Series : Control Engineering
2004, XVI, 416 p. 9 illus., Hardcover
ISBN: 3-7643-3779-6
About this textbook
This text is the first comprehensive treatment of structural
decompositions of various types of linear systems, including
autonomous, unforced or unsensed, strictly proper, non-strictly
proper, and descriptor or singular systems. Structural properties
play an important role in the understanding of linear systems and
also provide insight to facilitate the solution of control
problems related to stabilization, disturbance decoupling, robust
and optimal control. Applications can be extended to industrial
process control, aircraft and ship control, process automation
control, and many other types of engineering systems. The authors
employ a unique structural decomposition approach to break down
an overall system into various subsystems, each with distinct
features. The simplicity of these subsystems and their
interconnections lead to deep insight about the design of
feedback control systems for desired closed-loop performance,
stability, and robustness. All results and case studies are
presented in both continuous- and discrete-time settings.
Exercises, as well as MATLAB-based computational and design
algorithms utilizing the Linear Systems Toolkit, are included to
reinforce and demonstrate the concepts treated throughout the
book. Topics covered include: * Basic Concepts of Linear Systems
Theory * Decomposition of Unforced and/or Unsensed Systems,
Proper Systems and their Properties * Decomposition of Descriptor
Systems and their Properties * Cascade and Inner-Outer
Factorizations * Structural Assignment through Sensor/Actuator
Selections * State Feedback Control with Time-Scale and
Eigenstructure Assignment * Disturbance Decoupling with Static
Output Feedback Linear Systems Theory may be used as a textbook
for advanced undergraduate and graduate students in aeronautics
and astronautics, applied mathematics, chemical, electrical and
mechanical engineering. It may also serve as a valuable self-study
reference for researchers and engineering practitioners in areas
related to systems and control theory.
Table of contents
Introduction and Preview * Mathematical Background * Review of
Linear Systems Theory * Decompositions of Unforced and/or
Unsensed Systems * Decompositions of Proper Systems *
Decompositions of Descriptor Systems * Structural Mappings of
Bilinear Transformations * System Factorizations * Structural
Assignment via Sensor/Actuator Selection * Time-Scale and
Eigenstructure Assignment via State Feedback * Disturbance
Decoupling with Static Output Feedback * A Software Toolbox *
Bibliography * Index
Series : Applied and Numerical Harmonic Analysis
2005, XVI, 320 p. 30 illus., Hardcover
ISBN: 3-7643-3778-8
About this book
This volume, in honor of John J. Benedetto on the occasion of his
65th birthday, features invited articles which examine a wide
range of topics in harmonic analysis, number theory, weighted
norm inequalities, wavelet theory, time-frequency analysis, and
sampling theory. Benedetto has made fundamental and lasting
contributions to many areas of harmonic analysis and related
fields. Although the scope of the book is broad, chapters are
clustered by topic to provide authoritative expositions that will
be of lasting interest. The original papers collected here are
written by prominent, well-respected researchers and
professionals in the field. "Harmonic Analysis and its
Applications" pays tribute to Benedetto's many achievements
and expresses an appreciation for both the mathematical and
personal inspiration that he has given to so many students,
coauthors, and colleagues. Contributors include: A. Aldroubi, W.
Czaja, J.-P. Gabardo, H. Feichtinger, K. Groechenig, H. Heinig, J.
Lakey, D. Walnut, Y. Wang, G. Weiss, D. Labate, G. Zimmermann.
Table of contents
Frames and Atomic Decompositions / Aldroubi, Cabrelli, Molter *
Redundancy in the Frequency Domain / Baggett * The Gibbs
Phenomenon in Higher Dimensions / Benke * A Physical
Interpretation for Finite Tight Frames / Casazza, Fickus,
Kovacevic, Leon, Tremain * Density Results for Frames of
Exponentials / Casazza, Christensen, Linder, Li * Recent
Developments in the Balian-Low Theorem / Czaja * The Useful
Generalizations of Orthonormal Basis / Davis * An Axiomatic
Approach to Error Analysis / Feichtinger * Recent Advances in
Finite Frame Theory / Fickus, Kornelson * Some Problems Related
to the Distributional Zak Transform / Gabardo *
Pseudodifferential Operators for Pedestrians / Groechenig * The
Theory of Composite Wavelets / Guo, Labbate, Lim, Weiss, Wilson *
On Gabor Duality Characterizations / Hayashi, Li, Sorrels *
Linear Independence of Finite Gabor Systems / Heil * Differential
Inequalities in Weighted L^P Spaces / Heinig * Periodic
Nonuniform Sampling in Shift Invariant Spaces / Hogan, Lakey *
Spectra, Tiles, and the Fuglede Problem / Jorgensen, Wang *
Explicit Cross Sections of Singly Generated Group Actions /
Larson, Schulz, Speegle, Taylor * Sampling on Unions of One-Dimensional
Lattices / Walnut * Semidiscrete Multipliers / Zimmermann
Series : Progress in Mathematics , Vol. 234
2005, X, 278 p., Hardcover
ISBN: 3-76436-3850-4
About this book
This volume contains research and survey articles by well known
and respected mathematicians on differential geometry and
topology that have been collected and dedicated in honor of
Lieven Vanhecke, as a tribute to his many fruitful and inspiring
contributions to these fields. The papers, all written with the
necessary introductory and contextual material, describe recent
developments and research trends in spectral geometry, the theory
of geodesics and curvature, contact and symplectic geometry,
complex geometry, algebraic topology, homogeneous and symmetric
spaces, and various applications of partial differential
equations and differential systems to geometry. One of the key
strengths of these articles is their appeal to non-specialists,
as well as researchers and differential geometers. Contributors:
D.E. Blair; E. Boeckx; A.A. Borisenko; G. Calvaruso; V. Cortes; P.
de Bartolomeis; J.C. Diaz-Ramos; M. Djoric; C. Dunn; M.
Fernandez; A. Fujiki; E. Garcia-Rio; P.B. Gilkey; O. Gil-Medrano;
L. Hervella; O. Kowalski; V. Munoz; M. Pontecorvo; A.M. Naveira;
T. Oguro; L. Schafer; K. Sekigawa; C-L. Terng; K. Tsukada; Z.
Vla?ek; E. Wang; and J.A. Wolf.
Table of contents
* Preface * Acknowledgments * Authorsf Addresses * List of
Participants * D.E. Blair: Curvature of Contact Metric Manifolds
* E. Boeckx: A case for curvature: the unit tangent bundle * A.A.
Borisenko: Convex hypersurfaces in Hadamard manifolds * G.
Calvaruso: Contact metric geometry of the unit tangent sphere
bundle * V. Cortes and L. Schafer: Topological-antitopological
fusion equations, pluriharmonic maps and special Kahler manifolds
* P. de Bartolomeis: Z2 and Z-Deformation Theory for Holomorphic
and Symplectic Manifolds * J.C. Diaz-Ramos, E. Garcia-Rio and L.
Hervella: Total scalar curvatures of geodesic spheres and of
boundaries of geodesic disks * M. Djoric: Commutative condition
on the second fundamental form of CR submanifolds of maximal CR
dimension of a Kahler manifold * C. Dunn and P.B. Gilkey:
Curvature homogeneous pseudo-Riemannian manifolds which are not
locally homogeneous * M. Fernandez and V. Munoz: The Geography of
Non-formal Manifolds * A. Fujiki and M. Pontecorvo: On Hermitian
geometry of complex surfaces * O. Gil-Medrano: Unit vector fields
that are critical points of the volume and of the energy:
characterization and examples * O. Kowalski and Z. Vla?ek: On 3-dimensional
Riemannian manifolds with prescribed Ricci eigenvalues * A.M.
Naveira: Two problems in real and complex integral geometry * T.
Oguro and K. Sekigawa: Notes on the Goldberg conjecture in
dimension four * C-L. Terng and E. Wang: Curved flats, exterior
differential systems, and conservation laws * K. Tsukada:
Symmetric submanifolds of Riemannian symmetric spaces and
symmetric R-spaces * J.A. Wolf: Complex forms of Quaternionic
Symmetric Spaces
Series : Progress in Nonlinear Differential Equations and
Their Applications , Preliminary entry 1003
2005, Approx. 350 p. 10 illus., Hardcover
ISBN: 3-7643-4359-1
About this textbook
The study of shape optimization problems involves a wide area of
academic research and applications to the real world. In this
work these problems are treated from the classical and modern
perspectives and target a broad audience of graduate students in
pure and applied mathematics, as well as engineers requiring a
solid mathematical basis for the solution of practical problems.
Key topics: * Presents foundational introduction to shape
optimization theory * Studies some classical problems: the
isoperimetric problem and the Newton problem involving the best
aerodynamical shape, optimization problems over classes of convex
domains * Treats optimal control problems under a general scheme,
giving a topological framework, a survey of G-convergence,
problems governed by ODE * Examines shape optimization problems
with Dirichlet and Neumann condition on the free boundary, the
existence of classical solutions * Poses some open questions
Driven by several good examples and illustrations, the book
requires only a standard knowledge in the calculus of variations,
differential equations, and functional analysis.
Table of contents
Preface * Introduction to shape optimization theory and some
classical problems * Optimization problems over classes of convex
domains * Optimal control problems: a general scheme * Shape
optimization problems with Dirichlet condition on the free
boundary * Existence of classical solutions * Optimization
problems for functions of eigenvalues * Bibliography * Index
Series : Progress in Mathematical Physics , Vol. 40
2004, XXIV, 280 p., 77 illus. (72 line art, 5 halftones), 5
tables, Hardcover
ISBN: 3-7643-3339-1
About this book
One of the mathematical challenges of modern physics lies in the
development of new tools to efficiently describe different
branches of physics within one mathematical framework. This text
introduces precisely such a broad mathematical model, one that
gives a clear geometric expression of the symmetry of physical
laws and is entirely determined by that symmetry. The first three
chapters discuss the occurrence of bounded symmetric domains (BSDs)
or homogeneous balls and their algebraic structure in physics. It
is shown that the set of all possible velocities is a BSD with
respect to the projective group; the Lie algebra of this group,
expressed as a triple product, defines relativistic dynamics. The
particular BSD known as the spin factor is exhibited in two ways:
first, as a triple representation of the Canonical
Anticommutation Relations, and second, as a ball of symmetric
velocities. The associated group is the conformal group, and the
triple product on this domain gives a representation of the
geometric product defined in Clifford algebras. It is explained
why the state space of a two-state quantum mechanical system is
the dual space of a spin factor. Ideas from Transmission Line
Theory are used to derive the explicit form of the operator
Mobius transformations. The book further provides a discussion of
how to obtain a triple algebraic structure associated to an
arbitrary BSD; the relation between the geometry of the domain
and the algebraic structure is explored as well. The last chapter
contains a classification of BSDs revealing the connection
between the classical and the exceptional domains. With its
unifying approach to mathematics and physics, this work will be
useful for researchers and graduate students interested in the
many physical applications of bounded symmetric domains. It will
also benefit a wider audience of mathematicians, physicists, and
graduate students working in relativity, geometry, and Lie theory.
Table of contents
* Preface * List of Figures * List of Tables * Relativity Based
on Symmetry * The Real Spin Domain * The Complex Spin Factor and
Applications * The Classical Bounded Symmetric Domains * The
Algebraic Structure of Homogeneous Balls * Classification of JBW*-triple
Factors * References * Index