Neural networks convergence using physicochemical data

An investigation of the neural network convergence and prediction based on three optimization algorithms, namely, Levenberg-Marquardt, conjugate gradient, and delta rule, is described. Several simulated neural networks built using the above three algorithms indicated that the Levenberg-Marquardt optimizer implemented as a back-propagation neural network converged faster than the other two algorithms and provides in most of the cases better prediction. These conclusions are based on eight physicochemical data sets, each with a significant number of compounds comparable to that usually used in the QSAR/QSPR modeling. The superiority of the Levenberg-Marquardt algorithm is revealed in terms of functional dependence of the change of the neural network weights with respect to the gradient of the error propagation as well as distribution of the weight values. The prediction of the models is assessed by the error of the validation sets not used in the training process.     

A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation ofa thin cylindrical plate with clamped lateral side is performed.The problem is considered under the most general statement withthe plate being laminated and consisting of an arbitrary numberof nonhomogeneous and anisotropic (21 elastic moduli) layers.Explicit integral representations of the differential operatorswhich form the two-dimensional model of the plate are derived.In the case when the elastic moduli of each of the layers areconstant, these integral representations turn into algebraicones. The asymptotic procedure is justified with the help ofa weighted inequality of Korn's type. The error estimates obtainedgive a rigorous mathematical proof of both of Kirchhoff's hypotheses(kinematic and static) and shed light on the well-known intrinsicinconsistency of two of the hypotheses.