数学
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Theory and Applications of Higher-Dimensional Hadamard MatricesYang Yi XianThis is the first book on higher-dimensional hadamard matrices and their application in telecommunictions and information security .It is divided into three parts according to the dimensional walsh and Hadamard matrices .Fast algorithms,updated constructions,existence results,and their generalised forms are presented. The second part deals with the lower-dimenstional cases,e.g.3-,4-,and 6- dimensional Walsh and Hadamard matrices and transforms.One of the aims of this part is to simplify moving smoothly from 2-dimensional cases to the general higher-dimensional cases.This part concentrates on the 3-dimensional Hadamard and Walsh matrices.Constructions based upon direct multiplication,and upon recursive methods,perfect binary arrays are also introduced.Another important topic is the existence and construction of 3-dimensional Hadamard matrices of orders 4k and 4k +2 respectively,and a group of transforms based on 2-,3-,4-and 6-dimensional walsh-Hadamard matrices and their corresponding fast algorithms.The third part is the key part,which investigates the N-dimensional Hadamard matrices of order 2,which have been proved equivalent to the well known H-Boolean functions and the perfect binary arrays of order 2.This equivalence motivates a group of perfect results about the enumeration of higher-dimensional Hadamard matrices of order 2. Applications of these matrices to feed forward networking ,stream cipher,Bent functions and error correction cods are presented in turn.after introducing the definitions of the regular,proper,improper,and generalised higher-dimensional Hadamard matrices ,many theorems about the existence and constructions are presented.Perfect binary arrays,generalised perfect arrays,and the orthogonal desgns are also used to construct new higher-dimensional Hadamard matrices.The many open problems in the study of the theory of higher-dimensional Hadamard matrices which are also listed in the book will encourage further research.Audience This volume will appeal to researchers and graduate students whose work involves signal processing,coding,information security and applied discrete mathematics. -
形状生成理论Michael Leyton 著In this book, the author develops a generative theory of shape with two properties fundamental to intelligence: maximizing transfer of structure, and maximizing recoverability of generative operations. The theory is applied in considerable detail to CAD, perception, and robotics. A significant aspect of this book is the development of an object-oriented theory of geometry. This includes a group-theoretic formulation of object-oriented inheritance. In particular, a class of groups is developed called "unfolding groups", which define any complex shape as unfolded from a maximally collapsed version of itself called an "alignment kernel". The group is decomposed into levels corresponding to the inheritance hierarchy within the complex object. This achieves one of the main goals of the theory - the conversion of complexity into understandability. The advantages of the theory are demonstrated with lengthy studies of robot manipulators, perceptual organization, constructive solid geometry, assembly planning, architectural CAD, and mechanical CAD/CAM. -
寄情科学饶忠华主编本书是中国科普佳作百年选中的《寄情科学》,书中共分“文豪放言”、“寻幽探胜”、“生命物语”、“品味人生”、“绿色风情”、“科学之美”六部分,收录了我国著名的文字家茅盾、王蒙、黄宗英等人所作科普文章。 本书内容丰富,文笔生动流畅,融科学性、知识性及可读性于一体,非常值得一读。 -
高等代数专题研究学习指导书冯泰,周永胜,张清利 编按照高等代数专题研究多种媒体教材一体化设计方案的要求,本指导书每章分重难点解析、典型例题、自测题、自测题解答和教材习题解答五部分.高等代数专题研究是初等数学的理论基础,本课程涉及:什么是数,数的运算与映射的关系,不等式理论,多项式理论、因式分解,多项式根的求法与根的估计,初等排列组合的原理与应用,容斥原理和抽屉原理方面的知识等,知识面较广,内容较多.为了使学生能够顺利地学习相关的内容,在重难点解析部分对某些概念或定理、公式等作了较多的解释,并列举了大量例题印证或说明;自测题包括单项选择题、填空题、解答计算题和证明题,学生自己学完各章后,进行一次自我认识;教材中的部分习题有一定难度,在教材习题解答中给出稍细解答,一般题目只给答案.本课程的总体要求以该课程教学大纲为准,为此将《广播电视大学“本科开放教育”高等代数专题研究教学大纲》附上,供参考.教材中第六章“伽罗华理论”,教材和教学大纲中均加了“*”号,因时间关系,本书略去.教材中第四章“数论初步”,超出本课程的教学大纲,不做教学要求. -
模式识别 Pattern recognitionBernd Rading,Stefan Florczyk 著This edition includes discussion of Bayesian classification, Bayesian networks, linear and nonlinear classifier design (including neural networks and support vector machines), dynamic programming and hidden Markov models for sequential data, feature generation (including wavelets, principal component analysis, independent component analysis and fractals), feature selection techniques, basic concepts from learning theory, and clustering concepts and algorithms. This book considers classical and current theory and practice, of both supervised and unsupervised pattern recognition, to build a complete background for professionals and students of engineering. -
师从天才(美)罗伯特·卡尼格尔(Robert Kanigel)著;江载芬,闫鲜宁,张新颖译编辑推荐:本书关注的是现代科学中的师承关系链及其影响。作者罗伯特·卡尼格尔在书中把我们带进了一个充满智慧、趣味、竞争和创新的奇妙的科研王朝,展现了一个由美国国立卫生研究院(NIH)和约翰斯·霍普金斯大学的著名科学家群体构筑的世界,他们通过半个多世纪来在生物医学科学领域内的突破性贡献,赢得了拉斯克奖及诺贝尔奖。 -
动力系统基础及其方法陈绥阳,褚蕾蕾编著动力系统(DynamicalSystem)是拓扑空间上连续自映射迭代生成的系统。本书重点阐述拓扑动力系统(含符号动力系统、分形动力系统),微分动力系统和无穷维动力系统的基础理论知识与基本研究方法。这一理论与方法,已广泛而深入地应用于数学、统计学、物理、力学、信息与计算科学,以及许多工程领域。本书可作为数学类各专业的研究生教材,也可供以上相关专业的高年级学生及教学、科研人员参考。 -
大学数学王国荣主编大学数学(二)是培养本科学历小学教师(理科方向)使用的高等数学教材。目的是使他们具有较为坚实的数学分析基础知识。作为一元函数微积分的提高,我们在本书前三章编写了极限续论、无穷级数和微分方程,在本书的后四章编写了多元函数微积分的有关内容。前三章与后四章内容基本独立,可以根据教学时数或教学需要,直接进入后四章学习。 -
经济管理数学王孝成主编《经济管理数学》函数、极限与连续、导数与微分、中值定理与导数的应用、不定积分、定积分、多元函数微积分、无穷级数、微分方程初步等9章。每章附有习题。书末附有习题参考答案。 -
数学辞海《数学辞海》编辑委员会编《数学辞海》是当今世界最系统、最完备的大型学术性数学工具书,它是由大陆、台、港200余所院校和科研单位的1500余名专家教授(其中包括中国科学院院士30余人,博士生导师400余人),历时18年集体编纂而成的。全书包括100余个分支学科或专题项目,约1360万字,共分6卷,内容涵盖古今中外5000年的全部数学成果。其规模是前苏联同类辞书的2倍,是日本同类辞书的4倍。该书词条定义科学、准确,文字叙述简明、通俗,并具有实用性强及查找方便等特点。它是数学教师和科技工作者必备的工具书,也是教学专业学生、研究生、理工科大学生、中学生及数学爱好者难得的百科全书。
