On the cost of approximating all roots of a complex polynomial

This work examines the computational complexity of a homotopy algorithm in approximating all roots of a complex polynomialf. It is shown that, probabilistically, monotonic convergence to each of the roots occurs after a determined number of steps. Moreover, in all subsequent steps, each rootz is approximated by a complex numberx, where ifx ₀ =x, x _j =x _j–1 –f(x _j–1)/f(x _j–1),j = 1, 2,, then |x _j –z| < (1/|x ₀ –z|)|x _j–1–z|².     

Automated molecular design: A new fragment-joining algorithm

Summary A popular first step in the problem of structure-based, de novo molecule design is to identify regions where specific functional groups or chemical entities would be expected to interact strongly. When the three-dimensional structure of the receptor is not available, it may be possible to derive a pharmacophore giving the three-dimensional relationships between such chemical groups. The task then is to design synthetically feasible molecules which not only contain the required groups, but which can also position them in the desired relative orientation. One way to do this is to first link the groups using an acyclic chain. We have investigated the application of the tweak algorithm [Shenkin, P.S. et al., Biopolymers, 26 (1987) 2053] for generating families of acyclic linkers. These linking structures can subsequently be braced using a ring-joining algorithm [Leach, A.R. and Lewis, R.A., J. Comput. Chem., 15 (1994) 233], giving rise to an even wider variety of molecular skeletons for further studies.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

An investigation of the reliability of the Galerkin-Petrov method

It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 2¹ S and 3¹ S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.     

Validation steps for traceability of linear calibrated chemical measurements

Based on the new draft of the EURACHEM/CITAC Guide Traceability in Chemical Measurement, this publication describes how traceability can be achieved for chemical measurements using a linear calibration function. Traceability can be accomplished without larger expenditure, if the measurement is calibrated on the basis of appropriate reference standards and the linear regression employed is selected and validated statistically in a suitable form. The determination of nickel in aqua regia eluates of sediment samples, employed for an ICP-OES measurement, is used as a practical illustration of this approach.     

HPLC of antibiotics. 1. Streptolydigin and related compounds

Two new acyltetramic acids related to streptolydigin have been isolated from fermentations of Streptomyces lydicus. The principal members of this complex were resolved by TLC on silica gel. However, the methods of detection, permanganate spray or bioautography, were not suitable for both crude fermentation broths and purified extracts. Gas chromatography is unsuitable for the detection of either underivatized or silylated streptolydigins. High performance liquid chromatography (HPLC) particularly on triethylaminoethyl cellulose is rapid and sensitive and is the method of choice for the analysis of both crude and purified samples. Using high performance liquid chromatography, two components were detected in the complex, which are not observed using any of the other chromatographic procedures.     

Thermal degradation of polystyrene in the presence of hydrogen by catalyst in solution

For the first time, low temperature degradation (170-240 °C) of polystyrene in benzene is carried out in the presence of hydrogen using iron(III) oxide catalyst. The effect of temperature, catalyst loading and polymer loading on degradation are studied in hydrogen atmosphere. Degradation is also carried out at different initial hydrogen partial pressure. The time dependent molecular weight is calculated using viscosity average method. It is found that the degradation is enhanced considerably in the presence of hydrogen and followed random degradation chain scission. A random degradation kinetic model of Kelen [Kelen T. Polymer degradation. New York: Van Nostrand Reinhold Company; 1983.] is used to estimate the degradation rate constants. Empirical correlations are proposed to account for the effect of catalyst loading and initial hydrogen partial pressure on degradation. The true thermal degradation rate constants are calculated using these proposed correlations at given catalyst loading and initial hydrogen partial pressure with varying temperature. The frequency factor and activation energy are also determined using Arrhenius equation considering the true thermal degradation rate constants.     

Computation of suboptimal randomized strategies for steering the random motion of a point under partial observation

Consider the random motion in the plane of a pointM, whose velocityv=(v ₁,v ₂) is perturbed by an ²-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)= _u (u ₁,u ₂) _y (du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy, _y is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={ _y :y ²}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data.     

Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.     

Determination of acidic chlorinated pesticides in water: Comparison of official EPA method 515.1 and liquid-solid extraction HPLC/UV and HPLC/PBMS analyses

Summary A comparison of the official EPA method 515.1 for determination of chlorinated acidic pesticides and a modification of it is illustrated. Extraction of the analytes from water and their determination and quantitation is by gas chromatography-electron capture detection (GC-ECD), liquid chromatography-UV detection and liquid chromatography-particle beam mass spectrometry. Although HPLC-PBMS was found to be less sensitive than the GC-ECD method, it was, nevertheless, more sensitive than HPLC-UV. The modified method is simpler, quicker and allows more accurate determination of pesticides in aqueous samples.Deceased July 31, 1996