Abstract. Let L be a lattice and M a bounded distributive lattice. Let ConL denote the congruence lattice of L, P (M) the Priestley dual space of M , and L (M) the lattice of continuous order-preserving maps from P (M) to L with the discrete topology. It is shown that Con(L ) ∼= (ConL) P (ConM) Λ , the lattice of continuous order-preserving maps from P (ConM) to ConL with the Lawson topology. V...

Let H = −∆ + V be a Schrödinger operator on L(R) with real-valued potential V , and let H0 = −∆. If V has sufficient pointwise decay, the wave operators W± = s − limt→±∞ eitHe−itH0 are known to be bounded on L(R) for all 1 < p < ∞ if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on L(R) for...

We prove that there does not exist an orthonormal basis {bn} for L(R) such that the sequences {μ(bn)}, {μ(c bn)}, and {∆(bn)∆( bn)} are bounded. A higher dimensional version of this result that involves generalized dispersions is also obtained. The main tool is a time-frequency localization inequality for orthonormal sequences in L(R). On the other hand, for d > 1 we construct a basis {bn} for ...

We study the parameterized complexity of two families of problems: the bounded length disjoint paths problem and the bounded length cut problem. From Menger’s theorem both problems are equivalent (and computationally easy) in the unbounded case for single source, single target paths. However, in the bounded case, they are combinatorially distinct and are both NP-hard, even to approximate. Our r...

We show that the L-torsion of finite aspherical CW-complexes with boundedly measure equivalent fundamental groups agrees up to a factor given by the index of the measure equivalence.

If all bounded linear operators from L 1 into a Banach space X are Dunford-Pettis (i.e. carry weakly convergent sequences onto norm convergent sequences), then we say that X has the complete continuity property (CCP). The CCP is a weakening of the Radon-Nikod ym property (RNP). Basic results of Bourgain and Talagrand began to suggest the possibility that the CCP, like the RNP, can be realized a...

Motivated by the recent result of [EJT10] showing that MSO properties are Logspace computable on graphs of bounded tree-width, we consider the complexity of computing the determinant of the adjacency matrix of a bounded tree-width graph and prove that it is L-complete. It is important to notice that the determinant is neither an MSO-property nor counts the number of solutions of an MSO-predicat...

for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...

We give a new proof of the Dalang-Morton-Willinger theorem, relating the no-arbitrage condition in stochastic securities market models to the existence of an equivalent martingale measure with bounded density for a d-dimensional stochastic sequence (Sn) N n=0 of stock prices. Roughly speaking, the proof is reduced to the assertion that under the no-arbitrage condition for N = 1 and S ∈ L there ...

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). A finitely additive probability P on A such that P ∼ P0 and EP (X) = 0 for each X ∈ L is called EMFA (equivalent martingale finitely additive probability). In this paper, EMFA’s are investigated in case P0 is atomic. Existence of EMFA’s is characterized and a question raised in [3] is answered. Some res...