It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

Weconsider the Pottsmodelwith q colors on a sequence ofweighted graphs with adjacency matrices An , allowing for both positive and negative weights. Under a mild regularity condition on An we show that the mean-field prediction for the log partition function is asymptotically correct, whenever tr(An) = o(n). In particular, our results are applicable for the Ising and the Potts models on any seq...

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

We report our current research in a computer assisted methodology for synthesizing regular array processors using the Alpha language and design environment. The design process starts from an algorithmic level description of the function and nishes with a netlist of an array processor which performs the speciied function. To illustrate the proposed approach, we present the design of an array pro...

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Hoffman, Wolfe, and Ho...

In this paper we prove that random d–regular graphs with d ≥ 3 have traffic congestion of the order O(n log3d−1(n)) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ–hyperbolic for any non–negative δ almost surely as n→∞.

In 2006, Barát and Thomassen conjectured that the edges of every planar 4-regular 4-edgeconnected graph can be decomposed into claws. Shortly afterward, Lai constructed a counterexample to this conjecture. Using the small subgraph conditioning method of Robinson and Wormald, we find that a random 4-regular graph has a claw-decomposition asymptotically almost surely, provided that the number of ...

It has previously been shown that there exists a minimum degree ordering for regular grids that is considerably worse than nested dissection in terms of ll-in and operations for factorization 1]. This paper proves the existence of a minimum degree ordering for regular grids that has the same optimal asymptotic order complexity for ll-in and operation count as nested dissection. The analysis is ...

In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties eigenvalues and eigenfunctions for the strongly elliptic operator then obtain two existence theorems nontrivial solutions when nonlinearity is function with an asymptotically condition.