Subdifferential representation of homogeneous functions and extension of smoothness in Banach spaces

In this paper, we mainly consider proximal subdifferentials of lower semicontinuous functions defined on real Hilbert space and Clarke＇s subdifferentials of locally Lipschitzian functions defined on Banach space respectively, and obtain the generalized Euler identity of homogenous functions. Then, by introducing a multifunction F, we extend the smoothness of sphere and differentiability of norm function in Banach space.     

Comonotonic convex upper bound and majorization

When the dependence structure among several risks is unknown, it is common in the actuarial literature to study the worst dependence structure that gives rise to the riskiest aggregate loss. A central result is that the aggregate loss is the riskiest with respect to convex order when the underlying risks are comonotonic. Many proofs were given before. The objective of this article is to present a new proof using the notions of decreasing rearrangement and the majorization theorem, and give clear explanation of the relation between convex order, the theory of majorization and comonotonicity.     

Limit relations for three simple hyperbolic systems of conservation laws

This paper is concerned with the limit relations from the Euler equations of one‐dimensional compressible fluid flow and the magnetohydrodynamics equations to the simplified transport equations, where the δ‐shock waves occur in their Riemann solutions of the latter two equations. The objective is to prove that the Riemann solutions of the perturbed equations coming from the one‐dimensional simplified Euler equations and the magnetohydrodynamics equations converge to the corresponding Riemann solutions of the simplified transport equations as the perturbation parameterx ε tends to zero. Furthermore, the result can also be generalized to more general situations. Copyright © 2009 John Wiley & Sons, Ltd.     

二阶奇摄动拟线性微分系统的可解性

本文研究了一类二阶拟线件微分系统.利用边界层校正法,Green公式以及微分不等式理论,得到了一类一二阶拟线性微分系统两点边值问题的可解性条件.     

Synthesis and Characterization of Magnetic Polymer Microspheres

In this study, amino group–modified magnetic polymer microspheres were synthesized in a well‐shaped spherical form with a size range of 0.6 μm to 0.8 μm by mini‐emulsion polymerization. The morphology, composition, and thermal properties of the magnetic polymer microspheres were characterized by infrared (IR) spectra, transmission electron microscopy (TEM) photographs, particle size analysis, and thermogravimetric analysis (TGA) spectra. The results demonstrate that acrylic acid used for stabilizing the reaction system greatly affects the particle size, magnetite contents, and thermal stability of magnetic polymer microspheres.     

大型回热换热器的降温实验

大型低温配件的降温试验复杂和多变,文中针对大型回热换热器的降温进行了研究。将回热换热器置于特制的冷箱内,利用液氮作为冷源,氦气做为载冷剂为换热器提供降温条件;隔膜压缩机为循环氦气提供循环压力。试验前将换热器上面布置9支传感器,传感器所采集的数据自动记录并保存在上位机内,同时绘制降温曲线,为大型回热换热器的降温研究提供了数据。     

Facile Iron‐Mediated Dispersant‐Free Suspension Polymerization of Methyl Methacrylate via Reverse ATRP in Water

An iron‐mediated reverse ATRP of methyl methacrylate (MMA) is successfully carried out in water in the absence of any dispersants, using a water‐soluble 2,2′‐azobis(2‐methylpropionamidine) dihydrochloride (V‐50) as the initiator and the stabilizer, and using an oil‐soluble N,N‐butyldithiocarbamate ferrum (Fe(S₂CN(C₄H₉)₂)₃) as the catalyst without adding any additional ligands. Micron‐sized PMMA particles with UV light‐sensitive ‐S₂CN(C₄H₉)₂ end group are obtained, and monomer droplet nucleation and suspension polymerization mechanism are proposed. Polymerization results demonstrated typical “living”/controlled characteristics of ATRP: first‐order polymerization kinetics, linear increase of molecular weights with monomer conversion and narrow molecular weight distributions for the resultant PMMA particles. NMR spectroscopy and chain‐extension experiments under UV light irradiation confirm the attachment and livingness of UV light‐sensitive ‐S₂CN(C₄H₉)₂ group in the chain end.

     

Study of Morphology and Mechanical Properties of In Situ PP/PS Alloy

The in situ polypropylene (PP)/polystyrene (PS) alloy was prepared in the presence of dicumyl peroxide (DCP). Purified styrene (St) and pre‐polymerized styrene (PSt), forming a dispersed PS phase in the PP matrix would react with PP matrix to form PP‐g‐PS graft co‐polymers acting as a compatibilizer in these alloys, leading to the formation of in situ PP/PS alloys with in situ compatibilizer during reactive blending in a mixer. The morphology development of the alloy was examined by scanning electron microscopy (SEM) and was described using the characteristic length L and the average characteristic length L_m. The shape of the dispersed PS phase was regular and the distribution of PS particles was uniform. Tensile properties of the alloy were improved with mixing time and fluctuated in a certain composition range.     

认知无线电网络中提高传输层端到端吞吐率的跨层参数配置

在认知无线电网络中, 传输层端到端(TCP)吞吐率是衡量网络性能的重要指标. 前期相关研究大都具有以下两方面缺点: 第一, 大部分研究只考虑了协议底层参数来优化物理链路性能, 对传输层性能有所忽略; 第二, 目前的研究大都基于马尔可夫决策过程建模, 这需要网络具有完全知识, 使得这类模型的应用受到很大限制. 针对以上问题, 本文提出一种新的算法: 网络中每个节点通过联合配置物理层调制方式、发射功率、 链路层信道接入和TCP拥塞控制因子来找到传输层端到端近似最优吞吐率. 由于无线设备对环境感知存在误差, 本文将网络模型建模为部分可观测马尔可夫决策过程, 并将其转换成信念状态马尔可夫决策过程, 采用Q值迭代找到近似最优策略. 仿真分析表明, 提出的算法能在动态无线环境下以一定的误差限收敛于最优策略, 能在功率受限条件下, 有效提高传输层端到端吞吐率.     

像散椭圆高斯光束的M2因子矩阵的理论与实验研究

对像散椭圆高斯光束, 传统的M²因子测量采用M_x²和M_y²来描述光束质量. 当光束绕z轴旋转, M_x²和M_y²会随之变化, 单纯采用M_x²和M_y²来评价激光光束质量并不唯一. 为此采用了像散椭圆高斯光束的M²因子矩阵, 理论推导出了在同一坐标系下光场绕z轴旋转不同角度后的M²因子矩阵, 找出了光场旋转前后的M²因子矩阵元的不变量关系. 数值模拟、 实验测量得到M²因子矩阵主对角元随光斑旋转角度的变化轨迹曲线, 及反对角元随旋转角度的变化规律. 理论推导与实验结果相符. 结果表明, 像散椭圆高斯光束在主方向上时M_x²与M_y²之和最小; 在其他方向上的M_x², M_y²之和大于在主方向上的M_x², M_y²之和; 反对角元随旋转角度呈周期变化, 在主方向上为零. 关键词： M²因子矩阵')" href="#">M²因子矩阵 像散椭圆高斯光束 实验测量 矩阵光学