RSS 1.0Mathematics electronic theses and dissertations (MU)
The items in this collection are the theses and dissertations written by students of the Department of Mathematics. Some items may be viewed only by members of the University of Missouri System and/or University of Missouri-Columbia. Click on one of the browse buttons above for a complete listing of the works.
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Recent Submissions
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Quasilinear elliptic equations with sub-natural growth aand nonlinar potentials
(University of Missouri--Columbia, 2015)Necessary and sufficient conditions for the existence of finite energy and weak solutions are given. Sharp global pointwise estimates of solutions are obtained as well. We also discuss the uniqueness and regularity properties ... -
Frames and applications: distribution of frame coeficients, integer frames and phase retrieval
(University of Missouri--Columbia, 2015)The present dissertation is divided into two main areas: frame theoretic results and applications of frames. In particular, the beginning half develops the first detailed theory of the distribution of frame coefficients. ... -
Trace/extension operators in rough domains and applications to partial differential equations
(University of Missouri--Columbia, 2015)Trace and extension theory lay the foundation for solving a plethora of boundary value problems. In developing this theory, one typically needs well-behaved extension operators from a specified domain to the entire Euclidean ... -
Topics in geometric analysis and harmonic analysis on spaces of homogeneous type
(University of Missouri--Columbia, 2015)The present dissertation consists of three main parts. One theme underscoring the work carried out in this dissertation concerns the relationship between analysis and geometry. As a first illustration of the interplay ... -
Age-dependent Branching Processes and Applications to the Luria-Delbrck Experiment
(University of Missouri--Columbia, 2015)Microbial populations adapt to their environment by acquiring advantageous mutations, but in the early twentieth century, questions about how these organisms acquire mutations arose. The experiment of Salvador Luria and ... -
Counterexamples to Strichartz Type Inequalities
(University of Missouri--Columbia, 2013)The study of Strichartz s inequality is very important in the theory of nonlinear Shrodinger equations. The inequalities do not hold for all choice of constants. Many cases were settled. for instance, some cases were settled ... -
Quasi-Metric Geometry
([University of Missouri--Columbia], 2014) -
Expectation of p-norm of random matrices with heavy tails
([University of Missouri--Columbia], 2014)The p-norm (p > 2) of a random matrix whose entries are gaussian, subgaussian and log concave have been studied previously. We conjecture the following generalization of the above results for heavy tailed random matrices: ... -
On unimodality of Hilbert functions of Artinian level algebras of codimension 3 and type 2 and 3
([University of Missouri--Columbia], 2014)We prove the unimodality of the Hilbert Function for some classes of codimension three graded algebras of Cohen-Macaulay types 2 and 3. The method of proof uses the explicit structure theorems similar to the structure ... -
Results on the Collatz Conjecture
([University of Missouri--Columbia], 2014)Given a starting value, we can create a sequence using the rule that if the previous number, x, is even, then the next number is [x/2], and if the previous number, x, is odd, then the next number is [(3x+1)/2]. The collatz ... -
Generating sequences of valuations and applications
([University of Missouri--Columbia], 2014) -
Irrational behavior of algebraic discrete valuations
([University of Missouri--Columbia], 2014)We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities ... -
Lorentzian warped products and static space-times
(University of Missouri--Columbia, 1985) -
A vector treatment of the projective properties of plane curves
(University of Missouri, 1916) -
Limit of many molecules dynamics with rigorous macroscopic results
(University of Missouri--Columbia, 2013)The thesis builds on recent ideas that combine work by C.B. Morrey (1955) and D.W. Jepsen & D. ter Haar (1962) with more recent analytic techniques: measure disintegration, PDEs for measures, etc. (M.I. Vishik & A.V. ... -
Stability estimates for semigroups and partly parabolic reaction diffusion equations
(University of Missouri--Columbia, 2013)The purpose of my dissertation is the application of the methods of abstract theory of strongly continuous operator semigroups (and of evolution semigroups in particular) to study of the spectral properties of a class of ... -
Frames and projections
(University of Missouri--Columbia, 2013)In this dissertation we explore several ways in which the concept of projections arise infinite frame theory. In the first chapter we show that the Paulsen problem from frame theory is equivalent to a long standing open ... -
Groupoids and semigroupoids
(University of Missouri--Columbia, 2013)The theory of semigroupoids and groupoids makes the transition between arbitrary sets and groups. The usefulness of developing theory stems from various applications where a group structure is lacking, yet there exists ... -
Stochastically perturbed Navier-Stokes system on the rotating sphere
(University of Missouri--Columbia, 2013)We show the existence and uniqueness of an invariant measure for the kick-forced Navier-Stokes system on the 2-dimensional sphere, first without deterministic force and then with a time-independent deterministic force. The ... -
Fusion frame constructions and frame partitions
(University of Missouri--Columbia, 2013)Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Despite ...