Physical Sciences and Mathematics Commons^™

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.

Design And Analysis Of Efficient Algorithms To Solve The Maximum Concurrent Flow Problem, Farhad Shahrokhi

Dissertations

The maximum concurrent flow (MCFP) is a generalized commodity flow problem, where every pair of entities can send and receive flow Ma85 , BM86 , MS86 . We develop efficient labeling algorithms to solve the MCFP. We explore the combinatorial structure of the MCFP and show that the problem of associating costs (distances) to the edges so as to maximize the minimum cost of routing the concurrent flow is the dual of the MCFP. This duality covers max-flow min-cut theorem as a special case. Applications in packet switched networks At81 and cluster analysis Ma86 are discussed.

Alfred Tarski And Undecidable Theories, George F. Mcnulty

Faculty Publications

No abstract provided.

On The Laplacian, Frank A. Farris, James Ward Brown

Mathematics and Computer Science

In various applied mathematics courses one appearance of the Laplacian operator is in the study of heat distributions.

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.

Prophet Inequalities For Averages Of Independent Non-Negative Random Variables, Theodore P. Hill

Research Scholars in Residence

No abstract provided.

George Boole: His Life And Work (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: George Boole: His Life and Work by Desmond MacHale. (Profiles of Genius Series, 2.) xiii + 304 pp., illus., bibls., index. Dublin: Boole Press, 1985.

Keane Leads Us Olympiad Team To 1st Place Tie With Ussr, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

Optimal-Partitioning Inequalities For Nonatomic Probability Measures, John Elton, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

Suppose μ1,...,μn are nonatomic probability measures on the same measurable space (S, B). Then there exists a measurable partition {Si}ⁿ_i=1 of S such that μi(Si) ≥ (n + 1 - M)^-1 for all i = 1,...,n, where M is the total mass of Vⁿ_i=1μ1 (the smallest measure majorizing each μi). This inequality is the best possible for the functional M, and sharpens and quantifies a well-known cake-cutting theorem of Urbanik and of Dubins and Spanier. Applications are made to L1-functions, discrete allocation problems, statistical decision theory, …

Generalized Connectivity In Graphs, Ortrud R. Oellermann

Dissertations

The connectivity of a graph G is the minimum number of vertices in G whose deletion produces a disconnected or trivial graph, while the edge-connectivity of G is the minimum number of edges having this property. In this dissertation several generalizations and variations of these two parameters are introduced and studied.

Chapter I is an overview to the history of connectivity and provides a background for the chapters that follow. In Chapter II major n-connected subgraphs are introduced. Through this concept, the connectivities (of subgraphs) that are most representative in a given graph are studied.

Chapter III is devoted to …

Jacobi Moments In Applied Mathematics With Computer Applications, John A. Kapenga

Dissertations

This work provides solid asymptotic representations, sharp error bounds and stable recurrence methods (both three term and two dimensional) for the Jacobi moments. These moments are currently used in several areas of numerical analysis (numerical integration, integral equations and boundary value problems).

A powerful representation theorem, due to H. Gingold, which uses the Jacobi moments is extended and analyzed. Applications of this theorem to multi-turning point problems and several other areas are given.

For a number of important problems in mathematical physics it is not possible to prove that the currently employed methods of solution converge, or are valid in …

Scs 98: Z-Continuity, Z-Hypercompactness And Complete Distributivity, Marcel Erné

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

Mappings Of Anr's Whose Images Are Anr's, Jung-In Kang Choi

Doctoral Dissertations

Recently, R.J. Daverman and J.J. Walsh modified an example due to J. Taylor to obtain an example of a cell-like map from a compactum with non-trivial shape onto the Hilbert cube Q such that the non-degeneracy set is contained in the countable union of finite dimensional closed subsets of Q. Previously, G. Kozlowski proved that a cell-like map f: X' → X from a compact ANR X' onto a metric space X is a hereditary shape equivalence if there exists a sequence {B_n}∞_n=1 of finite dimensional closed subsets of X such that the non-degeneracy set is contained …

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

Faculty Publications

© 1986 by American Mathematical Society

Σary N=0, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai

Mathematics and Statistics Faculty Publications

Properties of measures associated with orthogonal polynomials are investigated in terms of the coefficients of the three term recurrence formula satisfied by the orthogonal polynomials.

On The Generalizations Of Gershgorin's Theorem, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper deals with generalization fo Gershgorin's theorem. This theorem is investigated and generalized in terms of contour integrals, directed graphs, convex analysis, and clock matrices.

These results are shown to apply to some specified matrices such as stable and stochastic matrices and some examples will show the relationship of eigenvalue inclusion regions among them.

A Truly Elementary Approach To The Bounded Convergence Theorem, Jonathan W. Lewin

Faculty and Research Publications

No abstract provided.

L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg

Mathematics and Statistics Faculty Publications

No abstract provided.

An Intrinsic Construction Of Fefferman's Cr Metric, Frank A. Farris

Mathematics and Computer Science

We construct a conformal class of Lorentz metrics naturally associated with an abstract definite CR structure. If the CR structure is that of a pseudoconvex boundary in Cn we prove that the intrinsically constructed metric is the same as that discovered by Fefferman using a solution to a complex Monge-Ampère equation. The construction presented here relies on formal solutions of a linear equation, dζ = 0, and provides a relatively simple procedure for computing the metric.

A Partial Integration Formula For Product Integrals Of Unbounded Operator-Valued Functions, Rhonda J. Hughes

Mathematics Faculty Research and Scholarship

The partial integration formula for product integrals of which the Trotter product formula is a consequence, is established for a wide class of unbounded operator-valued functions.

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.

Class Contradictions In The Indian Society., Ashok Kumar Nag Dr.

Doctoral Theses

Recognising the vastness of our subject it was felt necessary to limit the scope of the thesis in the following four ways(1) Agrarian classes have been left out.(2) Intra class contradictions have been analysed to a larger extent than inter class contradictions.(3) The historical process of Glass formation and the concomitant question of class consciousness have not been dealt with.(4) No direct reference has been made to the concept of mode of production.In other words, within the broad subject area suggested by the title, scope of the thesis has been narrowed down to the following identification and analysis of contradictions …

Optimum Sampling Strategies., T. V. Hanurav Dr.

Doctoral Theses

The advantages sample surveys over complete censuses are well known and seem to be fully appreaciated as is evidenced by the increasing use of sample surveys now a days as a means of collecting information.The use of probability theory to make rigorous inductive inferences has been well recognised for a long time. Such inferences can be made only when observations which form the basis of the infe- rence are generated by some chance mechanism, In traditional applica- tions, the statistician usually assume s or takes for granted some kind of chan ce mechanism behind the o bservations, where as in …

Computing The Largest Empty Rectangle, B. Chazelle, R. L. Drysdale, D. T. Lee

Dartmouth Scholarship

We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result [13] takes $O(N^2 )$ worst-case and $O(N\log ^2 N)$ expected time. This paper presents an $O(N\log ^3 N)$ time, $O(N\log N)$ space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones …

Problems Of Distribution In India's Development: An Empirical Analysis., M. Suryanarayana Dr.

Doctoral Theses

No abstract provided.

On Weighted Integrability Of Trigonometric Series And L¹-Convergence Of Fourier Series, William O. Bray, Caslav V. Stanojević

Mathematics and Statistics Faculty Research & Creative Works

Result concerning integrability of f(x)L(l/x)(g(x)L(l/x)), where f(x)(g(x)) is the pointwise limit of certain cosine (sine) series and L(•) is slowly vary in the sense of Karamata [5] is proved. Our result is an excludedďcase in more classical results (see [4]) and also generalizes a result of G. A. Fomin [1]. Also a result of Fomin and Telyakovskii [6] concerning L1-convergence of Fourier series is generalized. Both theorems make use of a generalized notion of quasi-monotone sequences. © 1986 American Mathematical Society.

Structural Interactions Of The Recursively Enumerable T- And W-Degrees, Rod G. Downey, M. Stob

University Faculty Publications and Creative Works

No abstract provided.

Aggregating Inductive Expertise, Daniel N. Osherson, Michael Stob, Scott Weinstein

University Faculty Publications and Creative Works

The aggregation problem is to design an inferential agent that makes intelligent use of the theories offered by a team of inductive inference machines working in a common environment. The present paper formulates several versions of the aggregation problem and investigates them from a recursion theoretic point of view.

Banach Spaces Of Functions Analytic In A Polydisc, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.