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...
Since their discovery in laboratory plasmas in the 1920s, Langmuir waves have been observed to be ubiquitous in plasma environments, particularly in space plasmas. From the greater solar wind to planetary foreshocks and the auroral ionosphere,...
Sorting very large datasets is a key subroutine in almost any application that is built on top of a large database. Two ways to sort out-of-core data dominate the literature: merging-based algorithms and partitioning-based algorithms. Within these...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
'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...
There are no Vassiliev invariants of degree one for classical knots. A. Henrich proved the existence of a sequence of three Vassiliev invariants of degree one for virtual knots. The invariants get stronger and stronger, and the final invariant is...
Pervasive computing leads to an increased integration between the real world and the computational world, and many applications in pervasive computing adapt to the user's context, such as the location of the user and relevant devices, the presence...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Î–[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...
Access control is a core component of any information-security strategy. Researchers have spent tremendous energy over the past forty years defining abstract access-control models and proving various properties about them. However, surprisingly...
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 Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
For many scientific applications, the data set cannot entirely fit in main memory. The data must reside out-of-core, i.e., on parallel disks. For many basic data-movement operations such as permuting, if the programmer does not design efficient...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
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...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
Public key infrastructure (Computer security). ; Computer networks -- Security measures. ; Operating systems (Computers). ; Microcomputers.
In 1976, Whitfield Diffie and Martin Hellman demonstrated how public key cryptography could enable secure information exchange between parties that do not share secrets. In order for public key cryptography to work in modern distributed...
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...
We provide a theoretical model for a design involving a dc voltage biased Josephson junction (JJ) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. We explore the rich classical dynamics of the resultant...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
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...
This thesis investigates a notion of Turing reducibility introduced by Winkler [8] that is total on all computably enumerable oracles. Groszek and Weber show in [7] that this is a new notion of reducibility and it is not transitive. They give su...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...