Analysis Commons^™

On A Paley-Wiener Theorem For The Zs-Akns Scattering Transform, Ryan D. Walker

Theses and Dissertations--Mathematics

In this thesis, we establish an analog of the Paley-Wiener Theorem for the ZS-AKNS scattering transform on a set of real potentials. We also demonstrate one application of our techniques to the study of an inverse spectral problem for a half-line Miura potential Schroedinger equation.

Analyzing And Solving Non-Linear Stochastic Dynamic Models On Non-Periodic Discrete Time Domains, Gang Cheng

Masters Theses & Specialist Projects

Stochastic dynamic programming is a recursive method for solving sequential or multistage decision problems. It helps economists and mathematicians construct and solve a huge variety of sequential decision making problems in stochastic cases. Research on stochastic dynamic programming is important and meaningful because stochastic dynamic programming reflects the behavior of the decision maker without risk aversion; i.e., decision making under uncertainty. In the solution process, it is extremely difficult to represent the existing or future state precisely since uncertainty is a state of having limited knowledge. Indeed, compared to the deterministic case, which is decision making under certainty, the ...

Regularity For Solutions To Parabolic Systems And Nonlocal Minimization Problems, Joe Geisbauer

Dissertations, Theses, and Student Research Papers in Mathematics

The goal of this dissertation is to contribute to both the nonlocal and local settings of regularity within the calculus of variations. We provide analogues of higher differentiability results in the context of Besov spaces for minimizers of nonlocal functionals. We also establish the Holder continuity of solutions to a system of parabolic partial differential equations.

Advisor: Mikil Foss

A Convexity Theorem For Symplectomorphism Groups, Seyed Mehdi Mousavi

Electronic Thesis and Dissertation Repository

In this thesis we study the existence of an infinite-dimensional analog of maximal torus in the symplectomorphism groups of toric manifolds. We also prove an infinite-dimensional version of Schur-Horn-Kostant convexity theorem. These results are extensions of the results of Bao-Raiu, Elhadrami, Bloch-Flachka-Ratiu and Bloch-El Hadrami-Flaschka-Raiu.

Math Moment, Paige S. Orland

Journal of Humanistic Mathematics

A short poem comparing Exponential and Logistic functions.

An Analysis Of Nonlocal Boundary Value Problems Of Fractional And Integer Order, Christopher Steven Goodrich

Dissertations, Theses, and Student Research Papers in Mathematics

In this work we provide an analysis of both fractional- and integer-order boundary value problems, certain of which contain explicit nonlocal terms. In the discrete fractional case we consider several different types of boundary value problems including the well-known right-focal problem. Attendant to our analysis of discrete fractional boundary value problems, we also provide an analysis of the continuity properties of solutions to discrete fractional initial value problems. Finally, we conclude by providing new techniques for analyzing integer-order nonlocal boundary value problems.

Adviser: Lynn Erbe and Allan Peterson

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Dissertations, Theses, and Student Research Papers in Mathematics

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to changes ...

Complex Absorbing Potential Method For Dirac Operators. Clusters Of Resonances, Jimmy Kungsman, Michael Melgaard

Articles

For both nonrelativistic and relativistic Hamiltonians, the Complex Absorbing Potential (CAP) method has been applied extensively to calculate resonances in Physics and Chemistry. We study clusters of resonances for the perturbed Dirac operator near the real axis and, in the semiclassical limit, we establish the CAP method rigorously by showing that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa.