Brock Theses
http://hdl.handle.net/10464/4
2019-10-16T04:20:15ZA Relation-Algebraic Approach to L - Fuzzy Topology
http://hdl.handle.net/10464/14542
A Relation-Algebraic Approach to L - Fuzzy Topology
Imangazin, Nurbek
Any science deals with the study of certain models of the real world. However, a model is always an abstraction resulting in some uncertainty, which must be considered. The theory of fuzzy sets is one way of formalizing one of the types of uncertainty that occurs when modeling real objects. Fuzzy sets have been applied in various real-world problems such as control system engineering, image processing, and weather forecasting systems.
This research focuses on applying the categorical framework of abstract L - fuzzy relations to L-fuzzy topology with ideas, concepts and methods of the theory of L-fuzzy sets. Since L-fuzzy sets were introduced to deal with the problem of approximate reasoning, t − norm based operations are essential in the definition of L - fuzzy topologies. We use the abstract theory of arrow categories with additional t − norm based connectives to define L - fuzzy topologies abstractly. In particular, this thesis will provide an abstract relational definition of an L - fuzzy topology, consider bases of topological spaces, continuous maps, and the first two separation axioms T0 and T1. The resulting theory of L - fuzzy topological spaces provides the foundation for applications and algorithms in areas such as digital topology, i.e., analyzing images using topological features.
Application of Density Functional Theory to Study the Mechanism of Alkali Metal Enolate Oxidation by N-sulfonyloxaziridines, Umpolung Amide Synthesis from Halo-Amino-Nitro Alkanes, Alkali-Metal Catalyzed Transfer Hydrogenation of Ketones, and Asymmetric Catalyzed Aza-Henry Reactions
http://hdl.handle.net/10464/14541
Application of Density Functional Theory to Study the Mechanism of Alkali Metal Enolate Oxidation by N-sulfonyloxaziridines, Umpolung Amide Synthesis from Halo-Amino-Nitro Alkanes, Alkali-Metal Catalyzed Transfer Hydrogenation of Ketones, and Asymmetric Catalyzed Aza-Henry Reactions
Foy, Hayden
Density functional theory (DFT) and other computational methods are useful tools for determining reaction mechanisms and the factors governing stereoselectivity. To illustrate the versatility of DFT methods, the following reactions were studied: (1) Li+, Na+, and K+ enolate addition to chiral N-sulfonyloxaziridines, stereoselectivity was found to be controlled by enolate, sulfonyl, and oxaziridine oxygen-cation chelation and steric contacts. From this study it was found that the mechanism proceeded in a SN¬1 rather than SN¬2 like fashion. (2) umpolung amide synthesis working from 1,1,1,1-halo-amino-nitro-alkanes leading to the finding that the amide oxygen originates from the nitro group but also from explicitly interacting water molecules in competing pathways. (3) alkali (Li+, Na+, and K+) metal-catalyzed transfer hydrogenation of acetophenone, the mechanism of which was found to proceed via a six-membered transition state affording direct hydrogen transfer to acetophenone generating the product phenylethanol. The TMEDA ligand had a profound effect in stabilizing the transition state which in turn, lowered the activation energy in comparison to the use of isopropanol ligands. Lastly, (4) asymmetric catalyzed Aza-Henry reactions. Controlling the stereoselectivity of such reactions catalyzed by HMeOQuin((Anth)Pyr)-BAM was an H-bonding manifold of specific hetero- and homonuclear hydrogen bonding motifs (N-H-O and N-H-N respectively) observed in the favored transition state structure (syn-(2S,3R)-TS(eq)). There was a central theme of sterics and other non-covalent interactions, such as - stacking or CH/ interactions, which also played significant roles in determining the stereoselectivity in the investigated reactions.
Objective reduction in many-objective optimization problems
http://hdl.handle.net/10464/14540
Objective reduction in many-objective optimization problems
Sen Gupta, Arpi
Many-objective optimization problems (MaOPs) are multi-objective optimization problems which have more than three objectives. MaOPs face significant challenges because of search efficiency, computational cost, decision making, and visualization. Many well-known multi-objective evolutionary algorithms do not scale well with an increasing number of objectives. The objective reduction can alleviate such difficulties. However, most research in objective reduction use non-dominated sorting or Pareto ranking. However, Pareto is effective in problems having less than four objectives. In this research, we use two approaches to objective reduction: random-based and linear coefficient-based. We use the sum of ranks instead of Pareto Ranking. When applied to many-objective problems, the sum of ranks has outperformed many other optimization approaches. We also use the age layered population structure (ALPS). We use ALPS in our approach to remove premature convergence and improve results. The performance of the proposed methods has been studied extensively on the famous benchmark problem DTLZ. The original GA and ALPS outperform the objective reduction algorithms in many test cases of DTLZ. Among all reduction algorithms, a linear coefficient based reduction algorithm provides better performance for some problems in this test suite. Random based reduction is not an appropriate strategy for reducing objectives.
Travelling Wave Solutions on a Non-zero Background for the Generalized Korteweg-de Vries Equation
http://hdl.handle.net/10464/14539
Travelling Wave Solutions on a Non-zero Background for the Generalized Korteweg-de Vries Equation
Nayeri, HamidReza
In presenting this thesis, we try to find all non-periodic travelling waves of the generalized Korteweg-de Vries (gKdV) equation
u_t +\alpha u^p u_x +\beta u_{xxx}=0
using an energy analysis method. Since the power p in the gKdV equation is arbitrary, we consider positive integer values for $p$. We first check the method for two cases where p=1 and p=2 which are known as the KdV and the mKdV equations, respectively.
Then, we look at the general case where p greater than or equal 3 is arbitrary.
By applying the energy analysis method on the KdV and the mKdV equations, we will find an explicit form of solitary waves on a non-zero background. Afterwards, we reparametrize the derived solutions in terms of speed and the background size to interpret these solutions physically. We also look at some limiting cases in which heavy-tailed and kink waves arise in the mKdV equation.
At last, we split up the gKdV equation into two cases of odd and even $p$ powers and apply a similar derivation. In each case, the implicit solutions are introduced and characterized by their features.