Mathematics Commons^™

On Some Class Of Hypersurfaces In \Bbb{E}^{N+1} Satisfying Chen's Equality, Ci̇han Özgür, Kadri̇ Arslan

Turkish Journal of Mathematics

In this paper we study pseudosymmetry type hypersurfaces in the Euclidean space \Bbb{E}^{n+1} satisfying B. Y. Chen's equality.

One Sided Banach Algebras, A. El Kinani, A. Najmi, Mohamed Oudadess

Turkish Journal of Mathematics

Many properties of two-sided algebras remain valid for one-sided algebras. Namely, any one sided Banach algebra is commutative modulo its Jacobson radical.

On Derivations Of Prime Gamma Rings, Mehmet Ali̇ Öztürk, Young Bae Jun, Kyung Ho Kim

Turkish Journal of Mathematics

We consider some results in a \Gamma-ring M with derivation which is related to Q, and the quotient \Gamma-ring of M.

Flat Marcinkiewicz Integral Operators, Hussain Al-Qassem, Ahmad Al-Salman

Turkish Journal of Mathematics

In this paper, we study Marcinkiewicz integral operators with rough kernels supported by surfaces of revolutions. We prove that our operators are bounded on L^p under certain convexity assumptions on our surfaces and under very weak conditions on the kernel.

On Some Properties Connecting Infinite Series, B. K. Lahiri, Pratulananda Das

Turkish Journal of Mathematics

We prove several theorems connecting infinite series of real terms in relation to Borel and Baire classification of sets and functions, connectedness of mappings, porosity character of sets etc.

Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego

Department of Math & Statistics Faculty Publications

For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤_spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …

Polynomial Continued Fractions, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher degree for both numerator and denominator polynomials, with particular attention given to cases in which the degrees are equal. We extend work of Ramanujan on continued fractions with rational limits and also consider cases where the limits are irrational.

A Density Property Of The Tori And Duality, Peter Loth

Mathematics Faculty Publications

In this note, a short proof of a recent theorem of D. Dikranjan and M. Tkachenko is given, and their result is extended.

Hilbert Spaces Induced By Toeplitz Covariance Kernels, Mihaela Teodora Matache, Valentin Matache

Faculty Books and Monographs

This is a book chapter that appeared in Stochastic Theory and Control by Bozenna Pasik-Duncan (ed.).

This volume contains almost all of the papers that were presented at the Workshop on Stochastic Theory and Control that was held at the Univ- sity of Kansas, 18–20 October 2001. This three-day event gathered a group of leading scholars in the ?eld of stochastic theory and control to discuss leading-edge topics of stochastic control, which include risk sensitive control, adaptive control, mathematics of ?nance, estimation, identi?cation, optimal control, nonlinear ?ltering, stochastic di?erential equations, stochastic p- tial di?erential equations, and stochastic theory and its …

Conversations Among Women In Mathematics (Program), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao

Mathematics Faculty Publications

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe

Mathematics Faculty Publications

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order di_erential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.

Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova

Mathematics Faculty Publications

The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved that the convergence is quadratic.

Third Kenneth C. Schraut Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

How To Keep Up With Mathematics (Abstract), Paul Campbell

Kenneth C. Schraut Memorial Lectures

You are a mathematics major perhaps because you are good at it and it’s useful, but more likely mainly because you enjoy it.

Most undergraduate mathematics is decades or even centuries old, in part because of the hierarchical nature of the subject. Meanwhile, your fellow students in biology and other sciences use textbooks that feature crucial work of the last five or ten years.

Recall, though, what you were told in orientation to college and often since: Much learning in college has to take place outside the classroom, at your own initiative. After your formal education ends, all mathematics learning …

Field Extensions Having The Unique Subfield Property, And G-Cogalois Extensions, Toma Albu

Turkish Journal of Mathematics

We present a short proof, based on Cogalois Theory, of a result due to Acosta de Orozco and Vélez (1982, J. Number Theory 15, 388-405) characterizing separable simple radical field extensions with the unique subfield property, and prove that these extensions are precisely the simple G--Cogalois extensions with a cyclic Kneser group.

K(Π, 1) For Artin Groups Of Finite Type, Colum Watt, Thomas Brady

Articles

This paper is a continuation of a programme to construct new K(π, 1)’s for Artin groups of finite type which began in [4] with Artin groups on 2 and 3 generators and was extended to braid groups in [3]. These K(π, 1)’s differ from those in [6] in that their universal covers are simplicial complexes. In [4] a complex is constructed whose top-dimensional cells correspond to minimal factorizations of a Coxeter element as a product of reflections in a finite Coxeter group. Asphericity is established in low dimensions using a metric of non-positive curvature. Since the nonpositive curvature condition is …

A Partial Order On The Orthogonal Group, Colum Watt, Thomas Brady

Articles

We define a natural partial order on the orthogonal group and completely describe the intervals in this partial order. The main technical ingredient is that an orthogonal transformation induces a unique orthogonal transformation on each subspace of the orthogonal complement of its fixed subspace.

On Unit Sum Numbers Of Rational Groups, Brendan Goldsmith, Christopher Meehan, S. Wallutis

Articles

The unit sum numbers of rational groups are investigated: the importance of the prime 2 being an automorphism of the rational group is discussed and other results are achieved by considering the number and distribution of rational primes which are, or are not, automorphisms of the group. Proof is given of the existence of rational groups with unit sum numbers greater than 2 but of finite value .

On Torsion And Mixed Minimal Abelian Groups, Brendan Goldsmith, S. O. Hogain

Articles

An abelian group is said to be minimal if it is isomorphic to all its subgroups of finite index. We obtain a complete characterisation of such groups in the torsion case; in the case of mixed groups of rank 1 we obtain a characterisation for some large classes of such groups.

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …

Some Irrational Generalised Moonshine From Orbifolds, Rossen Ivanov, Michael Tuite

Articles

We verify the Generalised Moonshine conjectures for some irrational modular functions for theMonster centralisers related to the Harada-Norton, Held, M12 and L3(3) simple groups based on certain orbifolding constraints. We find explicitly the fixing groups of the hauptmoduls arising in each case.

A Specht Module Analog For The Rook Monoid, Cheryl Grood

Mathematics & Statistics Faculty Works

The wealth of beautiful combinatorics that arise in the representation theory of the symmetric group is well-known. In this paper, we analyze the representations of a related algebraic structure called the rook monoid from a combinatorial angle. In particular, we give a combinatorial construction of the irreducible representations of the rook monoid. Since the rook monoid contains the symmetric group, it is perhaps not surprising that the construction outlined in this paper is very similar to the classic combinatorial construction of the irreducible Sn-representations: namely, the Specht modules.

Hat Derivatives, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

Definability, Canonical Models, And Compactness For Finitary Coalgebraic Modal Logic, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Behω(T) of coalgebras with morphisms preserving finitary behaviours is defined. We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Behω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.

Modal Predicates And Coequations, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

We show how coalgebras can be presented by operations and equations. This is a special case of Linton’s approach to algebras over a general base category X, namely where X is taken as the dual of sets. Since the resulting equations generalise coalgebraic coequations to situations without cofree coalgebras, we call them coequations. We prove a general co-Birkhoff theorem describing covarieties of coalgebras by means of coequations. We argue that the resulting coequational logic generalises modal logic.

Common Cause Failure Prediction Using Data Mapping, Paul H. Kvam, J. Glenn Miller

Department of Math & Statistics Faculty Publications

To estimate power plant reliability, a probabilistic safety assessment might combine failure data from various sites. Because dependent failures are a critical concern in the nuclear industry, combining failure data from component groups of different sizes is a challenging problem. One procedure, called data mapping, translates failure data across component group sizes. This includes common cause failures, which are simultaneous failure events of two or more components in a group. In this paper, we present methods for predicting future plant reliability using mapped common cause failure data. The prediction technique is motivated by discrete failure data from emergency diesel generators …

Levy-Like Continuity Theorems For Convergence In Distribution, Theodore P. Hill, Ulrich Krengel

Research Scholars in Residence

Levy’s classical continuity theorem states that if the pointwise limit of a sequence of characteristic functions exists, then the limit function itself is a characteristic function if and only if the limit function satisfies a single universal limit condition (in his case, the limit at zero is one), in which case the underlying measures converge weakly to the probability measure represented by the limit function. It is the purpose of this article to give a number of direct analogs of L´evy’s theorem for other probability-representing functions including moment sequences, maximal moment sequences, mean-residual-life functions, Hardy-Littlewood maximal functions, and failure-rate functions. …

Random Probability Measures With Given Mean And Variance Running Title: Random Probability Measures, Lisa Bloomer, Theodore P. Hill

Research Scholars in Residence

This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett’s Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.

Studying The Functional Genomics Of Stress Responses In Loblolly Pine With The Expresso Microarray Experiment Management System, Lenwood S. Heath, Naren Ramakrishnan, Ronald R. Sederoff, Ross W. Whetten, Boris I. Chevone, Craig Struble, Vincent Y. Jouenne, Dawei Chen, Leonel Van Zyl, Ruth Grene

Mathematics, Statistics and Computer Science Faculty Research and Publications

Conception, design, and implementation of cDNA microarray experiments present a variety of bioinformatics challenges for biologists and computational scientists. The multiple stages of data acquisition and analysis have motivated the design of Expresso, a system for microarray experiment management. Salient aspects of Expresso include support for clone replication and randomized placement; automatic gridding, extraction of expression data from each spot, and quality monitoring; flexible methods of combining data from individual spots into information about clones and functional categories; and the use of inductive logic programming for higher-level data analysis and mining. The development of Expresso is occurring in parallel with …