Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces

The boundedness and compactness of the products of differentiation and composition operators from Zygmund spaces to Bloch spaces and Bers spaces are discussed in this paper.     

Approximation numbers of weighted composition operators

We study the approximation numbers of weighted composition operators $f?w?(f°\phi )$ on the Hardy space $H^2$ on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight w can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples).     

Hypercyclic algebras for convolution and composition operators

We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as $\text{cos}(D)$, $D{e}^D$, or $e^D?aI$, where $0<a\le 1$. In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras.     

茂金属线性低密度聚乙烯的组成均匀性

茂金属线性低密度聚乙烯的组成均匀性徐旭荣徐君庭封麟先陈伟（浙江大学高分子科学与工程学系杭州３１００２７）（中国石化总公司石油化工科学研究院北京１０００８３）关键词线性低密度聚乙烯，组成均匀性，茂金属催化剂８０年代以来，茂金属催化剂得到迅速发展．...     

Phase relations in the system K2MoO4–KPO3–MoO3–Bi2O3: A new phosphate K3Bi5(PO4)6

Phase equilibrium in the pseudo-quaternary system K₂O–MoO₃–P₂O₅–Bi₂O₃ was studied as three-component solvent K₂MoO₄–KPO₃–MoO₃ containing 15 mol% Bi₂O₃ during slow cooling and spontaneous crystallization. The results of the investigation were shown on a composition diagram, which indicates the crystallization fields of K₂Bi(PO₄)(MoO₄), K₅Bi(MoO₄)₄, BiPO₄ and K₃Bi₅(PO₄)₆. New phosphate K₃Bi₅(PO₄)₆ was characterized by single-crystal X-ray diffraction (space group C2/c, a=17.680(4), b=6.9370(14), c=18.700(4) Å, β=113.79(3)°) and FTIR spectroscopy. The possibility of lone electron pair stereoactivity of bismuth was suggested using the calculations of characteristics of the Voronoi–Dirichlet polyhedra for K₃Bi₅(PO₄)₆ and K₂Bi(PO₄)(MoO₄).     

Aggregation of fuzzy preference relations to multicriteria decision making

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed fuzzy preference relation includes t-norms and t-conorms to take into account the relation between the criteria importance. Properties of the composition and new relation, giving a possibility to make a consistent choice or to rank the alternatives, are proved. An illustrative numerical study and comparative examples are presented.     

Preparation and properties of porous glass using fly ash as a raw material

The porous glasses were prepared by a conventional phase separation method using coal fly ash as a raw material, and the properties of these porous glasses were investigated. The composition of coal fly ash is basically composed of SiO₂–Al₂O₃–Fe₂O₃–CaO system and the SiO₂–B₂O₃–Al₂O₃–CaO–Na₂O system of glass was chosen as base glass composition. The pore diameter increases proportional to cube root of heating time (t^1/3), however, the early stage of phase separation is not clear. It is estimated that the rate determining step may be the diffusion process of structural units involving oxygen ions and the phase separation may take place by the nucleation and growth mechanism, and the relatively larger pores of above 1 μm can be obtained easily. The chemical composition of porous glasses is SiO₂–B₂O₃–Al₂O₃(–CaO–Na₂O). A relatively large amount of fly ash (>40%) can be used successfully for the preparation of porous glass.     

Contractible Lie groups over local fields

Let G be a Lie group over a local field of characteristic p > 0 which admits a contractive automorphism α : G → G (i.e., α ⁿ (x) → 1 as n → ∞, for each x ∈ G). We show that G is a torsion group of finite exponent and nilpotent. We also obtain results concerning the interplay between contractive automorphisms of Lie groups over local fields, contractive automorphisms of their Lie algebras, and positive gradations thereon. Some of the results extend to Lie groups over arbitrary complete ultrametric fields. Supported by the German Research Foundation (DFG), grants GL 357/2-1 and GL 357/6-1.     

Exotic cosmic family events. Aspects of observations and theories

Summary Against the background of the experimental reports obtained so far some very recent theoretical approaches to the understanding of the exotic family events in cosmic-ray physics have been traced in a comprehensive manner. The main trends in the observations have been highlighted and the limitations of the theoretical attempts have been pointed out.     

借多波长量测数据测定二元配合物组成

本文提出利用多波长量测数据测定二元配合物组成的新方法。首先以线性最小二乘求得各吸收组分吸收系数；继而应用多元线性回归获取各组分平衡浓度并据物料平衡求得配合物组成比及稳定常数。运用单纯形方法对５个体系测定结果进行了检验。