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Mathematics

Mathematics Faculty Publications

2001

Articles 1 - 8 of 8

Full-Text Articles in Physical Sciences and Mathematics

Composition Operators And A Pull-Back Measure Formula, Valentin Matache Sep 2001

Composition Operators And A Pull-Back Measure Formula, Valentin Matache

Mathematics Faculty Publications

A pull-back measure formula obtained in some particular cases by E. A. Nordgren and this author is generalized in the framework of boundary measures for zero-free Nevanlinna class fuctions on the unit polydisk. The formula is used to characterize the zero-free Nevanlinna class functions which are solutions of Schröder's equation induced by a polydisk automorphism ϕ (i.e. to determine the zero-free functionsf belonging to the Nevanlinna class which are solutions of the functional equationf ° π=λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author.

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A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler Jul 2001

A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler

Mathematics Faculty Publications

In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the …

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Topologically Pure Extensions, Peter Loth Jan 2001

Topologically Pure Extensions, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence 0→H →G→K→0 (*) in the category of locally compact abelian groups is said to be topologically pure if the induced sequence 0→nH→nG→nK→0 is proper short exact for all positive integers n. Some characterizations of topologically pure sequences in terms of direct decompositions, pure extensions and tensor products are established. A simple proof is given for a theorem on pure subgroups by Hartman and Hulanickl. Using topologically pure extensions, we characterize those splitting locally compact abelian groups whose torsion part is a direct sum of a compact …

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A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei Jan 2001

A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei

Mathematics Faculty Publications

We study approximations of the steady state Stokes problem governed by the power-law model for viscous incompressible non-Newtonian flow using the penalty formulation. We establish convergence and find error estimates

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Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang Jan 2001

Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang

Mathematics Faculty Publications

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.

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A Brunn-Minkowski Inequality For The Integer Lattice, Richard J. Gardner, Paolo Gronchi Jan 2001

A Brunn-Minkowski Inequality For The Integer Lattice, Richard J. Gardner, Paolo Gronchi

Mathematics Faculty Publications

A close discrete analog of the classical Brunn-Minkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a method for computing the exact lower bound in this situation, given the dimension of the lattice and the cardinalities of the two sets. These bounds in turn imply corresponding new bounds for the lattice point enumerator of the Minkowski sum of two convex lattice polytopes. A Rogers-Shephard type inequality for the …

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Numerical Ranges Of Composition Operators, Valentin Matache Jan 2001

Numerical Ranges Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 is a fixed point of the symbol. If 0 is not a fixed point of the symbol 1 is shown to be interior to the numerical range. Some composition operators whose …

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Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski Jan 2001

Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski

Mathematics Faculty Publications

We look for a parallel to the notion of “proper forcing” among λ-complete forcing notions not collapsing λ+. We suggest such a definition and prove that it is preserved by suitable iterations.

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