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2004

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Articles 241 - 270 of 318

Full-Text Articles in Mathematics

F-Invariant Submanifolds Of Kaehlerian Product Manifold, Mehmet Atçeken Jan 2004

F-Invariant Submanifolds Of Kaehlerian Product Manifold, Mehmet Atçeken

Turkish Journal of Mathematics

In this paper, the geometry of F-invariant submanifolds of a Kaehlerian product manifold is studied. The fundamental properties of these submanifolds are investigated such as pseudo umbilical, curvature invariant, totally geodesic, mixed geodesic submanifold and locally decomposable Riemannian product manifold.

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A Generalization Of A Result On Torsion-Free Groups With All Subgroups Subnormal, Tahi̇re Özen Jan 2004

A Generalization Of A Result On Torsion-Free Groups With All Subgroups Subnormal, Tahi̇re Özen

Turkish Journal of Mathematics

The main result in this paper is the following: Let G be a torsion-free locally nilpotent group and let F be a finitely generated subgroup of G. If every subgroup of G containing F is subnormal in G, then G is nilpotent.

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On Local Hörmander-Beurling Spaces, Jairo Villegas Jan 2004

On Local Hörmander-Beurling Spaces, Jairo Villegas

Turkish Journal of Mathematics

In this paper we aim to extend a result of Hörmander's, that \mathcal{B}_{p,k}^{loc}(\Omega)\subset\mathcal{C}^m(\Omega) if \frac{(1+\left \cdot\right )^m}{k}\in L_{p^\prime}, to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space \bigcap_{j=1}^\infty\mathcal{B}_{p_j,k_j}^{loc} (\Omega, E) (1\leq p_j\leq\infty, k_j=e^{j\omega}, j=1,2,\dots) is topologically isomorphic to \mathcal{E}_\omega(\Omega, E ). Moreover, it is well known that the union of Sobolev spaces \mathcal{H}_{s}^{loc}(\Omega) (=\mathcal{B}_{2,(1+ \cdot ^2)^{s/2}}^{loc}(\Omega)) coincides with the space \mathcal{D}^{\prime\,F}(\Omega) of finite order distributions on \Omega. We show that this is also verified in the context of vector valued Beurling ultradistributions.

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Integral Transforms, Convolution Products, And First Variations, Bong Jin Kim, Byoung Soo Kim, David Skough Jan 2004

Integral Transforms, Convolution Products, And First Variations, Bong Jin Kim, Byoung Soo Kim, David Skough

Department of Mathematics: Faculty Publications

We establish the various relationships that exist among the integral transform Fα,βF, the convolution product (F∗G)α, and the first variation δF for a class of functionals defined on K[0,T], the space of complex-valued continuous functions on [0,T] which vanish at zero.

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Discrete Approximations And Necessary Optimality Conditions For Functional-Differential Inclusions Of Neutral Type, Boris S. Mordukhovich, Lianwen Wang Jan 2004

Discrete Approximations And Necessary Optimality Conditions For Functional-Differential Inclusions Of Neutral Type, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper deals with necessary optimality conditions for optimal control systems governed by constrained functional-differential inclusions of neutral type. While some results are available for smooth control systems governed by neutral functional-differential equations, we are not familiar with any results for neutral functional-differential inclusions, even with smooth cost functionals in the absence of endpoint constraints. Developing the method of discrete approximations and employing advanced tools of generalized differentiation, we conduct a variational analysis of neutral functional-differential inclusions and obtain new necessary optimality conditions of both Euler-Lagrange and Hamiltonian types.

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Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam Jan 2004

Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam

Department of Math & Statistics Faculty Publications

We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) …

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A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam Jan 2004

A Nonlinear Random Coefficients Model For Degradation Testing, Suk Joo Bae, Paul H. Kvam

Department of Math & Statistics Faculty Publications

As an alternative to traditional life testing, degradation tests can be effective in assessing product reliability when measurements of degradation leading to failure can be observed. This article presents a degradation model for highly reliable light displays, such as plasma display panels and vacuum fluorescent displays (VFDs). Standard degradation models fail to capture the burn-in characteristics of VFDs, when emitted light actually increases up to a certain point in time before it decreases (or degrades) continuously. Random coefficients are used to model this phenomenon in a nonlinear way, which allows for a nonmonotonic degradation path. In many situations, the relative …

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Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg Jan 2004

Zeros Of Functions With Finite Dirichlet Integral, William T. Ross, Stefan Richter, Carl Sundberg

Department of Math & Statistics Faculty Publications

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

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Gamma-Set Domination Graphs. I: Complete Biorientations Of Q-Extended Stars And Wounded Spider Graphs, Kim A. S. Factor Jan 2004

Gamma-Set Domination Graphs. I: Complete Biorientations Of Q-Extended Stars And Wounded Spider Graphs, Kim A. S. Factor

Mathematics, Statistics and Computer Science Faculty Research and Publications

The domination number of a graph G, γ(G), and the domination graph of a digraph D, dom(D) are integrated in this paper. The γ-set domination graph of the complete biorientation of a graph G, domγ(G) is created. All γ-sets of specific trees T are found, and dom-γ(T) is characterized for those classes.

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Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall Jan 2004

Tree-Like Continua And 2-To-1 Maps, Jo Heath, Van C. Nall

Department of Math & Statistics Faculty Publications

It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.

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Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro Jan 2004

Prolongations And Cyclic Vectors, William T. Ross, Harold S. Shapiro

Department of Math & Statistics Faculty Publications

For functions belonging to invariant subspaces of the backward shift operator Bf = (f − f(0))/z on spaces of analytic functions on the unit disk D, we explore, in a systematic way, the continuation properties of these functions.

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The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson Jan 2004

The Backward Shift On The Space Of Chauchy Transforms, William T. Ross, Joseph A. Cima, Alec L. Matheson

Department of Math & Statistics Faculty Publications

This note examines the subspaces of the space of Cauchy transforms of measures on the unit circle that are invariant under the backward shift operator f --> z-1 (f—f (0)). We examine this question when the space of Cauchy transforms is endowed with both the norm and weak* topologies.

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Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz Jan 2004

Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.

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Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz Jan 2004

Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a nonelliptic indefinite operator. With the help of a few new estimates, the …

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A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan Jan 2004

A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give a new characterization of the approximate solution given by hybridized mixed methods for second order self-adjoint elliptic problems. We apply this characterization to obtain an explicit formula for the entries of the matrix equation for the Lagrange multiplier unknowns resulting from hybridization. We also obtain necessary and sufficient conditions under which the multipliers of the Raviart–Thomas and the Brezzi–Douglas–Marini methods of similar order are identical.

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Combinatorial Identities Deriving From The N-Th Power Of A 2 X 2 Matrix, James Mclaughlin Jan 2004

Combinatorial Identities Deriving From The N-Th Power Of A 2 X 2 Matrix, James Mclaughlin

Mathematics Faculty Publications

In this paper we give a new formula for the n-th power of a 2 × 2 matrix. More precisely, we prove the following: Let A = (a b c d) be an arbitrary 2 × 2 matrix, T = a + d its trace, D = ad − bc its determinant and define yn : = b X n/2c i=0 (n − i i )T n−2i (−D) i . Then, for n ≥ 1, A n = (yn − d yn−1 b yn−1 c yn−1 yn − a yn−1) . We use this formula together with an existing formula …

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A Theorem On Divergence In The General Sense For Continued Fractions, Douglas Bowman, James Mclaughlin Jan 2004

A Theorem On Divergence In The General Sense For Continued Fractions, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

If the odd and even parts of a continued fraction converge to different values, the continued fraction may or may not converge in the general sense. We prove a theorem which settles the question of general convergence for a wide class of such continued fractions. We apply this theorem to two general classes of q continued fraction to show, that if G(q) is one of these continued fractions and |q| > 1, then either G(q) converges or does not converge in the general sense. We also show that if the odd and even parts of the continued fraction K∞n=1an/1 converge to …

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On The Divergence Of The Rogers-Ramanujan Continued Fraction On The Unit Circle, Douglas Bowman, James Mclaughlin Jan 2004

On The Divergence Of The Rogers-Ramanujan Continued Fraction On The Unit Circle, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

This paper is an intensive study of the convergence of the Rogers-Ramanujan continued fraction. Let the continued fraction expansion of any irrational number t ∈ (0, 1) be denoted by [0, a1(t), a2(t), · · · ] and let the i-th convergent of this continued fraction expansion be denoted by ci(t)/di(t). Let S = {t ∈ (0, 1) : ai+1(t) ≥ φ di(t) infinitely often}, where φ = (√ 5 + 1)/2. Let YS = {exp(2πit) : t ∈ S}. It is shown that if y ∈ YS then the Rogers-Ramanujan continued fraction, R(y), diverges at y. S is an …

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The Wave Structure Function And Temporal Frequency Spread In Weak To Strong Optical Turbulence, Aaron J. Masino Jan 2004

The Wave Structure Function And Temporal Frequency Spread In Weak To Strong Optical Turbulence, Aaron J. Masino

Electronic Theses and Dissertations

This paper presents analytic expressions for the wave structure function, frequency spread of the temporal frequency spectrum, and the temporal frequency spectrum of optical signals propagating through a random medium, specifically the Earth’s atmosphere. The results are believed to be valid for all optical turbulence conditions. These expressions are developed using the Rytov approximation method. Generally, the validity of statistical quantities obtained via this method is restricted to conditions of weak optical turbulence. However, in this work, by using a modification of the effective atmospheric spectral model presented by Andrews et al. for scintillation index, wave structure function expressions have …

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The Effects Of The Cognitive Tutor Algebra On Student Attitudes And Achievement In A 9th Grade Algebra Course, Gary S. Plano Jan 2004

The Effects Of The Cognitive Tutor Algebra On Student Attitudes And Achievement In A 9th Grade Algebra Course, Gary S. Plano

Seton Hall University Dissertations and Theses (ETDs)

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Palindrome-Polynomials With Roots On The Unit Circle, John Konvalina, Valentin Matache Jan 2004

Palindrome-Polynomials With Roots On The Unit Circle, John Konvalina, Valentin Matache

Mathematics Faculty Publications

Given a polynomial f(x) of degree n, let fr(x) denote its reciprocal, i.e., fr(x) = xnf(1=x). If a polynomial is equal to its reciprocal, we call it a palindrome since the coefficients are the same when read backwards or forwards. In this mathematical note we show that palindromes whose coefficients satisfy a certain magnitude-condition must have a root on the unit circle...

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Simultaneous Data Perturbations And Analytic Center Convergence, Allen G. Holder Jan 2004

Simultaneous Data Perturbations And Analytic Center Convergence, Allen G. Holder

Mathematics Faculty Research

The central path is an infinitely smooth parameterization of the non-negative real line, and its convergence properties have been investigated since the middle 1980s. However, the central "path" followed by an infeasible-interior-point method relies on three parameters instead of one, and is hence a surface instead of a path. The additional parameters are included to allow for simultaneous perturbations in the cost and righ-hand side vectors. This paper provides a detailed analysis of the perturbed central path that is followed by infeasible-interior-point methods, and we characterize when such a path converges. We develop a set (Hausdorff) convergence property and show …

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Newton-Raphson Versus Fisher Scoring Algorithms In Calculating Maximum Likelihood Estimates, Andrew Schworer, Peter Hovey Jan 2004

Newton-Raphson Versus Fisher Scoring Algorithms In Calculating Maximum Likelihood Estimates, Andrew Schworer, Peter Hovey

Undergraduate Mathematics Day: Past Content

In this work we explore the difficulties and the means by which maximum likelihood estimates can be calculated iteratively when direct solutions do not exist. The Newton-Raphson algorithm can be used to do these calculations. However, this algorithm has certain limitations that will be discussed. An alternative algorithm, Fisher scoring, which is less dependent on specific data values, is a good replacement. The Fisher scoring method converged for data sets available to the authors, that would not converge when using the Newton-Raphson algorithm. An analysis and discussion of both algorithms will be presented. Their real world application on analysis of …

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Pebbling On Directed Graphs, Gayatri Gunda, Aparna Higgins Jan 2004

Pebbling On Directed Graphs, Gayatri Gunda, Aparna Higgins

Undergraduate Mathematics Day: Past Content

Consider a finite connected graph G whose vertices are labeled with non-negative integers representing the number of pebbles on each vertex. A pebbling move on a graph G is defined as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number f(G) of a connected graph is the least number of pebbles such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified but arbitrary vertex. We consider pebbling on directed graphs and study what configurations of directed graphs allow for pebbling …

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Newton’S Unfinished Business: Uncovering The Hidden Powers Of Eleven In Pascal’S Triangle, Robert Arnold, Tom Attenweiler, Christopher Brockman, Bethany Lesko, Christine Martinek, Colleen Mccormick, Jessica Mcquiston, Jessica Parker, Amy Rohmiller Jan 2004

Newton’S Unfinished Business: Uncovering The Hidden Powers Of Eleven In Pascal’S Triangle, Robert Arnold, Tom Attenweiler, Christopher Brockman, Bethany Lesko, Christine Martinek, Colleen Mccormick, Jessica Mcquiston, Jessica Parker, Amy Rohmiller

Undergraduate Mathematics Day: Past Content

Sir Isaac Newton once observed that the first five rows of Pascal’s Triangle, when concatenated, yield the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. Was he correct? While not all rows can simply be concatenated, the powers of eleven can still be easily derived from each. We have uncovered an algorithm the supports Newton’s claim and will prove its validity for all rows of the Triangle.

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2004 Vol. 1 Table Of Contents, University Of Dayton. Department Of Mathematics Jan 2004

2004 Vol. 1 Table Of Contents, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Past Content

No abstract provided.

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Some Interesting Multiples Of Nine: Use Your Digits To Get The Digits!, Kevin Hurley Jan 2004

Some Interesting Multiples Of Nine: Use Your Digits To Get The Digits!, Kevin Hurley

Undergraduate Mathematics Day: Past Content

We have unraveled two neat and powerful algorithms for calculating certain multiples of nine. These discussions might make for an interesting introduction to a number theory course, or a supplemental project in calculus or advanced algebra. The mathematics involved is within a student’s grasp, and the results are quite startling.

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Ramanujan Graphs In The Construction Of Ldpc Codes, Walter H. Chen Jan 2004

Ramanujan Graphs In The Construction Of Ldpc Codes, Walter H. Chen

Undergraduate Mathematics Day: Past Content

Low-density parity-check (LDPC) codes have recently become a popular interdisciplinary area of research. Widely unknown after their invention by Gallager in 1965, the existence of efficient encoding and decoding algorithms coupled with performance that operates near theoretical limits has led to the rediscovery of LDPC codes. This paper will address the reasoning and construction of LDPC codes with Ramanujan graphs.

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How Not To Get Lost While On A Random Walk, Robert Lewand Jan 2004

How Not To Get Lost While On A Random Walk, Robert Lewand

Undergraduate Mathematics Day: Past Content

What happens if you go on a random walk? Will you ever return home? Well, sometimes yes (probably) and sometimes no (probably). During this talk we will derive some elementary identities in favor you're not getting lost while on a random walk.

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2004 Alumni Presenters, University Of Dayton. Department Of Mathematics Jan 2004

2004 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

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