Statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable estimates of Lyapunov exponents χ in lower-dimensional Hamiltonian systems. This Letter explores the assumptions incorporated into these arguments. The predicted χ’s are insensitive to most details, but do depend sensitively on the nongeneric form of the auto-correlation function characte...

The aim of this paper is to introduce semi strong na continuous multifunctions and to obtain new results.

defined over Sobolev spaces is connected to the convexity of the potential w. In the scalar case, that is for functions u with domain or range in R, the functional I is weakly W 1,p lower semi-continuous (weakly * W ) if and only if w is convex, provided it is continuous and satisfies some growth conditions. The notion which replaces convexity in the vector case is quasi-convexity (introduced b...

Semi-algebraic proof systems were introduced in [1] as extensions of Lovász-Schrijver proof systems [2,3]. These systems are very strong; in particular, they have short proofs of Tseitin’s tautologies, the pigeonhole principle, the symmetric knapsack problem and the cliquecoloring tautologies [1]. In this paper we study static versions of these systems. We prove an exponential lower bound on th...

In this paper we will present class of new lower bounds for the Quadratic Semi-Assignment Problem (QSAP). These bounds are based on recent results about polynomially solvable cases, in particular we will consider the QSAP's whose quadratic cost coefficients define a reducible graph. Several lower bounds will be computationally compared, moreover we will present a method which improves these bou...

The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semiunbounded fan-in. It follows that the inclusions NC ⊆ SAC ⊆ AC are proper in the monotone setting, for every i ≥ 1. Mathematics Subject Classification. 68Q17, 68Q15.

In this paper we show that equi-lsc. functions from a topological vector space X to the extended reals are epi-compact without assuming the local compactness or the second countablity of the underlying space X. We also show that weakly equi-lower semicontinuous functions from a Banach space X to the extended reals are Mosco-compact. Finally, we apply these results to prove the Mosoc-compactness...

We define a convex extension of a lower-semicontinuous function to be a convex function that is identical to the given function over a pre-specified subset of its domain. Convex extensions are not necessarily constructible or unique. We identify conditions under which a convex extension can be constructed. When multiple convex extensions exist, we characterize the tightest convex extension in a...