2003V, 178 p. Hardcover
3-540-44219-7
This book presents mathematical models that
arise in current
photographic science. The book contains seventeen
chapters, each
dealing with one area of photographic science,
and a final
chapter containing exercises. Each chapter,
except the two
introductory chapters and the last one, begins
with general
background information at a level understandable
by graduate and
undergraduate students. It then proceeds
to develop a
mathematical model, using mathematical tools
such as ordinary
differential equations, partial differential
equations, and
stochastic processes. Next, some mathematical
results are
mentioned, often providing a partial solution
to problems raised
by the model. Finally, most chapters include
open problems. The
last chapter of the book contains "Modeling
and Applied
Mathematics" exercises based on the
material presented in
the earlier chapters.These exercises are
intended primarily for
graduate students and advanced undergraduates.
Keywords: coating flows, crystal growth,
gelation, image
formation, reaction diffusion systems
Contents: Sample Chapter for WWW: Chapter
10.
Series: Mathematics in Industry. Volume.
3
2003VI, 242 p. Softcover
3-540-44059-3
This book is an expanded version of lectures
given at a summer
school on symplectic geometry in Nordfjordeid,
Norway, in June
2001. The unifying feature of the book is
an emphasis on Calabi-Yau
manifolds. The first part discusses holonomy
groups and
calibrated submanifolds, focusing on special
Lagrangian
submanifolds and the SYZ conjecture. The
second studies Calabi-Yau
manifolds and mirror symmetry, using algebraic
geometry. The
final part describes compact hyperkahler
manifolds, which have a
geometric structure very closely related
to Calabi-Yau manifolds.
The book is an introduction to a very active
field of research,
on the boundary between mathematics and physics.
It is aimed at
graduate students and researchers in geometry
and string theory
and intended as an introductory text, requiring
only limited
background knowledge. Proofs or sketches
are given for many
important results. Moreover, exercises are
provided.
Keywords: calabi-yau manifolds, hyperkahler
manifolds, mirror
symmetry, special lagrangian submanifolds
Contents: I. Riemannian holonomy groups and
calibrated geometry
by Dominic Joyce.- II. Calabi-Yau manifolds
and mirror symmetry
by Mark Gross.- III. Compact hyperkahler
manifolds by Daniel
Huybrechts.- References.- Index.
Series: Universitext.
2003Approx. 415 pp. Hardcover
0-387-95407-4
The volume deals with the classical question
how from a sample
survey with observations on a variable conclusions
can be drawn
doncering the mean value of that variable
in the whole population.
It provides a novel and systematic treatement
of sampling theory
considered from the angel of athe samle autocorrelation
coefficient p (rho.)
Contents: Preface.- Notation and Introduction.-
Elementary
Statistic.- A "Normal" Approach
to Unequal Probability
Sampling.- A General rho Theory on Survey
Sampling.- Variance
Estimation for Some Standard Designs.- Multistage
and Cluster (Sub)Sampling.-
Some Speical (Sub)Cluster Sampling Designs.-
Estimation of the
Sample Autocorrelation Coeffcient pz.- Variance
Approximations.-
Systematic Sampling with Unequal Probabilities.-
The Regression
Estimator Revisited.- The General Restriction
Estimator in
Multisurvey Sampling.- Weighting Procedures.
Series: Springer Series in Statistics.
2003Approx. 250 pp. 106 figs. Softcover
0-387-95513-5
Learn to juggle numbers! This book is the
first comprehensive
account of the mathematical techniques and
results used in the
modelling of juggling patterns. This includes
all known and many
new results about juggling sequences and
matrices, the
mathematical skeletons of juggling patterns.
Many useful and entertaining tips and tricks
spice up the
mathematical menu presented in this book.
There are detailed
descriptions of jugglable and attractive
juggling sequences, easy
zero-gravity juggling, robot juggling, as
well as fun juggling of
words, anti-balls, and irrational numbers.
The book also includes novel, or at least
not very well known
connections with topics such as bell ringing,
knot theory, and
the many body problem. In fact, the chapter
on mathematical bell
ringing has been expanded into the most comprehensive
survey in
the literature of the mathematics used by
bell ringers.
Accessible at all levels of mathematical
sophistication, this is
a book for mathematically wired jugglers,
mathematical bell
ringers, combinatorists, mathematics educators,
and just about
anybody interested in beautiful and unusual
applications of
mathematics.
Keywords: Jonglieren, Juggling, Popular science
Contents: Juggling - an Introduction.- Simple
Juggling.-
Multiplex Juggling.- Multihand Juggling.-
Practical Juggling.-
Jingling, or, Ringing the Changes.- Juggling
Loose Ends.-
Appendix A: Stereograms of Hamiltonian Sycles.-
References.-
Index.
1st ed. 1980. 2nd printing2003VI, 139 p.
Hardcover
3-540-44237-5
The present book is an English translation
of "Arbres,
Amalgames, SL(2)", published in 1977
by J-P.Serre, and
written with the collaboration of H.Bass.
The first chapter
describes the "arboreal dictionary"
between graphs of
groups and group actions on trees. The second
chapter gives
applications to the Bruhat-Tits tree of SL(2)
over a local field.
Keywords: algebra, amalgams, graphs, groups
"In the case of an author like Serre,
there is almost no
need to underline the book's qualities of
elegance and precision:
over and above these, it provides abundant
links to other topics,
particularly by means of the remarks and
the numerous exercises
which, for the most part, are not easy to
solve, but genuinely
augment the content of the book. The greatest
quality of this
book however, is, in my opinion, that one
finds in it many new
and interesting ideas of very considerable
substance, but
presented in their very simplest form."
H. Behr, Frankfurt in: Jahresbericht der
DMV, (84/3) 1982
Contents: Chapter I: Trees and Amalgams:
Amalgams.- Trees.- Trees
and free groups.- Trees and amalgams.- Structure
of a group
acting on a tree.- Amalgams and fixed points
Chapter II: SL(2):The
tree of SL(2) over a local field.- Arithmetic
subgroups of the
groups GL(2) and SL(2) over a function field
of one variable.
Series: Springer Monographs in Mathematics.