We partially determine the necessary and su cient conditions on the entries of the intersection matrix of the transcendental lattice of algebraic K3 surface with Picard number 18 (X) 19 for the surface to doubly ...

Self-similar sets are one class of fractals that are invariant under geometric similarities. In this thesis, we study on self-similar sets. We give the definition of a self-similar set K and present the proof the existence ...

The properties of compact subsets of the real line which are in the class of Bounded Lebesgue Constants (BLC) are investigated. Knowing that any such set must have 1-dimensional Lebesgue measure zero and nowhere density, ...

We define the subgroup category, a category on the class of finite groups where the morphisms are given by the subgroups of the direct products and the composition is the star product. We also introduce some of its ...

In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we ...

Given a fusion system F defined on a p-group S, there exist infinite group models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G. If ...

We study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all the cases where an explicit generating set is known, we calculate the generic initial ideal of the Hilbert ideal ...

Of the 26 sporadic finite simple groups, 5 were discovered by E. Mathieu in 1861 and 1873 [1], [2]. These Mathieu groups are the focus of this thesis, where we will prove their simplicity using elementary methods. E. ...

Extremal problems in different function spaces have long been investigated. Ferguson provides a method, using Bergman projections, to solve certain types of extremal problems in Bergman spaces for 1 < p < ∞ in his work ...

Haar systems are generalizations of Haar measures on groups to groupoids. Naturally, important research directions in the field try to generalize the well known existence of a Haar measure on a locally compact group to the ...