Browsing Department of Mathematics by Title
Now showing items 1528 of 28

GlazmanKreinNaimark theory, leftdefinite theory, and the square of the Legendre polynomials differential operator.
(20160227)As an application of a general leftdefinite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the leftdefinite theory associated with the classical Legendre selfadjoint secondorder differential ... 
Global SL(2,R) representations of the Schrödinger equation with timedependent potentials.
(, 20120808)We study the representation theory of the solution space of the onedimensional Schrödinger equation with timedependent potentials that possess sl₂symmetry. We give explicit local intertwining maps to multiplier ... 
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 ... 
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 ... 
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 ... 
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 degenerate ... 
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 ... 
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= ...