Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).

Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Varieties of algebras arising from K-perfect m-cycle systems

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.

q-Leibniz Algebras

2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Free Bicommutative Algebras

2000 Mathematics Subject Classification: Primary 17A50, Secondary 16R10, 17A30, 17D25, 17C50.

Identifying programs to reduce road trauma to A.C.T. motorcyclists

A broad range of motorcycle safety programs and systems exist in Australia and New Zealand. These vary from statewide licensing and training systems run by government licensing and transport agencies to safety programs run in small communities and by individual rider groups. While the effectiveness of licensing and training has been reviewed and recommendations for improvement have been developed (e.g. Haworth & Mulvihill, 2005), little is known about many smaller or innovative programs, and their potential to improve motorcycle safety in the ACT.

Impacts of periodic tillage on soil C stocks : a synthesis

Long-term loss of soil C stocks under conventional tillage and accrual of soil C following adoption of no-tillage have been well documented. No-tillage use is spreading, but it is common to occasionally till within a no-till regime or to regularly alternate between till and no-till practices within a rotation of different crops. Short-term studies indicate that substantial amounts of C can be lost from the soil immediately following a tillage event, but there are few field studies that have investigated the impact of infrequent tillage on soil C stocks. How much of the C sequestered under no-tillage is likely to be lost if the soil is tilled? What are the longer-term impacts of continued infrequent no-tillage? If producers are to be compensated for sequestering C in soil following adoption of conservation tillage practices, the impacts of infrequent tillage need to be quantified. A few studies have examined the short-term impacts of tillage on soil C and several have investigated the impacts of adoption of continuous no-tillage. We present: (1) results from a modeling study carried out to address these questions more broadly than the published literature allows, (2) a review of the literature examining the short-term impacts of tillage on soil C, (3) a review of published studies on the physical impacts of tillage and (4) a synthesis of these components to assess how infrequent tillage impacts soil C stocks and how changes in tillage frequency could impact soil C stocks and C sequestration. Results indicate that soil C declines significantly following even one tillage event (1-11 % of soil C lost). Longer-term losses increase as frequency of tillage increases. Model analyses indicate that cultivating and ripping are less disruptive than moldboard plowing, and soil C for those treatments average just 6% less than continuous NT compared to 27% less for CT. Most (80%) of the soil C gains of NT can be realized with NT coupled with biannual cultivating or ripping. (C) 2007 Elsevier B.V. All rights reserved.