In a ring LAN, performance characteristics such as message transfer time, throughput, and bandwidth utilization depend on its station permutation. As ring LANs adopt fiber optics or other high speed transmission media, extend their geographical coverage, and hence contain more stations, such a dependency becomes more significant. The paper formulates the ring performance optimization problem associated with such a dependency, proves the NP-completeness of the problem, and establishes an integer programming model for solving the problem.< >

The authors consider the problem of finding u=u(x, t) and p=p(t) which satisfy u = Lu + p(t) + F(x, t, u, x, p(t)) in Q T=Ω×(0, T], u(x, 0)=ø(x), x∈Ω, u(x, t)=g(x, t) on ∂Ω×(0, T] and either ∫G(t) Φ(x,t)u(x,t)dx = E(t), 0 ⩽ t ⩽ T or u(x0, t)=E(t), 0≤t≤T, where Ω∋R n is a bounded domain with smooth boundary ∂Ω, x 0∈Ω, L is a linear elliptic operator, G(t)∋Ω, and F, ø, g, and E are known functions. For each of the two problems stated above, we demonstrate the existence, unicity and continuous dependence upon the data. Some considerations on the numerical solution for these two inverse problems are presented with examples.

A method is presented for the numerical solution of the diffusion equation ut = uxx + ƒ(x, t), 0 < x < 1, 0 < t ≤ T, subject to u(x, 0) = v(x), 0 < x < 1, and nonlocal boundary specifications u(0,t)=∫01φ(x,t)u(x,t)dx, 0<≤T,u(1,t)=∫01ψ(x,t)u(x,t)dx, 0<≤T. Some numerical experiments are also presented.

A finite-difference solution is demonstrated for an inverse problem of determining a control function p(t) in the parabolic partial differential equation ut=uxx+pu+f(x,t), 0