一类非线性奇摄动Robin问题解的渐近性态

利用渐近理论和微分不等式的方法,该文研究了一类非线性奇摄动Robin问题. 证明了其解的存在性,并得到了解的任意n 阶一致有效渐近展开式.     

Asymptotic properties of Rao's test for testing hypotheses in discrete parameter stochastic processes

Summary In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived.     

Curvature integrals under the Ricci flow on surfaces

In this paper, we consider the behavior of the total absolute and the total curvature under the Ricci flow on complete surfaces with bounded curvature. It is shown that they are monotone non-increasing and constant in time, respectively, if they exist and are finite at the initial time. As a related result, we prove that the asymptotic volume ratio is constant under the Ricci flow with non-negative Ricci curvature, at the end of the paper.      

Multiscale asymptotic method of optimal control on the boundary for heat equations of composite materials

In this paper, we study the optimal control on the boundary for parabolic equations with rapidly oscillating coefficients arising from the heat transfer problems and the optimal control on the boundary of composite materials or porous media. The multiscale asymptotic expansion of the solution for the problem in the case without any constraints is presented. We derive the proofs of all convergence results.     

Analysis of diffuse-layer effects on time-dependent interfacial kinetics

We investigate the subtle effects of the diffuse charged layer on interfacial kinetics by solving the governing equations for ion transport (Nernst–Planck) with realistic boundary conditions representing reaction kinetics (Butler–Volmer) and compact-layer capacitance (Stern) in the asymptotic limit =λ_D/L→0, where λ_D is the Debye screening length and L is the distance between the working and counter electrodes. Using the methods of singular perturbation theory, we derive the leading-order steady-state response to a nonzero applied current in the case of the oxidation of a neutral species into cations, without any supporting electrolyte. In certain parameter regimes, the theory predicts a reaction-limited current smaller than the classical diffusion-limited current; this over potential effect is not due to ohmic drop effects in the bulk of the cell but rather to antagonist processes involved in the surface charge transfer and diffuse layer charging respectively. We demonstrate that the charging of diffuse charge, since it is intimately coupled to the surface reaction and cannot be considered independently, plays a fundamental role in nonequilibrium surface reactions when the transport of one of the reacting species is coupled to the total interfacial response of the compact and diffuse layers.     

On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order

In the paper we study the existence of solutions of a nonlinear quadratic Volterra integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval. Moreover, we show that solutions of this integral equation are locally attractive.     

Hyperasymptotics and hyperterminants: Exceptional cases

A new method is introduced for the computation of hyperterminants. It is based on recurrence relations, and can also be used to compute the parameter derivatives of the hyperterminants. These parameter derivatives are needed in hyperasymptotic expansions in exceptional cases. Numerical illustrations and an application are included.     

Delay-dependent and delay-independent stability criteria for a delay differential system

For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.

     

On the jump behavior of distributions and logarithmic averages

The jump behavior and symmetric jump behavior of distributions are studied. We give several formulas for the jump of distributions in terms of logarithmic averages, this is done in terms of Cesàro-logarithmic means of decompositions of the Fourier transform and in terms of logarithmic radial and angular local asymptotic behaviors of harmonic conjugate functions. Application to Fourier series are analyzed. In particular, we give formulas for jumps of periodic distributions in terms of Cesàro–Riesz logarithmic means and Abel–Poisson logarithmic means of conjugate Fourier series.     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.