多重积分Nash平衡点的Lipschitz估计

设F（p，q）和G（p，q）在无穷远点的邻域内是分别关于p和q的近似凸函数，且具有二次增长．考虑由F和G构成的一对定义在Soblev空间中的泛函．本文利用blowup技巧，证明了这样一对泛函的Nash平衡点实际上是Lipschitz连续的．     

等高线图分析技术在GC／FTIR联用数据处理中的应用

在三种高聚物的裂解大口径毛细管气相色谱－傅里叶变换红外光谱联用分析（ＰｙＷＢＣＧＣ／ＦＴＩＲ）数据获得的基础上，介绍应用等高线图（ＣＴＤ）分析技术处理色谱重叠峰，并在该分析提供的信息指导下进行红外光谱累加及差减技术，获得了重叠峰中各纯物质较好信噪比的气相红外谱图并予以定性，显著了等高线图分析技术在联用数据中的优点，充分发挥了ＧＣ／ＦＴＩＲ联用特有的光谱分离离度优势。     

A nonmonotone adaptive trust region method for unconstrained optimization based on conic model

In this paper, we present a nonmonotone adaptive trust region method for unconstrained optimization based on conic model. The new method combines nonmonotone technique and a new way to determine trust region radius at each iteration. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments show that our algorithm is effective.     

Differential equation approach for the energy average of the scattering function

An exact differential equation is given to evaluate the energy average of the scattering function. The advantage of the differential equation as compared to the earlier methods based on series expansion is that one has to evaluate only single sums over the complex poles of the S-matrix. Using Wigner’s semicircle law for the distribution of the real parts of the poles of the scattering matrix, the earlier expression for the energy average of the scattering function is rederived.     

Symmetry reductions and new exact non-traveling wave solutions of potential Kadomtsev-Petviashvili equation with p-power

With the aid of Maple symbolic computation and Lie group method, PKPp equation is reduced to some (1+1)-dimensional partial differential equations, in which there are linear PDE with constant coefficients, nonlinear PDE with constant coefficients, and nonlinear PDE with variable coefficients. Using the separation of variables, homoclinic test technique and auxiliary equation methods, we obtain new abundant exact non-traveling solutions with arbitrary functions for the PKPp.     

纹影技术在直喷式柴油机燃烧过程研究中的应用

本文叙述了作者所设计建立的高速纹影摄影光路系统,给出了利用该系统所拍摄的纹影照片,并通过照片简单分析了柴油机缸内的喷雾和燃烧过程。结果表明,纹影技术是研究发动机缸内空气运动和喷雾燃烧过程的有效手段。     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

高阶剪切变形板理论K■rm■n型方程及在热后屈曲分析中的应用

本文基于Reddy高阶剪切变形板理论导出Karman型非线性大挠度方程并用于层合板热后屈曲分析．分析中计及板初始几何缺陷和热效应．给出了四边简支．对称正交铺设层合板在均匀或非均匀抛物型热分布作用下的后屈曲分析．采用摄动-Galerkin混合法确定板的热屈曲载荷与热后屈曲平衡路径．同时讨论了横向剪切变形，板长宽比，铺层数以及初始几何缺陷等各种参数变化的影响．     

一种解无约束优化问题的新的非单调自适应信赖域方法

本文提出了一种解无约束优化问题的新的非单调自适应信赖域方法.这种方法借助于目标函数的海赛矩阵的近似数量矩阵来确定信赖域半径.在通常的条件下,给出了新算法的全局收敛性以及局部超线性收敛的结果,数值试验验证了新的非单调方法的有效性.     

AlGaN薄膜的微区Raman散射光谱研究

利用微区Ｒａｍａｎ散射技术,对低压ＭＯＣＶＤ生长的不同Ａｌ组分的ＡｌｘＧａ１－ｘＮ薄膜（ｘ＝０,０．０７,０．１５）进行了背散射Ｚ（Ｘ,Ｘ）Ｚ－几何配制下的测量．Ａ１（ＬＯ）模式的声子频移随Ａｌ组分的变化关系为：ω（ＡｌｘＧａ１－ｘＮ）＝（１＋０．２２０ｘ）ω（ＧａＮ）．观察到了Ａ１（ＬＯ）模式由于空间相关效应引起的展宽．Ｅ２模式随Ａｌ组分的的增大产生的移动很微小,但趋于展宽．这被认为是Ｅ２模式的声子频移随Ａｌ组分的增加而增大与其受到的张应力导致的声子频移随Ａｌ组分的增加而减小共同作用的结果．在多种配置下,观察到了Ａｌ０．０７Ｇａ０．９３Ｎ薄膜的Ａ１（ＴＯ）模式、Ａ１（ＬＯ）模式、Ｅ１（ＴＯ）模式和Ｅ２模式．验证了ＡｌｘＧａ１－ｘＮ薄膜的Ｒａｍａｎ选择定则．表明ＡｌｘＧａ１－ｘＮ薄膜具有单模行为．