Lattice Sums Then And Now
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Lattice Sums Then And Now
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Author : Jonathan M. Borwein
language : en
Publisher:
Release Date : 2013
Lattice Sums Then And Now written by Jonathan M. Borwein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with MATHEMATICS categories.
"The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of knowledge that exists on lattice sums and their applications. The authors also provide commentaries on open questions, and explain modern techniques which simplify the task of finding new results in this fascinating and ongoing field. Lattice sums in one, two, three, four and higher dimensions are covered"--
Lattice Sums Then And Now
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Author : J. M. Borwein
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-05
Lattice Sums Then And Now written by J. M. Borwein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-05 with Mathematics categories.
This comprehensive overview of lattice sums is long overdue for a topic that is important in diverse areas of science.
Lattice Sums Then And Now
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Author : Professor Jonathan Borwein
language : en
Publisher:
Release Date : 2014-05-14
Lattice Sums Then And Now written by Professor Jonathan Borwein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Lattice theory categories.
This comprehensive overview of lattice sums is long overdue for a topic that is important in diverse areas of science.
Vector Partitions Visible Points And Ramanujan Functions
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Author : Geoffrey B. Campbell
language : en
Publisher: CRC Press
Release Date : 2024-05-29
Vector Partitions Visible Points And Ramanujan Functions written by Geoffrey B. Campbell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-29 with Mathematics categories.
Vector Partitions, Visible Points and Ramanujan Functions offers a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number theory and computational mathematics. It takes the reader up to research level, presenting new results alongside known classical results from integer partitions and areas of vector and multipartite partition theory. It also sets forth new directions for research for the more advanced reader. Above all, the intention of the book is to bring new inspiration to others who study mathematics and related areas. It is hoped that some new ideas will be launched to add value and insight into many of the classical and new theories surrounding partitions. The book is an appreciation of the many gifted authors of research into partitions over the past century and before, in the hope that more may come of this for future generations. Features Provides a step-by-step guide through the known literature on Integer and Vector Partitions, and a focus on the not so well-known Visible Point Vector identities Serves as a reference for graduate students and researchers in physics, applied mathematics, number theory and computational mathematics Offers a variety of practical examples as well as sets of exercises suitable for students and researchers Geoffrey B. Campbell completed his PhD at Australian National University in 1998 under the esteemed physicist Professor Rodney Baxter. His affiliation with the Australian National University Mathematical Sciences Institute has continued for over 30 years. Within that time frame, Geoffrey also served eight years as an Honorary Research Fellow at LaTrobe University Mathematics and Statistics Department in Melbourne. Currently he writes ongoing articles for the Australian Mathematical Society Gazette. Within the international scope, Geoffrey currently serves as a PhD external committee member for a mathematics graduate student at Washington State University in America. Geoffrey has built a career within Australian Commonwealth and State government departments, including as an Advisor at the Department of Prime Minister and Cabinet; as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.
Gratings Theory And Numeric Applications
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Author :
language : en
Publisher: Popov, Institut Fresnel
Release Date :
Gratings Theory And Numeric Applications written by and has been published by Popov, Institut Fresnel this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Density Functional Theory
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Author : Eric Cancès
language : en
Publisher: Springer Nature
Release Date : 2023-07-18
Density Functional Theory written by Eric Cancès and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with Mathematics categories.
Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.
Analytic Number Theory Modular Forms And Q Hypergeometric Series
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Author : George E. Andrews
language : en
Publisher: Springer
Release Date : 2018-02-01
Analytic Number Theory Modular Forms And Q Hypergeometric Series written by George E. Andrews and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-01 with Mathematics categories.
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
The Evaluation Of Certain Lattice Sums
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Author : George L. Hall
language : en
Publisher:
Release Date : 1958
The Evaluation Of Certain Lattice Sums written by George L. Hall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with categories.
Mathematical And Computational Methods In Photonics And Phononics
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Author : Habib Ammari
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-15
Mathematical And Computational Methods In Photonics And Phononics written by Habib Ammari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-15 with Photonics categories.
The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.
Pi The Next Generation
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Author : David H. Bailey
language : en
Publisher: Springer
Release Date : 2016-07-19
Pi The Next Generation written by David H. Bailey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-19 with Mathematics categories.
This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., “Is pi normal?”), articles presenting new and often amazing techniques for computing digits of pi (e.g., the “BBP” algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are “normal”). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe “quadratically convergent” algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore’s Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.
