Coefficients Definition and 753 Threads

What the title states. Is it possible? I can't seem to find a way (at least, from the massive stash of PDF files I downloaded about VLE/EOS) on how to employ NRTL activity coefficients with the Soave-Redlich-Kwong EOS. In other words, is there a way to get the activity coefficient models like...

Hi, I came across this statement while I was reading an article on resolution of vector in arbitrary basis. "v = αa + βb + γc ---(1) , where a, b and c are three independent vectors. we observe that the coefficient α cannot involve any overlap of v with either b or c ; β cannot involve any...

I have a numerical simulation where I'm randomly varying an input parameter. This results in variations in three output parameters: A, B and C. The output parameters can be assumed to have normal distributions, but are correlated to each other. If I calculate the mean and standard...

Hey! :o I have to solve the following initial and boundary value problem: $$u_t=u_{xx}, 0<x<L, t>0 (1)$$ $$u(0,t)=u_x(L,t)=0, t>0$$ $$u(x,0)=x, 0<x<L$$ I did the following: Using the method separation of variables, the solution is of the form: $u(x,t)=X(x)T(t)$ Replacing this at $(1)$, we...

Hey! :o Having the problem: $$v_t=v_{xx}, 0<x<1, t>0$$ $$v(0,t)=v_x(1,t)=0, t>0$$ $$v(x,0)=e^x-x$$ I have found that the solution of the problem is of the form $$v(x,t)=\sum_{n=0}^{\infty}{A_n \sin{(\frac{(2n+1) \pi x}{2})} e^{-(\frac{(2n +1) \pi}{2})^2t}}$$ Using the boundary condition...

I'm looking at how a l j1,j2,jm> state can be operated on by the ladder operators, changing the value of m, and how this state can be expressed as a linear combination of l j1, j2, m1, m2> states. Where the following relationships must be obeyed (x2): m=m1+m2 l j1-j2 l ≤ j ≤ j1+j2 So...

The question asks to use Fresnel's equations at normal incidence to find the ratio of the refractive indexes of the two materials. We are told equal energy is transmitted and reflected and that both media are non-magnetic and non-conducting dielectrics. So I know that the ratio of Er/Ei and...

Hey! :o I have to solve the following boundary value problem: $$u_{xx}+=u_{yy}=0, 0<x<a, 0<y<b$$ $$u_x(0,y)=u_x(a,y)=0, 0<y<b$$ $$u(x,0)=x, u_y(x,b)=0, 0<x<a$$ By using the method of separation of variables, the solution is of the form $u(x,y)=X(x)Y(y)$. By substituting this it the problem we...

Problem: Evaluate $$\mathop{\sum \sum}_{0\leq i<j\leq n} (-1)^{i-j+1}{n\choose i}{n\choose j}$$ Attempt: I wrote the sum as: $$\sum_{j=1}^{n} \sum_{i=0}^{j-1} (-1)^{i-j+1}{n\choose i}{n\choose j}$$ I am not sure how to proceed from here. I tried writing down a few terms but that doesn't seem...

Hi, I have looked everywhere. Can someone please point me in the right direction for solving a system of ODEs with variable coefficients? I managed to solve such system with constant coefficients.

Homework Statement 1) Find the general solution of y''+ω02=Ccos3(ωx) 2) Show there exists two frequencies at which resonance occurs and determine them The Attempt at a Solution I've tried the method of undetermined coefficients, assuming a solution of the form y=(Acos(ωx)+Bsin(ωx))3...

Homework Statement The task is to calculate the transmission probability when E<V0 given that the step potential barrier is of infinite length. Homework Equations So far it seems simple enough. For region I, where x<0, (we're assuming, as usual, that the particles/ waves are coming...

Most of this post is an overview. The actual question is at the end. Basically: If I am given crazy summations with lots of indices cycling through multiple matrices, is there a quick way I can implement this in Mathematica? So, I am doing a little bit of research into nonholonomic...

Homework Statement Problem: Find the first eight coefficients (i.e. a_0, a_1, a_2, ..., a_7) of the power series expansion y = ##Σ_{n = 0}^{∞}## [##a_n## ##x^n##] of the solution to the differential equation y'' + xy' + y = 0 subject to the initial-value conditions y(0) = 0, y'(0)...

Evaluate $\displaystyle\lower0.5ex{\mathop{\large \sum}_{n=2009}^{\infty}} \dfrac{1}{n \choose 2009}$.

Homework Statement I have got this circuit: I have to find coefficients k1 and k2, and time constants T1 and T2. Actually, we can see that T1 =R1*C1 and T2=R2*C2, but is it possible in this circuit or it's just theoretically time constants? I'm not sure, but as there is no amplifier in...

I have been trying to follow how the complex Fourier coefficients are obtained; the reference I am using is at www.thefouriertransform.com. However I am unable to follow the author's working exactly and wondered if anyone could help me see where I am going wrong. First, I understand that the...

Homework Statement A computer scientist has dropped a tiny pizza crumb onto a magnetic disk. Later, when it's turned on, the disk is rotating at 88 revolutions per second about its axis, which is vertical. The coefficients of kinetic and static friction between pizza crumbs and the disk are...

Using correlation coefficients as x in a regression?? I was reading an article in the Wall street journal and the author was using a rolling correlation coefficient, on a set of variables, as his predictor variable in a linear regression. Basically it was a uni-variate linear regression , y=...

Hey! :o $f(x)=\sum_{i=0}^{7}{a_ix^i}, g(x)=\sum_{i=0}^{5}{b_ix^i}$, $a_i, b_i$ are integer coefficients. The prime $p$ divides $a_0, a_1, a_2, a_3, a_4$ but it does not divide $a_5, a_6, a_7$. $p$ divides also $b_0, b_1, b_2$, but it does not divide $b_3, b_4, b_5$. $h(x)=f(x)g(x)$ Show that at...

Homework Statement consider y'' + 2y' - 3y = 1 + xe^x, find the particular solution The Attempt at a Solution so f(x) = 1 + xe^x f'(x) =e^x + xe^x f''(x) = 2e^x + xe^x so it looks like my particular solution is going to have a constant term, an e^x term and an xe^x term, so I can...

Homework Statement The value of ((^n C_0+^nC_3+...) - \frac{1}{2} (^nC_1+^nC_2+^nC_4+^nC_5+...))^2 + \frac{3}{4} (^nC_1-^nC_2+^nC_4-^nC_5...)^2 The Attempt at a Solution I can see that in the left parenthesis, the first bracket contains terms which are multiples of 3 and in the second...

Problem: Let $\displaystyle (3x^2+2x+c)^{12}=\sum_{r=0}^{24} A_rx^r$ and $\dfrac{A_{19}}{A_5}=\dfrac{1}{2^7}$, then $c$ is A)4 B)5 C)6 D)7 Attempt: One way I know of to solve such a problem is by using the multinomial theorem but I am reluctant to use it here. It would take a lot of time to...

Homework Statement "Suppose x[n] is a DT (discrete time) periodic signal with fundamental period N. Let us define x_{n}[n] to be x[n] for n ε {0, 1,2, ... , N-1} and zero elsewhere. Denote the Fourier transform of x_{n}[n] with X_{n}[e^jω]. How can one find the Fourier Series coefficients...

Hi, I want a software that can generate aerodynamic coefficients (CD, CL, CY,Cl,Cm,Cn, etc) I am aware of some specialized software (e.g. AVL, open source from MIT, LinAir Pro, commercial, etc). But was wondering whether I can use 'common' software like AutoCAD Mechanical or Solidworks...

How to find the Glebsch Gordan coefficients by matrix form. Let's suppose we have a two spin 1/2 particles, we get that (check attachment 1). These are the corresponding coefficients the classic way. Now if I want find them the matrix way, where the matrix should be diagonalized. How do I...

Homework Statement y'' + y = xsinx where y(0) = 0 and y'(0) = 1 Homework Equations yc = C1sinx + C2cosx The Attempt at a Solution So my attempt includes the yc which undoubtedly is correct. I now try to solve yp yp = Axsinx + Bxcosx y''p = A(2cosx - xsinx) + B(-2sinx -...

A 1000 kg car is moving at 10 m/s, the car applies the brakes and begins to skid and leave a mark. the first 4 m of the surface has a coefficient of 0.35 and after that the coefficient of friction is 0.2. What is the total distance the car will slide when coming to rest? Equations: F=ma...

Homework Statement Prove by induction that for any positive integers a, b, and n, (a choose 0)(b choose n) + (a choose 1)(b choose n-1) + ... + (a choose n)(b choose 0) = (a+b choose n) Homework Equations (x choose y) = (x!)/((x-y)!y!) The Attempt at a Solution I am able to do the...

Contemporary Abstract Algebra by Gallian This is Exercise 14 Chapter 3 Page 69 Question Let $G$ be the group of polynomials under the addition with coefficients from $Z_{10}$. Find the order of $f=7x^2+5x+4$ . Note: this is not the full question, I removed the remaining parts. Attempt...

Hello, I had a question about the method of undetermined coefficients for solving ODE's. I understand it is only useful for certain non-homogeneous functions, and those dictate specific guesses, but what if I had a sum or product of two valid functions, is the guess simply a sum or product of...

For a simple linear model: \alpha+\beta\times x=y If it is observed that y \in (-8.51,23.20) given x=4 The question is to give intervals of \alpha, \beta, which satisfy y \in (-8.51,23.20) given x=4. Is this problem identifiable? Can it be found the unique intervals for \alpha...

Homework Statement Compute the 2nd and 3rd Virial coefficients at 300K of Ar. Experimental parameters are mentioned in xlist and ylist below :) Homework Equations My professor has given a hit, which is as follows: "Use the data to determine the (z) compressability (sp?) and plot Z as a...

Homework Statement In oppgave 1 a) I am supposed to show that the given equality is true (namely that the isoterm compressibility coefficient partial-differentiated with regards to temperature = isobar coefficient differentiated with regards to pressure multiplied by minus one)...

hey pf! okay, so if you've studied PDEs you know the value of a Fourier series, and the difficulty of determining a Fourier coefficient. my question relates to finding this coefficient. briefly, i'll define a Fourier series as f(x)=\sum_{n=0}^{\infty} A_n\cos\frac{n\pi x}{L}+B_n\sin\frac{n\pi...

Homework Statement x(t) = 4 for 0 <x<1 and 0 otherwise and this process repeats for all values including negative. find X_0 and X_n and find the first 6th harmonics of the Fourier series in cosine form Homework Equations The Attempt at a Solution x_0 = 4/3 x_n =...

Greetings! Going throught Ballentine Ch.4 and the derivation of transmission/reflection coefficients. The math seems fairly straightforward: assuming a particle in a piecewise-constant potential, the solution of the correspondent time-independent SE is a piecewise-exponential wavefunction in...

Homework Statement Let ##f## be a ##2\pi## periodic function. Let ##\hat{f}(n)## be the Fourier coefficient of ##f## defined by $$ \hat{f}(n)=\frac{1}{2\pi}\int_{a}^{b}f(x)e^{-inx}dx. $$ for ##n\in\mathbb{N}##. If ##\overline{\hat{f}(n)}=\hat{f}(-n)## show that ##f## is real valued. The...

x = 1x x(x-1) = 1x^2 - 1x x(x-1)(x-2) = 1x^3 - 3x^2 + 2x x(x-1)(x-2)(x-3) = 1x^4 - 6x^3 + 11x^2 - 6x x(x-1)(x-2)(x-3)(x-4) = 1x^5 - 10x^4 + 35x^3 - 50x^2 + 24x ... So, I am looking for a short method how to find these coefficients ahead of each raisings of x: 1 1,-1 1,-3,2 1,-6,11,-6...

There is a trinomial theorem relationed with the Pascal's tetrahedron, so that... (x+y+z)^5= \\ +01x^5y^0z^0+05x^4y^1z^0+10x^3y^2z^0+10x^2y^3z^0+05x^1y^4z^0+01x^0y^5z^0 \\ +05x^4y^0z^1+20x^3y^1z^1+30x^2y^2z^1+20x^1y^3z^1+05x^0y^4z^1 \\ +10x^3y^0z^2+30x^2y^1z^2+30x^1y^2z^2+10x^0y^3z^2 \\...

Hello, 1. Homework Statement [/b] http://imageshack.com/a/img17/2531/gu44.png Uploaded with ImageShack.com[b] I'm trying to prove this but i didn't succeed Homework Equations The Attempt at a Solution For the t I multiplied by sin(θt) in the numerator and denominator and used...

I have found an expression for the estimated energy contribution a term |I> will bring to a wavefunction |K> \Delta E = \frac{|\langle I|\hat{H}| K\rangle|^2}{(E_K - \langle I |\hat{H}| I\rangle)} Is there a simple way to extract the coefficient that will be associated with |I>? Even a link...

Homework Statement In the dirac notation, inner product of <f|g> is given by ∫f(x)*g(x) dx. Why is there a 1/∏ attached to each coefficient an, which is simply the inner product of f and that particular basis vector: <cn|f>? Homework Equations The Attempt at a Solution

Given $f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0$, where $a_0, a_a,\cdots,a_n$ are all smaller than 4 and are integer, $a_n \in (0, 1, 2,\cdots)$. Given that $f(4)=2009$, find $f(1)$.

Background: My lab group has taken a number of measurements of gas levels over 15 minute period every 15 seconds. We actually used a gas sensor and computer interface to do it so it pretty much did all the work. In calculating the errors for the data, using the uncertainties given in the user...

Hi all, I am trying to figure out if there is a pre-existing theorem and proof of whether or not each of the binomial coefficients in a binomial expansion of (a +b)^n are divisible by n, particularly in the case where n is a prime number. Has this already been asked and answered somewhere in...

Homework Statement f(t) a continuously differentiable function twice over the circle T1 cr its Fourier coefficients and σn(f,t) partial sum of Fejer. a.Demonstrate that http://imageshack.us/a/img94/5992/ds35.png b. Consider k as -n≤k≤n , using cr coefficients calculate...

1. Background/theory We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then x1 + x2 + x3 = -p x1x2 + x2x3 + x3x1 = q x1x2x3 = -r 2. Problem statement Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r. That is, I'm supposed to find the discriminant of...

Something wrong with a "proof" relating to Laurent coefficients Homework Statement Let f(z) have an isolated singularity at z_0 and suppose that f(z) is bounded in some punctured neighborhood of z_0. Prove directly from the integral formula for the Laurent coefficients that a_(-j) = 0 for all...

Homework Statement I have 3 equations: \frac{\partial^2 u}{\partial t^2}+\frac{\partial^2 u}{\partial x \partial t}+\frac{\partial^2 u}{\partial x^2} \frac{\partial^2 u}{\partial t^2}+4\frac{\partial^2 u}{\partial x \partial t}+4\frac{\partial^2 u}{\partial x^2} \frac{\partial^2...