(Mathematics in Science and Engineering, Volume 209)
- Fractals generated from L-System including hybrid fractals
- Dimension calculation for L-system fractals
- Images & codes for L-system fractals
- Research directions in the area of L-system fractals
- Usage of various freely downloadable tools in this area
Description
The book covers all the fundamental aspects of generating
fractals through L-system. Also it provides insight to various
researches in this area for generating fractals through L-system
approach & estimating dimensions. Also it discusses various
applications of L-system fractals.
Key Features:
- Fractals generated from L-System including hybrid fractals
- Dimension calculation for L-system fractals
- Images & codes for L-system fractals
- Research directions in the area of L-system fractals
- Usage of various freely downloadable tools in this area
Contents
Preface
Contents
1. Introduction to Fractals
2. Fractals and L-System
3. Interactive Generation of Fractals Images
4. Generation of a Class of Hybrid Fractals
5. L-System Strings from Ramification Matrix
6. 3D Modeling of Realistic Plants
7. Fractals Dimension
8. Research Directions of L-Systems
Bibliography
Appendix A
Appendix B
Appendix C
Colour Section
Index
(Mathematics in Science and Engineering, Volume 210)
- Presents a unifying look on different equilibrium concepts and
also the present state of investigations in this field
- Describes static and dynamic input-output models, Walras,
Cassel-Wald, spatial price, auction market, oligopolistic
equilibrium models, transportation and migration equilibrium
models
- Covers the basics of theory and solution methods both for the
complementarity and variational inequality problems
- The methods are illustrated by applications and exercises to
economic equilibrium models
Description
The concept of equilibrium plays a central role in various
applied sciences, such as physics (especially, mechanics),
economics, engineering, transportation, sociology, chemistry,
biology and other fields. If one can formulate the equilibrium
problem in the form of a mathematical model, solutions of the
corresponding problem can be used for forecasting the future
behavior of very complex systems and, also, for correcting the
the current state of the system under control.
This book presents a unifying look on different equilibrium
concepts in economics, including several models from related
sciences.
Contents
Preface
Contents
List of Figures
1. Introduction
Part I : Models
2. Linear Models in Economics
3. Linear Dynamic Models of an Economy
4. Optimization and Equilibria
5. Nonlinear Economic Equilibrium Models
6. Transportation and Migration Models
Part II : Complementarity Problems
7. Complementarity with Z Properties
8. Applications
9. Complementarity with P Properties
10. Applications
Part III: Variational Inequalities
11. Theory of Variational Inequalities
12. Applications
13. Projection Type Methods
14. Applications of the Projection Methods
15. Regularization Methods
16. Direct Iterative Methods for Monotone Variational
Inequalities
17. Solutions to Exercises
Bibliography
Index
Series: Modern Birkhauser Classics
Originally published as volume 28 in the series: Progress in
Mathematics
1st ed. 1983. 4th printing, 2007, XIV, 236 p., 7 illus.,
Softcover
ISBN-10: 0-8176-4572-1
ISBN-13: 978-0-8176-4572-4
About this book
The first of a series of three volumes surveying the theory of
theta functions and its significance in the fields of
representation theory and algebraic geometry, this volume deals
with the basic theory of theta functions in one and several
variables, and some of its number theoretic applications.
Requiring no background in advanced algebraic geometry, the text
serves as a modern introduction to the subject.
Written for:
Graduate students and researchers in Mathematics and Physics
Table of contents
Introduction.- Introduction and Motivation: Theta Functions in
one Variable.- Basic Results on Theta Functions in several
Variables.
Series: Modern Birkhauser Classics
Originally published as volume 43 in the series: Progress in
Mathematics
1st ed. 1984. 4th printing, 2007, XIV, 272 p., 21 illus.,
Softcover
ISBN-10: 0-8176-4569-1
ISBN-13: 978-0-8176-4569-4
About this book
The second in a series of three volumes surveying the theory of
theta functions, this volume gives emphasis to the special
properties of the theta functions associated with compact Riemann
surfaces and how they lead to solutions of the Korteweg-de-Vries
equations as well as other non-linear differential equations of
mathematical physics.
This book presents an explicit elementary construction of
hyperelliptic Jacobian varieties and is a self-contained
introduction to the theory of the Jacobians. It also ties
together nineteenth-century discoveries due to Jacobi, Neumann,
and Frobenius with recent discoveries of Gelfand, McKean, Moser,
John Fay, and others.
A definitive body of information and research on the subject of
theta functions, this volume will be a useful addition to
individual and mathematics research libraries.
Table of contents
Introduction.- An Elementary Construction of Hyperelliptic
Jacobians.- Fay’s Trisecant Identity for Jacobian Theta
Functions.- Resolutions of Algebraic Equations by Theta Constants.-
Bibliography.
Series: Modern Birkhauser Classics
Originally published as volume 97 in the series: Progress in
Mathematics
1st ed. 1991. 3rd printing, 2007, VIII, 202 p., 2 illus.,
Softcover
ISBN-10: 0-8176-4570-5
ISBN-13: 978-0-8176-4570-0
About this book
This volume is the third of three in a series surveying the
theory of theta functions which play a central role in the fields
of complex analysis, algebraic geometry, number theory and most
recently particle physics.
Based on lectures given by the author at the Tata Institute of
Fundamental Research in Bombay, these volumes constitute a
systematic exposition of theta functions, beginning with their
historical roots as analytic functions in one variable (Volume I),
touching on some of the beautiful ways they can be used to
describe moduli spaces (Volume II), and culminating in a
methodical comparison of theta functions in analysis, algebraic
geometry, and representation theory (Volume III).
Researchers and graduate students in mathematics and physics will
find these volumes to be valuable additions to their libraries.
Table of contents
Preface.- Heisenberg groups in general.- The real Heisenberg
groups.- Finite Heisenberg groups and sections of line bundles on
abelian varieties.- Adelic Heisenberg groups and towers of
abelian varieties.- Algebraic theta functions.- Theta functions
with quadratic forms.- Riemann's theta relation.- The metaplectic
group and the full functional equation of $\vartheta$.- Theta
functions in spherical harmonics.- The homogeneous coordinate
ring of an abelian variety.