Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Active assembly (1)
- Backlund Transformation (1)
- Bilinear operator (1)
- Collaboration (1)
- Community of Practice (1)
-
- Conserved quantity (1)
- DNA tiling (1)
- Enlarged systems (1)
- Extremal combinatorics (1)
- Fractional integrals and derivatives (1)
- Fractional packings (1)
- Geometric Brownian motion (1)
- Grammian Solution (1)
- Grammian solution (1)
- Hamiltonian structure (1)
- Height sequence (1)
- Hierarchical assembly (1)
- Higher Education (1)
- Hirota Dierential Operator (1)
- Infinitely many symmetries (1)
- Infinitesimal generator (1)
- Integrable coupling (1)
- Lax pairs (1)
- Linear hypergraphs (1)
- Loop saturated assembly graphs (1)
- Lyapunov function (1)
- Matrix loop algebras (1)
- Middle additive operation (1)
- Non-homogeneous Poisson process (1)
- Nonlinear partial differential equations (1)
Articles 1 - 10 of 10
Full-Text Articles in Entire DC Network
On Algorithmic Fractional Packings Of Hypergraphs, Jill Dizona
On Algorithmic Fractional Packings Of Hypergraphs, Jill Dizona
USF Tampa Graduate Theses and Dissertations
Let F0 be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F0-packing of H is a family F of edge-disjoint copies of F0 which are subhypergraphs in H. Let nF0(H) denote the maximum size |F| of an F0-packing F of H. It is well-known that computing nF0(H) is NP-hard for nearly any choice of F0.
In this thesis, we consider the special case when F0 is a linear hypergraph, that is, when no two edges …
Wronskian, Grammian And Pfaffian Solutions To Nonlinear Partial Differential Equations, Alrazi Abdeljabbar
Wronskian, Grammian And Pfaffian Solutions To Nonlinear Partial Differential Equations, Alrazi Abdeljabbar
USF Tampa Graduate Theses and Dissertations
It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also variable coefficients under a certain constraint
(ut + α 1(t)uxxy + 3α 2(t)uxuy)x +α 3 (t)uty -α 4(t)uzz + α 5(t)(ux + α 3(t)uy) = …
Pfaffian And Wronskian Solutions To Generalized Integrable Nonlinear Partial Differential Equations, Magdy Asaad
Pfaffian And Wronskian Solutions To Generalized Integrable Nonlinear Partial Differential Equations, Magdy Asaad
USF Tampa Graduate Theses and Dissertations
The aim of this work is to use the Pfaffian technique, along with the Hirota bilinear method to construct different classes of exact solutions to various of generalized integrable nonlinear partial differential equations. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. The existence of multi-solitons, especially three-soliton solutions, is essential for information technology: it makes possible undisturbed simultaneous propagation of many pulses in both directions.
The derivation and solutions of integrable nonlinear partial differential equations in two spatial dimensions have been …
Team-Teaching Experiences Of A Mathematician And A Mathematics Teacher Educator: An Interpretative Phenomenological Case Study, Sarah K. Bleiler
Team-Teaching Experiences Of A Mathematician And A Mathematics Teacher Educator: An Interpretative Phenomenological Case Study, Sarah K. Bleiler
USF Tampa Graduate Theses and Dissertations
In recent years, experts and organizations involved in mathematics education have emphasized the importance of collaboration between mathematicians and mathematics teacher educators as a means of improving the professional preparation of mathematics teachers. While several such collaborative endeavors have been documented in the extant literature, most research reports have focused on the products, rather than the process, of collaboration. The purpose of this interpretative phenomenological case study is to gain an understanding of the lived experiences of a mathematician and a mathematics teacher educator as they engaged in a team-teaching collaboration within the context of prospective secondary mathematics teacher preparation. …
Self-Assembly Of Self-Similar Structures By Active Tiles, Daria Karpenko
Self-Assembly Of Self-Similar Structures By Active Tiles, Daria Karpenko
USF Tampa Graduate Theses and Dissertations
The natural capacity of DNA for molecular self-assembly has already been exploited to create DNA based tiles which can self-assemble into nano-scale arrays and carry out nano-scale computation. Thus far, however, all such self-assembly has been passive, in the sense that the binding capacities of a tile are never altered throughout the assembly. The idea of active tiles, tiles that can send signals to each other and activate latent binding sites, has been proposed but never incorporated into a formal model. Here, I present an extension of the existent abstract tile assembly model by defining an active tile assembly and …
Integrable Couplings Of The Kaup-Newell Soliton Hierarchy, Mengshu Zhang
Integrable Couplings Of The Kaup-Newell Soliton Hierarchy, Mengshu Zhang
USF Tampa Graduate Theses and Dissertations
By enlarging the spatial and temporal spectral problems within a certain Lie algebra, a hierarchy of integrable couplings of the Kaup-Newell soliton equations is constructed. The recursion operator of the resulting hierarchy of integrable couplings is explicitly computed. The integrability of the new coupling hierarchy is exhibited by showing the existence of infinitely many commuting symmetries.
Bi-Integrable And Tri-Integrable Couplings And Their Hamiltonian Structures, Jinghan Meng
Bi-Integrable And Tri-Integrable Couplings And Their Hamiltonian Structures, Jinghan Meng
USF Tampa Graduate Theses and Dissertations
An investigation into structures of bi-integrable and tri-integrable couplings is undertaken. Our study is based on semi-direct sums of matrix Lie algebras. By introducing new classes of matrix loop Lie algebras, we form new Lax pairs and generate several new bi-integrable and tri-integrable couplings of soliton hierarchies through zero curvature equations. Moreover, we discuss properties of the resulting bi-integrable couplings, including infinitely many commuting symmetries and conserved densities. Their Hamiltonian structures are furnished by applying the variational identities associated with the presented matrix loop Lie algebras.
The goal of this dissertation is to demonstrate the efficiency of our approach and …
Hamiltonian Sets Of Polygonal Paths In 4-Valent Spatial Graphs, Tilahun Abay Muche
Hamiltonian Sets Of Polygonal Paths In 4-Valent Spatial Graphs, Tilahun Abay Muche
USF Tampa Graduate Theses and Dissertations
Spatial graphs with 4–valent rigid vertices and two single valent endpoints, called assembly graphs, model DNA recombination processes that appear in certain species of ciliates. Recombined genes are modeled by certain types of paths in an assembly graph that make a ”oper pendicular ” turn at each 4–valent vertex of the graph called polygonal paths. The assembly number of an assembly graph is the minimum number of polygonal paths that visit each vertex exactly once. In particular, an assembly graph is called realizable if the graph has a Hamiltonian polygonal path.
An assembly graph ɣ^ obtained from a given …
Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu
Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu
USF Tampa Graduate Theses and Dissertations
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, …
Stochastic Hybrid Dynamic Systems: Modeling, Estimation And Simulation, Daniel Siu
Stochastic Hybrid Dynamic Systems: Modeling, Estimation And Simulation, Daniel Siu
USF Tampa Graduate Theses and Dissertations
Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems.
The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described …