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...

An additive and multiplicative privacy homomorphism is an encryption function mapping addition and multiplication of cleartext data into two operations on encrypted data. One such privacy homomorphism is introduced which has the novel property of seeming secure against a known-cleartext attack. An application to multilevel statistical computation is presented, namely classiied retrieval of exac...

An additive and multiplicative privacy homomorphism is an encryption function mapping addition and multiplication of cleartext data into two operations on encrypted data. One such privacy homomorphism is introduced which has the novel property of seeming secure against a known-cleartext attack. An application to multilevel statistical computation is presented, namely classified retrieval of exa...

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

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

‎let g=(v,e) be a simple connected graph with vertex set v and edge set e. the first, second and third zagreb indices of g are respectivly defined by: $m_1(g)=sum_{uin v} d(u)^2, hspace {.1 cm} m_2(g)=sum_{uvin e} d(u).d(v)$ and $ m_3(g)=sum_{uvin e}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in g and uv is an edge of g connecting the vertices u and v. recently, the first and second m...

We analyze nonlinear flows in randomly heterogeneous environments, which are characterized by state-dependent diffusion coefficients with spatially correlated structures. The prior Kirchhoff mapping is used to describe such systems by linear stochastic partial differential equations with multiplicative noise. These are solved through moment equations which are closed, alternatively, either by p...

Background: For psychiatric disorders, comorbidity is a rule rather than exception. Thus it is particularly important to study additive and multiplicative effects of multiple mental disorders on suicidal behaviors. Objectives: The aim of this study was to investigate the ethnic differences in multiplicative effects of mental disorders on suicidal ideation among Black adults in the United States...