Browsing by Department "Mathematics"
Now showing items 1-20 of 113
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(2013-08-01)Department: MathematicsWe consider various types of generalized bases in spaces of the type L^p(T), where T=[0,1]. More specifically, we determine whether there exists a system {f_n}_n, of the type under consideration, with the property f_n(t)>=0 ...
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(2014-06-26)Department: MathematicsThe work in this dissertation is about modeling the spread of an infectious disease in a closed community with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and ...
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(2023-06-14)Department: MathematicsThis thesis introduces and studies a natural generalization of the distortion function that applies to not necessarily finitely generated subgroups of finitely generated groups. We begin by computing this function in several ...
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(2023-06-14)Department: MathematicsThis thesis introduces and studies a natural generalization of the distortion function that applies to not necessarily finitely generated subgroups of finitely generated groups. We begin by computing this function in several ...
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(2012-06-25)Department: MathematicsThere is evidence that cancer develops when cells acquire a sequence of mutations. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. ...
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(2019-03-29)Department: MathematicsThis work is motivated by the problem of recovering the magnetization M of a rock sample from a given set of measurements for the magnetic field it generates. Modeling the magnetization by an R 3 -valued measure, we focus ...
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(2005-12-20)Department: MathematicsAn ordinary differential equations model for strep throat infection is constructed to compute the bacterial population densities of genotype combinations with binary switches in contingency genes. Theoretical analysis for ...
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(2018-07-11)Department: MathematicsLet V be a unitary vertex operator algebra (VOA) satisfying the following conditions: (1) V is of CFT type. (2) Every N-gradable weak V -module is completely reducible. (3) V is C2-cofinite. Let Rep(V)be the category of ...
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(2021-06-03)Department: MathematicsA holomorphic discrete series representation $(L_{\pi},H_{\pi})$ of a connected semi-simple real Lie group $G$ is associated with an irreducible representation $(\pi,V_{\pi})$ of its maximal compact subgroup $K$. The ...
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(2019-07-11)Department: MathematicsSplines have been used to approximate the solutions of differential equations for a while. In the first part of this thesis, adaptive algorithms based on the finite element method and splines on triangulations with hanging ...
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(2015-07-27)Department: MathematicsA general model of age-structured population dynamics of early humans is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear ...
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(2016-06-20)Department: MathematicsAmenability is a fundamental in operator algebras. The classification of von Neumann algebras by Alain Connes is a milestone in the theory. The study of amenable subalgebras in II1 factors has led to many important ...
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(2013-04-15)Department: MathematicsResiduated lattices, which generalize Boolean algebras and lattice-ordered groups, have been useful in the study of algebraic logic, particularly as an algebraic semantics for substructural logics. By equipping a residuated ...
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(2017-06-19)Department: MathematicsA fundamental problem in signal processing called signal reconstruction, or signal recovery, is the determination of a signal from a sequence of samples obtained from the signal. The sampling process can be viewed as ...
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(2022-05-18)Department: MathematicsComplex Hadamard matrices are biunitaries for spin model commuting squares. The corresponding subfactor standard invariant can be identified with the $1$-eigenspace of the angle operator defined by Vaughan Jones. We identify ...
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(2016-04-09)Department: MathematicsWe study annular algebras associated to a rigid C*-tensor category, a generalization of both Ocneanu's tube algebra and Jones' affine annular category. We show that all ``sufficiently large' annular algebras are strongly ...
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(2019-10-23)Department: MathematicsThe sphere packing problem asks for the densest collection of non-overlapping con- gruent spheres in Rn. In 2016, Viazovska proved that the E8 lattice is optimal for n = 8. Subsequently, she with Cohn, Kumar, Miller, and ...
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(2006-06-21)Department: MathematicsThis work studies the behavior of the minimal discrete Riesz s-energy and best-packing distance on rectifiable sets as the cardinality N of point configurations gets large. We extend known asymptotic results for the ...
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(2006-06-09)Department: MathematicsIn this dissertation we first study the Faber polynomials for a piecewise analytic Jordan curve $L$ without inner cusps (some extra conditions are additionally imposed on $L$). Let $Omega$ and $G$ be, repectively, the ...
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(2019-03-21)Department: MathematicsThe uncertainty principle implies that a function and its Fourier transform cannot both be well-localized. The Balian-Low theorem is a version of the uncertainty principle for generators of Gabor orthonormal bases. This ...