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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani
Precise Partitions Of Large Graphs, Pouria Salehi Nowbandegani
Electronic Theses and Dissertations
First by using an easy application of the Regularity Lemma, we extend some known results about cycles of many lengths to include a specified edge on the cycles. The results in this chapter will help us in rest of this thesis. In 2000, Enomoto and Ota posed a conjecture on the existence of path decomposition of graphs with fixed start vertices and fixed lengths. We prove this conjecture when |G| is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices. Furthermore, sharp minimum degree and degree sum conditions …
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva
Electronic Theses and Dissertations
Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford
Electronic Theses and Dissertations
Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …
Elements Of Convergence Approach Theory, William D. Trott
Elements Of Convergence Approach Theory, William D. Trott
Electronic Theses and Dissertations
We introduce two generalizations to convergence approach spaces of classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other. Characterizations are obtained for two alternative extensions of reg- ularity to convergence-approach spaces: regularity and strong regularity. Along the way, we give a brief overview of the theory of convergence spaces and of convergence approach spaces.
A Constructive Proof Of The Borel-Weil Theorem For Classical Groups, Kostiantyn Timchenko
A Constructive Proof Of The Borel-Weil Theorem For Classical Groups, Kostiantyn Timchenko
Electronic Theses and Dissertations
The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie algebra of a maximal torus of $G$.