Finite Definition and 1000 Threads

I am working on a problem on automorphism group of radical of finite group like this one: Here are what I know and what I don't know: ##Aut(R(G))## is an automorphism group, whose elements consist of isomorphic mappings from ##R(G)## to itself. For visualization purpose, I envision the...

What is the smallest positive integer n such that there are exactly 3 nonisomorphic Abelian group of order n

I am self-studying a class note on finite group and come across a problem like this: PROBLEM: Let ##G## be a dihedral group of order 30. Determine ##O_2(G),O_3(G),O_5(G), E(G),F(G)## and ##R(G).## Where ##O_p(G)## is the subgroup generated by all subnormal p-subgroups of ##G##; ##E(G)## is the...

hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ? please help me in this regard. thanks

After reading some of Einstein's writings on relativity I am confused as to why he finds it necessary that the universe is finite. In his "Relativity", Einstein explains that the ultimate Newtonian picture of the universe (matter in Euclidean space) would be one in which all mass were...

Hi, I bring a new algebraic challenge ;) Let $G$ be a finite group and $U,V,W\subset G$ arbitrary subsets of $G$. We will denote $N_{UVW}$ the number of triples $(x,y,z)\in U\times V \times W$ such that $xyz$ is the unity of $G$, say $e$. Now suppose we have three pairwise disjoint sets...

How can I use finite difference to discretize a system of fourth order differential equations? for example: y(4)+5y(3)-2y''+3y'-y=0

' I've got these solutions to the Schrödinger equation (##-\frac{\hbar} {2m} \frac {d^2} {dx^2} \psi(x) + V(x)*\psi(x)=E*\psi(x)##): x < -a: ##\psi(x)=C_1*e^(k*x)## -a < x < a: ##\psi(x)=A*cos(q*x)+B*sin(q*x)## x > a: ##\psi(x)=C_2*e^(-k*x)## ##q^2=\frac {2m(E+V_0)} {\hbar^2}## and ##k^2=\frac...

Homework Statement Let ##G## be a group such that its center ##Z(G)## has finite index. Prove that every conjugacy class has finite elements. Homework EquationsThe Attempt at a Solution I know that ##[G:Z(G)]<\infty##. If I consider the action on ##G## on itself by conjugation, each...

okay...if you accept that the sequence 1+2+3+4...=-1/12, I think I have determined a finite value of infinity. To find the value of the sums of all natural numbers up to a number, you can use the equation ((x^2)+x)/2. An example would be 4. 4+3+2+1=10. ((4^2)+4)/2 also equals 10. following...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with the proof of Corollary 2.2.4. Corollary 2.2.4 and its proof read as follows: In the second last paragraph of Bland's proof above we read: " ... ... If...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 2.2 on free modules and need help with the proof of Corollary 2.2.4. Corollary 2.2.4 and its proof read as follows: In the second last paragraph of Bland's proof above we read: " ... ... If...

Hi, I'm trying to covert a NFA to a regular expression and I've manged to come up with an answer but I don't think that it is right. Here's the question - http://i.imgur.com/NUHxTXY.png And here's my workings -...

It can be easily proved that Bose Einstein condensation can be got in infinite 2D. But what about finite 2D with extreme large "Volume" L^2 ?

$$F(z) = \sum_{n=0}^\infty a_n x^n $$ $$\partial_zF(z) = \sum_{n=0}^\infty (n+1)a_{n+1}x^n $$ So, we can begin to piece together some differential equations in terms of generating functions in order to satisfy some discrete recursion relation (which is the desired problem to solve). However I...

Consider a particle of mass m subject to the following potential function (taking Vo and L to be positive): V (x) = 40 Vo if x < 0; 0 if 0 < x < L/2; 2 Vo if L/2 < x < L; 40 Vo if x > L. (a) Derive the transcendental equation for energy eigenstates having an energy 2 Vo < E < 40 Vo. To simplify...

Homework Statement Consider a particle of mass m in the ground state of a potential well of width 2 a and depth. the particle was in the ground state of the potential well with V0 < Vcritical, which means the well is a narrow one. At t = 0 the bottom of the potential well is shifted down to Vo'...

So lately I've been thinking about whether or not it'd be possible to have the commutation relation [x,p]=i \hbar in a Hilbert Space of finite dimension d. Initially, I was trying to construct a lattice universe and a translation operator that takes a particle from one lattice point to the...

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 2: Linear Algebras and Artinian Rings, on Page 61 we find a definition of the length of a module. Some analysis follows, as does a statement of Theorem 2.5. I need help to understand...

Homework Statement Consider the Hamiltonian ##H=\begin{bmatrix} 0& \frac{-iw}{2}\\ \frac{iw}{2} & 0 \end{bmatrix}## Write the finite temperature density of the matrix ##\rho(T)## Homework Equations ##\beta=\frac{1}{kT}##The Attempt at a Solution The initial part of the problem had me find the...

Homework Statement Homework Equations V = q/(4*pi*E_0*r), when 0 is taken at infinity dV = -E*dsThe Attempt at a Solution a. The total charge of the rod is given by Q = lambda*L So the potential at P is given by V = (lambda*L)/(4*pi*E_0*y) b. We can calculate the electric field by...

Hi, I read in article: to incorporate the effects of the finite size of the nucleon, we considered an exponential form factor. I want to know what does "the finite size" mean? thank you

I am reading "Introduction to Ring Theory" by P. M. Cohn (Springer Undergraduate Mathematics Series) In Chapter 2: Linear Algebras and Artinian Rings we read the following on page 57: https://www.physicsforums.com/attachments/3149I am trying to gain an understanding of representations. I would...

I'm supposed to be doing a project. Here is what it says to do. I tried to copy and paste the directions in here but some of the equations are not turning out on this page as expected, so I have uploaded the project. Can anyone tell me how I need to start or what to do please? The...

I was reading the finite element method in engineering by Rao and in the first example he ends up with a matrix that is singular. The matrix is the following: \begin{pmatrix} 2 &-2 & 0\\ -2 & 3&-1\\ 0&-1& 1 \end{pmatrix} Which is a symmetric matrix as far as I can remember...

Hi guys , i am solving this equation by Finite difference method. (dt2/dx2 + dt2/dy2 )= -Q(x,y) i have developed a program on this to calculate the maximum temperature, when i change the mesh size the maximum temperature is also changing, Should the maximum temperature change with mesh...

I just completed a brief introduction to branch points in complex analysis, and I find it difficult to imagine/come up with functions with nonzero branch points. My difficulty is this: for the point to be considered a branch point, f(r,θ) and f(r,θ+2π) must be different for ANY closed path...

[The homework format does not appear on mobile] Problem: Show that a finite group of even order has elements of order 2 Attempt: The book gives a suggested approach that lead me to write the most round about, ugly proof I've ever written. Can't I just say: 1.) If G has even order, G/{1} has...

hello. I have a MATLAB skeleton provided because i want to model a distribution with a circular geometry. all in all, i want the 3d graph of the code to be some type of cylinder. This is the code: % flat step condition for ii=1:nHi, for jj=1:nHj, if (X(ii)/R_P)<1 &...

Homework Statement Plot the transient conduction of a material with k = 210 w/m K, Cp = 350 J/kg K, ρ = 6530 kg/m3 Where the material is a cylinder, with constant cross sectional area and is well insulated. The boundary conditions for the cylinder: T(0,t) = 330K T(l,t) = 299K...

Hello, I have an FSM which has 1 serial input and 4 outputs. The FSM must react to the table attaced in file. I can see that if the input is(for example)4 the output is 7(+3). I have to draw a state diagram(mealy). I can't solve it. Need some help Thanks

Hi, I would like to calculate the force between a finite coil and a nearby metal plate. A pulsed current is supposed to flow into the magnetic coil, which will generate a magnetic field near the coil. Due to this magnetic field, an Eddy current will be produced in a nearby metal plate and...

Homework Statement Two subgroups of G, H and K are conjugate if an element a in G exists such that aHa^-1= {aha^-1|elements h in H}= K Prove that if G is finite, then the number of subgroups conjugate to H equals |G|/|A|. Homework Equations A={elements a in G|aHa^-1=H} The Attempt...

Hi!, I'm working on a personal project: Solve the heat equation with the semi discretization method, using my own Mathematica's code, (W. Mathematica 9). The code: I'm having problems with the variable M (the number of steps). It works with M=1-5, but no further, I do not know what's going...

(I don't like the title, since it is a bit misleading. But, I couldn't think of a more descriptive title that fit in the length restrictions.) A recurring theme in a problem I am exploring is counting the number of subsets of size n in Z^{d}_{3} that have at least m mutually cohyperplanar...

Homework Statement Let G be a finite group with N , normal subgroup of G, and a, an element in G. Prove that if (a) intersect N = (e), then o(An) = o(a). Homework Equations The Attempt at a Solution (aN)^(o(a)) = a^(o(a)) * N = eN = N, but is the least power such that (aN)^m = N...

I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Section 6.5: Finite Fields, I need help with a statement of Beachy & Blair in Example 6.5.2 on page 298. Example 6.5.2 reads as follows:https://www.physicsforums.com/attachments/2858In the above...

I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Theorem 6.5.7. I need help with the proof of the Theorem. Theorem 6.5.7 and its proof read as follows:In the above proof, Beachy and Blair write: By Lemma 6.5.4, the set of all roots of $$f(x)$$ is...

I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Proposition 6.5.5. I need help with the proof of the proposition. Proposition 6.5.5 and its proof read as follows: In the proof of Proposition 6.5.5 Beachy and Blair write: " ... ... Since $$F$$ is...

I am reading Beachy and Blair's book: Abstract Algebra (3rd Edition) and am currently studying Theorem 6.5.2. I need help with the proof of the Theorem. Theorem 6.5.2 and its proof read as follows:In the conclusion of the proof, Beachy and Blair write the following: " ... ... Hence, since F...

As far as i understand the current big bang theory, it started as a extremely dense object, finite in size. But we still think (or well it is very accepted to belive) that the universe is infinite. I know inflation should be though as an expansion everywhere at the same time rather than the ball...

[SIZE="4"]Definition/Summary All finite fields are known; they are the Galois fields GF(p^n), where p is a prime. They have addition group Z(p)^n and multiplication group Z(p^n-1); their multiplication groups are cyclic. If p = 2, then addition and multiplication can be done very fast...

Homework Statement A cylindrical shell of radius a and length 2L is aligned around the z-axis from z= -L ot z = +L. A current I is distributed uniformly on the cylinder and moves around the cylinder's z-axis. Find the magnitude of the magnetic field at the origin. Homework Equations...

i am studying finite fields and trying to get an idea of the nature of finite fields. In order to achieve this understanding I am bring to determine the elements and the addition and multiplication tables of some finite fields of small order. For a start I am trying to determine the elements...

Ok here's a potential I invented and am trying to solve: V = -Vo in -b<x<b and 0 in -a<x<-b , b<x<a where b<a and ∞ everywhere elseI solved it twice and I got the same nonsensical transcendental equation for the allowed energies: \frac{-k}{\sqrt{z_0 - k^2}} \frac{e^{2kb} +...

Hello everyone, I am reading about the Finite Square Well in Griffiths Quantum Mechanics Text. Right now, I am reading about the case in which the particle can be in bound states, implying that it has an energy E < 0. After some derivations, the author comes across the equation \tan z =...

Hi guys, :smile: I am a mechanical engineer, and want to learn finite element analysis. I want to know what is the best book to start with. Assume I have no prior knowledge of the subject. :redface: Thanks, Sety.

Hi, I want to show that there exists a well ordering for every finite set. (I know if you add axiom of choice you can prove this theorem for infinite sets too but I think the finite sets do not need axiom of choice to become well ordered)

hy, there is nothing in Maxwells equations that would limit the speed of light. the only way one can get light speed, is to assume that em waves solve Maxwells equations and then one gets c as the square root of something out from Maxwells equations. the same goes for gravity waves, only...

This is a question about The Computational Capacity of the Universe by Seth Lloyd. It seems to me that arbitrary real numbers cannot be part of the state of the universe, since they carry an infinite amount of information. There are transition probabilities from the current state of the...