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Books > Science & Mathematics > Mathematics > General
This unique proceedings volume offers one of the very first truly
interdisciplinary conferences ever organized. More than 15 papers
in this volume are written by some of the most acclaimed
researchers in their field. Contributions range over a very wide
spectrum of disciplines: biology; computer science; economics;
education; health sciences; operations research; philosophy;
physics; psychology; mathematics; music and sociology.
This monograph evolved over the past five years. It had its origin
as a set of lecture notes prepared for the Ninth Summer School of
Mathematical Physics held at Ravello, Italy, in 1984 and was
further refined in seminars and lectures given primarily at the
University of Colorado. The material presented is the product of a
single mathematical question raised by Dave Kassoy over ten years
ago. This question and its partial resolution led to a successful,
exciting, almost unique interdisciplinary col laborative scientific
effort. The mathematical models described are often times
deceptively simple in appearance. But they exhibit a mathematical
richness and beauty that belies that simplicity and affirms their
physical significance. The mathe matical tools required to resolve
the various problems raised are diverse, and no systematic attempt
is made to give the necessary mathematical background. The unifying
theme of the monograph is the set of models themselves. This
monograph would never have come to fruition without the enthu siasm
and drive of Dave Eberly-a former student, now collaborator and
coauthor-and without several significant breakthroughs in our
understand ing of the phenomena of blowup or thermal runaway which
certain models discussed possess. A collaborator and former student
who has made significant contribu tions throughout is Alberto
Bressan. There are many other collaborators William Troy, Watson
Fulks, Andrew Lacey, Klaus Schmitt-and former students-Paul Talaga
and Richard Ely-who must be acknowledged and thanked."
Data Fusion and Data Mining for Power System Monitoring provides a
comprehensive treatment of advanced data fusion and data mining
techniques for power system monitoring with focus on use of
synchronized phasor networks. Relevant statistical data mining
techniques are given, and efficient methods to cluster and
visualize data collected from multiple sensors are discussed. Both
linear and nonlinear data-driven mining and fusion techniques are
reviewed, with emphasis on the analysis and visualization of
massive distributed data sets. Challenges involved in realistic
monitoring, visualization, and analysis of observation data from
actual events are also emphasized, supported by examples of
relevant applications. Features Focuses on systematic illustration
of data mining and fusion in power systems Covers issues of
standards used in the power industry for data mining and data
analytics Applications to a wide range of power networks are
provided including distribution and transmission networks Provides
holistic approach to the problem of data mining and data fusion
using cutting-edge methodologies and technologies Includes
applications to massive spatiotemporal data from simulations and
actual events
'Et moi, ..., si j'avait su comment en revenir, One service
mathematics has rendered the human race. It has put common sense
back je n'y serais point aile.' where it belongs, on the topmost
shelf next Jules Verne to the dusty canister labelled 'discarded n-
sense'. The series is divergent; therefore we may be Eric T. Bell
able to do something with it. O. Hcaviside Mathematics is a tool
for thought. A highly necessary tool in a world where both feedback
and non linearities abound. Similarly, all kinds of parts of
mathematics seNe as tools for other parts and for other sciences.
Applying a simple rewriting rule to the quote on the right above
one finds such statements as: 'One seIVice topology has rendered
mathematical physics .. .'; 'One service logic has rendered com
puter science .. .'; 'One service category theory has rendered
mathematics .. .'. All arguably true. And all statements obtainable
this way form part of the raison d'j tre of this series."
'The collection contains many delightful and enjoyable problems
that are either original or taken from old books, which are no
longer easily accessible. I especially like the detailed solutions,
which make it clear that the author has carefully re-examined all
the old problems and often discovered that the previously published
solutions were incomplete. Some problems are best solved with the
help of a computer, and can serve as original exercises in computer
programming. The book provides an enjoyable read, and should not be
missing in the library of any metagrobologist.'zbMATHDefinition of
metagrobolize: puzzle, mystify; puzzle out. Hence, metagrobology is
the study of puzzles and metagrobologist an expert in such study.
David Singmaster is possibly the world's best known
metagrobologist. He gained prominence in the 1980s with a booklet
on how to solve the Rubik's Cube.This book is a collection of over
200 problems that David Singmaster has composed since 1987. Some of
the math problems have appeared in his various puzzle columns for
BBC Radio and TV, Canadian Broadcasting, Focus (the UK popular
science magazine), Games and Puzzles, the Los Angeles Times,
Micromath, the Puzzle a Day memo pad and the Weekend Telegraph.
While some of these are already classics, many of the puzzles have
not been published elsewhere previously.Puzzle enthusiasts of all
ages will find here arithmetic problems, properties of digits;
monetary problems; alpha-metics; Diophantine problems; magic
figures; sequence problems; logical problems; geometric problems;
physics problems; combinatorial problems; geographic problems;
calendar problems; clock problems; dissection problems and verbal
problems.Can you solve it? Are you smarter than a metagrobologist?
Check out Alex Bellos's Monday Puzzle on The Guardian as he
features two sequence puzzles from the book.
On April 29, 1814 Napoleon landed on the island of Elba, surrounded
with a personal army of 1200 men. The allies, Russia, Prussia,
England and Austria,
hadforcedhimintoexileafteranumberofverycostlydefeats;hewasdeprived
ofallhistitles, butcouldkeepthetitleof"EmperorofElba."
Historytellsusthat each morning he took long walks in the sun,
reviewed his army each midday
anddiscussedworldmatterswithnewlyappointedadvisors,
followingthesame pattern everyday, to the great surprise of
Campbell, the British of?cer who was to keep an eye on him. All
this made everyone believe he was settled there for good.
Napoleononcesaid: Elbaisbeautiful, butabitsmall. Elbawasde?nitely a
source of inspiration; indeed, the early morning, March 6, 1815,
Metternich, the chancellor of Austria was woken up by one of his
aides with the stunning news that Napoleon had left Elba with his
1200 men and was marching to Paris with little resistance; A few
days later he took up his throne again in the Tuileries. In spite
of his insatiable hunger for battles and expansion, he is
remembered as an important statesman. He was a pioneer in setting
up much of the legal, administrative and political machinery in
large parts of continental Europe. We gathered here in a lovely and
quaint ?shing port, Marciana Marina on theislandofElba,
tocelebrateoneofthepioneersofintegrablesystems, Hirota Sensei,
andthisattheoccasionofhisseventiethbirthday. Trainedasaphysicist in
his home university Kyushu University, Professor Hirota earned his
PhD in '61 at Northwestern University with Professor Siegert in the
?eld of "Quantum Statistical mechanics." He wrote a widely
appreciated Doctoral dissertation on
"FunctionalIntegralrepresentationofthegrandpartitionfunction."
'The collection contains many delightful and enjoyable problems
that are either original or taken from old books, which are no
longer easily accessible. I especially like the detailed solutions,
which make it clear that the author has carefully re-examined all
the old problems and often discovered that the previously published
solutions were incomplete. Some problems are best solved with the
help of a computer, and can serve as original exercises in computer
programming. The book provides an enjoyable read, and should not be
missing in the library of any metagrobologist.'zbMATHDefinition of
metagrobolize: puzzle, mystify; puzzle out. Hence, metagrobology is
the study of puzzles and metagrobologist an expert in such study.
David Singmaster is possibly the world's best known
metagrobologist. He gained prominence in the 1980s with a booklet
on how to solve the Rubik's Cube.This book is a collection of over
200 problems that David Singmaster has composed since 1987. Some of
the math problems have appeared in his various puzzle columns for
BBC Radio and TV, Canadian Broadcasting, Focus (the UK popular
science magazine), Games and Puzzles, the Los Angeles Times,
Micromath, the Puzzle a Day memo pad and the Weekend Telegraph.
While some of these are already classics, many of the puzzles have
not been published elsewhere previously.Puzzle enthusiasts of all
ages will find here arithmetic problems, properties of digits;
monetary problems; alpha-metics; Diophantine problems; magic
figures; sequence problems; logical problems; geometric problems;
physics problems; combinatorial problems; geographic problems;
calendar problems; clock problems; dissection problems and verbal
problems.Can you solve it? Are you smarter than a metagrobologist?
Check out Alex Bellos's Monday Puzzle on The Guardian as he
features two sequence puzzles from the book.
Gauge theories have provided our most successful representations of
the fundamental forces of nature. How, though, do such
representations work? Interpretations of gauge theory aim to answer
this question. Through understanding how a gauge theory's
representations work, we are able to say what kind of world our
gauge theories reveal to us.
A gauge theory's representations are mathematical structures.
These may be transformed among themselves while certain features
remain the same. Do the representations related by such a gauge
transformation merely offer alternative ways of representing the
very same situation? If so, then gauge symmetry is a purely formal
property since it reflects no corresponding symmetry in
nature.
Gauging What's Real describes the representations provided by
gauge theories in both classical and quantum physics. Richard
Healey defends the thesis that gauge transformations are purely
formal symmetries of almost all the classes of representations
provided by each of our theories of fundamental forces. He argues
that evidence for classical gauge theories of forces (other than
gravity) gives us reason to believe that loops rather than points
are the locations of fundamental properties. In addition to
exploring the prospects of extending this conclusion to the quantum
gauge theories of the Standard Model of elementary particle
physics, Healey assesses the difficulties faced by attempts to base
such ontological conclusions on the success of these theories.
This fifth volume in the series of yearbooks by the Association of
Mathematics Educators in Singapore entitled Nurturing Reflective
Learners in Mathematics is unique in that it focuses on a single
theme in mathematics education. The objective is to encourage
teachers and researchers to advance reflection among students and
teachers in mathematics classrooms.Several renowned international
and Singapore researchers in the field have published their work in
this volume. The fifteen chapters of the book illustrate
evidence-based practices that school teachers and researchers can
experiment with in their own classrooms to bring about meaningful
learning outcomes. Three broad themes, namely fundamentals,
instructional tools, and approaches to teaching for nurturing
reflective learners in mathematics classrooms, shape the ideas in
these chapters. The book makes a significant contribution towards
the learning of mathematics. It is a good resource for mathematics
teachers, educators and research students.
Tsutomu Sasao - Kyushu Institute of Technology, Japan The material
covered in this book is quite unique especially for p- ple who are
reading English, since such material is quite hard to ?nd in the
U.S. literature. German and Russian people have independently
developed their theories, but such work is not well known in the
U.S. societies. On the other hand, the theories developed in the
U.S. are not conveyed to the other places. Thus, the same theory is
re-invented or re-discovered in various places. For example, the
switching theory was developed independently in the U.S., Europe,
and Japan, almost at the same time [4, 18, 19]. Thus, the same
notions are represented by di?- ent terminologies. For example, the
Shegalkin polynomial is often called complement-free ring-sum,
Reed-Muller expression [10], or Positive -
larityReed-Mullerexpression [19].Anyway,itisquitedesirablethatsuch
a unique book like this is written in English, and many people can
read it without any di?culties. The authors have developed a logic
system called XBOOLE.Itp- forms logical operations on the given
functions. With XBOOLE, the readers can solve the problems given in
the book. Many examples and complete solutions to the problems are
shown, so the readers can study at home. I believe that the book
containing many exercises and their solutions [9] is quite useful
not only for the students, but also the p- fessors.
For many decades, Martin Gardner, the Grand Master of mathematical
puzzles, has provided the tools and projects to furnish our
all-too-sluggish minds with an athletic workout. Gardner's problems
foster an agility of the mind as they entertain. This volume
presents a new collection of problems and puzzles not previously
published in book form. Martin Gardner has dedicated it to "all the
underpaid teachers of mathematics everywhere, who love their
subject and are able to communicate that love to their students."
This book offers an overview of advanced techniques to study
atmospheric dynamics by numerical experimentation. It is primarily
intended for scientists and graduate students working on
interdisciplinary research problems at the intersection of the
atmospheric sciences, applied mathematics, statistics and physics.
Scientists interested in adopting techniques from the atmospheric
sciences to study other complex systems may also find most of the
topics covered in the book interesting. The specific techniques
covered in the book have either proven or potential value in
solving practical problems of atmospheric dynamics.
Field Solutions on Computers covers a broad range of practical
applications involving electric and magnetic fields. The text
emphasizes finite-element techniques to solve real-world problems
in research and industry. After introducing numerical methods with
a thorough treatment of electrostatics, the book moves in a
structured sequence to advanced topics. These include
magnetostatics with non-linear materials, permanent magnet devices,
RF heating, eddy current analysis, electromagnetic pulses,
microwave structures, and wave scattering. The mathematical
derivations are supplemented with chapter exercises and
comprehensive reviews of the underlying physics. The book also
covers essential supporting techniques such as mesh generation,
interpolation, sparse matrix inversions, and advanced plotting
routines.
The second edition of a bestseller, Mathematical Techniques in GIS
demystifies the mathematics used in the manipulation of spatially
related data. The author takes a step-by-step approach through the
basics of arithmetic, algebra, geometry, trigonometry and calculus
that underpin the management of such data. He then explores the use
of matrices, determinants and vectors in the handling of geographic
information so that the data may be analyzed and displayed in
two-dimensional form either in the visualization of the terrain or
as map projections. See What's New in the Second Edition: Summaries
at the end of each chapter Worked examples of techniques described
Additional material on matrices and vectors Further material on map
projections New material on spatial correlation A new section on
global positioning systems Written for those who need to make use
geographic information systems but have a limited mathematical
background, this book introduces the basic statistical techniques
commonly used in geographic information systems and explains
best-fit solutions and the mathematics behind satellite
positioning. By understanding the mathematics behind the gathering,
processing, and display of information, you can better advise
others on the integrity of results, the quality of the information,
and the safety of using it.
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