In a pure functional language like Clean the values of the functional variables are constants; variables of functional programs do not change in time. Hence it seems that temporality has no meaning in functional programs. However, in certain cases (e.g. in interactive or distributed programs, or in ones that use IO) we would like to consider a series of values computed from each other as differ...

Van der Waals forces are among the weakest, yet most decisive interactions governing condensation and aggregation processes and the phase behaviour of atomic and molecular matter. Understanding the resulting structural motifs and patterns has become increasingly important in studies of the nanoscale regime. Here we measure the paradigmatic van der Waals interactions represented by the noble gas...

We propose a very simple modification of Kreisel’s modified realizability in order to computationally realize Markov’s Principle in the context of Heyting Arithmetic. Intuitively, realizers correspond to arbitrary strategies in Hintikka-Tarski games, while in Kreisel’s realizability they can only represent winning strategies. Our definition, however, does not employ directly game semantical con...

A purely atomic superprocess with dependent spatial motion is characterized as the pathwise unique solution of a stochastic partial differential equation, which is driven by a time-space white noise defining the spatial motion and a sequence of independent Brownian motions defining the branching mechanism. AMS Subject Classifications: Primary 60J80, 60G57; Secondary 60J35

The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial differential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measure-valued process which is the unique strong solution of a reconstructed, associated SDSPDE.

Throughout this paper A is a finite von Neumann algebra and tr :A −→ C is a finite normal faithful trace. Recall that a von Neumann algebra is finite if and only if it possesses such a trace. Let l2(A) be the Hilbert space completion of A which is viewed as a pre-Hilbert space by the inner product 〈a, b〉 = tr(ab∗). A finitely generated Hilbert A-module V is a Hilbert space V together with a lef...

Several necessary and suucient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any uniformly autocontinuous nite fuzzy measure is equivalent to a subadditive nite fuzzy measure. A furthe...

We prove that a Banach lattice X which does not contain the ln ∞uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology. 1980 Mathematics Subject Classification: Primary 46B03, 46B42.