In this paper, at first the elemantary and basic concepts of multiplicative discrete and continous differentian and integration introduced. Then for these kinds of differentiation invariant functions the general solution of discrete and continous multiplicative differential equations will be given. Finaly a vast class of difference equations with variable coefficients and nonlinear difference e...

‎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 take into account the stochastic Boiti–Leon–Manna–Pempinelli equation (SBLMPE), which is perturbed by a multiplicative Brownian motion. By applying He’s semi-inverse method and Riccati mapping method, we can acquire solutions of SBLMPE. Since utilized to explain incompressible liquid in fluid mechanics, acquired may be applied lot fascinating physical phenomena. To address how motion effects...

The fractional-stochastic Drinfel’d–Sokolov–Wilson equations (FSDSWEs) perturbed by the multiplicative Wiener process are studied. mapping method is used to obtain rational, hyperbolic, and elliptic stochastic solutions for FSDSWEs. Due importance of FSDSWEs in describing propagation shallow water waves, derived significantly more useful effective understanding various important challenging phy...

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume has nontrivial Under certain assumptions on $\Re$, we prove $\varphi$ is of the form $\psi + \tau$, where $\psi$ either an isomorphism or negative anti-isomorphism onto $\tau$ additive mapping into centre which maps commutat...

Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2...

In many situations, in all branches of physics, one encounters the power-like behavior of some variables, which is best described by a Tsallis distribution characterized by a nonextensivity parameter q and scale parameter T . However, there exist experimental results that can be described only by a Tsallis distributions, which are additionally decorated by some log-periodic oscillating factor. ...

Locally optimum detectors for weak random signals are derived for a generalized observation model incorporating signal-dependent and multiplicative noise. It is shown that the locally optimum random-signal detectors in the generalized observation model are interesting generalizations of those that would be obtained in the purely additive noisy signal model. Examples of explicit results for the ...

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stabil...

We prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.