Γ-Convergence of some super quadratic functionals with singular weights

We study the Γ-convergence of the following functional (p > 2)

Two-mechanism models ­ some aspects of modelling

Two-mechanism (or, generally, multi-mechanism) models have been studied for the last twenty years. Besides one-mechanism (or “Chaboche”) models, they are a useful tool for modelling inelastic behavior. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Are regularly estimable functionals always differentiable?

Summary. According to van der Vaart (1991), regularly estimable functionals k \kappa are necessarily differentiable, if lim_{t? 0}t^-1(k(P_t)-k(P₀)) \lim\limits_{t\to 0}t^{-1}(\kappa(P_t)-\kappa(P_0)) exists for every differentiable path. In the present paper, a comparable result is obtained under slightly weaker conditions. A counterexample shows that these conditions are minimal.     

Stability of isoperimetric type inequalities for some Monge–Ampère functionals

We investigate the stability of some inequalities of isoperimetric type related to Monge–Ampère functionals. In particular, firstly we prove the stability of a reverse Faber–Krahn inequality for the Monge–Ampère eigenvalue and its generalization. Then we give a stability result for the Brunn–Minkowski inequality and for a consequent Urysohn’s type inequality for the so-called \(n\) -torsional rigidity, a natural extension of the usual torsional rigidity.     

Quasilinearity of some composite functionals associated to Schwarz’s inequality for inner products

The quasilinearity of certain composite functionals associated to Schwarz’s celebrated inequality for inner products is investigated. Applications for operators in Hilbert spaces are given as well.     

Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices

In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results.     

Construction of the Lyapunov–Krasovskii Functionals for some Classes of Positive Delay Systems

A criterion is established for the diagonal stability of positive linear difference-differential systems with discrete and distributed delay. The problem is studied of existence of a common diagonal Lyapunov–Krasovskii functional for a family of these systems. The approach developed is used to obtain conditions of the absolute stability and estimates of the time of transient processes for nonlinear difference-differential systems with sector type nonlinearities.     

Do we self-regulate actions or perceptions? A test of two computational models

Self-regulation theories in applied psychology disagree about whether action or perceptions are the focus of regulation. Computational models based on the two conceptualizations were constructed and simulated. In one scenario, they performed identically and in conjunction with participants in a study of the goal-level effect (Vancouver et al., Organ Res Methods 8:100–127, 2005). In another scenario they created differentiating predictions and only the computational model based on the self-regulation of perceptions matched the data of participants. Implications for research and practice are discussed.

Regularity criterion to some liquid crystal models and the Landau-Lifshitz equations in R~3

We consider the regularity problem under the critical condition to some liquid crystal models and the Landau-Lifshitz equations. The Serrin type reularity criteria are obtained in the terms of the Besov spaces.     

Convergence and stability analysis of system of partial differential equations under Markovian structural perturbations–ii:vextor Lyapunov–like functionals

In this paper we employ the theory of dererministic ordinary differential inequalities together with the concept of vector Lyapunov–like functional to develop basic comparison theorems for system of partial differential equations of parabolic type under Markovian structural perturbations.These results will be utilized to give sufficient conditions for the convergence and stability of the solution process of the system.We also characterize the effects of the random structural perturbations on the qualitative properties of such system. Moreover,the Lyapunov–like functional approach provides a mechanism to characterize the diffusion effects on the qualitative properties of the system.     

Linear transformations to decrease computational requirements of solving some known linear programming models

Imposing additional weight restrictions increases the degeneracy and computational complexity of solving Data Envelopment Analysis (DEA) models, a known class of linear programming models. In this paper some linear transformations to reduce these problems are provided.     

Spectral instability for some Schr?dinger operators

Summary. We show that the condition numbers of isolated eigenvalues of typical non-self-adjoint differential operators such as the harmonic oscillator may be extremely large. We describe a stable procedure for computing the condition numbers for Schr?dinger operators in one dimension, and apply it to the complex resonances of a typical operator with a dilation analytic potential. Received October 9, 1998 / Revised version received September 13, 1999 / Published online 16 March 2000     

Almost periodic Szeg? cocycles with uniformly positive Lyapunov exponents

We exhibit examples of almost periodic Verblunsky coefficients for which Herman’s subharmonicity argument applies and yields the result that the associated Lyapunov exponents are uniformly bounded away from zero. As an immediate consequence of this result, we obtain examples of almost periodic Verblunsky coefficients for which the associated probability measure on the unit circle is pure point.     

On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov–Krasovskii functional

This paper is concerned with the problem of stability analysis of neural networks with interval time-varying delays. It is assumed that the lower bound of time-varying delays is not restricted to be zero. By constructing a newly augmented Lyapunov–Krasovskii functional which has not been proposed yet and utilizing some integral information on activation function as elements of augmented vectors, an improved stability criterion with the framework of linear matrix inequalities (LMIs) is introduced in Theorem 1. Based on the result of Theorem 1 and utilizing the property of the positiveness of Lyapunov–Krasovskii functional, a further relaxed stability condition will be proposed in Theorem 2. The effectiveness and less conservatism of the proposed theorems will be illustrated via three numerical examples.     

Design of a new dynamical core for global atmospheric models based on some efficient numerical methods

A careful study on the integral properties of the primitive hydrostatic balance equations for baroclinic atmosphere is carried out, and a new scheme to design the global adiabatic model of atmospheric dynamics is presented. This scheme includes a method of weighted equal-area mesh and a fully discrete finite difference method with quadratic and linear conservations for solving the primitive equation system. Using this scheme, we established a new dynamical core with adjustable high resolution acceptable to the available     

Do projections stay close together?

We estimate the rate of convergence of products of projections on K intersecting lines in . More generally, consider the orbit of a point under any sequence of orthogonal projections on K arbitrary lines in . Assume that the sum of the squares of the distances of the consecutive iterates is less than ε. We show that if ε tends to zero, then the diameter of the orbit tends to zero uniformly for all families of a fixed number K of lines. We relate this result to questions concerning convergence of products of projections on finite families of closed subspaces of ℓ₂.