We consider a constrained equational logic where the constraints are membership conditions t 2 s where s is interpreted as a regular tree language. Our logic includes a fragment of second order equational logic (without projections) where second order variables range over regular sets of contexts. The problem with constrained equational logics is the failure of the critical pair lemma. That is ...

We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear rod compressed by axial forces, and a planar circular ring subjected to uniform radial pressure on its outer perimeter. It is demonstrated that while spontaneous twi...

In the binary decision diagram–based terminal-pair network reliability analysis, the size of binary decision diagram heavily depends on the chosen edge ordering. From a theoretical point of view, finding the best ordering is an intractable task. Therefore, heuristics have been used to obtain reasonably good orderings. Among them, the breadth-first search heuristic typically outperforms other he...

Let be a distance-regular graph of diameter d, valency k and r := max{i | (ci , bi ) = (c1, b1)}. Let q be an integer with r + 1 ≤ q ≤ d − 1. In this paper we prove the following results: Theorem 1 Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 ≤ i ≤ q and for any pair of vertices at distance i ...

The concepts of k-pairable graphs and the pair length of a graph were introduced by Chen [Discrete Math. 287 (2004), 11–15] to generalize an elegant result of Graham et al. [Amer. Math. Monthly 101 (1994), 664– 667] from hypercubes and graphs with antipodal isomorphisms to a much larger class of graphs. A graph G is k-pairable if there is a positive integer k such that the automorphism group of...

We bound the diameter of a distance-regular graph in which two subdegrees are equal.

In the studies of acoustic waveguides in ocean, buckling of columns with variable cross sections in applied elasticity, transverse vibrations in non-homogeneous strings, etc., we encounter a new class of problems of the d2 yl X-2-rUl()Yl-"Yl defined on an interval [dl,d2] and type L lyldy L2Y2 + q2(x)y2 .y2 on the adjacent interval [d2, d3] satisfying certain matching conditions at the interfac...

The design, implementation and performance of a parallel algorithm for reduction of a matrix pair in block upper Hessenberg-Triangular form (Hr, T ) to upper Hessenberg-triangular form (H, T ) is presented. This reduction is the second stage in a two-stage reduction of a regular matrix pair (A, B) to upper Hessenberg-Triangular from. The desired upper Hessenberg-triangular form is computed usin...

We consider a reductive dual pair (G,G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K ′ C-orbits, where K ′ is a maximal compact subgroup of G′ and we describe the precise KC-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G,K). As an application, we pro...