Mathematics Commons^™

A Priori Lρ Error Estimates For Galerkin Approximations To Porous Medium And Fast Diffusion Equations, Dongming Wei, Lew Lefton

Mathematics Faculty Publications

Galerkin approximations to solutions of a Cauchy-Dirichlet prob-

lem governed by a generalized porous medium equation.

Composition Operators On Hardy Spaces Of A Half-Plane, Valentin Matache

Mathematics Faculty Publications

We consider composition operators on Hardy spaces of a half-plane. We mainly study boundedness and compactness. We prove that on these spaces there are no compact composition operators.

Inequalities For Solutions Of Multipoint Boundary Value Problems, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

The concept of concavity is generalized to functions, y, satisfying nth-order differential inequalities. … An analogous inequality for a related Green’s function is also obtained. These inequalities are useful in applications of certain cone theoretic fixed-point theorems.

An Algorithm To Determine Non-Perfect Colorings That Arise From Plane Crystallographic Groups, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

This paper presents a computer algorithm that assists us in our research on non-perfect colorings of plane crystallographic patterns.

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

Triple Positive Solutions For Multipoint Conjugate Boundary Value Problems, John M. Davis, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

For the nth order nonlinear differential equation y (n)(t)=f(y(t)), t [0,1], satisfying the multipoint conjugate boundary conditions, y (j)(ai) = 0,1 i k, 0 j n i - 1, 0 =a 1 a 2 a k = 1, and i=1 k n i =n, where f: [0, ) is continuous, growth condtions are imposed on f which yield the existence of at least three solutions that belong to a cone.

Error Estimation Of The Padé Approximation Of Transfer Functions Via The Lanczos Process, Zhaojun Bai, Qiang Ye

Mathematics Faculty Publications

Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix point of view. This approach simplifies the mathematical theory and derivation of the algorithm. Moreover, an explicit formulation of the approximation error of the PVL algorithm is given. With this error expression, one may implement the PVL algorithm that adaptively determines the number of Lanczos steps required to satisfy a prescribed error tolerance. …

The Eigenfunctions Of A Certain Composition Operator, Valentin Matache

Mathematics Faculty Publications

The composition operator on the classical Hardy space H2, induced by a hyperbolic disk automorphism is considered. It is investigated when a H2-function induces under the given operator a minimal invariant cyclic subspace. Theorems where we use the behaviour of this function in the neighbourhood of the fixed points of the hyperbolic automorphism in order to decide if the cyclic subspace mentioned above is minimal invariant or not, are obtained. The inner eigenfunctions of the operator under consideration are characterized.

Quadratic Convergence Of Approximate Solutions Of Two-Point Boundary Value Problems With Impulse, Vidya Doddaballapur, Paul W. Eloe, Yongzhi Zhang

Mathematics Faculty Publications

The method of quasilinearization, coupled with the method of upper and lower solutions, is applied to a boundary value problem for an ordinary differential equation with impulse that has a unique solution. The method generates sequences of approximate solutions which converge monotonically and quadratically to the unique solution. In this work, we allow nonlinear terms with respect to velocity; in particular, Nagumo conditions are employed.

Splitting In Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

No abstract provided.

A Boundary Value Problem For A System Of Ordinary Differential Equations With Impulse Effects, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

A two-point boundary value problem for a system of first-order ordinary differential equations with impulse effects is studied. The method of upper and lower solutions is employed to obtain the existence of a solution and a method of forced monotonicity is employed to obtain iterative improvement. The main result is illustrated with an application to the Liénard equation with periodic boundary conditions.

Normal Lattices And Coseparation Of Lattices, Barry B. Mittag

Mathematics Faculty Publications

No abstract provided.

Positive Solutions And Nonlinear Multipoint Conjugate Eigenvalue Problems, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

Values of λ are determined for which there exist solutions in a cone of the nth order nonlinear differential equation (see PDF) satisfying themultipoint boundary conditions (see PDF) where a and f are nonnegative valued, and where both (see PDF) exist.

Singular Nonlinear (N-1,1) Conjugate Boundary Value Problems, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

Solutions are obtained for the boundary value problem, y (n) + f(x,y) = 0, y (i)(0) = y(1) = 0, 0 i n – 2, where f(x,y) is singular at y = 0. An application is made of a fixed point theorem for operators that are decreasing with respect to a cone.

The Duals Of Warfield Groups, Peter Loth

Mathematics Faculty Publications

A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.

Building Home Plate: Field Of Dreams Or Reality?, Michael J. Bradley

Mathematics Faculty Publications

No abstract provided.

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe

Mathematics Faculty Publications

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.

Galois Module Structure Of Ideals In Wildly Ramified Cyclic Extensions Of Degree P2, Gove Griffith Elder

Mathematics Faculty Publications

For L/K, any totally ramified cyclic extension of degree p2 of local fields which are finite extensions of the field of p-adic numbers, we describe the Zp[Gal(L/K)]-module structure of each fractional ideal of L explicitly in terms of the 4p+1 indecomposable Zp[Gal(L/K)]-modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

Spectral Properties Of Operators Having Dense Orbits, Valentin Matache

Mathematics Faculty Publications

In the following H will denote a separable, infinite-dimensional, complex Hilbert space. The term operator will always mean linear, bounded operator on H. By invariant subspace we mean closed, invariant linear manifold. For a given operator T, the set of all invariant subspaces of T will be denoted LatT, since obviously it is a lattice. The set of all operators commuting with T is denoted {T}'. A subspace will be called hyperinvariant for T if it is invariant under any operator in {T}'.

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Mathematics Faculty Publications

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rⁿ into R that was strictly increasing with respect to the new order imposed on Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …

Singular Boundary Value Problems For Quasi-Differential Equations, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

Solutions are obtained of boundary value problems for Lny+f(x,L0y,…,Ln−2y), satisfying L2y(0)=Ln−1y(1)=0, 0≤i≤n−2, where Li, denotes the ith quasiderivative, and where f(x,y1,…,yn−1) has singularities at yi=0, 1≤i≤n−1.

Multipoint Boundary Value Problems For Functional Differential Equations, Paul W. Eloe, Johnny Henderson, Denise Taunton

Mathematics Faculty Publications

No abstract provided.

Positive Solutions For Higher Order Ordinary Differential Equations, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

Solutions that are positive with respect to a cone are obtained for the boundary value problem, u(n) + a(t)f(u) = 0, u(i)(0) = u(n−2)(1) = 0, 0 _ i _ n − 2, in the cases that f is either superlinear or sublinear. The methods involve application of a _xed point theorem for operators on a cone.

Operator Equations And Invariant Subspaces, Valentin Matache

Mathematics Faculty Publications

Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A² = B² and if A has non-trivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.

On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Mathematics Faculty Publications

The existence of bounded solutions and periodic solutions is studied for a system of infinite delay integral equations having nonlinear perturbations. An equivalent system of equations is obtained in terms of the resolvent kernel. Then the existence results are shown for the equivalent equations. Contraction principle, Schauder’s fixed point theorem, and monotone method are used in the study.

Beauty Bare, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

Positive Solutions And J-Focal Points For Two-Point Boundary Value Problems, Paul W. Eloe, Darrel Hankerson, Johnny Henderson

Mathematics Faculty Publications

Cone theory is applied to a class of two-point boundary value problems for ordinary differential equations. Criteria for the existence of extremal points are obtained. These criteria are in terms of the existence of nontrivial solutions that lie in a cone, and in terms of the spectral radius of an associated compact linear operator.

Splitting Of The Identity Component In Locally Compact Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this paper we are concerned with the splitting of the identity component G₀ in an LCA group G. As Pontrjagin duality shows, this splitting is to the splitting of the torsion part tA in a discrete abelian group A, if G is assumed to be compact.

A Statistical Theory Of Digital Circuit Testability, Sharad C. Seth, Vishwani D. Agrawal, Hassan Farhat

Mathematics Faculty Publications

When test vectors are applied to a circuit, the fault coverage increases. The rate of increase, however, could be circuit dependent. A relation between the average fault coverage and circuit testability is developed in this paper. The statistical formulation allows computation of coverage for deterministic and random vectors. We discuss the following applications of this analysis: determination of circuit testability from fault simulation, coverage prediction from testability analysis, prediction of test length, and test generation by fault sampling.

Changing Modes Of Thought: Non-Euclidean Geometry And The Liberal Arts, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.