Mathematics: Recent submissions
Now showing items 41-60 of 462
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Normal and paracompact spaces and their products
(University of Kansas, 1962-08-31) -
History of the Department of Mathematics of the University of Kansas, 1886-1970
(University of Kansas, Kansas University Endowment Association, 1976)Francis Huntington Snow, in 1866, was the first member of the faculty to teach mathematics in The University of Kansas. From this auspicious beginning, mathematics developed into one of the major departments in the University; ... -
Serre's Condition and Depth of Stanley-Reisner Rings
(University of Kansas, 2018-12-31)The aim of this work is to garner a deeper understanding of the relationship between depth of a ring and connectivity properties of the spectrum of that ring. We examine with particular interest the case where our ring is ... -
Decompositions of Simplicial Complexes
(University of Kansas, 2018-08-31)In this thesis we study the interplay between various combinatorial, algebraic, and topological properties of simplicial complexes. We focus on when these properties imply the existence of decompositions of the face poset. ... -
Analytical studies of standing waves in three NLS models
(University of Kansas, 2018-08-31)In this work, we present analytical studies of standing waves in three NLS models. We first consider the spectral stability of ground states of fourth order semi-linear Schrödinger and Klein-Gordon equations and semi-linear ... -
Parameter estimation for stochastic differential equations driven by fractional Brownian motion
(University of Kansas, 2018-05-31)This dissertation systematically considers the inference problem for stochastic differential equations (SDE) driven by fractional Brownian motion. For the volatility parameter and Hurst parameter, the estimators are ... -
Limit distributions for functionals of Gaussian processes
(University of Kansas, 2018-05-31)This thesis is devoted to the study of the convergence in distribution of functionals of Gaussian processes. Most of the problems that we present are addressed by using an approach based on Malliavin calculus techniques. ... -
Stability of Periodic Waves in Nonlocal Dispersive Equations
(University of Kansas, 2018-05-31)In this work consisting of joint projects with my advisor, Dr. Mathew Johnson, we study the existence and stability of periodic waves in equations that possess nonlocal dispersion, i.e. equations in which the dispersion ... -
Regularity of Stochastic Burgers’-Type Equations
(University of Kansas, 2018-05-31)In classical partial differential equations (PDEs), it is well known that the solution to Burgers' equation in one spatial dimension with positive viscosity can be solved by the so called Hopf-Cole transformation, which ... -
Optimal Time-Dependent Lower Bound On Density For Classical Solutions of 1-D Compressible Euler Equations
(Indiana University Mathematics Journal, 2017)For the compressible Euler equations, even when the initial data are uniformly away from vacuum, solution can approach vacuum in infinite time. Achieving sharp lower bounds of density is crucial in the study of Euler ... -
Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability
(Society for Industrial and Applied Mathematics, 2017)We construct various periodic traveling wave solutions of the Ostrovsky/Hunter--Saxton/short pulse equation and its KdV regularized version. For the regularized short pulse model with small Coriolis parameter, we describe ... -
Contributions to the theory of functions of a bicomplex variable
(University of Kansas, 1952) -
Accounting for Model Error from Unresolved Scales in Ensemble Kalman Filters by Stochastic Parameterization
(American Meteorological Society, 2017-08-23)The use of discrete-time stochastic parameterization to account for model error due to unresolved scales in ensemble Kalman filters is investigated by numerical experiments. The parameterization quantifies the model error ... -
Noncentral limit theorem for the generalized Rosenblatt process
(Institute of Mathematical Statistics, 2017)We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Rosenblatt processes Zγ with kernels defined by parameters γ taking values in a tetrahedral region Δ of $\RR^q$. We prove ... -
The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals
(Institute of Mathematical Statistics, 2017)The aim of this paper is to show an estimate for the determinant of the covariance of a two-dimensional vector of multiple stochastic integrals of the same order in terms of a linear combination of the expectation of the ... -
Formation enthalpies for transition metal alloys using machine learning
(Formation enthalpies for transition metal alloys using machine learning, 2017-06)The enthalpy of formation is an important thermodynamic property. Developing fast and accurate methods for its prediction is of practical interest in a variety of applications. Material informatics techniques based on ... -
Oscillation estimates of eigenfunctions via the combinatorics of noncrossing partitions
(Diamond Open Access Journals, 2017-09)We study oscillations in the eigenfunctions for a fractional Schrödinger operator on the real line. An argument in the spirit of Courant's nodal domain theorem applies to an associated local problem in the upper half plane ... -
Riemannian Geometry on Some Noncommutative Spaces
(University of Kansas, 2017-12-31)This dissertation enquires into how the theory and mechanism of Riemannian geometry can be introduced into and integrated with the existent ones in noncommutative geometry, a branch of mathematics inspired by the development ... -
Balancing domain decomposition by constraints algorithms for incompressible Stokes equations with nonconforming finite element discretizations
(University of Kansas, 2017-12-31)Hybridizable Discontinuous Galerkin (HDG) is an important family of methods, which combine the advantages of both Discontinuous Galerkin in terms of flexibility and standard finite elements in terms of accuracy and efficiency. ... -
A Comparison of Some Dimension Reduction Techniques with Varied Parameters
(University of Kansas, 2017-13-31)This paper presents and explains several methods of dimensionality reduction of data sets, beginning with the well known PCA and moving onto techniques that deal with data on a nonlinear manifold. Methods for handling data ...