Blenkinsop, T. /Kruhl, J. /Kupkov, M. /Dmowska, R. (eds. )

Fractals and Dynamic Systems in Geoscience.

Concepts and methods of fractal geometry penetrate various branches of human knowledge to
an increasing degree. This tendency is particularly striking in the geosciences,
because many processes occurring in and on the Earth result in time dependences and spatial
patterns that have a fractal character. The contributions in this volume arose from the
3rd International Symposium on Fractals and Dynamic Systems in Geosciences?, held at Stara Lesna,
Slovakia in June, 1997. The volume contains new ideas and applications of fractal geometry
in such diverse branches of geoscience as engineering geology, the physics of the lithosphere
(including faulting, seismicity, and fluid flow), and climate behavior.
June 2000 191 pp.
(Birkhauser) 3-7643-6309-6

Keller, K.

Invariant Factors, Julia Equivalences and the (abstract) Mandelbrot Set.

(Lecture Notes in Mathematics, Vol. 1732)
This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics.
The conceptual kernel is a self-contained abstract counterpart of connected quadratic
Julia sets which is built on Thurston's concept of a quadratic invariant lamination and
on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated
in the complex plane.
It is used to give rigorous proofs of some well-known and some partially new statements on
the structure of the Mandelbrot set. The text is intended for graduate students and researchers.
Some elementary knowledge in topology and in functions of one complex variable is assumed.
2000 205 pp.
(Springer) 3-540-67434-9

Morgan, F.

Geometric Measure Theory: a Beginner's Guide, 3rd ed.

Geometric measure theory has become increasingly essential to geometry as well as numerous and
varied physical applications. The third edition of this leading text/reference introduces the theory,
the framework for the study of crystal growth, clusters of soap bubbles, and similar structures
involving minimization of energy. Over the past thirty years, this theory has contributed to
major advances in geometry and analysis including, for example, the original proof of the
positive mass conjecture in cosmology.
This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time
in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters
lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture,
Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals.
The abundant illustrations, examples, exercises, and solutions in this book will
enhance its reputation as the most accessible introduction to the subject.
June 2000 400 pp.
(Academic) 0-12-506851-4

Hand, D. /Mannila, H. /Smyth, P.

Principles of Data Mining.

(Adaptive Computation and Machine Learning, Series)
The growing interest in data miming is motivated by a common problem across disciplines how
does one store, access, model, and ultimately, describe and understand very large data sets?
Historically, different aspects of data mining have been addressed independently by different
disciplines. This is the first truly Interdisciplinary text on data mining, blending
the contributions of information science, computer science, and statistics.
The book consists of three sections. The first, foundations, provides a tutorial overview of
the principles underlying data mining algorithms and their application. The presentation
emphasizes intuition rather than rigor. The second section, data mining algorithms, shows
how algorithms are constructed to solve specific problems in a principled manner.
The algorithms covered include trees and rules for classification and regression,
association rules, belief networks, classical statistical models, nonlinear models such as
neural networks, and local 杜emory-based? models. The third section shows how all of the
preceding analysis fits together when applied to real-world data mining problems.
Topics include the role of meta-data, how to handle missing data, and data preprocessing.
Sep. 2000 425 pp.
(M.I.T.) 0-262-08290-X

Ciarlet, P.

Mathematical Elasticity, Vol. III: Theory of Shells.

(Studies in Mathmatics and its Applications, Vol. 29)
The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional
theory of shells. To this end, it provides, without any recourse to any a priori assumptions of
a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and
linear shell theories, by means of asymptotic methods, with the thickness as the small parameter.
Contents Part A. Linear Shell Theory. 1. Three-dimensional linearized elasticity and Korn's inequalities
in curvilinear coordinates. 2. Inequalities of Korn's type on surfaces.
3. Asymptotic analysis of linearly elastic shells: Preliminaries and outline.
4. Linearly elastic elliptic membrane shells. 5. Linearly elastic generalized membrane shells.
6. Linearly elastic flexural shells. 7. Koiter's equations and other linear shell theories.
Part B. Nonlinear Shell Theory. 8. Asymptotic analysis of nonlinearly elastic shells: Preliminaries.
9. Nonlinearly elastic membrane shells. 10. Nonlinearly elastic flexural shells. 11. Koiter's
equations and other nonlinear shell theories.
Apr. 2000 666 pp.
(North Holland) 0-444-82891-5

Harel, D. /Kozen, D. /Tiuryn, J.

Dynamic Logic.

(Foundations of Computing Series, Series)
Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular
advantage of being strongly related to classical logic. Its variants constitute natural
generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic
(PDL) can be described as a blend of three complementary classical ingredients: propositional calculus,
modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL),
the propositional calculus is replaced by classical first-order predicate calculus.
Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value.
It can be used for formalizing correctness specifications and proving rigorously that those
specifications are met by a particular program. Other uses include determining the equivalence of
programs, comparing the expressive power of various programming constructs, and synthesizing programs
from specifications.
Oct. 2000 450 pp.
(M.I.T.) 0-262-08289-6

Pfaffenberger, B.

The Linux Dictionary and Quick Reference.

Linux use is growing like wildfire, and it's drawing in millions of users who already possess some
knowledge of Microsoft Windows 95/98/NT or Mac OS. These users already know the basic computer terns,
the likes of RAM and ROM. But they won't find definitions of bash, chown, emacs, grep, or root partition
in the standard computer dictionaries. The Linux system requires that a Linux user understand how
to access and program the core operating system. More than learning how to use a new operating system,
mastering Linux requires that a user from the Windows world experience an entirely new language of
operating system fundamentals and commands. The Linux Dictionary and Quick Reference is a high value
information resource for anyone using the Linux operating system. Linux, the Intel PC version of the
traditional Unix operating system, is rapidly expanding in the PC space dominated by the Windows
family of operating Systems.
Sep. 2000 450 pp.
(M. Kaufman) 0-12-533173-8