一种金属腔体中微波断层成像的最优分层非均一背景

针对基于金属腔体的微波断层成像系统,提出了一种最优分层非均一背景的设计方法.该方法使用一种新的微波断层成像积分算子评价方法和模拟退火法等最优化方法.首先,介绍了一种基于有限元法的微波断层成像积分算子计算方法.然后,提出一种新的微波断层成像积分算子度量,该度量可以综合评价整个积分算子奇异值谱,并通过一组仿真研究证明该度量与反演结果的误差具有相关性;该度量用一个数值综合评价一个积分算子,可以方便地应用于最优化算法中;利用模拟退火法选择圆形金属腔体中分层非均一背景的每一层介质的相对介电常数,从而获得一个最优分层非均一背景.最后,对尺寸小于半波长的圆柱目标和"凹"字形复杂目标进行仿真研究,仿真结果证明该最优分层非均一背景可以提高微波断层成像算法的收敛速度,提高反演结果的准确性.     

Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.      

Hansen Solubility Parameters in the Analysis of Solvent–Solvent Interactions by Inverse Gas Chromatography

The Flory–Huggins interaction parameters, for a solute with pure nonvolatile solvents and with binary mixtures of nonvolatile solvents were evaluated using Inverse Gas Chromatography (IGC) data at 403.15 K. The five solvents used have similar structure and nearly the same molar volume and their mixtures form regular solutions. The values were used to evaluate the Hansen solubility parameters (HSP) for the pure solvents and mixed solvent systems. The HSP are plotted as a function of composition of the polar solvent. The dispersion component, , and the polar component, , exhibited negative deviation whereas the hydrogen bonding component, , showed positive deviation in the four mixtures. However, the total solubility parameter was found to be almost linear with composition in the four binary systems. Further the total solubility parameter, , was used to calculate the molar excess heat of vaporization for the solvents (C78 + POH, C78 + PCN, C78 + TTF, and C78 + TMO) that was found to be negative for C78 (19,24-dioctadecyldotetracontane) + POH(18,23-dioctadecylhentetracontan-1-ol) and C78 + PCN(1-cyano-18,23-dioctadecylhentetracontane) systems and positive for C78 + TTF [19,24-bis(18,18,18-trifluorooctadecyl)-1,1,1,42,42,42-hexafluorodotetracontane), and C78 + TMO(17,22-bis-(16-methoxyhexadecyl)-1,38-dimethoxyoctatriacontane] and the other systems.     

Demonstration of Inverse Scattering Transform for DNLS Equation

Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as |λ| →∞, the usual inverse scattering transform (IST) must be revised. Beside the Kaup and Newell's approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ-2 or λ-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.     

与q形变玻色算符逆算符相关的相干态及其量子统计性质

讨论了ｑ形变玻色算符的广义逆算符作用于ｑ－相干态所得到的两类量子态的数学及量子统计性质。结果表明，ｑ－相干态的光子激发态不存在压缩但呈现反聚束效应，而ｑ－相干态的光子湮灭态却存在压缩但不呈现反聚束效应。     

体上GP矩阵的刻划

在文[2]～[6]的基础上,本文证明了体上 GP 矩阵的15种刻划,并给出了强 P 除环上GP 矩阵的一个充要条件及其群逆的一个显式。     

Demonstration of Soliton Solutions of DNLS Equation by Liouville Theorem

In the inverse scattering transform (IST), the reflectionless Jost solutions are combined by their analytic properties in the complex spectrum parameter plane, and then can be shown to satisfy the two Lax equations indeed by Liouville theorem. So the corresponding soliton solutions certainly satisfy the nonlinear equation by compatibility condition. Especially the multi-soliton solutions of DNLS equation can be demonstrated in this way. PACS Numbers: 05.45.Yv, 02.30.-f, 11.10.Ef     

单势阱粒子溢流模型中热力学量的涨落效应

采用相空间积分方法严格导出了各态历经条件下单势阱粒子溢流模型中系统温度和阱内粒子数涨落的解析表达式,着重讨论了热力学量涨落与总粒子数和势阱体积之间的关系.研究表明,系统总粒子数越少以及势阱体积越小,热力学涨落越显著,并且热力学涨落与阱内粒子的溢出密切相关.粒子的溢出和系统负比热及热力学大幅涨落的发生存在一一对应的关系,这一对应关系的根源可以从表观能量逆均分来理解.