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(2001)In Chapter 5, we prove two other equations on page 45 of Ramanujan's lost notebook by using the BauerMuir transformation and by using the method of successive approximation. Also, we prove several continued fractions of ...
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(20170710)We study taufunctions given as matrix elements for the action of loop groups, $\widehat{GL_n}$ on $n$component fermionic Fock space. In the simplest case, $n=2$, the taufunctions are equal to Hankel determinants and ...
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(2004)The second part of the thesis is devoted to the qualitative analysis of weighted operators, where the weights are obtained by almost everywhere sampling in a stationary stochastic process. The major theme of our investigation ...
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(20100820)In this thesis, we first use the ${\mathbb C^*}^2$action on the Hilbert scheme of two points on a Hirzebruch surface to compute all onepointed and some twopointed GromovWitten invariants via virtual localization, then ...
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(1967)
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(20170421)We introduce and study quasielliptic cohomology, a theory related to Tate Ktheory but built over the ring $\mathbb{Z}[q^{\pm}]$. In Chapter 2 we build an orbifold version of the theory, inspired by Devoto's equivariant ...
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(2003)In this thesis the notion of Schottky quasiconformal groups is introduced. We study Schottky quasiconformal groups and show that the limit set L(G) of any Schottky quasiconformal group G is uniformly perfect. Then the ...
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(1991)Nondifferentiable quasiconvex programming problems are studied using Clarke's subgradients. Several conditions sufficient for optimality are derived. Under certain regularity conditions on the constraint functions, we also ...
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(1995)Here we generalize quasigeodesics to multidimensional Alexandrov space with curvature bounded from below and prove that classical theorems of Alexandrov also hold for this case. Also we develop gradient curves as a tool ...
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(1995)In the first part of this thesis, we prove Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\sb4, E\sb4/E\sb6$ and other ...
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Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and Lfunctions (20150803)The focus of the first part of the thesis commences with an examination of two pages in Ramanujan's lost notebook, pages 336 and 335. A casual, or even more prolonged, examination of the strange formulas on these pages ...
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(20150121)In this dissertation, we study three problems about Ramsey theory. First, we prove a selfdual Ramsey theorem for parameter systems which is a generalization of the selfdual Ramsey theorem developed by Solecki. Second, ...
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(2000)Given an adapted probability measure on a locally compact group, there are a variety of support conditions which cause the concentration functions to go to zero. This work discusses the rate of this decay under many such ...
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(2003)Finally, this thesis uses dynamical systems techniques to prove already known results in continued fractions.
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(2008)Lattice varieties play an important role in several areas of mathematics. In this thesis we investigate the properties of rational points on lattice varieties over Witt vectors with algebraically closed residue field in ...
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