1-Overlap cycles for Steiner triple systems

A number of applications of Steiner triple systems (e.g. disk erasure codes) exist that require a special ordering of its blocks. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples of listing elements of a combinatorial family in a specific manner, and Godbole invented the following generalization of these in 2010. 1-overlap cycles require a set of strings to be ordered so that the last letter of one string is the first letter of the next. In this paper, we prove the existence of 1-overlap cycles for automorphism free Steiner triple systems of each possible order. Since Steiner triple systems have the property that each block can be represented uniquely by a pair of points, these 1-overlap cycles can be compressed by omitting non-overlap points to produce rank two universal cycles on such designs, expanding on the results of Dewar.     

Capelli identities for classical Lie algebras

We extend the Capelli identity from the Lie algebra to the other classical Lie algebras and . We employ the theory of reductive dual pairs due to Howe. Received: 12 February 1997 / in revised form: 24 July 1998     

Cancellative Orders

left order in Q and Q is a semigroup of left quotients of S if every q∈Q can be written as q=a^*b for some a, b∈S where a^* denotes the inverse of a in a subgroup of Q and if, in addition, every square-cancellable element of S lies in a subgroup of Q. Perhaps surprisingly, a semigroup, even a commutative cancellative semigroup, can have non-isomorphic semigroups of left quotients. We show that if S is a cancellative left order in Q then Q is completely regular and the {\cal D}-classes of Q are left groups. The semigroup S is right reversible and its group of left quotients is the minimum semigroup of left quotients of S. The authors are grateful to the ARC for its generous financial support.     

Optimization of the Production Medium for Biosynthesis of Antifungal Antibiotic Ak-111-81 by Phosphate-Deregulated Mutant of <Emphasis Type="Italic">Streptomyces hygroscopicus</Emphasis>

Experimental mathematical designs were applied for optimization of a nutrient medium for biosynthesis of the antifungal antibiotic AK-111-81 by phosphate-deregulated mutant of Streptomyces hygroscopicus 111-81. Antifungal antibiotic AK-111-81 possesses well-expressed activity against Fusarium graminearum and other phytopathogenic fungi. The level of the production of the antibiotic AK-111-81 on this medium is more than three times higher than on the initial medium. The optimized quantitative composition of the nutrient culture media is (g/l): glucose, 20; soy meal, 18; ammonium succinate, 3; CaCO₃, 1.     

The WADA Proficiency Testing Program as an integral part of the fight against doping in sport

This article provides a brief perspective of the World Anti-Doping Agency (WADA) in the context of the fight against doping in sport and of the WADA Proficiency Testing Program as an essential element of the World Anti-Doping Program. The WADA Proficiency Testing Program exists within the framework of the WADA-accredited laboratories and is aimed at improving the effectiveness of the fight against doping by testing the ability of the laboratories to reliably identify and measure the substances and methods defined in the WADA Prohibited List. The paper provides an overview of the WADA Proficiency Testing scheme with respect to organization, test composition and evaluation of anti-doping methods and techniques. Scientific research is mentioned in the context of WADA’s involvement in generating reference materials for improvement of analytical activities of the WADA-accredited laboratories. WADA’s funding of a reference material for 19-norandrosterone in human urine is illustrated as an example.     

Solvent effects in the polymerization of propylene catalyzed by octahedral complexes

The effect of solvents (toluene, dichloromethane, and hexane) was studied on the polymerization of propylene with the octahedral complexes bis(trimethylsilyl)benzamidinate titanium dichloride(a), bis(acetylacetonate) titanium dichloride(b), and bis(diethylamino) titanium di‐2‐(diphenylphosphanylamino)pyridine as catalytic precursors and methylalumoxane as the cocatalyst. For comparison, the polymerization was also performed in plain liquid propylene without the addition of any solvent. The obtained polymers were fractionated by refluxing hexane. The activity of the complexes and the molecular weights and tacticities of the whole polymers and their different fractions were the studied parameters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4505–4516, 2005     

A New Quantum Analog of the Brauer Algebra

We introduce a new algebra depending on two nonzero complex parameters z and q such that its specialization at z=q ⁿ and q=1 coincides the Brauer algebra. We show that the action of the new algebra commutes with the representation of the twisted deformation of the enveloping algebra U(o _n) in the tensor power of the vector representation.     

Idempotent bounded C-semigroups

A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups.