Euclidean Model of Space and Time

The aim of this work is to show that the currently widely accepted geometrical model of space and time based on the works of Einstein and Minkowski is not unique. The work presents an alternative geometrical model of space and time, a model which, unlike the current one, is based solely on Euclidean geometry. In the new model, the pseudo-Euclidean spacetime is replaced with a specific subset of four-dimensional Euclidean space. The work shows that four-dimensional Euclidean space allows explanation of known relativistic effects that are now explained in pseudo-Euclidean spacetime by Einstein’s Special Theory of Relativity (STR). It also shows simple geometric-kinematical nature of known relativistic phenomena and among others explains why we cannot travel backward in time. The new solution is named the Euclidean Model of Space and Time (EMST).

欧氏空间E^n中Pedoe不等式推广

应用距离几何的理论与方法,先证明了欧氏空间中n维单形的几个几何不等式,然后建立了加强形式的涉及两个单形棱长的n维Pedoe不等式和彭-常不等式以及k-n型Pedoe不等式和彭-常不等式.另外还建立了一个重要不等式.

欧氏空间中n维Pedoe不等式的推广及应用

利用距离几何的理论与方法,研究欧氏空间En中两个n维单形的棱长与体积的几何不等式,建立了n维单形两种加强形式的彭-常不等式,从而推广了En中n维Pedoe不等式.

基于纹理分析的笔迹识别系统

把手写笔迹作为一种纹理来看待,利用图象纹理处理技术和数学方法对笔迹的纹理信息进行鉴别,将笔迹识别问题转化为纹理识别.使用19个人的不同笔迹进行实验,采用游程长度分析法来提取这些笔迹的纹理特征,用欧氏距离分类器完成识别工作.取得了较好的效果.

单形中Weitzenbck不等式的稳定性

利用棱长引进了单形“偏正”度量的概念,获得了关于单形的Weitzenbck不等式的稳定性版本和张-杨不等式的稳定性版本.

长度关系与对称变换

利用长度关系给出了欧氏空间的变换为对称变换的若干个充要条件。

联系两个n维单形的不等式及应用

利用距离几何的理论与方法,研究了欧氏空间En中涉及两个单形棱长和体积的几何不等式问题,建立了涉及两个n维单形棱长与体积的两个几何不等式,推广了En中n维Pedoe不等式和彭-常不等式。

Rice Lognormal衰落信道中不同译码度量特性的比较

本文推导出了ＲｉｃｅＬｏｇｎｏｒｍａｌ 衰落信道中没有信道状态信息和具有信道状态信息两种情况下的最大似然译码度量，并同传统欧氏距离度量的成对错误概率进行了比较．数值计算结果表明：对于ＴＣＭＰＳＫ 方案，信道衰落特征（ｆＤＴ）对度量特性的影响几乎可以忽略．最后，讨论了ＲｉｃｅＬｏｇｎｏｒｍａｌ

Schwarz引理的几个推广与应用

给出了Schwarz引理的几个推广及应用.

Lorentz Transform in Multi-Dimensional Space

It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.

欧氏空间中升序变换半群的格林关系和正则元

设L(R^n)表示n维欧氏空间R^n的所有线性变换构成的集合,||α||表示向量α的欧氏长度,由欧氏长度建立起向量间的序关系.令:O+(R^n)={f∈L(R^n)|(?)α∈R^n,||f(α)||≥||α||},则O+(R^n)是欧氏空间R^n的所有升序变换构成的集合,其在交换的合成运算下构成一个半群,讨论了O+(R^n)的格林关系和正则元.

保欧氏度量偏序的变换

设L(R^n)表示n维欧氏空间R^n的所有线性变换构成的集合,‖ξ‖表示向量ξ的欧氏长度,由欧氏长度建立起向量间的序关系,令:PO(R^n)={f∈L(R^n)■|ξ,η∈R^(n×1),‖ξ‖≤‖η‖■‖f(ξ)‖≤‖f(η)‖}则PO(R^n)是欧氏空间R^n中保欧氏度量偏序变换构成的集合,讨论了PO(R^n)的结构,证明了保持这种序关系的变换由正交变换和伸缩变换组成.