In this paper, we consider ultrapowers of Banach algebras as and the product $${{\bigcirc }_{{(J,\mathcal{U})}}}$$ on second dual algebras. For a algebra A, show that if there is continuous derivation from A into itself, then (A**, ) it. Moreover, X**, where X A-bimodule, ultrapower X; i.e., $${{(X)}_{\mathcal{U}}}$$ . Ultra (character) amenability investigated it will be shown every inner, ult...

Contents Chapter 1. Introduction 5 1.1. The selective excitation transform 5 1.2. The problem of selective excitation pulse design 6 1.3. Examples 7 1.4. The discrete selective excitation transform (hard pulse approximation) 10 1.5. Main results: continuum theory 11 1.6. Main results: discrete theory 12 1.7. Energy Formulas 13 1.8. Algorithms 13 Chapter 2. Scattering theory 15 2.1. Preliminarie...

For the whole class of linear term rewriting systems and for each integer k, we define k-bounded rewriting as a restriction of the usual notion of rewriting. We show that the k-bounded uniform termination, the k-bounded termination, the inverse k-bounded uniform, and the inverse kbounded problems are decidable. The k-bounded class (BO(k)) is, by definition, the set of linear systems for which e...

In this paper, we introduce the notions of $(odot, oplus)$-derivations and $(ominus, odot)$-derivations for $MV$-algebras and discuss some related results. We study the connection between these derivations on an $MV$-algebra $A$ and the derivations on its boolean center. We characterize the isotone $(odot, oplus)$-derivations and prove that $(ominus, odot)$-derivations are isotone. Finally we d...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

A left-forbidding grammar, introduced in this paper, is a context-free grammar, where a set of nonterminal symbols is attached to each context-free production. Such a production can rewrite a nonterminal provided that no symbol from the attached set occurs to the left of the rewritten nonterminal in the current sentential form. The present paper discusses cooperating distributed grammar systems...

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...

BACKGROUND Patients with pulmonary hypertension due to left heart disease (PH-LHD) have overlapping clinical features with pulmonary arterial hypertension making diagnosis reliant on right heart catheterization (RHC). This study aimed to investigate computed tomography pulmonary angiography (CTPA) derived cardiopulmonary structural metrics, in comparison to magnetic resonance imaging (MRI) for ...

In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introd...

BACKGROUND The aim of the study was to derive and validate a novel risk score for early right-sided heart failure (RHF) after left ventricular assist device implantation. METHODS The EUROMACS (European Registry for Patients with Mechanical Circulatory Support) was used to identify adult patients undergoing continuous-flow left ventricular assist device implantation with mainstream devices. El...