A new approach to the character theory of the symmetric group
has been developed during the past fifteen years which is in many
ways more efficient, more transparent, and more elementary. In
this approach, each permutation is assigned a class function of
the corresponding symmetric group. Problems in character theory
can thereby be transferred into a completely different setting
and reduced to combinatorial problems on permutations in a
natural and uniform way.
This is the first account in book form entirely devoted to the
new “noncommutative method”. As a modern and comprehensive
survey of the classical theory the book contains such fundamental
results as the Murnaghan?Nakayama and Littlewood?Richardson rules
as well as more recent applications in enumerative combinatorics
and in the theory of the free Lie algebra. But it is also an
introduction to the vibrant theory of certain combinatorial Hopf
algebras such as the Malvenuto?Reutenauer algebra of permutations.
The three detailed appendices on group characters, the Solomon
descent algebra and the Robinson?Schensted correspondence makes
the material self-contained and suitable for undergraduate level.
Students and researchers alike will find that noncommutative
character theory is a source of inspiration and an illuminating
approach to this versatile field of algebraic combinatoric.
Contents:
Introduction to Group Characters
Co- and Bialgebras
Self-Duality
Algebra of Class Functions
Solomon Descent Algebra
Standard Young Tableaux
Malvenuto?Reutenauer Algebra of Permutations
Robinson?Schensted Algorithm
Plactic and Coplactic Relations
Schutzenberger’s Theorem
Greene Invariant
Poirier?Reutenauer Algebra of Tableaux
Jollenbeck’s Theorem
Littlewood?Richardson Rule
Murnaghan?Nakayama Rule
Skew Characters
Young Characters
Foulkes Characters
Descent Characters
Cyclic Characters
Kraskiewicz?Weyman Theorem
Readership: Undergraduate and graduate students in mathematics.
200pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 1-86094-511-2
The book presents basic structures, concepts and algorithms in
the area of multilayer optimizing control of industrial systems,
as well as the results of the research that was carried out by
the authors over the last two decades. The methodologies and
control algorithms are thoroughly illustrated by numerous
simulation examples. Also, the applications to several case study
examples are presented. These include ethylene distillation
column, vaporizer pilot scale plant, styrene distillation line
consisting of three columns and industrial furnace pilot scale
plant. A temporal decomposition is applied to the Integrated
Wastewater System case study to derive multilayer dynamic
optimizing controller with repetitive robust model predictive
control mechanism distributed over the layers operating in
different time scales.
Contents:
Multilayer Control
Optimizing Control Layer
Iterative Correction with Disturbance Estimation
Integrated System Optimization and Parameter Estimation (ISOPE)
ISOPE for Problems with Output Constraints
Iterative Algorithms for Dynamic Optimizing Control
Optimizing Control of Interconnected Systems
Readership: Researchers, graduate and postgraduate students, and
R&D engineers in control systems and advanced systems
engineering.
380pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 1-86094-514-7
With cutting-edge materials and minute electronic devices being produced
by the latest nanoscale fabrication technology, it is essential for scientists
and engineers to rely on first-principles (ab initio) calculation methods
to fully understand the electronic configurations and transport properties
of nanostructures. It is now imperative to introduce practical and tractable
calculation methods that accurately describe the physics in nanostructures
suspended between electrodes.
This timely volume addresses novel methods for calculating
electronic transport properties using real-space formalisms free
from geometrical restrictions. The book comprises two parts: The
first details the basic formalism of the real-space finite-difference
method and its applications. This provides the theoretical
foundation for the second part of the book, which presents the
methods for calculating the properties of electronic transport
through nanostructures sandwiched by semi-infinite electrodes.
Contents:
Foundations of Methodology
Solvers of the Poisson Equation and Related Techniques
Minimization Procedures of the Energy Functional
Timesaving Double-Grid Technique
Implementation for Systems under Various Boundary Conditions
Basic Scheme of the Overbridging Boundary-Matching Method
Inclusion of Norm-Conserving Pseudopotentials
Jellium Electrode Approximation
Green’s Function Formalism and the Overbridging Boundary-Matching
Scheme
Calculation Method Based on the Lippmann?Schwinger Equation
Formulas for Long-Range Potentials under Various Boundary
Conditions
Tight-Binding Approach Based on the Overbridging Boundary-Matching
Scheme
Readership: Graduate and post-graduate students and researchers
in computational, quantum and condensed matter physics, and
nanoscience.
250pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 1-86094-512-0
One of the most important features of nonlinear systems with
several degrees of freedom is the presence of internal resonances
at certain relations between natural frequencies of different
modes. This monograph is the first book devoted predominantly to
internal resonances in different mechanical systems including
those of practical importance.
The main purpose is to consider the internal resonances from the
general point of view and to elucidate their role in applied
nonlinear dynamics by using an efficient approach based on
introducing the complex representation of equations of motion (together
with the multiple scale method). Considered here are autonomous
and nonautonomous discrete two-degree-of-freedom systems,
infinite chains of particles, and continuous systems, including
circular rings and cylindrical shells. Specific attention is paid
to the case of one-to-one internal resonance in systems with
cubic and quadratic nonlinearities. Steady-state and
nonstationary regimes of motion, interaction of the internal and
external resonances at forced oscillations, and bifurcations of
steady-state modes and their stability are also studied.
Contents:
Single-Degree-of-Freedom Systems
Autonomous Two-Degree-of-Freedom Symmetric Cubic Systems with
Close Natural Frequencies
Nonautonomus Two-Degree-of-Freedom Cubic Systems with Close
Natural Frequencies
Nonlinear Flexural Free and Forced Oscillations of a Circular
Ring (with Account of Interaction of Conjugate Modes)
Localized Normal Modes in a Chain of Nonlinear Coupled
Oscillators
Nonlinear Dynamics of Coupled Oscillatory Chains
Nonlinear Dynamics of Strongly Non-Homogeneous Chains with
Symmetric Characteristics
Transversal Dynamics of One-Dimensional Chains on Nonlinear
Asymmetric Substrate
Readership: Researchers and graduate and post-graduate students
interested in nonlinear systems.
200pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 1-86094-510-4
This book discusses issues associated with the quantum
mechanical formulation of dissipative systems. It begins with an
introductory review of phenomenological damping forces, and the
construction of the Lagrangian and Hamiltonian for the damped
motion. It is shown, in addition to these methods, that classical
dissipative forces can also be derived from solvable many-body
problems. A detailed discussion of these derived forces and their
dependence on dynamical variables is also presented. The second
part of this book investigates the use of classical formulation
in the quantization of dynamical systems under the influence of
dissipative forces. The results show that, while a satisfactory
solution to the problem cannot be found, different formulations
represent different approximations to the complete solution of
two interacting systems. The third and final part of the book
focuses on the problem of dissipation in interacting quantum
mechanical systems, as well as the connection of some of these
models to their classical counterparts. A number of important
applications, such as the theory of heavy-ion scattering and the
motion of a radiating electron, are also discussed.
Contents:
Phenomenological Equations of Motion for Dissipative Systems
Lagrangian Hamiltonian and Hamilton?Jacobi Formulation of the
Classical Dissipative Systems
Noether's Theorem and Non-Noether Conservation Laws
Dissipative Forces Derived from Many-Body Problems
A Particle Coupled to a Field and the Damped Motion of a Central
Particle Coupled to a Heat Bath
Quantization of Dissipative Systems in General and of Explicitly
Time-Dependent Hamiltonians in Particular
Density Matrix and the Wigner Distribution Function for Damped
Systems
Path Integral Formulation of a Damped Harmonic Oscillator
Quantization of the Motion of an Infinite Chain
Heisenberg's Equations of Motion for a Particle Coupled to a Heat
Bath
Quantum Mechanical Models of Dissipative Systems and the Concept
of Optical Potential
Readership: Researchers and graduate students in applied
mathematics and theoretical physics.
350pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 1-86094-525-2
ISBN 1-86094-530-9(pbk)