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Articles 31 - 60 of 67
Full-Text Articles in Mathematics
On The Distribution Of Sums Of Residues, Jerrold R. Griggs
On The Distribution Of Sums Of Residues, Jerrold R. Griggs
Faculty Publications
No abstract provided.
Besov-Spaces On Domains In Rd, Ronald A. Devore, Robert C. Sharpley
Besov-Spaces On Domains In Rd, Ronald A. Devore, Robert C. Sharpley
Faculty Publications
No abstract provided.
Labeling Graphs With A Condition At Distance 2, Jerrold R. Griggs, Roger K. Yeh
Labeling Graphs With A Condition At Distance 2, Jerrold R. Griggs, Roger K. Yeh
Faculty Publications
No abstract provided.
A Family Of Complexes Associated To An Almost Alternating Map, With Applications To Residual Intersections, Andrew R. Kustin, Bernd Ulrich
A Family Of Complexes Associated To An Almost Alternating Map, With Applications To Residual Intersections, Andrew R. Kustin, Bernd Ulrich
Faculty Publications
No abstract provided.
Degree Of Adaptive Approximation, Ronald A. Devore, Ming Yu Xiang
Degree Of Adaptive Approximation, Ronald A. Devore, Ming Yu Xiang
Faculty Publications
We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.
Norms Of Positive Operators On Lp-Spaces, Ralph Howard, Anton R. Schep
Norms Of Positive Operators On Lp-Spaces, Ralph Howard, Anton R. Schep
Faculty Publications
No abstract provided.
On Two Function-Spaces Which Are Similar To L0, S J. Dilworth, D A. Trautman
On Two Function-Spaces Which Are Similar To L0, S J. Dilworth, D A. Trautman
Faculty Publications
No abstract provided.
Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson
Pursuing Analogies Between Differential Equations And Difference Equations, David L. Abrahamson
Faculty Publications
The study of ordinary differential equations has long been a staple in mathematics at both the undergraduate and graduate levels. Recently, instruction in the study of difference equations has widened, primarily due to the expanded role of the digital computer in mathematics. The two topics are inextricably linked at all levels, from elementary techniques through current research questions. Pursuing the analogies between these fields of study can only deepen the understanding of each. In particular, the study of many elementary topics in difference equations, requiring not even the use of calculus, can serve as a founda- tion for intuition and …
A Note On Roe's Characterization Of The Sine Function, Ralph Howard
A Note On Roe's Characterization Of The Sine Function, Ralph Howard
Faculty Publications
No abstract provided.
Interpolation Of Besov-Spaces, Ronald A. Devore, Vasil A. Popova
Interpolation Of Besov-Spaces, Ronald A. Devore, Vasil A. Popova
Faculty Publications
We investigate Besov spaces and their connection with dyadic spline approximation in Lp(Omega), 0 < p (less than or equal to) infinity. Our main results are: the determination of the interpolation spaces between a pair of Besov spaces; an atomic decomposition for functions in a Besov space; the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines.
The Twentieth Fermat Number Is Composite, Jeff Young, Duncan A. Buell
The Twentieth Fermat Number Is Composite, Jeff Young, Duncan A. Buell
Faculty Publications
The twentieth Fermat number, F20 = 22^20 +1, has been proven composite by machine computation.
Integer Squares With Constant Second Difference, Duncan A. Buell
Integer Squares With Constant Second Difference, Duncan A. Buell
Faculty Publications
The problem addressed is this: Do there exist nonconsecutive integers n0, n1, n2, . . ., such that the second differences of the squares of the ni are constant? Specifically, can that constant be equal to 2? A complete characterization of sequences of length four can be given. The question of whether or not sequences of length five exist is still open but the existence or nonexistence of such sequences can be described in a more algorithmic way than the simple statement of the problem.
Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan
Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan
Faculty Publications
No abstract provided.
Class Groups Of Quadratic Fields Ii, Duncan A. Buell
Class Groups Of Quadratic Fields Ii, Duncan A. Buell
Faculty Publications
A computation has been made of the noncyclic class groups of imaginary quadratic fields Q(√-D) for even and odd discriminants - D from 0 to - 25000000. Among the results are that 95% of the class groups are cyclic, and that -11203620 and -18397407 are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.
Approximation By Rational Functions, Ronald A. Devore
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
Alfred Tarski And Undecidable Theories, George F. Mcnulty
Faculty Publications
No abstract provided.
On The Atomic Decomposition Of H^1 And Interpolation, Robert Sharpley
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
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
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
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.
Inequalities Relating Sectional Curvatures Of A Submanifold To The Size Of Its 2nd Fndamental Form And Applications To Pinching Theorems For Submanifolds, Ralph Howard, S Walter Wei
Inequalities Relating Sectional Curvatures Of A Submanifold To The Size Of Its 2nd Fndamental Form And Applications To Pinching Theorems For Submanifolds, Ralph Howard, S Walter Wei
Faculty Publications
No abstract provided.
Interpolating Sequences On Curves, Samih Obaid, D. Rung
Interpolating Sequences On Curves, Samih Obaid, D. Rung
Faculty Publications
We established a condition on boundary curves (ending at points) lying either in the unit disc or the upper half plane which implies that any consecutively separated sequence, in the hyperbolic distance, lying on one of these curves is an interpolating sequence for bounded holomorphic functions.
Deformation And Linkage Of Gorenstein Algebras, Andrew R. Kustin, Matthew Miller
Deformation And Linkage Of Gorenstein Algebras, Andrew R. Kustin, Matthew Miller
Faculty Publications
General double linkage of Gorenstein algebras is defined. Rigidity, genericity, and regularity up to codimension six all pass across general double linkage. Rigid strongly unobstructed codimension four Gorenstein algebras which lie in different Herzog classes are produced.
The Expectation Of Success Using A Monte Carlo Factoring Method – Some Statistics On Quadratic Class Numbers, Duncan A. Buell
The Expectation Of Success Using A Monte Carlo Factoring Method – Some Statistics On Quadratic Class Numbers, Duncan A. Buell
Faculty Publications
A method has been proposed for factoring an integer N by using the structure of the class groups of quadratic fields of radicand – kN for various small multipliers k. We discuss the method and an implementation of the method, and various theoretical questions which have an impact on the practical use of the method in factoring. Some of the theoretical questions relate to the nature of class numbers and class groups; we present extensive statistical results on the class numbers and class groups of imaginary quadratic fields.
On The Differentiability Of Functions In Rn, Ronald A. Devore, Robert C. Sharpley
On The Differentiability Of Functions In Rn, Ronald A. Devore, Robert C. Sharpley
Faculty Publications
No abstract provided.
Error-Bounds For Gaussian Quadrature And Weighted-L1 Polynomial Approximation, Ronald A. Devore, L R. Scott
Error-Bounds For Gaussian Quadrature And Weighted-L1 Polynomial Approximation, Ronald A. Devore, L R. Scott
Faculty Publications
Error bounds for Gaussian quadrature are given in terms of the number of quadrature points and smoothness properties of the function whose integral is being approximated. An intermediate step involves a weighted-L' polynomial approximation problem which is treated in a more general context than that specifically required to bound the Gaussian quadrature error.
On First Countable, Countably Compact Spaces. I: (Omega-1,Omega-1-Star)-Gaps, Peter J. Nyikos, Jerry E. Vaughan
On First Countable, Countably Compact Spaces. I: (Omega-1,Omega-1-Star)-Gaps, Peter J. Nyikos, Jerry E. Vaughan
Faculty Publications
No abstract provided.
Metrizability And The Frechet-Urysohn Property In Topological Groups, Peter J. Nyikos
Metrizability And The Frechet-Urysohn Property In Topological Groups, Peter J. Nyikos
Faculty Publications
A question of Arhangel'skii, whether weakly first countable topological groups are metrizable, is answered in two ways: if the Hausdorff axiom is assumed, the answer is yes, but in general a weakly first countable topological group need not be pseudometrizable. The former result is obtained as a corollary of a more general sufficient condition for a sequential group to be Fr&chet-Urysohn. A general necessary and sufficient condition for a sequential group to be Frechet-Urysohn is given, and a number of questions are raised. Examples are given to show in what respect the theorems of the paper are the "best possible".
An Octic Reciprocity Law Of Scholz Type, Duncan A. Buell, Kenneth S. Williams
An Octic Reciprocity Law Of Scholz Type, Duncan A. Buell, Kenneth S. Williams
Faculty Publications
No abstract provided.
Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams
Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams
Faculty Publications
Let p ≡ 1 (mod 4) be a prime. A residue difference set modulo p is a set S = {ai} of integers ai such that (ai/p) = +1 and ((ai - aj)/p) = +1 for all i and j with i ≠ j, where (n/p) is the Legendre symbol modulo p. Let mp be the cardinality of a maximal such set S. The authors estimate the size of mp.