It has been shown by Voiculescu and Biane that the analytic subordination property holds for free additive and multiplicative convolutions. In this paper, we present an operatorial approach to subordination for free multiplicative convolutions. This study is based on the concepts of ‘freeness with subordination’, or ‘s-free independence’, and ‘orthogonal independence’, introduced recently in th...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

We prove that a class of stochastic differential equations with multiplicative noise has a unique solution in a noncommutative L2 space associated with a von Neumann algebra. As examples we consider usual L2 on a measure space, Hilbert-Schmidt operators and a hyperfinite II1-factor. A problem of finding an inverse of the solution is then discussed. Finally, we explain how a stochastic different...

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...

This paper proposes a novel approach to decentralized control with Plug and Play capabilities. Plug and Play allows a flexible addition and removal of subsystems to an existing plant. The proposed approach guarantees stability and robustness to a certain degree for systems with additive disturbances and multiplicative uncertainties. For the controller design, the plant is decomposed into subsys...

We consider a generalized adaptive and active adversary model for unconditionally secure Multi-Party Computation (MPC) in the zero error case. Cramer et al. proposed a generic approach to build a multiplicative Monotone Span Programs (MSP) – the special property of a Linear Secret Sharing Schemes (LSSS) that is needed to perform a multiplication of shared values. They give an efficient generic ...