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Clifford Algebras
  • Language: en
  • Pages: 635

Clifford Algebras

The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.

A First Course in Complex Analysis with Applications
  • Language: en
  • Pages: 471

A First Course in Complex Analysis with Applications

The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manor. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Algebraic Structures and Moduli Spaces
  • Language: en
  • Pages: 268

Algebraic Structures and Moduli Spaces

This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.

Complex Analysis
  • Language: en
  • Pages: 453

Complex Analysis

Designed for the undergraduate student with a calculus background but no prior experience with complex analysis, this text discusses the theory of the most relevant mathematical topics in a student-friendly manner. With a clear and straightforward writing style, concepts are introduced through numerous examples, illustrations, and applications. Each section of the text contains an extensive exercise set containing a range of computational, conceptual, and geometric problems. In the text and exercises, students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section devoted exclusively to the applications of complex analysis to science and engineering, providing students with the opportunity to develop a practical and clear understanding of complex analysis. The Mathematica syntax from the second edition has been updated to coincide with version 8 of the software. --

Challenges in the Construction of Highways in the Brazilian Amazonia Environment
  • Language: en

Challenges in the Construction of Highways in the Brazilian Amazonia Environment

  • Type: Book
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  • Published: 2020
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  • Publisher: Unknown

The construction of highways in the Brazilian Amazonia Region is always problematic, mainly because it involves environmental obstacles but also technical, economic, and natural challenges. The environmental issues concern the deforestation of the virgin forest and the resulting environmental impacts. The technical ones are related to the natural subgrade, formed by the geologically young alluvial soils that are plastic, being highly compressible or expansive, present in the vast Amazon Basin, whereas the economic issues refer to the final costs of inputs for the construction of the layers of the highway since granular soils and stony materials are located in limited areas that are distant f...

Combinatorial Algebraic Geometry
  • Language: en
  • Pages: 390

Combinatorial Algebraic Geometry

  • Type: Book
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  • Published: 2017-11-17
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  • Publisher: Springer

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.

Hasse-Schmidt Derivations on Grassmann Algebras
  • Language: en
  • Pages: 217

Hasse-Schmidt Derivations on Grassmann Algebras

  • Type: Book
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  • Published: 2016-07-08
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  • Publisher: Springer

This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert cal...

Perspectives in Representation Theory
  • Language: en
  • Pages: 384

Perspectives in Representation Theory

This volume contains the proceedings of the conference Perspectives in Representation Theory, held from May 12-17, 2012, at Yale University, in honor of Igor Frenkel's 60th birthday. The aim of the conference was to present current progress on the following (interrelated) topics: vertex operator algebras and chiral algebras, conformal field theory, the (geometric) Langlands program, affine Lie algebras, Kac-Moody algebras, quantum groups, crystal bases and canonical bases, quantum cohomology and K-theory, geometric representation theory, categorification, higher-dimensional Kac-Moody theory, integrable systems, quiver varieties, representations of real and -adic groups, and quantum gauge theories. The papers in this volume present representation theory connections to numerous other subjects, as well as some of the most recent advances in representation theory, including those which occurred thanks to the application of techniques in other areas of mathematics, and of ideas of quantum field theory and string theory.

Challenges in the Construction of Highways in the Brazilian Amazonia Environment
  • Language: en

Challenges in the Construction of Highways in the Brazilian Amazonia Environment

  • Type: Book
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  • Published: 2018
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  • Publisher: Unknown

The Chapter ,ÄúChallenges in the construction of highways in the Brazilian Amazonia environment: Part I: Identification of Engineering Problems,Äù dealt with the identification of Engineering problems concerning the implementation of road infrastructure in the Brazilian Amazon. This present chapter deals with Engineering solutions to overcome the obstacles mentioned in that previously chapter, focusing on alternatives that contemplate the use of the synthetic coarse aggregate of calcined clay (SCACC), recycled materials from ceramic waste, soil,Äìemulsion mixes, and chemical additives, in partial or total replacement of coarse and fine natural aggregates, in addition to the use of piled embankments, for the reinforcement of the natural subgrade in the presence of a very thick, soft soil layer in the foundation of the highway.

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
  • Language: en
  • Pages: 435

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry, category theory, gauge theory, and string theory has been closely related to generalizations of integral transforms of a more geometric character. "Fourier–Mukai and Nahm Transforms in Geometry and Mathematical Physics" examines the algebro-geometric approach (Fourier–Mukai functors) as well as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organized into a monograph. Key features: Basic constructions and definitions are presented in preliminary background chapters - Presentation explores applications and suggests several open questions - Extensive bibliography and index. This self-contained monograph provides an introduction to current research in geometry and mathematical physics and is intended for graduate students and researchers just entering this field.