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Applied Mathematics Commons™

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2010

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Articles 211 - 217 of 217

Full-Text Articles in Applied Mathematics

Quantitative Modelling Approaches For Ascorbic Acid Degradation And Non-Enzymatic Browning Of Orange Juice During Ultrasound Processing, Vasilis Valdramidis, Patrick J. Cullen, Brijesh Tiwari, Colm O’Donnell Jan 2010

Quantitative Modelling Approaches For Ascorbic Acid Degradation And Non-Enzymatic Browning Of Orange Juice During Ultrasound Processing, Vasilis Valdramidis, Patrick J. Cullen, Brijesh Tiwari, Colm O’Donnell

Articles

The objective of this study was to develop a deterministic modelling approach for non-enzymatic browning (NEB) and ascorbic acid (AA) degradation in orange juice during ultrasound processing. Freshly squeezed orange juice was sonicated using a 1,500 W ultrasonic processor at a constant frequency of 20 kHz and processing variables of amplitude level (24.4 – 61.0 μm), temperature (5 – 30 oC) and time (0 – 10 min). The rate constants of the NEB and AA were estimated by a primary model (zero and first order) while their relationship with respect to the processing factors was tested for a number of …

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Method Of Riemann Surfaces In Modelling Of Cavitating Flow, Anna Zemlyanova Jan 2010

Method Of Riemann Surfaces In Modelling Of Cavitating Flow, Anna Zemlyanova

LSU Doctoral Dissertations

This dissertation is concerned with the applications of the Riemann-Hilbert problem on a hyperelliptic Riemann surface to problems on supercavitating flows of a liquid around objects. For a two-dimensional steady irrotational flow of liquid it is possible to introduce a complex potential w(z) which allows to apply the powerful methods of complex analysis to the solution of fluid mechanics problems. In this work problems on supercavitating flows of a liquid around one or two wedges have been stated. The Tulin single-spiral-vortex model is employed as a cavity closure condition. The flow domain is transformed into an auxiliary domain with known …

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Orthogonal Grassmannians And Hermitian K-Theory In A¹-Homotopy Theory Of Schemes, Girja Shanker Tripathi Jan 2010

Orthogonal Grassmannians And Hermitian K-Theory In A¹-Homotopy Theory Of Schemes, Girja Shanker Tripathi

LSU Doctoral Dissertations

In this work we prove that the hermitian K-theory is geometrically representable in the A^1 -homotopy category of smooth schemes over a field. We also study in detail a realization functor from the A^1 -homotopy category of smooth schemes over the field R of real numbers to the category of topological spaces. This functor is determined by taking the real points of a smooth R-scheme. There is another realization functor induced by taking the complex points with a similar description although we have not discussed this other functor in this dissertation. Using these realization functors we have concluded in brief …

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Laguerre Arc Length From Distance Functions, David E. Barrett, Michael Bolt Jan 2010

Laguerre Arc Length From Distance Functions, David E. Barrett, Michael Bolt

University Faculty Publications and Creative Works

For the Laguerre geometry in the dual plane, invariant arc length is shown to arise naturally through the use of a pair of distance functions. These distances are useful for identifying equivalence classes of curves, within which the extremal curves are proved to be strict maximizers of Laguerre arc length among three-times differentiable curves of constant signature in a prescribed isotopy class. For smoother curves, it is shown that Laguerre curvature determines the distortion of the distance functions. These results extend existing work for the Möbius geometry in the complex plane. © 2010 International Press.

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Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene Jan 2010

Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene

Publications and Research

The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …

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Subgroups Of The Torelli Group, Leah R. Childers Jan 2010

Subgroups Of The Torelli Group, Leah R. Childers

LSU Doctoral Dissertations

Let Mod(Sg) be the mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces the well-known symplectic representation:

Mod(Sg) ---> Sp(2g, Z).
The kernel of this representation is called the Torelli group, I(Sg).

We will study two subgroups of I(Sg). First we will look at the subgroup generated by all SIP-maps, SIP(Sg). We will show SIP(Sg) is not I(Sg) and is in fact an infinite index subgroup of I(Sg). We will also classify which SIP-maps are in the kernel of the Johnson homomorphism and Birman-Craggs-Johnson homomorphism.

Then we will …

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Mathematical Models And Stability Analysis Of Cholera Dynamics, Shu Liao Jan 2010

Mathematical Models And Stability Analysis Of Cholera Dynamics, Shu Liao

Mathematics & Statistics Theses & Dissertations

In this dissertation, we present a careful mathematical study of several epidemic cholera models, including the model of Codeco [11] in 2001, that of Hartley, Morris and Smith [22] in 2006, and that of Mukandavire, Liao, Wang and Gaff et al. [60] in 2010. We formally derive the basic reproduction number R0 for each model by computing the spectral radius of the next generation matrix. We focus our attention on the stability analysis at the disease-free equilibrium which determines the short-term epidemic behavior, and the endemic equilibrium which determines the long-term disease dynamics. Particularly, we incorporate the Volterra-Lyapunov matrix …

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