Book Description:
The main aim of this monograph is to survey some recent results
obtained by the author related to reverses of the Schwarz,
triangle and Bessel inequalities. Some Gruss' type inequalities
for orthonormal families of vectors in real or complex inner
product spaces are presented as well. Generalizations of the Boas-Bellman,
Bombieri, Selberg, Heilbronn and Pecaric Inequalities for finite
sequences of vectors that are not necessarily orthogonal are also
provided. Two extensions of the celebrated Ostrowski's
inequalities for sequences or real numbers and the generalization
of Wagner's inequality in inner product spaces are pointed out.
Finally, some Gruss type inequalities for n-tuples of vectors in
inner product spaces and their natural applications for the
approximation of the discrete Fourier and Mellin transforms are
given as well.
Table of Contents:
Preface;
Part 1. Reverse Inequalities
Chapter 1. Reverses for the Schwarz Inequality
Chapter 2. Inequalities of the Gruss Type
Chapter 3. Reverses of Bessel's Inequality
Pat 2. Other Inequalities in Inner Product Spaces
Chapter 4. Generalisations of Bessel's Inequality
Chapter 5. Some Gruss' Type Inequalities for n-Tuples of Vectors
Chapter 6. Other Inequalities in Inner Product Spaces
Bibliography
Index.
Binding: Hardcover
Pub. Date: 2005
ISBN: 1-59454-529-4
Book Description:
The purpose of this book is to give a comprehensive introduction
to several inequalities in Inner Product Spaces that have
important applications in various topics of Contemporary
Mathematics such as: Linear Operators Theory, Partial
Differential Equations, Nonlinear Analysis, Approximation Theory,
Optimization Theory, Numerical Analysis, Probability Theory,
Statistics and other fields.
Table of Contents:
Preface
Chapter 1. Inequalities for Hermitian Forms
Chapter 2. Schwarz Related Inequalities
Chapter 3. Reverses for the Triangle Inequality
Chapter 4. Reverses for the Continous Triangle Inequality
Chapter 5. Reverses of the CBS and Heisenberg Inequalities
Chapter 6. Other Inequalities in Inner Product Spaces
Bibliography
Index
Binding: Hardback
Pub. Date: 2006
ISBN: 1-59454-903-6
Book Description:
In this book, generally speaking, some properties of
bitopological spaces generated by certain nonsymmetric functions
are studied. These functions, called ``probabilistic quasi-pseudo-metrics"
and ``fuzzy quasi-pseudo-metrics", are generalizations of
classical quasi-pseudo metrics. For the sake of completeness as
well as for convenience and easy comparison, most of the
introductory paragraphs are mainly devoted to fundamental notions
and results from the classical--deterministic or symmetric--theory.
Table of Contents:
CHAPTER I. INTRODUCTION
CHAPTER II. PRELIMINARY NOTIONS AND RESULTS
CHAPTER III. PROBABILISTIC QUASI-PSEUDO-METRIC SPACES
CHAPTER IV. EXAMPLES OF SPACES
CHAPTER V. TOPOLOGIES GENERATED BY METRICS
CHAPTER VI. RANDOM NORMED STRUCTURES
CHAPTER VII. QUASI-PSEUDO-METRIZATION IN SPACES
CHAPTER VIII. PROBABILISTIC METRICS AND DETERMINISTIC DISTANCE
FUNCTIONS
CHAPTER IX. COMPLETENESS IN PqpM-SPACES AND (PH)-SPACES
CHAPTER X. FUZZY QUASI-PSEUDO-METRIC SPACES
CHAPTER XI. PROBABILISTIC AND FUZZY CONTRACTIVE MAPPINGS
CHAPTER XII. CARTESIAN PRODUCTS OF FqpM-SPACES AND (PH)-SPACES
REFERENCES
SUBJECT INDEX
Binding: Flexback
Pub. Date: 2006
ISBN: 1-59454-917-6
Book Description:
The first chapter lists the basic results of orthogonal
polynomials, Jacobi, Laguerre, and Hermite polynomials, and
collects some frequently used theorems and formulas. As a base
and useful tool, the representation and quantitative theory of
Hermite interpolation is the subject of Chapter 2. The theory of
power orthogonal polynomials begins in Chapter 3: existence,
uniqueness, Characterizations, properties of zeros, and
continuity with respect to the measure and the indices are all
considered. Chapter 4 deals with Gaussian quadrature formulas and
their convergence. Chapter 5 is devoted to the theory of
ChristoRel type functions, which are related to Gaussian
quadrature formulas and is one of the important contents of power
orthogonal polynomials. The explicit representation of power
orthogonal polynomials is an interesting problem and is discussed
in Chapter 6. Chapter 7 is a detailed treatment of zeros in power
orthogonal polynomials. Chapter 8 is devoted to bounds and
inequalities of power orthogonal polynomials. In Chapters 9 and
10 we study asymptotics of general polynomials and power
orthogonal polynomials, respectively. In Chapter 11 we discuss
convergence of power orthogonal series, Lagrange and Hermite
interpolation, and two positive operators constructed by power
orthogonal polynomials. In Chapter 12 we investigate Gaussian
quadrature formulas for extended Chebyshev spaces. In Chapter 13
we give construction methods for power orthogonal polynomials and
Gaussian quadrature formulas; we also provide numerical results
and numerical tables.
Table of Contents:
Preface vii
1 Preliminaries
2 Hermite Interpolation
3 General Properties of Power Orthogonal Polynomials
4 Gaussian Quadrature Formulas
5 Christoel Type Functions
6 Explicit Expressions
7 Zeros of Power Orthogonal Polynomials
8 Bounds and Inequalities
9 Asymptotics of General Polynomials
10 Asymptotics of Power Orthogonal Polynomials
11 Interpolation and Power Orthogonal Series
12 Gaussian Quadrature Formulas for Extended Chebyshev Spaces
13 Construction Methods
Index
Binding: Hardcover
Pub. Date: March 2006
ISBN: 1-59454-855-2
Book Description:
Both current theory and practice in financial markets are
undergoing a strong pressure to include recently developed fields
of inquiry, namely market microstructure, transaction costs and
asymmetric information. This claim has been taking shape after
nearly thirty years of worthy research and empirical development
that laid sound groundwork to those promising subjects.
The purpose of this book is to introduce a new approach to work
out the returns from financial assets. Firstly, by means of the
concept of differential rates, which allow the breaking down of
the ordinary rate of return into components that are rates on
their own. Secondly, residual information sets are built up to
match each differential rate with its underlying information.
Table of Contents:
CHAPTER 1 ASYMMETRIC MARKETS AND INFORMATION SETS
CHAPTER 2 FINANCIAL ASSETS AND THEIR RATES OF RETURN
CHAPTER 3 DIFFERENTIAL RATES AND RESIDUAL INFORMATION SETS WITHIN
A TRANSACTION COSTS STRUCTURE
CHAPTER 4 THE BROKERAGE OF ASYMMETRIC INFORMATION
CHAPTER 5 NARROW AND BROAD DIFFERENTIAL RATES AND THEIR RESIDUAL
INFORMATION SETS
CHAPTER 6 TRANSACTIONAL ALGEBRAS AND THE EXTENT OF ARBITRAGE
CONSTRAINTS
CHAPTER 7 ARBITRAGE AND SEPARATION PORTFOLIOS WITHIN
TRANSACTIONAL ALGEBRAS
CHAPTER 8 ENLARGED SEPARATION PORTFOLIOS AND FINANCIAL SYNTHETICS
WITHIN TRANSACTIONAL ALGEBRAS
CHAPTER 9 CONFLICTS OF INTERESTS AND RESIDUAL INFORMATION SETS
CHAPTER 10 A TOOLBOX FOR PRACTITIONERS
Pub. Date: 2006
ISBN: 1-59454-872-2
Book Description:
The aim of this volume is to introduce new topics on the areas of
difference, differential, integrodifferential and integral
equations, evolution equations, control and optimization theory,
dynamic system theory, queuing theory and electromagnetism and
their applications.
Table of Contents:
Preface
1. On the Oscillation of Certain Second Order Differential
Equations (Ravi P. Agarwal and Said R. Grace)
2. A Method for Determining the Production Function (Corneliu
Anghel and Marius Boldea)
3. Existence Results for a Class of Difference Inclusions (N.C.
Apreutessi)
4. Existence of Solutions of Perturbed Fuzzy Integrodifferential
Equations (K. Balachandran and K. Kanagarajan)
5. Anti-Periodic Solutions for First Order Equations in Rn (Y.Q.
Chen, Y.J. Cho and L. Yang)
6. Positive Solutions for Second-Order Three-Point Boundary Value
Problems (Shijie Dong and Haiyun Zhou)
7. Existence and Uniqueness of Solution of Initial Value Problems
for Nonlinear First Order Impulsive Integro-Differential
Equations of Mixed Type in Banach Spaces (Lishan Liu and Fei Guo)
8. Interval Oscillation Criteria for Second Order Neutral Delay
Differential Equations (Fanwei Meng and Jizhong Wang)
9. Spectral Properties of Discrete Schrodinger Operator with
Quasi-Periodically Recurrent Potential (Koichiro Naito)
10. On Higher Order Differential Equation with Retarded Argument
(B.G. Pachpatte)
11. Controllability and H Control for Linear Continuous Time-Varying
Uncertain Systems (Vu N. Phat and Do Q. Vinh)
12. Exponential Attractor for an Adsorbate-Induced Phase
Transition Model with Periodic Boundary Conditions (Yasuhiro
Takei, Koichi Osaki, Tohru Tsujikawa and Atsushi Yagi)
13. Some Stability Results for the Solutions of Certain Fourth
Order Delay Differential Equations (Cemil Tunc)
14. Periodic Solutions of a Delayed Lotka-Volterra Type Model
with One Prey and two Predators (Rui Xu, Hanying Feng and Qiming
Liu)
15. Finite Difference Solutions of Landau-Lifshitz Equation with
Discontinuous External Field (Ganshan Yang and Qianshun Chang)
Binding: Flexback
Pub. Date: 2006
ISBN: 1-59454-876-5