A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

Twisted parafermions

A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted Z-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra A(2)((2)) is given.

On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified. (C) 2002 Elsevier Science (USA).

Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

Piggery pond sludge as a nitrogen source for crops. 1. Mineral N supply estimated from laboratory incubations and field application of stockpiled and wet sludge

Piggery pond sludge (PPS) was applied, as-collected (Wet PPS) and following stockpiling for 12 months ( Stockpiled PPS), to a sandy Sodosol and clay Vertosol at sites on the Darling Downs of Queensland. Laboratory measures of N availability were carried out on unamended and PPS-amended soils to investigate their value in estimating supplementary N needs of crops in Australia's northern grains region. Cumulative net N mineralised from the long-term ( 30 weeks) leached aerobic incubation was described by a first-order single exponential model. The mineralisation rate constant (0.057/week) was not significantly different between Control and PPS treatments or across soil types, when the amounts of initial mineral N applied in PPS treatments were excluded. Potentially mineralisable N (N-o) was significantly increased by the application of Wet PPS, and increased with increasing rate of application. Application of Wet PPS significantly increased the total amount of inorganic N leached compared with the Control treatments. Mineral N applied in Wet PPS contributed as much to the total mineral N status of the soil as did that which mineralised over time from organic N. Rates of CO2 evolution during 30 weeks of aerobic leached incubation indicated that the Stockpiled PPS was more stabilised (19-28% of applied organic C mineralised) than the Wet PPS (35-58% of applied organic C mineralised), due to higher lignin content in the former. Net nitrate-N produced following 12 weeks of aerobic non-leached incubation was highly correlated with net nitrate-N leached during 12 weeks of aerobic incubation (R-2 = 0.96), although it was

The number, morphology, and distribution of retinal ganglion cells and optic axons in the Australian lungfish Neoceratodus forsteri (Krefft 1870)

Australian lungfish Neoceratodus forsteri may be the closest living relative to the first tetrapods and yet little is known about their retinal ganglion cells. This study reveals that lungfish possess a heterogeneous population of ganglion cells distributed in a horizontal streak across the retinal meridian, which is formed early in development and maintained through to adult stages. The number and complement of both ganglion cells and a population of putative amacrine cells within the ganglion cell layer are examined using retrograde labelling from the optic nerve and transmission electron-microscopic analysis of axons within the optic nerve. At least four types of retinal ganglion cells are present and lie predominantly within a thin ganglion cell layer, although two subpopulations are identified, one within the inner plexiform and the other within the inner nuclear layer. A subpopulation of retinal ganglion cells comprising up to 7% or the total population are significantly larger (> 400 mu m(2)) and are characterized as giant or alpha-like cells. Up to 44% of cells within the retinal ganglion cell layer represent a population of presumed amacrine cells. The optic nerve is heavily fasciculated and the proportion of myelinated axons increases with body length from 17% in subadults to 74% in adults. Spatial resolving power, based on ganglion cell spacing, is low (1.6-1.9 cycles deg(-1), n = 2) and does not significantly increase with growth. This represents the first detailed study of retinal ganglion cells in sarcopterygian fish, and reveals that, despite variation amongst animal groups, trends in ganglion cell density distribution and characteristics of cell types were defined early in vertebrate evolution.