正交各向异性轴对称位势问题的Trefftz有限元分析

Trefftz有限元法（Trefftz finite element method, TFEM）因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元．在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入修正变分泛函并利用Gauss散度定理消除区域积分,最后根据驻值原理导得只含边界积分的单元刚度方程．数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.     

半平面压电体的Green函数及其应用

本文研究半平面压电体在线力、电荷和位错作用下的弹性场和电场，即Green函数．基于各向异性弹性力学中的Stroh方法和解析延拓理论，推导了Green函数的封闭形式的解．作为解的应用，分析了含半无限裂纹的无限大压电介质的机电耦合场，给出了应力和电位移强度因子的解析表达式．     

如何发现世界上最安静的敌潜艇

我们建立了一个数学模型；用以探测一个大型移动目标，譬如说一艘潜艇．并且计算出潜艇的大小和它移动的速度、方向．探测过程仅依赖于一个普通噪声环境受到的扰动我们作了一系列合理的假设，分析了潜艇的运动以及它对背景噪声场的影响．运动潜艇吸收、反射噪声声波，由此产生的多普勒效应，是原噪声场的一个扰动．这种扰动可被探测器（如压电麦克风）捕获．在对潜艇的形状与材料作了假设的基础上，我们推导出在一个单频单幅噪声场中潜艇回波的频谱分布．这个频谱分布类似伞形，简称伞形分布．频谱带宽可用于计算潜艇航速．伞形分布曲线下的面积可用于计算潜艇等效截面积，根据频谱的中心频率与噪声频率的差异，可计算出它的移动方向我们引入了对数频率坐标．基于卷积理论，计算出了在宽带噪声场中潜艇的回波．这样，通过反卷积，就可以简化为上述己解决的若这艘潜艇置于一单频单幅噪声场中应有的情况．根据反卷积后的回波分布，即可根据本文中提到的方法，得到需要的结果．我们还把这个模型推广到实际中，给出了一个伺服系统和一个可行的方案．文中最后就模型优缺点和问题本身的局限性作了讨论．考虑到实际的应用，提出了一些新的构想，并预想了这类问题今后可能的发展方向．     

Experimental Study on the Vortex-Induced Vibration of Fixed-Hinged Flexible Risers北大核心CSCD

海洋立管顶部常铰接于浮式平台下方,在海流激励下存在涡激振动响应,潜在疲劳失效的风险.该文采用非介入光学测试方法（高速摄像）,对布置于循环水槽中顶部铰接-底部固定的悬链线柔性立管进行了振动响应研究.实验结果表明,立管三个方向被激发的振动模态阶数与主导振动频率均随约化速度的增加而逐渐升高,平面外的最大均方根振幅在模态过渡时有先降后升的变化,与振动模态分支相呼应.流体与立管之间能量传递在不同方向的分布存在一定差异,导致不同步的模态过渡现象.平面内振动存在与平面外振动主导频率吻合的频率,根据其是否主导对应管段的平面内振动,将其分为强耦合和弱耦合两种模式.     

Poisson比为1/2材料中球形空穴突变和球形空穴萌生的分岔问题研究

研究Ｐｏｉｓｓｏｎ比为１／２的Ｈｏｏｋｅ材料中,空穴的突变和萌生现象·求解一个球对称几何非线性弹性力学的移动边界（ｍｏｖｉｎｇｂｏｕｎｄａｒｙ）问题,空穴为球形,远离空穴处为三向均匀拉伸应力状态,在当前构形上列控制方程;在当前构形边界上列边界条件·找到了这个自由边界问题的封闭解并得到空穴半径趋于零时的叉型分岔解·计算结果显示,在位移＿载荷曲线上存在一个切分岔型分岔点（或鞍结点型分岔点、极值型分岔点）,这个分岔点说明在外力作用下空穴会发生突变,即突然“长大”;当球腔半径趋于零时,这个切分岔转化为叉型分岔（或分枝型分岔）,这个叉型分岔可以解释实心球中的空穴萌生现象     

图的最大亏格与2-因子

图Ｇ的一个２因子Ｆ就是Ｇ的这样一个支撑子图，使其任何节点ｖ∈Ｖ的次ｄＦ（ｖ）＝２．易见，Ｇ的每个２因子均为无公共节点的圈之并．若Ｆ的每个圈的长均为３（或４），则称Ｇ含有一个三角形（或四边形）２因子．Ｍ．ｋ∨ｏｖｉｅｒａ［５］得到了含有三角形２因子的３－正则图的最大亏格．本文在３－正则图上，引进了扩张运算和讨论了与最大亏格和Ｂｅｔｉ亏数之间的关系．利用这些运算，得到了所有含四边形２因子的连通３－正则图是上可嵌入的，即γＭ（Ｇ）＝ｎ４（ｎ为Ｇ的节点数ｎ＝｜Ｖ（Ｇ）｜）．然后，基于此证明了含四边形２因子且所有节点ｖ∈Ｖ的次ｄＧ（ｖ）＝３（ｍｏｄ４）的图Ｇ均为上可嵌入的     

普适双变量随机气候模式的研究

该文对海气耦合双变量随机气候模式进行了系统研究，研究结果表明：（1）无论是考虑只有大气子系统的随机作用还是同时考虑大气子系统和海洋子系统的双扰动，对给定的扰动频率，海气气候系统对大气的扰动作用相当于一个十分简单的线性放大器；对于不同的扰动频率，在能量上海温的变化将随大气的扰动做4次幂的非线性响应;（2）若同时考虑大气子系统和海洋子系统的随机扰动，在满足细致平衡条件下可以求出系统定态的概率分布。否则，只有当扰动为弱噪声时，才能用级数展开法近似求出系统的概率分布。     

求部分分式待定常数的几个规则及简便求法

有理函数分解为部分分式，往往要确定部分分式中的待定常数，常用的方法是用赋值法或比较法进行。下面讨论几个规则及简便的求法。假设为真分式，且P（x）与Q（x）无公共因子。从例1中可以看出，Ak（k＝1，2，…，m）实际上等于中去掉Q（x）里的因子（x－a。），然后将x—a。代入后所得的值。利用这种方法进行心算可以很容易“读出”A。的值。如。。Th。。。。。Q；（。）。。，。，；。＃。。＃。。g证明用（x－a广乘（3）式的两端，得令x、a，两端取极限，注意到。即右端的极限为k！B。。，两端除以k！，即由（4）式知，当是一0时，有…     

梢涡流场中气泡轨迹及形态数值模拟

针对气泡在舰船尾迹涡流场运动特性,根据其是否为尾涡所捕获,将数值模拟过程分为两个阶段:准球状运动阶段和非球状运动阶段．分别应用单向耦合质点粒子追踪法（PTM）和边界元法（BEM）模拟这两个阶段,将第1阶段结束的物理量作为第2阶段的初始条件,从而完成整个数值模拟过程．在已有数值研究结果和实验数据基础上,探讨空化发生条件,追踪尾迹空泡运动轨迹,模拟尾迹气泡的运动、变形、溃灭等,以及被尾涡捕获后的撕裂等运动特性,旨在为优化设计尾流场提供参考．     

飞行器结构噪声致振试验及声振耦合响应分析

以高超声速飞行器X-43A为研究对象,建立其有限元结构模型,在动力学实验室进行飞行器结构模型的固有频率测试,通过固有频率计算与试验结果对比,二者误差在1%左右,这表明所建立的结构有限元模型是比较准确的．在高声强混响室进行飞行器结构噪声致振试验,得到飞行器结构测点加速度功率谱密度(power spectral density, PSD)和舱内声场噪声声压级,通过声振耦合数值模拟计算结果与试验值对比,结果表明:数值模拟计算方法对振动噪声环境预测是比较可靠的,结构振动响应与舱内噪声响应的有限元分析与试验结果趋势上较为一致,低频段吻合较好;高频外噪声场引起的飞行器弹性腔体结构振动占据结构振动响应的主要成分,尤其是以结构低阶振动为主,而外噪声场传递到封闭腔体内的噪声也主要是通过结构腔体弹性壁板的低阶振动传播,即使外噪声激励是宽频的,封闭舱内响应噪声的频率主分量仍然是结构的低阶模态振动．     

基于肤色模型法的人脸定位技术研究

基于JAVA语言对人脸识别首要环节的定位技术进行代码开发,在传统肤色模型法的基础上,对采集到的大量图像进行深入研究,运用图像精准化微调和图像增强处理的方法,提高了传统肤色模型法在实际运用中的精准率,实现了人脸在视频图像中的定位。     

自然电位测井的数学模型

自然电位测井是石油开发中一种常用而重要的测井方法。自然电位函数的数学模型可归结为具有间断交界面条件的椭圆型等位面边值问题,在交界面交汇点处,自然电位的跳跃通常不满足相容性条件,此时,这个边值问题不存在分块H1*解,不能使用有限元素法直接求解。本文介绍这一测井方法的数学模型及数值求解方法。     

关于单调亚紧空间

In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fó-subspaces. For a generalized ordered (GO)-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X* is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.     

Supersymmetric p-branes at finite temperature

The regularized free energy of open and closed supersymmetric p-branes in (D – 1)-dimensional flat space is calculated by the method of quasiclassical quantization. The critical temperature, indicating a phase transition, is obtained. It is shown that the quantum properties of bosonic p-branes (open and closed) with p = D – 1 are identical to the properties of a massless scalar particle.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 36–40, 1990.     

The joint embedding property in normal open induction

The models of normal open induction are those discretely ordered rings, integrally closed in their fraction field whose nonnegative part satisfy Peano's induction axioms for open formulas in the language of ordered semirings.

It is known that neither open induction nor the usually studied stronger fragments of arithmetic (where induction for quantified formulas is allowed), have the joint embedding property.

We prove that normal models of open induction have the joint embedding property.     

The inverse scattering problem for a partially coated cavity with interior measurements

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.     

Non-accretive Schrödinger operators and exponential decay of their eigenfunctions

We consider non-self-adjoint electromagnetic Schrödinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.     

On catastrophe and cavitation for spherical cavity

This work deals with catastrophe of a spherical cavity and cavitation of a spherical cavity for Hooke material with 1/2 Poisson's ratio. A nonlinear problem, which is the Cauchy traction problem, is solved analytically. The governing equations are written on the deformed region or on the present configuration. And the conditions are described on moving boundary. A closed form solution is found. Furthermore, a bifurcation solution in closed form is given from the trivial homogeneous solution of a solid sphere. The results indicate that there is a tangent bifurcation on the displacement-load curve for a sphere with a cavity. On the tangent bifurcation point, the cavity grows up suddenly, which is a kind of catastrophe. And there is a pitchfork bifurcation on the displacement-load curve for a solid sphere. On the pitchfork bifurcation point, there is a cavitation in the solid sphere.     

Reconstruction of a penetrable cavity and the external obstacle

The inverse acoustic scattering of point sources by a penetrable cavity and the external obstacle is considered. Making use of the internal measurements of scattered field on a closed curve inside the cavity, we first derive a factorization method which provides a rigorous characterization of the support of the cavity without knowing the external object. Then under the condition of the cavity is known in advance, we show that the linear sampling method can be applied to recover the outside obstacle with the help of some Green function.     

Completion of the mixed unit interval graphs hierarchy

We describe the missing class of the hierarchy of mixed unit interval graphs. This class is generated by the intersection graphs of families of unit intervals that are allowed to be closed, open, and left‐closed‐right‐open. (By symmetry, considering closed, open, and right‐closed‐left‐open unit intervals generates the same class.) We show that this class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic‐time algorithms that recognize graphs from this class and produce a corresponding interval representation if one exists. We also show that the algorithm from Shuchat et al. [8] directly extends to provide a quadratic‐time algorithm to recognize the class of mixed unit interval graphs.