In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥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...
DC-to-DC converters -- Design and construction. Electric inductors -- Design and construction. Thin film devices -- Design and construction. Microprocessors -- Power supply. Microfabrication. Transients (Dynamics).
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...
Coding theory. Characters of groups. Error-correcting codes (Information theory). Polynomials.
We introduce vector-valued character theory, a higher dimensional generalization of character theory. We then use vector-valued characters to extend the MacWilliams equivalence theorem for linear codes to a class of additive codes, called...
In an undercooled environment any protuberance or bump on a planar solid/liquid interface that extends into the melt enhances its growth since the surrounding temperature gradient is greater than that about the planar surface. Consequently, the...
Membrane docking and fusion are essential steps in intracellular vesicular trafficking. The underlying molecular mechanisms are highly conserved between organisms. Yeast homotypic vacuole fusion has become a paradigm in studying this fundamental...
Plants -- Effect of iron on. Iron -- Metabolism -- Molecular aspects. Chloroplasts. Plant mitochondria. Homeostasis. Plant enzymes. Reduction (Chemistry). Iron chelates.
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...