We prove that entropy solutions of heterogeneous ultra-parabolic equations satisfying a traceability condition admit strong traces at t = 0. In particular, this property is satisfied by entropy solutions to heterogeneous scalar conservation laws. The tools that we are using are (Panov’s extension of) H-measures and the kinetic approach.

We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of two Gross-Pitaevskii equations with variable scattering lengths. We show that rogue wave solutions exist only for certain combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations of these coefficients that adm...

We introduce session automata, an automata model to process data words, i.e., words over an infinite alphabet. Session automata support the notion of fresh data values, which are well suited for modeling protocols in which sessions using fresh values are of major interest, like in security protocols or ad-hoc networks. Session automata have an expressiveness partly extending, partly reducing th...

The implication problem for saturated conditional independence statements is studied in the presence of fixed and undetermined sets of incomplete random variables. Here, random variables are termed incomplete since they admit missing data. Two different notions of implication arise. In the classic notion of V -implication, a statement is implied jointly by a set of statements and a fixed set V ...

Data-flow models are convenient to represent signal processing systems. They precisely reflect the data-dependencies and numerous algorithms exist to compute a static schedule that optimizes a given criterion especially for parallel implementations. Once deployed the data-flow models must be refined with constraints imposed by the environment and the execution platform. In this paper, we show h...

Using algebraic approach we find new solutions of N-component nonlinear Schrödinger equations with mixed signs of nonlinear coefficients. Explicit expressions are given for the cases N = 2 and N = 3. These solutions admit singularities for certain fixed values of the spatial variable.  2004 Elsevier B.V. All rights reserved.

Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. Performances of an MDP are evaluated by a payoff function. The controller of the MDP seeks to optimize those performances, using optimal strategies. There exists various ways of measuring performances, i.e. various classes of payoff functions. For example, average performances can be evaluated ...

The implication problem for saturated conditional independence statements is studied in the presence of fixed and undetermined sets of incomplete random variables. Here, random variables are termed incomplete since they admit missing data. Two different notions of implication arise. In the classic notion of V -implication, a statement is implied jointly by a set of statements and a fixed set V ...

A philosopher has argued that there can be no such thing as a provably correct system. Some software reliability and safety experts believe that no system can have a software reliability of 1. These claims are related, and they are both mistaken, which we prove with a simple counterexample. But is this the only kind of counterexample? An interesting question arises: which types of systems admit...

We study the conditions for the fivebrane worldvolume theory in D=11 to admit supersymmetric solitons with non-vanishing self-dual three-form. We construct some new soliton solutions consisting of “superpositions” of calibrated surfaces, self-dual strings and instantons.