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  • An adaptive spot placement method on Cartesian grid for pencil beam scanning proton therapy 

    Lin, Bowen; Fu, Shujun; Lin, Yuting; Rotondo, Ronny L.; Huang, Weizhang; Li, Harold H.; Chen, Ronald C.; Gao, Hao (IOP Publishing, 2021-12-02)
    Pencil beam scanning proton radiotherapy (RT) offers flexible proton spot placement near treatment targets for delivering tumoricidal radiation dose to tumor targets while sparing organs-at-risk. Currently the spot placement ...
  • Unique Factorization Domains in Commutative Algebra 

    Huang, Yongjian (Department of Mathematics, University of Kansas, 2021-05-20)
    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 ...
  • Initial-boundary value problems for a reaction-diffusion equation 

    Himonas, A. Alexandrou; Mantzavinos, Dionyssios; Yan, Fangchi (American Institute of Physics, 2019-08-27)
    A novel approach that utilizes Fokas’s unified transform is employed for studying a reaction-diffusion equation with power nonlinearity formulated either on the half-line or on a finite interval with data in Sobolev spaces. ...
  • A General Stochastic Volatility Model on VIX Options 

    Cui, Yanhao (University of Kansas, 2019-12-31)
    Abstract In this dissertation, we study a general stochastic volatility model for the VIX options (Chicago Board Options Exchange) volatility index, which is a stochastic differential equation with 8 unknown parameters. ...
  • On the Generation of Stable Kerr Frequency Combs in the Lugiato--Lefever Model of Periodic Optical Waveguides 

    Hakkaev, Sevdzhan; Stanislavova, Milena; Stefanov, Atanas G. (Society for Industrial and Applied Mathematics, 2019-03-07)
  • The Korteweg-de Vries equation on an interval 

    Himonas, A. Alexandrou; Mantzavinos, Dionyssios; Yan, Fangchi (American Institute of Physics, 2019-05-08)
    The initial-boundary value problem (IBVP) for the Korteweg-de Vries (KdV) equation on an interval is studied by extending a novel approach recently developed for the well-posedness of the KdV on the half-line, which is ...
  • Finitary isomorphisms of Poisson point processes 

    Soo, Terry; Wilkens, Amanda (Institute of Mathematical Statistics, 2019-10-22)
    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 measure-preserving ...
  • A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes 

    Aalipour, Ghodratollah; Duval, Art M.; Kook, Woong; Lee, Kang-Ju; Martin, Jeremy L. (Elsevier, 2018-03-26)
    We present a version of the weighted cellular matrix-tree 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 

    Braun, Benjamin; Corrales, Hugo; Corry, Scott; Puente, Luis David García; Glass, Darren; Kaplan, Nathan; Martin, Jeremy L.; Musiker, Gregg; Valencia, Carlos E. (Elsevier, 2018-07-27)
    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 

    Hallam, Joshua; Martin, Jeremy L.; Sagan, Bruce E. (Elsevier, 2018-11-01)
    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 Gaussian-cluster percolation model 

    Dorpalen-Barry, Galen; Hettle, Cyrus; Livingston, David C.; Martin, Jeremy L.; Nasr, George D.; Vega, Julianne; Whitlatch, Hays (Elsevier, 2020-12-18)
    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 

    Adeniran, Ayomikun; Butler, Steve; Dorpalen-Barry, Galen; Harris, Pamela E.; Hettle, Cyrus; Liang, Qingzhong; Martin, Jeremy L.; Nam, Hayan (Electronic Journal of Combinatorics, 2020-06-12)
    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 ...
  • Optimal Energy Decay for the Damped Klein-Gordon Equation 

    Malhi, Satbir Singh (University of Kansas, 2019-08-31)
    In this dissertation we study the long time dynamics of damped Klein-Gordon and damped fractional Klein-Gordon equations using $C_0$- Semigroup theory and its application. The $C_0$-semigroups are used to solve a large ...
  • Sharp time asymptotics for the quasi-geostrophic equation, the Boussinesq system and near plane waves of reaction-diffusion models 

    Hadadifard, Fazel (University of Kansas, 2019-5-31)
    Through this dissertation we present the sharp time decay rates for three equations, namely quasi--geostrophic equation (SQG), Boussinesq system (BSQ) and plane wave of general reaction-diffusion models. In addition, in ...
  • Interval parking functions 

    Colaric, Emma; DeMuse, Ryan; Martin, Jeremy L.; Yin, Mei (Elsevier, 2020-11-16)
    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, ...
  • A canonical form for the differential equations of curves in n-dimensional space 

    Smith, Ronald Gibson (University of Kansas, 1930-05-31)
  • Normal determinants and expansions in modified sequences 

    Larkin, James Richard (University of Kansas, 1952-05-31)
  • Asymptotic-lp Banach Spaces and the Property of Lebesgue 

    Gaebler, Harrison (2020-06-15)
    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 ...
  • Efficient Tunnel Detection with Waveform Inversion of Back-scattered Surface Waves 

    Wang, Yao (University of Kansas, 2019-05-31)
    An efficient subsurface imaging method employing back-scattered surface waves is developed to detect near-surface underground elastic-wave velocity anomalies, such as tunnels, sinkholes, fractures, faults, and abandoned ...

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