Abstract: The globally exponentially stable conditions for delayed parabolic neural networks with variable coefficients are considered in this paper. We first derive the globally exponentially stable condition for delayed parabolic neural networks with variable coefficients based on delay differential inequality combining with Young inequality. Compared with the method of Lyapunov functionals a...

This paper deals with the problem of observer-based stabilization for linear systems with parameter inequality. A new design methodology is proposed thanks to a judicious use of the famous Young relation. This latter leads to a less restrictive synthesis condition, expressed in term of Linear Matrix Inequality (LMI), than those available in the literature. Numerical comparisons are provided in ...

We summarize results on the Penrose inequality bounding the ADM-mass or the Bondi mass in terms of the area of an outermost apparent horizon for asymptotically flat initial data of Einstein’s equations. We first recall the proof, due to Geroch and to Jang and Wald, of monotonicity of the Geroch-Hawking mass under a smooth inverse mean curvature flow for data with non-negative Ricci scalar, whic...

In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the $(n+1)$-dimensional Euclidean unit ball. Then solve some related isoperimetric type problems convex hypersurfaces, which lead to new Alexandrov–Fenchel inequalities. particular, $n = 2$ obtain a Minkowski-type inequality and 3$ an optimal Willmore-type inequality. To prove these estimates, employ specifica...

As the struggle continues to explain the relatively high rates of infant mortality (IMR) exhibited in the United States, a renewed emphasis is being placed on the role of possible 'contextual' determinants. Cross-sectional and short time-series studies have found that higher income inequality is associated with higher IMR at the state level. Yet, descriptively, the longer-term trends in income ...

In this paper, we provide a su cient condition for asymptotic stability of a system with a single time delay in a state expressed as an linear matrix inequality(LMI). We consider a time delay as a inverse uncertainty con guration.

In this paper, we introduce an iterative process which converges strongly to a common element of solutions of variational inequality problems for γ-inverse strongly monotone mappings and common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive nonself mappings, and hence obtain related convergence theorems in Banach spaces. Mathematics Subject Classification: 47H09...

1 Linear algebra 2 1.1 Inner product, norm, distance, and orthogonality . . . . . . . . . 2 1.2 Angle and inequality . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Vector projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Basics of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . ....

In this note, we derive non trivial sharp bounds related to the weighted harmonic-geometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of a symmetric positive definite matrix and an inequality related to the coefficients of polynomials with positive roots.

A parabolic equation or inequality in an infinite domain is considered. The lateral Cauchy data for this equation are assumed to be given at an arbitrary smooth lateral surface. An inverse problem of the interest of this paper consists in an estimate of the unknown initial condition via these Cauchy data.