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Books > Science & Mathematics > Mathematics
The Workshop for Women in Graph Theory and Applications was held at
the Institute for Mathematics and Its Applications (University of
Minnesota, Minneapolis) on August 19-23, 2019. During this five-day
workshop, 42 participants performed collaborative research, in six
teams, each focused on open problems in different areas of graph
theory and its applications. The research work of each team was led
by two experts in the corresponding area, who prior to the
workshop, carefully selected relevant and meaningful open problems
that would yield high-quality research and results of strong
impact. As a result, all six teams have made significant
contributions to several open problems in their respective areas.
The workshop led to the creation of the Women in Graph Theory and
Applications Research Collaboration Network, which provided the
framework to continue collaborating and to produce this volume.
This book contains six chapters, each of them on one of the
different areas of research at the Workshop for Women in Graph
Theory and Applications, and written by participants of each team.
This book discusses quantum theory as the theory of random
(Brownian) motion of small particles (electrons etc.) under
external forces. Implying that the Schroedinger equation is a
complex-valued evolution equation and the Schroedinger function is
a complex-valued evolution function, important applications are
given. Readers will learn about new mathematical methods (theory of
stochastic processes) in solving problems of quantum phenomena.
Readers will also learn how to handle stochastic processes in
analyzing physical phenomena.
In China, lots of excellent maths students take an active part in
various maths contests and the best six senior high school students
will be selected to form the IMO National Team to compete in the
International Mathematical Olympiad. In the past ten years China's
IMO Team has achieved outstanding results - they won the first
place almost every year.The authors of this book are coaches of the
China national team. They are Xiong Bin, Yao Yijun, Qu Zhenhua et
al. Those who took part in the translation work are Zhao Wei and
Zhou Tianyou.The materials of this book come from a series of two
books (in Chinese) on Forward to IMO: A Collection of Mathematical
Olympiad Problems (2019-2020). It is a collection of problems and
solutions of the major mathematical competitions in China. It
provides a glimpse of how the China national team is selected and
formed.
This monograph explores classical electrodynamics from a
geometrical perspective with a clear visual presentation
throughout. Featuring over 200 figures, readers will delve into the
definitions, properties, and uses of directed quantities in
classical field theory. With an emphasis on both mathematical and
electrodynamic concepts, the author's illustrative approach will
help readers understand the critical role directed quantities play
in physics and mathematics. Chapters are organized so that they
gradually scale in complexity, and carefully guide readers through
important topics. The first three chapters introduce directed
quantities in three dimensions with and without the metric, as well
as the development of the algebra and analysis of directed
quantities. Chapters four through seven then focus on
electrodynamics without the metric, such as the premetric case,
waves, and fully covariant four-dimensional electrodynamics.
Complementing the book's careful structure, exercises are included
throughout for readers seeking further opportunities to practice
the material. Directed Quantities in Electrodynamics will appeal to
students, lecturers, and researchers of electromagnetism. It is
particularly suitable as a supplement to standard textbooks on
electrodynamics.
This book is the essential companion to Counting (2nd Edition)
(World Scientific, 2013), an introduction to combinatorics for
secondary to undergraduate students. The book gives solutions to
the exercises in Counting (2nd Edition). There is often more than
one method to solve a particular problem and the authors have
included alternative solutions whenever they are of interest. The
rigorous and clear solutions will aid the reader in further
understanding the concepts and applications in Counting (2nd
Edition). An introductory section on problem solving as described
by George P lya will be useful in helping the lay person understand
how mathematicians think and solve problems.
This contributed volume presents some of the latest research
related to model order reduction of complex dynamical systems with
a focus on time-dependent problems. Chapters are written by leading
researchers and users of model order reduction techniques and are
based on presentations given at the 2019 edition of the workshop
series Model Reduction of Complex Dynamical Systems - MODRED, held
at the University of Graz in Austria. The topics considered can be
divided into five categories: system-theoretic methods, such as
balanced truncation, Hankel norm approximation, and reduced-basis
methods; data-driven methods, including Loewner matrix and
pencil-based approaches, dynamic mode decomposition, and
kernel-based methods; surrogate modeling for design and
optimization, with special emphasis on control and data
assimilation; model reduction methods in applications, such as
control and network systems, computational electromagnetics,
structural mechanics, and fluid dynamics; and model order reduction
software packages and benchmarks. This volume will be an ideal
resource for graduate students and researchers in all areas of
model reduction, as well as those working in applied mathematics
and theoretical informatics.
The 4th World Congress on Genetics, Geriatrics and
Neurodegenerative Diseases Research (GeNeDis 2020) focuses on the
latest major challenges in scientific research, new drug targets,
the development of novel biomarkers, new imaging techniques, novel
protocols for early diagnosis of neurodegenerative diseases, and
several other scientific advances, with the aim of better, safer,
and healthier aging. Computational methodologies for implementation
on the discovery of biomarkers for neurodegenerative diseases are
extensively discussed. This volume focuses on the sessions from the
conference regarding computational biology and bioinformatics.
This book presents the emerging regime of zero refractive index
photonics, involving metamaterials that exhibit effectively zero
refractive index. Metamaterials are artificial structures whose
optical properties can be tailored at will. With metamaterials,
intriguing and spellbinding phenomena like negative refraction and
electromagnetic cloaking could be realized, which otherwise seem
unnatural or straight out of science fiction. Zero index
metamaterials are also seen as a means of boosting nonlinear
properties and are believed to have strong prospects for being
useful in nonlinear optical applications. In summary, this book
highlights almost everything currently available on zero index
metamaterials and is useful for professionally interested and
motivated readers.
This book provides application of multi criteria decision making
techniques for managerial discretion. With this book, a concerted
platform has been provided for several peers and other management
organizations to understand and implement these tools and deal with
the practical problems in a better way so as to provide more robust
managerial decision making.
This book summarizes research being pursued within the Research
Unit FOR 2089, funded by the German Research Foundation (DFG), the
goal of which is to develop the scientific base for a paradigm
shift towards dimensioning, structural realization and maintenance
of pavements, and prepare road infrastructure for future
requirements. It provides a coupled thermo-mechanical model for a
holistic physical analysis of the pavement-tire-vehicle system:
based on this model, pavement structures and materials can be
optimized so that new demands become compatible with the main goal
- durability of the structures and the materials. The development
of these new and qualitatively improved modelling approaches
requires a holistic procedure through the coupling of theoretical
numerical and experimental approaches as well as an
interdisciplinary and closely linked handling of the coupled
pavement-tire-vehicle system. This interdisciplinary research
provides a deeper understanding of the physics of the full system
through complex, coupled simulation approaches and progress in
terms of improved and, therefore, more durable and sustainable
structures.
This proceedings gather a selection of peer-reviewed papers
presented at the 8th International Conference on Fracture Fatigue
and Wear (FFW 2020), held as a virtual conference on 26-27 August
2020. The contributions, prepared by international scientists and
engineers, cover the latest advances in and innovative applications
of fracture mechanics, fatigue of materials, tribology, and wear of
materials. In addition, they discuss industrial applications and
cover theoretical and analytical methods, numerical simulations and
experimental techniques. The book is intended for academics,
including graduate students and researchers, as well as industrial
practitioners working in the areas of fracture fatigue and wear.
The unique and fully-integrated Access to Foundation workbooks for
Pearson Edexcel GCSE (9-1) Mathematics provide structured support
for your low-attaining students to help them gain confidence and
fluency in basic Number, Geometry (including Measures) and
Statistics (including Probability) before they progress to the
Foundation GCSE Maths course. The write-on Number Workbook helps
students focus with learning objectives, key points as well as
worked examples to guide them through solutions with worked
examples. Lots of carefully stepped practice questions build
students' confidence and then support stretch with 'extend
questions'. There are chapter summaries to support revision, topic
tests to check fluency, and self-assessment charts to help students
track and take ownership of their own progression. Key features
also include a baseline entry test (previous NC Levels 3-5 ),
Progress to Foundation test to move on to the full Foundation
course, and a flexible scheme of work.
The book is about strong axioms of infi nity in set theory (also
known as large cardinal axioms), and the ongoing search for natural
models of these axioms. Assuming the Ultrapower Axiom, a
combinatorial principle conjectured to hold in all such natural
models, we solve various classical problems in set theory (for
example, the Generalized Continuum Hypothesis) and uncover a theory
of large cardinals that is much clearer than the one that can be
developed using only the standard axioms.
This book provides a broad, interdisciplinary overview of
non-Archimedean analysis and its applications. Featuring new
techniques developed by leading experts in the field, it highlights
the relevance and depth of this important area of mathematics, in
particular its expanding reach into the physical, biological,
social, and computational sciences as well as engineering and
technology. In the last forty years the connections between
non-Archimedean mathematics and disciplines such as physics,
biology, economics and engineering, have received considerable
attention. Ultrametric spaces appear naturally in models where
hierarchy plays a central role - a phenomenon known as
ultrametricity. In the 80s, the idea of using ultrametric spaces to
describe the states of complex systems, with a natural hierarchical
structure, emerged in the works of Fraunfelder, Parisi, Stein and
others. A central paradigm in the physics of certain complex
systems - for instance, proteins - asserts that the dynamics of
such a system can be modeled as a random walk on the energy
landscape of the system. To construct mathematical models, the
energy landscape is approximated by an ultrametric space (a finite
rooted tree), and then the dynamics of the system is modeled as a
random walk on the leaves of a finite tree. In the same decade,
Volovich proposed using ultrametric spaces in physical models
dealing with very short distances. This conjecture has led to a
large body of research in quantum field theory and string theory.
In economics, the non-Archimedean utility theory uses probability
measures with values in ordered non-Archimedean fields. Ultrametric
spaces are also vital in classification and clustering techniques.
Currently, researchers are actively investigating the following
areas: p-adic dynamical systems, p-adic techniques in cryptography,
p-adic reaction-diffusion equations and biological models, p-adic
models in geophysics, stochastic processes in ultrametric spaces,
applications of ultrametric spaces in data processing, and more.
This contributed volume gathers the latest theoretical developments
as well as state-of-the art applications of non-Archimedean
analysis. It covers non-Archimedean and non-commutative geometry,
renormalization, p-adic quantum field theory and p-adic quantum
mechanics, as well as p-adic string theory and p-adic dynamics.
Further topics include ultrametric bioinformation, cryptography and
bioinformatics in p-adic settings, non-Archimedean spacetime,
gravity and cosmology, p-adic methods in spin glasses, and
non-Archimedean analysis of mental spaces. By doing so, it
highlights new avenues of research in the mathematical sciences,
biosciences and computational sciences.
This book provides a comprehensive examination of preconditioners
for boundary element discretisations of first-kind integral
equations. Focusing on domain-decomposition-type and multilevel
methods, it allows readers to gain a good understanding of the
mechanisms and necessary techniques in the analysis of the
preconditioners. These techniques are unique for the discretisation
of first-kind integral equations since the resulting systems of
linear equations are not only large and ill-conditioned, but also
dense. The book showcases state-of-the-art preconditioning
techniques for boundary integral equations, presenting up-to-date
research. It also includes a detailed discussion of Sobolev spaces
of fractional orders to familiarise readers with important
mathematical tools for the analysis. Furthermore, the concise
overview of adaptive BEM, hp-version BEM, and coupling of FEM-BEM
provides efficient computational tools for solving practical
problems with applications in science and engineering.
This book includes up-to-date contributions in the broadly defined
area of probabilistic analysis of voting rules and decision
mechanisms. Featuring papers from all fields of social choice and
game theory, it presents probability arguments to allow readers to
gain a better understanding of the properties of decision rules and
of the functioning of modern democracies. In particular, it focuses
on the legacy of William Gehrlein and Dominique Lepelley, two
prominent scholars who have made important contributions to this
field over the last fifty years. It covers a range of topics,
including (but not limited to) computational and technical aspects
of probability approaches, evaluation of the likelihood of voting
paradoxes, power indices, empirical evaluations of voting rules,
models of voters' behavior, and strategic voting. The book gathers
articles written in honor of Gehrlein and Lepelley along with
original works written by the two scholars themselves.
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