The Will of the People

The paper discusses the cybernetic mechanisms whereby our institutions fail to translate the will of the people into effective policies, and those by which the will of the people is an attenuated version of human potentiality in the first place. A systemic model is developed to account for the observed phenomena in terms of a cybernetic theory of the management process, and this is then exemplified from current dilemmas facing humankind. The model is subsequently extended to encompass the theory of viable systems, the principle of self-reference, and a model of self-hood which promotes new concepts that close the model into its starting point of human potential. The total approach bears on the capability of individuals, groups, institutions, societies and nations to realize themselves, and to thwart the dangers in which our civilization is plunged.     

Serum lithium determinations using flameless atomic absorption spectroscopy

The use of lithium salts and lithium carbonate in particular, in the control and treatment of certain types of psychiatric patients requires a means of monitoring lithium levels in serum. The currently accepted theraputic concentrations cover the range 0.5–1.5 milliequiv-alents of lithium per liter (mEq/l.) of serum with toxic symptoms reported above 1.5–2.0 mEq/l. Atomic absorption spectroscopy has been the method of choice for this analysis for several years and with the development of flameless methods the smaller samples may be used and multiple determinations made in about the same time required for a single determination using an air-acetylene flame and aspiration technique. The standard deviation of the flameless method is approximately 5% relative over the range of interest, 0.5–2.0 mEq/l. A comparison of results is made using a Perkin-Elmer Model 303 AA unit and a Varian Model AA5 with Model 63 Carbon Rod Atomizer.     

Rational Cherednik algebras and Hilbert schemes

Let H_c be the rational Cherednik algebra of type A_n-1 with spherical subalgebra U_c=eH_ce. Then U_c is filtered by order of differential operators, with associated graded ring where W is the nth symmetric group. We construct a filtered Z-algebra B such that, under mild conditions on c:• the category B-qgr of graded noetherian B-modules modulo torsion is equivalent to U_c-mod;• the associated graded Z-algebra has grB-lqgr?coh Hilb(n), the category of coherent sheaves on the Hilbert scheme of points in the plane.This can be regarded as saying that U_c simultaneously gives a non-commutative deformation of h⊕h^*/W and of its resolution of singularities Hilb(n)→h⊕h^*/W. As we show elsewhere, this result is a powerful tool for studying the representation theory of H_c and its relationship to Hilb(n).     

Automating the Partition of Indexes

Abstract

In this article we show how attention to the structure of a particular algebraic calculation can lead to the simple implementation of powerful computer algebra tools. The creation of partitions for a set of indexes is required for the implementation of many theoretical structures. This may be difficult to do by hand even when the number of indexes is only moderately large. These partitions arise through the action of differentiation and so we mimic differentiation in a computer algebra package to create partitions of indexes. The strategies employed are extended to the creation of complementary set partitions, their reduction to equivalence classes, and the implementation of Edgeworth expansions and the exlog relations.