Spelling suggestions: "subject:"geometric function theory"" "subject:"eometric function theory""
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Cauchy transforms of self-similar measures. / CUHK electronic theses & dissertations collectionJanuary 2002 (has links)
by Dong Xinhan. / "March 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 113-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.
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Applications of the fourier transform to convex geometryYaskin, Vladyslav, January 2006 (has links)
Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.
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Topics in functional analysis and convex geometryYaskina, Maryna, January 2006 (has links)
Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.
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Polynomial equations and solvability: A historical perspectiveRiggs, Laurie Jan 01 January 1996 (has links)
No description available.
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Convolutions and Convex Combinations of Harmonic Mappings of the DiskBoyd, Zachary M 01 June 2014 (has links) (PDF)
Let f_1, f_2 be univalent harmonic mappings of some planar domain D into the complex plane C. This thesis contains results concerning conditions under which the convolution f_1 ∗ f_2 or the convex combination tf_1 + (1 − t)f_2 is univalent. This is a long-standing problem, and I provide several partial solutions. I also include applications to minimal surfaces.
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The class number one problem in function fieldsHarper, John-Paul 12 1900 (has links)
Thesis (MComm)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More
precisely I give a survey of the current state of research into extensions of a rational function
field over a finite field with principal ring of integers. I focus particularly on the quadratic
case and throughout draw analogies and motivations from the classical number field situation.
It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of
quadratic extensions of the rational numbers and the corresponding rings of integers. More
recently however work has been done in the situation of function fields in which the arithmetic
is very similar.
I begin with an introduction into the arithmetic in function fields over a finite field and
prove the analogies of many of the classical results. I then proceed to demonstrate how the
algebra and arithmetic in function fields can be interpreted geometrically in terms of curves
and introduce the associated geometric language. After presenting some conjectures, I proceed
to give a survey of known results in the situation of quadratic function fields. I present also
a few results of my own in this section. Lastly I state some recent results regarding arbitrary
extensions of a rational function field with principal ring of integers and give some heuristic
results regarding class groups in function fields. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek
ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam
oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in
besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke
getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese
uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek
het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van
funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is.
Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en
bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in
funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot
die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds
vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my
eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n
rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied
is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.
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A study of the geometric and algebraic sewing operationsPenfound, Bryan 10 September 2010 (has links)
The sewing operation is an integral component of both Geometric Function Theory and Conformal Field Theory and in this thesis we explore the interplay between the two fields. We will first generalize Huang's Geometric Sewing Equation to the quasi-symmetric case. That is, given specific maps g(z) and f^{-1}(z), we show the existence of the sewing maps F_{1}(z) and F_{2}(z). Second, we display an algebraic procedure using convergent matrix operations showing that the coefficients of the Conformal Welding Theorem maps F(z) and G(z) are dependent on the coefficients of the map phi(z). We do this for both the analytic and quasi-symmetric cases, and it is done using a special block/vector decomposition of a matrix representation called the power matrix. Lastly, we provide a partial result: given specific maps g(z) and f^{-1}(z) with analytic extensions, as well as a particular analytic map phi(z), it is possible to provide a method of determining the coefficients of the complementary maps.
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A study of the geometric and algebraic sewing operationsPenfound, Bryan 10 September 2010 (has links)
The sewing operation is an integral component of both Geometric Function Theory and Conformal Field Theory and in this thesis we explore the interplay between the two fields. We will first generalize Huang's Geometric Sewing Equation to the quasi-symmetric case. That is, given specific maps g(z) and f^{-1}(z), we show the existence of the sewing maps F_{1}(z) and F_{2}(z). Second, we display an algebraic procedure using convergent matrix operations showing that the coefficients of the Conformal Welding Theorem maps F(z) and G(z) are dependent on the coefficients of the map phi(z). We do this for both the analytic and quasi-symmetric cases, and it is done using a special block/vector decomposition of a matrix representation called the power matrix. Lastly, we provide a partial result: given specific maps g(z) and f^{-1}(z) with analytic extensions, as well as a particular analytic map phi(z), it is possible to provide a method of determining the coefficients of the complementary maps.
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The Lie symmetries of a few classes of harmonic functions /Petersen, Willis L., January 2005 (has links) (PDF)
Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (leaves 112-113).
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Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular TypeCoiculescu, Ion 05 1900 (has links)
In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.
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