求解集中载荷作用下厚矩形板弯曲的新方法

应用功的互等定理法(RTM)于求解厚矩形板的弯曲问题,得到了任意一点作用集中荷载矩形厚板弯曲问题的解析解,并将分析过程和结果与普通解析法进行了比较.其结果表明,这是求解厚矩形板弯曲的简单、通用的有效新方法.     

非齐次空间上Tb定理必要条件的证明

Tb定理是Calderón-Zygmund 算子的L2有界性的一个充要条件,为了完善Tb定理的结果,对Calderón-Zygmund算子T在非齐次空间上Tb定理条件下定义在Lipschitz函数上的双线性型作了介绍,利用双线性型的不等式估计,给出了在这种情况下的Tb定理的必要条件的一种证明,即若Tb1属于某个BMOpλ(μ), 则Tb1∈RBMO(μ).这个结论是对非齐次空间上Tb定理的补充.     

Chernoff-Type Direct Product Theorems

Consider a challenge-response protocol where the probability of a correct response is at least α for a legitimate user and at most β<α for an attacker. One example is a CAPTCHA challenge, where a human should have a significantly higher chance of answering a single challenge (e.g., uncovering a distorted letter) than an attacker; another example is an argument system without perfect completeness. A natural approach to boost the gap between legitimate users and attackers is to issue many challenges and accept if the response is correct for more than a threshold fraction, for the threshold chosen between α and β. We give the first proof that parallel repetition with thresholds improves the security of such protocols. We do this with a very general result about an attacker’s ability to solve a large fraction of many independent instances of a hard problem, showing a Chernoff-like convergence of the fraction solved incorrectly to the probability of failure for a single instance. Russell Impagliazzo: Research partially supported by NSF Awards CCR-0515332 and CNS-0716790. Views expressed are not endorsed by the NSF. Ragesh Jaiswal: Research partially supported by NSF Awards CCR-0515332, CCF-0634909, CNS-0524765 and CNS-0716790. Views expressed are not endorsed by the NSF.     

高斯定理的直观教学

高斯定理是一个非常重要的基本定理,也是麦克斯韦电磁场理论的基础之一.学生对高斯定理的掌握与理解会直接影响其对电磁场理论课程的学习效果.而现有教材给出高斯定理的证明要么不够严谨,要么因抽象需要高度的空间想象力.为此,本文提出一种新的证明方法--"光影"证明法,可以直观形象地证明高斯定理,使学生较容易理解高斯定理.     

近距离高频单站定位技术

介绍了电离层参数的模式化预测方法和实时反演、重构技术,导出基于多层准抛物模型的电离层虚高公式,并给出基于Martyn等效理论的高频单站定位迭代算法,利用实测数据验证了算法在近距离上的实用性,即在约600～1200km范围内单站定位误差不超过5％。     

改进的干涉仪测向方法研究

提出了一种基于长短基线匹配的干涉仪测向方法。该方法根据中国剩余定理,借鉴了长短基线干涉仪测向原理,利用短基线相位差测量解决相位模糊的问题,长基线相位差测量提高测向的精度。对长短基线的匹配选取、测向能力以及抗噪声性能进行了理论分析和仿真。试验结果表明,新方法与其他方法相比,适应能力强、运算量小、精度高,在低信噪比下仍具有良好的估计精度,适于硬件实现。     

浅议高等数学的学习方法

本文讨论了在学习高等数学的过程中,应注意的四个方面。即:一、深刻理解基本概念,为掌握基本公式奠定基础;二、牢固掌握基本定理、公式,为灵活掌握计算方法培养基本功;三、灵活运用基本的计算方法,为解决实际问题训练能力;四、重视数学知识的应用,为培养创新能力奠定基础。     

The evidence algorithm and problems of representation and processing of mathematical computer knowledge

A series of research works on the realization of the “evidence algorithm” program initiated by V. M. Glushkov in the sixties is described. The works are planned in the context of a new understanding of the theorem-proving problem and according to modern trends in information technologies and computer science. Translated from Kibemetika i Sistemnyi Analiz, No. 6, pp. 9–17, November–December, 1999.     

倍压整流电路原理仿真及应用

利用戴维南定理巧妙地分析了典型的二倍压电路与多级倍压电路产生原理，并通过电子电路仿真软件Muhisim10．0进行了仿真。最后，通过故障实例介绍了实际应用。     

Automatic Discovery of Theorems in Elementary Geometry

We present here a further development of the well-known approach to automatic theorem proving in elementary geometry via algorithmic commutative algebra and algebraic geometry. Rather than confirming/refuting geometric statements (automatic proving) or finding geometric formulae holding among prescribed geometric magnitudes (automatic derivation), in this paper we consider (following Kapur and Mundy) the problem of dealing automatically with arbitrary geometric statements (i.e., theses that do not follow, in general, from the given hypotheses) aiming to find complementary hypotheses for the statements to become true. First we introduce some standard algebraic geometry notions in automatic proving, both for self-containment and in order to focus our own contribution. Then we present a rather successful but noncomplete method for automatic discovery that, roughly, proceeds adding the given conjectural thesis to the collection of hypotheses and then derives some special consequences from this new set of conditions. Several examples are discussed in detail.