In this paper, we study the generalized derivation of a Lie sub-algebra algebra polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant and Euler field, under some conditions sub-algebra.

We present a derivation of Gosper's algorithm which permits generalization to higher-order recurrences with constant least and most signiicant coeecients. Like Gosper's algorithm, the generalized algorithm requires only "rational" operations (such as gcd and resultant computations) but no factorization.

Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...

A general derivation of the multi-pion correlation function for completely chaotic source is given. Its effects on the pion multiplicity distribution, twopion interferometry are studied. A generalized multi-pion correlation function for a partially coherent source is also discussed.

The present paper introduces and discusses generalized scattered context grammars that are based upon sequences of productions whose left-hand sides are formed by nonterminal strings, not just single nonterminals. It places two restrictions on the derivations in these grammars. More specifically, let k be a positive integer. The first restriction requires that all rewritten symbols occur within...

The notion of co derivations of ranked bigroupoids is discussed by Alshehri et al. in press , and their generalized version is studied by Jun et al. under review press . In particular, Jun et al. under review press studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked ...

We show that a quaternary Jordan derivation on a quaternary Banach algebra associated with the equation f( x+ y + z 4 ) + f( 3x− y − 4z 4 ) + f( 4x+ 3z 4 ) = 2f(x) . is satisfied in generalized Hyers–Ulam stability.

The main purpose of this note is to characterize the operators T ∈ B(H) which are orthogonal (in the sense of James) to the range of a generalized derivation for non-normal operators A,B ∈ B(H).

We prove some theorems in the setting of a 3-prime near-ring admitting a suitably constrained generalized derivation, thereby extending some known results on derivations. Moreover, we give an example proving that the hypothesis of 3-primeness is necessary.

This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized Kähler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized Kähler geometry...