Gives undergraduate and graduate students alike a vivid idea of connection
theory in action for many-body systems
Shows that geometric mechanics for many-body systems works well in
dealing with the falling cat problem
Adapts geometric mechanics for the falling cat problem in the formulation of
the port-controlled Hamiltonian system
The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control
are in action together. As is well known, cats can almost always land on their feet when tossed
into the air in an upside-down attitude. If cats are not given a non-vanishing angular
momentum at an initial instant, they cannot rotate during their motion, and the motion they
can make in the air is vibration only. However, cats accomplish a half turn without rotation
when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly
understand rotations and vibrations. The connection theory in differential geometry can provide
rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats
are not easy to treat mechanically. A feasible way to approach the question of the falling cat is
to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid
bodies, which can approximate the body of a cat. In this book, the connection theory is applied
first to a many-body system to show that vibrational motions of the many-body system can
result in rotations without performing rotational motions and then to the cat model consisting
of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems
and of jointed rigid bodies must be set up.
Due 2021-05-10
X, 190 p. 25 illus.
Softcover
ISBN 978-981-16-0687-8
Product category : Monograph
Series : Lecture Notes in Mathematics
Mathematics : Differential Geometry
This book is an outgrowth of the conference ?gRegulators IV: An International Conference on
Arithmetic L-functions and Differential Geometric Methods?h that was held in Paris in May 2016.
Gathering contributions by leading experts in the field ranging from original surveys to pure
research articles, this volume provides comprehensive coverage of the frontmost developments
in the field of regulator maps. Key topics covered are: Additive polylogarithms Analytic torsions
Chabauty-Kim theory Local Grothendieck-Riemann-Roch theorems Periods Syntomic regulator
The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O.
Gregory, A. Langer, B. Lawrence, X. Ma, S. Muller, N. Otsubo, W. Raskind, J. Raimbault, D. Rossler,
S. Shen, N. Triantafillou, S. Unver and J. Vonk.
Due 2021-06-22
1st ed. 2021, Approx. 290 p.
Hardcover
ISBN 978-3-030-65202-9
Product category : Proceedings
Series : Progress in Mathematics
Mathematics : Number Theory
Offers a unified and friendly approach to enumerative combinatorics through
formal languages
Showcases the authors' unique perspective and insightful examples
Illuminates the important connection between discrete mathematics and
computer science
Engages readers through numerous exercises, examples, and applications
This textbook introduces enumerative combinatorics through the framework of formal
languages and bijections. By starting with elementary operations on words and languages, the
authors paint an insightful, unified picture for readers entering the field. Numerous concrete
examples and illustrative metaphors motivate the theory throughout, while the overall approach
illuminates the important connections between discrete mathematics and theoretical computer
science. Beginning with the basics of formal languages, the first chapter quickly establishes a
common setting for modeling and counting classical combinatorial objects and constructing
bijective proofs. From here, topics are modular and offer substantial flexibility when designing a
course. Chapters on generating functions and partitions build further fundamental tools for
enumeration and include applications such as a combinatorial proof of the Lagrange inversion
formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal
formulas, and the combinatorics that lie behind the classical Cayley?Hamilton theorem. The
remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring,
exponential structures, matching and distinct representatives, with each topic opening many
doors to further study. Generous exercise sets complement all chapters, and miscellaneous
sections explore additional applications. Lessons in Enumerative Combinatorics captures the
authors' distinctive style and flair for introducing newcomers to combinatorics. The
conversational yet rigorous presentation suits students in mathematics and computer science
at the graduate, or advanced undergraduate level
Due 2021-07-18
1st ed. 2021, XIV, 426 p. 319 illus.
Hardcover
ISBN 978-3-030-71249-5
Product category : Graduate/advanced undergraduate textbook
Series : Graduate Texts in Mathematics
Mathematics : Discrete Mathematics
Proceedings of the Eighth China-Japan-Korea International Symposium on
Ring Theory
The Eighth China-Japan-Korea International Symposium on Ring Theory, Nagoya
University, Nagoya, Japan, 26 - 31 August 2019
https://doi.org/10.1142/12099 | January 2021
Pages: 256
Since 1991, the group of ring theorists from China and Japan, joined by Korea from 1995 onwards, took turns to hold the quadrennial international conferences (sometimes also referred to as symposiums). As the proceedings of the eighth conference held in Nagoya, Japan in 2019, this volume consists of a collection of articles by invited speakers (survey) and general speakers (survey and original), all of which were refereed by world experts.
The survey articles show the trends of current research and offer clear, thorough explanations that are ideal for researchers also in other specialized areas of ring theory. The original articles display new results, ideas and tools for research investigations in ring theory.
The articles cover major areas in ring theory, such as: structures of rings, module theory, homological algebra, groups, Hopf algebras, Lie theory, representation theory of rings, (non-commutative) algebraic geometry, commutative rings (structures, representations), amongst others.
This volume is a useful resource for researchers ? both beginners and advanced experts ? in ring theory.
Invited Lectures (Survey Articles):
On Cyclotomic Quiver Hecke Algebras of Affine Type (S Ariki)
Divisibility Properties of the Quotient Ring of the Polynomial Ring D[X,Y,U,V] Modulo (XV ? YU) (G W Chang)
On the Hochschild Cohomology of Differential Graded Categories (B Keller)
Color Hom-Lie Bialgebras (I Bakayoko and S-Q Oh)
Introduction to Auslander-Bridger Theory for Unbounded Projective Complexes over Commutative Noetherian Rings (Y Yoshino)
General Lectures (Survey Articles):
The Jordan?Holder Property, Grothendieck Monoids and Bruhat Inversions (H Enomoto)
Action Functor Formalism (K Shimizu)
Boolean Graphs ? A Survey (T S Wu)
General Lectures (Original Articles):
On Two-Sided Harada Rings Constructed from QF Rings (Y Baba)
Morita Theory on ?-Representations of Rings (N Hijriati, S Wahyuni and I E Wijayanti)
An Application of Hochschild Cohomology to the Moduli of Subalgebras of the Full Matrix Ring II (K Nakamoto and T Torii)
On Generalized Nakayama?Azumaya Lemma and NAS-Modules (M Sato)
A Baer?Kaplansky Theorem in Additive Categories (S Crivei, D Keskin Tutuncu and R Tribak)
Leibniz Conformal Algebras of Rank Three (Z Wu)
Graduate students and researchers involved in areas of ring theory and
representation theory of algebras.
https://doi.org/10.1142/12168 | May 2021
Pages: 230
ISBN: 978-981-123-254-1 (hardcover)
This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.
The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform material and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
Preface
Introduction
Fundamentals:
Continuum Mechanics
Groupoids
Algebroids
Material Groupoid:
Material Algebroid
Material Distributions
Appendices:
Distributions
Connections
Principal Bundles
Bibliography
Index
Graduate and postgraduate students interested in Continuum Mechanics, Mathematical
Physics and Differential Geometry. Researchers in Elasticity, Applied Mathematics
and Differential Geometry. And those taking a master or doctorate course
that seeks the interaction between mathematics and mechanical engineering.
.
https://doi.org/10.1142/11968 | July 2021
Pages: 440
ISBN: 978-981-122-537-6 (hardcover)
ISBN: 978-981-122-766-0 (softcover)
Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.
Rather than focussing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics is similar?
The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics throughout as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.
As the book progresses, advanced material is sprinkled for further detailed exploration. This is to keep it interesting for the readers and to showcase non-trivial examples where mathematics and physics augment one another.
Introduction
Ordinary Differential Equations
The Hamiltonian Formalism of Classical Mechanics
Banach & Hilbert Spaces
Linear Operators
The Fourier Transform
Schwartz Functions and Tempered Distributions
Green's Functions
Quantum Mechanics
Variational Calculus
Appendices:
A Primer on Measure Theory
Functional Calculus
Advanced undergraduate and graduate students of mathematics and physics
with an interest in mathematical physics. Instructors can use it to design
a comprehensive course on differential equations after paring down some
of the material. Or alternatively, it also serves as a good basis for more
specialized classes on, e.g., quantum mechanics or electromagnetism that
place more emphasis on the necessary mathematics.
High School 1
https://doi.org/10.1142/12087 | May 2021
Pages: 500
ISBN: 978-981-122-985-5 (hardcover)
ISBN: 978-981-123-142-1 (softcover)
he series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 most influential educational brand in China.
The series is in line with the mathematics cognition and intellectual development level of the students in the corresponding grade. The volume lines up the topics in each chapter and introduces a variety of concepts and methods to provide with the knowledge, then gradually transitions to the competition level. The content covers all the hot topics of the competition.
In each chapter, there are packed with many problems including some real competition questions which students can use to verify their abilities. Selected detailed answers are provided. Some of the solutions are from national training team and national team members, their wonderful solutions being the feature of this series.
Concepts and Arithmetic of Sets
Number of Elements in aFinite Set
Quadratic Functions
Graphs and Properties of Functions
Powers, Exponentials and Logarithms
Functions with Absolute Values
The Maximum and Minimum of a Function
Properties of Inequalities
Basic Inequalities
Solving Inequalities
Miscellaneous Problems on Inequalities
Concepts and Properties of Trigonometric Functions
Identical Transformation in Trigonometry
Trigonometric Inequalities
Extrema of Trigonometric Expressions
Inverse Trigonometric Functions and Trigonometric Equations
The Sine Law and the Cosine Law
Concepts and Arithmetic of Vectors
Angles and Distances in Space
Cross Section, Folding and Spreading
Projection and the Area Projection Theorem
Partition of Sets
Miscellaneous Problems on Quadratic Functions
Extremum of Discrete Objects
Simple Function Iteration and Functional Equations
Constructing Functions to Solve Problems
Vector and Geometry
Tetrahedrons
The Five Centers of a Triangle
Some Famous Theorems in Plane Geometry
The Extremal Principle
Secondary school students engaged in mathematical competition, coaches in mathematics teaching, and teachers setting up math elective courses.