1/r dT/dr + d2T/dθ2 = 0. How do I implement dT/dr || [r = 0] = 0? Also, what should I do about 1/r? This is actually the first time I am going to attack FDF in polar/cylindrical coordinates. I can finite-difference the base equation fairly decently; I am just...

Hi, I'm preparing for an exam, and I'm going over past papers. I've solved parts a & b of this question without any problems, however I'm finding it hard to understand part c. I thought of shifting the boundary conditions so I'd have 0 and L in the place of ± L/2, but that would not work...

In reviewing some calculations, I've arrived at the series: ##S(d)=-\frac 1 {d-1}+\frac 1 2 \frac{d-2}{d-3}-\frac 1 8 \frac{(d-2)(d-4)}{d-5}+\frac 1 {48} \frac{(d-2)(d-4)(d-6)}{d-7}+\dots ## Its an infinite series but because I'm interested in its values for even ##d##s, its actually a finite...

I have completed a 2D finite difference code in MATLAB that has a domain of (0,1)x(0,1) and has Dirichlet Boundary Conditions of value zero along the boundary. I get convergence rates of 2 for second order and 4 for fourth order. My issue now is that I'm now wanting to change the domain to a...

Homework Statement Hi everybody! I am asked to calculate how much of the total radiated power of a light bulb at temperature ##T=2300##K is contained within ##400##nm and ##750##nm. I am also given the average emissivity of tungsten ##\epsilon_\text{ave}=0.288## and the emissivity within the...

If I have this right, when we have exact certainty of a particle's momentum, the bounds of this particle's location cannot be determined. Now there are some who believe in a universe of finite volume and so this particle has to be within this volume. So there seems to be a contradiction. Does...

I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?

I need help trying to set up this problem. I want to find the capacitance between a point charge and a finite plate (or disk) as the point moves from above the center of the plate to some distance off the plate. I have been able to simulate this problem using FEM, however, there should be a...

Hi, Physics forum! Just a little push of my doubts I hope somebody could help me with my confusion of one of our home works. I know that all boundary conditions are zero. My doubt is how do I interpret (x,y,0)=0.01 source in the figure? Where is it located in the grid. I am hoping someone...

<Moderation note: edited LaTex code> E.g. A rotation by a finite angle θ is constructed as n consecutive rotations by θ/n each and taking the limit n→∞. $$ \begin{pmatrix} x' \\ y' \\ \end{pmatrix} =\lim_{x \to \infty} (I + \frac{\theta}{n} L_z )^n \begin{pmatrix} x...

Hello guys, I was reading some models about the topology and size of the universe (always a controversial topic), then a question came to my mind. It is predicted that our universe will expand until it reaches heat death. Can a closed, finite universe also reach heat death and be described by...

There are lots of measurements showing strong temperature ($T$) dependence of Hall coefficient ($R_H$) in correlated materials (eg. cuprate superconductors and other oxide materials) and such plots are available in many recent experimental papers. However, I could not find any $R_H$ vs $T$ plot...

Homework Statement Homework Equations I could really use a push on how to approach this problem. My primary problem is it asks for the heat flux into the page, which makes no sense to me as that is the z direction and this is in the x/y plane. If anyone could explain this problem and maybe...

I am using the Finite Difference Method to solve Poisson's equation \frac{\partial \phi}{\partial z^2} = \frac{\rho}{\epsilon} To do it is discretized according to the Finite Difference Approximation of the second order derivative yielding the following set of equations for each grid point...

Hey! Let $C$ be an algebraic closure of $F$ and let $f\in F[x]$ be separable. Let $K\leq C$ be the splitting field of $f$ over $F$ and let $E\leq C$ be a finite and separable extension of $F$. I want to show that the extension $KE/F$ is finite and separable. We have that $KE$ is the smallest...

Homework Statement Suppose that ##H## and ##K## are subgroups of finite index in the (possibly infinite) group ##G## with ##|G : H|m## and ##|G:K|=n##. Prove that ##lcm(m,n) \le |G : H \cap K | < mn##. Homework EquationsThe Attempt at a Solution I was able to get the upper bound on ##|G : H...

Hi guys, Based on what I know about the status of modern cosmology the question whether the universe is infinite or finite in extent is still open. Are there any plausible models in which the universe is finite and closed, despite the curvature being close to flat? Thanks in advance.

Homework Statement Give an example of each, or state that the request is impossible: 1) A finite set that contains its infimum, but not its supremum. 2) A bounded subset of ℚ that contains its supremum, but not its infimum. Homework EquationsThe Attempt at a Solution I either understand this...

Homework Statement I read somewhere that if ##\{A_i\}## is a collection of subsets in some topological space ##X## that is locally finite, then ##\overline{\bigcup A_i} = \bigcup \overline{A}_i##, but I am having difficulty showing this. Homework EquationsThe Attempt at a Solution I already...

I need to take a look at some references about QFT at finite density but I can't find anything, or at least I don't know where to look. I should emphasize that what I need is QFT at zero temperature and finite density so it seems to me QFT in finite temperature books may not be what I need or...

How would I design a non-trivial algebraic function of degree 4 containing a branch at the origin with the (finite) power expansion: ##w(z)=1+0.5 z-1/4 z^{1/2}+3/4 z^{1/4}##? having the form ## f(z,w)=a_0+a_1 w+a_2 w^2+a_3 w^3+a_4 w^4=0## with the ##a_i ## ( preferably not fractional)...

What does it mean when a limit is finite

Homework Statement Which algebraic expressions must be solved when you use finite difference approximation to solve the following Possion equation inside of the square : $$U_{xx} + U_{yy}=F(x,y)$$[/B] $$0<x<1$$ $$0<y<1$$ Boundary condition $$U(x,y)=G(x,y)$$ Homework Equations Central...

Homework Statement I'm currently working on a homework set for my intermediate QM class and for some reason I keep drawing a blank as to what to do on the first problem. I'm given three potentials, V(x), the first is of the form {A+Bexp(-Cx^2)}, the others I'll leave out. I'm asked to draw the...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.3 ... ... Lemma 1.3 reads as follows...

Suppose $G$ is an infinite group and $H$ is an infinite subgroup of $G$. Let $g\in G$. Suppose $\forall h\in H\ \exists h'\in H$ such that $gh=h'g$. Can we conclude that $gH=Hg$? What if $G$ and $H$ are of finite orders?

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.2 ... ... Lemma 1.2 reads as follows...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with some aspects of the proof of Lemma 1.2 ... ... Lemma 1.2 reads as follows: My questions related to the above proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with another aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: My questions regarding Bresar's proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with another aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: My questions regarding Bresar's proof...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...

I am reading Matej Bresar's book, "Introduction to Noncommutative Algebra" and am currently focussed on Chapter 1: Finite Dimensional Division Algebras ... ... I need help with the an aspect of the proof of Lemma 1.1 ... ... Lemma 1.1 reads as follows: In the above text, at the start of the...

Hi, I'm attempting to solve the 3D poisson equation ∇ ⋅ [ ε(r) ∇u ] = -ρ(r) Using a finite difference scheme. The scheme is simple to implement in 3D when ε(r) is constant, and I have found an algorithm that solves for a non-constant ε(r) in 2D. But I am having trouble finding an algorithm...

Homework Statement An electron is enclosed in a potential well, whose walls are ##V_0 = 8.0eV## high. If the energy of the ground state is ##E = 0.50eV##, approximate the width of the well. Answer: ##0.72nm## Homework Equations For an electron in a potential well, whose energy is less than...

In my simulation I have a wire with a fixed current flowing, I observed if I change the diameter of the wire the magnetic field (B) in a fixed point of the space also changes, is it correct?

Hello I am trying to prove that $\mathbb{Q}$ is not a finite set. I proceed with path of proof by contradiction. Suppose that $\mathbb{Q}$ is a finite set. Then $\exists\; n \in \mathbb{N}$ such that $I_n \sim \mathbb{Q}$, where \[ I_n = \{i \in \mathbb{Z^{+}} |\; i \leq n\} \] This means that...

Suppose I want to solve the time-independent Schrödinger equation (ħ2/2m ∂2/∂x2 + V)ψ = Eψ using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...