Series: NATO Science Series II: Mathematics, Physics and
Chemistry , Vol. 237
2006, Approx. 345 p.,
Hardcover ISBN-10: 1-4020-5402-5 ISBN-13: 978-1-4020-5402-0
Softcover ISBN-10: 1-4020-5403-3 ISBN-13: 978-1-4020-5403-7
Due: November 2006
About this book
Written for graduate students and researchers alike, this set of
lectures provides a structured introduction to the concept of
equidistribution in number theory. This concept is of growing
importance in many areas, including cryptography, zeros of L-functions,
Heegner points, prime number theory, the theory of quadratic
forms, and the arithmetic aspects of quantum chaos.
The volume brings together leading researchers from a range of
fields, whose accessible presentations reveal fascinating links
between seemingly disparate areas.
Written for:
Students and researchers in Number Theory and its applications
Table of contents
Series: Mathematics and Its Applications , Vol. 585
First edition, translated, revised and extended; original title:
Ecuatu diferentiale cu aplicatii ia mecanica constuctubor, Ed.
Tehnica, Bucharest, Romania, 1999; published by arrangement with
EDITURA TEHNICA, Bucharest, ROMANIA
2007, X, 488 p., Hardcover
ISBN-10: 1-4020-5439-4
ISBN-13: 978-1-4020-5439-6
About this book
The present book has its source in the authorsf wish to create
a bridge between the mathematical and the technical disciplines,
which need a good knowledge of a strong mathematical tool. The
necessity of such an interdisciplinary work drove the authors to
publish a first book to this aim with Editura Tehnica, Bucharest,
Romania.
The present book is a new, English edition of the volume
published in 1999. It contains many improvements concerning the
theoretical (mathematical) information, as well as new topics,
using enlarged and updated references. Only ordinary differential
equations and their solutions in an analytical frame were
considered, leaving aside their numerical approach.
The problem is firstly stated in its mechanical frame. Then the
mathematical model is set up, emphasizing on the one hand the
physical magnitude playing the part of the unknown function and
on the other hand the laws of mechanics that lead to an ordinary
differential equation or system. The solution is then obtained by
specifying the mathematical methods described in the
corresponding theoretical presentation. Finally a mechanical
interpretation of the solution is provided, this giving rise to a
complete knowledge of the studied phenomenon.
The number of applications was increased, and many of these
problems appear currently in engineering.
Written for:
Mechanical and civil engineers, physicists, applied
mathematicians, astronomers and students. The prerequisites are
courses of elementary analysis and algebra, as given at a
technical university. On a larger scale, all those interested in
using mathematical models and methods in various fields, like
mechanics, civil and mechanical engineering, and people involved
in teaching or design will find this work indispensable.
Keywords:
Bernoulli-Euler equation
Cauchy problem
Eigenvalues
Lagrange, Clairaut, Riccati
ODE, LEM
Ordinary Differential Equations
Sturm-Liouville problems
Taylor series expansion
Table of contents
Series: Lecture Notes in Mathematics , Vol. 1900
2007, Approx. 175 p., Softcover
ISBN-10: 3-540-40902-5
ISBN-13: 978-3-540-40902-1
About this book
Spin glass theory is going through a stunning period of progress
while finding exciting new applications in areas beyond
theoretical physics, in particular in combinatorics and computer
science. This collection of state-of-the-art review papers
written by leading experts in the field covers the topic from a
wide variety of angles. The topics covered are mean field spin
glasses, including a pedagogical account of Talagrand's proof of
the Parisi solution, short range spin glasses, emphasizing the
open problem of the relevance of the mean-field theory for
lattice models, and the dynamics of spin glasses, in particular
the problem of ageing in mean field models.
The book will serve as a concise introduction to the state of the
art of spin glass theory, useful to both graduate students and
young researchers, as well as to anyone curious to know what is
going on in this exciting area of mathematical physics.
Written for:
Researchers and graduate students
Keywords:
Sherrington-Kirkpatrick model
ageing
disordered systems
random energy model
spin glasses
Series: Springer Monographs in Mathematics
2007, Approx. 250 p., Hardcover
ISBN-10: 3-540-36822-1
ISBN-13: 978-3-540-36822-9
About this book
Following Quillen's approach to complex cobordism, the authors
introduce the notion of oriented cohomology theory on the
category of smooth varieties over a fixed field. They prove the
existence of a universal such theory (in characteristic 0) called
Algebraic Cobordism. Surprisingly, this theory satisfies the
analogues of Quillen's theorems: the cobordism of the base field
is the Lazard ring and the cobordism of a smooth variety is
generated over the Lazard ring by the elements of positive
degrees. This implies in particular the generalized degree
formula conjectured by Rost. The book also contains some examples
of computations and applications.
Table of contents
Introduction.- I. Cobordism and oriented cohomology.- 1.1.
Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3.
Relations with complex cobordism. - II. The definition of
algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2.
Oriented functors of geometric type. 2.3. Some elementary
properties. 2.4. The construction of algebraic cobordism. 2.5.
Some computations in algebraic cobordism.- III. Fundamental
properties of algebraic cobordism. 3.1. Divisor classes. 3.2.
Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5.
The projective bundle formula. 3.6. The extended homotopy
property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak
homology and Chern classes. 4.2. Algebraic cobordism and K-theory.
4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5.
Comparison with the Chow groups. V. Oriented Borel-Moore homology.
5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented
theories.- VI. Functoriality. 6.1. Refined cobordism. 6.2.
Intersection with a pseudo-divisor. 6.3. Intersection with a
pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i.
morphisms. 6.6. Refined pull-back and refined intersections. VII.
The universality of algebraic cobordism. 7.1. Statement of
results. 7.2. Pull-back in Borel-Moore homology theories. 7.3.
Universality 7.4. Some applications.- Appendix A: Resolution of
singularities.- References.- Index.- Glossary of Notation.
Series: Sources and Studies in the History of Mathematics and
Physical Sciences
2007, VIII, 224 p., Hardcover
ISBN-10: 1-84628-593-3
ISBN-13: 978-1-84628-593-6
About this book
The Scottish mathematician Colin MacLaurin (1698-1746) is best
known for developing and extending Newtonfs work in calculus,
geometry and gravitation; his 2-volume work "Treatise of
Fluxions" (1742) was the first systematic exposition of
Newtonfs methods. It is well known that MacLaurin was awarded
prizes by the Royal Academy of Sciences, Paris, for his earlier
work on the collision of bodies (1724) and the tides (1740);
however, the contents of these essays are less familiar ?
although some of the material is discussed in the Treatise of
Fluxions - and the essays themselves often hard to obtain. This
book presents these important works in translation for the first
time, preceded by a translation of MacLaurinfs MA dissertation
on gravity (Glasgow, 1713) which provides evidence of his early
study of Newtonian principles.
In his essentially descriptive discussion of gravity MacLaurin
ranges over planetary orbits, vortices and theology. His
discussion of collisions includes a disputatious account of what
should be understood by the force of a moving body, a contentious
topic at the time. The essay on the tides has the original
version of his celebrated theorem on the equilibrium of a
spheroidal fluid mass and employs a remarkable combination of
geometry and calculus to determine forces of attraction.
The aim is to make this material more generally accessible to
researchers and students in mathematics and physics, and indeed
to anyone with an interest in the historical development of these
subjects. A general introduction puts the works in context and
gives an outline of MacLaurin's career. Each translation is then
accompanied by an introduction and a series of notes and
appendices in which individual results are analysed, both in
modern terms and from a historical point of view. Background
material is also provided.
Table of contents
General Introduction.- Part I: MacLaurin on Gravity.- Part II:
MacLaurin on Collisions.- Part III: MacLaurin on the Tides.-
References.- Index.
Series: Springer Monographs in Mathematics
2007, VIII, 152 p., 7 illus., Hardcover
ISBN-10: 0-387-35073-X
ISBN-13: 978-0-387-35073-8
About this book
This monograph presents a self contained mathematical treatment
of the initial value problem for shock wave solutions of the
Einstein equations in General Relativity. The first two chapters
provide background for the introduction of a locally intertial
Glimm Scheme, a non-dissipative numerical scheme for
approximating shock wave solutions of the Einstein equations in
spherically symmetric spacetimes. What follows is a careful
analysis of this scheme providing a proof of the existence of (shock
wave) solutions of the spherically symmetric Einstein equations
for a perfect fluid, starting from initial density and velocity
profiles that are only locally of bounded total variation. The
book covers the initial value problems for Einstein's
gravitational field equations with fluid sources and shock wave
initial data. It has a clearly outlined goal: proving a certain
local existence theorem. Concluding remarks are added and
commentary is provided throughout. The book will be useful to
graduate students and researchers in mathematics and physics.
Table of contents
Introduction.- The Initial Value Problem in Special Relativity.-
A Shock Waves Formulation of Einstein Equations.- Existence and
Consistency for the Initial Value Problem.- Bibliography