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Articles 21781 - 21810 of 27447

Full-Text Articles in Physical Sciences and Mathematics

2005 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics Jan 2005

2005 Undergraduate Mathematics Day Poster, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

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2005 Program And Abstracts, University Of Dayton. Department Of Mathematics Jan 2005

2005 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

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Zeros Of The Jost Function For A Class Of Exponentially Decaying Potentials, Daphne Gilbert, Alain Kerouanton Jan 2005

Zeros Of The Jost Function For A Class Of Exponentially Decaying Potentials, Daphne Gilbert, Alain Kerouanton

Articles

We investigate the properties of a series representing the Jost solution for the differential equation $-y''+q(x)y=lambda y$, $x geq 0$, $q in mathrm{L}({mathbb{R}}^{+})$. Sufficient conditions are determined on the real or complex-valued potential $q$ for the series to converge and bounds are obtained for the sets of eigenvalues, resonances and spectral singularities associated with a corresponding class of Sturm-Liouville operators. In this paper, we restrict our investigations to the class of potentials $q$ satisfying $|q(x)| leq ce^{-ax}$, $x geq 0$, for some $a>0$ and $c$ greator than 0.

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Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson Jan 2005

Where Does It All End? Boundaries Beyond Euclidean Space, Jonathan Thompson

Inquiry: The University of Arkansas Undergraduate Research Journal

No abstract provided.

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Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan Jan 2005

Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees …

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Asymptotic Methods In The Spectral Analysis Of Sturm-Liouville Operators, Daphne Gilbert Jan 2005

Asymptotic Methods In The Spectral Analysis Of Sturm-Liouville Operators, Daphne Gilbert

Articles

Gilbert, D.: Asymptotic Methods in the Spectral Analysis of Sturm-Lioville Operators.Sturm-Liouville theory : Past and Present, 2005, pp 121-136.

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Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz Jan 2005

Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this note, we provide a conveniently implementable basis for simplicial Nédélec spaces of any order in any space dimension. The main feature of the basis is that it is expressed solely in terms of the barycentric coordinates of the simplex.

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Modeling The Evolution Of Inhomogeneities, Marek Elźanowski, Serge Preston Jan 2005

Modeling The Evolution Of Inhomogeneities, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

A model of an anelastic evolution law of a defective continuum is discussed, emphasizing the role of the Clausius-Duhem inequality in selecting admissible processes.

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A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia Jan 2005

A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We study real Smirnov functions and investigate a certain *-closed subalgebra of the Smirnov class N^+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space H^p ∩ H^p [overscore over the second H^p]. This leads to a natural analog of the Riesz projection on a certain quotient space of L^p for p ϵ (0, 1). We also study a Herglotz-like integral transform for singular measures on the unit circle ∂D.

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Microarray Data From A Statistician’S Point Of View, Johanna S. Hardin Jan 2005

Microarray Data From A Statistician’S Point Of View, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

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Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia Jan 2005

Inner Matrices And Darlington Synthesis, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We describe and parameterize the solutions of the scalar valued Darlington synthesis problem. In the case of rational data we derive a simple procedure for producing all possible solutions.

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A Map On The Space Of Rational Functions, G. Boros, J. Little, V. Moll, Edward Mosteig, R. Stanley Jan 2005

A Map On The Space Of Rational Functions, G. Boros, J. Little, V. Moll, Edward Mosteig, R. Stanley

Mathematics, Statistics and Data Science Faculty Works

We describe dynamical properties of a map defined on the space of rational functions. The fixed points of F are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials.

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Derived Categories And The Analytic Approach To General Reciprocity Laws. Part I, Michael Berg Jan 2005

Derived Categories And The Analytic Approach To General Reciprocity Laws. Part I, Michael Berg

Mathematics, Statistics and Data Science Faculty Works

We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations of n-Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. Subsequently, we begin to investigate conditions on associated sheaves and a derived category of sheaf complexes specifically designed for an attack on Hecke's eighty-year-old challenge.

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Commensurability Classes Of Twist Knots, Jim Hoste, Patrick D. Shanahan Jan 2005

Commensurability Classes Of Twist Knots, Jim Hoste, Patrick D. Shanahan

Mathematics, Statistics and Data Science Faculty Works

In this paper we prove that if MK is the complement of a non-fibered twist knot K in S3, then MK is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by D. Calegari and N. Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.

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From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber Jan 2005

From Loop Groups To 2-Groups, John C. Baez, Danny Stevenson, Alissa S. Crans, Urs Schreiber

Mathematics, Statistics and Data Science Faculty Works

We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism called the "Jacobiator". Similarly, a Lie 2-group is a categorified version of a Lie group. If G is a simply-connected compact simple Lie group, there is a 1-parameter family of Lie 2-algebras g_k each having Lie(G) as its Lie algebra of objects, but with a Jacobiator built from the canonical 3-form on G. There appears to be no Lie 2-group …

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On The Structure Of Graphs With Non-Surjective L(2,1)-Labelings, John P. Georges, David W. Mauro Jan 2005

On The Structure Of Graphs With Non-Surjective L(2,1)-Labelings, John P. Georges, David W. Mauro

Faculty Scholarship

For a graph G, an L(2,1)-labeling of G with span k is a mapping $L \right arrow \{0, 1, 2, \ldots, k\}$ such that adjacent vertices are assigned integers which differ by at least 2, vertices at distance two are assigned integers which differ by at least 1, and the image of L includes 0 and k. The minimum span over all L(2,1)-labelings of G is denoted $\lambda(G)$, and each L(2,1)-labeling with span $\lambda(G)$ is called a $\lambda$-labeling. For $h \in \{1, \ldots, k-1\}$, h is a hole of Lif and only if h …

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Commutative Quartic P-Galois Extensions Over A Field Of Characteristic Not 2, Atsushi Nakajima Jan 2005

Commutative Quartic P-Galois Extensions Over A Field Of Characteristic Not 2, Atsushi Nakajima

Turkish Journal of Mathematics

In [2], K. Kishimoto introduced the notion of P-Galois extensions and gave some fundamental properties of these extensions. P-Galois extensions relate Hopf Galois extensions, and the author treated these topics in [5]. Moreover, the cubic P-Galois extensions over a field were completely determined in [6]. Continuing [5] and [6], we classify commutative quartic P-Galois extensions over a field of characteristic not 2.

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On A Class Of Para-Sakakian Manifolds, Ci̇han Özgür Jan 2005

On A Class Of Para-Sakakian Manifolds, Ci̇han Özgür

Turkish Journal of Mathematics

In this study, we investigate Weyl-pseudosymmetric Para-Sasakian manifolds and Para-Sasakian manifolds satisfying the condition C \cdot S=0.

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Characterizations Of Augmented Graded Rings, Mashhoor Refai, Fida A. M. Moh'd Jan 2005

Characterizations Of Augmented Graded Rings, Mashhoor Refai, Fida A. M. Moh'd

Turkish Journal of Mathematics

In this paper, we introduce some characterizations for augmented graded rings in special cases.

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On Banach Lattice Algebras, Ayşe Uyar Jan 2005

On Banach Lattice Algebras, Ayşe Uyar

Turkish Journal of Mathematics

In this study, without using the assumption a^{-1} > 0, it is shown that E is lattice - and algebra - isometric isomorphic to the reals R whenever E is a Banach lattice f-algebra with unit e, e = 1, in which for every a > 0 the inverse a^{-1} exists. Subsequently, an alternative proof to a result of Huijsmans is given for Banach lattice algebras.

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Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth Jan 2005

Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth

Mathematics Faculty Publications

In this note, we prove that in a Hausdorff topological abelian group, the closed subgroup generated by all compact elements is equal to teh closed subgroup generated by all compact elements which are topologically p-torsion for some prime p. In particular, this yields a new, short solution to a question raised by Armacost [A]. Using Pontrjagin duality, we obtain new descriptions of the identity component of a locally compact abelian group.

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Kinetic Structure Simulations Of Nematic Polymers In Plane Couette Cells. Ii: In-Plane Structure Transitions, M. Gregory Forest, Ruhai Zhou, Qi Wang Jan 2005

Kinetic Structure Simulations Of Nematic Polymers In Plane Couette Cells. Ii: In-Plane Structure Transitions, M. Gregory Forest, Ruhai Zhou, Qi Wang

Mathematics & Statistics Faculty Publications

Nematic, or liquid crystalline, polymer (LCP) composites are composed of large aspect ratio rod-like or platelet macromolecules. This class of nanocomposites exhibits tremendous potential for high performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. Fibers made from nematic polymers have set synthetic materials performance standards for decades. The current target is to engineer multifunctional films and molded parts, for which processing flows are shear-dominated. Nematic polymer films inherit anisotropy from collective orientational distributions of the molecular constituents and develop heterogeneity on length scales that are, as yet, not well understood and thereby uncontrollable. Rigid LCPs in …

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A Template Functional-Gage Design Using Parameter-File Table In Autodesk Inventor, Cheng Lin, Moustafa Moustafa Jan 2005

A Template Functional-Gage Design Using Parameter-File Table In Autodesk Inventor, Cheng Lin, Moustafa Moustafa

Engineering Technology Faculty Publications

A systematic approach using Autodesk Inventor to design the functional gages of Geometric Dimensioning & Tolerancing (GD&T) is presented. The gages can be used to check straightness, angularity, perpendicularity, parallelism, and position tolerances of a part when geometric tolerances are specified with Maximum Material Condition (MMC). Four steps are proposed to accomplish the task: (1) creation of two-dimensional (2-D) initial template files, (2) generation of hierarchical folders for the template files, (3) creation a 3-D gage model from a specific template file, and (4) dimensioning and generation of the gage drawing. Results show that, by following this approach, students can …

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Rational Hyperholomorphic Functions In R4, Daniel Alpay, Michael Shapiro, Dan Volok Jan 2005

Rational Hyperholomorphic Functions In R4, Daniel Alpay, Michael Shapiro, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of Cauchy-Kovalevskaya quotients of polynomials, the second in terms of realizations and the third in terms of backward-shift invariance. Also introduced and studied are the counterparts of the Arveson space and Blaschke factors.

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Applications Of Bimatrices To Some Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2005

Applications Of Bimatrices To Some Fuzzy And Neutrosophic Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematical tools which can give the hidden pattern of the problem under investigation. This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. …

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Continued Radicals, Jamie Johnson Jan 2005

Continued Radicals, Jamie Johnson

Masters Theses & Specialist Projects

If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the …

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Feedback Classification Of Multi-Input Nonlinear Control Systems, Issa Amadou Tall Jan 2005

Feedback Classification Of Multi-Input Nonlinear Control Systems, Issa Amadou Tall

Articles and Preprints

We study the feedback group action on multi-input nonlinear control systems with uncontrollable mode. We follow slightly an approach proposed in Kang and Krener [W. Kang and A. J. Krener, SIAM J. Control. Optim., 30 (1992), pp. 1319–1337] which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes, on one hand, the results obtained in the single-input case and, on the other hand, those recently obtained by the same author in the controllable case. We illustrate our results by studying the Caltech Multi-Vehicle Wireless Testbed (MVWT) and the prototype …

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Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam Jan 2005

Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) Growing up as a child in southern England, my early memories of snow include trudging home from school with my father, gazing at the seemingly enormous snowdrifts that smoothed the hedgerows, fields and bushes, while listening to the soft “scrunch” of the snow under my Wellington boots. In the country, snow stretching as far as I could see was not a particularly uncommon sight. The quietness of the land under a foot of snow seemed eerie. I cannot remember the first time I looked at snowflakes per se; my interests as a small child were primarily in their …

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An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov Jan 2005

An Explicit Mapping Between The Frequency Domain And The Time Domain Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov

Articles

Explicit expressions are presented that describe the input-output behaviour of a nonlinear system in both the frequency and the time domain. The expressions are based on a set of coefficients that do not depend on the input to the system and are universal for a given system. The anharmonic oscillator is chosen as an example and is discussed for different choices of its physical parameters. It is shown that the typical approach for the determination of the Volterra Series representation is not valid for the important case when the nonlinear system exhibits oscillatory behaviour and the input has a pole …

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Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov Jan 2005

Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov

Articles

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.

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