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Books > Science & Mathematics > Mathematics > Geometry > General
The work of the Japanese sculptor Toshimasa Kikuchi (born in 1979)
is somehow bewilderingly obvious. Trained in the restoration of
Buddhist statues, mastering to perfection the techniques of
classical Japanese statuary, he carves pure forms in wood -
geometric, hydrodynamic or figurative. His scientific repertory is
of all time (mathematics, engineering, natural history), but his
preferred materials and techniques are firmly grounded in tradition
(Japanese hinoki cypress, urushi lacquer, kinpaku gold leaf). The
installation he presents for his Carte Blanche at the musee Guimet
in Paris, brings together a series of slender sculptures in
lacquered wood of mathematical objects, in the tradition of the
celebrated photographs that Man Ray took of them. These abstract
forms, hanging from the ceiling like mobiles or laid on the floor
like devotional objects, take shape through a virtuosity and
craftsmanship seldom found in contemporary art. The book is
lavishly illustrated by the Japanese photographer Tadayuki
Minamoto, who was able to capture the magnificence of the
mathematical abstraction of the works of Kikuchi; by photographs
and paintings by Man Ray; and with fascinating mathematical objects
from the Institut Henri Poincare, Paris, photographed by the French
photographer Bertrand Michau. It is essential reading for lovers of
surrealism and of the early years of twentieth-century abstraction
as well as for all who are intrigued by the close relationship
between art and mathematics.
In the two-volume set 'A Selection of Highlights' we present basics
of mathematics in an exciting and pedagogically sound way. This
volume examines many fundamental results in Geometry and Discrete
Mathematics along with their proofs and their history. In the
second edition we include a new chapter on Topological Data
Analysis and enhanced the chapter on Graph Theory for solving
further classical problems such as the Traveling Salesman Problem.
Physics/Mathematics
Every advanced undergraduate and graduate student of physics
must master the concepts of vectors and vector analysis. Yet most
textbooks cover this topic by merely repeating the
introductory-level treatment based on a limited algebraic or
analytic view of the subject.
By contrast, Geometrical Vectors introduces a more sophisticated
approach, which not only brings together many loose ends of the
traditional treatment, but also leads directly into the practical
use of vectors in general curvilinear coordinates by carefully
separating those relationships which are topologically invariant
from those which are not. Based on the essentially geometric nature
of the subject, this approach builds consistently on students'
prior knowledge and geometrical intuition.
Written in an informal and personal style, Geometrical Vectors
provides a handy guide for any student of vector analysis. Clear,
carefully constructed line drawings illustrate key points in the
text, and a set of problems is provided at the end of each chapter
(except the Epilogue) to deepen understanding of the material
presented. Pertinent physical examples are cited to show how
geometrically informed methods of vector analysis may be applied to
situations of special interest to physicists.
The term "stereotype space" was introduced in 1995 and denotes a
category of locally convex spaces with surprisingly elegant
properties. Its study gives an unexpected point of view on
functional analysis that brings this fi eld closer to other main
branches of mathematics, namely, to algebra and geometry. This
volume contains the foundations of the theory of stereotype spaces,
with accurate definitions, formulations, proofs, and numerous
examples illustrating the interaction of this discipline with the
category theory, the theory of Hopf algebras, and the four big
geometric disciplines: topology, differential geometry, complex
geometry, and algebraic geometry.
The first part of this book introduces the Schubert Cells and
varieties of the general linear group Gl (k^(r+1)) over a field k
according to Ehresmann geometric way. Smooth resolutions for these
varieties are constructed in terms of Flag Configurations in
k^(r+1) given by linear graphs called Minimal Galleries. In the
second part, Schubert Schemes, the Universal Schubert Scheme and
their Canonical Smooth Resolution, in terms of the incidence
relation in a Tits relative building are constructed for a
Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic
where algebra and algebraic geometry, combinatorics, and group
theory interact in unusual and deep ways.
From two authors who embrace technology in the classroom and value
the role of collaborative learning comes "College Geometry Using
The Geometer's Sketchpad." The book's truly discovery-based
approach guides readers to learn geometry through explorations of
topics ranging from triangles and circles to transformational,
taxicab, and hyperbolic geometries. In the process, readers hone
their understanding of geometry and their ability to write rigorous
mathematical proofs.
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.
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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R4,470
Discovery Miles 44 700
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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.
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