Theory of Nonparametric Tests


Mathematics

Thorsten Dickhaus, “Theory of Nonparametric Tests”
David Acheson, “The Calculus Story: A Mathematical Adventure”
de Souza Sánchez Filho, Emil, “Tensor Calculus for Engineers and Physicists”
Dardha, Ornela, “Type Systems for Distributed Programs: Components and Sessions”
Numerical Simulation in Applied Geophysics (Lecture Notes in Geosystems Mathematics and Computing) by Juan Enrique Santos

Thorsten Dickhaus, “Theory of Nonparametric Tests”

English | ISBN: 3319763148 | 2018 | 142 pages | PDF, EPUB | 4 MB

This textbook provides a self-contained presentation of the main concepts and methods of nonparametric statistical testing, with a particular focus on the theoretical foundations of goodness-of-fit tests, rank tests, resampling tests, and projection tests. The substitution principle is employed as a unified approach to the nonparametric test problems discussed. In addition to mathematical theory, it also includes numerous examples and computer implementations. The book is intended for advanced undergraduate, graduate, and postdoc students as well as young researchers. Readers should be familiar with the basic concepts of mathematical statistics typically covered in introductory statistics courses.

David Acheson, “The Calculus Story: A Mathematical Adventure”

English | ISBN: 0198804547 | 2017 | PDF | 208 pages | 12 MB

Calculus is the key to much of modern science and engineering. It is the mathematical method for the analysis of things that change, and since in the natural world we are surrounded by change, the development of calculus was a huge breakthrough in the history of mathematics. But it is also something of a mathematical adventure, largely because of the way infinity enters at virtually every twist and turn…
In The Calculus Story David Acheson presents a wide-ranging picture of calculus and its applications, from ancient Greece right up to the present day. Drawing on their original writings, he introduces the people who helped to build our understanding of calculus. With a step by step treatment, he demonstrates how to start doing calculus, from the very beginning.

de Souza Sánchez Filho, Emil, “Tensor Calculus for Engineers and Physicists”

English | 2016 | ISBN-10: 3319315196 | 345 pages | EPUB | 5 MB

Presents concepts in a straightforward way, while maintaining a great level of rigor
Provides 56 solved exercises and a select set of unsolved problems with answers
Presents a didactic and concise text suited to undergraduate and graduate students
Enriches understanding of tensor calculus applied to all technical sciences and engineering disciplines, providing the reader with complete illustrations that supplement the presented concepts
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces.
The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step.
Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors.
Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.

Dardha, Ornela, “Type Systems for Distributed Programs: Components and Sessions”

English | 2016 | ISBN-10: 946239203X | 192 pages | EPUB | 4 MB

A new technique based on types for the consistency of dynamic reconfigurations
Innovative technique based on encodings for the safety properties in complex distributed systems
Powerful analysis of progress and deadlock freedom of communication in complex distributed systems
In this book we develop powerful techniques based on formal methods for the verification of correctness, consistency and safety properties related to dynamic reconfiguration and communication in complex distributed systems. In particular, static analysis techniques based on types and type systems are an adequate methodology considering their success in guaranteeing not only basic safety properties, but also more sophisticated ones like deadlock or lock freedom in concurrent settings.The main contributions of this book are twofold.i) We design a type system for a concurrent object-oriented calculus to statically ensure consistency of dynamic reconfigurations.ii) We define an encoding of the session pi-calculus, which models communication in distributed systems, into the standard typed pi-calculus. We use this encoding to derive properties like type safety and progress in the session pi-calculus by exploiting the corresponding properties in the standard typed pi-calculus.

Numerical Simulation in Applied Geophysics (Lecture Notes in Geosystems Mathematics and Computing) by Juan Enrique Santos

English | 20 Jan. 2017 | ISBN: 3319484567 | 309 Pages | PDF | 3.53 MB

This book presents the theory of waves propagation in a fluid-saturated porous medium (a Biot medium) and its application in Applied Geophysics. In particular, a derivation of absorbing boundary conditions in viscoelastic and poroelastic media is presented, which later is employed in the applications.
The partial differential equations describing the propagation of waves in Biot media are solved using the Finite Element Method (FEM).


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