New Developments in Environmental Exposure Assessment in the EU Pesticide Regulatory Process

The paper discusses key aspects of the European Union (EU) regulatory policy for environmental exposure assessment of agricultural pesticide active substances (a.s.) in soil and water, which is examined in the context of the EU Authorisations Directive (91/414/EEC). For agricultural pesticide regulation within EU Member States (MS), the Authorisations Directive will gradually replace existing national systems. Discussion is concentrated on this directive, looking in particular at the Uniform Principles therein and the possible ways that these decision-making guidelines are being developed into a workable regulatory framework. The aim in this process of negotiated development involving the Member States, the Agrochemical Industry and the European Commission (EC), is to identify any questions or data requirements that will be needed for agricultural pesticides.     

Quasimin and quasisaddlepoint for vector optimization

For a constrained multicriteria optimization problem with differentiable functions, but not assuming any convexity, vector analogs of quasimin, Kuhn-Tucker point, and (suitably defined) vector quasisaddlepoint are shown to be equivalent. A constraint qualification is assumed. Similarly, a proper (by Geoffrion's definition) weak minimum is equivalent to a Kuhn–Tucker point with a strictly positive multiplier for the objective, and also to a vector quasisaddlepoint with an attached stability property. Under generalized invex hypotheses, these properties reduce to proper minimum and stable saddlepoint. Various known results are thus unified.     

Some Extensions of Nonconvex Economic Modeling: Invexity,Quasimax, and New Stability Conditions

There are many applications in economics of nonlinear programming, usually under convexity assumptions. Some nonconvex models have also been discussed extensively in order to relax the restrictive assumption of convexity. The applicability can be extended considerably by further generalization to invexity and of maximum to quasimax. Some qualitatively different effects may occur with nonconvex models, such as nonunique optima at different objective levels and jumps in the consumption function, which have economic significance. This paper describes these effects and relates them to mathematical concepts.Thanks are due to Professor F. Giannessi for correcting a number of details of thepresentation     

Extension of orderings on -fields

An analysis is made of the ways in which a total ordering of the set of symmetric elements of a skew field with involution can be extended to an ordering of a larger set of elements. This is done for several different types of orderings found in the literature.

     

Converse duality in Banach space

Two theorems on converse duality are obtained for mathematical programs in Banach spaces. The proofs are based on a Banach-space generalization of the F. John necessary condition for a constrained minimum. No use is made of Kuhn-Tucker constraint qualifications. In the second theorem, the primal program contains a nonlinear equality constraint, and a converse duality theorem is obtained, using a modified concept of convexity; this result appears new, even for finite-dimensional programs. The results are applied to a problem in optimal control.     

Simple modules for groups with abelian Sylow 2-subgroups are algebraic

An algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if G is a group with abelian Sylow 2-subgroups and K is a field of characteristic 2, then every simple KG-module is algebraic.     

A Generalization of the Transportation Method of Linear Programming

The transportation method of linear programming is extended to a more general class of problem, for which the "stepping-stone method" of Charnes and Cooper fails. The method is applicable to various problems in the optimum scheduling of production and transport.This paper reviews the relevant theory, and then describes an efficient computational method, applicable to computers of moderate capacity. Many features of the transportation method are retained. In particular, the amount of information which must be retained, at each stage of calculation, is much less, for a large problem, than is required for the simplex or revised simplex methods.     

Existence and continuity of solutions for vector optimization

Conditions are obtained for the existence of a weak minimum for constrained vector optimization, with a less restrictive compactness hypothesis than usual. Conditions are also derived for the upper and lower semicontinuity of the multifunction describing weak minimum points. The results are applicable to semi-infinite vector optimization.