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Books > Science & Mathematics > Mathematics > Geometry > General
This book reports on an original approach to problems of loci. It
shows how the theory of mechanisms can be used to address the locus
problem. It describes the study of different loci, with an emphasis
on those of triangle and quadrilateral, but not limited to them.
Thanks to a number of original drawings, the book helps to
visualize different type of loci, which can be treated as curves,
and shows how to create new ones, including some aesthetic ones, by
changing some parameters of the equivalent mechanisms. Further, the
book includes a theoretical discussion on the synthesis of
mechanisms, giving some important insights into the correlation
between the generation of trajectories by mechanisms and the
synthesis of those mechanisms when the trajectory is given, and
presenting approximate solutions to this problem. Based on the
authors' many years of research and on their extensive knowledge
concerning the theory of mechanisms, and bridging between geometry
and mechanics, this book offers a unique guide to mechanical
engineers and engineering designers, mathematicians, as well as
industrial and graphic designers, and students in the
above-mentioned fields alike.
This book consists of three volumes. The first volume contains
introductory accounts of topological dynamical systems, fi
nite-state symbolic dynamics, distance expanding maps, and ergodic
theory of metric dynamical systems acting on probability measure
spaces, including metric entropy theory of Kolmogorov and Sinai.
More advanced topics comprise infi nite ergodic theory, general
thermodynamic formalism, topological entropy and pressure.
Thermodynamic formalism of distance expanding maps and
countable-alphabet subshifts of fi nite type, graph directed Markov
systems, conformal expanding repellers, and Lasota-Yorke maps are
treated in the second volume, which also contains a chapter on
fractal geometry and its applications to conformal systems.
Multifractal analysis and real analyticity of pressure are also
covered. The third volume is devoted to the study of dynamics,
ergodic theory, thermodynamic formalism and fractal geometry of
rational functions of the Riemann sphere.
The book consists of articles based on the XXXVIII Bialowieza
Workshop on Geometric Methods in Physics, 2019. The series of
Bialowieza workshops, attended by a community of experts at the
crossroads of mathematics and physics, is a major annual event in
the field. The works in this book, based on presentations given at
the workshop, are previously unpublished, at the cutting edge of
current research, typically grounded in geometry and analysis, with
applications to classical and quantum physics. For the past eight
years, the Bialowieza Workshops have been complemented by a School
on Geometry and Physics, comprising series of advanced lectures for
graduate students and early-career researchers. The extended
abstracts of the five lecture series that were given in the eighth
school are included. The unique character of the
Workshop-and-School series draws on the venue, a famous historical,
cultural and environmental site in the Bialowieza forest, a UNESCO
World Heritage Centre in the east of Poland: lectures are given in
the Nature and Forest Museum and local traditions are interwoven
with the scientific activities. The chapter "Toeplitz Extensions in
Noncommutative Topology and Mathematical Physics" is available open
access under a Creative Commons Attribution 4.0 International
License via link.springer.com.
From a review of the second edition:
"This book covers many interesting topics not usually covered in
a present day undergraduate course, as well as certain basic topics
such as the development of the calculus and the solution of
polynomial equations. The fact that the topics are introduced in
their historical contexts will enable students to better appreciate
and understand the mathematical ideas involved...If one constructs
a list of topics central to a history course, then they would
closely resemble those chosen here."
(David Parrott, Australian Mathematical Society)
This book offers a collection of historical essays detailing a
large variety of mathematical disciplines and issues; it 's
accessible to a broad audience. This third edition includes new
chapters on simple groups and new sections on alternating groups
and the Poincare conjecture. Many more exercises have been added as
well as commentary that helps place the exercises in context.
This book covers methods of Mathematical Morphology to model and
simulate random sets and functions (scalar and multivariate). The
introduced models concern many physical situations in heterogeneous
media, where a probabilistic approach is required, like fracture
statistics of materials, scaling up of permeability in porous
media, electron microscopy images (including multispectral images),
rough surfaces, multi-component composites, biological tissues,
textures for image coding and synthesis. The common feature of
these random structures is their domain of definition in n
dimensions, requiring more general models than standard Stochastic
Processes.The main topics of the book cover an introduction to the
theory of random sets, random space tessellations, Boolean random
sets and functions, space-time random sets and functions (Dead
Leaves, Sequential Alternate models, Reaction-Diffusion),
prediction of effective properties of random media, and
probabilistic fracture theories.
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Asymptotic, Algebraic and Geometric Aspects of Integrable Systems
- In Honor of Nalini Joshi On Her 60th Birthday, TSIMF, Sanya, China, April 9-13, 2018
(Paperback, 1st ed. 2020)
Frank Nijhoff, Yang Shi, Dajun Zhang
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R4,363
Discovery Miles 43 630
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Ships in 10 - 15 working days
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This proceedings volume gathers together selected works from the
2018 "Asymptotic, Algebraic and Geometric Aspects of Integrable
Systems" workshop that was held at TSIMF Yau Mathematical Sciences
Center in Sanya, China, honoring Nalini Joshi on her 60th birthday.
The papers cover recent advances in asymptotic, algebraic and
geometric methods in the study of discrete integrable systems. The
workshop brought together experts from fields such as asymptotic
analysis, representation theory and geometry, creating a platform
to exchange current methods, results and novel ideas. This volume's
articles reflect these exchanges and can be of special interest to
a diverse group of researchers and graduate students interested in
learning about current results, new approaches and trends in
mathematical physics, in particular those relevant to discrete
integrable systems.
Hermitian symmetric spaces are an important class of manifolds that
can be studied with methods from Kahler geometry and Lie theory.
This work gives an introduction to Hermitian symmetric spaces and
their submanifolds, and presents classifi cation results for real
hypersurfaces in these spaces, focusing on results obtained by
Jurgen Berndt and Young Jin Suh in the last 20 years.
This book provides a lucid introduction to both modern differential
geometry and relativity for advanced undergraduates and first-year
graduate students of applied mathematics and physical sciences.
This book meets an overwhelming need for a book on modern
differential geometry and relativity that is student-friendly, and
which is also suitable for self-study. The book presumes a minimal
level of mathematical maturity so that any student who has
completed the standard Calculus sequence should be able to read and
understand the book. The key features of the book are: Detailed
solutions are provided to the Exercises in each chapter; Many of
the missing steps' that are often omitted from standard
mathematical derivations have been provided to make the book easier
to read and understand; A detailed introduction to Electrodynamics
is provided so that the book is accessible to students who have not
had a formal course in this area; In its treatment of modern
differential geometry, the book employs both a modern,
co-ordinate-free approach, and the standard co-ordinate-based
approach. This makes the book attractive to a large audience of
readers. Also, the book is particularly attractive to professional
non-specialists who would like an easy to read introduction to the
subject.
The volume reports on interdisciplinary discussions and
interactions between theoretical research and practical studies on
geometric structures and their applications in architecture, the
arts, design, education, engineering, and mathematics. These
related fields of research can enrich each other and renew their
mutual interest in these topics through networks of shared
inspiration, and can ultimately enhance the quality of geometry and
graphics education. Particular attention is dedicated to the
contributions that women have made to the scientific community and
especially mathematics. The book introduces engineers, architects
and designers interested in computer applications, graphics and
geometry to the latest advances in the field, with a particular
focus on science, the arts and mathematics education.
The study of the geometry of structures that arise in a variety of
specific natural systems, such as chemical, physical, biological,
and geological, revealed the existence of a wide range of types of
polytopes of the highest dimension that were unknown in classical
geometry. At the same time, new properties of polytopes were
discovered as well as the geometric patterns to which they obey.
There is a need to classify these types of polytopes of the highest
dimension by listing their properties and formulating the laws to
which they obey. The Classes of Higher Dimensional Polytopes in
Chemical, Physical, and Biological Systems explains the meaning of
higher dimensions and systematically generalizes the results of
geometric research in various fields of knowledge. This book is
useful both for the fundamental development of geometry and for the
development of branches of science related to human activities. It
builds upon previous books published by the author on this topic.
Covering areas such as heredity, geometry, and dimensions, this
reference work is ideal for researchers, scholars, academicians,
practitioners, industry professionals, instructors, and students.
This collection of contributions originates from the
well-established conference series "Fractal Geometry and
Stochastics" which brings together researchers from different
fields using concepts and methods from fractal geometry. Carefully
selected papers from keynote and invited speakers are included,
both discussing exciting new trends and results and giving a gentle
introduction to some recent developments. The topics covered
include Assouad dimensions and their connection to analysis,
multifractal properties of functions and measures, renewal theorems
in dynamics, dimensions and topology of random discrete structures,
self-similar trees, p-hyperbolicity, phase transitions from
continuous to discrete scale invariance, scaling limits of
stochastic processes, stemi-stable distributions and fractional
differential equations, and diffusion limited aggregation.
Representing a rich source of ideas and a good starting point for
more advanced topics in fractal geometry, the volume will appeal to
both established experts and newcomers.
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