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Articles 20671 - 20700 of 27475

Full-Text Articles in Physical Sciences and Mathematics

The Center Of Some Braid Groups And The Farrell Cohomology Of Certain Pure Mapping Class Groups, Craig A. Jensen, Yu Qing Chen, Henry H. Glover Jan 2007

The Center Of Some Braid Groups And The Farrell Cohomology Of Certain Pure Mapping Class Groups, Craig A. Jensen, Yu Qing Chen, Henry H. Glover

Mathematics Faculty Publications

In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the primary part of the Farrell cohomology groups of certain mapping class groups are elementary abelian groups. At the end we compute the primary part of the Farrell cohomology of a few pure mapping class groups.

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The Euler Characteristic Of The Whitehead Automorphism Group Of A Free Product, Craig A. Jensen, Jon Mccammond, John Meier Jan 2007

The Euler Characteristic Of The Whitehead Automorphism Group Of A Free Product, Craig A. Jensen, Jon Mccammond, John Meier

Mathematics Faculty Publications

A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms...

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Vorticity Dynamics And Sound Generation In Two-Dimensional Fluid Flow, Raymond J. Nagem, Guido Sandri, David Uminsky Jan 2007

Vorticity Dynamics And Sound Generation In Two-Dimensional Fluid Flow, Raymond J. Nagem, Guido Sandri, David Uminsky

Mathematics

An approximate solution to the two-dimensional incompressible fluid equations is constructed by expanding the vorticity field in a series of derivatives of a Gaussian vortex. The expansion is used to analyze the motion of a corotating Gaussian vortex pair, and the spatial rotation frequency of the vortex pair is derived directly from the fluid vorticity equation. The resulting rotation frequency includes the effects of finite vortex core size and viscosity and reduces, in the appropriate limit, to the rotation frequency of the Kirchhoff point vortex theory. The expansion is then used in the low Mach number Lighthill equation to derive …

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Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott Jan 2007

Relationships Between Braid Length And The Number Of Braid Strands, Cornelia A. Van Cott

Mathematics

For a knot K, let ℓ(K,n) be the minimum length of an n–stranded braid representative of K. Fixing a knot K, ℓ(K,n) can be viewed as a function of n, which we denote by ℓK(n). Examples of knots exist for which ℓK(n) is a nonincreasing function. We investigate the behavior of ℓK(n), developing bounds on the function in terms of the genus of K. The bounds lead to the conclusion that for any knot K the function ℓK(n) is eventually stable. We study the stable behavior of ℓK(n), with stronger results for homogeneous knots. For knots of nine or fewer …

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Π01 Classes And Strong Degree Spectra Of Relations, John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denise R. Hirschfeldt, Carl G. Jockusch, Timothy H. Mcnicholl, Sarah Pingrey Jan 2007

Π01 Classes And Strong Degree Spectra Of Relations, John Chisholm, Jennifer Chubb, Valentina S. Harizanov, Denise R. Hirschfeldt, Carl G. Jockusch, Timothy H. Mcnicholl, Sarah Pingrey

Mathematics

We study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear order. Countable Π01 subsets of 2w and Kolmogorov complexity play a major role in the proof.

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Unbounded Regions Of Infinitely Logconcave Sequences, David Uminsky, Karen Yeats Jan 2007

Unbounded Regions Of Infinitely Logconcave Sequences, David Uminsky, Karen Yeats

Mathematics

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Boros and Moll in [1] that the binomial coefficients are ∞-logconcave.

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The Relaxed Game Chromatic Index Of K-Degenerate Graphs, Charles Dunn Jan 2007

The Relaxed Game Chromatic Index Of K-Degenerate Graphs, Charles Dunn

Faculty Publications

The (r, d)-relaxed coloring game is a two-player game played on the vertex set of a graph G. We consider a natural analogue to this game on the edge set of G called the (r, d)-relaxed edge-coloring game. We consider this game on trees and more generally, on k-degenerate graphs. We show that if G is k-degenerate with ∆(G) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆+k−1 and d≥2k2 + 4k.

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Sonia Kovalevsky Math For Girls Day General Information, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings Jan 2007

Sonia Kovalevsky Math For Girls Day General Information, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

PowerPoint presentation about Lincoln University Sonia Kovalevsky (LUSK) Math for Girls Day.

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The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner Jan 2007

The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. …

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Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner Jan 2007

Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.

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Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler Jan 2007

Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider the differentiability of weak solutions of linear parabolic equations with respect to parameters and initial data. under natural assumptions, it is shown that solutions possess as much differentiability with respect to the data as do the terms appearing in the equation. The derivatives are shown to satisfy the appropriate sensitivity equations. The theoretical results are illustrated with an example.

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Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner Jan 2007

Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

Oscillation and nonoscillation properties of second order Sturm-Liouville dynamic equations on time scales — for example, second order self-adjoint differential equations and second order Sturm-Liouville difference equations — have attracted much interest. Here we consider a given homogeneous equation and a corresponding equation with forcing term. We give new conditions implying that the latter equation inherits the oscillatory behavior of the homogeneous equation. We also give new conditions that introduce oscillation of the inhomogeneous equation while the homogeneous equation is nonoscillatory. Finally, we explain a gap in a result given in the literature for the continuous and the discrete case. …

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Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner Jan 2007

Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques we establish some oscillation criteria for the second order Emden-Fowler dynamic equation on a time scale. Such equations contain the classical Emden-Fowler equation as well as their discrete counterparts. The classical oscillation results of Atkinson (in the superlinear case) and Belohorec (in the sublinear case) are extended in this paper to Emden-Fowler dynamic equations on any time scale.

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The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du Jan 2007

The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du

Mathematics and Statistics Faculty Research & Creative Works

The dynamic laws of quantized vortex interactions in the Ginzburg-Landau-Schrödinger equation (GLSE) are analytically and numerically studied. A review of the reduced dynamic laws governing the motion of vortex centers in the GLSE is provided. The reduced dynamic laws are solved analytically for some special initial data. By directly simulating the GLSE with an efficient and accurate numerical method proposed recently in [Y. Zhang, W. Bao, and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation, European J. Appl. Math., to appear], we can qualitatively and quantitatively compare quantized vortex interaction patterns of the GLSE with those from the …

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On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le Jan 2007

On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

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On The Complete Join Of Permutative Combinatorial Rees–Sushkevich Varieties, Edmond W. H. Lee Jan 2007

On The Complete Join Of Permutative Combinatorial Rees–Sushkevich Varieties, Edmond W. H. Lee

Mathematics Faculty Articles

A semigroup variety is a Rees–Sushkevich variety if it is contained in a periodic variety generated by 0-simple semigroups. The collection of all permutative combinatorial Rees–Sushkevich varieties constitutes an incomplete lattice that does not contain the complete join J of all its varieties. The objective of this article is to investigate the subvarieties of J. It is shown that J is locally finite, non-finitely generated, and contains only finitely based subvarieties. The subvarieties of J are precisely the combinatorial Rees–Sushkevich varieties that do not contain a certain semigroup of order four.

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Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro Jan 2007

Green And Poisson Functions With Wentzell Boundary Conditions, José-Luis Menaldi, Luciano Tubaro

Mathematics Faculty Research Publications

We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-di erential operator with Wentzell boundary conditions.

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Modeling Immune Response To Bacterial Infection, Carla Roth Jan 2007

Modeling Immune Response To Bacterial Infection, Carla Roth

The Journal of Undergraduate Research

Mathematical models have begun to play an important role in the study of biology. We will examine this role further by analyzing a specific model of the innate immune system's response to a bacterial infection. Beginning with the biological background of the model, we will move into an explanation of a specific model of this situation followed by a critique of the model and future work to be done with the topic.

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Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich Jan 2007

Discrete Approximations, Relaxation, And Optimization Of One-Sided Lipschitzian Differential Inclusions In Hilbert Spaces, Tzanko Donchev, Elza Farkhi, Boris S. Mordukhovich

Mathematics Research Reports

We study discrete approximations of nonconvex differential inclusions in Hilbert spaces and dynamic optimization/optimal control problems involving such differential inclusions and their discrete approximations. The underlying feature of the problems under consideration is a modi- fied one-sided Lipschitz condition imposed on the right-hand side (i.e., on the velocity sets) of the differential inclusion, which is a significant improvement of the conventional Lipschitz continuity. Our main attention is paid to establishing efficient conditions that ensure the strong approximation (in the W^1,p-norm as p greater than or equal to 1) of feasible trajectories for the one-sided Lipschitzian differential inclusions under. consideration by …

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Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno Jan 2007

Inversion For Non-Smooth Models With Physical Bounds, Partha S. Routh, Leming Qu, Mrinal K. Sen, Phil D. Anno

Mathematics Faculty Publications and Presentations

Geological processes produce structures at multiple scales. A discontinuity in the subsurface can occur due to layering, tectonic activities such as faulting, folding and fractures. Traditional approaches to invert geophysical data employ smoothness constraints. Such methods produce smooth models and thefore sharp contrasts in the medium such as lithological boundaries are not easily discernible. The methods that are able to produce non-smooth models, can help interpret the geological discontinuity. In this paper we examine various approaches to obtain non-smooth models from a finite set of noisy data. Broadly they can be categorized into approaches: (1) imposing non-smooth regularization in the …

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Actors, Objects, Contextures, Morphograms, Rudolf Kaehr Jan 2007

Actors, Objects, Contextures, Morphograms, Rudolf Kaehr

Rudolf Kaehr

Systematic and historic overview and critics of actor and object oriented programming.

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From Dialogues To Polylogues, Rudolf Kaehr Jan 2007

From Dialogues To Polylogues, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

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On The Eigenvalues Of Some Tridiagonal Matrices, Carlos Fonseca Jan 2007

On The Eigenvalues Of Some Tridiagonal Matrices, Carlos Fonseca

Carlos Fonseca

No abstract provided.

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Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun Jan 2007

Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun

Xiao-Jun Yang

The dynamic feature of high buildings is discussed in the present study with the application of ANSYS，the large finite element analysis software，aimed at the analysis of dynamic response of high buildings．Based on the case of a 15一story-building，a model of beam and shell 3-D finite element structure is built and the frequency of structure and the mode of vibration are computed in the study；furthermore，the structural dynamic response is discussed under different seismic waves with the use of the history analysis method．The results show that the more intense the seismic wave is，the bigger is the dynamic response of the buildings．The information can …

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Existence Of Double Walsh Series Universal In Weighted Spaces, Sergo Armenak Episkoposian (Yepiskoposyan) Jan 2007

Existence Of Double Walsh Series Universal In Weighted Spaces, Sergo Armenak Episkoposian (Yepiskoposyan)

Sergo Armenak Episkoposian (Yepiskoposyan)

No abstract provided.

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On Greedy Algorithms With Respect To Generalized Walsh System, Sergo Armenak Episkoposian (Yepiskoposyan) Jan 2007

On Greedy Algorithms With Respect To Generalized Walsh System, Sergo Armenak Episkoposian (Yepiskoposyan)

Sergo Armenak Episkoposian (Yepiskoposyan)

No abstract provided.

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Graphics With Pgf And Tikz, Andrew Mertz, William Slough Jan 2007

Graphics With Pgf And Tikz, Andrew Mertz, William Slough

Andrew Mertz

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a fine line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.

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Graphics With Tikz, Andrew Mertz, William Slough Jan 2007

Graphics With Tikz, Andrew Mertz, William Slough

Andrew Mertz

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a thin line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.

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Programming With Perltex, Andrew Mertz, William Slough Jan 2007

Programming With Perltex, Andrew Mertz, William Slough

Andrew Mertz

PerlTEX couples two well-known worlds—the Perl programming language and the LATEX typesetting system. The resulting system provides users with a way to augment LATEX macros with Perl code, thereby adding programming capabilities to LATEX that would otherwise be difficult to express. In this paper, we illus- trate the use of PerlTEX with a variety of examples and explain the associated Perl code. Although Perl may perhaps be best known for its string manipula- tion capabilities, we demonstrate how PerlTEX indirectly provides support for “programming” graphics through the use of additional packages such as TikZ.

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A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler Jan 2007

A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler

Bruce Kessler

If a large number of educated people were asked, ``What was your most exciting class?'', odds are that very few of them would answer ``Trigonometry.'' The subject is generally presented in a less-than-exciting fashion, with the repeated caveat that ``you'll need this when you take calculus,'' or ``this has lots of applications'' without ever really seeing many of them. This manuscript addresses how the author is trying to change this tradition by exposing casual students from kindergarten to college to Joseph Fourier's secret, that nearly any function can be built out of sine and cosine curves. And music serves as …

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