martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

Martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. In this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed to deal with a special type of boundary conditions and to verify the pathwise...

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.

Diversity partitioning has become a popular method for analyzing patterns of alpha and beta diversity. A recent evaluation of the method emphasized a distinction between additive and multiplicative partitioning and further advocated the use of multiplicative partitioning based on a presumed independence between alpha and beta. Concurrently, additive partitioning was criticized for producing dep...

In this paper we obtain asymptotic expansion for the geometric mean of values positive strongly multiplicative function $f$ satisfying $f(p)=\alpha(d)\,p^d+O(p^{d-\delta})$ any prime $p$ with $d$ real and $\alpha(d),\delta>0$.

We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Betaand Gam...

We count algebraic points of bounded height and degree on the graphs certain functions analytic unit disk, obtaining a bound which is polynomial in logarithm multiplicative height. combine this work with $p$-adic methods to obtain, for each positive $\varepsilon$, an upper form $cD^{3n/4 + \varepsilon n}$ number irreducible factors $P^{\circ n}(X)-P^{\circ n}(\alpha)$ over $K$, where $K$ field,...

In 2013, Huczynska, Mullen, Panario and Thomson introduced the concept of k-normal elements: an element $$\alpha \in {\mathbb {F}}_{q^n}$$ is over $${\mathbb {F}}_q$$ if greatest common divisor polynomials $$g_{\alpha }(x)= \alpha x^{n-1}+\alpha ^qx^{n-2}+\cdots +\alpha ^{q^{n-2}}x+\alpha ^{q^{n-1}}$$ $$x^n-1$$ in {F}}_{q^n}[x]$$ has degree k, generalizing normal elements (normal usual sense 0-...

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...