The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.     

含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

Quantum Lax Operators and Discrete 2+1-Dimensional Integrable Models

A specific quantum Lax operator, forming a quantum U _q (sl n) chain, is suggested. The intertwining R L L relation is proved. The invariant local 2+1-dimensional reformulation of the auxiliary linear problem for the L-operator is discussed.     

Hochschild Cohomologies of the Algebra of Smooth Functions

Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation.     

Extended Cesàro operators on Bergman spaces

We define an extended Cesàro operator T_g with holomorphic symbol g in the unit ball B of Cⁿ. For a large class of weights w we characterize those g for which T_g is bounded (or compact) from Bergman space L^p_a,w(B) to L^q_a,w(B), 0<p,q<∞. In addition, we obtain some results about equivalent norms, the norm of point evaluation functionals, and the interpolation sequences on L^p_a,w(B).     

无界区域R1上推广的B-BBM方程的整体吸引子

本文研究了无界区域R^1上推广的B—BBM方程的长时间动力学行为，证明了该方程整体吸引子的存在性．     

A new proof for Rockafellar's characterization of maximal monotone operators

We provide a new and short proof for Rockafellar's characterization of maximal monotone operators in reflexive Banach spaces based on S. Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter for proving their result on the representation of a maximal monotone operator by convex functions.

     

基于指数分布的进化策略

典型的进化策略受自然进化过程的启发而成为求解全局优化问题的重要方法。传统的ES变异算子作为一个主要的进化技术是建立在正态分布的随机变量基础上的，本文提出了基于指数分布的进化策略由于采用了新的变异算子有效地减少了产生探试解的成本，从而优于传统的进化策略。     

齐次~Morrey-Herz 空间上分数次积分算子高阶交换子的有界性

在齐次Morrey-Herz空间上建立了高阶交换子~$T^{m}_{b,l}$ 和 ~$M^{m}_{b,l}$的有界性，其中~$T^{m}_{b,l}$ 和 ~$M^{m}_{b,l}$ 是由分数次积分算子和分数次极大算子分别与~BMO($R^{n}$)函数生成的高阶交换子.     

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.