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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 …

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

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

Σary N=0, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

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

Faculty Publications

© 1986 by American Mathematical Society

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 Articles

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.

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.

Untitled (Subject: Reverberation), Richard C. Heyser

Unpublished Writings

In this paper, Richard C. Heyser explains how sound reverberates and why he developed a time delay spectrometer (TDS) to measure sound.

A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice, Erica Flapan

Pomona Faculty Publications and Research

We begin by giving several definitions. A knot K in S³ is said to be amphicheiral if there is an orientation-reversing diffeomorphism h of S³ which leaves K setwise invariant. Suppose, in addition, that K is given an orientation. ThenK is said to be positive amphicheiral if h preserves the orientation of K. If, in addition, the diffeomorphism h is an involution then K is strongly positive amphicheiral. Finally, we say a knot is slice if it bounds a smooth disc in B⁴. In this note we shall give a smooth example of …

Analysis Of A Worst Case Oil Spill Eis, Galveston, Gail Elizabeth Meisner

Marine Affairs Theses and Major Papers

On July 8, 1980, the Galveston district of the U.S. Army Corps of Engineers (Corps) issued the permits required for the construction of an onshore deepwater port. The proposed port expansion project has been the subject of extensive controversy and litigation. The primary conflict has centered on the exclusion of a worst case oil spill analysis, as required by recent Council on Environmental Quality (CEQ) regulations. A rational-deductive approach to this decision leads to the conclusion that the economically and environmentally favored choice would have been to include the worst case analysis in the initial Environmental Impact Statement (EIS). Because …

Containerized Cargo Flow Analysis Between The United States And The Far East, Bi-Chou Wei

Marine Affairs Theses and Major Papers

Within less than a decade, containerization has revolutionized maritime general cargo transportation throughout major world trade routes, especially the trade routes between the Far East and the United States. Few commodity flow studies have focused on this latest innovation in maritime transport. To most of the rapidly developing state-owned Far East shipping industries, an understanding of container flow variation and port calling preference with U.S. seaports has become essential in order to maximize investments and to rationalize services. By applying 1974, 1977, and 1980 Far East/U.S. container flow data, this study intends to explore the non-physical and economic elements which …

Ua66/10/2 Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

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

Faculty Publications

No abstract provided.

Reliable Computation In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

This talk concerns computation by systems whose components exhibit noise (that is, errors committed at random according to certain probabilistic laws). If we aspire to construct a theory of computation in the presence of noise, we must possess at the outset a satisfactory theory of computation in the absence of noise.

A theory that has received considerable attention in this context is that of the computation of Boolean functions by networks (with perhaps the strongest competition coming from the theory of cellular automata; see [G] and [GR]). The theory of computation by networks associates with any two sets Q and …

Perfect Numbers And Mersenne Primes, Barry A. Delello

Retrospective Theses and Dissertations

No abstract provided.

On A Generalization Of The Corona Problem, Graziano Gentili, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Let g, f_l,...., f_m EH ^(A). We provide conditions on f_l,...,f_m in order that Ig(z) lIf_i(z)l+...+If_m (z)I, for all z in 4, imply that g, or g², belong to the ideal generated by f_l,....,f_m in H.

Realising Rings As Endomorphism Rings: The Impact Of Logic, Brendan Goldsmith

Articles

No abstract available

Camc Examines America, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

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 r^th power residues, r ≥ 2, r even.