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Articles 181 - 210 of 288

Full-Text Articles in Mathematics

A General Theory Of Almost Convex Functions, S J. Dilworth, Ralph Howard, James W. Roberts Mar 2006

A General Theory Of Almost Convex Functions, S J. Dilworth, Ralph Howard, James W. Roberts

Faculty Publications

No abstract provided.

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Maldi-Tof Baseline Drift Removal Using Stochastic Bernstein Approximation, Joseph Kolibal, Daniel Howard Jan 2006

Maldi-Tof Baseline Drift Removal Using Stochastic Bernstein Approximation, Joseph Kolibal, Daniel Howard

Faculty Publications

Stochastic Bernstein (SB) approximation can tackle the problem of baseline drift correction of instrumentation data. This is demonstrated for spectral data: matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF) data. Two SB schemes for removing the baseline drift are presented: iterative and direct. Following an explanation of the origin of the MALDI-TOF baseline drift that sheds light on the inherent difficulty of its removal by chemical means, SB baseline drift removal is illustrated for both proteomics and genomics MALDI-TOF data sets. SB is an elegant signal processing method to obtain a numerically straightforward baseline shift removal method as it includes a …

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Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao Jan 2006

Adaptive Finite Element Methods For Elliptic Pdes Based On Conforming Centroidal Voronoi-Delaunay Triangulations, Lili Ju, Max Gunzburger, Weidong Zhao

Faculty Publications

A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi–Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, …

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Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer Jan 2006

Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer

Faculty Publications

Size regulation is a crucial feature in many biological systems, with misregulation leading to dysplasia or hyperplasia. The recent discovery of counting factor (CF) in Dictyostelium discoideum will lead to a greater understanding of how the system regulates the size of a group of cells. In this paper we mathematically model the known effects of CF using two different models: a cellular automata model and a discrete continuum hybrid model. With the use of these models we are able to understand how modulation of adhesion and motile forces by CF can facilitate stream breakup. In addition, the modelling suggests a …

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Particular Solutions For Axisymmetric Helmholtz-Type Operators, A.S. Muleshkov, M.A. Golberg, C.S. Chen Nov 2005

Particular Solutions For Axisymmetric Helmholtz-Type Operators, A.S. Muleshkov, M.A. Golberg, C.S. Chen

Faculty Publications

In this paper, we consider the solution of the axisymmetric heat equation with axisymmetric data in an axisymmetric domain in R-3. To solve this problem, we remove the time-dependence by various transform or time-stepping methods. This converts the problem to one of a sequence of modified inhomogeneous Helmholtz equations. Generalizing previous work, we consider solving these equations by boundary-type methods. In order to do this, one needs to subtract off a particular solution, so that one obtains a sequence of modified homogeneous Helmholtz equations. We do this by modifying the usual Dual Reciprocity Method (DRM) and approximating the right-hand sides …

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Conjugacy Classes And Finite P-Groups, Edith Adan-Bante Oct 2005

Conjugacy Classes And Finite P-Groups, Edith Adan-Bante

Faculty Publications

Let G be a finite p-group, where p is a prime number, and a ∈ G. Denote by Cl(a) = {gag−1| g ∈ G} the conjugacy class of a in G. Assume that |Cl(a)| = p n . Then Cl(a) Cl(a−1) = {xy | x ∈ Cl(a), y ∈ Cl(a−1)} is the union of at least n(p − 1) + 1 distinct conjugacy classes of G.

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Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy Feb 2005

Graphs Whose Minimal Rank Is Two: The Finite Fields Case, Wayne Barrett, Hein Van Der Holst, Raphael Loewy

Faculty Publications

Let F be a finite field, G = (V,E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n × n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with p^t elements, p does not = 2, it is shown that mr(F,G) ≤ 2 if and only if the complement of G is the join of a complete graph with either the union of at most …

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Hyperbolic Sets That Are Not Locally Maximal, Todd L. Fisher Dec 2004

Hyperbolic Sets That Are Not Locally Maximal, Todd L. Fisher

Faculty Publications

This paper addresses the following topics relating to the structure of hyperbolic sets: First, hyperbolic sets that are not contained in locally maximal hyperbolic sets. Second, the existence of a Markov partition for a hyperbolic set. We construct new examples of hyperbolic sets which are not contained in locally maximal hyperbolic sets. The first example is robust under perturbations and can be constructed on any compact manifold of dimension greater than one. The second example is robust, topologically transitive, and constructed on a 4-dimensional manifold. The third example is volume preserving and constructed on R4. We show that every hyperbolic …

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Outerplanar Crossing Numbers, The Circular Arrangement Problem And Isoperimetric Functions, Eva Czabarka, Ondrej Sykora, Laszlo A. Szekely, Imrich Vrt'o Nov 2004

Outerplanar Crossing Numbers, The Circular Arrangement Problem And Isoperimetric Functions, Eva Czabarka, Ondrej Sykora, Laszlo A. Szekely, Imrich Vrt'o

Faculty Publications

We extend the lower bound in [15] for the outerplanar crossing number (in other terminologies also called convex, circular and one-page book crossing number) to a more general setting. In this setting we can show a better lower bound for the outerplanar crossing number of hypercubes than the best lower bound for the planar crossing number. We exhibit further sequences of graphs, whose outerplanar crossing number exceeds by a factor of log n the planar crossing number of the graph. We study the circular arrangement problem, as a lower bound for the linear arrangement problem, in a general fashion. We …

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How Cellular Movement Determines The Collective Force Generated By The Dictyostelium Discoideum Slug, J. C. Dallon, H. G. Othmer Nov 2004

How Cellular Movement Determines The Collective Force Generated By The Dictyostelium Discoideum Slug, J. C. Dallon, H. G. Othmer

Faculty Publications

How the collective motion of cells in a biological tissue originates in the behavior of a collection of individuals, each of which responds to the chemical and mechanical signals it receives from neighbors, is still poorly understood. Here we study this question for a particular system, the slug stage of the cellular slime mold Dictyostelium discoideum. We investigate how cells in the interior of a migrating slug can effectively transmit stress to the substrate and thereby contribute to the overall motive force. Theoretical analysis suggests necessary conditions on the behavior of individual cells, and computational results shed light on experimental …

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Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer Sep 2004

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

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Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer Sep 2004

Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer

Faculty Publications

No abstract provided.

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Products Of Characters And Finite P-Groups Ii, Edith Adan-Bante Apr 2004

Products Of Characters And Finite P-Groups Ii, Edith Adan-Bante

Faculty Publications

Let p be a prime number. Let G be a finite p-group and χ ∈ Irr(G). Denote by the -χ ∈ Irr(G) complex conjugate of χ . Assume that χ(1) = pn. We show that the number of distinct irreducible constituents of the product of χ-χ is at least 2n(p−1)+1.

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Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka Feb 2004

Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka

Faculty Publications

No abstract provided.

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Anatomy Of A Chaotic Attractor: Subtle Model-Predicted Patterns Revealed In Population Data, Aaron A. King, R. F. Costantino, J. M. Cushing, Shandelle M. Henson, Robert A. Desharnais, Brian Dennis Jan 2004

Anatomy Of A Chaotic Attractor: Subtle Model-Predicted Patterns Revealed In Population Data, Aaron A. King, R. F. Costantino, J. M. Cushing, Shandelle M. Henson, Robert A. Desharnais, Brian Dennis

Faculty Publications

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn from chaotic insect populations, we show quantitatively that chaos manifests itself as a tapestry of identifiable and predictable patterns woven together by stochasticity. We show too that the mixture of patterns an experimentalist can expect to see depends on the scale of the system under study.

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A Thermoviscoelastic Beam Model For Brakes, Kenneth Kuttler, J. Bajkowski, J. R. Fernandez, M. Shillor Jan 2004

A Thermoviscoelastic Beam Model For Brakes, Kenneth Kuttler, J. Bajkowski, J. R. Fernandez, M. Shillor

Faculty Publications

A model for the dynamic thermomechanical behavior of a viscoelastic beam which is in frictional contact with a rigid rotating wheel is presented. It describes a simple braking system in which the wheel comes to a stop as a result of the frictional traction generated by the beam. Friction is modelled with a temperature and slip rate dependent coefficient of friction. Frictional heat generation is taken into account as well as the wheel temperature evolution, and the wear of the beam's contacting end. The model is formulated as a variational inequality. A FEM numerical scheme for the model is described, …

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Explaining And Predicting Patterns In Stochastic Population Systems, Shandelle M. Henson, Aaron A. King, R. F. Costantino, J. M. Cushing, Brian Dennis, Robert A. Desharnais Aug 2003

Explaining And Predicting Patterns In Stochastic Population Systems, Shandelle M. Henson, Aaron A. King, R. F. Costantino, J. M. Cushing, Brian Dennis, Robert A. Desharnais

Faculty Publications

Lattice effects in ecological time-series are patterns that arise because of the inherent discreteness of animal numbers. In this paper, we suggest a systematic approach for predicting lattice effects. We also show that an explanation of all the patterns in a population time-series may require more than one deterministic model, especially when the dynamics are complex.

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The Topology Of Hyperbolic Attractors On Compact Surfaces, Todd L. Fisher Jun 2003

The Topology Of Hyperbolic Attractors On Compact Surfaces, Todd L. Fisher

Faculty Publications

Suppose M is a compact surface and M is a nontrivial mixing hyperbolic attractor for some f 2 Diff(M). We show that if is a hyperbolic set for some g 2 Diff(M), then is a nontrivial mixing hyperbolic attractor or repeller for g.

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Minimal Graphs In R3 Over Convex Domains, Michael Dorff Jun 2003

Minimal Graphs In R3 Over Convex Domains, Michael Dorff

Faculty Publications

Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust's theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent analytic mappings, this family of convolution surfaces is much larger than just the family of associated surfaces. Also, this generalization guarantees that all the resulting surfaces are over close-toconvex domains. In particular, all the associate surfaces and certain Goursat transformation surfaces …

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Every Three-Point Set Is Zero Dimensional, David L. Fearnley, J. W. Lamoreaux, David L. Fearnley Jan 2003

Every Three-Point Set Is Zero Dimensional, David L. Fearnley, J. W. Lamoreaux, David L. Fearnley

Faculty Publications

This paper answers a question of Jan J. Dijkstra by giving a proof that all three-point sets are zero dimensional. It is known that all two-point sets are zero dimensional, and it is known that for all n > 3, there are n-point sets which are not zero dimensional, so this paper answers the question for the last remaining case.

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Odd Perfect Numbers Have A Prime Factor Exceeding 10^7, Paul M. Jenkins Jan 2003

Odd Perfect Numbers Have A Prime Factor Exceeding 10^7, Paul M. Jenkins

Faculty Publications

It is proved that every odd perfect number is divisible by a prime greater than 10^7.

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An Extension Of Elton's L(1)(N) Theorem To Complex Banach Spaces, S J. Dilworth, Joseph P. Patterson Sep 2002

An Extension Of Elton's L(1)(N) Theorem To Complex Banach Spaces, S J. Dilworth, Joseph P. Patterson

Faculty Publications

No abstract provided.

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Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka Jan 2002

Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka

Faculty Publications

For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula …

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A Sufficient Condition For The Uniqueness Of Positive Steady State To A Reaction Diffusion System, Joon Hyuk Kang, Yun Oh Jan 2002

A Sufficient Condition For The Uniqueness Of Positive Steady State To A Reaction Diffusion System, Joon Hyuk Kang, Yun Oh

Faculty Publications

In this paper, we concentrate on the uniqueness of the positive solution for the general elliptic system { Δu + u(g1(u) - g 2(v)) = 0 in R+ × Ω, Δν + v(h 1(u) - h2(v)) = 0 u|∂Ω = v| ∂Ω = 0. This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

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Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu Dec 2001

Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu

Faculty Publications

We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.

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Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini Oct 2001

Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini

Faculty Publications

We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of TGF. Our work extends a previously developed model which considers the interactions between fibroblasts and extracellular matrix, composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix can direct the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGF to alter the properties of the fibroblasts. Thus we are able to simulate experiments …

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Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert Sep 2001

Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert

Faculty Publications

WE CONSIDER FACTORS INFLUENCING the build-up of corrugations on dirt roads and the reactions of vehicles to them. We suggest that corrugations are (at least in part) a consequence of a natural tangential oscillation of the tread surface of the car lure that occurs when the vehicle is being driven or braked. Secondly, we suggest that the unpleasant vibration experienced by a vehicle passing over a corrugated road is the result of a beat produced by the difference of the frequency of oscillation of its own tyres and the frequency of the stimulation received by the vehicle due to passage …

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Blowup In A Mass-Conserving Convection-Diffusion Equation With Superquadratic Nonlinearity, Todd L. Fisher, Christopher P. Grant Apr 2001

Blowup In A Mass-Conserving Convection-Diffusion Equation With Superquadratic Nonlinearity, Todd L. Fisher, Christopher P. Grant

Faculty Publications

A nonlinear convection-diffusion equation with boundary conditions that conserve the spatial integral of the solution is considered. Previous results on nite-time blowup of solutions and on decay of solutions to the corresponding Cauchy problem were based on the assumption that the nonlinearity obeyed a power law. In this paper, it is shown that assumptions on the growth rate of the nonlinearity, which take the form of weak superquadraticity and strong superlinearity criteria, are suffcient to imply that a large class of nonnegative solutions blow up in nite time.

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An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing Jan 2001

An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing

Faculty Publications

We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.

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Gravitational Descendants And The Moduli Space Of Higher Spin Curves, Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob Jan 2001

Gravitational Descendants And The Moduli Space Of Higher Spin Curves, Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob

Faculty Publications

The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of r-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a priori analog in the theory of Gromov-Witten invariants), in terms of the multiplicativity of the virtual class. We prove that the Descent Axiom holds in the convex case, and consequently in genus zero.

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