Sufficient conditions for the existence of at least one solution of anti-periodic boundary value problems for nonlinear functional difference equations are established. We allow f to be at most linear, superlinear or sublinear in obtained results.

Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors.

We consider a generalized form of the coupon collection problem in which a random number, S, of balls is drawn at each stage from an urn initially containing n white balls (coupons). Each white ball drawn is colored red and returned to the urn; red balls drawn are simply returned to the urn. The question considered is then: how many white balls (uncollected coupons) remain in the urn after the ...

In the problem size-ensemble size plane, fixed-sized and scaled-sized paradigms have been the subsets of primary interest to the parallel processing community. A problem with the newer scaled-sized model is that execution time increases for problems where operation complexity grows faster than storage complexity. The fixed time model is introduced, which, unlike the scaled model, implies the ne...

In the distributed subgraph-freeness problem, we are given a graph H , and asked to determine whether the network graph contains H as a subgraph or not. Subgraph-freeness is an extremely local problem: if the network had no bandwidth constraints, we could detect any subgraph H in |H| rounds, by having each node of the network learn its entire |H|-neighborhood. However, when bandwidth is limited...

We develop and analyze a superlinearly convergent aane-scaling interior-point Newton method for innnite-dimensional problems with pointwise bounds in L p-space. The problem formulation is motivated by optimal control problems with L p-controls and pointwise control constraints. The nite-dimensional convergence theory by Coleman and Li (SIAM J. Optim., 6 (1996), pp. 418{445) makes essential use ...

The Central Limit Theorem is studied for stationary sequences that are sums of countable collections of linear processes. Two sets of sufficient conditions are obtained. One restricts only the coefficients and is shown to be best possible among such conditions. The other involves an interplay between the coefficients and the distribution functions of the innovations and is shown to be necessary...

In this paper we deal with the solution, by means of preconditioned conjugate gradient (PCG) methods, of n × n symmetric Toeplitz systems An(f)x = b with nonnegative generating function f . Here the function f is assumed to be continuous and strictly positive, or is assumed to have isolated zeros of even order. In the first case we use as preconditioner the natural and the optimal τ approximati...

Regularized and stabilized sequential quadratic programming (SQP) methods are two classes of methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a stabilized SQP method has been proposed that allows convergence to points satisfying certain secondorder KKT conditions (Report CCoM 13-04, Center f...