Relativistic complex Burgers-Schrödinger and Nonliner Schrödinger equations are constructed. In the non-relativistic limit they reduce to the standard Burgers and NLS equations respectively and are integrable at any order of relativistic corrections. 1 General Burgers-Schrödinger Hierarchy The relativistic linear Schrödinger equation has been discussed at the early years of quantum mechanics bu...

Given a T-indistinguishability operator E defined between some fuzzy subsets of a universe of discourse X, this paper studies three ways to generate an indistinguishability operator on X compatible with E inspired by the tools used in approximate reasoning and on the duality principle. Of special interest are the cases when the fuzzy subsets determine a partition and a hard-partition of the uni...

Abstract Let Ω be a compact Hausdorff space, let E be a Banach space, and let C(Ω, E) stand for the Banach space of all E-valued continuous functions on Ω under supnorm. In this paper we study when nuclear operators on C(Ω, E) spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if F is a Banach space and if T : C(Ω, E) → F is a ...

We discuss the exact chiral symmetry and its spontaneous breakdown in lattice QCD with the Dirac operators satisfying the GinspargWilson relation. The axial vector current, which turns out to be related to the vector current simply by the insertion of the operator γ5(1−aD), is explicitly constructed in the case of the Neuberger-Dirac operator. We also consider an Euclidean proof of the Nambu-Go...

ly, we may think of a differential operator ~ on M as a mapping on the smooth functions on M. That is, let C~(M) denote the space of smooth real-valued functions on M. Then 3' : C~(M) ~ C~(M). Bifurcations on Hemispheres 215 In our extension theory we consider only those operators that respect the symmetries on M and N. We define these operators as follows. There is a natural action of ISO(M) o...

Let E, F be exact operator spaces (for example subspaces of the C *-algebra K(H) of all the compact operators on an infinite dimensional Hilbert space H). We study a class of bounded linear maps u: E → F * which we call tracially bounded. In particular, we prove that every completely bounded (in short c.b.) map u: E → F * factors boundedly through a Hilbert space. This is used to show that the ...

Memory logics are modal logics whose semantics is specified in terms of relational models enriched with additional data structure to represent memory. The logical language is then extended with a collection of operations to access and modify the data structure. In this paper we study their satisfiability and the model checking problems. We first give sound and complete tableaux calculi for the ...

Abstract. We investigate the sample paths regularity of operator scaling α-stable random fields. Such fields were introduced in [6] as anisotropic generalizations of self-similar fields and satisfy the scaling property {X(cx);x ∈ R} (fdd) = {cX(x);x ∈ R} where E is a d× d real matrix and H > 0. In the case of harmonizable operator scaling random fields, the sample paths are locally Hölderian an...

We establish some versions of fixed-point theorem in a Frechet topological vector space E. The main result is that every map A BC where B is a continuous map and C is a continuous linear weakly compact operator from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Kra...