Generalized Fourier-Feynman Transforms, Convolution Products, And First Variations On Function Space,
2010
Dankook University
Generalized Fourier-Feynman Transforms, Convolution Products, And First Variations On Function Space, Seung Jun Chang, Jae Gil Choi, David Skough
Department of Mathematics: Faculty Publications
In this paper we examine the various relationships that exist among the first variation, the convolution product and the Fourier-Feynman transform for functionals of the form F(x) = f((α1, x), . . . , (αn, x)) with x in a very general function space Ca,b[0,T].
Mesoscopic Methods In Engineering And Science,
2010
Old Dominion University
Mesoscopic Methods In Engineering And Science, Alfons Hoekstra, Li-Shi Luo, Manfred Krafczyk
Mathematics & Statistics Faculty Publications
(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the …
High Accuracy Multiscale Multigrid Computation For Partial Differential Equations,
2010
University of Kentucky
High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang
University of Kentucky Doctoral Dissertations
Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques …
Matrix Singular Value Decomposition,
2010
University of North Florida
Matrix Singular Value Decomposition, Petero Kwizera
UNF Graduate Theses and Dissertations
This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is …
Quantitative Modelling Approaches For Ascorbic Acid Degradation And Non-Enzymatic Browning Of Orange Juice During Ultrasound Processing,
2010
Technological University Dublin
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 …
Method Of Riemann Surfaces In Modelling Of Cavitating Flow,
2010
Louisiana State University and Agricultural and Mechanical College
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 …
Orthogonal Grassmannians And Hermitian K-Theory In A¹-Homotopy Theory Of Schemes,
2010
Louisiana State University and Agricultural and Mechanical College
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 …
Laguerre Arc Length From Distance Functions,
2010
University of Michigan, Ann Arbor
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.
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum,
2010
CUNY Kingsborough Community College
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 …
Subgroups Of The Torelli Group,
2010
Louisiana State University and Agricultural and Mechanical College
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 …
Mathematical Models And Stability Analysis Of Cholera Dynamics,
2010
Old Dominion University
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 …
