Semi-revision is a model of belief change that differs from revision in that a new formula is not always accepted. Later, Fuhrmann defined multiple semi-revision by replacing a new formula with a set of formulae as the new information, which results in a merging operator called a partial meet merging operator. The problem for the partial meet merging operator is that it needs additional informa...

Given V a finite set, a self–adjoint operator on C(V ), K, is called elliptic if it is positive semi–definite and its lowest eigenvalue is simple. Therefore, there exists a unique, up to sign, unitary function ω ∈ C(V ) satisfying K(ω) = λω and then K is named (λ, ω)–elliptic. Clearly, a (λ, ω)–elliptic operator is singular iff λ = 0. Examples of elliptic operators are the so–called Schrödinger...

New method to determine semi-analytical solutions of one-dimensional contaminant transport problem with nonlinear sorption is described. This method is based on operator splitting approach where the convective transport is realized exactly and the diffusive transport by finite volume method. The exact solutions for all sorption isotherms of Freundlich and Langmuir type are presented for the cas...

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...

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...

We prove that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi-finite von Neumann algebra. This complements Junge’s recent result that it admits such an embedding in the non semi-finite case. ——————– In remarkable recent work [5], Marius Junge proves that the operator Hilbert space OH (from [8], see also [9]) embeds completely isomorphically (c.i...

In this paper it is shown that if T ∈ L(H) satisfies (i) T is a pure hyponormal operator; (ii) [T ∗, T ] is of rank-two; and (iii) ker [T ∗, T ] is invariant for T , then T is either a subnormal operator or the Putinar’s matricial model of rank two. More precisely, if T |ker [T∗,T ] has the rank-one self-commutator then T is subnormal and if instead T |ker [T∗,T ] has the ranktwo self-commutato...

In arbitrary dimension, in the discrete setting of finite-differences we prove a Carleman estimate for a semi-discrete parabolic operator, in which the large parameter is connected to the mesh size. This estimate is applied for the derivation of a (relaxed) observability estimate, that yield some controlability results for semi-linear semi-discrete parabilic equations. Sub-linear and super-line...

Let A' be a compact C -manifold. Let || ||, || || denote the supremum norm and the C -norm, respectively, and let \P \ be a Markovian semigroup on C(X). The semigroup's infinitesimal generator A, with domain 3), is defined by Af= lim Q t~ (P'f f), whenever the limit exists in || ||. Theorem. Assume that \P s preserves C -junctions and that the restriction of {PA to C2(X), I I' is strongly conti...