Maximum principle for mean-field jump–diffusion stochastic delay differential equations and its application to finance

This paper investigates a stochastic optimal control problem with delay and of mean-field type, where the controlled state process is governed by a mean-field jump–diffusion stochastic delay differential equation. Two sufficient maximum principles and one necessary maximum principle are established for the underlying system. As an application, a bicriteria mean–variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques. Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier, which are as elegant as those in the classical mean–variance problem without delays.     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Synthesis,characterization, and thermal properties of phosphorus‐containing,wholly aromatic thermotropic copolyesters

A series of phosphorus‐containing, wholly aromatic thermotropic copolyesters from acetylated 2‐(6‐oxide‐6H‐dibenz〈c,e〉〈1,2〉oxa phosphorin‐6‐yl)‐1,4‐dihydroxy phenylene, p‐acetoxybenzoic acid, terephthalic acid, and isophthalic acid were prepared by melting polycondensation. The structure and basic properties of the polymers, such as the glass‐transition temperature (T_g), melting temperature (T_m), thermal stability, crystallinity, and liquid crystallinity, were investigated with Fourier transform infrared, elemental analysis, differential scanning calorimetry (DSC), thermogravimetric analysis, wide‐angle X‐ray diffraction, and hot‐stage polarizing optical microscopy. The copolyesters had relatively high T_g values ranging from 183 to 192°C. The T_m values obtained from DSC curves for samples P‐20 and P‐25 were 290 and 287°C, respectively (where the number in the sample name indicates the molar fraction of the phosphorus‐containing monomer in the reactants). The initial flow temperatures of other samples observed with hot‐stage polarizing microscopy were 271–290°C. The 5% degradation temperatures in nitrogen ranged from 431 to 462°C, and the char yields at 640°C were 41–52%. All the copolyesters, except P‐40, were thermotropic and nematic. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1278–1284, 2002     

A novel approach for fit analysis of thermal protective clothing using three-dimensional body scanning

The garment fit played an important role in protective performance, comfort and mobility. The purpose of this study is to quantify the air gap to quantitatively characterize a three-dimensional (3-D) garment fit using a 3-D body scanning technique. A method for processing of scanned data was developed to investigate the air gap size and distribution between the clothing and human body. The mesh model formed from nude and clothed body was aligned, superimposed and sectioned using Rapidform software. The air gap size and distribution over the body surface were analyzed. The total air volume was also calculated. The effects of fabric properties and garment size on air gap distribution were explored. The results indicated that average air gap of the fit clothing was around 25–30 mm and the overall air gap distribution was similar. The air gap was unevenly distributed over the body and it was strongly associated with the body parts, fabric properties and garment size. The research will help understand the overall clothing fit and its association with protection, thermal and movement comfort, and provide guidelines for clothing engineers to improve thermal performance and reduce physiological burden.     

Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators

We consider infinite-dimensional port-Hamiltonian systems described on jet bundles. Based on a power balance relation we introduce the port-Hamiltonian system representation using differential operators regarding the structural mapping, the dissipation mapping and the input mapping. In contrast to the well-known representation on the basis of the underlying Stokes–Dirac structure our approach is not necessarily based on using energy-variables which leads to a different port-Hamiltonian representation of the analyzed partial differential equations. The presented constructions will be specialized to mechanical systems to which class also the presented examples belong.     

Bi2—xPbxSr2Ca2Cu3Oy系高Tc超导体相变的研究

用DSC研究了高T_e超导体B_(2-r)Pb_rSr_2Ca_2Cu_sO_v(x=0,0.2,0.4,0.6)从室温至600℃范围内的相变。在320℃和440℃附近有二个吸热蜂,每一个峰对应一个相变过程。440℃附近的相变是不可递的,其原子激活能为1.37eV,是由高T_e相向低T_e相的转变。而320℃附近的相变则与超结构的形成有关。     

自适应混合多目标分布估计进化算法

针对多目标分布估计算法全局收敛性较弱的缺陷,提出了一种自适应混合多目标分布估计进化算法。其基本思想是:在多目标分布估计算法中引入全局收敛性较强的差分进化算法,当函数变化率较大时,用分布估计算法产生新种群;当函数变化率较小即算法可能陷入局部收敛时,用差分进化算法产生新种群。理论分析和数值实验结果表明,这种混合算法不仅具有良好的全局收敛性,而且解的分布性和均匀性较没有考虑目标函数变化率的混合多目标分布估计算法也有了一定程度的提高。     

基于祖冲之类方法的多体动力学方程保能量保约束积分

针对一类多体动力学问题导出的微分 代数方程,提出一种保能量、保约束的算法.该算法基于祖冲之类方法和欧拉中点保辛差分,利用祖冲之类方法保证在时间格点上精确满足约束方程,避免约束违约问题;并进一步证明该算法在时间格点上可以精确保能量.数值算例进一步验证该算法的可靠性.     

D.s.c. investigation of the states of water in poly(vinyl alcohol-co-itaconic acid) membranes

The state of water in water-swollen poly(vinyl alcohol-co-itaconic acid) membranes, having various water contents from 0.31 to 0.83, was investigated by d.s.c. measurements and compared with those in water-swollen poly(vinyl alcohol) membranes. The amount of freezing water in the membranes was estimated by use of a relationship between the phase transition temperature and the enthalpy of the crystallization of supercooled water. The melting temperature of the water in the membranes immersed in urea and NaCl 0–2 mol l^?1 aqueous solutions was also determined by d.s.c. analysis. The present study proposes a method for estimating the solubilities of urea and NaCl in both of the freezing and the non-freezing water using the melting point depression of the freezing water in the membranes immersed in the solute solution.