In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
This research extends previous findings that the behavior of individuals high as compared to low in Private Self-consciousness, an individual difference in self-awareness, is more influenced by subtle primes. Manipulations of self-awareness were...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Ζ[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
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...
Fc receptors. Dendritic cells. Immune recognition.
Three types of Fc receptors for IgG, FcyRI (CD64), FcyRII (CD32), and FcyRIII (CD 16) are expressed differentially on blood leukocytes. In particular, CD64 and CD32 are constitutively expressed on mononuclear phagocytes of the human myeloid system....
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...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Α is an order of level M in H , we define theta series for each ideal I of Α using the reduced norm on H. Using harmonic analysis...
Prior research has shown that people with high and low self-esteem respond differently to rejection and failure. These differential responses may be due to the expectations people hold about their future acceptance by others and may be linked to...
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...
Chapter 1: Munchnones and mesoionic heterocycles The reactivity, regioselectivity, and synthetic applications of munchnones (1,3-oxazolium-5-olates) is a common theme which runs through Chapters 2-5. The definition, structure, and reactivity of...
Lung cancer is the leading cause of cancer-related death in the USA and worldwide causing 160,000 and 1.5 million deaths per year, respectively. Due to the late stage of diagnosis, poor efficacy of chemotherapies (targeted and pleiotropic), and...
Many protocols for adoptive T cell therapy (ACT) include preparative conditioning strategies to deplete host lymphocytes prior to T cell infusion. Total body irradiation and high-dose chemotherapy regimens not only relieve immunosuppression, but...
A new type of analytic expansion for use in stability calculations is presented and applied to the question of the stability of laminar solutions of the Navier-Stokes equation. This leads in a natural way to a model of the transition from laminar...
Studies presented in this dissertation focus on the transcriptional targets and cellular functions of [Delta]Np63[alpha], the predominant TP63 isoform expressed in epithelial stem cell compartments. TP63, a member of the p53 family of...
The Mixed Lineage Leukemia (MLL1) gene was first cloned as a hot spot of chromosomal translocations in acute leukemia. More than 70 fusion proteins of MLL1 have been described in both lymphoid and myeloid leukemia and many are highly associated...
Internet -- Security measures. Public key infrastructure (Computer security). Digital signatures. Peer-to-peer architecture (Computer networks) -- Security measures.
The Internet has become a virtual place where people not only operate in isolation but also interact with other Internet users. Collaborative systems are becoming more popular. Applications now being introduced could provide better remote education...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by 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...
This thesis explores practical and theoretical aspects of several privacy-providing technologies, including tools for anonymous web-browsing, verifiable electronic voting schemes, and private information retrieval from databases. State-of-art...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
The cortical cytoskeleton mediates a range of cellular activities such as endocytosis, cell motility, and the maintenance of cell rigidity. In yeast cells, prominent cortical structures called eisosomes generate specialized domains termed MCCs to...
Sensing light from the environment using photoreceptors is of great adaptive significance to eukaryotes. A prominent feature of the photochemistry of these receptors is the photocycle length, the time taken to decay from the initial signaling light...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...