Barton, R.R., The Pennsylvania State University, University Park, PA, USA
1999. Approx. 210 pp.
0-387-94750-7
Most texts on the design of experiments focus on the analysis of
experimental data, not on the creation of the
design. Graphical Methods for Experimental Design presents a
strategic view of the planning of experiments, and
provides a number of graphical tools that are useful for
justifying the effort required for experimentation,
identifying variables and candidate statistical models, selecting
the set of run conditions and for assessing the
quality of the design. In addition, the graphical framework for
creating fractional factorial designs is used to
present experimental results in a way that is easier to
understand than a set of model coefficients. The text
merely assumes a basic knowledge of statistics and matrices,
while many of the graphical techniques are accessible
without any knowledge of statistical models, requiring only some
familiarity with the plotting of functions and with
the concept of projection from elementary mechanical drawing.
Contents: Introduction.- Planning for a Designed Experiment.-
Design-Plots for Factorial and
Fractional-Factorial Designs.- Designing Experiments
Graphically.- Assessing Experiment Designs.- Presenting
Results Graphically.
Series: Lecture Notes in Statistics.VOL. 143
Beltrami, E., State University of New York at Stony Brook, NY, USA
1999. Approx 150 pp. 25 figs.
0-387-98737-1
In this fascinating book, mathematician Ed Beltrami takes a close
enough look at randomness to make it
mysteriously disappear. The results of coin tosses, it turns out,
are determined from the start, and only our
incomplete knowledge makes them look random. "Random"
sequences of numbers are more elusive, but Godel
undecidability theorem informs us that we will never know. Those
familiar with quantum indeterminacy assert that
order is an illusion, and that the world is fundamentally random.
Yet randomness is also an illusion. Perhaps order
and randomness, like waves and particles, are only two sides of
the same (tossed) coin.
Contents: Preface; 1. The Taming of Chance; 2. Uncertainty and
Information; 3. Janus-Faced Randomness; 4.
Algorithms, Information, and Chance; 5. The Edge of Randomness;
Sources and Further Readings; Technical
Notes; Appendix A: Geometric Sums; Appendix B: Binary Numbers; C:
Logarithms; References.
Bachmann, G., Polytechnic University, Brooklyn, NY, USA
Beckenstein, E., St. John's University, Staten Island, NY, USA
Narici, L., St. Johns University, Jamaica, NY, USA
1999. Approx. 510 pp. 31 figs.
0-387-98899-8
This book is intended as an introduction to classical Fourier
analysis, Fourier series, the Fourier transform, and
Fourier sine and cosine transforms. The topics are developed
slowly for the reader who has never seen them
before, with a preference for clarity of exposition over elegance
in stating and proving results. More recent
developments, such as the discrete and fast Fourier transforms
and wavelets, are covered in the last two chapters,
where the approach is elementary, intended for the novice reader.
The first three, short, chapters present
requisite background material, and these could be read as a short
course in functional analysis. The text includes
many historical notes to place the material in a cultural and
mathematical context; from the fact that Jean Baptiste
Joseph Fourier was the nineteenth, but not the last, child in his
family to the impact that Fourier series have had
on the evolution of the concept of the integral.
Contents: Metric and Normed Spaces.- Analysis.- Bases.- Fourier
Series.- The Fourier Transform.- The
Discrete and Fast Fourier Transforms.- Wavelets.
Series: Universitext.
Prokhorov, Y.V., Steklov Mathematical Institute, Moscow,
Russia,
Statulevicius, V., Lithuanian Academy of Sciences, Vilnius,
Lithuania
(Eds.)
1999. Approx. 320 pp.
3-540-57045-4
The book is a collection of research level surveys on certain
topics in probability theory, which will be of interest
to graduate students and researchers.
Keywords: Limit theorems, large deviations
Contents: Preface.- Part I. Classical-Type Theorems for Sums of
Independent Random Variables (V.V. Petrov).-
Part II. The Accuracy of Gaussian Approximation in Banach Spaces
(V. Bentkus, F. G?tze, V. Paulauskas, A.
Rackauskas).- Part III. Approximation of Distributions of Sums of
Weakly Dependent Random Variables by the
Normal Distribution (J. Sunklodas).- Part IV. Refinements of the
Central Limit Theorem for Homogeneous Markov
Chains (P. Gudynas).- Part V. Limit Theorems on Large Deviations
(L. Saulis, V. Satulevicius).- Author Index.-
Subject Index.
Buchmann, J., Technische Universit?t Darmstadt, Germany
Hoeholdt, T., Technical University of Denmark, Lyngby, Denmark
Stichtenoth, H., Universit?t Gesamthochschule Essen, Germany
Tapia-Recillas, H., Universidad Autonoma
Metropolitana-Iztapalapa, Mexico
(Eds.)
1999. Approx. 266 pp.
3-540-66248-0
This book contains 23 contributions presented at the
"International Conference on Coding Theory, Cryptography
and Related Areas (ICCC)", held in Guanajuato, Mexico, in
April 1998.
It comprises a series of research papers on various aspects of
coding theory (geometric-algebraic, decoding,
exponential sums, etc.) and cryptography (discrete logarithm
problem, public key cryptosystems, primitives,
etc.), as well as in other research areas, such as codes over
finite rings and some aspects of function fields and
algebraic geometry over finite fields.
The book contains new results on the subject, never published in
any other form. It will be useful to students,
researchers, professionals, and tutors interested in this area of
research.
Keywords: algebraic - geometric coding theory, cryptography,
finite fields
Brilon, W., Ruhr-Universit?t Bochum, Germany
Huber, F., Bergische Universit?t-Gesamthochschule Wuppertal,
Germany
Schreckenberg, M., Gerhard-Mercator-Universit?t, Duisburg,
Germany
Wallentowitz, H., Institut f?r Kraftfahrwesen, Aachen, Germany
(Eds.)
Simulation - Economics - Environment
1999. X, 450 pp.
3-540-66295-2
The book deals with modern aspects of traffic theory and its
applications to real world problems. In 17 articles
various new developments are reported. The topics range from
microscopic computer simulation of traffic flow
simulations to air pollution in urban street networks. The
articles, with many illustrations are aimed at interested
students as well as experts in the field. The current status of
the work in this research area is presented by
well-known experts.
Keywords: Traffic theory, traffic simulation
Contents: Preface.- List of Participants.- Economic Factors of
Traffic Generation.- Traffic Generation.- Traffic
Flow Theory, Networks.- Environmental Effects
Flenner, H., Ruhr-Universit?t Bochum, Germany
O'Carroll, L., University of Edinburgh, UK
Vogel, W.
1999. VI, 306 pp.
3-540-66319-3
The central topic of the book is refined Intersection Theory and
its applications, the central tool of investigation
being the St?ckrad-Vogel Intersection Algorithm, based on the
join construction. This algorithm is used to
present a general version of Bezout's Theorem, in classical and
refined form. Connections with the Intersection
Theory of Fulton-MacPherson are treated, using work of van Gastel
employing Segre classes. Bertini theorems
and Connectedness theorems form another major theme, as do
various measures of multiplicity. We mix local
algebraic techniques as e.g. the theory of residual intersections
with more geometrical methods, and present a
wide range of geometrical and algebraic applications and
illustrative examples. The book incorporates methods
from Commutative Algebra and Algebraic Geometry and therefore it
will deepen the understanding of Algebraists
in geometrical methods and widen the interest of Geometers in
major tools from Commutative Algebra.
Keywords: Intersection theory, join varieties, connectedness
theorems, residual
intersections, Bezout ' s theorem .
Series: Springer Monographs in Mathematics.
Azema, J., Universite Pierre et Marie Curie, Paris, France
Emery, M., Universite Louis Pasteur, Strasbourg, France
Ledoux, M., Universite Paul Sabatier, Toulouse, France
Yor, M., Universite Pierre et Marie Curie, Paris, France
(Eds.)
1999. VII, 418 pp.
3-540-66342-8
Besides topics traditionally found in the S?minaire de
Probabilit?s (Martingale Theory, Stochastic Processes,
questions of general interest in Probability Theory), this volume
XXXIII presents nine contributions to the study
of filtrations up to isomorphism. It also contains three graduate
courses: Dynamics of stochastic algorithms, by M.
Benaim; Simulated annealing algorithms and Markov chains with
rare transitions, by O. Catoni; and Concentration
of measure and logarithmic Sobolev inequalities, by M. Ledoux.
These up to date courses present the state of the
art in three matters of interest to students in theoretical or
applied Probability Theory, and to researchers as well.
Keywords: Stochastic integrals, diffusion, Brownian motion,
Brownian filtration
Contents: Articles by: M. Arnaudon; S. Beghdadi-Sakrani; N.
Belili; M. Benaim; A. Bentaleb; W. Brannath; O.
Catoni; K. Chr?tien, F. Delbaen; B. De Meyer; L. Dubins; N.
Eisenbaum; M. ?mery; A. Es-Sahib; P. Grandits;
H. Heinich; J. Kallsen; D. Kurtz; M. Ledoux; B. Maisonneuve; M.
Morayne; J. Pitman; M. Pratelli; W.
Schachermayer; K. Tabisz; K. Takaoka; H. Tsukahara; J. Warren; S.
Watanabe
Series: Lecture Notes in Mathematics.VOL. 1709
Klir, G.J., Binghampton University - SUNY, Binghampton, NY,
USA
Wierman, M.J., Creighton University, Omaha, NE, USA
Elements of Generalized Information Theory
2nd corr. ed. 1999. XV, 170 pp. 11 figs., 10 tabs.
3-7908-1242-0
The book is an overview of the development of basic ideas and
mathematical results regarding measures and
principles of uncertainty-based information formalized within the
framework of classical set theory, probability
theory, fuzzy set theory, possibility theory, and the
Dempster-Shafer theory of evidence.
The book contains many new results, which had until now not been
available in a single monograph. The book is
very useful for researchers, but it can also be used as a
graduate text.
Keywords: Information theory, uncertainty, probability theory,
fuzzy logic
Contents: Introduction: Significance of Uncertainty; Uncertainty
and Information.- Uncertainty
Formalizations: Classical Sets: Terminology and Notation; Fuzzy
Set Theory. Fuzzy Operations. Fuzzy
Subsethood. Cylindric Extensions. Types of Fuzzy Sets; Fuzzy
Measure Theory; Evidence Theory. Upper and
Lower Probabilities; Probability Theory; Possibility Theory;
Overview of Uncertainty Theories.- Uncertainty
Measures: Nonspecifity. Hartley Function. U-uncertainty.
Nonspecifity in Evidence Theory. Nonspecifity of
Sets in n-Dimensional Euclidean Space. Generalized Hartley-Like
Measures of Nonspecifity ; Conflict. Shannon
Entropy. Entropy-Like Measure in Evidence Theory. Conflict in
Possibility Theory; Aggregate Uncertainty in
Evidence Theory. General Algorithm. for Computing Function AU.
Computing Function AU in Possibility Theory;
Fuzziness; Summary of Uncertainty Measures.- Principles of
Uncertainty: Principle of Minimum Uncertainty;
Principle of Maximum Uncertainty; Principle of Uncertainty
Invariance. Probability-Possibility Transformations.
Approximations of Fuzzy Sets. Approximations in Evidence Theory.
Revised Probability-Possibility
Transformations; Summary of Uncertainty Principles.- Conclusions:
Appraisal of Current Results; Unresolved
Problems; Future Directions.
Series: Studies in Fuzziness and Soft Computing.VOL. 15
Drensky, V., Bulgarian Academy of Sciences, Sofia, Bulgaria
A Graduate Course in Algebra
1999. Approx. 240 pp.
981-4021-48-2
The book is devoted to the combinatorial theory of polynomial
algebras, free associative and free Lie algebras,
and algebras with polynomial identities. It also examines the
structure of automorphism groups of free and
relatively free algebras. It is based on graduate courses and
short cycles of lectures presented by the author at
several universities and its goal is to involve the reader as
soon as possible in the research area, to make him or
her able to read books and papers on the considered topics. It
contains both classical and contemporary results
and methods. A specific feature of the book is that it includes
as its inseparable part more than 250 exercises and
examples with detailed hints (50 % of the numbered statements),
some of them treating serious mathematical
results. The exposition is accessible for graduate and advanced
undergraduate students with standard background
on linear algebra and some elements of ring theory and group
theory. The professional mathematician working in
the field of algebra and other related topics also will find the
book useful for his or her research and teaching.
Contents: Introduction 1. Commutative, Associative and Lie
Algebras: Basic properties of algebras; Free
algebras; The Poincar?-Birkhoff-Witt theorem. 2. Algebras with
Polynomial Identities: Definitions and examples of
PI-Algebras; Varieties and relatively free algebras; The theorem
of Birkhoff. 3. The Specht Problem: The finite
basis property; Lie algebras in characteristic 2. 4. Numerical
Invariants of T-Ideals: Graded vector spaces;
Homogeneous and multilinear polynomial identities; Proper
polynomial identities. 5. Polynomial Identities of
Concrete Algebras: Polynomial identities of the Grassmann
algebra; Polynomial identities of the upper triangular
matrices. 6. Methods of Commutative Algebra: Rational Hilbert
series; Nonmatrix polynomial identities;
Commutative and noncommutative invariant theory. 7. Polynomial
Identities of the Matrix Algebras: The
Amitsur-Levitzki theorem; Generic matrices; Central polynomials;
Various identities of matrices. 8. Multilinear
Polynomial Identities: The codimension theorem of Regev; Algebras
with polynomial growth of codimensions; The
Nagata-Higman theorem; The theory of Kemer. 9. Finitely Generated
PI-Algebras: The problems of Burnside and
Kurosch; The Shirshov theorem; Growth of algebras and
Gelfand-Kirillov dimension; Gelfand-Kirillov dimension of
PI-Algebras. 10. Automorphisms of Free Algebras: Automorphisms of
groups and algebras; The polynomial algebra
in two variables; The free associative algebra of rank two;
Exponential automorphisms; Automorphisms of relatively
free algebras. 11. Free Lie Algebras and Their Automorphisms:
Bases and subalgebras of free Lie algebras;
Automorphisms of free Lie algebras; Automorphisms of relatively
free Lie algebras. 12. The Method of
Representation Theory: Representations of finite groups; The
symmetric group; Multilinear polynomial identities;
The action of the general linear group; Proper polynomial
identities; Polynomial identities of matrices.
Pilyugin, S.Y., St. Petersburg State University, Russia
1999. XVII, 271 pp.
3-540-66299-5
This book is an introduction to the theory of shadowing of
approximate trajectories in dynamical systems by exact
ones. This is the first book completely devoted to the theory of
shadowing. It shows the importance of shadowing
theory for both the qualitative theory of dynamical systems and
the theory of numerical methods. Shadowing
Methods allow us to estimate differences between exact and
approximate solutions on infinite time intervals and to
understand the influence of error terms. The book is intended for
specialists in dynamical systems, for researchers
and graduate students in the theory of numerical methods.
Keywords: dynamical systems differential equatins shadowing
hyperbolic set
Contents: Chapter 1. Shadowing Near an Invariant Set 1.1 Basic
Definitions 1.2 Shadowing Near a Hyperbolic Set
for a Diffeomorphism 1.2.1 Hyperbolic Sets 1.2.2 The Classical
Shadowing Lemma 1.2.3 Shadowing for a Family of
Approximate Trajectories 1.2.4 The Method of Bowen 1.3 Shadowing
for Mappings of Banach Spaces 1.3.1
Shadowing for a Sequence of Mappings 1.3.2 Conditions of
Uniqueness 1.3.3 Application to the Classical
Shadowing Lemma 1.3.4 Theorems of Chow-Lin-Palmer and
Steinlein-Walther 1.3.5 Finite-Dimensional Case 1.4
Limit Shadowing 1.4.1 Limit Shadowing Property 1.4.2 Lp-Shadowing
1.4.3 The Sacker-Sell Spectrum and
Weighted Shadowing 1.4.4 Asymptotic Pseudotrajectories 1.5
Shadowing for Flows Chapter 2. Topologically
Stable, Structurally Stable, and Generic Systems 2.1 Shadowing
and Topological Stability 2.2 Shadowing in
Structurally Stable Systems 2.2.1 The Case of a Flow 2.2.2 The
Case of a Diffeomorphism 2.3 Shadowing in
Two-Dimensional Diffeomorphisms 2.4 Co-Genericity of Shadowing
for Homeomorphisms Chapter 3. Systems with
Special Structure 3.1 One-Dimensional Systems 3.2 Linear and
Linearly Induced Systems 3.3 Lattice Systems 3.4
Global Attractors for Evolution Systems Chapter 4. Numerical
Applications of Shadowing 4.1 Finite Shadowing 4.2
Periodic Shadowing for Flows 4.3 Approximation of Spectral
Characteristics 4.3.1 Evaluation of Upper Lyapunov
Exponents 4.3.2 Approximation of the Morse Spectrum 4.4
Discretizations of PDEs 4.4.1 Shadowing in
Discretizations 4.4.2 Discretization Errors on Unbounded Time
Intervals
Series: Lecture Notes in Mathematics.VOL. 1706