Mathematics Commons^™

A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler

Mathematics Faculty Publications

This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with a class of continuous, orthogonal, compactly-supported scaling functions that contain piecewise linears on a uniform triangulation of $\R^2$. This class of scaling functions is a generalization of a set of scaling functions first constructed by Donovan, Geronimo, and Hardin. A specific set of scaling functions and associated multiwavelets with symmetry properties will be constructed.

P-Cross-Section Bodies, Richard J. Gardner, Apostolos Giannopoulos

Mathematics Faculty Publications

If K is a convex body in Eⁿ, its cross-section body CK has a radial function in any direction u is ∈ S^n-1 equal to the maximal volume of hyperplane sections of K orthogonal to u. A generalization called the p-cross-section body C_pK of K, where p > -1, is introduced. The radial function of C_pK in any direction u ∈ S^n-1 is the pth mean of the volumes of hyperplane sections of K orthogonal to u through points in K. It is shown that C …

Classroom Capsules: Additivity ⊕ Homogeneity, Michael J. Bradley, Michael St. Vincent, David L. Finn

Mathematics Faculty Publications

A Classroom Capsule is a short article that contains a new insight on a topic taught in the earlier years of undergraduate mathematics.

An Analytic Solution To The Busemann-Petty Problem On Sections Of Convex Bodies, Richard J. Gardner, Alexander Koldobsky, Thomas Schlumprecht

Mathematics Faculty Publications

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in Rⁿ with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n - 1)-dimensional X-ray) gives the ((n - 1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in Rⁿ and leads to a unified analytic solution to the Busemann-Petty problem: Suppose that K and L are two origin-symmetric convex bodies in Rⁿ such that the …

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.

Extremal Graphs For Weights, Béla Bollobás, Paul Erdös, Amites Sarkar

Mathematics Faculty Publications

Given a graph G = (V,E) and α ∈ R, we write wα(G)=∑_xyϵEdG(x)^αdG(y)^α, and study the function w_α(m) = max {w_α(G): e(G) = m}. Answering a question from Bollobás and Erdös (Graphs of external weights, to appear), we determine w_i(m) for every m, and we also give bounds for the case α ≠ 1.

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.

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.

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.

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.