Griogor A Barsegian

Gamma-Lines

On the Geometry of Real and Complex Functions

• Gebundenes Buch

Produktbeschreibung

To a large extent, the history of mathematics and the study of solutions of f(x)=a=const for functions f(x) of one real or complex variable are intertwined. Therefore, it is surprising that we know little about solutions of u(x,y)=A=const for functions of two real variables. These two solutions, called level of sets, are important in physics, biology, and economics, as they map appropriate processes described by the function u(x,y) for given parameters (x,y). This text explores the a-points concept along with the Gamma-lines concept and generalizes the notion of levels of sets and a-points. The general methods proposed are useful to both physicists and engineers.

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Produktdetails

• Verlag: Taylor & Francis Ltd (Sales)
• Seitenzahl: 192
• Erscheinungstermin: 15. August 2002
• Englisch
• Abmessung: 244mm x 153mm x 16mm
• Gewicht: 408g
• ISBN-13: 9780415269698
• ISBN-10: 0415269695
• Artikelnr.: 23400305

Autorenporträt

Barsegian, Griogor A.

Inhaltsangabe

Preface. Tangent Variation Principle. Satellite Principles. Modification of
Length-area Principle. Tangent Variation Principle. Estimates for
collections of Gamma-Lines. Estimates of lengths of Gamma-Lines for
angular-quasiconformal mappings. Remarks on applying of estimates of L (D,
Gamma). Nevanlinna and Ahilfors Theories. Additions. Basic concepts and
outcomes of Nevanlinna Value Distribution theory and Ahlfors theory of
covering surfaces. Geometric deficient values. On some additions to L.
Ahlfor's theory of covering surfaces. Bounds of some integrals. Gamma-Lines
Approach in the Theory of Meromorphic Functions. Principle of closeness of
sufficiently large sets of Alpha-points of meromorphic functions.
Integrated Version of the Principle. Connections with known classes of
functions. Distribution of Gamma-Lines for Functions Meromorphic in C.
Applications. The main results on distribution of Gamma-Lines. "Wingdings"
of Gamma-Lines. Average lengths of Gamma-Lines along concentric circles and
the deficient values. Distribution of Gamma-Lines and value distribution of
subclasses of modules and real parts of mermorphic functions. The number of
Gamma-Lines crossing rings. Distribution of Gelfond points. Nevalinna's
dream-description of transcendental ramification of Riemann surfaces. The
proximity property of Alpha-points of meromorphic functions. A proof of the
proximity property of Alpha-points based only on investigation of
Gamma-Lines. Some Applied Problems. Gamma-Lines in Physics. On the cross
road of value distribution, Gamma-Lines, free boundary theories and applied
mathematics. "Pointmaps" of physical processes and Alpha-points of general
classes of functions Principles. Nevanlinna and Ahilfors Theories.
Additions. Gamma-Lines Approach in the Theory of Meromorphic Functions.
Distribution of Gamma-Lines for Functions Mermorphic in C. Applications.
Some Applied Problems.