Nonhomogeneous waring equations

It is proved that for an arbitrary positive integer k the equation n=x²+y²+z³+u³+v⁴+w¹⁴+t^4k+1 has a positive integer solution for all sufficiently large n. Bibliography: 6 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 226, 1996, pp. 65–68.     

High performance liquid chromatographic determination of Picumast and two active metabolites in plasma using on-line sample preparation.

A method for determining Picumast, an antiallergic drug, in plasma by HPLC and column switching has been developed. The system consisted of two precolumns, an analytical column, three pumps, an autosampler and a fluorescence detector. The precolumns (17 x 4.6 mm i.d.) were packed with LiChroprep RPR (a moderately polar reversed phase) and the analytical column with Nucleosil ODS (RP 18, 5 microns). The columns were connected according to the alternating precolumn technique. The mobile phase consisted of 30% CH3CN/70% 0.05 M KH2PO4, pH 2.5, with a flow gradient. Detection wavelengths were 333 nm for excitation and 383 nm for emission. The retention times of Picumast, M1 and M2 were 12, 3.6 and 4.0 min, respectively. Total run time was 15 min. The limit of detection was 3 ng/mL for M1 and 1 ng/mL for M2 and Picumast using an injection volume of 150 microL. The recoveries vary between 89% and 97% with standard deviations between 2.4 and 3.3%.     

Wave attenuation in an elastic medium

This article examines the propagation of viscoelastic (elastic) waves in a medium consisting of two layers of finite thickness. It is found that there is a mechanical effect manifest in the monotonic dependence of the damping factor on the parameters of the system. These dependences have distinct maxima and minima, thus making it possible to optimize the damping properties of systems by varying their geometric parameters.Translated from Dinamicheskie, Sistemy, No. 4, pp. 57–62, 1985.     

COSMIC(90): An improved molecular mechanics treatment of hydrocarbons and conjugated systems

Summary Four modifications to the COSMIC molecular mechanics force field are described, which greatly increase both its versatility and the accuracy of calculated conformational energies. The Hill non-bonded van der Waals potential function has been replaced by a two-parameter Morse curve and a new H-H potential, similar to that in MM3, incorporated. Hydrocarbon energies in particular are much improved.A simple iterative Hückel pi-electron molecular orbital calculation allows modelling of conjugated systems. Calculated bond lengths and rotational barriers for a series of conjugated hydrocarbons and nitrogen heterocycles are shown to be as accurate as those determined by the MM2 SCF method.Explicit hydrogen-bonding potentials for H-bond acceptor-donor atom pairs have been included to give better hydrogen bond energies and lengths. The van der Waals radii of protonic hydrogens are reduced to 0.5 Å and the energy well depth is increased to 1.0 kcal mol^-1.Two new general atom types, N⁺ _sp ² and O^- _sp ³ , have been introduced which allow a wide variety of charged conjugated systems to be studied. A minimum of parameterisation is required, as the new types are easily included in the Hückel scheme which automatically adjusts bond and torsional parameters according to the defined bond-order relationships.     

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

On the strong monotonicity of power indices

The problem of choosing a power index which better describes a control situation could be solved by the property of strong monotonicity. We prove this property for some of the best known power indices.sponsored by Committee 10 of C.N.R.     

Mössbauer spectra and magnetic properties of Sm2 (Co,Fe)17 alloys

Hyperfine Interactions - Sm2(Co1?x Fe x )17 alloys form the basis of a new class of permanent magnets. We have investigated these materials with57Fe Mössbauer spectroscopy. Alloys...