A transitive triple, (a, b, c), is defined to be the set {(a, b), (b, c), (a, c)} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D, β), where D is a set of v points and β is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of β. An antiautomorphism of ...

Let A and B be two finite subsets of a field F. In this paper we provide a nontrivial lower bound for |{a + b: a ∈ A, b ∈ B, and P (a, b) 6= 0}| where P (x, y) ∈ F[x, y].

1. Basic Concepts and Facts (1.1) A semigroup is an ordered pair (G, ?) where G is a nonempty set and ? is a binary operation on G satisfying: (G1) a ? (b ? c) = (a ? b) ? c, ∀a, b, c ∈ G. A semigroup G is a monoid if it also satisfies: (G2) G has an element e (sometimes denoted by 1G, called the identity of G), such that e ? a = a ? e = a, ∀a ∈ G. A monoid is a group if (G3) below is satisfied...

DOI: 10.1007/s11424-015-2240-3 Received: 8 November 2012 / Revised: 1 July 2014 c ©The Editorial Office of JSSC & Springer-Verlag Berlin Heidelberg 2015 Abstract Let k be a positive integer. For any positive integer x = ∑∞ i=0 xi2 , where xi = 0, 1, we define the weight w(x) of x by w(x) := ∑∞ i=0 xi. For any integer t with 0 < t < 2 k − 1, let St := {(a, b) ∈ Z2|a+ b ≡ t (mod 2 − 1), w(a)+w(b)...

A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J and Skill...

Vancouver, October 2005. Bridging the Gap between Technology and Users: Leveraging Machine Translation in a Visual Data Triage Tool Thomas Hoeft Nick Cramer M. L. Gregory Elizabeth Hetzler Pacific Northwest National Laboratory Pacific Northwest National Laboratory Pacific Northwest National Laboratory Pacific Northwest National Laboratory 902 Battelle Blvd. 902 Battelle Blvd. 902 Battelle Blvd....

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

polyaniline and polyamide (nylon 6,6) nanocomposites with silva were prepared by in-situ oxidativepolymerization of aniline monomers in the presence of ag salt nano particles of silver (nps) were symthesieedby controlled reduction of ag+ ions kith sodium borohydride at room temperature. nylon 6,6 wax loaded withag nanoparfieles by erdrapment of ag+ ions into the polymer network, followed by red...

in order to determine the prevalence, incidence and odd ratio of hbv, 681 serum samples were collected from 54 laboratory personnel in tehran in both private and governmental sectors. the samples were tested for hbsag and ab using elisa technique. the results showed that the prevalence of hbsag and ab among clinical laboratory personnel was 2.3 and 20 percent respectively. the prevalence of hbs...