in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

This paper considers a formalisation of classical logic using general introduction rules and elimination rules. It proposes definition `maximal formula', `segment' segment' suitable to the system, gives reduction procedures for them. is then shown that deductions in system convert into normal form, i.e. contain neither maximal formulas nor segments, form satisfy subformula property. Tarski's Ru...

In this paper, we investigate the general properties of lattice spin models with emerging fermionic excitations in any dimensions. We argue that fermions always come in pairs and their creation operator always has a string-like structure with the newly created particles appearing at the endpoints of the string. The physical implication of this structure is that the fermions always couple to a n...

The variety of semantical approaches that have been invented for logic programs for reasoning about inconsistent databases is quite broad. Especially, we are interested in an ontological encapsulation of a many-valued logics with negation, based on bilattices, into a 2-valued logic: this new approach is a minimilistic one based on the concept of the semantic reflection. We define a Model theore...

Let Jα k be a real power of the integration operator Jk defined on Sobolev space W k p [0, 1]. We investigate the spectral properties of the operator Ak = ⊕n j=1 λjJ α k defined on ⊕n j=1W k p [0, 1]. Namely, we describe the commutant {Ak} ′, the double commutant {Ak} ′′ and the algebra AlgAk. Moreover, we describe the lattices LatAk and HypLatAk of invariant and hyperinvariant subspaces of Ak,...

The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The ...

A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become weakly vanishing functions of the Quadratic and Linear Constraints. The implication of this result is that (formal) Dirac consistency of the Quantum Operator C...

Abstract Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number classes algebras which result from enriching (subreducts of) Heyting with special modal operator, known in the literature as nucleus . Among these various structures, for we employ umbrella term intuitionistic , some have been studied since at least 1970s, usually within framework topology a...

In this paper we introduce a theoretical framework and a logical application for analyzing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of bo...