Finite-element grid improvement by minimization of stiffness matrix trace

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.     

Resonant neutron filters in elemental analysis and radiography

Translated from Atomnaya Énergiya, Vol. 67, No. 4, pp. 271–274, October, 1989.     

Multifunctional alkylphenol additive

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, pp. 14–15, February, 1989.     

Relation of registration with yield and termination of first lactation in dairy goats

First lactation records of 9941 Alpine, 2383 LaMancha, 11,203 Nubian, 3714 Saanen, and 4649 Toggenburg dairy goat does were obtained from the USDA to evaluate relation of registration (purebred, American, or grade) with lactation yield traits (mature equivalent milk and fat yields) and with reason for termination of lactation (normal, sold for dairy, or culled). Does were grouped by age at first kidding (11 through 16 mo or 21 through 26 mo) and by calendar year (1976 through 1978, 1979 through 1981, or 1982 through 1984). Data were analyzed within breed and year group for yield traits and within breed for reason of termination. Registration and age at first kidding accounted for little variation in mature equivalent milk and fat yields or in reason for termination.     

Computing hysteresis points of nonlinear equations depending on two parameters

A direct method is described for computing a hysteresis point (double turning point) corresponding to a cusp point of a system ofn nonlinear equations inn variables depending on two parameters. By addition of two equations a minimally extended system ofn+2 nonlinear equations is constructed for which the hysteresis point is an isolated solution. An efficient implementation of Newton's method is presented not requiring evaluations of second derivatives of the original problem. Two numerical examples show the efficiency of theQ-quadratically convergent method.