Value Distribution Theory

Value Distribution Theory
Author: Yang Lo
Publisher: Springer
Total Pages: 0
Release: 2013-10-03
Genre: Mathematics
ISBN: 9783662029176

It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 A

Nevanlinna’s Theory of Value Distribution

Nevanlinna’s Theory of Value Distribution
Author: William Cherry
Publisher: Springer Science & Business Media
Total Pages: 224
Release: 2001-04-24
Genre: Mathematics
ISBN: 9783540664161

This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. Authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its number theoretic digressions These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.

Distribution Theory of Runs and Patterns and Its Applications

Distribution Theory of Runs and Patterns and Its Applications
Author: James C. Fu
Publisher: World Scientific
Total Pages: 174
Release: 2003
Genre: Mathematics
ISBN: 9810245874

A rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics.

Extreme Value Distributions

Extreme Value Distributions
Author: Samuel Kotz
Publisher: World Scientific
Total Pages: 195
Release: 2000
Genre: Mathematics
ISBN: 1860944027

This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."

Distributions

Distributions
Author: J.J. Duistermaat
Publisher: Springer Science & Business Media
Total Pages: 455
Release: 2010-08-09
Genre: Mathematics
ISBN: 0817646752

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.

Meromorphic Functions over non-Archimedean Fields

Meromorphic Functions over non-Archimedean Fields
Author: Pei-Chu Hu
Publisher: Springer Science & Business Media
Total Pages: 308
Release: 2000-09-30
Genre: Mathematics
ISBN: 9780792365327

This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research. Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.

Results in Distribution Theory and Its Applications Inspired by Quantile Generated Probability Distributions

Results in Distribution Theory and Its Applications Inspired by Quantile Generated Probability Distributions
Author: Clement Ampadu
Publisher: Lulu.com
Total Pages: 106
Release: 2018-12
Genre: Science
ISBN: 0359249957

The q_T-X family of distributions induced by V is inspired by [Clement Boateng Ampadu, Quantile-Generated Family of Distributions: A New Method for Generating Continuous Distributions, Fundamental Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 1, 2018, Pages 13-34]. This book investigates some properties and applications of a somewhat dual to the EG T-X family of distributions that appeared in [Suleman Nasiru, Peter N. Mwita and Oscar Ngesa, Exponentiated Generalized Transformed-Transformer Family of Distributions, Journal of Statistical and Econometric Methods, vol.6, no.4, 2017, 1-17]. A notable feature of the book are the exercise sets, and the section "Further Developments", which invites the reader to begin his or her own investigative inquiry into quantile generated probability distributions.

Value Distribution Theory and Related Topics

Value Distribution Theory and Related Topics
Author: Grigor A. Barsegian
Publisher: Springer Science & Business Media
Total Pages: 331
Release: 2006-05-02
Genre: Mathematics
ISBN: 1402079516

The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

Uniqueness Theory of Meromorphic Functions

Uniqueness Theory of Meromorphic Functions
Author: Chung-Chun Yang
Publisher: Springer Science & Business Media
Total Pages: 590
Release: 2004-10-04
Genre: Mathematics
ISBN: 9781402014482

This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish mathematician, early in the 1920's, research in the field has developed rapidly over the past three decades with a great deal of fruitful results. This book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results. In addition, useful skills and simple proofs are introduced. This book is suitable for higher level and graduate students who have a basic grounding in complex analysis, but will also appeal to researchers in mathematics.