let a be a unital algebra over a field of characteristic zero. we show that every derivation from( ) n m a into its dual ( ) n m a ∗ is the sum of an inner derivation and a derivation induced by a derivationfrom a into a∗

The primary aim of this paper is to answer the question: what are the highest-order fiveor nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the oneand two-dimensional Poisson equation on uniform, quasi-uniform, and non-uniform face-to-face hyper-rectangular grids and directly prove the existence or non-...

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

The paper presents logical derivation algorithms that can be applied to inversion of polynomially computable discrete functions. The proposed approach is based on the fact that it is possible to organize DPLL derivation on a small subset of variables appeared in a CNF which encodes the algorithm computing the function. The experimental results showed that arrays of conflict clauses generated by...

Asymptotic approximation formulas for polynomials of the type Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi with integer order real parameters are obtained via hyperbolic functions. The derivation is done using principle saddle point expansion appropriate function about a point.

in this paper, we introduce the notion of derivation on krasner hyperrings as follows: the function d : r  r isa derivation on a krasner hyperring r if for all , , ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). then, we investigate some fundamental properties of derivation on krasnerhyperings and prime krasner hyperrings. also, we introduce differential krasner hy...

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}