Element Definition and 836 Threads

I am really stuck with how to prove that the only element in Sn (with n>=3) commuting with all the other elements of this group is the identity permutation id. I have no idea what I am supposed to do with it, i know why S3 has only one element that commutes but i don't know how to prove it...

I have gone through Beam Element analysis in several books on FEA. 80% of books have a particular Stiffness matrix, while a very small number of books have a matrix which is subtly different in sign. http://www.flickr.com/photos/66943862@N06/7195680680/in/photostream/lightbox Most books have...

Let \begin{equation*} A=% \begin{bmatrix} 0 & 1 & \cdots & n-1 & n \\ 1 & 0 & \cdots & n-2 & n-1 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ n-1 & n-2 & \cdots & 0 & 1 \\ n& n-2 & \cdots & 1 & 0% \end{bmatrix}% \end{equation*}. How can you prove that det(A)=[(-1)^n][n][2^(n-1)]? Thanks.

What is the maximum order of an element modulo n, where n is a product of two odd, distinct primes? Let t be the smallest positive integer such that xt = 1 mod n I've have been searching around on the web, but I don't really understand this concept. Some of the keyword I have found to be...

why does peak of fire of a matchstick face upwards ie away from ground.why is it not effected by gravity,is there any reason other than pressure considerations.

Dear all, I have written a code for dynamic analysis of a mechanical structure. My primary purpose is to find natural frequencies of the structure. When I test my code for a cantilever bar whose natural frequencies are known analytically, I found a big difference between the the first...

Hi, i do a motorsport where a normal cooling system for the engine cannot be used as it gets damage so we use solid water tanks along the bulkhead of the car, these arent the greatest as they tend to get hot as they're not really a cooling system at all. My idea would be to make a water tank...

Wigner-Eckart theorem and "reduced matrix element" Hello, I am studying the Wigner-Eckart theorem and I have found some difficulties understanding the reduced matrix element of a spherical tensor. In fact, a spherical tensor is commonly defined through its transformation properties, and I...

Dear all, I have written a code for structural analysis using the finite element method. For some reason, I directly started with 3D elements ( hexahedron). I used to believe that the code was fine but recently i realized that the results ( deformation, natural frequency,..) strongly depend...

I've been reading a Kabbalah book written by Yehuda Berg. "The power of Kabbalah" And it's basically explaining the universe and everything about it from the text of the zohar. And the Kaballah explains in the first few pages that Humans main core element Is Desire and in the book it quotes "If...

Hi all, A fixed-free bar has a single natural frequency. When we discretize such a bar in the finite element method, then the natural frequencies are the eigenvalues and an nχn matrix where n is the number of the degree of freedom which is usually large. Thus we obtain up to n natural...

Homework Statement The rotation matrix below describes a beam element which is rotated around three axes x,y and z. Derive the rotation matrix. http://img194.imageshack.us/img194/3351/60039512.png http://img808.imageshack.us/img808/159/64794596.png Homework Equations -The Attempt at a...

So, as the title describes, I am trying to build an infrared heating element for my own heating panel. I want to use this heater to cure an epoxy at 350F that is about 5" away. I'm an EE so the wiring and such will be simple but the heating calculations are beyond my area of expertise. Here is...

Hi all, I need to do a dynamic structural analysis using finite element method and I have a question about the mass matrix. Question: I have the force per nodes and I need to calculate the displacement of each node at a given time. For this purpose, it seems that I need to distribute the...

Hello, If we know the value of the field variables at the nodes of hexahedral element. How one finds the value at the center of the element. The hexahedral element is trilinear and solved using 2x2x2 gauss quadrature rule.

Folks, I have a query regarding the attached circuit. In order to design a rectifier, I was trying different structures. So, I started with the attached circuit without delay elements. I have used a cap at the NMOS, so that the cap will gets charged. But I don't want the cap to discharge...

So I just started learning to use the finite element package abaqus for modelling beam tip deflection under different loading conditions. I think I understand the theory behind it but was wondering if some one could answer a few questions about it to further my understanding. Firstly, how do...

Homework Statement Let R be a ring in which 1_R = 0_R .Show that R has only one element.Homework Equations The Attempt at a Solution I'm trying to show that a*0_r=a*1_r implies a*0_r=0_r. if 0=0+0=>a*0=a*(0+0)=a*0+a*0=a*1_r+a*1_r=2a=>a*0=2a= >a=0...is this correct? If not Is there something I...

Homework Statement I'm trying to write a proof ot demonstrate that every finite domain contains an identity element.Homework Equations The Attempt at a Solution If I can think of the operation from the ring as a mapping...like x->yx..where y are just values from the domain and then to consider...

How can I prove that every finite domain has an identity element? How should I think about the problem and what should I take into consideration?

I need to make a 1 metre long heating element from NiChrome Wire. The wire I have is 0.9mm with resistance of 1.7ohms per metre. Can I wire it straight to the mains with a light dimmer switch in place to limit the power?

I recently saw the Evaluated Nuclear Data File provided by Brookhaven national lab., where in i saw the plot of "Neutron Energy Vs cross section (total)" for different elements. http://www.nndc.bnl.gov/sigma/index.jsp?as=1&lib=endfb7.0&nsub=10 Now what i am interested in is, can we derive or...

Hello, I have been following this forum for some time now, but this is the first time I participate. I would appreciate if you could give me a hand in understanding the results of a finite element analysis of an automotive component we have designed. The analysis results indicate that the...

I'm studying a particular system but to ease the understanding let me take a general approach. 1) Suppose I have a system comprised of N=10^10 elements. Assuming now that I deal a damage to a random element for every timestep, I want to figure out how the damages are distributed in the...

I'm working through my rheology notes and there is a fairly basic part that I don't understand at all. If you have two neighbouring points in a liquid P(x,y,z) and $$Q(x + \Delta{x}, y + \Delta{y}, z + \Delta{z})$$ now if the velocity components of P are given as (u, v, w) then $$u_Q = u_P +...

Homework Statement Which of following statements are TRUE or FALSE. Why? In any group G with identity element e a) for any x in G, if x2 = e then x = e. b) for any x in G, if x2 = x then x = e. c) for any x in G there exists y in G such that x = y2. d) for any x, y in G there exists z...

I'm writing a script to simulate the transport of ion beam in a Thomson Spectrometer. My concern is that the program doesn't allow the passage of higher charge states through out the pinholes that I use to collimate the beam. I mean if I want to simulate a 3 charge states beam of C ions I will...

Please teach me this: In chapter 18.4 Peskin&Schoeder(QFT) they consider the annihilation of electron and positron to hadron.Ignoring the mass of the electron,we have: σ(e^{+}e^{-})=(1/2s)ImM(e^{+}e^{-}→e^{+}e^{-}). We have...

Ok what is your favorite element? My list includes einsteinium, seaborgium, lawrencium, fermium, and uranium. First four because they bear the name of my favorite scientists. Uranium because it is so versatile.

Homework Statement Let F|K be a field extension. If v e F is algebraic over K(u) for some u e F and v is transcendental over K, then u is algebraic over K(v).Homework Equations v transcendental over K implies K(v) iso to K(x). Know also that there exists f e K(u)[x] with f(v) = 0.The Attempt at...

Hungerford says that But if we take K = ℝ and K(x_{1}) = ℝ(i) = ℂ, we have that i is not in ℝ yet is algebraic over ℝ. Guess I'm missing something here. Is it that this need not be true for simple extensions if the primitive element is algebraic over the field?

There seem to be several methods for calculating the orbital element. Newcomb, Laplace, Lagrange, Gauss, Olbers, ... I'm sure over time a new method came to light. However, what basically was the difference between a new method and the one it replaced? Improvements in calculations (computer)...

Hi Could anyone point me in the right direction? I'm employed at a small firm, only three employees at the time being. Our competencies spans from architecture to programming. We're in need of somebody who can help us create a finite element solution which we can implement in the cad...

Homework Statement Over time (0s ≤ t < ∞), charge enters an element according to q(t) = 7.5C · (1 − e(+t/τ)). 1. What is the current into the element as a function of time? (Find a symbolic answer!) 2. What is the unit of τ? 3. Prove that the unit of the result indeed is A. The...

Hi guys, I think this is a simple question for mathematica experts. How can I maximize the extracted value from a list given a index that has to respect some constrains? For example: S = {4,2,3,5} Maximize[{Extract[S,x], x<= 3, x>=1},{x}] I would like 4 is returned instead of...

Hi there, As part of my paper I need to define the minimum non-zero element of some set. In particular I have, \begin{equation} \zeta(j):= \displaystyle \min_{\substack{ k\in1..\kappa\\ t\in 1..\kappa+1,~i \in \mathcal I^{t,j},\\ b_i^{t,j} \mod \theta_k \neq 0}} b_i^{t,j} \mod...

Hello, I am looking for a good source of information about design of machines (static failure, fatigue theory, design of shafts and keys, spur gears, etc..). Maybe some free online material or lecture notes? It seems like a fairly difficult course but I could find very few information so far...

Please help me, I need to derive exciton-photon interaction. Here, we are using second quantization. Please refer to this paper http://prb.aps.org/abstract/PRB/v75/i3/e035405 Hamiltonian of electron-photon is H_{el-op}=\sum_k D_k c^+_{kc}c_{kv}(a+a^+) c^+_{kc}c_{kv} are creation of...

Homework Statement Hello, I'm having a problem in multiplying two vectors together in a specific way in Fortran. I can do it in Matlab, but can't work out how to do it in Fortran. The problem is that i want to multiply two vectors together, but only each element by it's corresponding...

Hello all, Just recently my one Professor has been depicting the BJT transistor with a capacitor joining the base and emitter portion of the transistor. The transistor is of npn configuration, however, he has yet to say anything regarding the capacitor. Is this "capacitor" a characteristic of...

I use a popcorn popper to roast coffee beans. I'd like to be able to vary the heat of the heating element (as inexpensively as possible). My thought is to connect into the internal wiring of the popper to the heating element and run a wire out to connect to some type of external controller...

Valence electrons of a transition element... Here is the electron config. for Iron (Fe) 1s2 2s2 2p6 3s2 3p6 4s2 3d6. I have two questions about this I've been on for hours... #1 Which subshell (4s or 3d) has the highest subshell? -You can say that the 3d has higher energy because you write...

This has been bugging me and I just can't seem to figure out a solid answer. My electric stove has different sized heating elements where the size comes from just a longer heating element. It looks like this: http://www.sausagemaker.com/ProductImages/41516.jpg When I measure the...

Good books that explain the "Why" element. Hi there, I'm in a bit of a pickle. I'm currently in what I think is the equivilent to the American Senior year. I am kind of angry with my maths teacher. While she is good she "Teaches to the exam". It really nettles me. Does anyone know any good...

Homework Statement At 1000 deg C and 10 torr, the densit of a certain element in the gaseous state is 2.55×10^-3 g/L. The element is: Homework Equations The Attempt at a Solution So, i took the the density equation, that of which is derived from the ideal gas law, and rearranged...

Hello, I am trying to solve the shallow water equations using finite element method. Can anyone explain me how to treat nonlinear term in the Galerkin equation? so for example in the equation for the velocity we will have the term u\nabla v where u and v are the velocity components. For...

Prove that the set of integers has neither a greatest nor a least element. I was given a hint: There are 2 different non existence results to prove, so prove them as separate propositions or claims. Divide into cases using the definition of the set of integers. So I was kind of confused...

Let G be an abelian group containing elements a and b of order m and n, respectively. Show that G contains an element of order [m,n] (the LCM of m and n). This is true when (m,n)=1, because mn(a+b) = e, and if |a+b|=h, then h|mn. Now, hm(a+b) →m|h and similarly I find that n|h. But (m,n)=1...

Hi everyone I need to heat up an area 0.5m^3 (100cm x 100cm x 50cm). Would anybody know of any formulas I could use to calculate what wattage heating element id need to heat this area up to 100 degrees C within say 30 minutes. Thanks

Hi. I need to: prove the group (Zp*,x) has exactly one element of order 2. Here, p is prime and (Zp*,x) is the set {1, 2,..., p-1} under multiplication modulo p. Any help would be much appreciated!