Download or read book Structural Additive Theory written by David J. Grynkiewicz and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

Download or read book Structural Additive Theory written by David Grynkiewicz and published by Springer. This book was released on 2013-06-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​Nestled between number theory, combinatorics, algebra and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e., sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

Download or read book Additive Combinatorics written by Terence Tao and published by Cambridge University Press. This book was released on 2006-09-14 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Download or read book Theory and Practice of Additive Manufacturing written by Tuhin Mukherjee and published by John Wiley & Sons. This book was released on 2023-09-26 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory and Practice of Additive Manufacturing Discover the ins and outs of additive manufacturing in this student-friendly textbook Also known as 3D printing, additive manufacturing is a process by which layers of material are added to create three-dimensional objects guided by a digital model. It has revolutionized the design and manufacture of customized products, facilitating the rapid, flexible production of a huge range of goods. It promises to revolutionize manufacturing engineering, shorten industrial supply chains, and more. Theory and Practice of Additive Manufacturing provides the first introduction to this subject designed specifically for students. Balancing the underlying theories behind additive manufacturing with concrete applications, it guides readers through basic processes, essential tools and materials, and more. The result is ideal for readers looking to bring additive manufacturing to bear on engineering or industry careers of almost any kind. Theory and Practice of Additive Manufacturing features: Over 100 worked-out example problems Detailed discussion of the emerging digital tools including mechanistic modeling, machine learning, and more Commitment to pedagogy and reinforcement geared toward student learning outcomes Theory and Practice of Additive Manufacturing is ideal for undergraduate and graduate students and instructors in introductory additive manufacturing courses, as well as practicing engineers and researchers working in industries that use additive manufacturing technologies, including aerospace, automotive, and consumer goods.

Download or read book Additive Structures and Randomness in Combinatorics written by Christoph Spiegel and published by . This book was released on 2020 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Combinatorics, Combinatorial Number Theory, Structural Additive Theory and Additive Number Theory are just some of the terms used to describe the vast field that sits at the intersection of Number Theory and Combinatorics and which will be the focus of this thesis. Its contents are divided into two main parts, each containing several thematically related results.The first part deals with the question under what circumstances solutions to arbitrary linear systems of equations usually occur in combinatorial structures..The properties we will be interested in studying in this part relate to the solutions to linear systems of equations.A first question one might ask concerns the point at which sets of a given size will typically contain a solution. We will establish a threshold and also study the distribution of the number of solutions at that threshold, showing that it converges to a Poisson distribution in certain cases.Next, Van der Waerden's Theorem, stating that every finite coloring of the integers contains monochromatic arithmetic progression of arbitrary length, is by some considered to be the first result in Ramsey Theory. Rado generalized van der Waerden's result by characterizing those linear systems whose solutions satisfy a similar property and Szemerédi strengthened it to a statement concerning density rather than colorings. We will turn our attention towards versions of Rado's and Szemerédi's Theorem in random sets, extending previous work of Friedgut, Rödl, Ruciński and Schacht in the case of the former and of Conlon, Gowers and Schacht for the latter to include a larger variety of systems and solutions.Lastly, Chvátal and Erdo¿s suggested studying Maker-Breaker games. These games have deep connections to the theory of random structures and we will build on work of Bednarska and Luczak to establish the threshold for how much a large variety of games need to be biased in favor of the second player. These include games in which the first player wants to occupy a solution to some given linear system, generalizing the van der Waerden games introduced by Beck.The second part deals with the extremal behavior of sets with interesting additive properties. In particular, we will be interested in bounds or structural descriptions for sets exhibiting some restrictions with regards to either their representation function or their sumset.First, we will consider Sidon sets, that is sets of integers with pairwise unique differences. We will study a generalization of Sidon sets proposed very recently by Kohayakawa, Lee, Moreira and Rödl, where the pairwise differences are not just distinct, but in fact far apart by a certain measure. We will obtain strong lower bounds for such infinite sets using an approach of Cilleruelo. As a consequence of these bounds, we will also obtain the best current lower bound for Sidon sets in randomly generated infinite sets of integers of high density. Next, one of the central results at the intersection of Combinatorics and Number Theory is the Freiman-Ruzsa Theorem stating that any finite set of integers of given doubling can be efficiently covered by a generalized arithmetic progression. In the case of particularly small doubling, more precise structural descriptions exist. We will first study results going beyond Freiman's well-known 3k-4 Theorem in the integers. We will then see an application of these results to sets of small doubling in finite cyclic groups.Lastly, we will turn our attention towards sets with near-constant representation functions. Erdo¿s and Fuchs established that representation functions of arbitrary sets of integers cannot be too close to being constant. We will first extend the result of Erdo¿s and Fuchs to ordered representation functions. We will then address a related question of Sárközy and Sós regarding weighted representation function.

Download or read book Combinatorial Number Theory and Additive Group Theory written by Alfred Geroldinger and published by Springer Science & Business Media. This book was released on 2009-06-04 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Download or read book Probabilistic Structural Dynamics written by Yu-Kweng Lin and published by McGraw Hill Professional. This book was released on 2004 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic structural dynamics is a new approach to building calculations that satisfy safety requirements while at the same time driving new efficiencies. This text provides a tutorial to these new methods.

Download or read book Additive Combinatorics written by Bela Bajnok and published by CRC Press. This book was released on 2018-04-27 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods. The book is divided into five parts which are compared to a meal. The first part is called Ingredients and includes relevant background information about number theory, combinatorics, and group theory. The second part, Appetizers, introduces readers to the book’s main subject through samples. The third part, Sides, covers auxiliary functions that appear throughout different chapters. The book’s main course, so to speak, is Entrees: it thoroughly investigates a large variety of questions in additive combinatorics by discussing what is already known about them and what remains unsolved. These include maximum and minimum sumset size, spanning sets, critical numbers, and so on. The final part is Pudding and features numerous proofs and results, many of which have never been published. Features: The first book of its kind to explore the subject Students of any level can use the book as the basis for research projects The text moves gradually through five distinct parts, which is suitable both for beginners without prerequisites and for more advanced students Includes extensive proofs of propositions and theorems Each of the introductory chapters contains numerous exercises to help readers

Download or read book Combinatorial and Additive Number Theory IV written by Melvyn B. Nathanson and published by Springer Nature. This book was released on 2021-08-12 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Download or read book Handbook of Learning and Cognitive Processes Volume 5 written by William Estes and published by Psychology Press. This book was released on 2014-06-20 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1978 Volume 5 of this Handbook reflects a single theoretical orientation, that characterized by the term human information processing in the literature at the time, but which ranges over a very broad spectrum of cognitive activities. The first two chapters give some overall picture of the background, goals, method, and limitations of the information-processing approach. The remaining chapters treat in detail some principal areas of application – visual processing, mental chronometry, representation of spatial information in memory, problem solving, and the theory of instruction. The first three volumes of the Handbook presented an overview of the field, followed by treatments of conditioning, behavior theory, and human learning and retention. With the fourth volume, the focus of attention shifted from the domain of learning theory to that of cognitive psychology.

Download or read book Environmental Modelling written by Keith Beven and published by CRC Press. This book was released on 2010-02-25 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty in the predictions of science when applied to the environment is an issue of great current relevance in relation to the impacts of climate change, protecting against natural and man-made disasters, pollutant transport and sustainable resource management. However, it is often ignored both by scientists and decision makers, or interpreted as a conflict or disagreement between scientists. This is not necessarily the case, the scientists might well agree, but their predictions would still be uncertain and knowledge of that uncertainty might be important in decision making. Environmental Modelling: An Uncertain Future? introduces students, scientists and decision makers to: the different concepts and techniques of uncertainty estimation in environmental prediction the philosophical background to different concepts of uncertainty the constraint of uncertainties by the collection of observations and data assimilation in real-time forecasting techniques for decision making under uncertainty. This book will be relevant to environmental modellers, practitioners and decision makers in hydrology, hydraulics, ecology, meteorology and oceanography, geomorphology, geochemistry, soil science, pollutant transport and climate change. A companion website for the book can be found at www.uncertain-future.org.uk

Download or read book Structure and Randomness in Complexity Theory and Additive Combinatorics written by Seyed Kaave Hosseini and published by . This book was released on 2019 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation involves the interplay between structure, randomness, and pseudorandomness in theoretical computer science and additive combinatorics. Such interplay in particular materializes when one is extracting algebraic structure in scenarios where only weak combinatorial information is available. We develop new tools to address some problems of this type where the objects are sumsets and its bilinear generalizations, set of large Fourier spectra, and protocols in communication complexity. Later we move on to constructions of objects with certain pseudorandom properties. We construct a highly irregular set showing the limits of regularity lemma in the algebraic setting which is a major tool in pseudorandomness. Moreover, we introduce a new framework to construct pseudorandom generators and give some applications.

Download or read book Personality Research Methods and Theory written by Patrick E. Shrout and published by Psychology Press. This book was released on 2014-04-04 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Donald W. Fiske's professional life and collaborations are themselves a textbook in the development of the field of personality. From the field's early origins in personnel selection, rating accuracy, and psychotherapy outcomes, to its current status of theoretical and methodological maturity -- complete with mid-life crises -- the field has been fundamentally changed by Fiske's work, and the changes have influenced generations of scholars. This festschrift is a celebration of Fiske's impact, but not merely of his impact on the history of personality research. Instead, the volume focuses on ongoing debates and issues that have been framed or influenced by Fiske's work. The festschrift's three sections are organized around three themes in Fiske's writings -- themes that also correspond to three periods in his career. This volume examines current thinking about what can be known about personality, how constructs relevant to personality psychology are best measured, and how to approach specific research problems in personality and related fields. The contributors create an eminent cross-section of the development and current status of personality methods. In addition to Fiske's eminent contemporaries, the contributors to this volume include Fiske's former students, collaborators, and his two children, both of whom are behavioral scientists. The accomplishments of his students, colleagues, and children testifies to the range of psychologists who have benefited from his scholarly and practical wisdom. This collection is a valuable textbook for an advanced graduate course as well as appealing as a scholarly resource. Many of the contributors are renown psychological leaders who have made available their latest original thoughts. The book concludes with an essay by Fiske offering his perspective on the central themes: behavioral and social science metatheory, methods, and strategies.

Download or read book The Theory of 2 structures written by Andrzej Ehrenfeucht and published by World Scientific. This book was released on 1999 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of 2-structures provides a convenient framework for decomposition and transformation of mathematical systems where one or several different binary relationships hold between the objects of the system. In particular, it forms a useful framework for decomposition and transformation of graphs. The decomposition methods presented in this book correspond closely to the top-down design methods studied in theoretical computer science. The transformation methods considered here have a natural interpretation in the dynamic evolution of certain kinds of communication networks. From the mathematical point of view, the clan decomposition method presented here, also known as modular decomposition or substitution decomposition, is closely related to the decomposition by quotients in algebra. The transformation method presented here is based on labelled 2-structures over groups, the theory of which generalizes the well-studied theory of switching classes of graphs. This book is both a text and a monograph. As a monograph, the results concerning the decomposition and transformation of 2-structures are presented in a unified way. In addition, detailed notes on references are provided at the end of each chapter. These notes allow the reader to trace the origin of many notions and results, and to browse through the literature in order to extend the material presented in the book. To facilitate its use as a textbook, there are numerous examples and exercises which provide an opportunity for the reader to check his or her understanding of the discussed material. Furthermore, the text begins with preliminaries on partial orders, semigroups, groups and graphs to the extent needed for the book.

Download or read book Modules and the Structure of Rings written by Golan and published by Routledge. This book was released on 2017-10-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.

Download or read book Unified Theory of Concrete Structures written by Thomas T. C. Hsu and published by John Wiley & Sons. This book was released on 2010-03-16 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unified Theory of Concrete Structures develops an integrated theory that encompasses the various stress states experienced by both RC & PC structures under the various loading conditions of bending, axial load, shear and torsion. Upon synthesis, the new rational theories replace the many empirical formulas currently in use for shear, torsion and membrane stress. The unified theory is divided into six model components: a) the struts-and-ties model, b) the equilibrium (plasticity) truss model, c) the Bernoulli compatibility truss model, d) the Mohr compatibility truss model, e) the softened truss model, and f) the softened membrane model. Hsu presents the six models as rational tools for the solution of the four basic types of stress, focusing on the significance of their intrinsic consistencies and their inter-relationships. Because of its inherent rationality, this unified theory of reinforced concrete can serve as the basis for the formulation of a universal and international design code. Includes an appendix and accompanying website hosting the authors’ finite element program SCS along with instructions and examples Offers comprehensive coverage of content ranging from fundamentals of flexure, shear and torsion all the way to non-linear finite element analysis and design of wall-type structures under earthquake loading. Authored by world-leading experts on torsion and shear

Download or read book Soil Health and Environmental Sustainability written by Pravat Kumar Shit and published by Springer Nature. This book was released on 2022-09-27 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the measurement, monitoring, mapping and modelling of soil pollution and land resources. This book explores state-of-the-art techniques based on open sources software & R statistical programming and modelling in modern geo-computation techniques specifically focusing on the recent trends in data mining/machine learning techniques and robust modelling in soil resources. Soil and agricultural systems are an integral part of the global environment and human well‐being, providing multiple goods and services essential for people worldwide and crucial for sustainable development. Soil contamination is an environmental hazard and has become a big issue related to environmental health. The challenge of the twenty-first century is to reduce the contaminant load and bring it to below permissible level. The contamination is not only a problem affecting local environments at the place of occurrence but also spreading to other regions because of easy transportation of pollutants. This leads to direct and indirect contamination of land and aquatic systems, surface water and groundwater, inducing significant risks for natural ecosystems. In this context, the spatial modelling, prediction, efficient use, risk assessment, protection and management of soil resources in the agriculture system are the key to achieving sustainable development goals and ensuring the promotion of an economically, socially and environmental sustainability future. The aim of this book on soil contaminants and environmental health: application of geospatial technology is to identify the soil and sediment quality, sources of contaminants and risk assessment and focuses on the decision-making and planning point of view through GIS data management techniques. This book covers major topics such as spatial modelling in soil and sediments pollution and remediation; radioactive wastes, microbiology of soil and sediments, soil salinity and sodicity, pollution from landfill sites, soil erosion and contamination from agricultural activities, heavy metal pollution and health risk; environmental impact and risk assessment, sustainable land use, landscape management and governance, soil degradation and risk assessment, agricultural soil pollution, pollution due to urban activities, soil pollution by industrial effluents and solid wastes, pollution control and mitigation in extreme environments. The content of this book is of interest to researchers, professionals and policy-makers whose work is in soil science and agriculture practices. The book equips with the knowledge and skills to tackle a wide range of issues manifested in geographic data, including those with scientific, societal and environmental implications.