Series: Mathematics and Its Applications, Vol. 583
2006, Approx. 350 p. 144 illus., Hardcover
ISBN: 0-387-30413-4
About this boo
Although some examples of phase portraits of quadratic systems
can already be found in the work of Poincare, the first paper
dealing exclusively with these systems was published by Buchel in
1904. By the end of the 20th century an increasing flow of
publications resulted in nearly a thousand papers on the subject.
This book attempts to give a presentation of the advance of our
knowledge of phase portraits of quadratic systems, paying special
attention to the historical development of the subject. The book
organizes the portraits into classes, using the notions of finite
and infinite multiplicity and finite and infinite index.
Classifications of phase portraits for various classes are given
using the well-known methods of phase plane analysis.
Written for:
Mathematics graduate systems and researchers studying quadratic
systems.
Table of contents
1. Introduction.- 2. Critical Points in Quadratic Systems.- 3.
Isoclines, Critical Points and Classes of Quadratic Systems.- 4.
Analyzing Phase Portraits of Quadratic Systems.- 5. Phase
Portraits of Quadratic Systems in the Class mf = 0.- 6. Quadratic
Systems with a Center Point.- 7. Limit Cycles in Quadratic
Systems.- 8. Phase Portraits of Quadratic Systems in the Class mf
= 1.- 9. Phase Portraits of Quadratic Systems in the Class mf = 2.-
10. Phase Portraits of Quadratic Systems in the Class mf = 3.- 11.
Phase Portraits of Quadratic Systems in the Class mf = 4.-
References.
Series: Lecture Notes in Mathematics, Vol. 1883
2006, Approx. 450 p., Softcover
ISBN: 3-540-31062-2
About this book
Special functions and orthogonal polynomials in particular have
been around for centuries. Can you imagine mathematics without
trigonometric functions, the exponential function or polynomials?
In the twentieth century the emphasis was on special functions
satisfying linear differential equations, but this has now been
extended to difference equations, partial differential equations
and non-linear differential equations.
The present set of lecture notes containes seven chapters about
the current state of orthogonal polynomials and special functions
and gives a view on open problems and future directions. The
topics are: computational methods and software for quadrature and
approximation, equilibrium problems in logarithmic potential
theory, discrete orthogonal polynomials and convergence of Krylov
subspace methods in numerical linear algebra, orthogonal rational
functions and matrix orthogonal rational functions, orthogonal
polynomials in several variables (Jack polynomials) and
separation of variables, a classification of finite families of
orthogonal polynomials in Askey’s scheme using Leonard pairs,
and non-linear special functions associated with the Painleve
equations.
Written for:
Researchers and graduate students interested in classification,
computation and applications
Table of contents
Walter Gautschi: Orthogonal polynomials, quadrature, and
approximation: computational methods and software (in Matlab).-
Andrei Martinez Finkelshtein: Equilibrium problems potential
theory in the complex plane.- Bernhard Beckermann: Discrete
orthogonal polynomials and superlinear convergence of Krylov
subspace methods in numerical linear algebra.- Adhemar Bultheel,
P. Gonzalez-Vera, E. Hendriksen, O. Njastad: Orthogonal rational
functions on the unit circle: From the scalar to the matrix case.-
Vadim B. Kuznetsov: Orthogonal polynomials and separation of
variables.- Paul Terwilliger: An algebraic approach to the Askey
scheme of orthogonal polynomials.- Peter A. Clarkson: Painleve
equations, nonlinear special functions.
Series: Studies in Fuzziness and Soft Computing, Vol. 196
2006, XIII, 270 p. 78 illus., Hardcover
ISBN: 3-540-30841-5
About this book
This book combines material from our previous books FP (Fuzzy
Probabilities: New Approach and Applications,Physica-Verlag, 2003)
and FS (Fuzzy Statistics, Springer, 2004), plus has about one
third new results. From FP we have material on basic fuzzy
probability, discrete (fuzzy Poisson,binomial) and continuous (uniform,
normal, exponential) fuzzy random variables. From FS we included
chapters on fuzzy estimation and fuzzy hypothesis testing related
to means, variances, proportions, correlation and regression. New
material includes fuzzy estimators for arrival and service rates,
and the uniform distribution, with applications in fuzzy queuing
theory. Also, new to this book, is three chapters on fuzzy
maximum entropy (imprecise side conditions) estimators producing
fuzzy distributions and crisp discrete/continuous distributions.
Other new results are: (1) two chapters on fuzzy ANOVA (one-way
and two-way); (2) random fuzzy numbers with applications to fuzzy
Monte Carlo studies; and (3) a fuzzy nonparametric estimator for
the median.
Written for:
Engineers, researchers, and students in Fuzziness and Applied
Mathematics.
2006, Approx. 435 p. 14 illus., Hardcover
ISBN: 3-540-30265-4
About this textbook
Recently, quantum information theory has been developing through
a fusion of results from various research fields. This requires
that understanding of basic results on diverse topics, and
derived from different disciplinary perspectives, is required for
appreciating the overall picture. Intended to merge key topics
from both the information-theoretic and quantum- mechanical
viewpoints, this graduate-level textbook provides a unified
viewpoint of quantum information theory and lucid explanations of
those basic results, so that the reader fundamentally grasps
advances and challenges. For example, advanced topics in quantum
communication such as quantum teleportation, superdense coding,
quantum state transmission (quantum error-correction), and
quantum encryption especially benefit from this unified approach.
Unlike earlier treatments, the text requires knowledge of only
linear algebra, probability theory, and quantum mechanics, while
it treats the topics of quantum hypothesis testing and the
discrimination of quantum states, and quantum channel coding (message
transmission) with the minimal amount of math needed to convey
their essence. Solving the more than 240 exercises provides
readers with practice that not only enriches their knowledge of
quantum information theory, but also can equip them with the
techniques necessary for pursuing their own research in this
field.
Written for:
Advanced students
Table of contents
Introduction.- 1. Mathematical Formulation of Quantum Systems.- 2.
Information Quantities and Parameter Estimation in Classical
System.- 3. Quantum Hypothesis Testing and Discrimination of
Quantum States.- 4. Classical-Quantum Channel Coding (Message
Transmission).- 5. State Evolution and Trace Preserving
Completely Positive Maps.- 6. Quantum Information Geometry and
Quantum Estimation.- 7. Quantum Measurements and State Reduction.-
8. Entanglement and Locality Restrictions.- 9. Analysis of
Quantum Communication Protocols.- 10. Source Coding in Quantum
System.- A. Limits and Linear Algebra.- B. Proofs of Theorems and
Lemmas.- C. Hints and Brief Solutions to Exercises.
Series: Studies in Fuzziness and Soft Computing, Vol. 198
2006, X, 195 p. 3 illus., 1 in colour., Hardcover
ISBN: 3-540-31695-7
About this book
This research monograph presents basic foundational aspects for a
theory of statistics with fuzzy data, together with a set of
practical applications. Fuzzy data are modeled as observations
from random fuzzy sets. Theories of fuzzy logic and of random
closed sets are used as basic ingredients in building statistical
concepts and procedures in the context of imprecise data,
including coarse data analysis. The monograph also aims at
motivating statisticians to look at fuzzy statistics to enlarge
the domain of applicability of statistics in general.
Hung T. Nguyen is a professor of Mathematical Sciences at New
Mexico State University, USA.
Berlin Wu is a professor of Mathematical Sciences at National
Chengchi University, Taipei, Taiwan.
Written for:
Researchers, engineers, graduate students in Soft Computing,
Fuzziness and Statistics
Table of contents
Introduction.- Set-valued Data.- Modeling of fuzzy data.- Random
fuzzy sets.- Aspect of statistical Inference.- Convergence of
random fuzzy sets.- Fuzzy Statistical Analysis and Estimation.-
Testing Hypothesis with Fuzzy Data.- Fuzzy Time Series Analysis
and Forecasting.