题目4953 · 数学
Boundary Eigenvalue 3
For y'' + λ y = 0 on [0,1] with y'(0)=0 and y(1)=0, what is the 1-th positive eigenvalue?
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中文题目For y'' + λ y = 0 on [0,1] with y'(0)=0 and y(1)=0, what is the 1-th positive eigenvalue?
打开 →For y'' + λ y = 0 on [0,1.5] with y(0)=0 and y(1.5)=0, what is the 2-th positive eigenvalue?
打开 →For y'' + lambda y = 0 on [0,L] with y(0)=0 and y(L)=0, the first positive eigenvalue is lambda_1 = (pi/L)^2. If lambda_1 = 4*pi^2, what is L?
打开 →For y'' + lambda y = 0 on [0,L] with Dirichlet endpoints, the first positive eigenvalue is lambda_1 = (pi/L)^2. If lambda_1 = pi^2/4, what is L?
打开 →On an undirected graph, each edge $\{u,v\}$ has a positive conductance $c_{uv}=c_{vu}$. The chain moves from $u$ to $v$ with probability \[ P(u,v)=\frac{c_{uv}}{\sum_w c_{uw}}. \] Find the stationary distribution.
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