应用激光全息干涉术及有限元法对2050热连轧机机座自振特性的三维分析

根据相似理论,进行了宝山钢铁总厂热轧厂2050热连轧精轧机机座自振特性的三维模拟研究,并应用全息干涉术进行了前三阶主振型分析.本文还进行了三维有限元数值分析与模拟值进行了映照.二者结果是吻合的.     

基于HBP估计的宏观经济统计数据诊断方法实证研究

HBP估计是具有高失效点的稳健估计方法,根据生产函数模型,利用LMS和MCD估计方法对浙江省相关年份的GDP进行了定量诊断,发现研究期间的GDP存在异常点和高杠杆点,并对异常点进行了验证,对高杠杆点进行了分析,解释了高杠杆点的产生原因。同时利用RLS估计方法对模型进行回归,根据回归结果对异常点进行了修正。     

基于神经网络的我国猪肉年度消费需求量预测研究

主要运用神经网络对中国猪肉年度消费需求量的预测问题进行了研究.首先对畜产品预测方法进行了综述,对神经网络预测原理进行了介绍,然后分别建立GM(1,1)、ARIMA模型、GRNN神经网络模型,GA-GRNN神经网络模型模型对猪肉消费量进行了预测,最后对模型进行了集成.结果表明,优化后的GA-GRNN模型预测误差率显著降低,集成模型在稳定性和精度方面均比较理想.     

丙型肝炎中免疫模型的动力学分析

对肝炎C病毒与宿主细胞及免疫反应之间关系的动力系统进行了分析,得到了模型平衡点的存在条件,并对复杂的平衡点进行了数值模拟,模拟结果显示系统是趋于渐进稳定的.而且对染病初期,进行抗病毒治疗的数学模型也进行了数值模拟,并且能够达到预期的效果.     

不同参数下Galton板实验的探讨及仿真

介绍了 Galton板实验的实验现象和物理背景 ,建立了细致的概率模型对实验进行了分析 ,并基于模型对不同参数下的 Galton板实验进行了探讨 ,还利用 MATLAB编制了仿真软件 ,对结论进行了验证 .     

基于GOMPERTZ函数的上证综合指数预测的实证研究

对基于G om pertz函数的上证综合指数进行预测的可行性进行了分析,同时,在对上证综合指数的具体走势及实际数据进行研判的基础上,对牛市行情下上证综合指数的运行进行了预测的实证研究,得出了相应的结论,并提出了该预测方法进一步完善之处和可进一步深入研究的问题.     

双层线性分式规划求顶点的算法

基于双层线性分式规划的性质,讨论了上层不带约束的双层线性分式规划模型,给出了求其所有顶点的算法.此算法为进一步进行双层线性分式规划的灵敏度分析打下了坚实的基础,通过例子对算法进行了检验,并利用结果进行了灵敏度分析.     

确定观测站点预报雨量的两种方法

对2005年高教社杯全国大学生数学建模竞赛C题"雨量预报方法的评价"的解决方法进行了讨论.给出了确定观测站点预报雨量的距离权重法与插值法,并进行了比较.同时,对预报质量的进一步提高进行了探讨.     

计算机蠕虫病毒传播的数学模型分析

建立了一种计算机病毒传播的数学模型,并利用微分方程理论进行了分析,得到了计算机病毒消除的阈值,并进行了数值模拟.     

基于多属性群决策模型的评教方法

对高校学生网上评教存在的主要问题进行了分析,给出了网上评教的信息处理新方法.首先利用信息熵和正态分布函数对学生可信度函数进行了定义,再根据可信度大小对学生评价的权重进行了分配,最后利用加权算术平均算子对课程班的得分进行集结.数值算例分析了方法的有效性、合理性和可操作性.     

Noncommutative geometry and conformal geometry. III. Vafa–Witten inequality and Poincaré duality

This paper is the third part of a series of papers whose aim is to use the framework of twisted spectral triples to study conformal geometry from a noncommutative geometric viewpoint. In this paper we reformulate the inequality of Vafa–Witten [42] in the setting of twisted spectral triples. This involves a notion of Poincaré duality for twisted spectral triples. Our main results have various consequences. In particular, we obtain a version in conformal geometry of the original inequality of Vafa–Witten, in the sense of an explicit control of the Vafa–Witten bound under conformal changes of metrics. This result has several noncommutative manifestations for conformal deformations of ordinary spectral triples, spectral triples associated with conformal weights on noncommutative tori, and spectral triples associated with duals of torsion-free discrete cocompact subgroups satisfying the Baum–Connes conjecture.     

A volume comparison theorem for Finsler manifolds

Let be a symmetric Finsler manifold, endowed with the Busemann volume form, and let be its unit disk bundle endowed with the canonical symplectic volume form. It is shown that , where is the volume of the unit disk in . Moreover, equality holds if and only if is Riemannian.

     

等周问题的一个初等证明

本文把欧氏平面，半球面和非欧面之中，不含给定边界，含有给定边界和含有边界而且在其上给定端点这样三种等周问题、给以初等、统一的证明。其要点在于把它们的存在性和唯一性简明扼要地归结到下述初等引理，即一个给定凹边边长的四边形的面积以四顶共圆时为其唯一的极大     

Projectively flat Finsler 2-spheres of constant curvature

After recalling the structure equations of Finsler structures on surfaces, I define a notion of "generalized Finsler structure" as a way of microlocalizing the problem of describing Finsler structures subject to curvature conditions. I then recall the basic notions of path geometry on a surface and define a notion of "generalized path geometry" analogous to that of "generalized Finsler structure". I use these ideas to study the geometry of Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature K and whose geodesic path geometry is projectively flat, i.e., locally equivalent to that of straight lines in the plane. I show that, modulo diffeomorphism, there is a 2-parameter family of projectively flat Finsler structures on the sphere whose Finsler-Gauss curvature K is identically 1.     

TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.     

On contact tops and integrable tops

In this paper, we introduce a geometric structure called top, which is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of l-forms (e.g., of contact and integrable forms) with particular properties with respect to the metric. We classify the manifolds which admit tops and we describe the associated metrics.     

On Mascheroni's La geometria del compasso at the beginning of the 19th century

Lorenzo Mascheroni's 1797 work La geometria del compasso, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.     

Riemann-Finsler Geometry with Applications to Information Geometry

Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce Riemann-Finsler geometry, by which we establish Information Geometry on a much broader base, so that the potential applications of Information Geometry will be beyond statistics.     

The complexity of plane hyperbolic incidence geometry is ∀∃∀∃

We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ???, but that there is an axiom system, all of whose axioms are ???? sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)