In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

In the first half of this paper, a Fubini type identity in law which was previously developed by two of the authors between quadratic functionals of Brownian motion is extended in two directions: an analogue of this identity in law holds when Brownian motion is replaced by a symmetric stable process of any order a E (0,2), provided the function: x -* x2 is replaced by: x -> I x la; such Fubini ...

For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the Bell inequality holds, unless non-local interactions exist between certain parts of the setup. Here we show that in nonlinear systems the Bell inequality can be violated by non-local effects that are arbitrarily weak. Then we show that the quantum result of the existing Einstein-PodolskyRosen-type experiments can be r...

0. Introduction. The purpose of this chapter is to give a detailed account of the known evidence ([Be1], §5) for Beilinson’s conjecture concerning the values at s = 2 of L-functions of modular forms of weight two. We do not discuss here the results concerning the L-values at other integers s ≥ 2 (for which see [Be2]), nor do we treat the case of the product of two modular curves (also to be fou...

1 Hamiltonian Cycle “Non-local” problems can also be NP-hard. Recall that a Hamilton cycle is one where all vertices is visited exactly once. Name: HC Input: A graph G. Output: Does G contain a Hamiltonian cycle? In other words, HC is asking whether the longest cycle in G has length n. This problem is “non-local” in the sense that the constraint involves all vertices (a.k.a. global). Theorem 1....

Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The...

In this paper we settle the open problem of proving Prohorov’s theorem for transition probabilities (alias Young measures) in its most general form, viz. in the case where the transition probabilities act into a completely regular Suslin space. Among others, the present author and C. Castaing have considered this problem (in [9, p. 5.17] it is said to seem ”difficult”). Versions of Prohorov’s t...

Let (; x) be an eigenpair of the Hermitian matrix A of order n and let (; u) be a Ritz pair from a subspace K of C 2. Saad has given a simple inequality bounding sin \(x; u) in terms of sin \(x; K). In this note we show that this inequality can be extended to an equally simple inequality for eigenspaces of non-Hermitian matrices. ABSTRACT Let (; x) be an eigenpair of the Hermitian matrix A of o...

The assumptions needed to prove Cox’s Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural. I recently wrote a paper (Halpern, 1999) casting doubt on how compelling a justification for probability is provided by Cox’s celebrated theorem (Cox, 1946). I have received (w...