Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 61-64). Available also in a digital version from Dissertation Abstracts.

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Three end-member clinopyroxenes from the NaM13+Si2O6 series (M1 = Al, Fe and Ga) have been examined by single-crystal X-ray diffraction at pressures up to 11 GPa. NaGaSi2O6 was also examined with Raman spectroscopy to 16.5 GPa. NaAlSi2O6 (jadeite) and NaFeSi2O6 (aegirine) are naturally occurring minerals. NaGaSi2O6 is synthetic. Various characteristics of each of the three clinopyroxenes as a function of pressure are reported, including bulk moduli (K0), unit cell volumes, atomic positions, and bond lengths.The compressibilities of a selection of clino- and orthopyroxenes from the literature were examined and considered in terms of M2-O3 bonding and unit cell volumes. As predicted by previous workers, pyroxene compressibilities generally correlate with unit cell volumes at ambient conditions. Compressibilities are also found, however, to be significantly affected by the relationship of M2-O3 bonds with the sense of rotation of silica tetrahedra upon compression. Two such relationships are observed: sympathetic, where the corner of the SiO4 tetrahedron tilts toward M2, and antipathetic, where the corner of the tetrahedron tilts away from M2. All interatomic separations in pyroxenes decrease with pressure, but sympathetic-type separations decrease more than expected based on isotropic scaling of the unit cell. Pyroxene structures may have one of several M2-O3 bond configurations: none, one, two or four bonds, and none, only sympathetic, only antipathetic, or a mixture of both types of bonds. Structures with antipathetic bonds are significantly stiffer than structures without, all else constant. The sympathetic/antipathetic bond hypothesis represents a new, previously unrecognized, first-order control on pyroxene compressibility.M1 size controls ambient unit cell volumes of clinopyroxenes. However, M1 size does not correlate well with pyroxene bulk moduli. Applying the idea of sympathetic and antipathetic M2-O3 bonding, much of the dispersion in a plot of M1 cation size versus bulk modulus can be explained. The three NaM13+Si2O6 clinopyroxenes examined in this study exhibit very similar behavior under compression. All show signs of approaching a C2/c -> C2/c phase transition at ~20 GPa. All exhibit unit strain ellipsoids with similar orientations and dimensions. All have identical bond topologies and bulk moduli that correlate with their ambient unit cell volumes.

Morrison has constructed a geometric relationship between K3 surfaces with large Picard number and abelian surfaces. In particular, this establishes that the period spaces of certain families of lattice polarized K3 surfaces (which are closely related to the moduli spaces of lattice polarized K3 surfaces) and lattice polarized abelian surfaces are identical. Therefore, we may study the moduli spaces of such K3 surfaces via the period spaces of abelian surfaces. In this thesis, we will answer the following question: from the moduli space of abelian surfaces with endomorphism structure (either a Shimura curve or a Hilbert modular surface), there is a natural map into the moduli space of abelian surfaces, and hence into the period space of abelian surfaces. What sort of relationship exists between the moduli spaces of abelian surfaces with endomorphism structure and the moduli space of lattice polarized K3 surfaces? We will show that in many cases, the endomorphism ring of an abelian surface is just a subring of the Clifford algebra associated to the N\'eron-Severi lattice of the abelian surface. Furthermore, we establish a precise relationship between the moduli spaces of rank 18 polarized K3 surfaces and Hilbert modular surfaces, and between the moduli spaces of rank 19 polarized K3 surfaces and Shimura curves. Finally, we will calculate the moduli space of E_8^2 + <4>-polarized K3 surfaces as a family of elliptic K3 surfaces in Weierstrass form and use this new family to find families of rank 18 and 19 polarized K3 surfaces which are related to abelian surfaces with real multiplication or quaternionic multipliction via the Shioda-Inose construction. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2011-08-12 14:38:04.131

<p>The Torelli group Tg of a closed orientable surface Sg of genus g >1 is the group</p><p>of isotopy classes of orientation-preserving diffeomorphisms of Sg which act trivially</p><p>on its first integral homology. The hyperelliptic Torelli group TDg is the subgroup</p><p>of Tg whose elements commute with a fixed hyperelliptic involution. The finiteness</p><p>properties of Tg and TDg are not well-understood when g > 2. In particular, it is not</p><p>known if T3 is finitely presented or if TD3 is finitely generated. In this thesis, we begin</p><p>a study of the finiteness properties of genus 3 Torelli groups using techniques from</p><p>complex analytic geometry. The Torelli space T3 is the moduli space of non-singular</p><p>genus 3 curves equipped with a symplectic basis for the first integral homology and is</p><p>a model of the classifying space of T. Each component of the hyperelliptic locus T hyp 3</p><p>in T3 is a model of the classifying space for TD3. We will investigate the topology</p><p>of the zero loci of certain theta functions and thetanulls and explain how these are</p><p>related to the topology of T3 and T3 hyp. We show that the zero locus in h 2 x C2 </p><p>of any genus 2 theta function is isomorphic to the universal cover of the universal framed genus 2 curve of compact type and that it is homotopy equivalent to an infinite bouquet of 2-spheres. We also derive a necessary and sufficient condition for the zero locus of any genus 3 even thetanull to be homotopy equivalent to a bouquet of 2-spheres and 3-spheres.</p> / Dissertation

Thesis (Ph.D.)--McMaster University (Canada), 1995. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6295. Adviser: I. Hambleton.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 44-48).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 20-21). Also available in electronic version. Access restricted to campus users.

Thesis (doctoral)--Bonn, 1998. / Pages 10, 68 and 102 blank. Includes bibliographical references (p. 103-105).

SILVA, Joserlan Perote da. Existência de moduli para equivalência Hölder de funções analíticas. 2016. 51 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016. / Submitted by Erivan Almeida (eneiro@bol.com.br) on 2016-05-12T17:30:37Z No. of bitstreams: 1 2016_tese_jpsilva.pdf: 588345 bytes, checksum: 0d431d35b6066546720c644c4271be15 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-05-13T11:08:29Z (GMT) No. of bitstreams: 1 2016_tese_jpsilva.pdf: 588345 bytes, checksum: 0d431d35b6066546720c644c4271be15 (MD5) / Made available in DSpace on 2016-05-13T11:08:29Z (GMT). No. of bitstreams: 1 2016_tese_jpsilva.pdf: 588345 bytes, checksum: 0d431d35b6066546720c644c4271be15 (MD5) Previous issue date: 2016 / In this work, we show that Hölder equivalence of analytic functions germs (C2, 0) → (C, 0)admits continuous moduli. More precisely, we constructed an invariant of the Hölder equivalence of such germs that varies continuously in a family ft : (C2, 0) → (C, 0). For a single germ ft the invariant of ft is given in terms of the leading coefficients of the asymptotic expansion of ft along the branches of generic polar curve of ft . / Neste trabalho, mostramos que equivalência Hölder de germes de funções analíticas (C2, 0) → (C, 0) admite moduli contínuo. Mais precisamente, construimos um invariante da equivalência Hölder de tais germes que varia continuamente numa família ft : (C2, 0) → (C, 0). Para um único germe ft o invariante de ft é dado em termos dos coeficientes principais das expansões assintóticas de ft ao longo dos ramos da curva polar genérica de ft.