April 2004, ISBN 1-4020-1990-4, Hardbound
Book Series: NONLINEAR PHENOMENA AND COMPLEX SYSTEMS : Volume 10
This book contains the lectures given at the Second Conference on
Dynamics and Randomness held at the Centro de Modelamiento
Matematico of the Universidad de Chile, from December 9-13, 2003.
This meeting brought together mathematicians, theoretical
physicists, theoretical computer scientists, and graduate
students interested in fields related to probability theory,
ergodic theory, symbolic and topological dynamics. The courses
were on:
Some Aspects of Random Fragmentations in Continuous Times;
Metastability of Ageing in Stochastic Dynamics;
Algebraic Systems of Generating Functions and Return
Probabilities for Random Walks;
Recurrent Measures and Measure Rigidity;
Stochastic Particle Approximations for Two-Dimensional Navier
Stokes Equations; and
Random and Universal Metric Spaces.
The intended audience for this book is Ph.D. students on
Probability and Ergodic Theory as well as researchers in these
areas. The particular interest of this book is the broad areas of
problems that it covers. We have chosen six main topics and asked
six experts to give an introductory course on the subject
touching the latest advances on each problem.
May 2004, ISBN 1-4020-2186-0, Hardbound
Do formulas exist for the solution to algebraical equations in
one variable of any degree like the formulas for quadratic
equations? The main aim of this book is to give new geometrical
proof of Abel's theorem, as proposed by Professor V.I. Arnold.
The theorem states that for general algebraical equations of a
degree higher than 4, there are no formulas representing roots of
these equations in terms of coefficients with only arithmetic
operations and radicals.
A secondary, and more important aim of this book, is to acquaint
the reader with two very important branches of modern mathematics:
group theory and theory of functions of a complex variable.
This book also has the added bonus of an extensive appendix
devoted to the differential Galois theory, written by Professor A.G.
Khovanskii.
As this text has been written assuming no specialist prior
knowledge and is composed of definitions, examples, problems and
solutions, it is suitable for self-study or teaching students of
mathematics, from high school to graduate.
Contents
Preface for the English edition; V.I. Arnold. Preface.
Introduction.
1: Groups. 1.1. Examples. 1.2. Groups of transformations. 1.3.
Groups. 1.4. Cyclic groups. 1.5. Isomorphisms. 1.6. Subgroups. 1.7.
Direct product. 1.8. Cosets. Lagrange's theory. 1.9. Internal
automorphisms. 1.10. Normal subgroups. 1.11. Quotient groups. 1.12.
Commutant. 1.13. Homomorphisms. 1.14. Soluble groups. 1.15.
Permutations.
2: The complex numbers. 2.1. Fields and polynomials. 2.2. The
field of complex numbers. 2.3. Uniqueness of the field of complex
numbers. 2.4. Geometrical descriptions of the field of complex
numbers. 2.5. The trigonometric form of the complex numbers. 2.6.
Continuity. 2.7. Continuous curves. 2.8. Images of curves: the
basic theorem of the algebra of complex numbers. 2.9. The Riemann
surface of the function w = ăz. 2.10. The Riemann surfaces of
more complicated functions. 2.11. Functions representable by
radicals. 2.12. Monodromy groups of multi-valued functions. 2.13.
Monodromy groups of functions representable by radicals. 2.14.
The Abel theorem.
3: Hints, Solutions and Answers. 3.1.Problems of Chapter 1. 3.2.
Problems of Chapter 2. Drawings of Riemann surfaces; F. Aicardi.
Appendix. Solvability of equations by explicit formulae; A.
Khovanskii. A.1. Explicit solvability of equations. A.2.
Liouville's theory. A.3. Picard-Vessiot's theory. A.4.
Topological obstructions for the representation of functions by
quadratures. A.5. -functions. A.6. Monodromy group. A.7.
Obstructions for the representability of functions by quadratures.
A.8. Solvability of algebraic equations. A.9. The monodromy pair.
A.10. Mapping of the semi-plane to a polygon bounded by arcs of
circles. A.11. Topological obstructions for the solvability of
differential equations. A.12. Algebraic functions of several
variables. A.13. Functions of several complex variables
representable by quadratures and generalized quadratures. A.14. -germs.
A.15. Topological obstruction for the solvability of the
holonomic systems of linear differential equations. A.16.
Topological obstruction for the solvability of the holonomic
systems of linear differential equations. Bibliography.
Appendix; V.I. Arnold.
Index.
May 2004, ISBN 1-4020-7899-4, Hardbound
Markov chains have increasingly become useful way of capturing
stochastic nature of many economic and financial variables.
Although the hidden Markov processes have been widely employed
for some time in many engineering applications e.g. speech
recognition, its effectiveness has now been recognized in areas
of social science research as well. The main aim of Hidden Markov
Models: Applications to Financial Economics is to make such
techniques available to more researchers in financial economics.
As such we only cover the necessary theoretical aspects in each
chapter while focusing on real life applications using
contemporary data mainly from OECD group of countries. The
underlying assumption here is that the researchers in financial
economics would be familiar with such application although
empirical techniques would be more traditional econometrics.
Keeping the application level in a more familiar level, we focus
on the methodology based on hidden Markov processes. This will,
we believe, help the reader to develop more in-depth
understanding of the modeling issues thereby benefiting their
future research.
Contents
List of Figures. List of Tables.
Dedication. Acknowledgements.
1: Introduction. 1. Introduction. 2. Markov Chains. 3. Passage
Time. 4. Markov Chains and the Term Structure of Interest Rates.
5. State Space Methods and Kalman Filter. 6. Hidden Markov Models
and Hidden Markov Experts. 7. HMM Estimation Algorithm. 8. HMM
Parameter Estimation. 9. HMM Most Probable State Sequence:
Viterbi Algorithm. 10. HMM Illustrative examples.
2: Volatility in Growth Rate of Real GDP. 1. Introduction. 2.
Models. 3. Data. 4. Empirical Results. 5. Conclusion.
3: Linkages among G7 Stock Markets. 1. Introduction. 2. Empirical
Technique. 3. Data. 4. Empirical Results. 5. Conclusion.
4: Interplay between Industrial Production and Stock Market. 1.
Introduction. 2. Markov Switching Heteroscedasticity Model of
Output and Equity. 3. Data. 4. Empirical Results. 5. Conclusion.
5: Linking Inflation and Inflation Uncertainty. 1. Introduction.
2. Empirical Technique. 3. Data. 4. Empirical Results. 5.
Conclusion.
6: Exploring Permanent and Transitory Components of Stock Return.
1. Introduction. 2. Markov Switching Heteroscedasticity Model of
Stock Return. 3. Data. 4. Empirical Results. 5. Conclusion.
7: Exploring the Relationship between Coincident Financial Market
Indicators. 1. Introduction. 2. Markov Switching Coincidence
Index Model. 3. Data. 4. Empirical Results. 5. Conclusion.
References. Index.
July 2004, ISBN 1-4020-2172-0, Paperback
July 2004, ISBN 1-4020-2171-2, Hardbound
Book Series: NATO SCIENCE SERIES: II: Mathematics, Physics and
Chemistry : Volume 152
A compendium of novel information on molecular-scale science and
the application of nanocarbon, nanosilicon and biopolymer
integrated nanosystems.
During the 20th century, molecular-scale science and
nanotechnology developed rapidly, leading to the construction of
innovative materials - nanosystens from molecules (fullerenes),
supramolecules (nanotubes, peapods, polymers, biopolymers (DNA,
protein and their complexes) and semiconductor nanoparticles (nano-Si,
SiOx, Si/SiGe dots, metal nanowires). This book presents exciting
new developments of the early 21st century. Significant progress
has been made in nanotechnology of building blocks for integrated
nanosystems, single and assembled molecules, nanoparticles
characterisation, and multifunctional applications of nanosystems.
The realisation and the application of novel multifunctional
nanosystems in electronics, optics, biomedicine (nano-bioelectronic
devices based on DNA and proteins, silicon nanocrystal memory
devices, monolithically integrated silicon photonics,
nanocapsules, biosensor nanosystems) are described by well known
experts.
This multi-disciplinary, scientific display of cutting-edge
research across the entire spectrum of nanoscience and
nanotechnology of inorganic, and organic systems, as well as
systems for electronics photonics, and spintronics demonstrates
that researching nanocarbon, nanosilicon, biomolecular integrated
nanosystems, and developing their new applications, is a complex
and exiting topic that will continue to attract scientists and
engineers for many years to come.