Mathematics

Conformal Groups in Geometry and Spin Structures By Pierre Anglès

Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics By Rafał Abłamowicz, Bertfried Fauser

Statistical Data Analytics :

Foundations for Data Mining, Informatics, and Knowledge Discovery

Delayed and Network Queues

The Mathematical-Function Computation Handbook: Programming Using the MathCW Portable Software Library By Prof. Nelson H.F. Beebe

Conformal Groups in Geometry and Spin Structures By Pierre Anglès

English | PDF | 2008 | 307 Pages | ISBN : 0817635122 | 12.19 MB

Conformal groups play a key role in geometry and spin structures. This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley and progressing to recent research in spinors and conformal geometry.

Key topics and features:

This text is suitable for a course in mathematical physics at the advanced undergraduate and graduate levels. It will also benefit researchers as a reference text.

Clifford Algebras and their Applications in Mathematical Physics Volume 1: Algebra and Physics By Rafał Abłamowicz, Bertfried Fauser

English | PDF | 2000 | 470 Pages | ISBN : 1461271169 | 36.5 MB

The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E 0, the latter forming four trans lation invariant part of its total angular (four) momentum M.

Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.

Statistical Data Analytics : Foundations for Data Mining, Informatics, and Knowledge Discovery

English | 2015 | ISBN: 111861965X | 487 Pages | PDF | 3.8 MB

A comprehensive introduction to statistical methods for data mining and knowledge discovery.

Applications of data mining and ‘big data’ increasingly take center stage in our modern, knowledge-driven society, supported by advances in computing power, automated data acquisition, social media development and interactive, linkable internet software. This book presents a coherent, technical introduction to modern statistical learning and analytics, starting from the core foundations of statistics and probability. It includes an overview of probability and statistical distributions, basics of data manipulation and visualization, and the central components of standard statistical inferences. The majority of the text extends beyond these introductory topics, however, to supervised learning in linear regression, generalized linear models, and classification analytics. Finally, unsupervised learning via dimension reduction, cluster analysis, and market basket analysis are introduced.

Extensive examples using actual data (with sample R programming code) are provided, illustrating diverse informatic sources in genomics, biomedicine, ecological remote sensing, astronomy, socioeconomics, marketing, advertising and finance, among many others.

Statistical Data Analytics:

– Focuses on methods critically used in data mining and statistical informatics. Coherently describes the methods at an introductory level, with extensions to selected intermediate and advanced techniques.

– Provides informative, technical details for the highlighted methods.

– Employs the open-source R language as the computational vehicle – along with its burgeoning collection of online packages – to illustrate many of the analyses contained in the book.

– Concludes each chapter with a range of interesting and challenging homework exercises using actual data from a variety of informatic application areas.

This book will appeal as a classroom or training text to intermediate and advanced undergraduates, and to beginning graduate students, with sufficient background in calculus and matrix algebra. It will also serve as a source-book on the foundations of statistical informatics and data analytics to practitioners who regularly apply statistical learning to their modern data.

Delayed and Network Queues

English | 2016 | ISBN: 1119022134 | 415 Pages | PDF | 7.3 MB

Presents an introduction to differential equations, probability, and stochastic processes with real-world applications of queues with delay and delayed network queues.

Featuring recent advances in queueing theory and modeling, Delayed and Network Queues provides the most up-to-date theories in queueing model applications. Balancing both theoretical and practical applications of queueing theory, the book introduces queueing network models as tools to assist in the answering of questions on cost and performance that arise throughout the life of a computer system and signal processing. Written by well-known researchers in the field, the book presents key information for understanding the essential aspects of queues with delay and networks of queues with unreliable nodes and vacationing servers.

Beginning with simple analytical fundamentals, the book contains a selection of realistic and advanced queueing models that address current deficiencies. In addition, the book presents the treatment of queues with delay and networks of queues, including possible breakdowns and disruptions that may cause delay. Delayed and Network Queues also features:

– Numerous examples and exercises with applications in various fields of study such as mathematical sciences, biomathematics, engineering, physics, business, health industry, and economics

– A wide array of practical applications of network queues and queueing systems, all of which are related to the appropriate stochastic processes

– Up-to-date topical coverage such as single- and multiserver queues with and without delays, along with the necessary fundamental coverage of probability and difference equations

– Discussions on queueing models such as single- and multiserver Markovian queues with balking, reneging, delay, feedback, splitting, and blocking, as well as their role in the treatment of networks of queues with and without delay and network reliability

Delayed and Network Queues is an excellent textbook for upper-undergraduate and graduate-level courses in applied mathematics, queueing theory, queueing systems, probability, and stochastic processes. The book is also an ideal reference for academics and practitioners in mathematical sciences, biomathematics, operations research, management, engineering, physics, business, economics, health industry, and industrial engineering.

The Mathematical-Function Computation Handbook: Programming Using the MathCW Portable Software Library By Prof. Nelson H.F. Beebe

English | PDF | 2017 | 1145 Pages | ISBN : 3319641093 | 29.7 MB

This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision.

Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built

C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions.

This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw

are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.