Consider a selfadjoint unbounded operator D on a Hilbert space H and a one parameter norm continuous family of selfadjoint bounded operators {A(t) | t ∈ R} that converges in norm to asymptotes A± at ±∞. Then under certain conditions [RoSa95] that include the assumption that the operators {D(t) = D + A(t), t ∈ R} all have discrete spectrum then the spectral flow along the path {D(t)} can be show...

Crawford, T., and Levene, C. I. (1952). 7. Path. Bact., 64, 523. Duguid, J. B. (1946). Ibid., 58, 207. Gunning, A. J., Pickering, G. W., Robb-Smith, A. H. T., and Russell, R. W. R. (1964a). Quart. 7. Med., 33, 133. (1964b). Ibid., 33, 155. McLetchie, N. G. B. (1952). Amner. 7. Path., 28, 413. Ross, J. P. (1936). Proc. roy. Soc. Med., 29, 872. Russell, R. W. R. (1963). Lancet, 2, 1354. Skovborg,...

Given two rooted, labeled trees P and T the tree path subsequence problem is to determine which paths in P are subsequences of which paths in T . Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.

— In this paper an algorithm for obtaining a Hamiltonian path from a shortest spanning tree ofa complete weighted graph isproposed. As a conséquence, two inequalities between the costs ofa shortest Hamiltonian path and a shortest spanning tree Tin the symmetrie EucUdean case are proposed. These inequalities involve the diameter of T or the number of terminal vertices of T and they become equali...

In a graph G with non-negative edge lengths, let P be a shortest path from a vertex s to a vertex t. We consider the problem of computing, for each edge e on P , the length of a shortest path in G from s to t that avoids e. This is known as the replacement paths problem. We give a linearspace algorithm with O(n log n) running time for n-vertex planar directed graphs. The previous best time boun...

A path to high assurance solutions C r y p t o l : T h e L a n g u a g e o f C r y p t o g r a p h y

ABSTRACT We propose a modified penalty embedding for solving complementarity problem (LCP). This embedding is a special one parametric optimization problem P(t), t∈[0,1]. Under the condition (A3) (a modified Enlarged Mangasarian Fromovitz Constrait Qualification), (A4) (P(t) is JongenJonker -Twilt regular) and two technical assumptions (A1) and (A2) there exists a path in the set of stationary ...

This article will generally follow the notation and terminology defined in [1]. A digraph is called strongly connected or strong if for every pari of vertices u and v there exists a directed path from u to v and a directed path from v to u. Let k be a positive integer. A digraph G is k-connected if the removal of any set of fewer than k vertices results in a strong digraph. A tournament with n ...