First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints

In this paper we consider a mathematical program with semidefinite cone complementarity constraints (SDCMPCC). Such a problem is a matrix analogue of the mathematical program with (vector) complementarity constraints (MPCC) and includes MPCC as a special case. We first derive explicit formulas for the proximal and limiting normal cone of the graph of the normal cone to the positive semidefinite cone. Using these formulas and classical nonsmooth first order necessary optimality conditions we derive explicit expressions for the strong-, Mordukhovich- and Clarke- (S-, M- and C-)stationary conditions. Moreover we give constraint qualifications under which a local solution of SDCMPCC is a S-, M- and C-stationary point. Moreover we show that applying these results to MPCC produces new and weaker necessary optimality conditions.     

Fe2O3掺杂Ce0.8Nd0.2O1.9固体电解质的结构与导电性能

采用溶胶-凝胶法合成SiO2含量小于50×10-6的Ce0.8Nd0.2O1.9(NDC)陶瓷粉体,并将少量Fe2O3加入到NDC体系中,讨论Fe2O3的掺杂对其微观结构及电性能的影响。通过X射线衍射(XRD)等手段对氧化物进行结构表征,交流阻抗谱(AC)测试电性能。研究表明,Fe2O3的掺杂显著提高NDC陶瓷材料的致密度;相比于NDC而言,加入Fe2O3后材料的晶界电导率提高约12倍,总电导率提高约6倍。     

探究学习的历史沿革

本文总结了探究学习的历史起源及国内外的发展现状 ,以期帮助广大教师更好地了解探究学习 ,应对国家新一轮课程教材改革。     

Parallel Plate Interferometer with a Reflecting Mirror for Measuring Angular Displacement

A parallel plate interferometer with a reflecting mirror for measuring angular displacement is proposed. A deflection angle of a beam caused by an angular displacement is amplified by use of a reflecting mirror to increase the optical path difference (OPD) in the plane-parallel plate, which provides high sensitivity of the phase measurement. Detection of light transmitted through the plane-parallel plate with a position sensitive detector (PSD) enables high accurate measurement of the initial angle of incidence to the plane-parallel plate with insensitivity to stray light. The improved parallel plate interferometer achieves a measurement repeatability of 10⁻⁸ rad.     

Viscoelastic interfacial properties of compatibilized poly(ε‐caprolactone)/polylactide blend

Poly(ε‐caprolactone)/polylactide blend (PCL/PLA) is an interesting biomaterial because the two component polymers show good complementarity in their physical properties. However, PCL and PLA are incompatible thermodynamically and hence the interfacial properties act as the important roles controlling the final properties of their blends. Thus, in this work, the PCL/PLA blends were prepared by melt mixing using the block copolymers as compatibilizer for the studies of interfacial properties. Several rheological methods and viscoelastic models were used to establish the relations between improved phase morphologies and interfacial properties. The results show that the interfacial behaviors of the PCL/PLA blends highly depend on the interface‐located copolymers. The presence of copolymers reduces the interfacial tension and emulsified the phase interface, leading to stabilization of the interface and retarding both the shape relaxation and the elastic interface relaxation. As a result, besides the relaxation of matrices (τ_m) and the shape relaxation of the dispersed PLA phase (τ_F), a new relaxation behavior (τ_β), which is attribute to the relaxation of Marangoni stresses tangential to the interface between dispersed PLA phase and matrix PCL, is observed on the compatibilized blends. In contrast to that of the diblock copolymers, the triblock copolymers show higher emulsifying level. However, both can improve the overall interfacial properties and enhance the mechanical strength of the PCL/PLA blends as a result. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 756–765, 2010     

Transition temperature reduction for CdS nanoparticles under high pressure

The structure transition of nanoparticles has a significant effect on their practical applications. In this study, the transition temperature of CdS nanoparticles with the size of 3–5 nm from sphalerite to wurtzite structure is significantly reduced to 150 °C under a high pressure of 1 GPa, much lower than that 300–400 °C for CdS nanoparticles and 600 °C for bulk CdS under room pressure. The lower transition temperature leads to an ultrafine grain size d = 5 nm for the formed wurtzite phase as compared with that d = 33 nm yielded under room pressure with a similar transition volume fraction of ~80%. The underlying physical mechanism is discussed.     

Strong Semismoothness of the Fischer-Burmeister SDC and SOC Complementarity Functions

We show that the Fischer-Burmeister complementarity functions, associated to the semidefinite cone (SDC) and the second order cone (SOC), respectively, are strongly semismooth everywhere. Interestingly enough, the proof relys on a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix.The author’s research was partially supported by Grant R146-000-035-101 of National University of Singapore.The author’s research was partially supported by Grant R314-000-042/057-112 of National University of Singapore and a grant from the Singapore-MIT Alliance.Mathematics Subject Classification (2000): 90C33, 90C22, 65F15, 65F18     

碳纳米管在聚对苯二甲酸丙二酯/乙烯-醋酸乙烯酯共聚物不相容共混体系中的选择性分散

采用熔融共混法制备了碳纳米管(CNT)填充改性的聚对苯二甲酸丙二酯(PTT)/乙烯-醋酸乙烯酯共聚物(EVA)三元复合材料.通过扫描电子显微镜(SEM)、透射电子显微镜(TEM)、接触角测量仪、旋转流变仪等研究了该复合材料中碳纳米管的分布、不相容的相形态以及流变和力学性能.研究结果表明,与EVA相比,PTT组分具有较低...     

Morphology evolution of nanocomposites based on poly(phenylene sulfide)/poly(butylene terephthalate) blend

Poly(phenylene sulfide) (PPS)/poly(butylene terephthalate) (PBT) (60/40 w/w) blend nanocomposites (PPS/PBTs) were prepared by direct melt compounding of PPS, PBT, and organoclay. The morphology and rheology of PPS/PBTs were investigated using scanning electron microscope and transmission electron microscope as well as parallel plate rheometer. The intercalated clay tactoids are selectively located in the continuous PBT phase due to their nice affinity. A novel morphology evolution of the immiscible blend matrices is observed with increase of clay loadings. Small addition of clay increases the discrete PPS spherulite domain size. With increasing loading levels, the PPS phase transform to the fibrous structure and finally, to the partial laminar structure at the high loading levels, in which shows a characteristic of large‐scaled phase separation. The presence of clay, however, does not impede the coalescence of the PPS phase because the phase size increases with increasing clay loadings. The elasticity and blend ratio of two matrices are proposed as the important roles on the morphological evolution. Moreover, the laminar structure of PPS phase is very sensitive to the steady shear flow and is easy to be broken down to spherulite droplet at the low shear rate. However, high shear level is likely to facilitate the coalescence of those PPS phase and finally to phase inversion, both contributing to increases of the dynamic modulus after steady shear flow. In conclusion, the morphology of the immiscible polymer blend nanocomposites depends strongly on both the clay loadings and shear history. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1265–1279, 2008