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Summability Theory and Its Applications

Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded convergent in the Pringsheim's sense both convergent in the Pringsheim's sense and bounded and regularly convergent double sequences in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course or as a key text for special Analysis seminars.

GBP 130.00

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Concise Encyclopedia of Coding Theory

Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then coding theory has grown into a discipline with many practical applications (antennas networks memories) requiring various mathematical techniques from commutative algebra to semi-definite programming to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level with definitions examples and many references. The book is divided into three parts: Part I fundamentals: cyclic codes skew cyclic codes quasi-cyclic codes self-dual codes codes and designs codes over rings convolutional codes performance bounds Part II families: AG codes group algebra codes few-weight codes Boolean function codes codes over graphs Part III applications: alternative metrics algorithmic techniques interpolation decoding pseudo-random sequences lattices quantum coding space-time codes network coding distributed storage secret-sharing and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

GBP 74.99

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The Theory of Statistical Implicative Analysis Or the Implausibility of Falsehood ... When the Exception Confirms the Rule

This book summarizes the methods and concepts of Statistical Implicative Analysis (SIA) created by Régis Gras in the 1980s to study in a new way the behavioural responses of French pupils to mathematics tests. Using a multidimensional non-symmetrical data analysis method SIA crosses a set of subjects or objects with a set of variables. It effectively complements traditional correlational and psychometric methods. SIA through its various extensions is today presented as a broad Artificial Intelligence method aimed at extracting trends and possible causalities in the form of rules from a set of variables. It is based on the unlikeliness of the existence of these relationships i. e. on the relative weakness of their counter-examples compared to what chance alone would produce. It establishes a dual topological relationship between the set of subjects and the set of variables. Many applications of this approach driving forces or crucibles for the development of SIA have concerned and still concern various fields such as didactics evaluation and assessment psychology sociology medicine biology economics art history and others. Key Features: Presents the foundations and representations of SIA Provides extensions of variable sets and subjects Includes a bonus exercise | The Theory of Statistical Implicative Analysis Or the Implausibility of Falsehood . When the Exception Confirms the Rule

GBP 120.00

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Geometric Modeling and Mesh Generation from Scanned Images

Cutting-Edge Techniques to Better Analyze and Predict Complex Physical PhenomenaGeometric Modeling and Mesh Generation from Scanned Images shows how to integrate image processing geometric modeling and mesh generation with the finite element method (FEM) to solve problems in computational biology medicine materials science and engineering. Based on the author’s recent research and course at Carnegie Mellon University the text explains the fundamentals of medical imaging image processing computational geometry mesh generation visualization and finite element analysis. It also explores novel and advanced applications in computational biology medicine materials science and other engineering areas. One of the first to cover this emerging interdisciplinary field the book addresses biomedical/material imaging image processing geometric modeling and visualization FEM and biomedical and engineering applications. It introduces image-mesh-simulation pipelines reviews numerical methods used in various modules of the pipelines and discusses several scanning techniques including ones to probe polycrystalline materials. The book next presents the fundamentals of geometric modeling and computer graphics geometric objects and transformations and curves and surfaces as well as two isocontouring methods: marching cubes and dual contouring. It then describes various triangular/tetrahedral and quadrilateral/hexahedral mesh generation techniques. The book also discusses volumetric T-spline modeling for isogeometric analysis (IGA) and introduces some new developments of FEM in recent years with applications.

GBP 46.99

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Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials

Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials provides a practical introduction to unconditional approaches to planning randomised clinical trials particularly aimed at drug development in the pharmaceutical industry. This book is aimed at providing guidance to practitioners in using average power assurance and related concepts. This book brings together recent research and sets them in a consistent framework and provides a fresh insight into how such methods can be used. Features: A focus on normal theory linking average power expected power predictive power assurance conditional Bayesian power and Bayesian power. Extensions of the concepts to binomial and time-to-event outcomes and non-inferiority trials An investigation into the upper bound on average power assurance and Bayesian power based on the prior probability of a positive treatment effect Application of assurance to a series of trials in a development program and an introduction of the assurance of an individual trial conditional on the positive outcome of an earlier trial in the program or to the successful outcome of an interim analysis Prior distribution of power and sample size Extension of the basic approach to proof-of-concept trials with dual success criteria Investigation of the connection between conditional and predictive power at an interim analysis and power and assurance Introduction of the idea of surety in sample sizing of clinical trials based on the width of the confidence intervals for the treatment effect and an unconditional version.

GBP 99.99

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Mathematical Theory of Subdivision Finite Element and Wavelet Methods

This book provides good coverage of the powerful numerical techniques namely finite element and wavelets for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore an overview of essential content such as vector spaces norm inner product linear operators spectral theory dual space and distribution theory etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method lifting scheme and error estimation technique etc. Features: • Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. • Presents a range of workout examples for better comprehension of spaces and operators. • Algorithms are presented to facilitate computer programming. • Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area. | Mathematical Theory of Subdivision Finite Element and Wavelet Methods

GBP 105.00

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