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.     

Structures and syntheses of layered and framework amine-bearing uranyl phosphate and uranyl arsenates

Two hydrated uranyl arsenates and a uranyl phosphate were synthesized by hydrothermal methods in the presence of amine structure-directing agents and their structures determined: (N₂C₆H₁₄)[(UO₂)(AsO₄)]₂(H₂O)₃, DabcoUAs, {NH(C₂H₅)₃}[(UO₂)₂(AsO₄)(AsO₃OH)], TriethUAs, and (N₂C₄H₁₂)(UO₂)[(UO₂)(PO₄)]₄(H₂O)₂, PiperUP. Intensity data were collected at room temperature using MoKα X-radiation and a CCD-based area detector. The crystal structures were refined by full-matrix least-squares techniques on the basis of F² to agreement indices (DabcoUAs, TriethUAs, PiperUP) wR₂=5.6%, 8.3%, 7.2% for all data, and R₁=2.9%, 3.3%, 4.0%, calculated for 1777, 5822, 9119 unique observed reflections (|F_o|?4σ_F), respectively. DabcoUAs is monoclinic, space group C2/m, Z=2, a=18.581(1), b=7.1897(4), c=7.1909(4) Å, β=102.886(1)°, V=936.43(9) Å³, D_calc=3.50 g/cm³. TriethUAs is monoclinic, space group P2₁/n, Z=4, a=9.6359(4), b=18.4678(7), c=10.0708(4) Å, β=92.282(1)°, V=1790.7(1) Å³, D_calc=3.41 g/cm³. PiperUP is monoclinic, space group Pn, Z=2, a=9.3278(4), b=15.5529(7), c=9.6474(5) Å, β=93.266(1)°, V=1397.3(1) Å³, D_calc=4.41 g/cm³. The structure of DabcoUAs contains the autunite-type sheet formed by the sharing of vertices between uranyl square bipyramids and arsenate tetrahedra. The triethylenediammonium cations are located in the interlayer along with two H₂O groups and are disordered. Both TriethUAs and PiperUP contain sheets formed of uranyl pentagonal bipyramids and tetrahedra (arsenate and phosphate, respectively) with the uranophane sheet-anion topology. In TriethUAs, triethlyammonium cations are located in the interlayer. In PiperUP, the sheets are connected by a uranyl pentagonal bipyramid that shares corners with phosphate tetrahedra of adjacent sheets, resulting in a framework with piperazinium cations and H₂O groups in the cavities of the structure.     

Bessel框架及其摄动

本文进一步研究了Bessel框架的性质,给出其稳定性和摄动的几个有意义的结果。     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.

     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.