Salapaka, M.V., Iowa State University, Ames,
IA, USA
Dahleh, M., University of California, Santa
Barbara, CA, USA
2000. XV, 167 pp. 17 figs.
1-85233-256-5
Series: Lecture Notes in Control and Information
Sciences.VOL. 252
This book develops the necessary mathematical
background and
basic results in control theory that are
needed to
set up and solve a class of multiple objective
control design
problems. Exact solutions for certain problems
are
provided, as well as approximations to more
general problems.
This book is intended for engineering and
mathematics graduate students who are interested
in control
theory and the application of functional
analysis and
optimization tools to engineering problems.
Contents: Topology.- Functions on Vector
Spaces.- Convex
Analysis.- Paradigm for Control Design.-
SISO
l1/H2 Problem.- A Composite Performance Measure.-
MIMO Design:
The Square Case.- Multiple-input
Multiple-output Systems.- Robust Performance.-
References.-
Index.
Passot, T., Nice, France / Sulem, P.-L., Nice, France (Eds.)
Proceedings of the Workshop Held in Nice,
France, 1-4 December
1998
1999. X, 385 pp.
3-540-66697-4
Series: Lecture Notes in Physics.vol. 536
This book is of interest to researchers in
astrophysics and the
planetary sciences. It surveys the current
knowledge on the propagation of nonlinear
waves and the
development of a turbulent dynamics in
magnetohydrodynamic flows. The authors emphasize
how the
theoretical understanding of MHD waves and
turbulence is related to the description
of media where the
presence of an ambient magnetic field is
known to play
an essential role. These effects are important
in the physics of
various space plasmas such as the magnetosphere,
the solar wind, the solar corona, the interplanetary
and
interstellar media, etc. The authors treat
fundamental
aspects as revealed by asymptotic analysis,
numerical
simulations, and observations in the solar
wind.
Keywords: MHD : magnetohydrodynamics, magnetosphere,
Alfven waves, space physics, plasma waves,
solar wind .
Contents: From the contents: Nonlinear Dispersive
Alfv?n Waves.-
Wistler Solitons, Their Radiation and the
Self-Focusing of Whistler Wave Beams.- Alfv?n
Wave Filamentation
and Plasma Heating.- Nonlinear
Quasiresonant Alfv?n Oscillations in One-dimensional
Magnetic
Cavity.- On the Reflection of Alfv?n Waves
in
the Inhomogeneous Solar Wind.- Relativistic
Alfv?n Soliton and
Acceleration of Cosmic Rays.- Reduced Models
of Magnetohydrodynamic Turbulence in the
Interstellar Medium and
the Solar Wind.- Alfv?nic Turbulence and
Wave Propagation in the Corona and Heliosphere.-
Nonlinear Alfv?n
Wave Interaction with Large-Scale
Heliospheric Current Sheet.- Coherent Electrostatic
Nonlinear
Waves in Collisionless Space Plasmas.- Modeling
the Dissipation Range of Magnetofluid Turbulence.-
A Weak
Turbulence Theory for Incompressible MHD.-
Shell
Models for Magnetohydrodynamic Turbulence.
Iarrobino, A., Northeastern University, Boston,
MA, USA
Kanev, V., Institute of Mathematics, Sofia,
Bulgaria
1999. XXXI, 345 pp.
3-540-66766-0
Series: Lecture Notes in Mathematics.VOL. 1721
This book treats the theory of representations
of homogeneous
polynomials as sums of powers of linear forms.
The
first two chapters are introductory, and
focus on binary forms
and Waring's problem. Then the author's recent
work is presented mainly on the representation
of forms in three
or more variables as sums of powers of relatively
few linear forms. The methods used are drawn
from seemingly
unrelated areas of commutative algebra and
algebraic
geometry, including the theories of determinantal
varieties, of
classifying spaces of Gorenstein-Artin algebras,
and
of Hilbert schemes of zero-dimensional subschemes.
Of the many
concrete examples given, some are calculated
with the aid of the computer algebra program
"Macaulay", illustrating the abstract
material. The
final chapter
considers open problems. This book will be
of interest to
graduate students, beginning researchers,
and seasoned
specialists. Prerequisite is a basic knowledge
of commutative
algebra and algebraic geometry.
Keywords: determinantal Variety power sums
Gorenstein algebra
Hilbert scheme catalecticant matrix
Contents: Introduction: Informal History
and Brief Outline.-
Catalecticant Varieties: Forms and Catalecticant
Matrices. Sums of Powers and Linear Forms,
and Gorenstein
Algebras. Tangent Spaces to Catalecticant
Schemes.
The Locus PS(s,j;r) of Sums of Powers, and
Determinantal Loci of
Catalecticant Matrices.- Catalecticant
Varieties and the Punctual Hilbert Scheme:
Forms and
Zero-Dimensional SchemesI: Basic Results,
and the
Case r = 3. Forms and Zero-Dimensional Schemes,
II: Annihilating
Schemes and Reducible Gor(T).
Connectedness and Components of the Determinantal
Locus
PVs(u,v;r). Closures of the Variety Gor(T),
and the
Parameter Space G(T) of Graded Algebras.-
Questions and
Problems.- Appendix A: Divided Rings and
Polynomial Rings.- Appendix B: Height Three
Gorenstein Ideals.-
Appendix C: The Gotzmann Theorems and
the Hilbert Scheme (Anthony Iarrobino and
S.L. Kleiman).-
Appendix D: Exemples of "Macaulay"
Scripts.-
Appendix E: Concordance with the 1996 Version.
McCutcheon, R., University of Maryland, MD, USA
1999. VI, 160 pp.
3-540-66809-8
Series: Lecture Notes in Mathematics.VOL. 1722
This book, suitable for graduate students
and professional
mathematicians alike, didactically introduces
methodologies due to Furstenberg and others
for attacking
problems in chromatic and density Ramsey
theory via
recurrence in topological dynamics and ergodic
theory,
respectively. Many standard results are proved,
including
the classical theorems of van der Waerden,
Hindman, and
Szemer?di. More importantly, the presentation
strives
to reflect the extent to which the field
has been streamlined
since breaking onto the scene around twenty
years
ago. Potential readers who were previously
intrigued by the
subject matter but found it daunting may
want to give
a second look.
Keywords: Ramsey theory, ergodic theory,
topological dynamics
Contents: Ramsey Theory and Topological Dynamics.-
Infinitary
Ramsey Theory.- Density Ramsey Theory.-
Three Ergodic Roth Theorems.- Multiple Recurrence.
Ferrard, J.-M., Lyon, France / Lemberg, H., Paris, France (Eds.)
1999. Approx. 400 pp.
2-287-59685-2
The aim of this book is to present basic
and advanced
mathematical concepts using the graphical
and traditional
calculator, the TI 92 and the TI 89. These
mathematical concepts
are commonly taught at some stage of the
first
three years of college curricula; Analysis
(approximations,
convergence, differential equations, etc.)
Linear
Algebra (orthogonality, reduction, etc.).
The idea behind this
book is totally original and will teach the
reader not
only all the necessary theorems and examples,
but illustrations
of the calculator screens and the programs
(short
versions) will allow the reader to visualize
these new concepts
directly from the book, or on the calculator,
leading to a better understanding through
"seeing" and
"touching" the mathematical lesson
being taught.
Fields: Functional Analysis,Operator Theory;
Mathematics, general
Written for: Students, teachers
Book category: Undergraduate Textbook
Publication language: English
Janich, K., Universitat Regensburg
5. Aufl. 1999. IX, 123 S. 100 Abb.
3-540-66152-2
Die Funktionentheorie behandelt die Analysis
komplexer
Ver?nderlicher. Dieses Buch, geschrieben
im bekannten
J?nich-Stil, bietet f?r Studenten im Grundstudium
eine straffe
und kompakte, dabei stets mathematisch pr?zise
erste Einf?hrung. Ausgehend vom Cauchyschen
Integralsatz wird der
Leser an die grundlegenden Begriffe und
S?tze herangef?hrt: Cauchyformel, Potenz-
und Laurentreihen,
Monodromiesatz, Umlaufszahl, Residuensatz,
S?tze
von Mittag-Leffler, Weierstra? und Riemann.
Viele Abbildungen und
kommentierte ?bungsaufgaben erleichtern die
Lekt?re. Ein auch f?r Studenten der Physik
und Informatik
hervorragend geeigneter Text!
Schlagworte: Holomorphe Funktionen, Cauchyscher
Integralsatz,
Residuenkalk?l, S?tze von Mittag-Leffler,
Weierstra? und Riemann
Reihe: Springer-Lehrbuch.
Elworthy, K.D., University of Warwick, UK
Le Jan, Y., Universite Paris Sud, Orsay,
France
Li, X.-M., University of Connecticut, Storrs,
CT, USA
1999. IV, 118 pp.
3-540-66708-3
Series: Lecture Notes in Mathematics.VOL. 1720
Stochastic differential equations, and Hoermander
form
representations of diffusion operators, can
determine a
linear connection associated to the underlying
(sub)-Riemannian
structure. This is systematically described,
together with its invariants, and then exploited
to discuss
qualitative properties of stochastic flows,
and analysis
on path spaces of compact manifolds with
diffusion measures. This
should be useful to stochastic analysts,
especially those with interests in stochastic
flows, infinite
dimensional analysis, or geometric analysis,
and also to
researchers in sub-Riemannian geometry. A
basic background in
differential geometry is assumed, but the
construction of the connections is very direct
and itself gives
an intuitive and concrete introduction. Knowledge
of stochastic analysis is also assumed for
later chapters.
Keywords: Stochastic differential equations,
sub-Riemannian
geometry, path space, differential forms,
connections
Contents: Construction of connections.- The
infinitesimal
generators and associated operators.- Decomposition
of noise and Itering.- Application: Analysis
on spaces of paths.-
Stability of stochastic dynamical systems.-
Appendices.
Croisille, J.-P., Universite de Metz, France
Lebeau, G., Ecole Polytechnique, Palaiseau,
France
1999. VI, 134 pp.
3-540-66810-1
Series: Lecture Notes in Mathematics.VOL. 1723
This monograph presents the mathematical
description and
numerical computation of the high-frequency
diffracted
wave by an immersed elastic wave with normal
incidence. The
mathematical analysis is based on the explicit
description of the principal symbol of the
pseudo-differential
operator connected with the coupled linear
problem
elasticity/fluid by the wedge interface.
This description is
subsequently used to derive an accurate numerical
computation of diffraction diagrams for different
incoming waves
in the fluid, and for different wedge angles.
The
method can be applied to any problem of coupled
waves by a wedge
interface. This work is of interest for any
researcher concerned with high frequency
wave scattering,
especially mathematicians, acousticians,
engineers.
Keywords: diffraction, wave equation, scattering,
numerical
analysis, acoustics
Contents: Introduction.- Notation and results.-
The spectral
function.- Proofs of the results.- Numerical
algorithm.- Numerical results.