UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item The differential geometry associated with a given area metric(1943) Wagner, Thomas Charles Gordon; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item Theorems on stability and convergence in numerical solutions of partial differential equations(1951) O'Brien, George Gerald; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item On the structure of locally connected plane continua on which it is possible to define a pointwise periodic homeomorphism which is not almost periodic(1950) Haywood, Stuart Troy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item Hyperconformal transformations(1937) Alrich, George Frederick; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item An arc problem(1951) Boyer, Jean Marie; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item Infinite processes in Greek mathematics(1943) Vedova, George Clarence; Digital Repository at the University of Maryland; University of Maryland (College Park, Md)Item An Exposition of Stochastic Integrals and Their Application to Linearization Coefficients(2009) Kuykendall, John Bynum; Slud, Eric V; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Stochastic integration is introduced as a tool to address the problem of finding linearization coefficients. Stochastic, off-diagonal integration against a random spectral measure is defined and its properties discussed, followed by a proof that two formulations of Ito's Lemma are equivalent. Diagonals in R<\bold>n<\super> are defined, and their relationship to partitions of {1, ..., n} is discussed. The intuitive notion of a stochastic integral along a diagonal is formalized and calculated. The relationship between partitions and diagonals is then exploited to apply Moebius inversion to stochastic integrals over different diagonals. Diagonals along which stochastic integrals may be nonzero with positive probability are shown to correspond uniquely to diagrams. This correspondence is used to prove the Diagram Formula. Ito's Lemma and the Diagram Formula are then combined to calculate the linearization coefficients for Hermite Polynomials. Finally, future work is suggested that may allow other families of linearization coefficients to be calculated.Item Regularized Variable Selection in Proportional Hazards Model Using Area under Receiver Operating Characteristic Curve Criterion(2009) Wang, Wen-Chyi; Yang, Grace L; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The goal of this thesis is to develop a statistical procedure for selecting pertinent predictors among a number of covariates to accurately predict the survival time of a patient. There are available many variable selection procedures in the literature. This thesis is focused on a more recently developed “regularized variable selection procedure”. This procedure, based on a penalized likelihood, can simultaneously address the problem of variable selection and variable estimation which previous procedures lack. Specifically, this thesis studies regularized variable selection procedure in the proportional hazards model for censored survival data. Implementation of the procedure requires judicious determination of the amount of penalty, a regularization parameter λ, on the likelihood and the development of computational intensive algorithms. In this thesis, a new criterion of determining λ using the notion of “the area under the receiver operating characteristic curve (AUC)” is proposed. The conventional generalized cross-validation criterion (GCV) is based on the likelihood and its second derivative. Unlike GCV, the AUC criterion is based on the performance of disease classification in terms of patients' survival times. Simulations show that performance of the AUC and the GCV criteria are similar. But the AUC criterion gives a better interpretation of the survival data. We also establish the consistency and asymptotic normality of the regularized estimators of parameters in the partial likelihood of proportional hazards model. Some oracle properties of the regularized estimators are discussed under certain sparsity conditions. An algorithm for selecting λ and computing regularized estimates is developed. The developed procedure is then illustrated with an application to the survival data of patients who have cancers in head and neck. The results show that the proposed method is comparable with the conventional one.Item Abundance of escaping orbitsin a family of anti-integrable limitsof the standard map(2009) De Simoi, Jacopo; Dolgopyat, Dmitry; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We give quantitative results about the abundance of escaping orbits in a family of exact twist maps preserving Lebesgue measure on the cylinder T × R; geometrical features of maps of this family are quite similar to those of the well-known Chirikov-Taylor standard map, and in fact we believe that the techniques presented in this work can be further improved and eventually applied to studying ergodic properties of the standard map itself. We state conditions which assure that escaping orbits exist and form a full Hausdorff dimension set. Moreover, under stronger conditions we can prove that such orbits are not charged by the invariant measure. We also obtain prove that, generically, the system presents elliptic islands at arbitrarily high values of the action variable and provide estimates for their total measure.Item OPTIMAL APPROXIMATION SPACES FOR SOLVING PROBLEMS WITH ROUGH COEFFICIENTS(2009) Li, Qiaoluan Helen; Osborn, John E.; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The finite element method has been widely used to solve partial differential equations by both engineers and mathematicians for the last several decades. This is due to its well-known effectiveness when applied to a wide variety of problems. However, it has some practical drawbacks. One of them is the need for meshing. Another is that it uses polynomials as the approximation basis functions. Commonly, polynomials are also used by other numerical methods for partial differential equations, such as the finite difference method and the spectral method. Nevertheless, polynomial approximations are not always effective, especially for problems with rough coefficients. In the dissertation, a suitable approximation space for the solution of elliptic problems with rough coefficients has been found, which is named as generalized L-spline space. Theoretically, I have developed generalized L-spline approximation spaces, where L is an operator of order m with rough coefficients, have proved the interpolation error estimate, and have also proved that the generalized L-spline space is an optimal approximation space for the problem L*Lu=f with certain operator L, by using n-widths as the criteria. Numerically, two problems have been tested and the relevant error estimate results are consistent with the shown theoretical results. Meshless methods are newly developed numerical methods for solving partial differential equations. These methods partially eliminate the need of meshing. Meshless methods are considered to have great potential. However, the need for effective quadrature schemes is a major issue concerning meshless methods. In our recently published paper, we consider the approximation of the Neumann problem by meshless methods, and show that the approximation is inaccurate if nothing special (beyond accuracy) is assumed about the numerical integration. We then identify a condition - referred to as the zero row sum condition. This, together with accuracy, ensure the quadrature error is small. The row sum condition can be achieved by changing the diagonal elements of the stiffness matrix. Under row sum condition we derive an energy norm error estimate for the numerical solution with quadrature. In the dissertation, meshless methods are discussed and quadrature issue is explained. Two numerical experiments are presented in details. Both theoretical and numerical results indicate that the error has two components; one due to the meshless methods approximation and the other due to quadrature.