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This volume consists of a collection of chapters by recognized experts to provide a comprehensive fundamental theoretical continuum treatment of constitutive laws used for modelling the mechanical and coupled-field properties of various types of solid materials. It covers the main types of solid material behaviour, including isotropic and anisotropic nonlinear elasticity, implicit theories, viscoelasticity, plasticity, electro- and magneto-mechanical interactions, growth, damage, thermomechanics, poroelasticity, composites and homogenization. The volume provides a general framework for research in a wide range of applications involving the deformation of solid materials. It will be of considerable benefit to both established and early career researchers concerned with fundamental theory in solid mechanics and its applications by collecting diverse material in a single volume. The readership ranges from beginning graduate students to senior researchers in academia and industry.

Mechanics. --- Mechanics, Applied. --- Mathematical physics. --- Continuum physics. --- Solid Mechanics. --- Mathematical Applications in the Physical Sciences. --- Classical and Continuum Physics. --- Elastic solids. --- Continuum mechanics --- Mechanics --- Solids --- Statics --- Physical mathematics --- Physics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Classical field theory --- Continuum physics --- Mathematics --- Field theory (Physics)

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This book systematically introduces readers to computational granular mechanics and its relative engineering applications. Part I describes the fundamentals, such as the generation of irregular particle shapes, contact models, macro-micro theory, DEM-FEM coupling, and solid-fluid coupling of granular materials. It also discusses the theory behind various numerical methods developed in recent years. Further, it provides the GPU-based parallel algorithm to guide the programming of DEM and examines commercial and open-source codes and software for the analysis of granular materials. Part II focuses on engineering applications, including the latest advances in sea-ice engineering, railway ballast dynamics, and lunar landers. It also presents a rational method of parameter calibration and thorough analyses of DEM simulations, which illustrate the capabilities of DEM. The computational mechanics method for granular materials can be applied widely in various engineering fields, such as rock and soil mechanics, ocean engineering and chemical process engineering.

Mechanics. --- Mechanics, Applied. --- Continuum physics. --- Ocean engineering. --- Theoretical and Applied Mechanics. --- Classical and Continuum Physics. --- Offshore Engineering. --- Deep-sea engineering --- Oceaneering --- Submarine engineering --- Underwater engineering --- Engineering --- Marine resources --- Oceanography --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Equipment and supplies --- Granular materials --- Bulk solids --- Materials

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There are numbers of all kinds: rational, real, complex, p-adic, and more. The p-adic numbers are not as well known as the others, but they play a fundamental role in number theory and in other parts of mathematics, capturing information related to a chosen prime number p. They also allow us to use methods from calculus and analysis to obtain results in algebra and number theory. This book is an elementary introduction to p-adic numbers. Most other books on the subject are written for more advanced students; this book provides an entryway to the subject for students with an undergraduate mathematics education. Readers who want to have an idea of and appreciation for the subject will probably find what they need in this book. Readers on the way to becoming experts can begin here before moving on to more advanced texts. This third edition has been thoroughly revised to correct mistakes, make the exposition clearer, and call attention to significant aspects that are usually reserved for advanced books. The most important addition is the integration of mathematical software for computations with p-adic numbers and functions. A final chapter includes a selection of problems for further exploration. From the reviews of the first and second editions: "Perhaps the most suitable text for beginners" - The Mathematical Gazette "This text perfectly fulfills what it proposes" - Mathematical Reviews "An extraordinarily nice manner to introduce the uninitiated to the subject" - Mededelingen van het wiskundig genootschap "If I had to recommend one book on the subject to a student – or even to a fully grown mathematician ...– it would still be this book" - MAA Reviews.

p-adic numbers. --- Numbers, p-adic --- Number theory --- p-adic analysis --- Number theory. --- Algebra. --- Field theory (Physics). --- Mathematical analysis. --- Analysis (Mathematics). --- Number Theory. --- Field Theory and Polynomials. --- Analysis. --- Number study --- Numbers, Theory of --- Algebra --- 517.1 Mathematical analysis --- Mathematical analysis --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Field theory (Physics)

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This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title "Multigraded Algebra and Applications" (ISBN 978-3-319-90493-1). .

Commutative algebra. --- Commutative rings. --- Algebraic geometry. --- Combinatorics. --- Graph theory. --- Algebra. --- Field theory (Physics). --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Graph Theory. --- Field Theory and Polynomials. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Mathematical analysis --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Combinatorics --- Algebra --- Algebraic geometry --- Geometry --- Rings (Algebra) --- Extremal problems --- Geometry, Algebraic. --- Combinatorial analysis. --- Field theory (Physics)

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Capturing Adriano Garsia's unique perspective on essential topics in algebraic combinatorics, this book consists of selected, classic notes on a number of topics based on lectures held at the University of California, San Diego over the past few decades. The topics presented share a common theme of describing interesting interplays between algebraic topics such as representation theory and elegant structures which are sometimes thought of as being outside the purview of classical combinatorics. The lectures reflect Garsia’s inimitable narrative style and his exceptional expository ability. The preface presents the historical viewpoint as well as Garsia's personal insights into the subject matter. The lectures then start with a clear treatment of Alfred Young's construction of the irreducible representations of the symmetric group, seminormal representations and Morphy elements. This is followed by an elegant application of SL(2) representations to algebraic combinatorics. The last two lectures are on heaps, continued fractions and orthogonal polynomials with applications, and finally there is an exposition on the theory of finite fields. The book is aimed at graduate students and researchers in the field.

Algebra. --- Field theory (Physics). --- Group theory. --- Commutative algebra. --- Commutative rings. --- Field Theory and Polynomials. --- Group Theory and Generalizations. --- Commutative Rings and Algebras. --- Rings (Algebra) --- Algebra --- Groups, Theory of --- Substitutions (Mathematics) --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematics --- Mathematical analysis --- Combinatorial analysis --- Field theory (Physics) --- Combinatorics --- Algebraic fields. --- Polynomials. --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory