Recent content by ymhiq

Excuse me all of you. Finally I got the mistake I made solved. It was an incorrect solutions of ƒ'(x0-α∇ƒ(x0))=-5+30α-24α2 .

Oh! Excuse me! You are right! However I made a mistake when I wrote the original problem. Let me write it again. I have to minimize the function ƒ(x1,x2)=(x1-1)2+x23-x1x2. The initial point is [1,1]T.

1. Homework Statement I have to minimize the function (x1-1)2+x23+x1x2 by the steepest descent method. The initial point is [1,1]T Homework EquationsThe Attempt at a Solution The gradient of this function is ∇ƒ(x1,x2)=[2(x1-1)-x2 3x22-x1]. This...

Homework Statement How do you explain that crystalline melting temperature Tf of PE is greater than the Tf of PEO? How do you explain that the glass transition temperature of PP is lower than the glass transition temperatures of PVC and PS? Homework Equations None The Attempt at a Solution...

Thanks a lot HallsofIvy, I was here before your suggestions: -\int^{1}_{0}v(x)a(x)\frac{d[u^{2}(x)]}{dx^{2}}dx-\int^{1}_{0}v(x)\frac{d[a(x)]}{dx}\frac{d[u(x)]}{dx}dx=\int^{1}_{0}v(x)f(x)dxI applied them on the integrals of the LHS of this equation and did the math, I came up with this...

Homework Statement Hello, I have to demonstrate that multiplying a differential equation: -d/dx[a(x)*d/dx{u(x)}]=f(x), 0<x<1 subject to u(0)=0 and u(1)=0. by some function v(x) and integrating over an interval [0,1], I get a new equation that can be used in an optimisation problem, that...

Homework Statement Toluene (C6H5CH3) is hydrogenated according to the two simultaneous chemical reactions C6H5CH3 + H2 → C6H6 + CH4 2C6H5CH3 + H2 → (C6H5)2 + 2CH4 Initially, the reactor contains 40% toluene and 60% H2 (% mole). At the end of the operation, the reactor contains 10% toluene and...

Would it be correct if I'd wrote something like: Kc = k+/k- = Ka/[{(ƩCj)^(-ƩSj)}*{∏(P^Sj)}*{∏(∅j^Sj)}] ? Here, P is total pressure and ∅j is the fugacity coefficient of j.

Yes, Indeed. All of them are equilibrium constants for chemical reactions. Kc is the most used. It is based on concentration or molarities. Kc=∏(cj^Sj) where Sj is the stoichiometric coefficient of j chemical compound and Cj is its concentration. Concentration is often written as [j]. It has...

Thanks for your reply, I knew that but my doubt is exactly if Ke=Ka=Kc=Kx=Kp=(k+/k-) but in advance I Know that Ka≠Kc≠Kx≠Kp so the statement Ke=k+/k- is valid only valid for Kc according to my findings in literature. What about the others equilibrium constants? Is this statement valid for them...

Is the statement Ke=k+/k- valid for all equilibrium constants like Ka, Kx, Kp, Kc? All of the expressions I have found for this statement relate Kc, k+ and k- only.