Search results
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Title
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Goodness-of-Fit Tests Under Permutations
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Author
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Chen, Chen
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Date Created
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2019
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Subjects--Topical
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Statistics, Mathematics, Information science
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Description
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Several new goodness-of-fit tests are proposed on countable alphabets, where certain fundamental statistical concepts associated with random variables, such as cumulative distribution functions, characteristic functions and moments, may not exist....
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Title
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Inverse source problems for elliptic and parabolic equations
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Author
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Li, Qitong
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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In this dissertation, we solve two inverse problems. The first one is the inverse source problem for the Helmholtz equation that governs the wave propagating in anisotropic media. The second one is to recover the initial condition for parabolic eq...
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Title
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Neumann functions and image systems of the Laplacian in the spheroidal geometry
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Author
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Edmiston, Robert
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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We apply the method of image charges from electrostatics to the study of the Neumannfunction for the Laplace operator, equivalent to the Green's function with a Neumannboundary condition imposed. Such an analysis has previously been given for the ...
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Title
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Number Rings and Dedekind Domains
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Author
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Harrison, Mary
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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In this paper, we study number rings and their factorization properties. We begin with an introduction to number fields and number rings. Then we consider the ring Z[i], which is a unique factorization domain, where each element factors uniquely i...
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Title
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ON THE DISCRETE SPECTRUM OF EXTERIOR ELLIPTIC PROBLEMS.
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Author
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Puri, Rajan
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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In this dissertation, we present three new results in the exterior elliptic problems with the variable coefficients that describe the process in inhomogeneous media in the presence of obstacles. These results concern perturbations of the operator ...
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Title
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On the spectral theory of 1-D Schrodinger operator with random sparse potentials
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Author
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Cook, Thomas
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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The goal of this dissertation is to develop a spectral theory for the Schr\"odinger operator with sparse random potential. To do this, we will first reformulate theories for sparse deterministic potentials. This includes a general development of t...
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Title
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Population Dynamics with Immigration
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Author
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Han, Dan
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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The paper contains the complete analysis of the Galton-Watson models with immigration, including the processes in the random environment, stationary or nonstationary ones. We also study the branching random walk on Zd with immigration and prove th...
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Title
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Quantification of Profile Measurement Data
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Author
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Javidpour, Farid
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Date Created
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2019
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Subjects--Topical
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Mechanical engineering, Mathematics, Civil engineering
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Description
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Parts with complicated freeform shapes have been attracting more attention in industrial applications in recent decades. In most systems, the functional performance of these parts is directly related to the conformity of their profile with the des...
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Title
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SCHWARZ METHODS FOR FOURTH-ORDER PROBLEMS CONTAINING SINGULARITIES
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Author
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Palta, Birce
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Date Created
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2019
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Subjects--Topical
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Mathematics
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Description
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We develop numerical methods for analysis of fourth-order partial differential equations on domains with angular corners. For the finite element analysis of fourth-order partial differential equations, we have to use smoother basis functions whose...
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Title
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SOLUTION OF A 1-D INVERSE PROBLEM BY THE CONVEXIFICATION METHOD
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Author
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Abney, Ray
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Date Created
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2019
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Subjects--Topical
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Mathematics, Physics
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Description
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In this thesis, we demonstrate a method outlined by Dr. Mikhail Klibanov for solving a 1-D coefficient inverse problem by the convexification method. Our inverse problem in question concerns finding buried bombs, where the dielectric constants of ...
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Title
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Understanding the Probability Literacy of High School Students
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Author
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Coon, Fred
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Date Created
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2019
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Subjects--Topical
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Mathematics--Study and teaching, Education, Mathematics
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Description
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This multi-case study examined high school students’ probability literacy, with focus on randomness, independence, and sample space. Task-based interviews were used with ten high school students. A Levels of Understanding Matrix (LUM), that was cr...