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Browsing Graduate School by Author "Mathematics."

Rogers, James W., Jr.
In this dissertation, we explore highly efficient and accurate finite difference methods for the numerical solution of variable coefficient partial differential
equations arising in electromagnetic wave applications. We ...

Jones, Leslie Braziel.
We explore the endpoint structure of the inverse limit space of unimodal maps such that the restriction of the map to the ωlimit set of the critical point is topologically conjugate to an adding machine. These maps fall ...

Bruder, Andrea S.
It is well known that, for –α, –β, –α – β – 1 ∉ ℕ, the Jacobi polynomials {Pn(α,β)(x)} ∞ n=0 are orthogonal on ℝ with respect to a bilinear form of the type(f,g)μ = ∫ℝfgdμ, for some measure μ. However, for negative integer ...

Hamilton, Brent (Brent A.)
(, )
We study asymptotic behavior arising in inverse limit spaces of dendrites. In particular, the inverse limit is constructed with a single unimodal bonding map, for which points have unique itineraries and the critical point ...

Lyons, Jeffrey W.
(Mathematical Sciences Publishers.International Publications.Academic Publications., )
In this dissertation, we investigate boundary data smoothness for solutions of
nonlocal boundary value problems over discrete and continuous domains. Essentially, we show that under certain conditions partial derivatives ...

Hartsock, Gail.
(, )
It follows from a formula by Kostant that the difference between the highest weights of consecutive parabolic Verma modules in the BernsteinGelfandGelfandLepowsky resolution of the trivial representation is a single ...

Neugebauer, Jeffrey T.
(, )
The theory of u₀positive operators with respect to a cone in a Banach space is applied to the linear differential equations u⁽⁴⁾ + λ₁p(x)u = 0 and u⁽⁴⁾ + λ₂q(x)u = 0, 0 ≤ x ≤ 1, with each satisfying the boundary conditions ...

Pruett, W. Andrew.
We develop a system of canonical reduced decompositions of minimal coset representatives of quotients corresponding to cominuscule flag varieties and affine Grassmannians. This canonical decomposition allows, in the first ...

Liu, Xueyan, 1978.
(, )
In this dissertation, we investigate the existence and uniqueness of boundary value problems for the third and nth order differential equations by matching solutions. Essentially, we consider the interval [a, c] of a BVP ...

Sutherland, Shawn M., 1984
(, )
In this dissertation, we prove the existence of positive solutions to two classes of three point right focal singular boundary value problems of at least fourth order.

Maroun, Mariette.
(Orlando, FL : International Publications., )
In this dissetation, we seek positive solutions for the n^th order ordinary differential equation, y^(n)=f(x,y), satisfying the right focal boundary conditions, y^(i)(0)=y^(n2)(p)=y^(n1)(1)=0, i=0,...,n3, where p is a ...

Wagner, Bradley M.
(, )
Let P be an arbitrary partially ordered set and I(P) its incidence space. Then F(P) is the finitary incidence algebra and I(P) is a bimodule over it. Consequently we can form D(P) = FI(P) ⊕ I(P) the idealization of I(P). ...

Ehrke, John E.
We apply a wellknown fixed point theorem to guarantee the existence of a
positive solution and bounds for solutions for second, third, fourth, and nth order
families of boundary value problems. We begin by characterizing ...

Jackson, Billy, 1978
In this work, we examine linear systems theory in the arbitrary time scale setting by considering Laplace transforms, stability, controllability, and realizability. In particular, we revisit the definition of the Laplace ...

Franco, Jose A.
(, )
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 ...

Williams, Brian R. (Brian Robert), 1982
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 ...

Cornelius, Alexander Nelson.
Much is known about inverse limits of compact spaces with continuous bonding
maps. When the requirement that the bonding maps be continuous functions is relaxed,
to allow for upper semicontinuous setvalued functions, ...

Tuncer, Davut.
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 ...

Hopkins, Britney.
In this work, we discuss multiplicity results for nonhomogeneous evenorder boundary value problems on both discrete and continuous domains. We develop a method for establishing existence of positive solutions by transforming ...

Aceves, Kelly Fouts.
(, )
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 ...