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Discovering Evolution Equations with Applications Volume 1-Deterministic Equations

Discovering Evolution Equations with Applications Volume 1-Deterministic Equations

Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists even those with minimal prior exposure to analysis the foundation to understand what evolution equations are and how to work with them in various areas of practice. After presenting the essentials of analysis the book discusses homogenous finite-dimensional ordinary differential equations. Subsequent chapters then focus on linear homogenous abstract nonhomogenous linear semi-linear functional Sobolev-type neutral delay and nonlinear evolution equations. The final two chapters explore research topics including nonlocal evolution equations. For each class of equations the author develops a core of theoretical results concerning the existence and uniqueness of solutions under various growth and compactness assumptions continuous dependence upon initial data and parameters convergence results regarding the initial data and elementary stability results. By taking an applications-oriented approach this self-contained conversational-style book motivates readers to fully grasp the mathematical details of studying evolution equations. It prepares newcomers to successfully navigate further research in the field. | Discovering Evolution Equations with Applications Volume 1-Deterministic Equations

GBP 74.99
1

Handbook of Item Response Theory Volume 1: Models

Handbook of Item Response Theory Volume 1: Models

Drawing on the work of internationally acclaimed experts in the field Handbook of Item Response Theory Volume One: Models presents all major item response models. This first volume in a three-volume set covers many model developments that have occurred in item response theory (IRT) during the last 20 years. It describes models for different response formats or response processes the need of deeper parameterization due to a multilevel or hierarchical structure of the response data and other extensions and insights. In Volume One all chapters have a common format with each chapter focusing on one family of models or modeling approach. An introductory section in every chapter includes some history of the model and a motivation of its relevance. Subsequent sections present the model more formally treat the estimation of its parameters show how to evaluate its fit to empirical data illustrate the use of the model through an empirical example and discuss further applications and remaining research issues. | Handbook of Item Response Theory Volume 1: Models

GBP 66.99
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An Illustrated Introduction to Topology and Homotopy Solutions Manual for Part 1 Topology

An Illustrated Introduction to Topology and Homotopy Solutions Manual for Part 1 Topology

This solution manual accompanies the first part of the book An Illustrated Introduction toTopology and Homotopy by the same author. Except for a small number of exercises inthe first few sections we provide solutions of the (228) odd-numbered problemsappearing in first part of the book (Topology). The primary targets of this manual are thestudents of topology. This set is not disjoint from the set of instructors of topologycourses who may also find this manual useful as a source of examples exam problems etc. | An Illustrated Introduction to Topology and Homotopy Solutions Manual for Part 1 Topology

GBP 36.99
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Handbook of Approximation Algorithms and Metaheuristics Methologies and Traditional Applications Volume 1

Handbook of Approximation Algorithms and Metaheuristics Methologies and Traditional Applications Volume 1

Handbook of Approximation Algorithms and Metaheuristics Second Edition reflects the tremendous growth in the field over the past two decades. Through contributions from leading experts this handbook provides a comprehensive introduction to the underlying theory and methodologies as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction relaxation local ratio approximation schemes randomization tabu search evolutionary computation local search neural networks and other metaheuristics. It also explores multi-objective optimization reoptimization sensitivity analysis and stability. Traditional applications covered include: bin packing multi-dimensional packing Steiner trees traveling salesperson scheduling and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization computational geometry and graphs problems as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering networks (sensor and wireless) communication bioinformatics search streams virtual communities and more. About the EditorTeofilo F. Gonzalez is a professor emeritus of computer science at the University of California Santa Barbara. He completed his Ph. D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma the Pennsylvania State University and the University of Texas at Dallas before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling graph algorithms computational geometry message communication wire routing etc. | Handbook of Approximation Algorithms and Metaheuristics Methologies and Traditional Applications Volume 1

GBP 44.99
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Canonical Problems in Scattering and Potential Theory Part 1 Canonical Structures in Potential Theory

Canonical Problems in Scattering and Potential Theory Part 1 Canonical Structures in Potential Theory

Although the analysis of scattering for closed bodies of simple geometric shape is well developed structures with edges cavities or inclusions have seemed until now intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified. The first volume Canonical Structures in Potential Theory develops the mathematics solving mixed boundary potential problems for structures with cavities and edges. The second volume Acoustic and Electromagnetic Diffraction by Canonical Structures examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures. | Canonical Problems in Scattering and Potential Theory Part 1 Canonical Structures in Potential Theory

GBP 56.99
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Performance Analysis of Queuing and Computer Networks

Performance Analysis of Queuing and Computer Networks

Performance Analysis of Queuing and Computer Networks develops simple models and analytical methods from first principles to evaluate performance metrics of various configurations of computer systems and networks. It presents many concepts and results of probability theory and stochastic processes. After an introduction to queues in computer networks this self-contained book covers important random variables such as Pareto and Poisson that constitute models for arrival and service disciplines. It then deals with the equilibrium M/M/1/∞queue which is the simplest queue that is amenable for analysis. Subsequent chapters explore applications of continuous time state-dependent single Markovian queues the M/G/1 system and discrete time queues in computer networks. The author then proceeds to study networks of queues with exponential servers and Poisson external arrivals as well as the G/M/1 queue and Pareto interarrival times in a G/M/1 queue. The last two chapters analyze bursty self-similar traffic and fluid flow models and their effects on queues.

GBP 59.99
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Performance Reliability and Availability Evaluation of Computational Systems Volume I Performance and Background

Performance Reliability and Availability Evaluation of Computational Systems Volume I Performance and Background

This textbook intends to be a comprehensive and substantially self-contained two-volume book covering performance reliability and availability evaluation subjects. The volumes focus on computing systems although the methods may also be applied to other systems. The first volume covers Chapter 1 to Chapter 14 whose subtitle is ``Performance Modeling and Background. The second volume encompasses Chapter 15 to Chapter 25 and has the subtitle ``Reliability and Availability Modeling Measuring and Workload and Lifetime Data Analysis. This text is helpful for computer performance professionals for supporting planning design configuring and tuning the performance reliability and availability of computing systems. Such professionals may use these volumes to get acquainted with specific subjects by looking at the particular chapters. Many examples in the textbook on computing systems will help them understand the concepts covered in each chapter. The text may also be helpful for the instructor who teaches performance reliability and availability evaluation subjects. Many possible threads could be configured according to the interest of the audience and the duration of the course. Chapter 1 presents a good number of possible courses programs that could be organized using this text. Volume I is composed of the first two parts besides Chapter 1. Part I gives the knowledge required for the subsequent parts of the text. This part includes six chapters. It covers an introduction to probability descriptive statistics and exploratory data analysis random variables moments covariance some helpful discrete and continuous random variables Taylor series inference methods distribution fitting regression interpolation data scaling distance measures and some clustering methods. Part II presents methods for performance evaluation modeling such as operational analysis Discrete-Time Markov Chains (DTMC) and Continuous Time Markov Chains (CTMC) Markovian queues Stochastic Petri nets (SPN) and discrete event simulation. | Performance Reliability and Availability Evaluation of Computational Systems Volume I Performance and Background

GBP 120.00
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Analytical Similarity Assessment in Biosimilar Product Development

Analytical Similarity Assessment in Biosimilar Product Development

This book focuses on analytical similarity assessment in biosimilar product development following the FDA’s recommended stepwise approach for obtaining totality-of-the-evidence for approval of biosimilar products. It covers concepts such as the tiered approach for assessment of similarity of critical quality attributes in the manufacturing process of biosimilar products models/methods like the statistical model for classification of critical quality attributes equivalence tests for critical quality attributes in Tier 1 and the corresponding sample size requirements current issues and recent developments in analytical similarity assessment.

GBP 48.99
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Theoretical Statistics

Theoretical Statistics

A text that stresses the general concepts of the theory of statistics Theoretical Statistics provides a systematic statement of the theory of statistics emphasizing general concepts rather than mathematical rigor. Chapters 1 through 3 provide an overview of statistics and discuss some of the basic philosophical ideas and problems behind statistical procedures. Chapters 4 and 5 cover hypothesis testing with simple and null hypotheses respectively. Subsequent chapters discuss non-parametrics interval estimation point estimation asymptotics Bayesian procedure and deviation theory. Student familiarity with standard statistical techniques is assumed.

GBP 180.00
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Python for Scientific Computing and Artificial Intelligence

Python for Scientific Computing and Artificial Intelligence

Python for Scientific Computing and Artificial Intelligence is split into 3 parts: in Section 1 the reader is introduced to the Python programming language and shown how Python can aid in the understanding of advanced High School Mathematics. In Section 2 the reader is shown how Python can be used to solve real-world problems from a broad range of scientific disciplines. Finally in Section 3 the reader is introduced to neural networks and shown how TensorFlow (written in Python) can be used to solve a large array of problems in Artificial Intelligence (AI). This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modelling. Features: No prior experience of programming is required Online GitHub repository available with codes for readers to practice Covers applications and examples from biology chemistry computer science data science electrical and mechanical engineering economics mathematics physics statistics and binary oscillator computing Full solutions to exercises are available as Jupyter notebooks on the Web Support Material GitHub Repository of Python Files and Notebooks: https://github. com/proflynch/CRC-Press/ Solutions to All Exercises: Section 1: An Introduction to Python: https://drstephenlynch. github. io/webpages/Solutions_Section_1. html Section 2: Python for Scientific Computing: https://drstephenlynch. github. io/webpages/Solutions_Section_2. html Section 3: Artificial Intelligence: https://drstephenlynch. github. io/webpages/Solutions_Section_3. html

GBP 52.99
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Introduction to Mathematical Modeling and Computer Simulations

Introduction to Mathematical Modeling and Computer Simulations

Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions making it accessible for first- and second-year students. Chapter 1 and the Preface of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4. 0 license available at http://www. taylorfrancis. com/books/e/9781315277240

GBP 44.99
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Introduction to Statistical Methods for Financial Models

Introduction to Statistical Methods for Financial Models

This book provides an introduction to the use of statistical concepts and methods to model and analyze financial data. The ten chapters of the book fall naturally into three sections. Chapters 1 to 3 cover some basic concepts of finance focusing on the properties of returns on an asset. Chapters 4 through 6 cover aspects of portfolio theory and the methods of estimation needed to implement that theory. The remainder of the book Chapters 7 through 10 discusses several models for financial data along with the implications of those models for portfolio theory and for understanding the properties of return data. The audience for the book is students majoring in Statistics and Economics as well as in quantitative fields such as Mathematics and Engineering. Readers are assumed to have some background in statistical methods along with courses in multivariate calculus and linear algebra. | Introduction to Statistical Methods for Financial Models

GBP 44.99
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Algorithm Design: A Methodological Approach - 150 problems and detailed solutions

Algorithm Design: A Methodological Approach - 150 problems and detailed solutions

A bestseller in its French edition this book is original in its construction and its success in the French market demonstrates its appeal. It is based on three principles: (1) An organization of the chapters by families of algorithms: exhaustive search divide and conquer etc. On the contrary there is no chapter devoted only to a systematic exposure of say algorithms on strings. Some of these will be found in different chapters. (2) For each family of algorithms an introduction is given to the mathematical principles and the issues of a rigorous design with one or two pedagogical examples. (3) For the most part the book details 150 problems spanning seven families of algorithms. For each problem a precise and progressive statement is given. More importantly a complete solution is detailed with respect to the design principles that have been presented; often some classical errors are pointed out. Roughly speaking two-thirds of the book is devoted to the detailed rational construction of the solutions. | Algorithm Design: A Methodological Approach - 150 problems and detailed solutions

GBP 48.99
1

Real and Complex Analysis

Real and Complex Analysis

Presents Real & Complex Analysis Together Using a Unified ApproachA two-semester course in analysis at the advanced undergraduate or first-year graduate levelUnlike other undergraduate-level texts Real and Complex Analysis develops both the real and complex theory together. It takes a unified elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide. By presenting real and complex analysis together the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1 000 exercises the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website. This book offers a unique comprehensive presentation of both real and complex analysis. Consequently students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.

GBP 59.99
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Raspberry Pi OS System Administration with systemd and Python A Practical Approach

Raspberry Pi OS System Administration with systemd and Python A Practical Approach

The second in a new series exploring the basics of Raspberry Pi Operating System administration this installment builds on the insights provided in Volume 1 to provide a compendium of easy-to-use and essential Raspberry Pi OS system administration for the novice user with specific focus on Python and Python3. The overriding idea behind system administration of a modern 21st-century Linux system such as the Raspberry Pi OS is the use of systemd to ensure that the Linux kernel works efficiently and effectively to provide these three foundation stones of computer operation and management: computer system concurrency virtualization and secure persistence. Exercises are included throughout to reinforce the readers’ learning goals with solutions and example code provided on the accompanying GitHub site. This book is aimed at students and practitioners looking to maximize their use of the Raspberry Pi OS. With plenty of practical examples projects and exercises this volume can also be adopted in a more formal learning environment to supplement and extend the basic knowledge of a Linux operating system. | Raspberry Pi OS System Administration with systemd and Python A Practical Approach

GBP 44.99
1

Introduction to non-Kerr Law Optical Solitons

Introduction to non-Kerr Law Optical Solitons

Despite remarkable developments in the field a detailed treatment of non-Kerr law media has not been published. Introduction to non-Kerr Law Optical Solitons is the first book devoted exclusively to optical soliton propagation in media that possesses non-Kerr law nonlinearities. After an introduction to the basic features of fiber-optic communications the book outlines the nonlinear Schrödinger equation (NLSE) conserved quantities and adiabatic dynamics of soliton parameters. It then derives the NLSE for Kerr law nonlinearity from basic principles the inverse scattering transform and the 1-soliton solution. The book also explains the variational principle and Lie transform. In each case of non-Kerr law solitons the authors develop soliton dynamics evaluated integrals of motion and adiabatic dynamics of soliton parameters based on multiple-scale perturbation theory. The book explores intra-channel collision of optical solitons in both Hamiltonian and non-Hamiltonian type perturbations. In addition it examines the stochastic perturbation of optical solitons the corresponding Langevin equations and optical couplers followed by an introduction to optical bullets. Establishing a basis in an important yet insufficiently documented subject Introduction to non-Kerr Law Optical Solitons will help fuel advances in optical communication systems.

GBP 56.99
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Mathematical Principles of the Internet Volume 2 Mathematics

Mathematical Principles of the Internet Volume 2 Mathematics

This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead they cover a partial panorama and the key principles. Volume 1 explores Internet engineering while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes and an effort has been made to make this work succinct yet self-contained. Elements of information theory algebraic coding theory cryptography Internet traffic dynamics and control of Internet congestion and queueing theory are discussed. In addition stochastic networks graph-theoretic algorithms application of game theory to the Internet Internet economics data mining and knowledge discovery and quantum computation communication and cryptography are also discussed. In order to study the structure and function of the Internet only a basic knowledge of number theory abstract algebra matrices and determinants graph theory geometry analysis optimization theory probability theory and stochastic processes is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering. | Mathematical Principles of the Internet Volume 2 Mathematics

GBP 44.99
1

Innovative Methods for Rare Disease Drug Development

Innovative Methods for Rare Disease Drug Development

In the United States a rare disease is defined by the Orphan Drug Act as a disorder or condition that affects fewer than 200 000 persons. For the approval of orphan drug products for rare diseases the traditional approach of power analysis for sample size calculation is not feasible because there are only limited number of subjects available for clinical trials. In this case innovative approaches are needed for providing substantial evidence meeting the same standards for statistical assurance as drugs used to treat common conditions. Innovative Methods for Rare Disease Drug Development focuses on biostatistical applications in terms of design and analysis in pharmaceutical research and development from both regulatory and scientific (statistical) perspectives. Key Features: Reviews critical issues (e. g. endpoint/margin selection sample size requirements and complex innovative design). Provides better understanding of statistical concepts and methods which may be used in regulatory review and approval. Clarifies controversial statistical issues in regulatory review and approval accurately and reliably. Makes recommendations to evaluate rare diseases regulatory submissions. Proposes innovative study designs and statistical methods for rare diseases drug development including n-of-1 trial design adaptive trial design and master protocols like platform trials. Provides insight regarding current regulatory guidance on rare diseases drug development like gene therapy.

GBP 44.99
1

Meaningful Futures with Robots Designing a New Coexistence

Meaningful Futures with Robots Designing a New Coexistence

Soon robots will leave the factories and make their way into living rooms supermarkets and care facilities. They will cooperate with humans in everyday life taking on more than just practical tasks. How should they communicate with us? Do they need eyes a screen or arms? Should they resemble humans? Or may they enrich social situations precisely because they act so differently from humans? Meaningful Futures with Robots: Designing a New Coexistence provides insight into the opportunities and risks that arise from living with robots in the future anchored in current research projects on everyday robotics. As well as generating ideas for robot developers and designers it also critically discusses existing theories and methods for social robotics from different perspectives - ethical design artistical and technological – and presents new approaches to meaningful human-robot interaction design. Key Features: Provides insights into current research on robots from different disciplinary angles with a particular focus on a value-driven design. Includes contributions from designers psychologists engineers philosophers artists and legal scholars among others. Licence line: Chapters 1 3 12 and 15 of this book are available for free in PDF format as Open Access from the individual product page at www. crcpress. com. They have been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4. 0 license. | Meaningful Futures with Robots Designing a New Coexistence

GBP 44.99
1

Advanced Number Theory with Applications

Advanced Number Theory with Applications

Exploring one of the most dynamic areas of mathematics Advanced Number Theory with Applications covers a wide range of algebraic analytic combinatorial cryptographic and geometric aspects of number theory. Written by a recognized leader in algebra and number theory the book includes a page reference for every citing in the bibliography and more than 1 500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout the text begins with coverage of algebraic number theory binary quadratic forms Diophantine approximation arithmetic functions p-adic analysis Dirichlet characters density and primes in arithmetic progression. It then applies these tools to Diophantine equations before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture including Thue–Siegel–Roth theorem Hall’s conjecture the Erdös–Mollin-–Walsh conjecture and the Granville–Langevin Conjecture. In the appendix the author reviews sieve methods such as Eratothesenes’ Selberg’s Linnik’s and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.

GBP 69.99
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R Companion for Sampling Design and Analysis Third Edition

R Companion for Sampling Design and Analysis Third Edition

The R Companion for Sampling: Design and Analysis designed to be read alongside Sampling: Design and Analysis Third Edition by Sharon L. Lohr (SDA; 2022 CRC Press) shows how to use functions in base R and contributed packages to perform calculations for the examples in SDA. No prior experience with R is needed. Chapter 1 tells you how to obtain R and RStudio introduces basic features of the R statistical software environment and helps you get started with analyzing data. Each subsequent chapter provides step-by-step guidance for working through the data examples in the corresponding chapter of SDA with code output and interpretation. Tips and warnings help you develop good programming practices and avoid common survey data analysis errors. R features and functions are introduced as they are needed so you can see how each type of sample is selected and analyzed. Each chapter builds on the knowledge developed earlier for simpler designs; after finishing the book you will know how to use R to select and analyze almost any type of probability sample. All R code and data sets used in this book are available online to help you develop your skills analyzing survey data from social and public opinion research public health crime education business agriculture and ecology. | R Companion for Sampling Design and Analysis Third Edition

GBP 28.99
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SAS Software Companion for Sampling Design and Analysis Third Edition

SAS Software Companion for Sampling Design and Analysis Third Edition

The SAS® Software Companion for Sampling: Design and Analysis designed to be read alongside Sampling: Design and Analysis Third Edition by Sharon L. Lohr (SDA; 2022 CRC Press) shows how to use the survey selection and analysis procedures of SAS® software to perform calculations for the examples in SDA. No prior experience with SAS software is needed. Chapter 1 tells you how to access the software introduces basic features and helps you get started with analyzing data. Each subsequent chapter provides step-by-step guidance for working through the data examples in the corresponding chapter of SDA with code output and interpretation. Tips and warnings help you develop good programming practices and avoid common survey data analysis errors. Features of the SAS software procedures are introduced as they are needed so you can see how each type of sample is selected and analyzed. Each chapter builds on the knowledge developed earlier for simpler designs; after finishing the book you will know how to use SAS software to select and analyze almost any type of probability sample. All code is available on the book website and is easily adapted for your own survey data analyses. The website also contains all data sets from the examples and exercises in SDA to help you develop your skills through analyzing survey data from social and public opinion research public health crime education business agriculture and ecology | SAS® Software Companion for Sampling Design and Analysis Third Edition

GBP 28.99
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Introduction to Functional Data Analysis

Introduction to Functional Data Analysis

Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework. The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors as well as for MS and PhD students in other disciplines including applied mathematics environmental science public health medical research geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems. The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA 2) functional regression models 3) sparse and dependent functional data and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus linear algebra distributional probability theory foundations of statistical inference and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

GBP 44.99
1

Combinatorial Nullstellensatz With Applications to Graph Colouring

Combinatorial Nullstellensatz With Applications to Graph Colouring

Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to tackle combinatorial problems in diverse areas of mathematics. This book focuses on the applications of this theorem to graph colouring. A key step in the applications of Combinatorial Nullstellensatz is to show that the coefficient of a certain monomial in the expansion of a polynomial is nonzero. The major part of the book concentrates on three methods for calculating the coefficients: Alon-Tarsi orientation: The task is to show that a graph has an orientation with given maximum out-degree and for which the number of even Eulerian sub-digraphs is different from the number of odd Eulerian sub-digraphs. In particular this method is used to show that a graph whose edge set decomposes into a Hamilton cycle and vertex-disjoint triangles is 3-choosable and that every planar graph has a matching whose deletion results in a 4-choosable graph. Interpolation formula for the coefficient: This method is in particular used to show that toroidal grids of even order are 3-choosable r-edge colourable r-regular planar graphs are r-edge choosable and complete graphs of order p+1 where p is a prime are p-edge choosable. Coefficients as the permanents of matrices: This method is in particular used in the study of the list version of vertex-edge weighting and to show that every graph is (2 3)-choosable. It is suited as a reference book for a graduate course in mathematics. | Combinatorial Nullstellensatz With Applications to Graph Colouring

GBP 52.99
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Component-Based Software Engineering Methods and Metrics

Component-Based Software Engineering Methods and Metrics

This book focuses on a specialized branch of the vast domain of software engineering: component-based software engineering (CBSE). Component-Based Software Engineering: Methods and Metrics enhances the basic understanding of components by defining categories characteristics repository interaction complexity and composition. It divides the research domain of CBSE into three major sub-domains: (1) reusability issues (2) interaction and integration issues and (3) testing and reliability issues. This book covers the state-of-the-art literature survey of at least 20 years in the domain of reusability interaction and integration complexities and testing and reliability issues of component-based software engineering. The aim of this book is not only to review and analyze the previous works conducted by eminent researchers academicians and organizations in the context of CBSE but also suggests innovative efficient and better solutions. A rigorous and critical survey of traditional and advanced paradigms of software engineering is provided in the book. Features: In-interactions and Out-Interactions both are covered to assess the complexity. In the context of CBSE both white-box and black-box testing methods and their metrics are described. This work covers reliability estimation using reusability which is an innovative method. Case studies and real-life software examples are used to explore the problems and their solutions. Students research scholars software developers and software designers or individuals interested in software engineering especially in component-based software engineering can refer to this book to understand the concepts from scratch. These measures and metrics can be used to estimate the software before the actual coding commences. | Component-Based Software Engineering Methods and Metrics

GBP 105.00
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