Existence and uniqueness of bounded weak solution for non‐linear parabolic boundary value problem with equivalued surface

In this paper, we discuss the existence and uniqueness of bounded weak solution for non‐linear parabolic boundary value problem with equivalued surface and correct the mistake in Zhang Xu (Math. Meth. Appl. Sci. 1999; 22 : 259). The approach is based on L^∞ estimate of solution. Copyright © 2004 John Wiley & Sons, Ltd.     

Solution representations for a wave equation with weak dissipation

We consider the Cauchy problem for the weakly dissipative wave equation □v+μ/1+t v_t=0, x∈?ⁿ, t≥0 parameterized by μ>0, and prove a representation theorem for its solutions using the theory of special functions. This representation is used to obtain L_p–L_q estimates for the solution and for the energy operator corresponding to this Cauchy problem. Especially for the L₂ energy estimate we determine the part of the phase space which is responsible for the decay rate. It will be shown that the situation depends strongly on the value of μand that μ=2 is critical. Copyright © 2004 John Wiley & Sons, Ltd.     

Bootstraps of sums of independent but not identically distributed stochastic processes

A central limit theorem is developed for sums of independent but not identically distributed stochastic processes multiplied by independent real random variables with mean zero. Weak convergence of the Hoffmann–Jørgensen–Dudley type, as described in van der Vaart and Wellner (Weak Convergence and Empirical Processes, Springer, New York, 1996), is utilized. These results allow Monte Carlo estimation of limiting probability measures obtained from application of Pollard's (Empirical Processes: Theory and Applications, IMS, Hayward, CA, 1990) functional central limit theorem for empirical processes. An application of this theory to the two-parameter Cox score process with staggered entry data is given for illustration. For this process, the proposed multiplier bootstrap appears to be the first successful method for estimating the associated limiting distribution. The results of this paper compliment previous bootstrap and multiplier central limit theorems for independent and identically distributed empirical processes.     

Marcinkiewicz积分交换子在Herz型空间中的弱型估计

用μΩ表示Marcinkiewicz积分,μΩ,b表示μΩ与函数b∈BMO(R~n)生成的交换子．本文证明了交换子μΩ,b是从Herz型Hardy空间H■_q~(n(1-(1/q)),p)(R~n)到弱Herz空间W■_q~(n(1-(1/q)),p)(R~n)有界的,其中0＜p≤1,1＜q＜∞．     

Al0.22Ga0.78N/GaN二维电子气中的弱局域和反弱局域效应

通过磁输运测量研究了Al_0.22Ga_0.78N/GaN二维电子气的电子相干散射中的弱局域和反弱局域化现象.在外加弱磁场的情况下，该系统表现出正-负磁阻的变化，说明在Al_0.22Ga_0.78N/GaN异质结中存在晶体场引起的电子自旋-轨道散射.同时讨论了二维电子气中不同的散射时间对温度的依赖关系，实验得到的非弹性散射时间与温度成反比，表明非弹性散射机理主要来源于小能量转移的电子-电子散射. 关键词： 二维电子气 弱局域 磁阻     

Local dominance and local recombination in MOEAs on 0/1 multiobjective knapsack problems

This work studies and compares the effects on performance of local dominance and local recombination applied with different locality in multiobjective evolutionary algorithms on combinatorial 0/1 multiobjective knapsack problems. For this purpose, we introduce a method that creates a neighborhood around each individual and assigns a local dominance rank after alignment of the principle search direction of the neighborhood by using polar coordinates in objective space. For recombination a different neighborhood determined around a random principle search direction is created. The neighborhood sizes for dominance and recombination are separately controlled by two different parameters. Experimental results show that the optimum locality of dominance is different from the optimum locality of recombination. Additionally, it is shown that the performance of the algorithm that applies local dominance and local recombination with different locality is significantly better than the performance of algorithms applying local dominance alone, local recombination alone, or dominance and recombination globally as conventional approaches do.     

The characteristic of convexity of a Banach space and normal structure

We present some sufficient conditions for normal structure of Banach spaces and their dual spaces in terms of the characteristic of convexity, the James constant, and the coefficient of weak orthogonality. Many known results are improved and strengthened. We also show that some of our results are sharp.     

Stable approximation of solutions to irregular nonlinear operator equations in a Hilbert space under large noise

The class of regularized Gauss-Newton methods for solving inexactly specified irregular nonlinear equations is examined under the condition that additive perturbations of the operator in the problem are close to zero only in the weak topology. By analogy with the well-understood conventional situation where the perturbed and exact operators are close in norm, a stopping criterion is constructed ensuring that the approximate solution is adequate to the errors in the operator.     

On the existence of weak solutions to the equations of non‐stationary motion of heat‐conducting incompressible viscous fluids

This paper is concerned with the equations of non‐stationary motion in 3D of heat‐conducting incompressible viscous fluids with temperature‐dependent viscosity. The conservation of internal energy includes the usual dissipation term. We prove the existence of a ‘weak solution with defect measure’ to the system of PDEs under consideration. Our method of proof is based on a regularization of the equations of conservation of momentum. Copyright © 2006 John Wiley & Sons, Ltd.     

The Stability of Set of Solutions for Symmetric Vector Quasi-Equilibrium Problems

In this paper, the stability of the set of solutions for symmetric vector quasi-equilibrium problems is discussed. Then, we prove a generic stability theorem and give an existence theorem for essentially connected components of the set of solutions for symmetric vector quasi-equilibrium problems. Finally, we apply these results to vector weak saddle point problems with constraints. This research was partially supported by the Natural Science Foundation of China (Grant number: 10561007) and Natural Science Foundation of Jiangxi Province, China.