Parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network

The parallel dynamics of the asymmetric extremely diluted Ashkin-Teller neural network is studied using signal-to-noise analysis techniques. Evolution equations for the order parameters are derived, both at zero and finite temperature. The retrieval properties of the network are discussed in terms of the four-spin coupling strength and the temperature. It is shown that the presence of a four-spin coupling enhances the retrieval quality. Received 10 November 1999     

On the topological complexity of DC-sets

A DC-set is a set defined by means of convex constraints and one additional inverse convex constraint. Given an arbitrary closed subsetM of the Euclideann-space, we show that there exists a DC-set in (n+1)-space being homeomorphic to the given setM. Secondly, for any fixedn2, we construct a compactn-dimensional manifold with boundary, which is a DC-set and which has arbitrarily large Betti-numbersr _k fork n–2.     

Predicting Noninertial Effects with Linear and Nonlinear Eddy-Viscosity, and Algebraic Stress Models

Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coroiolis-modified eddy-viscosity model, a realizable nonlinear eddy-viscosity model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the validation of the turbulence models. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.     

Smoothing by mollifiers. Part II: nonlinear optimization

This article complements the paper (Jongen, Stein, Smoothing by mollifers part I: semi-infinite optimization J Glob Optim doi:), where we showed that a compact feasible set of a standard semi-infinite optimization problem can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties. In the special case of nonlinear programming this function is constructed as the mollification of the finite min-function which describes the feasible set. In the present article we treat the correspondences between Karush–Kuhn–Tucker points of the original and the smoothed problem, and between their associated Morse indices.      

X-ray treatment at 5 MeV and above

There is agreement in the scientific community that X-ray treatment of food at 7.5 MeV can be safe. Possible process improvements for treating at higher than 5 MeV X-rays have been re-visited. Monte Carlo methods have been applied to simulate the X-ray conversion process and to calculate dose distributions in homogeneous phantoms. Experimental data obtained using X-rays produced with a Rhodotron TT200 at 5 and 10 MeV verifies a representative set of data which is calculated with the presented method.

With this qualified Monte Carlo tool, calculations at 7.5 MeV incident electron energy were performed. The analysis gives special attention to higher photon yield, improved product penetration, as well as surface and edge effects.     

Characterization of strong stability for C-stationary points in MPCC

We study mathematical programs with complementarity constraints (MPCC). Special focus will be on C-stationary points. Under the Linear Independence Constraint Qualification we characterize strong stability of C-stationary points (in the sense of Kojima) by means of first and second order information of the defining functions. It turns out that strong stability of C-stationary points allows a possible degeneracy of bi-active Lagrange multipliers. Some relations to other stationarity concepts (such as A-, M-, S- and B-stationarity) are shortly discussed.     

On regular minimax optimization

We consider functions of maximum type (max functions for short), subject to (in)equality constraints. The space dimension is finite, and the maximum is taken over a compact manifold with boundary. Effective local minimization algorithms based on Newton's method can be derived in the case where a local minimum is nondegenerate (in a two-level sense). In fact, nondegeneracy refers on the one hand to a local (implicit) reduction of the original max function to another one, where the maximum is taken over a finite set. On the other hand, it refers to strict complementarity and nondegeneracy of the underlying quadratic form with respect to the reduced stationary situation. As the main goal, we show that the set ofn-parameter families of functions, for which the stationary points of the corresponding max function are nondegenerate, constitutes an open and dense subset in the space of alln-parameter families (the topology used takes derivatives up to second order into account). An application to approximation problems of Chebyshev type is presented.     

Crystal Structures and Thermal Behaviour of Lanthanide(III) Hexanoate 1, 10‐Phenanthroline Complexes, [M(C5H11CO2)3(phen)] and [Tm(C5H11CO2)2(NO3)(phen)]

Lanthanide(III) hexanoate 1, 10‐phenanthroline complexes crystallise in the space group P2₁/n. The compounds consist of dimers, whereby two lanthanide ions are held together by two bidentate bridging and two tridentate bridging carboxylate groups. The first coordination sphere of the lanthanide ions is completed by one bidentate chelating carboxylate group and by one bidentate 1, 10‐phenanthroline molecule, resulting in the coordination number 9. The dimers have a spherical form, which has important consequences for the thermal properties of complexes. The basic idea behind the preparation of this type of compounds is the stabilisation of the ionic lanthanide layer, so that the smaller lanthanide ions (from which the normal alkanoates do not show mesomorphism because they are too small) show liquid crystallinity. The stabilisation of the ionic layer was successful, expressed by the high melting temperatures, but mesomorphism is not observed. The absence of mesomorphism is related to the isotropic structure of the compounds. A lower symmetry is obtained when a hexanoate group is replaced by a nitrate group. Thulium(III) dihexanoate nitrate 1, 10‐phenanthroline crystallises in the space group P1¯. However, this compound also shows a spherical dimeric structure, but no mesomorphism.     

Gas chromatographic determination of the pesticide dodemorph for assessment of occupational exposure.

As part of a health hazard survey of occupational exposure to pesticides in greenhouse growing of ornamentals, analytical methods are developed and validated for measurement of exposure of workers to the fungicide dodemorph. A gas chromatographic method is developed using on-column injection and nitrogen-phosphorus detection for quantification. Methods for the determination of (potential) dermal exposure by the analysis of foliar dislodgeable residues and cotton gloves are validated with respect to background, analytical recovery, stability, limit of detection, and between-day coefficients of variation. Analytical recovery from 'foliar dislodgeable residue solutions' and cotton gloves is more than 95%. Dodemorph in 'foliar dislodgeable residue solutions' and on cotton gloves is stable for at least five and six months, respectively, when stored in the refrigerator. Between-day coefficients of variation are 6% for both matrices. The limit of detection is 3 micrograms per leaf sample and 150 micrograms per pair of gloves. Institute of Occupational Medicine (IOM) samplers, designed for the collection of a defined inspirable fraction of aerosols, are tested for sampling air-borne dodemorph. IOM samplers equipped with glass-fiber or cellulose filters appear unsuitable for reliable sampling of the fungicide because of breakthrough or breakdown during sampling.