‎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...

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.

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

We describe a quantum algorithm to estimate the $\ensuremath{\alpha}$-Renyi entropy of an unknown density matrix $\ensuremath{\rho}\ensuremath{\in}{\mathbb{C}}^{d\ifmmode\times\else\texttimes\fi{}d}$ for $\ensuremath{\alpha}\ensuremath{\ne}1$ by combining recent technique singular value transformations with method estimating normalized traces in one clean qubit model. consider oracular input mo...