Dautray, R., Paris, France
Lions, J.-L., College de France, Paris, France
: Integral Equations and Numerical Methods
1st ed. 1990. 2nd printing 1999. X, 494 pp. 67 figs.
3-540-66100-X
The advent of high-speed computers has made it possible for the
first time to calculate values from models
accurately and rapidly. Researchers and engineers thus have a
crucial means of using numerical results to modify
and adapt arguments and experiments along the way. Every facet of
technical and industrial activity has been
affected by these developments. The objective of the present work
is to compile the mathematical knowledge
required by researchers in mechanics, physics, engineering,
chemistry and other branches of application of
mathematics for the theoretical and numerical resolution of
physical models on computers. Since the publication in
1924 of the "Methoden der mathematischen Physik" by
Courant and Hilbert, there has been no other
comprehensive and up-to-date publication presenting the
mathematical tools needed in applications of
mathematics in directly implementable form.
Contents: Mixed Problems and Tricomi Equation.- Integral
Equations.- Numerical Methods for Stationary
Problems.- Approximation of Integral Equations by Finite
Elements. Error Analysis.- Appendix: Singular
Integrals.- Bibliography.- Table of Notations.- Index.- Contents
of Volumes 1-3, 5, 6.
Dautray, R., Paris, France
Lions, J.-L., College de France, Paris, France
Physical Origins and Classical Methods
1st ed. 1990. 2nd printing 1999. XVIII, 722 pp.
3-540-66097-6
These 6 volumes - the result of a 10 year collaboration between
the authors, two of France's leading scientists
and both distinguished international figures - compile the
mathematical knowledge required by researchers in
mechanics, physics, engineering, chemistry and other branches of
application of mathematics for the theoretical
and numerical resolution of physical models on computers. Since
the publication in 1924 of the "Methoden der
mathematischen Physik" by Courant and Hilbert, there has
been no other comprehensive and up-to-date
publication presenting the mathematical tools needed in
applications of mathematics in directly implementable
form. The advent of large computers has in the meantime
revolutionised methods of computation and made this
gap in the literature intolerable: the objective of the present
work is to fill just this gap. Many phenomena in
physical mathematics may be modeled by a system of partial
differential equations in distributed systems: a model
here means a set of equations, which together with given boundary
data and, if the phenomenon is evolving in
time, initial data, defines the system. The advent of high-speed
computers has made it possible for the first time
to calculate values from models accurately and rapidly.
Researchers and engineers thus have a crucial means of
using numerical results to modify and adapt arguments and
experiments along the way. Every facet of technical
and industrial activity has been affected by these developments.
Modeling by distributed systems now also
supports work in many areas of physics (plasmas, new materials,
astrophysics, geophysics), chemistry and
mechanics and is finding increasing use in the life sciences. The
main physical examples examined in the 6
volumes are presented in Chapter I: Classical Fluids and the
Navier-Stokes System; Linear Elasticity, Linear
Viscoelasticity, Electromagnetism and Maxwell's Equation,
Neutronics, and Quantum Physics. Then a first
examination of the mathematical models is given. Chapter II is
devoted to the study of the Laplacian operator by
methods which only use classical tools.
Contents: I: Physical Examples.- II: The Laplace Operator.
Dautray, R., Paris, France
Lions, J.-L., College de France, Paris, France
Spectral Theory and Applications
1st ed. 1990. 2nd printing 1999. X, 542 pp. 4 figs.
3-540-66099-2
The advent of high-speed computers has made it possible for the
first time to calculate values from models
accurately and rapidly. Researchers and engineers thus have a
crucial means of using numerical results to modify
and adapt arguments and experiments along the way. Every facet of
technical and industrial activity has been
affected by these developments. The objective of the present work
is to compile the mathematical knowledge
required by researchers in mechanics, physics, engineering,
chemistry and other branches of application of
mathematics for the theoretical and numerical resolution of
physical models on computers. Since the publication in
1924 of the "Methoden der mathematischen Physik" by
Courant and Hilbert, there has been no other
comprehensive and up-to-date publication presenting the
mathematical tools needed in applications of
mathematics in directly implementable form.
Contents: Spectral Theory.- Examples in Electromagnetism and
Quantum Physics.- Appendix: Some Spectral
Notions.- Bibliography.- Table of Notations.- Index.
Dautray, R., Paris, France
Lions, J.-L., College de France, Paris, France
Evolution Problems I
1st ed. 1992. 2nd printing 1999. XIV, 742 pp. 38 figs.
3-540-66101-8
These 6 volumes - the result of a 10 year collaboration between
the authors, two of France's leading scientists
and both distinguished international figures - compile the
mathematical knowledge required by researchers in
mechanics, physics, engineering, chemistry and other branches of
application of mathematics for the theoretical
and numerical resolution of physical models on computers. Since
the publication in 1924 of the "Methoden der
mathematischen Physik" by Courant and Hilbert there has been
no other comprehensive and up-to-date
publication presenting the mathematical tools needed in
applications of mathematics in directly implementable
form. The advent of large computers has in the meantime
revolutionised methods of computation and made this
gap in the literature intolerable: the objective of the present
work is to fill just this gap. Many phenomena in
physical mathematics may be modeled by a system of partial
differential equations in distributed systems: a model
here means a set of equations, which together with given boundary
data and, if the phenomenon is evolving in
time, initial data, defines the system. The advent of high-speed
computers has made it possible for the first time
to calculate values from models accurately and rapidly.
Researchers and engineers thus have a crucial means of
using numerical results to modify and adapt arguments and
experiments along the way. Every facet of technical
and industrial activity has been affected by these developments.
Modeling by distributed systems now also
supports work in many areas of physics (plasmas, new materials,
astrophysics, geophysics), chemistry and
mechanics and is finding increasing use in the life sciences.
Contents: XIV: Evolution Problems: Cauchy Problems in IR n.- XV:
Evolution Problems: The Method of
Diagonalisation.- XVI: Evolution Problems: The Method of Laplace,
Transformation.- XVII: Evolution Problems:
The Method of Semigroups.- XVIII: Evolution Problems:Variational
Methods.
Dautray, R., Paris, France
Lions, J.-L., College de France, Paris, France
Evolution Problems II
1st ed. 1993. 2nd printing 1999. XII, 588 pp. 33 figs.
3-540-66102-6
These six volumes - the result of a ten year collaboration
between the authors, two of France's leading scientists
and both distinguished international figures - compile the
mathematical knowledge required by researchers in
mechanics, physics, engineering, chemistry and other branches of
application of mathematics for the theoretical
and numerical resolution of physical models on computers. Since
the publication in 1924 of the Methoden der
mathematischen Physik by Courant and Hilbert, there has been no
other comprehensive and up-to-date
publication presenting the mathematical tools needed in
applications of mathematics in directly implementable
form. The advent of large computers has in the meantime
revolutionised methods of computation and made this
gap in the literature intolerable: the objective of the present
work is to fill just this gap. Many phenomena in
physical mathematics may be modeled by a system of partial
differential equations in distributed systems: a model
here means a set of equations, which together with given boundary
data and, if the phenomenon is evolving in
time, initial data, defines the system. The advent of high-speed
computers has made it possible for the first time
to caluclate values from models accurately and rapidly.
Researchers and engineers thus have a crucial means of
using numerical results to modify and adapt arguments and
experiments along the way. Every fact of technical and
industrial activity has been affected by these developments.
Modeling by distributed systems now also supports
work in many areas of physics (plasmas, new materials,
astrophysics, geophysics), chemistry and mechanics and is
finding increasing use in the life sciences. Volumes 5 and 6
cover problems of Transport and Evolution.
Contents: XIX: The Linearised Navier-Stokes Equations.- XX:
Numerical Methods for Evolution Problems.-
XXI: Transport.
Chen, Y., Singapore
Wen, C., Nanyang Technological University, Singapore
Convergence, Robustness and Applications
1999. XII, 199 pp. 69 figs.,
1-85233-190-9
DM 108,-
(Recommended Retail Price)
This book provides readers with a comprehensive coverage of
iterative learning control. The book can be used as
a text or reference for a course at graduate level and is also
suitable for self-study and for industry-oriented
courses of continuing education.
Ranging from aerodynamic curve identification robotics to
functional neuromuscular stimulation, Iterative Learning
Control (ILC), started in the early 80s, is found to have wide
applications in practice. Generally, a system under
control may have uncertainties in its dynamic model and its
environment. One attractive point in ILC lies in the
utilisation of the system repetitiveness to reduce such
uncertainties and in turn to improve the control
performance by operating the system repeatedly. This monograph
emphasises both theoretical and practical
aspects of ILC. It provides some recent developments in ILC
convergence and robustness analysis. The book also
considers issues in ILC design. Several practical applications
are presented to illustrate the effectiveness of ILC.
The applied examples provided in this monograph are particularly
beneficial to readers who wish to capitalise the
system repetitiveness to improve system control performance.
Contents: Introduction.- High-Order Iterative Learning Control of
Uncertain Nonlinear Systems with State
Delays.- High-Order P-type Iterative Learning Controller Using
Current Iteration Tracking Error.- Iterative
Learning Control of Uncertain Nonlinear Discrete-time Systems
Using Current Iteration Tracking Error.- Iterative
Learning Control of Uncertain Nonlinear Discrete-time Feedback
Systems with Saturation.- Initial State Learning
Method for Iterative Learning Control of Uncertain Time-varying
Systems.- High-order Terminal Iterative
Learning Control with An application to a Rapid Thermal Process
for Chemical Vapor Deposition.- Designing
Iterative Learning Controller via Noncausal Filtering.- High
Precision Iterative Learning Control of Permanent
Magnetic Linear Motor with Less Modeling Effort.- Iterative
Learning Identification with An Application to
Aerodynamic Drag Coefficient Curve Extraction Problem.- Iterative
Learning Control of Functional Neuromuscular
Stimulation Systems.- Conclusions and Future Research.-
References.- Index.
Series: Lecture Notes in Control and Information Sciences.VOL.
248
Koecher, M.
Krieg, A., RWTH Aachen, Germany
Walcher, S., Technische Universitat Munchen, Germany
(Eds.)
1999. IX, 173 pp.
3-540-66360-6
This volume contains a re-edition of Max Koecher famous Minnesota
Notes. The main objects are homogeneous,
but not necessarily convex, cones. They are described in terms of
Jordan algebras. The central point is a
correspondence between semisimple real Jordan algebras and
so-called omega-domains. This leads to a
construction of half-spaces which give an essential part of all
bounded symmetric domains. The theory is
presented in a concise manner, with only elementary
prerequisites. The editors have added notes on each chapter
containing an account of the relevant developments of the theory
since these notes were first written.
Keywords: Jordan algebra, half - space, omega - domain,
automorphism group, domain of positivity
Contents: Domains of Positivity.-Omega Domains.-Jordan
Algebras.-Real and Complex Jordan
Algebras.-Complex Jordan Algebras.- Jordan Algebras and Omega
Domains.-Half-Spaces.-Appendix: The
Bergman kernel function.
Series: Lecture Notes in Mathematics.VOL. 1710
Arnold, B., University of
California, Riverside, CA, USA
Castillo, E., Universidad de Cantabria, Santander, Spain
Sarabia, J.M., Universidad de Cantabria, Santander, Spain
1999. Approx. 430 pp.
0-387-98761-4
The concept of conditional specification of distributions is not
new but, except in normal families, it has not been
well developed in the literature. Computational difficulties
undoubtedly hindered or discouraged developments in
this direction. However, such roadblocks are of dimished
importance today. Questions of compatibility of
conditional and marginal specifications of distributions are of
fundamental importance in modeling scenarios.
Models with conditionals in exponential families are particularly
tractable and provide useful models in a broad
variety of settings.
Contents: Conditional Specification.- Basic Theorems.- Exact and
Almost-Exact Compatibility in Discrete
Distributions.- Distributions with Normal Conditionals.-
Conditionals in Exponential Families.- Other Conditionally
Specified Families.- Impossible Models.- Characterizations
Involving Conditional Moments.- Multivariate
Extensions.- Parameter Estimation in Conditionally Specified
Models.- Simulations.- Marginal and Conditional
Specification of Distributions.- Conditional Survival Models.-
Bivariate Extreme Models Based on CS.- Bayesian
Analysis Using Conditionally Specified Models.- Conditional
Specification of Simultaneous Equation Models.-
Other Conditional Specification Cases.
Series: Springer Series in Statistics.