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Articles 241 - 264 of 264
Full-Text Articles in Entire DC Network
The Commutant Of A Certain Compression, William T. Ross
The Commutant Of A Certain Compression, William T. Ross
Department of Math & Statistics Faculty Publications
Let G be any bounded region in the complex plane and K Ϲ G be a simple compact arc of class C1. Let A2(G\K) (resp. A2(G)) be the Bergman space on G\K (resp. G). Let S be the operator multiplication by z on A2(G\K) and C = PN S│N be the compression of S to the semi-invariant subspace N = A2(G\K) Ɵ A2(G). We show that the commutant of C* is the set of all operators …
A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab
A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1,d2 ∈ D, d1 ≠ d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic if the underlying group is. Difference sets a.re important in design theory because they a.re equivalent to symmetric (v, k, λ) designs with a regular automorphism group. Abelian difference sets arise naturally in …
Almost Difference Sets And Reversible Divisible Difference Sets, James A. Davis
Almost Difference Sets And Reversible Divisible Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
Let G be a group of order mn and N a subgroup of G of order n. If D is a k-subset of G, then D is called a (m, n, k, λ1, λ2) divisible difference set (DDS) provided that the differences dd'-1 for d, d' ∈ D, d ≠ d' contain every nonidentity element of N exactly λ1 times and every element of G - N exactly λ2 times. Difference sets are used to generate designs, as described by [4] and [9]. D will be …
Construction Of Relative Difference Sets In P-Groups, James A. Davis
Construction Of Relative Difference Sets In P-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
Jungnickel (1982) and Elliot and Butson (1966) have shown that (pj+1,p,pj+1,pj) relative difference sets exist in the elementary abelian p-group case (p an odd prime) and many 2-groups for the case p = 2. This paper provides two new constructions of relative difference sets with these parameters; the first handles any p-group (including non-abelian) with a special subgroup if j is odd, and any 2-group with that subgroup if j is even. The second construction shows that if j is odd, every abelian group …
A Generalization Of Kraemer's Result On Difference Sets, James A. Davis
A Generalization Of Kraemer's Result On Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
Kraemer has shown that every abelian group of order 22d+ 2 with exponent less than 22d+ 3 has a difference set. Generalizing this result, we show that any nonabelian group with a central subgroup of size 2d+ 1 together with an exponent-like condition will have a difference set.
An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis
An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
An exponent bound is presented for abelian (pi+j, pi, pi+j, pi) relative difference sets: this bound can be met for i≤j.
[Introduction To] The Vax Book: An Introduction, John R. Hubbard
[Introduction To] The Vax Book: An Introduction, John R. Hubbard
Bookshelf
This book is an expansion of the book, A Gentle Introduction to the Vax System. The purpose of the book is to guide the novice, step-by-step, through the initial stages of learning to use the Digital Equipment Corporation's Vax computers, running under the VMS operating system (Version 5.0 or later). As a tutorial for beginners, this book assumes no previous experience with computers.
Difference Sets In Abelian 2-Groups, James A. Davis
Difference Sets In Abelian 2-Groups, James A. Davis
Department of Math & Statistics Faculty Publications
Examples of difference sets are given for large classes of abelian groups of order 22d + 2. This fills in the gap of knowledge between Turyn's exponent condition and Dillon's rank condition. Specifically, it is shown thatℤ/(2d)×ℤ/(2d+2) andℤ/(2d+1)×Z/(2d+1) both admit difference sets, and these have many implications.
A Result On Dillon's Conjecture In Difference Sets, James A. Davis
A Result On Dillon's Conjecture In Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
Dillon has conjectured that any group of order 22d+2 with a normal subgroup isomorphic to Z2d+1 will have a difference set. He was able to show that this is true if the subgroup is central: this paper extends that idea to noncentral subgroups.
Some Non-Existence Results On Divisible Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
Some Non-Existence Results On Divisible Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
Department of Math & Statistics Faculty Publications
In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches:
(i) character sum arguments similar to the work of Turyn [25] for ordinary difference sets,
(ii) involution arguments, and
(iii) multipliers in conjunction with results on ordinary difference sets.
Among other results, we show that an abelian affine difference set of odd order s (s not a perfect square) in G can exist only if the Sylow 2-subgroup of G is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd …
Analytic Continuation In Bergman Spaces And The Compression Of Certain Toeplitz Operators, William T. Ross
Analytic Continuation In Bergman Spaces And The Compression Of Certain Toeplitz Operators, William T. Ross
Department of Math & Statistics Faculty Publications
Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A2 (G\K) and A2(G) be the Bergman spaces on G\K, respectively G and define N = A2(G\K) Ɵ A2 (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of aG that do not intersect K. This result will be used to discuss the Fredholm theory of the operator Cf = PNTf│N, where f ϵ C(G) …
A Note On Nonabelian (64, 28, 12) Difference Sets, James A. Davis
A Note On Nonabelian (64, 28, 12) Difference Sets, James A. Davis
Department of Math & Statistics Faculty Publications
The existence of difference sets in abelian 2-groups is a recently settled problem [5]; this note extends the abelian constructs of difference sets to nonabelian groups of order 64.
A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
A Note On Intersection Numbers Of Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott
Department of Math & Statistics Faculty Publications
We present a condition on the intersection numbers of difference sets which follows from a result of Jungnickel and Pott [3]. We apply this condition to rule out several putative (non-abelian) difference sets and to correct erroneous proofs of Lander [4] for the nonexistence of (352, 27, 2)- and (122, 37, 12)-difference sets.
On Uniform And Relative Distribution In The Brauer Group, Gary R. Greenfield
On Uniform And Relative Distribution In The Brauer Group, Gary R. Greenfield
Department of Math & Statistics Technical Report Series
In this progress/technical report our objective is twofold. First, to formalize and expand upon remarks appearing in [7] concerning the relativization of the fundamental identity in the setting of the Brauer group of a ring, and second to exhibit a construction which shows how to interpret uniform distribution as a homological phenomenon.
Partially Confluent Maps And N-Ods, Van C. Nall
Partially Confluent Maps And N-Ods, Van C. Nall
Department of Math & Statistics Faculty Publications
Let f : X-->Y be a map between topological spaces. A Wf-set in Y is a continuum in Y which is the image under f of a continuum in X. The map f is partially confluent if each continuum in Y is the union of a finite number of Wf-sets, and n-partially confluent if each continuum in Y is the union of n Wf-sets. In this paper, it is shown that every partially confluent map onto an n-cell is weakly confluent. Also, the relationship between partially confluent maps and continua which …
Maps Which Preserve Graphs, Van C. Nall
Maps Which Preserve Graphs, Van C. Nall
Department of Math & Statistics Faculty Publications
In 1976 Eberhart, Fúgate, and Gordh proved that the weakly confluent image of a graph is a graph. A much weaker condition on the map is introduced called partial confluence, and it is shown that the image of a graph is a graph if and only if the map is partially confluent.
In addition, it is shown that certain properties of one-dimensional continua are preserved by partially confluent maps, generalizing theorems of Cook and Lelek, Tymchatyn and Lelek, and Grace and Vought. Also, some continua in addition to graphs are shown to be the images of partially confluent maps only.
[Introduction To] A Gentle Introduction To The Vax System, John R. Hubbard
[Introduction To] A Gentle Introduction To The Vax System, John R. Hubbard
Bookshelf
This book was written originally for students enrolled in computer science courses at the University of Richmond. Very few had worked on a large time-sharing system like the VAX.
The purpose of this book is to help the novice become comfortable using any of the Digital Equipment Corporations VAX computers, from the Micro-VAX to the powerful VAX 8000 system. The book is meant to be used as a tutorial.
Weak Confluence And W-Sets, Van C. Nall
Weak Confluence And W-Sets, Van C. Nall
Department of Math & Statistics Faculty Publications
A mapping between continua is weakly confluent if for each subcontinuum K of the range some component of the preimage of K maps onto K. Class [W] is the class of all continua which are the images of weakly confluent maps only. The notion of Class [W] was introduced by Andrej Lelek in 1972. Since then it has been widely explored and some characterizations of these continua have been given. J. Grispolakis and E. D. Tymchatyn have given a characterization in terms of hyperspaces [4]. J. Davis has shown that acyclic atriodic continua are in Class [W]i therefore, atriodic tree-like …
Approximation Of Compact Homogeneous Maps, John R. Hubbard
Approximation Of Compact Homogeneous Maps, John R. Hubbard
Department of Math & Statistics Faculty Publications
Within the clasp of continuous homogeneous maps between Banach spaces, it is proved that every compact map can be uniformly approximated by finite-rank maps. This result is obtained by means of the classical metric projection on Banach spaces.
Air Force Rotc At The University Of Richmond, 1951-1957, Robert J. Dandridge
Air Force Rotc At The University Of Richmond, 1951-1957, Robert J. Dandridge
Honors Theses
In the summer of 1950, after the seriousness of the Korean conflict had become evident, a special committee appointed three years earlier by the Executive Committee of the Board of Trustees was reactivated for the purpose of considering "the feasibility of applying for a Reserve Office Training Corps unit" for the University of Richmond. This special committee, called the ROTC Committee, after thorough study, rendered a unanimous recommendation to the Board that a unit of Army ROTC be applied for. The application was completed and mailed to the Department of the Army. Approval of the application was not long in …
Four Dimensional Graphs Of Complex Functions, Malcom Lee Murrill
Four Dimensional Graphs Of Complex Functions, Malcom Lee Murrill
Master's Theses
Complex functions of a single complex variable involve four unknowns, two independent and two dependent variables, and thus cannot be adequately represented in two- or three- dimensional space. Various geometric constructions in both two and three dimensions have been devised in the past, however, in attempts to illuminate complex function theory. The standard and most useful, of these representations is that developed by Gauss and Riemann employing two complex planes simultanesously. These show the correspondence between a particular curve or region in the object plane and its image, as mapped by a given transformation, in the image plane.
A Historical Survey Of Methods Of Solving Cubic Equations, Minna Burgess Connor
A Historical Survey Of Methods Of Solving Cubic Equations, Minna Burgess Connor
Master's Theses
It has been said that the labor-saving devices ot this modern age have been made possible by the untiring efforts of lazy men. While working with cubic equations, solving them according to the standard methods appearing in modern text-books on the theory of equations, it became apparent, that in many cases, the finding of solutions was a long and tedious process involving numerical calculations into which numerous errors could creep. Confessing to laziness, and having been told at an impressionable age that "any fool can do it the hard way but it takes a genius to find the easy …
The Existence Theorem Of Ordinary Differential Equations, Harris J. Dark
The Existence Theorem Of Ordinary Differential Equations, Harris J. Dark
Master's Theses
There are a great many devices for solving differential equations of certain special forms. But there is a large number of classes of differential equations that are not included in these special forms and cannot be integrated by quadratures or other purely elementary methods. When mathematicians were forced to abandon their cherished hope of finding a method for expressing the solution of every differential equation in terms of a finite number of known functions or their integrals they turned their attention to the question of whether a differential equation in general had a solution at all, and, if so, of …
Gauss' Hypergeometric Equation, William R. Smith
Gauss' Hypergeometric Equation, William R. Smith
Master's Theses
As early as the seventeenth century the English mathematician, john Wallis (1616-1703), used the term "hypergeometric" to describe a series which he was studying. This series, ∑(a)(a+b)(a+2b)…(a+n-1b), is quite different from the usual geometric series, hence the term, "hyper" (=above) plus "geometric," was used to signify that the series was of greater complexity than the geometric series. Wallis did not consider his series a power series or a function of x.
In 1769 this series received a remarkable development at the hands of Loonhard Euler who, following the example of Wallis, applied the word "hypergeometric" to it. He observed that …