Browsing Department of Mathematics by Title
Now showing items 1937 of 37

Indecomposability in inverse limits.
(20101008)Topological inverse limits play an important in the theory of dynamical systems and in continuum theory. In this dissertation, we investigate classical inverse limits of Julia sets and setvalued inverse limits of arbitrary ... 
Krylov methods for solving a sequence of large systems of linear equations.
(20150722)Consider solving a sequence of linear systems A_{(i)}x^{(i)}=b^{(i)}, i=1, 2, ... where A₍ᵢ₎ ϵℂⁿᵡⁿ and b⁽ⁱ⁾ϵℂⁿ using some variations of Krylov subspace methods, like GMRES. For a single system Ax=b, it is wellknown that ... 
The leftdefinite spectral analysis of the legendre type differential equation.
(20100202)Littlejohn and Wellman developed a general abstract leftdefinite theory for a selfadjoint operator A that is bounded below in a Hilbert space (H,(‧,‧)). More specifically, they construct a continuum of Hilbert spaces ... 
Local automorphisms of finitary incidence algebras.
(20170707)Let $R$ be a commutative, indecomposable ring with identity and let $(P,\le)$ be a locally finite partially ordered set. Let $FI(P)$ denote the finitary incidence algebra of $(P,\le)$ over $R$. In this case, the finitary ... 
On a ring associated to F[x].
(, 20130924)For a ﬁeld F and the polynomial ring F [x] in a single indeterminate, we deﬁne Ḟ [x] = {α ∈ End_F(F [x]) : α(ƒ) ∈ ƒF [x] for all ƒ ∈ F [x]}. Then Ḟ [x] is naturally isomorphic to F [x] if and only if F is inﬁnite. If F ... 
On BirmanHardyRellichtype inequalities.
(20190724)In 1961, Birman proved a sequence of inequalities on the space of mtimes continuously di↵erentiable functions of compact support Cm 0 ((0, 1)) ⇢ L2((0, 1)), containing the classical (integral) Hardy inequality and the ... 
Orbit structures of homeomorphisms.
(, 20121129)In this dissertation we answer the following question: If X is a Cantor set and T: X → to X is a homeomorphism, what possible orbit structures can T have? The answer is given in terms of the orbit spectrum of T. If X is a ... 
Polynomial preconditioning with the minimum residual polynomial.
(20191217)Krylov subspace methods are often used to solve large, sparse systems of linear equations Ax=b. Preconditioning can help accelerate the Krylov iteration and reduce costs for solving the problem. We study a polynomial ... 
Preconditioning mixed finite elements for tide models.
(20190724)We describe finite element methods for the linearized rotating shallow water equations which govern tides. Symplectic Euler and CrankNicolson timestepping strategies have good energy preservation properties, which is ... 
Quadratic Lyapunov theory for dynamic linear switched systems.
(, 20140128)In this work, a special class of timevarying linear systems in the arbitrary time scale setting is examined by considering the qualitative properties of their solutions. Building on the work of J. DaCunha and A. Ramos, ... 
Restarting the Lanczos algorithm for large eigenvalue problems and linear equations.
(20081002)We are interested in computing eigenvalues and eigenvectors of large matrices and in solving large systems of linear equations. Restarted versions of both the symmetric and nonsymmetric Lanczos algorithms are given. For ... 
Similarity of blocks in parabolic category O and a wonderful correspondence for modules of covariants.
(20180713)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.
(20170708)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.
(, 20121129)In this work we explore various piston configurations with different types of potentials. We analyze Laplacetype 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.
(20190715)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 updownwind finite difference methods for solving Heston stochastic volatility equations.
(20190715)This dissertation explores effective and efficient computational methodologies for solving twodimensional Heston stochastic volatility option pricing models with multiple financial engineering applications. Dynamically ... 
The sixthorder Krall differential expression and selfadjoint operators.
(20190322)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 selfadjoint operator in L2 \mu(1, 1) ... 
Uniqueness implies uniqueness and existence for nonlocal boundary value problems for fourth order differential equations.
(20060707)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.
(20060729)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= ...