Abstract In this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of implementation. The NOM is based on so-called support, dual-support, operators, operate energy functional ensuring stability. generalization conventional differential operators. Combined with weighed residuals variational principles, esta...

‎let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module‎. ‎we study the set‎ ‎$dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$‎. ‎in the case $ex=pa$‎, ‎$dec_{pa}(pa)$ is the well-known apostol algebra of $pa$‎. ‎we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...

in this paper, a viscous flow simulation is presented using the lattice boltzmann equation (lbe). a finite volume approach is adapted to discretize the lbe on a cell-centered, arbitrary shaped, rectangular tessellation. the formulation includes upwind scheme and high order descretization schemes for the flux term and collision operator respectively. a consistent open and solid boundary treatmen...

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...

We study the operator growth in open quantum systems with dephasing dissipation terms, extending Krylov complexity formalism of Phys. Rev. X 9, 041017. Our results are based on dissipative $q$-body Sachdev-Ye-Kitaev (SYK$_q$) model, governed by Markovian dynamics. introduce a notion ''operator size concentration'' which allows diagrammatic and combinatorial proof asymptotic linear behavior two ...

Let D be the open unit disk in the complex plane C. Denote by H(D) the class of all functions analytic on D. An analytic self-map φ : D → D induces the composition operator Cφ on H(D), defined by Cφ ( f ) = f (φ(z)) for f analytic on D. It is a well-known consequence of Littlewood’s subordination principle that the composition operator Cφ is bounded on the classical Hardy and Bergman spaces (se...

The concepts of fuzzy θ-open (θ-closed)sets and fuzzy θ-closure operator are introduced and discussed in intuitionistic fuzzy topological spaces. As applications of these concepts, certain functions are characterized in terms of intuitionistic fuzzy θ-closure operator.

Our aim in this paper is to make explicit the operator theory of the heuristic open Bosonic string and to abstract a suitable field algebra for the string. This is done on a Fock-Krein space and we examine integrability and J-unitary implementability of all the defining transformations of the string, i.e. time translations, gauge transformations and Poincare transformations. The results obtaine...