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Full-Text Articles in Physical Sciences and Mathematics
Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao
Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao
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In this dissertation, we address several research problems in statistical inference. We obtain results in the following four directions: linear model selection, minimax estimation of linear functionals, Bayes type estimators for the survival functions based on right censored data, and estimation of survival functions based on doubly censored data.
Automorphic Decompositions Of Graphs, Robert Beeler
Automorphic Decompositions Of Graphs, Robert Beeler
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Let G and H be graphs. A G-decomposition D of a graph H is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. It is well known that a graceful labelling (or more generally a rho-valuation) of a graph G induces a cyclic G-decomposition of a complete graph. We will extend these notions to that of a general valuation in a cyclic group. Such valuations yield decompositions of circulant graphs. We will show that every graph has a valuation and hence is a …
Planning, Scheduling, And Timetabling In A University Setting, Christine Kraft
Planning, Scheduling, And Timetabling In A University Setting, Christine Kraft
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Methods and procedures for modeling university student populations, predicting course enrollment, allocating course seats, and timetabling final examinations are studied and proposed. The university enrollment model presented uses a multi-dimensional state space based on student demographics and the Markov property, rather than longitudinal data to model student movement. The procedure for creating adaptive course prediction models uses student characteristics to identify groups of undergraduates whose specific course enrollment rates are significantly different than the rest of the university population. Historical enrollment rates and current semester information complete the model for predicting enrollment for the coming semester. The course prediction model …
Numerical Approximation Of Shear-Thinning And Johnson-Segalman Viscoelastic Fluid Flows, Jason Howell
Numerical Approximation Of Shear-Thinning And Johnson-Segalman Viscoelastic Fluid Flows, Jason Howell
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In this work computational approaches to the numerical simulation of steady-state viscoelastic fluid flow are investigated. In particular, two aspects of computing viscoelastic flows are of interest: 1) the stable computation of high Weissenberg number Johnson-Segalman fluids and 2) low-order approaches to simulating the flow of fluids obeying a power law constitutive model.
The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. For the nonlinear Johnson-Segalman constitutive model, defect-correction and continuation methods are examined …
Permutation Decoding Of Codes From Graphs And Designs, Padmapani Seneviratne
Permutation Decoding Of Codes From Graphs And Designs, Padmapani Seneviratne
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Permutation decoding is a technique, developed by Jessie McWilliams in 1960's. It involves finding a set of automorphisms of the code, called a PD-set. If such a set exists and if the generator matrix of the code is in standard form then a simple algorithm using this set can be followed to correct the maximum number of errors of which the code is capable. Primarily this method was used originally on cyclic codes and Golay codes.
In this dissertation we study binary codes formed from an adjacency matrix of some classes of graphs and apply the permutation decoding method to …
Estimates Related To The Arithmetic Of Elliptic Curves, Bryan Faulkner
Estimates Related To The Arithmetic Of Elliptic Curves, Bryan Faulkner
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This dissertation presents results related to two problems in the arithmetic of elliptic curves.
Feng and Xiong equate the nontriviality of the Selmer groups associated with congruent number curves to the presence of certain types of partitions of graphs associated with the prime factorization of n. The triviality of the Selmer groups associated to the congruent number curve implies that the curve has rank zero which in turn implies n is noncongruent. We extend the ideas of Feng and Xiong in order to compute the Selmer groups of congruent number curves.
We prove an average version of a generalization of …
Equitable Efficiency In Multiple Criteria Optimization, Vijay Singh
Equitable Efficiency In Multiple Criteria Optimization, Vijay Singh
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Equitable efficiency in multiple criteria optimization was introduced mathematically in the middle of nineteen-nineties. The concept tends to strengthen the notion of Pareto efficiency by imposing additional conditions on the preference
structure defining the Pareto preference. It is especially designed to solve multiple criteria problems having commensurate criteria where different criteria values can be compared directly.
In this dissertation we study some theoretical and practical aspects of equitably efficient solutions. The literature on equitable efficiency is not very extensive and provides very limited number of ways of generating such solutions. After introducing
some relevant notations, we develop some scalarization based …
Random Vectors Over Finite Fields, Shannon Lockard
Random Vectors Over Finite Fields, Shannon Lockard
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The study of random objects is a useful one in many applications and areas of mathematics. The Probabilistic Method, introduced by Paul Erdos and his many collaborators, was first used to study the behavior of random graphs and later to study properties of random objects. It has developed as a powerful tool in combinatorics as well as finding applications in linear algebra, number theory, and many other areas. In this dissertation, we will consider random vectors, in particular, dependency among random vectors. We will randomly choose vectors according to a specified probability distribution. We wish to determine how many vectors …