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Physical Sciences and Mathematics Commons™

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Selected Works

2007

Applied Mathematics

Articles 1 - 14 of 14

Full-Text Articles in Physical Sciences and Mathematics

Trends In Uspto Office Actions, Ron D. Katznelson Nov 2007

Trends In Uspto Office Actions, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

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A Stable Algorithm For Flat Radial Basis Functions On A Sphere, Bengt Fornberg, Cecile M. Piret Nov 2007

A Stable Algorithm For Flat Radial Basis Functions On A Sphere, Bengt Fornberg, Cecile M. Piret

Cecile M Piret

When radial basis functions (RBFs) are made increasingly flat, the interpolation error typically decreases steadily until some point when Runge-type oscillations either halt or reverse this trend. Because the most obvious method to calculate an RBF interpolant becomes a numerically unstable algorithm for a stable problem in the case of near-flat basis functions, there will typically also be a separate point at which disastrous ill-conditioning enters. We introduce here a new method, RBF-QR, which entirely eliminates such ill-conditioning, and we apply it in the special case when the data points are distributed over the surface of a sphere. This algorithm …

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A Large-Scale Rheumatoid Arthritis Genetic Study Identifies Association At Chr 9q33.2, Steven J. Schrodi May 2007

A Large-Scale Rheumatoid Arthritis Genetic Study Identifies Association At Chr 9q33.2, Steven J. Schrodi

Steven J Schrodi

No abstract provided.

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Using Math In Cell Biology: A Tale Of Two Channel Types, Borbala Mazzag Mar 2007

Using Math In Cell Biology: A Tale Of Two Channel Types, Borbala Mazzag

Borbala Mazzag

No abstract provided.

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Lanchester's Equations In Three Dimensions, Christina Spradlin, Greg Spradlin Mar 2007

Lanchester's Equations In Three Dimensions, Christina Spradlin, Greg Spradlin

Gregory S. Spradlin

This paper generalizes Lanchester's equations of warfare to partial differential equations involving time and two spatial variables. Unlike in Lanchester's original ordinary differential equations, the distribution of armies over the battlefield must be considered. Four different modes of attack are introduced, generalizing Lanchester's equations for area fire and for direct fire. The effect of the distribution of forces and their movement on the outcome is considered, and numerical simulations given.

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Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant Dec 2006

Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant

Tim Marchant

The increase in temperature in compost piles/landfill sites due to micro-organisms undergoing exothermic reactions is modelled. A simplified model is considered in which only biological self-heating is present. The heat release rate due to biological activity is modelled by a function which is a monotonic increasing function of temperature over the range 0⩽T⩽a, whilst for T⩾a it is a monotone decreasing function of temperature. This functional dependence represents the fact that micro-organisms die or become dormant at high temperatures. The bifurcation behaviour is investigated for 1-d slab and 2-d rectangular slab geometries. In both cases there are two generic steady-state …

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Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant Dec 2006

Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant

Tim Marchant

Solitary wave interaction for a higher-order version of the nonlinear Schrödinger (NLS) equation is examined. An asymptotic transformation is used to transform a higher-order NLS equation to a higher-order member of the NLS integrable hierarchy, if an algebraic relationship between the higher-order coefficients is satisfied. The transformation is used to derive the higher-order one- and two-soliton solutions; in general, the N-soliton solution can be derived. It is shown that the higher-order collision is asymptotically elastic and analytical expressions are found for the higher-order phase and coordinate shifts. Numerical simulations of the interaction of two higher-order solitary waves are also performed. …

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Asymptotic Solitons On A Non-Zero Mean Level., Tim Marchant Dec 2006

Asymptotic Solitons On A Non-Zero Mean Level., Tim Marchant

Tim Marchant

The collision of solitary waves for a higher-order modified Korteweg-de Vries (mKdV) equation is examined. In particular, the collision between solitary waves with sech-type and algebraic (which only exist on a non-zero mean level) profiles is considered. An asymptotic transformation, valid if the higher-order coefficients satisfy a certain algebraic relationship, is used to transform the higher-order mKdV equation to an integrable member of the mKdV hierarchy. The transformation is used to show that the higher-order collision is asymptotically elastic and to derive the higher-order phase shifts. Numerical simulations of both elastic and inelastic collisions are performed. For the example covered …

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Numerical Simulation Of Contaminant Flow In A Wool Scour Bowl., Tim Marchant Dec 2006

Numerical Simulation Of Contaminant Flow In A Wool Scour Bowl., Tim Marchant

Tim Marchant

Wool scouring is the process of washing dirty wool after shearing. Our model numerically simulates contaminant movement in a wool scour bowl using the advection–dispersion equation. This is the first wool scour model to give time-dependent results and to model the transport of contaminants within a single scour bowl. Our aim is to gain a better understanding of the operating parameters that will produce efficient scouring. Investigating the effects of varying the parameters reveals simple, interesting relationships that give insight into the dynamics of a scour bowl.

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Computational Modeling Of Calcium Dynamics Near Heterogeneous Release Sites, Borbala Mazzag, Zachary Cooper, Michael Greenwood Dec 2006

Computational Modeling Of Calcium Dynamics Near Heterogeneous Release Sites, Borbala Mazzag, Zachary Cooper, Michael Greenwood

Borbala Mazzag

Background: Calcium is known to play an important role in many physiological
processes, such as egg fertilization and heart muscle functions.
Several recent theoretical studies ([4], [1]) investigated calcium dynamics
near so-called release sites – clusters of calcium-regulated channels on
the intracellular calcium stores. Interest in the synchronized openings of
channels within a release site has increased because these openings are
thought to be the building blocks of global calcium events.
Methods: We conduct computational studies of the effect of heterogeneity
in the make-up of the release site on the resulting calcium dynamics.
We introduce heterogeneity into the model of …

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Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter J.S. S, Leetsch C. Hsu Dec 2006

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter J.S. S, Leetsch C. Hsu

Tian-Xiao He

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

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Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles K. Chui, Qingtang Jiang Dec 2006

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles K. Chui, Qingtang Jiang

Tian-Xiao He

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

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Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He Dec 2006

Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He

Tian-Xiao He

No abstract provided.

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The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter J.S. Shiue, Leetsch C. Hsu Dec 2006

The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter J.S. Shiue, Leetsch C. Hsu

Tian-Xiao He

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.

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