Relations Definition and 540 Threads

I'm struggling to derive some thermodynamic equations from this http://my.safaribooksonline.com/book/chemical-engineering/9780132441902/thermodynamic-properties-from-volumetric-data/ch03lev1sec1" : Homework Statement I'm trying to derive all the equations from 3.8 to 3.14 for Pressure...

Dear Sirs, I have discovered these two formulas: p = (1-v^2/c^2) * dKE / dv v = dKE / dp where p – momentum; v – velocity; KE – kinetic energy. Everywhere are used relations with full energy instead of kinetic. Therefore would be nice to know why these two are not used...

Homework Statement Show that: [p,x] = -iħ, Show that: [p,x^n] = -niħ x^(n-1), n>1 Show that: [p, A] = -iħ dA/dx Where p = -iħ d/dx, and A = A(x) is a differentiable function of x. Homework Equations [p,x] = px - xp; The Attempt at a Solution So far I understand part of each...

Virtually every treatment of quantum mechanics brings up the canonical commutation relations (CCR); they go over what the Poisson bracket is and how it relates to a phase space / Hamiltonian mechanics, and then say "then, you replace that with ih times the commutator, and replace the dynamical...

"Open" and "closed" relations We know that if we have convergent sequences (xn) and (yn) in simply ordered metric space, then xn\leqyn implies that the limits x and y have x\leqy. Also, xn<yn. My instinct on noting this is to say that "<" is an "open relation" on that metric space, and that...

Homework Statement Deciede if the following are equivalence relations on Z. If so desribe the eqivalence classes i) a\equiv b if \left|a\right| = \left|b\right| ii) a\equiv b if b=a-2 Homework Equations The Attempt at a Solution i) \left|a\right| = \left|a\right| so its...

Let Q be the group of rational numbers with respect to addition. We define a relation R on Q via aRb if and only if a − b is an even integer. Prove that this is an equivalence relation. I am very stumped with this and would welcome any help Thank you

Hello, I have a sequence of polynomials defined in the following way: P_k(x) = \frac{\partial^k}{\partial x^k}e^{s(x)}\vert_{x=0} Essentially the polynomial Pk is the k-th derivative of \exp(s(x)) evaluated at x=0. The function s(x) is a polynomial of 2nd degree in x. In mathematica I...

Hello, I need to measure the complex-optical conductivity of some materials. The problem is that I can only measure the imaginary part of the complex conductivity only for limited wavelengths between 1030 nm and 2300 nm. From Kramers-Kronig relations, we know that the real and imaginary...

Homework Statement I have a trouble understanding what would be the output when for example we say let's input the signal x(k*n) or x(n-n0) to the system... this has given me problems when having to solve systems for which I have to check the property of time invariance suppose we have a...

Hi, this is my first time posting here, and I am trying to prove the following proofs and I do not know how to start: Suppose R and S are relations on set A 1. If R is reflexive and R is a subset of S, then S is reflexive. 2. If R is symmetric and R is a subset of S, then S is symmetric. 3...

Hi, I'm hopng someone can help me. I've begun working my way through Lahiri's "A first book of quantum field theory". In chapter 3 he shows the Fourier decomposition of the free field is given by \phi(x) = \int \frac{d^3 P}{\sqrt{(2\pi)^3 2E_p}} (a(p) e^{-ip\cdot x} + a^D(p) e^{ip...

Homework Statement a_n+3a_{n-1}-10a_{n-2}=2^n The Attempt at a Solution I missed the lectures that addressed how to solve these kinds of problems, and while studying my recommended textbook it only went as far as solving recurrence relations that are equal to 0 as opposed to 2n. I...

Homework Statement The conductivity of a plasma is defined as \sigma = i\frac{Ne^{2}}{m\omega} where N is the electron density. a) Prove the refractive index is: n = \sqrt{1- (\frac{\omega}{\omega_{p}})^{2}} with \omega_{p} = \sqrt{\frac{Ne^{2}}{m\epsilon_{0}}} b) Show the Attenuation...

(This could maybe turn out to be a little longer post, so I'll bold my questions) Hi, I was reading a little about affine geometry, and something bothered me. Namely, in some books, there were some paragraphs that were written like "blabla, let's observe an affine plane for instance, and...

I know that determining functions from relations can be easy. A relation is a function if every x has a unique y or every first coordinate(domain) of the ordered pair has exactly one second coordinate(range). What I don't know is if the repetition of an ordered pair affect the set at all...

EDIT: fixed TeX issues Hi, I'm learning about the correspondence in string theory between the geometry of Calabi-Yau manifolds and melting crystals. I care more about the math and know almost nothing about string theory, so navigating the literature littered with so much string theory jargon...

According to Dyson, Feynman in 1948 related to him a derivation, which, from 1) Newton's: m\ddot{x}_i=F_i(x,\dot{x},t) 2) the commutator relations: [x_i,x_j]=0m[x_i,\dot{x}_j]=i\hbar\delta_{ij} deduces: 1) the 'Lorentz force': F_i(x,\dot{x},t)=E_i(x,t)+\epsilon_{ijk}\dot{x}_j B_k(x,t) 2)...

One of my dilemmas about <standard> quantum mechanics is spelled out in the sequel: If the position and momentum observables of a single-particle quantum system in 3D are described by the self-adjoint linear operators Q_i and P_i on a seperable Hilbert space \mathcal{H} subject to the...

EDIT: fixed minus sign issue =) Hey, I have what is probably a rather trivial question but I just want to ensure that I'm on the right track :) If I have a wave equation of the form -\psi''(r) +A(r) \psi(r) = 0 then one can invoke (in suitable circumstances) the semi-classical...

More questions about "Relations" I have some more questions... 1) How do I exactly define an equivalence relation? I know it needs to be reflexive, symmetric, and transitive. That's too much to check for, and it's very confusing. There must be something else. No? This is important, because I...

Trying to prepare for an exam... 4) Let f : A -> B be any function from the set A to the set B. How is the equivalence relation ~f on A defined? 5. Let f : R -> R, x -> x^2, (Couldn't find the R symbol - real numbers) be the parabola function. What does the partition for the equivalence...

Homework Statement [PLAIN]http://img812.imageshack.us/img812/5261/unleduqi.png Homework Equations The Attempt at a Solution Can anyone help with part (a)ii, is pk=(1/2)^k? I can't see how to find qk

I would like to work out the following commutation relations (assuming I have the operators right...:-p) (1) \left[\hat{p}^{\alpha},\hat{p}_{\beta}\right] (2) \left[\hat{p}_{\alpha},\hat{L}^{\beta\gamma}\right] (3) \left[\hat{L}^{\alpha\beta},\hat{L}_{\gamma\delta}\right] where...

A uniform film of oil 0.13 mm thick separates two circular discs, each 150 mm diameter and mounted coaxially. Find the torque required to rotate one disc relative to the other at a steady speed of 400 rev/min if the oil has a viscosity of 0.14 Pa.s. (Ignore edge effects at the rim of the...

I am totally new to this area, and have some major trouble understanding how recurrence relations were derived from the problems, what to do and what's not. Really appreciate any guidance!For example: Give a Ternary String (containing only 0s, 1s, or 2s), we have to find out the recurrence...

Are the absolute magnitude of stars relevant (calculated) with it's mass and rotational velocity? I understand that the mass of a star has a relation to it's size... regardless of this.. I need to know if mass and rotational velocity combined are used to determine anything for stars. Furthermore...

I was talking with a friend earlier today about the idea that at absolute zero, particles essentially stop moving. I know that this makes sense since temperature is defined as average kinetic energy, which, if this equals 0, implies no movement. That made me think, however, about the...

Hello, all, the most important results that I know in this topic is the Gauss-Bonnet Theorem (and hence the classification of compact orientable surfaces) and also the Poincare-Hopf index theorem. But there are still some fundamental problems I don't understand. For example, is the...

How is this accomplished? How can one derive equations for stress in terms of strain from equations of strain in terms of stress or vice versa?

Hi, If we have an orthonormal basis, how can we show that the relation \sum|x><x| = Identity? I see this in Quantum Mechanics but I'm not sure how to prove it. Thank you.

Homework Statement Use the reciprocity relations and known transforms to compute the Fourier Transform of the given function. f(x)=\frac{1}{1+x^{2}} Homework Equations With the help of the table of Fourier transforms, write the given functions as F(f). The Attempt at a Solution...

Hey, I have had a lot of trouble understanding how one obtains a Maxwell relation. So let's say in general I know(from a specific problem) T ds = dE - F dL where F is a tension and L is a length, E is the energy T is the temperature and S is the entropy of a system. In a specific...

Hi, All: I am given two groups G,G', and their respective presentations: G=<g1,..,gn| R1,..,Rm> ; G'=<g1,..,gn| R1,..,Rm, R_(m+1),...,Rj > i.e., every relation in G is a relation in G', and they both have the same generating set. Does this relation (as a...

Homework Statement Let Z be the set of all integers. Then, S is a relation on the set Z x Z defined by: for (a1, a2), (b1, b2) belong to Z x Z, (a1, a2)S(b1, b2) <-> a1b2 = a2b1. Homework Equations The Attempt at a Solution The actual problem is about symmetry...

Homework Statement The relation R on the set of all groups defined by HRK if and only if H is a subgroup of K is an equivalence relation. Homework Equations Subgroup: has identity, closed under * binary relation, has inverse for each element. Equivalence relation: transitive, symmetric...

1. I am trying to practice solving recurrence relations but get stuck when it comes to generalizing the last part of them and would be grateful if someone could offer some help. I'm not very good with series which is why I may be having some problems with them. Here are a few examples if its...

\textup{A 2 x 7 rectangle has tiling with 1 x 1 and 1 x 2 tiles (singletons and doubletons).} \textup{How many such tilings of a 2 x 7 grid are there?} \textup{Let }a_{n}\textup{ be the number of tilings of a 2 x n grid using 1 x 1 and 1 x 2 tiles so that the} \textup{two rightmost squares...

Homework Statement Consider the following binary relations on the naturals (non-negative integers). Which ones are reflexive? Symmetric? Anti-symmetric? Transitive? Partial orders? a) A(x,y) true if and only if y is even b) B(x,y) true if and only if x < y c) C(x,y) true if and only...

I try to calculate refractive index of experimental spectral data using Kramers-Kronig relations but didn’t succeed. I need your expert advice and help to solve this problem. Data and expression for KK relation is give in worksheet, where alpha(omwga) is in cm-1. Solution through Matlab or...

Hello guys, I am new to this forum. I have a question: A relation can be subset of some other relation? For example? I have the relations X: A <---> B Y: B <---> C Z: A <---> C X...

I don't understand how a left (right) Green relation is a right (left) congruence. xLy <=> Sx = Sy (Green's Left Relation): where we join 1 to S if it doesn't have identity. Left Congruence: aPb ==> caPcb for some c in the semigroup S. Take this example table: * a|b|c a|a|b|c...

If you have a Grassman number \eta that anticommutes with the creation and annihilation operators, then is the expression: <0|\eta|0> well defined? Because you can write this as: <1|a^{\dagger} \eta a|1>=-<1| \eta a^{\dagger} a|1> =-<1|\eta|1> But if \eta is a constant, then...

1. Let R be a relation on X that satisfies a) for all a in X, (a,a) is in R b) for a,b,c in X, if (a,b) and (b,c) in R, then (c,a) in R. Show that R is an equivalence relation. 2. In order for R to be an equivalence relation, the following must be true: 1) for all a in X, (a,a) is...

Where, on the internet, can one learn the method to solving equations modulus a number? I'd like to learn the method for finding such relations as this special case for the Erdos-Straus Conjecture, with n ≡ 2 (mod 3). Also, what is the technical name for finding the mod n relations in an...

First this is my first attempt at using latex to ask a question, so my appologies if the statements come out strange. I'll edit as needed. Homework Statement Let R and S be relations on a set A. Prove that if R \subseteq S, then R^{n} \subseteq S^{n} for all n \geq 1 Homework Equations...

Homework Statement A = {0, 1, 2, 3, 4 ,5} Let R be a binary relation on set A such that: R = {(0,1), (1,0), (1,3), (2,2), 2,1), 2,5), (4,4)} a. Make a Directed Graph for the relation R on A b. What must be added to R to make it reflexive/symmetric?

In Srednicki's book, he discusses quantizing a non-interacting spin-0 field \phi(x) by defining the KG Lagrangian, and then using it to derive the canonical conjugate momentum \pi(x) = \dot{\phi}(x). Then, he states that, by analogy with normal QM, the commutation relations between these fields...

Homework Statement I'm solving the quantum harmonic oscillator. And I'm solving Schrodinger equation. So I came up to one part where I have to use power series method of solving DE (that or Frobenius would probably work just fine). Now I have the recurrence relation...

Homework Statement [PLAIN]http://img530.imageshack.us/img530/6672/linn.jpg The Attempt at a Solution For parts (a) and (b) I've found the eigenvalues to be -\frac{1}{3} and -1 with corresponding eigenvectors \begin{bmatrix} -1 \\ 3 \end{bmatrix} and \begin{bmatrix} -1 \\ 1...