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Articles 1 - 10 of 10
Full-Text Articles in Entire DC Network
New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal
New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal
Department of Math & Statistics Faculty Publications
Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays.
A Note On New Semi-Regular Divisible Difference Sets, James A. Davis, Jonathan Jedwab
A Note On New Semi-Regular Divisible Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
We give a construction for new families of semi-regular divisible difference sets. The construction is a variation of McFarland's scheme [5] tor noncyclic difference sets.
Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis
Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis
Department of Math & Statistics Faculty Publications
Yang's comment [C] is based on a lemma which claims to construct an s0 x s1 x s2 x ... x s, perfect binary array (PBA) from an s0s1 x s2 x ... x sr PBA.
Symmetric Designs, Difference Sets, And A New Way To Look At Macfarland Difference Sets, John Bowen Polhill Jr.
Symmetric Designs, Difference Sets, And A New Way To Look At Macfarland Difference Sets, John Bowen Polhill Jr.
Honors Theses
In this paper, the topics of symmetric designs and difference sets are discussed both separately and in relation to each other. Then an approach to MacFarland Difference Sets using the theory behind homomorphisms from groups into the complex numbers is introduced. This method is contrasted with the method of finding this type of difference set used by E.S. Launder in his book Symmetric Designs: An Algebraic Approach.
Topics In Cyclotomic And Quadratic Fields, Pam Mellinger
Topics In Cyclotomic And Quadratic Fields, Pam Mellinger
Honors Theses
This paper introduces cyclotomic and quadratic fields and explores some of their properties and applications to problems in number theory. After some preliminary definitions and theorems, the paper looks at the relationship between quadratic and cyclotomic fields, at Kummer's lemma on units in the pth cyclotomic field, and at the Quadratic Reciprocity Law and its applications to diophantine equations.
Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis
Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis
Department of Math & Statistics Faculty Publications
A perfect binary array (PBA) is an r-dimensional matrix with elements ±I such that all out-of-phase periodic autocorrelation coefficients are zero. The two smallest sizes for which the existence of a PBA is undecided, 2 x 2 x 3 x 3 x 9 and 4 x 3 x 3 x 9, are ruled out using computer search and a combinatorial argument.
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 …
Computational Problems With Binomial Failure Rate Model And Incomplete Common Cause Failure Reliability Data, Paul H. Kvam
Computational Problems With Binomial Failure Rate Model And Incomplete Common Cause Failure Reliability Data, Paul H. Kvam
Department of Math & Statistics Faculty Publications
In estimating the reliability of a system of components, it is ordinarily assumed that the component lifetimes are independently distributed. This assumption usually alleviates the difficulty of analyzing complex systems, but it is seldom true that the failure of one component in an interactive system has no effect on the lifetimes of the other components. Often, two or more components will fail simultaneously due to a common cause event. Such an incident is called a common cause failure (CCF), and is now recognized as an important contribution to system failure in various applications of reliability. We examine current methods for …
Weak-Star Limits On Polynomials And Their Derivatives, William T. Ross, Joseph A. Ball
Weak-Star Limits On Polynomials And Their Derivatives, William T. Ross, Joseph A. Ball
Department of Math & Statistics Faculty Publications
Let μ and v be regular finite Borel measures with compact support in the real line ℝ and define the differential operator D :L ∞(μ) → L ∞(v) with domain equal to the polynomials P by Dp = p′. In this paper we will characterize the weak-star closure of the graph of D in ∞(μ) ⊕ ∞(y). As a consequence we will characterize when D is closable (i.e. the weak-star closure of G contains no non-zero elements of the form o ⊕ g) and when g is weak-star dense in L∞(μ) ⊕ …