拉格朗日中值定理的一个新证法

本文给出了利用坐标旋转法证明拉格朗日中值定理的一种新方法。即从罗尔定理出发，采用坐标旋转法及隐函数、复合函数求导法则，证明拉格朗日中值定理，由于该证明方法从直观的几何意义入手，因此，其证明过程更加清晰、易懂。     

一个新非线性方程组解的存在性定理

作为微积分中连续函数介值定理在n维欧氏空间Rn中的推广,G.Aumann建立了一个定义于n维矩形上非线性方程组解的存在性定理,J.Rohn利用Brouwer不动点定理,把定理推广到定义域为紧凸集的情形。利用Brouwer拓扑度理论,证明定理中凸性条件进一步减弱为星形区域时,其结论仍然成立。     

Lagrange中值定理的证明

通过从Lagrange中值定理的结论、条件、几何意义三个方面的分析，提出了构造辅助函数的思路和方法，并利用辅助函数证明了Lagrange中值定理。     

中值定理的应用探讨

通过典型例题，对微分中值定理，积分中值定理在求特殊函数的极限及有关命题，证明等式、不等式方面做了深刻地阐述，探讨怎样正确、理解、应用好中值定理。     

Zp上的遍历定理

在密码学和编码理论中，学习伪随机序列和遍历变换十分重要。通过应用组合的性质，对其进行变形，使得在满足引理1的条件下，对乙上的遍历定理进行了证明。     

n阶非线性常微分方程n点边值问题解的存在唯一性

n阶非线性常微分方程n点边值问题解的存在唯一性早在20世纪50年代就有人开始研究，所得结果都是在条件及其复杂，假设了一些边值问题解的存在性或唯一性(甚至包括其自身的)的基础上得到的，这给应用带来了困难。至今还没有人得到条件简单明了的便于应用的存在唯一性定理。这篇文章成功地将上述边值问题转化成了积分方程问题．并利用格林函数，不动点定理得到了较好的存在唯一性结果。为研究n阶非线性常微分方程非线性n点边值问题奠定了基础。     

带有双闭环滤波器的有限时间稳定变结构制导律

 在末制导过程中,为了取得较高的命中精度,制导律必须使视线(LOS)角速率较快收敛。为了提高制导律的性能,在假设未知不确定时变项有界的前提下,对带有双闭环滤波器的变结构制导律进行了研究。提出的变结构制导律能够使视线角速率及其一阶导数在有限时间内收敛至滑动模态域内,得到更加精确的等效控制并有效克服干扰的影响。通过引入高阶滑动模态,对有关定理进行了重新证明,简化了证明过程,加强了定理的结论,弱化了定理成立的条件。最后利用数值仿真验证了所研究方法的有效性。     

熵损失下无失效数据的 Bayes估计

讨论了在熵损失下定时截尾数据的Bayes估计问题，将无失效数据看作逐次定时截尾试验的结果，进而得到无失效数据的Bayes估计，利用相关定理证明该估计是容许的。通过数值例子，进一步说明所得估计的合理性。     

一个均衡调整算法

本文对任务分配问题提出一个新算法－均衡调整算法，该算法具有变异性，均稀性以及均衡持久性，并以均衡定理的形式加以论述和证明，从而证明了均衡调整算法的正确性。     

凸曲线的求长问题

本文给出并证明了凸函数的一个新的性质（文中引理及其证明），依此证明了凸曲线是可以求出长度的曲线（文中定理及其证明）及凸函数是可以积分的函数。     

利用边界测点求解二维稳态导热逆问题

针对导热逆问题求解中的测点的选择提出了不同的方式,即采用边界测点取代内部测点进行导热逆问题的求解.通过数值计算揭示了测点选择不当将导致逆问题计算的失败及原因,验证了采用边界测点求解二维稳态导热逆问题的可行性.采用本文提出的方式将使逆问题的应用更为实际、合理.     

ISAR imaging of targets at low elevation angles

The problem of inverse synthetic aperture radar (ISAR) image reconstruction of targets at low elevation angle is considered. In this geometric condition the main causes affecting the reconstructed ISAR image are the multipath effect due to the reflection of the Earth's surface and the angular motions of the target produced by external action like wind, fast maneuvering, and sea waves as in the case of ships. The aim of this work is to analyze the effects that the multipath and the target angular motions jointly produce on the ISAR image. The results show that multipath generates some artifacts in the image whereas the target oscillations undergo a spatial-dependent blurring of the point spread function of the ISAR system. These theoretical results are validated by presenting some numerical examples relevant to aircrafts and ships in rectilinear or circular motion. A wide discussion on possible solutions of this problem is made in the conclusion     

基于优化技术的叶型反方法改进设计

在势流函数反方法设计叶型的过程中,通过分析叶片表面速度分布对叶型形状的影响规律,发现采用局部区域速度分布调整,可有效的克服以往反方法设计叶型中易出现的非物理解现象,并针对叶型前缘和尾缘的几何封闭问题分别建立了优化目标函数,借助流场求解中的优化迭代技术获得了具有良好气动性能并满足几何约束的叶型设计结果。对典型叶型的三个设计算例表明:所研究的叶型反问题优化设计方法,具有设计精度较高,适用范围较宽,工程应用性较好等优点。      

Inverse simulation as a tool for flight dynamics research—Principles and applications

The technique of inverse simulation is finding application in many and varied fields. As the name implies this technique is used to calculate the control action required to achieve a specified system response. The field of aircraft flight dynamics is particularly suited to this form of simulation as the question of what control actions must the pilot (or automatic flight control system) take for the aircraft to fly along a particular trajectory (a landing approach, for example) is often asked. This paper looks specifically at the application of inverse simulation in flight dynamics. The aim is not only to give an overview of the various techniques and applications but also to provide guidance to potential users of the technique on several of the physical and numerical features often observed in the results. An extensive review of the methodologies used within the family of inverse simulations is presented followed by a formal treatment of the theoretical development of inverse simulation as an established technique. A case study involving the inverse simulation of a helicopter flying a slalom manoeuvre is presented to demonstrate the application of inverse simulation in a flight dynamics analysis. An important feature of the use of inverse simulation is that it is necessary to define the output response required—in the case of flight dynamics the required flight path has to be modelled. Some of the methods used are documented, and their validity discussed. The paper also gives an insight into the types of problem which can be addressed by inverse simulation by detailing some of the many applications to which it has been put in the past. These include studies of rotorcraft handling qualities, performance and design, and pilot modelling as well as model validation. An important element of this paper is the formal, theoretical analysis of some of the numerical and physical features exhibited by inverse simulation which should aid potential users to interpret their results. The work presented in this paper shows a clear evolution of inverse simulation from its initial days when the mathematical models used were relatively simple into a mature analytical technique able to incorporate state of the art mathematical models and be applied to real flight dynamics problems.     

有摩擦弹性接触问题的增量数值解法

 指出应用全量变分法于有摩擦弹性接触问题是不能普遍适用的，提出了这一类问题增量变分法的数值解法和适用于增量法的库伦摩擦力的正则条件。对可转变的边界条件限于较简单的有限个离散点的情况，可采用状态试凑法来确定可变约束条件的状态。数值计算结果表明了本文提出的增量方法的正确性。     

混合初边值问题解的渐近性质及其差分解

 本文讨论了当t→∞时拟线性方程组初边值解的一些渐近性质。在假设非定常问题的解唯一、定常问题的解存在时,对同一边界条件,证明了当t→∞时非定常方程组的解趋于定常问题的解,讨论了用差分方法求解这种问题时,边界点上一些量的精确算法;为了消除在物体尖角附近出现的局部非物理解,得到正确解,我们还给出了一个简单的耗散型物面边界格式;最后给出了一些尖角凹形体的算例。     

辽宁省经济发展方案与指标的分析

本文利用辽宁省1997年投入产出表对辽宁省经济发展的几个问题做了初步的优化分析，得出了具有一定指导性意义的结论。     

Marangoni boundary layers

This paper deals with the theory of Marangoni boundary layers developing near the free surface of a nonuniformly heated liquid.

In the Introduction the notion of a thermocapillary effect is considered, and the conditions, under which thermocapillary flow is dominant, are elucidated. The similarity criteria of the problems are revealed, and the effects resulting from melt convection are considered.

In the second section the mathematical aspects of the theory of Marangoni boundary layers are considered. The boundary layer effect on the form of a free surface is investigated, and some examples are presented.

In Section 3 a qualitative flow pattern in a Marangoni boundary layer is analyzed, similarities and differences in the problems of Prandtl and Marangoni boundary layer theory are discussed. The possibility of Marangoni boundary layer degeneration at the outer boundary, as well as the initiation of flow containing a counter-stream zone are emphasized.

The fourth section outlines the calculation scheme on the basis of boundary-layer theory for convective flows with directed crystallization and in the absence of mass forces. Some examples are presented.

In the fifth section some problems of the theory of Marangoni boundary layers that need further investigation are discussed.     

现代自然层流翼型的设计方法

本文介绍一种设计跨声速自然层流翼型的计算流体力学(CFD)方法。本方法采用“正反迭代、余量修正”设计原理,通过将跨声速翼型设计软件NPU-TD2D中的反设计程序进行改进,并与含有层、湍流混合边界层修正的跨声速层流翼型计算程序DLRBGKWALZ耦合,实现了在跨声速粘性流动条件下直接设计层流翼型。亚、超临界的设计实例和风洞验证表明,本方法可以在几个设计迭代内设计出压力分布、转捩位置及气动参数均准确收敛于设计目标的新翼型,是一种设计现代自然层流翼型的有效而实用的CFD方法。     

Is information security an oxymoron?

Although weaknesses have been demonstrated in some security techniques (encryption, protocols, mobile code such as Java, etc.), current security technology is quite strong in many areas. Despite this, information security has proved difficult to achieve in large modern software systems. Many problems have been reported in which supposedly secure systems have been penetrated and, in some cases, significant damage done. One problem considered is a buffer-overrun attack. The idea called a 〈wrapper〉 which is a layer of software that logically surrounds a software artifact and enhances the functionality of the artifact in some way, is then discussed. Most proposals for the use of wrappers assume that their presence is transparent to the artifact being wrapped. In other words, the artifact sees its operating environment as unchanged and the artifact does not have to be modified in i order to permit it to be wrapped. Wrappers have been proposed as an approach to dealing with deficiencies in existing systems, deficiencies in security for example. The use of shells as a feasible solution to the problem of security is also considered