Mathematics Scholarly Works
Browse by
Recent Submissions

Unique Factorization Domains in Commutative Algebra
(Department of Mathematics, University of Kansas, 20210520)In this project, we learn about unique factorization domains in commutative algebra. Most importantly, we explore the relation between unique factorization domains and regular local rings, and prove the main theorem: If R ... 
Initialboundary value problems for a reactiondiffusion equation
(American Institute of Physics, 20190827)A novel approach that utilizes Fokas’s unified transform is employed for studying a reactiondiffusion equation with power nonlinearity formulated either on the halfline or on a finite interval with data in Sobolev spaces. ... 
On the Generation of Stable Kerr Frequency Combs in the LugiatoLefever Model of Periodic Optical Waveguides
(Society for Industrial and Applied Mathematics, 20190307) 
The Kortewegde Vries equation on an interval
(American Institute of Physics, 20190508)The initialboundary value problem (IBVP) for the Kortewegde Vries (KdV) equation on an interval is studied by extending a novel approach recently developed for the wellposedness of the KdV on the halfline, which is ... 
Finitary isomorphisms of Poisson point processes
(Institute of Mathematical Statistics, 20191022)As part of a general theory for the isomorphism problem for actions of amenable groups, Ornstein and Weiss (J. Anal. Math. 48 (1987) 1–141) proved that any two Poisson point processes are isomorphic as measurepreserving ... 
A weighted cellular matrixtree theorem, with applications to complete colorful and cubical complexes
(Elsevier, 20180326)We present a version of the weighted cellular matrixtree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply ... 
Counting arithmetical structures on paths and cycles
(Elsevier, 20180727)Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag(d)A)r = 0, where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical ... 
Increasing spanning forests in graphs and simplicial complexes
(Elsevier, 20181101)Let G be a graph with vertex set {1,...,n}. A spanning forest F of G is increasing if the sequence of labels on any path starting at the minimum vertex of a tree of F forms an increasing sequence. Hallam and Sagan showed ... 
A positivity phenomenon in Elser's Gaussiancluster percolation model
(Elsevier, 20201218)Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideration of numerical graph invariants which we ... 
Enumerating Parking Completions Using Join and Split
(Electronic Journal of Combinatorics, 20200612)Given a strictly increasing sequence t with entries from [n] := {1, . . . , n}, a parking completion is a sequence c with t + c = n and {t ∈ t  t 6 i} + {c ∈ c  c 6 i} > i for all i in [n]. We can think of t as ... 
Interval parking functions
(Elsevier, 20201116)Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair (a, ... 
Asymptoticlp Banach Spaces and the Property of Lebesgue
(20200615)The primary contribution of this work is to nearly characterize the Property of Lebesgue for Banach spaces that behave in a global asymptotic sense like lp. This generalizes a number of individual results that are collected ... 
PLANETARY ORBITS IN CONSTANT CURVATURE PLANES
(University of Kansas, 20191109)A law of gravitation is defined and justified for constant curvature planes and it is demonstrated that Kepler’s three laws of planetary motion have natural analogs in this new context. 
MASS IN HYPERBOLIC 3SPACE
(University of Kansas, 20190113)Contents: 1. A hyperbolic Theorem of Pappus. 2. A hyperbolic version of Newton’s Theorem that the center of gravity and the center of mass of the uniform sphere are identical. 3. A hyperbolic version of the ... 
MASS IN THE HYPERBOLIC PLANE
(University of Kansas, 20190217)Archimedes computed the center of mass of several regions and bodies [Dijksterhuis], and this fundamental physical notion may very well be due to him. He based his investigations of this concept on the notion of moment ... 
MASS IN HYPERBOLIC GEOMETRY
(University of Kansas, 20080313)Archimedes computed the center of mass of several regions and solid bodies [Dijksterhuis], and this fundamental physical notion may very well be due to him. He based his investigations of this concept on the notion of ... 
HYPERBOLIC CENTROIDS OF SOME REGIONS
(University of Kansas, 20060117)Explicit expressions for the centroids of hyperbolic pie shapes and isosce les triangles are found and compared to their Euclidean analogs. 
Large Deviations for Stochastic Heat Equation with Rough Dependence in Space
(Bernoulli Society, 20170727)In this paper we establish a large deviation principle for the nonlinear one dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian ... 
History of the Department of Mathematics of the University of Kansas, 18861970
(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; ... 
Optimal TimeDependent Lower Bound On Density For Classical Solutions of 1D 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 ...