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Articles 1 - 7 of 7

Full-Text Articles in Physical Sciences and Mathematics

Approximation By Rational Functions, Ronald A. Devore Dec 1986

Approximation By Rational Functions, Ronald A. Devore

Faculty Publications

Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f' is in L log L on a finite interval, then f can be approximated in the uniform norm by rational functions of degree n to an error 0(1/n) on that interval.


Alfred Tarski And Undecidable Theories, George F. Mcnulty Dec 1986

Alfred Tarski And Undecidable Theories, George F. Mcnulty

Faculty Publications

No abstract provided.


Sequence Alignment With Matched Sections, Jerrold R. Griggs, Philip J. Hanlon, Michael S. Waterman Oct 1986

Sequence Alignment With Matched Sections, Jerrold R. Griggs, Philip J. Hanlon, Michael S. Waterman

Faculty Publications

In molecular biology, two finite sequences are compared by displaying one sequence written over another in an alignment. The number of alignments of two sequences is related to the Stanton-Cowan numbers. This paper gives asymptotics for the number of alignments of two sequences of length n with matching sections of size at least b.


On The Atomic Decomposition Of H^1 And Interpolation, Robert Sharpley May 1986

On The Atomic Decomposition Of H^1 And Interpolation, Robert Sharpley

Faculty Publications

© 1986 by American Mathematical Society


Nonexistence Of Stable Harmonic Maps To And From Certain Homogeneous Spaces And Submanifolds Of Euclidean-Space, Ralph Howard, S Walter Wei Mar 1986

Nonexistence Of Stable Harmonic Maps To And From Certain Homogeneous Spaces And Submanifolds Of Euclidean-Space, Ralph Howard, S Walter Wei

Faculty Publications

Call a compact Riemannian manifold M a strongly unstable manifold if it is not the range or domain of a nonconstant stable harmonic map and also the homotopy class of any map to or from M contains elements of arbitrarily small energy. If M is isometrically immersed in Euclidean space, then a condition on the second fundamental form of M is given which implies M is strongly unstable. As compact isotropy irreducible homogeneous spaces have "standard" immersions into Euclidean space this allows a complete list of the strongly unstable compact irreducible symmetric spaces to be made.


Multivariate Rational Approximation, Ronald A. Devore, Xiang Ming Yu Jan 1986

Multivariate Rational Approximation, Ronald A. Devore, Xiang Ming Yu

Faculty Publications

No abstract provided.


Sequences In Power Residue Classes, Duncan A. Buell, Richard H. Hudson Jan 1986

Sequences In Power Residue Classes, Duncan A. Buell, Richard H. Hudson

Faculty Publications

Using A. Weil’s estimates the authors have given bounds for the largest prime P0 such that all primes P > P0 have sequences of quadratic residues of length m. For m ≤ 8 the smallest prime having m consecutive quadratic residues is ≡ 3(mod 4) and P0 ≡ 1 (mod 4). The reason for this phenomenon is investigated in this paper and the theory developed is used to successfully uncover analogous phenomena for rth power residues, r ≥ 2, r even.