几何直观在线性代数教学中的应用

本文强调了几何直观在线性代数教学中的作用 ,通过例子从代数概念的引入、代数性质的几何解释、代数理论应用的直观分析几个方面加以说明 .     

Deformations of Real Rational Dynamics in Tropical Geometry

In this paper we study analytic properties of orbits given by real rational functions. We introduce some comparison methods which allow us to compare the real rational dynamics with automata given by (max, +) functions, passing through a kind of scale transform in tropical geometry. Such a scale transform gives a one-to-one correspondence of presentations between automata and real rational functions. We study invariant properties of the real rational dynamics under change of presentations of automata.     

Automata in Groups and Dynamics and Induced Systems of PDE in Tropical Geometry

In this paper we develop a dynamical scaling limit from rational dynamics to automata in tropical geometry. We compare these dynamics and induce uniform estimates of their orbits. We apply these estimates to introduce a comparison analysis of theory of automata groups in geometric group theory with analysis of rational dynamics and some hyperbolic PDE systems. Frameworks of characteristic properties of automata groups are inherited to the corresponding rational or PDE dynamics. As an application we study the Burnside problem in group theory and translate the property as the infinite quasi-recursiveness in rational dynamics.     

Ensemble Graphics

One graphic can convey a lot of information and several graphics linked together in a coherent ensemble can convey even more. This article describes the principles underlying ensemble graphics, their key dimensions, and where they are of most use. Ensemble graphics must have strong common themes and carefully constructed layouts. Appropriate interactive tools are important. Ensembles can be used flexibly for EDA or in a more structured fashion for supporting modeling and for presentations.     

对象标识统一化程度影响物流资源整合的系统动力学分析

为了分析对象标识统一化程度对物流资源整合的影响,提出利用系统动力学理论建立反馈模型。采用2002年以来国家统计局和《中国现代物流发展报告》的数据,设计模型变量,并进行回归,以确定变量关系方程式。在该模型中采用物流资源利用率、企业间合作比例、物流行业总收益作为衡量物流资源整合水平的指标,运用Vensim仿真对象标识统一化程度与三者之间的相互影响。模拟结果显示对象标识统一化程度对物流资源利用率、企业间合作比例和物流行业总收益均有正向影响。该研究表明提升对象标识统一化程度可以有效提高企业间的沟通,促进物流资源整合水平的提高,实现物流产业对经济增长的可持续拉动作用。     

Geometry of Real Grassmann Manifolds. IV

Classical geodesic embeddings in the Grassmann manifold are described algebraically by means of the exterior algebra (V). The group I ₀(G ⁺) of isometries of the Grassmannian is described without the theory of Lie groups and algebras. Interior and exterior properties of Grassmann manifolds are proved with the help of the equivariant Plücker embedding. The isomorphism type of the group of twists of the Grassmann manifold around an arbitrary geodesic is described. Bibliography: 16 titles.     

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.     

Geometry of real grassmann manifolds. Part III

A canonical decomposition for an element of the tangent bundle of the Grassmann manifold G _p,n ⁺ in its Plücker model is constructed. This decomposition is used for introducing the notion of stationary angles between oriented planes. The relation with the stationary angles in the nonoriented case is established. An explicit formula for the exponential mapping is given, which allows calculating the diameter and the injectivity radius of the manifold G _p,n ⁺ . The problem of uniqueness of the canonical decomposition is reduced to a similar problem on the decomposition of bivectors that realizes their mass (the latter has earlier been solved by the author). The techniques developed are used for describing the structure of the closure of an arbitrary geodesic in the manifolds G _p,n ⁺ and G_p,n. (For the manifolds G_p,n, this result was announced by Wong without proof.) Bibliography: 11 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 246, 1997, pp. 108–129. Translated by N. Yu. Netsvetaev.     

Symplectic Geometry

Book Review

Symplectic GeometryA. T. Fomenko: Advanced Studies in Contemporary Mathematics, Volume 5, Gordon and Breach Science Publishers, 1988, 387 pp     

Pseudoquaternion Geometry

We describe complex holomorphic transformations of a quaternion vector space taking left quaternion lines to left quaternion lines and real linear transformations of the quaternion plane simultaneously preserving the sets of left and right quaternion lines.     

Trends in Computer Graphics

The increasing use of powerful interactive microcomputer systems will lead to a much wider use of graphics. This paper presents the basis of interactive computing using graphics terminals, as a contribution to increasing the understanding of this area. In particular, the raster terminal is presented in some detail as a powerful and relatively cheap display.     

The Language of Graphics

Abstract

We describe a system, called the Graphics Production Library (GPL), that implements a language for quantitative graphics. The structure of this system differs from existing statistical graphics, visualization, and mapping systems. Instead of treating a graphics display as a viewer for underlying data, GPL treats data as an accessory to viewing a graph. GPL is based on the mathematical definition of the graph of a function and uses that definition to organize data linked to the graph.