In this paper, the linear quadratic regulation problem for discrete-time systems with state delays and multiplicative noise is considered. The necessary and sufficient condition for the problem admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference equations. Our approach is based on the maximum...

abstract soil contamination by heavy metals is yet one of the most important environmental concerns. among heavy metals, nickel and cadmium have dangerous influences on human, animals and plants. the objective of this study was to derive a new model for simultaneous phytoextraction of ni and cd from contaminated soils. consequently, a macroscopic model was derived by combining yield reduction f...

Various scholars have lately employed a wide range of strategies to resolve specific types symmetrical fractional differential equations. In this paper, we propose new identity for multiplicatively differentiable functions; based on identity, establish some multiplicative Bullen-type inequalities convex functions. Some applications the obtained results are given.

We show that the trace formula interpretation of the explicit formulas expresses the counting function N(q) of the hypothetical curve C associated to the Riemann zeta function, as an intersection number involving the scaling action on the adèle class space. Then, we discuss the algebraic structure of the adèle class space both as a monoid and as a hyperring. We construct an extension Rconvex of...

Several architectures have been proposed to enhance point-to-point architectures with the addition of multiple bus systems. In particular, we consider an architecture for a massively parallel system where processors are connected solely by buses. These archi-tectures can use the power of bus technologies, providing a way to interconnect much more processors in a simple and eecient manner. In th...

Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS. In this paper, we propose the new concept of a 3-multiplicative LSSS, and establish its relationship with strongly multiplic...

Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS. In this paper, we propose the new concept of 3-multiplicative LSSS, and establish its relationship with strongly multiplicat...

A numerical approach for the approximation of inertial manifolds of stochastic evolutionary equations with multiplicative noise is presented and illustrated. After splitting the stochastic evolutionary equations into a backward and a forward part, a numerical scheme is devised for solving this backward-forward stochastic system, and an ensemble of graphs representing the inertial manifold is co...

This work is concerned with existence of weak solutions to discontinuous stochastic differential equations driven by multiplicative Gaussian noise and sliding mode control dynamics generated by stochastic differential equations with variable structure, that is with jump nonlinearity. The treatment covers the finite dimensional stochastic systems and the stochastic diffusion equation with multip...