Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- 3-line graph (1)
- Complete graph (1)
- Derived graphs (1)
- Differential quadrature (1)
- Edge coloring (1)
-
- Fluorescence Recovery After Photobleaching (1)
- Gaussian quadrature rule (1)
- Graph (1)
- Graph theory (1)
- Hamiltonian cycles (1)
- Hamiltonian digraph (1)
- Hamiltonian extension (1)
- Hamiltonian graph (1)
- Information-transfer paths (1)
- KSS (1)
- Kinetics photobleaching (1)
- Krylov Subspace Spectral (1)
- Line graph (1)
- Local method (1)
- Matrix decomposition (1)
- Multiple frame shrinkage (1)
- Multiwavelet shrinkage (1)
- Nonlinear diffusion. (1)
- Orthogonal Polynomials (1)
- Peterson graph (1)
- Polynomial Particular Solutions (1)
- Proper coloring (1)
- Radial basis function (1)
- Rainbow coloring (1)
- Rainbow connection (1)
Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Structures Of Derived Graphs, Khawlah Hamad Alhulwah
Structures Of Derived Graphs, Khawlah Hamad Alhulwah
Dissertations
One of the most familiar derived graphs are line graphs. The line graph L(G) of a graph G is the graph whose vertices are the edges of G where two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. One of the best- known results on the structure of line graphs deals with forbidden subgraphs by Beineke. A characterization of graphs whose line graph is Hamiltonian is due to Harary and Nash-Williams. Iterated line graphs of almost all connected graphs were shown to be Hamiltonian by Chartrand. The girth of a graph G …
Color-Connected Graphs And Information-Transfer Paths, Stephen Devereaux
Color-Connected Graphs And Information-Transfer Paths, Stephen Devereaux
Dissertations
The Department of Homeland Security in the United States was created in 2003 in response to weaknesses discovered in the transfer of classied information after the September 11, 2001 terrorist attacks. While information related to national security needs to be protected, there must be procedures in place that permit access between appropriate parties. This two-fold issue can be addressed by assigning information-transfer paths between agencies which may have other agencies as intermediaries while requiring a large enough number of passwords and rewalls that is prohibitive to intruders, yet small enough to manage. Situations such as this can be represented by …
Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, Daniel Watson
Radial Basis Function Differential Quadrature Method For The Numerical Solution Of Partial Differential Equations, Daniel Watson
Dissertations
In the numerical solution of partial differential equations (PDEs), there is a need for solving large scale problems. The Radial Basis Function Differential Quadrature (RBFDQ) method and local RBF-DQ method are applied for the solutions of boundary value problems in annular domains governed by the Poisson equation, inhomogeneous biharmonic equation, and the inhomogeneous Cauchy-Navier equations of elasticity. By choosing the collocation points properly, linear systems can be obtained so that the coefficient matrices have block circulant structures. The resulting systems can be efficiently solved using matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). For the local RBFDQ method, the …
Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, Thir R. Dangal
Numerical Solution Of Partial Differential Equations Using Polynomial Particular Solutions, Thir R. Dangal
Dissertations
Polynomial particular solutions have been obtained for certain types of partial differential operators without convection terms. In this dissertation, a closed-form particular solution for more general partial differential operators with constant coefficients has been derived for polynomial basis functions. The newly derived particular solutions are further coupled with the method of particular solutions (MPS) for numerically solving a large class of elliptic partial differential equations. In contrast to the use of Chebyshev polynomial basis functions, the proposed approach is more flexible in selecting the collocation points inside the domain. Polynomial basis functions are well-known for yielding ill-conditioned systems when their …
Solution Of Pdes For First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami
Solution Of Pdes For First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami
Dissertations
We solve the first order reaction-diffusion equations which describe binding-diffusion kinetics using a photobleaching scanning profile of a confocal laser scanning microscope approximated by a Gaussian laser profile. We show how to solve these equations with prebleach steady-state initial conditions using a time-domain method known as a Krylov Subspace Spectral (KSS) method. KSS methods are explicit methods for solving time- dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of their stability and their superior scalability. These advantages are obtained by applying Gaussian quadrature rules in the spectral domain developed by Golub and Meurant. …
Highly Hamiltonian Graphs And Digraphs, Zhenming Bi
Highly Hamiltonian Graphs And Digraphs, Zhenming Bi
Dissertations
A cycle that contains every vertex of a graph or digraph is a Hamiltonian cycle. A graph or digraph containing such a cycle is itself called Hamiltonian. This concept is named for the famous Irish physicist and mathematician Sir William Rowan Hamilton. These graphs and digraphs have been the subject of study for over six decades. In this dissertation, we study graphs and digraphs with even stronger Hamiltonian properties, namely highly Hamiltonian graphs and digraphs.
Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson
Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson
Dissertations
As a result of stiff systems of ODEs, difficulties arise when using time stepping methods for PDEs. Krylov subspace spectral (KSS) methods get around the difficulties caused by stiffness by computing each component of the solution independently. In this dissertation, we extend the KSS method to a circular domain using polar coordinates. In addition to using these coordinates, we will approximate the solution using Legendre polynomials instead of Fourier basis functions. We will also compare KSS methods on a time-independent PDE to other iterative methods. Then we will shift our focus to three families of orthogonal polynomials on the interval …
Correspondence Between Multiwavelet Shrinkage/Multiple Wavelet Frame Shrinkage And Nonlinear Diffusion, Hanan Ali Alkhidhr
Correspondence Between Multiwavelet Shrinkage/Multiple Wavelet Frame Shrinkage And Nonlinear Diffusion, Hanan Ali Alkhidhr
Dissertations
There are numerous methodologies for signal and image denoising. Wavelet, wavelet frame shrinkage, and nonlinear diffusion are effective ways for signal and image denoising. Also, multiwavelet transforms and multiple wavelet frame transforms have been used for signal and image denoising. Multiwavelets have important property that they can possess the orthogonality, short support, good performance at the boundaries, and symmetry simultaneously. The advantage of multiwavelet transform for signal and image denoising was illustrated by Bui et al. in 1998. They showed that the evaluation of thresholding on a multiwavelet basis has produced good results. Further, Strela et al. have showed that …