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Articles 22441 - 22470 of 27436

Full-Text Articles in Physical Sciences and Mathematics

Coloring Graphs With Crossings, Wei Zhao Jan 2003

Coloring Graphs With Crossings, Wei Zhao

Honors Theses

No abstract provided.

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On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue Jan 2003

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

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Open Problems From The Linz2000 Closing Session, Lawrence Stout Jan 2003

Open Problems From The Linz2000 Closing Session, Lawrence Stout

Scholarship

No abstract provided.

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2003 Program And Abstracts, University Of Dayton. Department Of Mathematics Jan 2003

2003 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Program and abstracts of papers presented at the 2003 Undergraduate Mathematics Day at the University of Dayton

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2003 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics Jan 2003

2003 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

Poster of Undergraduate Mathematics Day events held Saturday, November 1, 2003.

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Curvature (Abstract), Chikako Mese Jan 2003

Curvature (Abstract), Chikako Mese

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

We may have an intuitive idea of what it means for surfaces to be curved, but what does it mean for higher dimensional spaces to be curved?

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A Mathematical Model For Simplifying Representations Of Objects In A Geographic Information System, Gabriel Perrow Jan 2003

A Mathematical Model For Simplifying Representations Of Objects In A Geographic Information System, Gabriel Perrow

Electronic Theses and Dissertations

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that …

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U(1)-Invariant Special Lagrangian 3-Folds In {\Mathbb C}^3 And Special Lagrangian Fibrations, Dominic Joyce Jan 2003

U(1)-Invariant Special Lagrangian 3-Folds In {\Mathbb C}^3 And Special Lagrangian Fibrations, Dominic Joyce

Turkish Journal of Mathematics

This is a survey of the author's series of three papers [8, 9, 10] on special Lagrangian 3-folds (SL 3-folds) in {\mathbb C}^3 invariant under the U(1)-action (z_1,z_2,z_3)e^{i\theta}z_1, e^{-i\theta}z_2,z_3), and their sequel {\mathbb C} [11] on special Lagrangian fibrations and the SYZ Conjecture. We briefly present the main results of these four long papers, giving some explanation and motivation, but no proofs. The aim is to make the results and ideas accessible to String Theorists and others who have an interest in special Lagrangian 3-folds and fibrations, but have no desire to read pages of technical analysis. Let N be …

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On Locally M-Pseudoconvex A^*-Algebras, A. El Kinani Jan 2003

On Locally M-Pseudoconvex A^*-Algebras, A. El Kinani

Turkish Journal of Mathematics

We consider classical A^*-algebras in the context of locally pseudoconvex algebras. Results concerning the auxiliary topology and A^* -algebras of the first kind are given.

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A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat Jan 2003

A Multilevel Discontinuous Galerkin Method, Jay Gopalakrishnan, Guido Kanschat

Mathematics and Statistics Faculty Publications and Presentations

A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.

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A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan Jan 2003

A Schwarz Preconditioner For A Hybridized Mixed Method, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the ux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners for the lowest order case of the Raviart-Thomas method have been constructed previously by exploiting its connection with a nonconforming method, our approach is different, in that we use a new variational characterization of the Lagrange multiplier equation. This allows us to …

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A Few Weight Systems Arising From Intersection Graphs, Blake Mellor Jan 2003

A Few Weight Systems Arising From Intersection Graphs, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

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A Geometric Interpretation Of Milnor's Triple Invariants, Blake Mellor, Paul Melvin Jan 2003

A Geometric Interpretation Of Milnor's Triple Invariants, Blake Mellor, Paul Melvin

Mathematics, Statistics and Data Science Faculty Works

Milnor's triple linking numbers of a link in the 3-sphere are interpreted geometrically in terms of the pattern of intersections of the Seifert surfaces of the components of the link. This generalizes the well known formula as an algebraic count of triple points when the pairwise linking numbers vanish.

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Finding Common Ground: Collaboration Across The Disciplines In The Scholarship Of Teaching, Elaine K. Yakura, Curtis D. Bennett Jan 2003

Finding Common Ground: Collaboration Across The Disciplines In The Scholarship Of Teaching, Elaine K. Yakura, Curtis D. Bennett

Mathematics, Statistics and Data Science Faculty Works

Many recent writings on the scholarship of teaching discuss the need to locate this scholarship within the disciplines. The authors argue that while scholarship within the disciplines is important, it should not come at the expense of work across the disciplines. They demonstrate the usefulness of cross-disciplinary collaboration for the scholarship of teaching and learning through the specific example of how collaboration contributed to their understanding of the role of such scholarship in the teaching of mathematics and negotiations courses. The authors also outline some of the pitfalls of cross-disciplinary collaboration, and they offer suggestions for beginning collaborative initiatives.

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On Regular Graphs Optimally Labeled With A Condition At Distance Two, John P. Georges, David W. Mauro Jan 2003

On Regular Graphs Optimally Labeled With A Condition At Distance Two, John P. Georges, David W. Mauro

Faculty Scholarship

For positive integers $j \geq k$, the $\lambda_{j,k}$-number of graph Gis the smallest span among all integer labelings of V(G) such that vertices at distance two receive labels which differ by at least k and adjacent vertices receive labels which differ by at least j. We prove that the $\lambda_{j,k}$-number of any r-regular graph is no less than the $\lambda_{j,k}$-number of the infinite r-regular tree $T_{\infty}(r)$. Defining an r-regular graph G to be $(j,k,r)$-optimal if and only if $\lambda_{j,k}(G) = \lambda_{j,k}(T_{\infty}(r))$, we establish the equivalence between $(j,k,r)$-optimal graphs and r-regular bipartite …

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Robustly Transitive Sets And Heterodimensional Cycles, Christian Bonatti, Lorenzo J. Díaz, Enrique R. Pujals, Jorge Rocha Jan 2003

Robustly Transitive Sets And Heterodimensional Cycles, Christian Bonatti, Lorenzo J. Díaz, Enrique R. Pujals, Jorge Rocha

Publications and Research

It is known that all non-hyperbolic robustly transitive sets Λφ have a dominated splitting and, generically, contain periodic points of different indices. We show that, for a C1-dense open subset of diffeomorphisms φ, the indices of periodic points in a robust transitive set Λφ form an interval in ℕ. We also prove that the homoclinic classes of two periodic points in Λφ are robustly equal. Finally, we describe what sort of homoclinic tangencies may appear in Λφ by studying its dominated splittings.

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A Monopole Homology For Integral Homology 3-Spheres, Weiping Li Jan 2003

A Monopole Homology For Integral Homology 3-Spheres, Weiping Li

Turkish Journal of Mathematics

To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded (monopole) homology MH_*(Y, I_{\eta}(\Theta; \eta_0)) whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow I_{\eta}(\Theta; \eta_0), where \Theta is the unique U(1)-reducible monopole of the Seiberg-Witten equation on Y and \eta_0 is a reference perturbation datum. The definition uses the moduli space of monopoles on Y \times {\mathbb R} introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology MH_*(Y, I_{\eta}(\Theta; \eta_0)) is invariant among Riemannian metrics with same I_{\eta}(\Theta; \eta_0). This provides a chamber-like structure for …

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On Cofinite Subgroups Of Mapping Class Groups, Mustafa Korkmaz Jan 2003

On Cofinite Subgroups Of Mapping Class Groups, Mustafa Korkmaz

Turkish Journal of Mathematics

For every positive integer n, we exhibit a cofinite subgroup \Gamma_n of the mapping class group of a surface of genus at most two such that \Gamma_n admits an epimorphism onto a free group of rank n. We conclude that H^1 (\Gamma_n; {\mathbb Z}) has rank at least n and the dimension of the second bounded cohomology of each of these mapping class groups is the cardinality of the continuum. In the case of genus two, the groups \Gamma_n can be chosen not to contain the Torelli group. Similarly for hyperelliptic mapping class groups. We also exhibit an automorphism of …

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On L_{P}-Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali Jassim Mohammad Jan 2003

On L_{P}-Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali Jassim Mohammad

Turkish Journal of Mathematics

In the present paper, we study some direct results in L_{p} -approximation by a linear combination of a new sequence of linear positive operators. The error in the approximation is estimated in terms of the higher order integral modulus of smoothness using some properties of the Steklov means.

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Pushouts Of Profinite Crossed Modules And Cat^1-Profinite Groups, Murat Alp, Özgün Gürmen Jan 2003

Pushouts Of Profinite Crossed Modules And Cat^1-Profinite Groups, Murat Alp, Özgün Gürmen

Turkish Journal of Mathematics

In this paper, we presented a brief review of crossed modules [7], cat^1-groups [6], pullback crossed modules [4], pullback cat^1-group [1], profinite crossed modules [5], cat^1-profinite groups [5], pullback profinite crossed modules [5], pullback cat^1-profinite groups [3]. We defined the pushout cat^1-profinite groups and gave the left adjoint constructions.

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Partitioning Regular Polygons Into Circular Pieces I: Convex Partitions, Mirela Damian, Joseph O'Rourke Jan 2003

Partitioning Regular Polygons Into Circular Pieces I: Convex Partitions, Mirela Damian, Joseph O'Rourke

Computer Science: Faculty Publications

We explore an instance of the question of partitioning a polygon into pieces, each of which is as “circular” as possible, in the sense of having an aspect ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. The problem is rich even for partitioning regular polygons into convex pieces, the focus of this paper. We show that the optimal (most circular) partition for an equilateral triangle has an infinite number of pieces, with the lower bound approachable to any accuracy desired by a …

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The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis Jan 2003

The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis

Mathematics Faculty Publications

A residuated lattice is an ordered algebraic structure [formula] such that is a lattice, is a monoid, and \ and / are binary operations for which the equivalences [formula] hold for all a,b,c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as "dividing" on the right by b and "dividing" on the left by a. The class of all residuated lattices is denoted by ℛℒ The study of such objects originated in the context of the theory of ring ideals in the 1930s. The …

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On String Topology Of Three Manifolds, Hossein Abbaspour Jan 2003

On String Topology Of Three Manifolds, Hossein Abbaspour

Dissertations, Theses, and Capstone Projects

In this dissertation we establish a connection between some aspects of the string topology of three dimensional manifolds and their topology and geometry using the theory of the prime decomposition and characteristic surfaces.

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Crowded And Selective Ultrafilters Under The Covering Property Axiom, Krzysztof Ciesielski Jan 2003

Crowded And Selective Ultrafilters Under The Covering Property Axiom, Krzysztof Ciesielski

Faculty & Staff Scholarship

In the paper we formulate an axiom CPA_{prism}^{game}, which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to \omega1, while \continuum=\omega2: the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number u. We will also show that CPA_{prism}^{game} implies the existence of crowded and selective ultrafilters as well as nonselective P-points. In addition we prove that under CPA_{prism}^{game} every …

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Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek Jan 2003

Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek

Articles and Preprints

We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analyzing, step by step, the action of homogeneous transformations on the homogeneous part of the same degree of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and a dual canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms (resp., their dual canonical forms) coincide. We give an explicit construction of transformations bringing …

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Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen Jan 2003

Protocols For Disease Classification From Mass Spectrometry Data, Michael Wagner, Dayanand Naik, Alex Pothen

Mathematics & Statistics Faculty Publications

We report our results in classifying protein matrix-assisted laser desorption/ionizationtime of flight mass spectra obtained from serum samples into diseased and healthy groups. We discuss in detail five of the steps in preprocessing the mass spectral data for biomarker discovery, as well as our criterion for choosing a small set of peaks for classifying the samples. Cross-validation studies with four selected proteins yielded misclassification rates in the 10-15% range for all the classification methods. Three of these proteins or protein fragments are down-regulated and one up-regulated in lung cancer, the disease under consideration in this data set. When cross-validation studies …

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Simplicity Of Ultragraph Algebras, Mark Tomforde Jan 2003

Simplicity Of Ultragraph Algebras, Mark Tomforde

Dartmouth Scholarship

In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an ultragraph algebra to be purely infinite and to be AF. Using these techniques we also produce an example of an ultragraph algebra which is neither a graph algebra nor an Exel-Laca algebra. We conclude by proving that the C*-algebras of ultragraphs with no sinks are Cuntz-Pimsner algebras.

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Boundary Volume And Length Spectra Of Riemannian Manifolds: What The Middle Degree Hodge Spectrum Doesn't Reveal, Carolyn S. Gordon, Juan P. Rossetti Jan 2003

Boundary Volume And Length Spectra Of Riemannian Manifolds: What The Middle Degree Hodge Spectrum Doesn't Reveal, Carolyn S. Gordon, Juan P. Rossetti

Dartmouth Scholarship

No abstract provided.

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Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp Jan 2003

Category Of Nonlinear Evolution Equations, Algebraic Structure, And R-Matrix, Zhijun Qiao, Cewen Cao, Walter Strampp

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper we deal with the category of nonlinear evolution equations ~NLEEs! associated with the spectral problem and provide an approach for constructing their algebraic structure and r-matrix. First we introduce the category of NLEEs, which is composed of various positive order and negative order hierarchies of NLEEs both integrable and nonintegrable. The whole category of NLEEs possesses a generalized Lax representation. Next, we present two different Lie algebraic structures of the Lax operator: one of them is universal in the category, i.e., independent of the hierarchy, while the other one is nonuniversal in the hierarchy, i.e., dependent on …

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Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath Jan 2003

Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.

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