Now showing items 35-42 of 42

• #### Similarity of blocks in parabolic category O and a wonderful correspondence for modules of covariants. ﻿

(2018-07-13)
Let (g,k) be the pair of complexified Lie algebras corresponding to an irreducible Hermitian symmetric space of noncompact type. Then we have an associated triangular decomposition g = p− ⊕ k ⊕ p+, and q = k ⊕ p+ is a ...
• #### Solving degenerate stochastic Kawarada partial differential equations via adaptive splitting methods. ﻿

(2017-07-08)
In this dissertation, we explore and analyze highly effective and efficient computational procedures for solving a class of nonlinear and stochastic partial differential equations. We are particularly interested in ...
• #### Spectral functions for generalized piston configurations. ﻿

(, 2012-11-29)
In this work we explore various piston configurations with different types of potentials. We analyze Laplace-type operators P=-g^ij ∇^E_i ∇ ^E_j+V where V is the potential. First we study delta potentials and rectangular ...
• #### Spectral properties of quantum graphs with symmetry. ﻿

(2019-07-15)
Quantum graphs were first introduced as a simple model for studying quantum mechanics in geometrically complex systems. For example, Pauling used quantum graphs to study organic molecules by viewing the atomic nuclei as ...
• #### Stable up-downwind finite difference methods for solving Heston stochastic volatility equations. ﻿

(2019-07-15)
This dissertation explores effective and efficient computational methodologies for solving two-dimensional Heston stochastic volatility option pricing models with multiple financial engineering applications. Dynamically ...
• #### The sixth-order Krall differential expression and self-adjoint operators. ﻿

(2019-03-22)
We first provide an overview of classical GNK Theory for symmetric, or symmatrizable, differential expressions in L2((a, b);w). Then we review how this theory was applied to find a self-adjoint operator in L2 \mu(-1, 1) ...
• #### Uniqueness implies uniqueness and existence for nonlocal boundary value problems for fourth order differential equations. ﻿

(2006-07-07)
In this dissertation, we are concerned with uniqueness and existence of solutions of certain types of boundary value problems for fourth order differential equations. In particular, we deal with uniqueness implies uniqueness ...
• #### Uniqueness implies uniqueness and existence for nonlocal boundary value problems for third order ordinary differential equations. ﻿

(2006-07-29)
For the third order ordinary differential equation, $y'''=f(x,y,y',y'')$, it is assumed that, for some $m\geq 4$, solutions of nonlocal boundary value problems satisfying $y(x_1)=y_1,\ y(x_2)=y_2,$ \[y(x_m)-\sum_{i= ...