Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures

In this paper we examine the bi-Hamiltonian structure of the generalized KdV-hierarchies. We verify that both Hamiltonian structures take the form of Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated system. Classical extended conformal algebras are obtained from the second Poisson bracket. In particular, we construct the $W_n^l$ algebras, first discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.Comment: 41 page

Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies

Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of De Groot et al, reductions based upon graded regular elements of arbitrary Heisenberg subalgebras are considered. We show that, in the case of the nontwisted loop algebra $\ell(gl_n)$, graded regular elements exist only in those Heisenberg subalgebras which correspond either to the partitions of $n$ into the sum of equal numbers $n=pr$ or to equal numbers plus one $n=pr+1$. We prove that the reduction belonging to the grade $1$ regular elements in the case $n=pr$ yields the $p\times p$ matrix version of the Gelfand-Dickey $r$-KdV hierarchy, generalizing the scalar case $p=1$ considered by DS. The methods of DS are utilized throughout the analysis, but formulating the reduction entirely within the Hamiltonian framework provided by the classical r-matrix approach leads to some simplifications even for $p=1$.Comment: 43 page

First report of facial eczema in sheep in South Africa

The occurrence of facial eczema in sheep in the Republic of South Africa is reported for the first time. The disease in this country is similar to that described in New Zealand and Australia. To date it has only been diagnosed in Merino sheep on artificial pastures in the Humansdorp area of the Cape Province. The fungus Pithomyces chartarum (Berk. & Curt.) M. B. Ellis was isolated from grass litter in these pastures. One of these isolates was shown to produce sporidesmin and the typical clinical and histopathological signs of facial eczema were reproduced upon dosing this culture to a lamb.The articles have been scanned in colour with a HP Scanjet 5590;300dpi. adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format

Nature’s nations: the shared conservation history of Canada and the USA

Historians often study the history of conservation within the confines of national borders, concentrating on the bureaucratic and political manifestations of policy within individual governments. Even studies of the popular expression of conservationist ideas are generally limited to the national or sub-national (province, state, etc.) scale. This paper suggests that conservationist discourse, policy and practice in Canada and the USA were the products of a significant cross-border movement of ideas and initiatives derived from common European sources. In addition, the historical development of common approaches to conservation in North America suggests, contrary to common assumptions, that Canada did not always lag behind the USA in terms of policy innovation. The basic tenets of conservation (i.e. state control over resource, class-based disdain for subsistence hunters and utilitarian approaches to resource management) have instead developed at similar time periods and along parallel ideological paths in Canada and the USA