Recent content by sigh1342

Homework Statement Show that S is open if and only if ∀x ∈ S, ∃ a open ball B(x; r)(r > 0) such that B(x; r) ⊂ S And what we have is , let X be normed space, S ⊂X , Then S is close if and only if $$∀{x_{n}}⊂X, s.t. x_{n}->x \in X$$, x∈ S. A set S is open if and only if X\S is close...

um,, I just want to know how can I find such K and f... Thanks you.:)

Homework Statement I found that the blurred image is always presented by $$A=Ku+f$$, where u is the perfect image source, and the K is transformation (blurring, sampling) and f is the noising . The question I want to know is how can we find such K, or f when we blurred the image , for...

Actually the method I want to use need the boundary condition be all zero. like the 1D case , $$u_{xx}=0 ,a<x<b, u(a)=\alpha, u(b)=\beta$$ the we can use $$u'=u-\beta+\frac{(x-b)(\beta-\alpha)}{a-b}$$ so $$u'_{xx}=0 , a<x<b , u'(a)=0, u'(b)=0$$ I would want to find whether there are similar...

I want to find some application of the laplace equation on semi-infinite plate on physics where the PDE is looke like $$u_{xx}+u_{yy}=f , for a<x<\infty , c<y<d$$ $$u(a,y)=g(y), u(x,c)=f_{1}(x), u(x,d)=f_{2}(x)$$ $$\lim_{x->\infty} f(x)=\lim_{x->\infty} f_{1}(x)=\lim_{x->\infty}...

Homework Statement now I have a PDE $$u_{xx}+u_{yy}=0,for 0<x,y<1$$ $$u(x,0)=x,u(0,y)=y^2,u(x,1)=0,u(1,y)=y$$ Then I want to know whether there are some method to make the PDE become homogeneous boundary condition. $$i.e. u|_{\partialΩ}=0$$

Homework Statement In$$ M/M/1/FCFS/c/\infty $$ I don't know what is offered load and effective load. Wiki say offered load is equal to the expected number in the system, and I found offered load is equal to the ρ=λ/μ, where λ is the average arrive rate. And the μ is the average service time...

Oh I find that the value $$x^tAx$$ that I was computed is wrong . :frown: Thanks you so much :-p

Homework Statement show SOR iteration method converges for the system. $$6x+4y+2z=11$$ $$4x+7y+4z=3$$ $$2x+4y+5=-3$$ Homework Equations if the coeff. matrix is positive definite matrix and 0≤ω≤2. Then SOR converge for any initial guess. Or if $$ρ(T_{ω})$$≥|ω-1|, then SOR converge...

For possion equation $$u_{xx}+u_{yy}=f$$ I know the general five point scheme is in the form $$a_{1}U_{i,j-1}+a_{2}U_{i-1,j}+a_{3}U_{i,j}+a_{4}U_{i+1,j}+a_{5}U_{i,j+1}=f_{i,j}$$ But , is there have the form...

it's ok now , I got it , no need to answer this post , thank you lol

shooting method for non-linear equation(urgent) Homework Statement for shooting method , in non-linear equation, we're find $$t_{k}=t_{k-1}-\frac{[y(b,t_{k-1})-β](t_{k-1}-t_{k-2})}{y(b,t_{k-1})-y(b,t_{k-2})}$$ but how can we find the $$y(b,t_{k})$$ ? I am suppose to use Euler method for...

second order pde -- on invariant? What the meaning for a second order pde is rotation invariant? Is all second order pde are rotation invariant? or only laplacian?

Thanks Ray. Following your approach, I've found there are 14 patterns in total. So is that the total number of pipes, z = sum(i = 1 to 14) x_i and my objective is to minimize z on x_i's? And how about the constraints? I don't know how to make use of the proportion(2:4:1) to establish my...

Homework Statement A factory has stocked a lot of pipes (sufficient). Each standard pipe is 5-meter long. But this kind of pipe cannot be used directly. We should cut them into three types: 140cm, 95cm and 65cm. In addition, the proportion of these three types of pipes must be 2:4:1. In...