Series: Springer Optimization and Its Applications , Vol. 6
2007, XIV, 238 p., 84 illus., Hardcover
ISBN-10: 0-387-45673-2
ISBN-13: 978-0-387-45673-7
About this book
In one sense, the problem of finding the densest packing of
congruent circles in a square is easy to understand. But on
closer inspection, this problem reveals itself to be an
interesting challenge of discrete and computational geometry with
all its surprising structural forms and regularities. This book
summarizes results achieved in solving the circle packing problem
over the past few years, providing the reader with a
comprehensive view of both theoretical and computational
achievements. Typically illustrations of problem solutions are
shown, elegantly displaying the results obtained.
Beyond the theoretically challenging character of the problem,
the solution methods developed in the book also have many
practical applications.
One especially important feature of the book is the inclusion on
an enclosed CD of all the open source programming codes used.
Since the codes can be worked with directly, they will enable the
reader to improve on them and solve problem instances that still
remain challenging, or to use them as a starting point for
solving related application problems.
Table of contents
Preface.- Glossary of Symbols.- 1. Introduction and Problem
History.- 2. Problem Definitions and Formulations.- 3. Bounds for
the Optimum Values.- 4. Approximate Circle Packings Using
Optimization Methods.- 5. Other Methods for Finding Approximate
Circle Packings.- 6. Interval Methods for Validating Optimal
Solutions.- 7. The First Fully Interval-based Optimization Method.-
8. The Improved Version of the Interval Optimization Method.- 9.
Interval Methods for Verifying Structural Optimality.- 10.
Repeated Patterns in Circle Packings.- 11. Minimal Polynomials of
Point Arrangements.- 12. About the Codes Used.- Appendix A.
Currently Best Known Results for Packing Congruent Circles in a
Square.- Bibliography.- Related Web Sites.- List of Figures.-
List of Tables.- Index.
Series: Lecture Notes in Mathematics , Vol. 830
2007, X, 166 p., Softcover
ISBN-10: 3-540-46944-3
ISBN-13: 978-3-540-46944-5
About this book
The first half of this book contains the text of the first
edition of LNM volume 830, Polynomial Representations of GLn.
This classic account of matrix representations, the Schur
algebra, the modular representations of GLn, and connections with
symmetric groups, has been the basis of much research in
representation theory.
The second half is an Appendix, and can be read independently of
the first. It is an account of the Littelmann path model for the
case gln. In this case, Littelmann's 'paths' become 'words', and
so the Appendix works with the combinatorics on words. This leads
to the representation theory of the 'Littelmann algebra', which
is a close analogue of the Schur algebra. The treatment is self-contained;
in particular complete proofs are given of classical theorems of
Schensted and Knuth.
Table of contents
Series: Sources and Studies in the History of Mathematics and
Physical Sciences
2007, XIV, 226 p., 11 illus., Hardcover
ISBN-10: 0-387-46408-5
ISBN-13: 978-0-387-46408-4
About this book
This book offers a detailed history of parametric statistical
inference. Covering the period between James Bernoulli and R.A.
Fisher, it examines: binomial statistical inference; statistical
inference by inverse probability; the central limit theorem and
linear minimum variance estimation by Laplace and Gauss; error
theory, skew distributions, correlation, sampling distributions;
and the Fisherian Revolution. Lively biographical sketches of
many of the main characters are featured throughout, including
Laplace, Gauss, Edgeworth, Fisher, and Karl Pearson. Also
examined are the roles played by DeMoivre, James Bernoulli, and
Lagrange.
Table of contents
Introduction.- The Three Revolutions in Parametric Statistical
Inference.- James Bernoulli’s Law of Large Numbers for the
Binomial, 1713, and its Generalization.- De Moivre's Normal
Approximation to the Binomial, 1733, and its Generalizations.-
Bayes's Posterior Distribution of the Binomial Parameter and His
Rule for Inductive Inference, 1764.- Laplace’s Theory of
Inverse Probability, 1774-1786.- A Nonprobabilistic Interlude:
The Fitting of Equations to Data, 1750-1805.- Gauss’s
Derivation of the Normal Distribution and the Method of Least
Squares, 1809.- Credibility and Confidence Intervals by Laplace
and Gauss.- The Multivariate Posterior Distribution.- Edgeworth’s
Genuine Inverse Method and the Equivalence of Inverse and Direct
Probability in Large Samples, 1908 and 1909.- Criticisms of
Inverse Probability.- Laplace’s Central Limit Theorem and
Linear Minimum Variance Estimation.- Gauss’s Theory of Linear
Minimum Variance Estimation.- The Development of a Frequentist
Error Theory.- Skew Distributions and the Method of Moments.-
Normal Correlation and Regression.- Sampling Distributions Under
Normality, 1876-1908.- Fisher's Early papers, 1912-1921.- The
revolutionary paper, 1922.- Studentization, the F Distribution
and the Analysis of Variance, 1922-1925.- The Likelihood
Function, Ancillarity and Conditional Inference .- References.-
Subject Index.- Author Index.
Series: Classics in Mathematics
Originally published as Volume 274 in the series: Grundlehren der
mathematischen Wissenschaften
Reprint of the 1st ed. 1985. Corr. 2nd Printing Berlin Heidelberg
New York 1994, 2007, XII, 525 p., 7 illus., Softcover
ISBN-10: 3-540-49937-7
ISBN-13: 978-3-540-49937-4
From the reviews:
"Volumes III and IV complete L. Hormander's treatise on
linear partial differential equations. They constitute the most
complete and up-to-date account of this subject, by the author
who has dominated it and made the most significant contributions
in the last decades.....It is a superb book, which must be
present in every mathematical library, and an indispensable tool
for all - young and old - interested in the theory of partial
differential operators."
L. Boutet de Monvel in Bulletin of the American Mathematical
Society, 1987
"This treatise is outstanding in every respect and must be
counted among the great books in mathematics. It is certainly no
easy reading (...) but a careful study is extremely rewarding for
its wealth of ideas and techniques and the beauty of presentation."
J. Bruning in Zentralblatt MATH, 1987
Table of contents
Contents: Second Order Elliptic Operators.- Pseudo-Differential
Operators.- Elliptic Operators on a Compact Manifold without
Boundary.- Boundary Problems for Elliptic Differential Operators.-
Symplectic Geometry.- Some Classes of (Micro-)Hypoelliptic
Operators.- The Strictly Hyperbolic Cauchy Problem.- The Mixed
Dirichlet-Cauchy Problem for Second Order Operators.- Appendix B:
Some Spaces of Distributions.- Appendix C: Some Tools from
Differential Geometry.- Bibliography.- Index.- Index of Notation.
Series: Communications and Control Engineering
2007, Approx. 515 p., 10 illus., Hardcover
ISBN-10: 1-84628-604-2
ISBN-13: 978-1-84628-604-9
About this book
Matrices are effective tools for the modelling and analysis of
dynamical systems. Professor Kaczorek gives an overview of new
results in the application of polynomial and rational matrices to
continuous- and discrete-time systems. The book is self-contained,
beginning with important basics such as the Cayley?Hamilton
theorem and definitions and elementary operations of polynomial
and rational matrices and moving on to cover such topics as:
* normal matrices (including their realisation);
* rational and algebraic polynomial matrix equations;
* perfect observers for and realisation of linear systems; and
* new results on positive linear discrete- and continuous-time
systems with delays.
The text is rounded off with an appendix describing fundamental
definitions and theorems relevant to controllability and
observability in linear systems.
Polynomial and Rational Matrices will be valuable to researchers
in control and/or system theory and will provide useful reference
material for graduates studying courses in electronic and
computer engineering, mechatronics and electrical engineering.
Table of contents
Polynomial Matrices.- Rational Functions and Matrices.- Normal
Matrices and Systems.- Problem of Realisation of Normal Matrices.-
Singular and Cyclic Normal Systems.- Matrix Polynomial Equations,
Rational and Algebraic Matrix Equations.- Realization Problem and
Perfect Observers of Singular Systems.- Positive Linear Systems
with Delays.- Appendix: Selected Problems of Controllability and
Observability of Linear Systems.