Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1933. / Sonderabdruck aus den "Schriften des Mathematischen Seminars und des Instituts für angewandte Mathematik der Universität Berlin, Band 1"--T.p. verso. Vita. Includes bibliographical references.

Thesis (M.A.)--Kutztown State College, 1975. / Source: Masters Abstracts International, Volume: 45-06, page: 3173. Typescript. Abstract precedes thesis as [2] preliminary leaves. Includes bibliographical records (leaves 56-58).

O objetivo principal deste trabalho é o estudo das funções univalentes e de suas propriedades. Este estudo é direcionado principalmente aos polinômios univalentes e à investigação de prolemas extremos envolvendo seus coeficientes, seus zeros e suas propriedades geométricas. Encontramos uma relação interessante entre os polinômios univalentes e os polinômios univalentes definida por Suffridge. Geramos várias funções univalentes estreladas e convexas através de suas propriedades geométricas e da localização de seus zeros. / The main aim of this work is the study of univalent functions and their properties. This study is focused speciall on the univalent polynomials and theinvestigation of extremal problems involving their coefficients, zeros and geometric properties. We find a very ineresting relation between univalent polynomials through a class of univalent starlike and convex functions involving their geometric properties and the location of their zeros.

O objetivo principal deste trabalho é o estudo das funções univalentes e de suas propriedades. Este estudo é direcionado principalmente aos polinômios univalentes e à investigação de prolemas extremos envolvendo seus coeficientes, seus zeros e suas propriedades geométricas. Encontramos uma relação interessante entre os polinômios univalentes e os polinômios univalentes definida por Suffridge. Geramos várias funções univalentes estreladas e convexas através de suas propriedades geométricas e da localização de seus zeros. / The main aim of this work is the study of univalent functions and their properties. This study is focused speciall on the univalent polynomials and theinvestigation of extremal problems involving their coefficients, zeros and geometric properties. We find a very ineresting relation between univalent polynomials through a class of univalent starlike and convex functions involving their geometric properties and the location of their zeros.

A planar harmonic mapping is a complex-valued function ƒ : D → C of the form ƒ(x+iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as ƒ = h+g where h and g are both analytic; the function w = g'/h' is called the dilatation of ƒ. This thesis considers the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping p;(z) = z/(1-z) with respective dilatations e^iθz and e^ipz, θ, p ∈ R. We prove that any such convolution is univalent. We also derive a convolution identity that extends this result to shears of p(z) = z/(1-z) in other directions.

We study universal integral means spectra of certain classes of univalent functions defined on subsets of the complex plane. After reformulating the definition of the integral means spectrum of a univalent function in terms of membership in weighted Bergman spaces, we describe the Hilbert space techniques that can be used to estimate universal means spectra from above. Finally, we show that the method of norm expansion used in that context can be applied in a more general setting to reproducing kernel spaces in order to explicitly compute kernel functions. / <p>QC 20101117</p>

The preparation and thermophysical properties of some In(I), Ga(I) and Ag(I) substituted NZP type materials were explored. Many compositions with the NZP framework show low and negative thermal expansion. Previously reported material, GaZr2(PO4(3, transforms from one NZP related phase into another NZP type phase due to oxidation under air above 300oC. In addition, it exhibits hysteresis under inert atmosphere; the cell parameters are different on heating and cooling cycles for a given temperature. The synthesis, and characterization of a new material, InZr2(PO4)3, is outlined. It crystallizes in space group R -3 c. In addition, as GaZr2(PO4)3, it oxidizes above 300oC under air and exhibits hysteresis under inert atmosphere. Furthermore, the synthesis of AgTixZr2-x(PO4)3 solid solution compositions, their ion exchange characteristics with Ga(I) and their thermophysical properties are described. Thermal expansion anisotropy (the difference between a and c ) of the solid solutions decreases as the bigger ion, Zr4+, is substituted by the smaller one, Ti4+. Thermal expansion characteristics of GaZr2(PO4)3, InZr2(PO4)3 and AgZr2(PO4)3 are compared with MZr2(PO4)3 ( M = Li, Na, K, Rb, Cs). Ionic radii for Ga(I) and In(I) in a six coordinate oxygen environment were proposed.

<p>We study universal integral means spectra of certain classes of univalent functions defined on subsets of the complex plane. After reformulating the definition of the integral means spectrum of a univalent function in terms of membership in weighted Bergman spaces, we describe the Hilbert space techniques that can be used to estimate universal means spectra from above. Finally, we show that the method of norm expansion used in that context can be applied in a more general setting to reproducing kernel spaces in order to explicitly compute kernel functions.</p>

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2005. / Includes bibliographical references (leaves 112-113).

This thesis presents an account of the cubical sets model of homotopy type theory using an internal type theory for elementary topoi. Homotopy type theory is a variant of Martin-Lof type theory where we think of types as spaces, with terms as points in the space and elements of the identity type as paths. We actualise this intuition by extending type theory with Voevodsky's univalence axiom which identifies equalities between types with homotopy equivalences between spaces. Voevodsky showed the univalence axiom to be consistent by giving a model of homotopy type theory in the category of Kan simplicial sets in a paper with Kapulkin and Lumsdaine. However, this construction makes fundamental use of classical logic in order to show certain results. Therefore this model cannot be used to explain the computational content of the univalence axiom, such as how to compute terms involving univalence. This problem was resolved by Cohen, Coquand, Huber and Mortberg, who presented a new model of type theory in Kan cubical sets which validated the univalence axiom using a constructive metatheory. This meant that the model provided an understanding of the computational content of univalence. In fact, the authors present a new type theory, cubical type theory, where univalence is provable using a new "glueing" type former. This type former comes with appropriate definitional equalities which explain how the univalence axiom should compute. In particular, Huber proved that any term of natural number type constructed in this new type theory must reduce to a numeral. This thesis explores models of type theory based on the cubical sets model of Cohen et al. It gives an account of this model using the internal language of toposes, where we present a series of axioms which are sufficient to construct a model of cubical type theory, and hence a model of homotopy type theory. This approach therefore generalises the original model and gives a new and useful method for analysing models of type theory. We also discuss an alternative derivation of the univalence axiom and show how this leads to a potentially simpler proof of univalence in any model satisfying the axioms mentioned above, such as cubical sets. Finally, we discuss some shortcomings of the internal language approach with respect to constructing univalent universes. We overcome these difficulties by extending the internal language with an appropriate modality in order to manipulate global elements of an object.