一个函数不等式的加强与延伸

从一个常见的不等式谈起,分析了多种证明方法,运用该不等式推导出了多个重要结论,对不等式进行了扩充和加强,解释了蕴含的意义,显示了该不等式的重要性和深刻性.     

基于粗糙集的患者满意度评价模型及其实证分析

在文献阅读及实地调研的基础上,本文提出了患者满意度的定义,建立了影响患者满意度的指标体系,介绍了粗糙集的相关概念及利用粗糙集进行评价的步骤,提出了新的约简方法,构建了基于粗糙集的患者满意度评价模型并进行了实证分析,得出了影响患者满意度的关键指标,并计算了关键指标权重,对江西省十个医院进行了综合评价值的计算.     

交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

关于举办2012年中学生数学奥林匹克夏令营活动的启事

从1996年至今,华中师范大学数学与统计学学院已成功举办多届全国中学生数学奥林匹克夏令营活动,培养了大批优秀的数学竞赛选手,他们经过权威名师的指点,既丰富了理论知识,更掌握了实践经验,为走上成功明确了航向,在国内、国际数学竞赛中取得了令人瞩目的成绩。我院已成为全国数学奥林匹克活动的重要培训基地,吸引了众多优秀中学生云集武汉参     

网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

系统动力学在城市污水再生回用系统中的应用

用系统动力学方法研究了城市污水回用系统.首先分析了影响城市污水回用系统的诸多因素以及它们之间的相互关系,探讨了污水再生回用系统行为和结构的特点,确定了系统中因素之间的定量关系,建立了城市污水回用系统动力学(SD)模型,并介绍了模型的检验方法.同时给出了SD模型的具体应用实例,对西北地区的某一城市的污水回用进行了预测和分析,提出了符合该城市发展的污水回用方案.     

压板松动时大型发电机端部绕组的主共振与分岔

研究了大型汽轮发电机定子端部固定绕组的压板松动时,位于两侧压板间某段绕组的振动问题．首先,采用分离变量法,给出了发电机运行时定子端部绕组区域的磁感应强度表达式,并给出了绕组所受电磁力及与松动压板间摩擦力的计算式．其次,建立了研究绕组非线性振动问题的力学分析模型,采用多尺度法对主共振情形进行了解析求解,推得了稳态运动下的幅频响应方程,并对定常解的稳定性及分岔奇异性进行了研究,得到了稳定性的判定条件及分岔方程的转迁集．最后,针对工程实际问题进行了计算,给出了相应的幅频响应曲线图,并进行了分析讨论．     

红树林自然保护区湿地生态系统的数学模型及其应用

研究了红树林自然保护区自然环境和人类社会活动对于生态系统的影响,考虑了生物之间的相互关系,将生物量、生物生长的面积等作为主要指标,建立了常微分方程组模型,对生态系统的变化情况进行了描述,借助稳定性分析对方程进行了研究,并进行了数值模拟。根据理论分析和数值模拟的结果,对保护区的林木恢复工作提出了合理的建议。     

求解资源受限项目调度问题的人工鱼群算法

提出了将人工鱼群算法应用于求解资源受限项目调度问题中的构想,建立了求解资源受限项目调度问题的人工鱼群算法模型,设计了一种标准随机键编码方式,构建了人工鱼的觅食行为、聚群行为、追尾行为和随机行为四种基本算子,采用了正向逆向局部改进技术和精英保留策略,并给出了算法流程。应用PSPLIB标准问题库对该算法进行了大量的测试,并与其他算法进行了比较,验证了该算法的有效性。     

基于干扰管理理论的航空备件模型参量扰动性分析

概述了干扰管理理论的内涵、意义以及目标,依据未来不确定因素引起飞机备件需求量变化以及备件供应时限性增强的实际情况,创建了时限一致度算子,优化了备件需求泊松分布模型,提高了备件供应的精确度,并选取了优化后的模型中的多个参量,进行了多因素的扰动性分析,最后构造了算例,验证了本方法的科学性和有效性.     

R4(C)中平均曲率方向平行的Bonnet曲面

本文利用[5]的方法,对R⁴(C)中平均曲率方向平行的Bonnet曲面引入了半测地等温 参数,并给出了一个分类结果.     

R_1~3中混合型曲面保主曲率等距变形

本文研究了Minkowski空间R_(1)~3曲面的等距变形问题.建立了R_(1)~3中曲面的共形、等距等概念.推广了O.Bonnet和S.S.Chern关于欧氏空间的结论.对R_(1)~3出现的新情况——曲面的中曲率梯度类光作了一定探讨,得出的主要结果为:非平坦的、允许保主曲率等距变形的曲面一定不是W-曲面.     

Tangential developable surfaces as bonnet surfaces

We study the real Bonnet surfaces which accept one unique nontrivial isometry that preserves the mean curvature, in the three-dimensional Euclidean space. We give a general criterion for these surfaces and use it to determine the tangential developable surfaces of this kind. They are determined implicitly by elliptic integrals of the third kind. Only the tangential developable surfaces of circular helices are explicit examples for which we completely determine the above unique nontrivial isometry. Dedication Dedicated to Siuping Ho for all her invaluable support and encouragement.     

Global geometry and topology of spacelike stationary surfaces in the 4-dimensional Lorentz space

For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space, one can naturally introduce two Gauss maps and a Weierstrass-type representation. In this paper we investigate the global geometry of such surfaces systematically. The total Gaussian curvature is related with the surface topology as well as the indices of the so-called good singular ends by a Gauss–Bonnet type formula. On the other hand, as shown by a family of counterexamples to Osserman?s theorem, finite total curvature no longer implies that Gauss maps extend to the ends. Interesting examples include the deformations of the classical catenoid, the helicoid, the Enneper surface, and Jorge–Meeks? k-noids. Each family of these generalizations includes embedded examples in the 4-dimensional Lorentz space, showing a sharp contrast with the 3-dimensional case.     

R13中混合型曲面保主曲率等距变形

本文研究了Minkowski空间R₁³曲面的等距变形问题.建立了R₁³中曲面的共形、等距等概念.推广了O.Bonnet和S.S.Chern关于欧氏空间的结论.对R₁³出现的新情况——曲面的中曲率梯度类光作了一定探讨,得出的主要结果为:非平坦的、允许保主曲率等距变形的曲面一定不是W-曲面.     

Global results on Bonnet Surfaces

The local theory of the Bonnet Surfaces in the three dimensional Euclidean Space of the type of non-constant mean curvature that admit infinitely many non-trivial and geometrically distinct isometries preserving the mean curvature has been developed, in the literature, under the assumption that the surfaces contain no umbilic points and no critical points of the mean curvature function. Here, we prove that these restrictions do not create any difference from the possible global results, except in one case in which we prove that the set of the umbilic points, known to consist of exactly one point, is equal to the set of the critical points of the mean curvature function. Furthermore, we show that the index of this umbilic point, as isolated singularity of the foliation of the principal curves is one. In our proofs we use: (a) An intrinsic characterization of these surfaces, which we derive in a manner easier and including more details than those already found in the literature. From this characterization we conclude that all surfaces of this type are analytic. (b) The harmonic functions of the angles by which the respected isometries rotate the principal frames, which we compute.Dedicated to the memory of my great benefactors: my first important mathematics teacher and motivator, my uncle Michael Ioannou Roussos ( November, 1992), and his wife, my aunt Evanggelia Michael Roussou-Gavala ( May, 1994), for their invaluable support.     

Bonnet Surfaces with Constant Curvature

We classify Bonnet surfaces with constant curvature in 3-dimensional space forms and show that they are parametrized by curves in 2-dimensional space forms with specific geodesic curvature.     

Spectral transformation of constant mean curvature surfaces in H3 and Weierstrass representation

By using the method of integrable system, we study the deformation of constant mean curvature surfaces in three-dimensional hyperbolic space form H3. We also obtain a Weierstrass representation formula of the constant mean curvature surfaces with mean curvature greater than 1.     

Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian space forms.      

The problem of non-trivial isometries of surfaces preserving principal curvatures

In this paper we deal with the Bonnet problem of determining the surfaces in the Euclidean three dimensional space which can admit at least one nontrival isometry that preserves the principal curvatures(Bonnet surfaces). The problem is considered locally and examined in the general case. The main results are: (a) Necessary and sufficient condition for a surface to be a Bonnet surface is that it admits a special isothermal parameter system. (b) Complete solution of the problem in the class of the isothermic surfaces. Moreover: These results and the methods used provide a new efficient and elegant manner of proving the, already known, fact that all helicoidal surfaces are Bonnet surfaces and determine the already known developable Bonnet surfaces.