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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
Ergodic Properties Of Countable Extensions, Samuel Joshua Roth
Ergodic Properties Of Countable Extensions, Samuel Joshua Roth
Open Access Dissertations
First, we study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a non-decreasing semiconjugacy to an interval map of constant slope in terms of the existence of an eigenvector of an operator acting on a space of measures. Then we give examples, both Markov and non-Markov, for which the criterion is violated. ^ Next, we establish a criterion for the existence of a constant slope map on the extended real line conjugate to a given countably piecewise monotone interval map. We require the given interval map to be continuous, Markov, …
Heat Trace And Heat Content Asymptotics For Schrodinger Operators Of Stable Processes/Fractional Laplacians, Luis Guillermo Acuna Valverde
Heat Trace And Heat Content Asymptotics For Schrodinger Operators Of Stable Processes/Fractional Laplacians, Luis Guillermo Acuna Valverde
Open Access Dissertations
Let V be a bounded and integrable potential over Rd and 0 < α ≤ 2. We show the existence of an asymptotic expansion by means of Fourier Transform techniques and probabilistic methods for the following quantities [special characters omitted] and [special characters omitted] as t ↓ 0. These quantities are called the heat trace and heat content in Rd with respect to V, respectively. Here, p((α)/ t)(x, y) and p( HV/t)(x, y) denote, respectively, the heat kernels of the heat semigroups with infinitesimal generators given by (-Δ)(α/2) and HV = (-Δ)(α/2) + V. The former operator is known as the fractional Laplacian whereas the latter one is known as the fractional Schrödinger Operator. ^ The study …
Orderability And Rigidity In Contact Geometry, Peter Weigel
Orderability And Rigidity In Contact Geometry, Peter Weigel
Open Access Dissertations
We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold (&Sgr;, ξ = ker(α)). Previous results (see [1]) show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable (&Sgr;, α) with dim(&Sgr;) ≥ 7, there exists a Liouville-fillable contact structure ξ' on &Sgr; which admits no positive loop at all. Further, ξ' can be chosen to agree with ξ' on the complement of a Darboux ball. We then define a relative version of orderability for a Legendrian submanifold, and discuss the relationship between the two …
Permutohedra, Configuration Spaces And Spineless Cacti, Yongheng Zhang
Permutohedra, Configuration Spaces And Spineless Cacti, Yongheng Zhang
Open Access Dissertations
It has been known that the configuration space F(R2, n) of n distinct ordered points in R2 deformation retracts to a regular CW complex with n!permutohedra Pn as the top dimensional cells. In this paper, we show that there exists a similar but different permutohedral structure of the spaceCact(n) of spineless cacti with n lobes. Based on these structures, direct homotopy equivalences between F (R2, n) and Cact(n) are then given. It is well known that the little 2-discs space D2(n) is homotopy equivalent toF(R2, n). …
Uncertainty Quantification And Calibration Of Physical Models, Xian He
Uncertainty Quantification And Calibration Of Physical Models, Xian He
Open Access Dissertations
An ecosystem model is a representation of a real complex ecological system, and is usually described by sophisticated mathematical models. Terrestrial Ecosystem Model (TEM) is one of the ecosystem models, that describes the dynamics of car- bon, nitrogen, water and other vegetation related variables. There are uncertainties in the TEM which are attributed to inaccurate input data, insufficient knowledge of the parameters, inherent randomness and simplification of the physical model. Quantification of uncertainty of such an ecosystem model is computationally very heavy. Bayesian calibration method has been used as an efficient way to calibrate and quantify uncertainties of the computer …
Parallel Symmetric Eigenvalue Problem Solvers, Alicia Marie Klinvex
Parallel Symmetric Eigenvalue Problem Solvers, Alicia Marie Klinvex
Open Access Dissertations
Sparse symmetric eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and spectral reordering, for example. Often, the large size of these problems requires the development of eigensolvers that scale well on parallel computing platforms. In this dissertation, we describe two such eigensolvers, TraceMin and TraceMin-Davidson. These methods are different from many other eigensolvers in that they do not require accurate linear solves to be performed at each iteration in order to find the smallest eigenvalues and their associated eigenvectors. After introducing these closely related eigensolvers, we discuss alternative methods for solving the saddle point …
Investigating Synergy: Mathematical Models For The Coupled Dynamics Of Hiv And Hsv-2 And Other Endemic Diseases, Christina M Alvey
Investigating Synergy: Mathematical Models For The Coupled Dynamics Of Hiv And Hsv-2 And Other Endemic Diseases, Christina M Alvey
Open Access Dissertations
This dissertation presents epidemiological models that investigate synergy: synergy between HIV and HSV-2 or between humans and mosquitoes in a malaria study. Each of the three coupled disease models addresses different epidemiological questions with regard to gender or disease structure in the context of sexually-transmitted diseases (STDs), while the malaria model focuses on age-structure of the human population. ^ Mounting evidence indicates that HSV-2 infection may increase susceptibility to HIV infection and that co-infection may increase infectiousness. Accordingly, antiviral treatment of people with HSV-2 may mitigate the incidence of HIV in populations where both pathogens occur. To better understand the …
Applications Of Microlocal Analysis To Some Hyperbolic Inverse Problems, Andrew J Homan
Applications Of Microlocal Analysis To Some Hyperbolic Inverse Problems, Andrew J Homan
Open Access Dissertations
This thesis compiles my work on three inverse problems: ultrasound recovery in thermoacoustic tomography, cancellation of singularities in synthetic aperture radar, and the injectivity and stability of some generalized Radon transforms. Each problem is approached using microlocal methods. In the context of thermoacoustic tomography under the damped wave equation, I show uniqueness and stability of the problem with complete data, provide a reconstruction algorithm for small attenuation with complete data, and obtain stability estimates for visible singularities with partial data. The chapter on synthetic aperture radar constructs microlocally several infinite-dimensional families of ground reflectivity functions which appear microlocally regular when …
Functional Inequalities And The Curvature Dimension Inequality On Totally Geodesic Foliations, Bumsik Kim
Functional Inequalities And The Curvature Dimension Inequality On Totally Geodesic Foliations, Bumsik Kim
Open Access Dissertations
We discover following analytic / geometric properties on Riemannian foliations with bundle-like metric and totally geodesic leaves, or shortly, totally geodesic foliations. Under a certain curvature condition, we obtain (1) Sobolev-isoperimetric inequalities, global Poincar\'e inqualities, and a lower bound for Cheeger's isoperimetric constant, (2) Poincar\'e inequalities on balls and uniqueness of positive(or $L^p,p\geq 1$) solutions for the subelliptic heat equation, (3) A lower bound for the first non-zero eigenvalue of sub-Laplacians (Lichnerowicz theorem), and Obata's sphere theorem. In this context, the curvature condition is a sub-Riemannian analogue of lower bounds for Ricci curvature tensor. Earlier, it is given by Baudoin-Garofalo's …
A Pure-Jump Market-Making Model For High-Frequency Trading, Chi Wai Law
A Pure-Jump Market-Making Model For High-Frequency Trading, Chi Wai Law
Open Access Dissertations
We propose a new market-making model which incorporates a number of realistic features relevant for high-frequency trading. In particular, we model the dependency structure of prices and order arrivals with novel self- and cross-exciting point processes. Furthermore, instead of assuming the bid and ask prices can be adjusted continuously by the market maker, we formulate the market maker's decisions as an optimal switching problem. Moreover, the risk of overtrading has been taken into consideration by allowing each order to have different size, and the market maker can make use of market orders, which are treated as impulse control, to get …
G-Frobenius Manifolds, Byeongho Lee
G-Frobenius Manifolds, Byeongho Lee
Open Access Dissertations
The goal of this dissertation is to introduce the notion of G-Frobenius manifolds for any finite group G. This work is motivated by the fact that any G-Frobenius algebra yields an ordinary Frobenius algebra by taking its G-invariants. We generalize this on the level of Frobenius manifolds. To define a G-Frobenius manifold as a braided-commutative generalization of the ordinary commutative Frobenius manifold, we develop the theory of G-braided spaces. These are defined as G-graded G-modules with certain braided-commutative "rings of functions", generalizing the commutative rings of power series on ordinary vector spaces. As the genus zero part of any ordinary …
A P-Adic Spectral Triple, Sumedha Hemamalee Rathnayake
A P-Adic Spectral Triple, Sumedha Hemamalee Rathnayake
Open Access Dissertations
We construct a spectral triple for the C*-algebra of continuous functions on the space of p-adic integers. On the technical level we utilize a weighted rooted tree obtained from a coarse grained approximation of the space combined with the forward derivative D on the tree. Our spectral triple satisfies the properties of a compact spectral metric space and the metric on the space of p-adic integers induced by the spectral triple is equivalent to the usual p-adic metric. Furthermore, we show that the spectrum of the operator D*D is closely related to the roots of a certain …
Modeling, Optimization, And Sensitivity Analysis Of A Continuous Multi-Segment Crystallizer For Production Of Active Pharmaceutical Ingredients, Bradley James Ridder
Modeling, Optimization, And Sensitivity Analysis Of A Continuous Multi-Segment Crystallizer For Production Of Active Pharmaceutical Ingredients, Bradley James Ridder
Open Access Dissertations
We have investigated the simulation-based, steady-state optimization of a new type of crystallizer for the production of pharmaceuticals. The multi-segment, multi-addition plug-flow crystallizer (MSMA-PFC) offers better control over supersaturation in one dimension compared to a batch or stirred-tank crystallizer. Through use of a population balance framework, we have written the governing model equations of population balance and mass balance on the crystallizer segments. The solution of these equations was accomplished through either the method of moments or the finite volume method. The goal was to optimize the performance of the crystallizer with respect to certain quantities, such as maximizing the …
A 2-Categorical Extension Of The Reshetikhin--Turaev Theory, Yu Tsumara
A 2-Categorical Extension Of The Reshetikhin--Turaev Theory, Yu Tsumara
Open Access Dissertations
We concretely construct a 2-categorically extended topological quantum field theory that extends the Reshetikhin-Turaev TQFT to cobordisms with corners. The source category will be a well chosen 2-category of decorated cobordisms with corners and the target bicategory will be the Kapranov-Voevodsky 2-vector spaces.