Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
The Euler '-function and Carmichael -function are extremely important in modern number theory, and much work has been devoted to studying the distribution and arithmetic properties of the values of each function. One interesting unresolved question...
The study of twin primes gives rise to several famously difficult problems in number theory--in fact, we still cannot definitively say whether there are infinitely many twin primes. In this work, we consider a related problem, namely: What is the...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over [Special characters omitted.] [x ] of xn - 1 for some positive integer n. In this thesis, we will examine two natural questions concerning the divisors...
Dendritic cells. Biological response modifiers. Immune response -- Regulation. T cells. CD antigens. Dendritic Cells -- Immunology. Receptors
Dendritic cells (DCs) are professional antigen-presenting cells (APCs) that regulate antigen-specific T cell activation or tolerance. The maturation state of DCs is critical since immature DCs are believed to induce T cell tolerance whereas mature...
Retinal degeneration -- Genetic aspects. Photoreceptors -- Molecular aspects. Cell death.
Endocytosis.
Rhodopsin.
NF-kappa B (DNA-binding protein)
Cellular signal transduction.
In humans, progressive loss of vision accompanies many inherited retinal degenerative disorders. In many cases, the affected genes are known. However the molecular pathway of photoreceptor cell death is still elusive. In this thesis, I describe the...
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...