用泛函观点看LEBESGUE积分

从泛函分析观点来看Lebesgue积分,使得Lebesgue积分可以用泛函分析最简单最基本的方法独立导出．基本做法是将Riemann对于区间[0,1]上的连续函数的积分看成连续函数空间C[0,1]上的连续线性泛函,再将它“自然”延拓到C[0,1]在积分范数意义下的完备化空间,而这个完备化空间正是Lebesgue可积函数空间L1[0,1]．     

Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure

In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure. Therefore, it resolves a long-standing question.     

Investigation of formation mechanism of Ti3SiC2 by high pressure and high-temperature synthesis

ABSTRACT

In this paper, synthesis of titanium silicon carbide (Ti₃SiC₂) under high pressure and high-temperature condition has been investigated by using the reactant systems Ti/Si/C, Ti/SiC/TiC, Ti/SiC/C and Ti/TiC/Si. Results reveal that Ti/TiC/Si is unsuited to the synthesis of Ti₃SiC₂ under a high pressure of 2.0?GPa, while an elemental mixture of Ti/Si/C is applicable. By the addition of Al, Ti₃SiC₂ with 95.8?wt% purity was obtained from elemental mixture with a large excess of silicon. The optimum experimental parameters were determined as Ti/Si/Al/C having the molar ratio of 3:1.5:0.5:1.9, holding at 2.0?GPa and 1300?°C for 60?min.     

Approximation characteristics for diagonal operators in different computational settings

First we study several extremal problems on minimax, and prove that they are equivalent. Then we connect this result with the exact values of some approximation characteristics of diagonal operators in different settings, such as the best n-term approximation, the linear average and stochastic n-widths, and the Kolmogorov and linear n-widths. Most of these exact values were known before, but in terms of equivalence of these extremal problems, we present a unified approach to give them a direct proof.     

Theoretical predictions of the electronic and optical properties of single and coupled (In,Ga)As/GaAs quantum dots

We show how an atomistic pseudopotential plus many-body configuration interaction theory can address the main spectroscopic features of self-assembled dots including, excitons, trions, biexcitons, fine-structure, charging spectra as well as electric-field dependence of entanglement in dot molecules.     

江苏-西部能源需求-供给模型及其动力学分析

根据江苏省能源需求与西部能源供给及江苏省能源进口量之间相互支持、相互制约的复杂关系建立了江苏-西部能源需求-供给系统．分析了系统的稳态、周期、分叉、混沌等若干动力学行为．通过调节参数可以使系统处于稳定发展或周期震荡区域中．基于Silnikov定理,应用待定系数法,求出了能源系统的同宿轨的表达式．证明了在两个平衡点处均有Silnikov型的同宿轨．根据Silnikov定理确保了能源系统有Smale马蹄和马蹄形混沌．     

A solvent-controlled highly efficient Pd-C catalyzed hydrogenolysis of benzaldehydes to methylbenzenes via a novel ‘acetal pathway’

Pd-C catalyzed hydrogenolysis of benzaldehydes to methylbenzenes has been described to proceed via a ‘benzenemethanol pathway’. In this article, a novel ‘acetal pathway’ was first revealed by a systematic study when lower alcohols were used as solvents and a solvent-controlled highly efficient procedure was established.     

等离子体喷涂层的正电子湮没研究

本文用正电子湮没技术对等离子体喷涂铜基合金压缩形变的微观缺陷进行了测量。对等离子体喷涂合金，随着压缩量的增加，正电子寿命变短，这一现象与常规合金中观察到的情况相反。     

Strontium‐based initiator system for ring‐opening polymerization of cyclic esters

An amino isopropoxyl strontium (Sr‐PO) initiator, which was prepared by the reaction of propylene oxide with liquid strontium ammoniate solution, was used to carry out the ring‐opening polymerization (ROP) of cyclic esters to obtain aliphatic polyesters, such as poly(ε‐caprolactone) (PCL) and poly(L ‐lactide) (PLLA). The Sr‐PO initiator demonstrated an effective initiating activity for the ROP of ε‐caprolactone (ε‐CL) and L‐lactide (LLA) under mild conditions and adjusted the molecular weight by the ratio of monomer to Sr‐PO initiator. Block copolymer PCL‐b‐PLLA was prepared by sequential polymerization of ε‐CL and LLA, which was demonstrated by ¹H NMR, ¹³C NMR, and gel permeation chromatography. The chemical structure of Sr‐PO initiator was confirmed by elemental analysis of Sr and N, ¹H NMR analysis of the end groups in ε‐CL oligomer, and Fourier transform infrared (FTIR) spectroscopy. The end groups of PCL were hydroxyl and isopropoxycarbonyl, and FTIR spectroscopy showed the coordination between Sr‐PO initiator and model monomer γ‐butyrolactone. These experimental facts indicated that the ROP of cyclic esters followed a coordination‐insertion mechanism, and cyclic esters exclusively inserted into the Sr–O bond. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1934–1941, 2003