A.M. Mathai's Books

An Introduction to Geometrical Probability

Distributional Aspects with Applications

By: A.M. Mathai

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An Introduction to Geometrical Probability

Distributional Aspects with Applications

By: A.M. Mathai

A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.

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Page Count

580

Publisher

CRC Press

Published Date

ISBN 10

9056996819

ISBN 13

9789056996819

Special Functions for Applied Scientists

By: A.M. Mathai,H.J. Haubold

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Special Functions for Applied Scientists

By: A.M. Mathai,H.J. Haubold

This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.

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Page Count

480

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387758941

ISBN 13

9780387758947

Erdélyi–Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

By: A. M. Mathai,H. J. Haubold

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Erdélyi–Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

By: A. M. Mathai,H. J. Haubold

This book focuses on Erdélyi–Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdélyi–Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics. A major mathematical objective of this book is specifically to examine a new definition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a definition for the case of real-valued scalar functions of several matrices.

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Page Count

132

Publisher

Springer

Published Date

ISBN 10

9811311595

ISBN 13

9789811311598

The H-Function

Theory and Applications

By: A.M. Mathai,Ram Kishore Saxena,Hans J. Haubold

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The H-Function

Theory and Applications

By: A.M. Mathai,Ram Kishore Saxena,Hans J. Haubold

TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.

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Page Count

276

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441909168

ISBN 13

9781441909169

Fractional and Multivariable Calculus

Model Building and Optimization Problems

By: A.M. Mathai,H.J. Haubold

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Fractional and Multivariable Calculus

Model Building and Optimization Problems

By: A.M. Mathai,H.J. Haubold

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable functions). Illustrative examples, input-output process, optimal recovery of functions and approximations are given; each section lists an ample number of exercises to heighten understanding of the material. Chapter three discusses deterministic/mathematical and optimization models evolving from differential equations, difference equations, algebraic models, power function models, input-output models and pathway models. Fractional integral and derivative models are examined. Chapter four covers non-deterministic/stochastic models. The random walk model, branching process model, birth and death process model, time series models, and regression type models are examined. The fifth chapter covers optimal design. General linear models from a statistical point of view are introduced; the Gauss–Markov theorem, quadratic forms, and generalized inverses of matrices are covered. Pathway, symmetric, and asymmetric models are covered in chapter six, the concepts are illustrated with graphs.

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Page Count

243

Publisher

Springer

Published Date

ISBN 10

3319599933

ISBN 13

9783319599939

Jacobians of Matrix Transformations and Functions of Matrix Argument

By: A. M. Mathai

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Jacobians of Matrix Transformations and Functions of Matrix Argument

By: A. M. Mathai

This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with lots of worked examples, aimed at self-study. Some exercises are also given, at the end of each section.The book is a valuable reference for statisticians, engineers, physicists, econometricians, applied mathematicians and people working in many other areas. It can be used for a one-semester graduate level course on Jacobians and functions of matrix argument.

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Page Count

452

Publisher

World Scientific

Published Date

ISBN 10

9810230958

ISBN 13

9789810230951

THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume II (ICT and Engineering)

By: Dr. Shahana A. M., Dr. A. Sivakumar & Mr. V. Parthiban

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THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume II (ICT and Engineering)

By: Dr. Shahana A. M., Dr. A. Sivakumar & Mr. V. Parthiban

IOTA is a novel cryptocurrency that uses distributed ledger technology based on directed acyclic graph data structure. Security of cryptocurrencies ought to be scrutinized in order to acquire esteemed security, attain trust, and accomplish indelible adoption. Although IOTA prefers resilient security controls, IOTA security is not yet well explored. Among all the propounded IOTA vulnerabilities that have been identified, we pragmatically exploit replay attack against IOTA. It further analyze the attack to perceive its impact. Attack methodology and proof of concept for the replay attack is presented. Our proposed exploitation methodology is based upon address reuse, while IOTA in default mode does not reuse addresses. Distrust and privation of balance can be some of the severe impacts of this vulnerability. This system introduces the Crypto Terminal, a new open device for securing blockchain wallets.

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Page Count

292

Publisher

Lulu Publication

Published Date

ISBN 10

1300395826

ISBN 13

9781300395829

THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume I (Social Science and ICT)

By: Dr. Shahana A. M., Dr. A. Sivakumar & Mr. V. Parthiban

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THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume I (Social Science and ICT)

By: Dr. Shahana A. M., Dr. A. Sivakumar & Mr. V. Parthiban

Uncertainty is a circumstance in one’s life. Individual differ in their approach to handle uncertainty. Intolerance to uncertainty is influenced by various factors, such as personality, cognitive aspects and uncertainty, neuro biological aspects of uncertainty. When one understands how intolerance to uncertainty is developed and makes individual vulnerable. We can strength the psychological mind set to face uncertainty.

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Page Count

343

Publisher

Lulu Publication

Published Date

ISBN 10

1300397241

ISBN 13

9781300397243

The H-Function

Theory and Applications

By: A.M. Mathai,Ram Kishore Saxena,Hans J. Haubold

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The H-Function

Theory and Applications

By: A.M. Mathai,Ram Kishore Saxena,Hans J. Haubold

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Page Count

276

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441909168

ISBN 13

9781441909169

Fractional and Multivariable Calculus

Model Building and Optimization Problems

By: A.M. Mathai,H.J. Haubold

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Fractional and Multivariable Calculus

Model Building and Optimization Problems

By: A.M. Mathai,H.J. Haubold

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Page Count

243

Publisher

Springer

Published Date

ISBN 10

3319599933

ISBN 13

9783319599939

Erdélyi–Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

By: A. M. Mathai,H. J. Haubold

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Erdélyi–Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

By: A. M. Mathai,H. J. Haubold

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Page Count

132

Publisher

Springer

Published Date

ISBN 10

9811311595

ISBN 13

9789811311598

An Introduction to Geometrical Probability

Distributional Aspects with Applications

By: A.M. Mathai

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An Introduction to Geometrical Probability

Distributional Aspects with Applications

By: A.M. Mathai

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Solve jigsaw puzzle

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Page Count

580

Publisher

CRC Press

Published Date

ISBN 10

9056996819

ISBN 13

9789056996819

Quadratic Forms in Random Variables

By: A.M. Mathai,Serge B. Provost

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Quadratic Forms in Random Variables

By: A.M. Mathai,Serge B. Provost

Textbook for a one-semester graduate course for students specializing in mathematical statistics or in multivariate analysis, or reference for theoretical as well as applied statisticians, confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

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Page Count

424

Publisher

CRC Press

Published Date

ISBN 10

0824786912

ISBN 13

9780824786915

Erdélyi-Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

By: A. M. Mathai,H. J. Haubold

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Erdélyi-Kober Fractional Calculus

From a Statistical Perspective, Inspired by Solar Neutrino Physics

By: A. M. Mathai,H. J. Haubold

This book focuses on Erdelyi-Kober fractional calculus from a statistical perspective inspired by solar neutrino physics. Results of diffusion entropy analysis and standard deviation analysis of data from the Super-Kamiokande solar neutrino experiment lead to the development of anomalous diffusion and reaction in terms of fractional calculus. The new statistical perspective of Erdelyi-Kober fractional operators outlined in this book will have fundamental applications in the theory of anomalous reaction and diffusion processes dealt with in physics. A major mathematical objective of this book is specifically to examine a new definition for fractional integrals in terms of the distributions of products and ratios of statistically independently distributed positive scalar random variables or in terms of Mellin convolutions of products and ratios in the case of real scalar variables. The idea will be generalized to cover multivariable cases as well as matrix variable cases. In the matrix variable case, M-convolutions of products and ratios will be used to extend the ideas. We then give a definition for the case of real-valued scalar functions of several matrices.

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Page Count

122

Published Date

ISBN 10

9811311609

ISBN 13

9789811311604

Book's by A.M. Mathai

An Introduction to Geometrical Probability

An Introduction to Geometrical Probability

Special Functions for Applied Scientists

Special Functions for Applied Scientists

Erdélyi–Kober Fractional Calculus

Erdélyi–Kober Fractional Calculus

The H-Function

The H-Function

Fractional and Multivariable Calculus

Fractional and Multivariable Calculus

Jacobians of Matrix Transformations and Functions of Matrix Argument

Jacobians of Matrix Transformations and Functions of Matrix Argument

THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume II (ICT and Engineering)

THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume II (ICT and Engineering)

THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume I (Social Science and ICT)

THE OPPORTUNITIES OF UNCERTAINTIES: FLEXIBILITY AND ADAPTATION NEEDED IN CURRENT CLIMATE Volume I (Social Science and ICT)

The H-Function

The H-Function

Fractional and Multivariable Calculus

Fractional and Multivariable Calculus

Erdélyi–Kober Fractional Calculus

Erdélyi–Kober Fractional Calculus

An Introduction to Geometrical Probability

An Introduction to Geometrical Probability

Quadratic Forms in Random Variables

Quadratic Forms in Random Variables

Erdélyi-Kober Fractional Calculus

Erdélyi-Kober Fractional Calculus

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