Let PG(s, t) denote a shortest path between two nodes s and t in an undirected graph G with nonnegative edge weights. A detour at a node u ∈ PG(s, t) = (s, . . . , u, v, . . . , t) is defined as a shortest path PG−e(u, t) from u to t which does not make use of (u, v). In this paper, we focus on the problem of finding an edge e = (u, v) ∈ PG(s, t) whose removal produces a detour at node u such t...

A digraph G = (V, E) with a distinguished set T ⊆ V of terminals is called inner Eulerian if for each v ∈ V − T the numbers of arcs entering and leaving v are equal. By a T -path we mean a simple directed path connecting distinct terminals with all intermediate nodes in V −T . This paper concerns the problem of finding a maximum T -path packing, i.e. a maximum collection of arc-disjoint T -path...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger's equation, which is half of the defining equations of Bohmian mechanics. I try ...

Let D be an open subset of a real uniformly smooth Banach space E. Suppose T : D̄ → E is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where D̄ denotes the closure ofD. Then, it is proved that (i) D̄ ⊆ (I + r(I −T)) for every r > 0; (ii) for a given y0 ∈ D, there exists a unique path t → yt ∈ D̄, t ∈ [0,1], satisfying yt := tT yt + (1− t)y0. Moreover, if F(T) = ∅ o...

In this paper we consider the following modification of the iterative search problem. We are given a tree T , so that a dynamic catalog C(v) is associated with every tree node v. For any x and for any node-to-root path π in T , we must find the predecessor of x in ∪v∈πC(v). We present a linear space dynamic data structure that supports such queries in O(t(n) + |π|) time, where t(n) is the time ...

Feynman's path integrals provide a hidden variable description of quantum mechanics (and quantum field theories). The expectation values defined through path integrals obey Bell's inequalities in Euclidean time, but not in Minkowski time. This observation allows us to pinpoint the origin of violation of Bell's inequalities in quantum mechanics. It is common, and often more convenient, to study ...