Correspondence On the Similarity of the Entropy Power Inequality The preceeding equations allow the entropy power inequality and the Brunn-Minkowski Inequality to be rewritten in the equivalent form (4) where X' and Y' are independent normal variables with corresponding entropies H(X') = H(X) and H(Y') = H(Y). Verification of this restatement follows from the use of (1) to show that Abstract-Th...

Let L(H) denote the C∗-algebra of adjointable operators on a Hilbert C∗-module H. In this paper, we introduce generalized Cauchy–Schwarz inequality for in L(H). More precisely, an operator A∈L(H) is said to satisfy if there exists ν∈(0,1) such that ‖⟨Ax,y⟩‖≤(‖Ax‖‖y‖)ν(‖Ay‖‖x‖)1−ν(x,y∈H).We investigate various properties which inequality. particular, prove A satisfies has polar decomposition, th...

Given a list of N states with probabilities 0 < p1 ≤ · · · ≤ pN , the average conditional algorithmic information Ī to specify one of these states obeys the inequality H ≤ Ī < H + O(1), where H = − pj log2 pj and O(1) is a computer-dependent constant. We show how any universal computer can be slightly modified in such a way that the inequality becomes H ≤ Ī < H + 1, thereby eliminating the comp...

This paper studies the problems of H∞ output tracking performance analysis and controller design for networked control systems (NCSs) with time delay and packet dropout. By defining new Lyapunov function and using the discrete Jensen inequality, linear matrix inequality (LMI)-based H∞ output tracking performance analysis and controller design are presented. The adoption of the discrete Jensen i...

In this paper, the author examines Holder’s inequality and related inequalities in probability. The paper establishes new inequalities in probability that generalize previous research in this area. The author places Beckenbach’s (1950) inequality in probability, from which inequalities are deduced that are similar to Brown’s (2006) inequality along with Olkin and Shepp (2006). For convenience, ...

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

This paper describes the robust output feedback ∞ H fuzzy control design for a class of nonlinear stochastic systems. The system dynamic is modelled by type ô It − stochastic differential equations. For general nonlinear stochastic systems, the ∞ H ontrol can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonline...

The concept of η-invex set is explored and the concept of T-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended to H-spaces and differentiable n-manifolds. The solution of complementarity problem is also studied in the presence of fixed ...

• An inequality constrained optimization problem is an optimization problem in which the constraint set D can be represented as D = U ∩ {x ∈ R | h(x) ≥ 0}, where h : R → R. We refer to the functions h = (h1, . . . , hl) as inequality constraints. • An optimization problem with mixed constraints is an optimization problem in which the constraint set D can be represented as D = U ∩ {x ∈ R | g(x) ...