Numerical comparison of several variable-metric algorithms

The paper compares the numerical performances of the LDL decomposition of the BFGS variable-metric algorithm, the Dennis-Mei dogleg algorithm on the BFGS update, and Davidon's projections with the BFGS update with the straight BFGS update on a number of standard test problems. Numerical results indicate that the standard BFGS algorithm is superior to all of the more complex strategies.This research was supported by the National Science Foundation under Research Grant No. MCS77-07327.     

A method for calibration and validation subset partitioning

This paper proposes a new method to divide a pool of samples into calibration and validation subsets for multivariate modelling. The proposed method is of value for analytical applications involving complex matrices, in which the composition variability of real samples cannot be easily reproduced by optimized experimental designs. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. The proposed technique is illustrated in a case study involving the prediction of three quality parameters (specific mass and distillation temperatures at which 10 and 90% of the sample has evaporated) of diesel by NIR spectrometry and PLS modelling. For comparison, PLS models are also constructed by full cross-validation, as well as by using the Kennard-Stone and random sampling methods for calibration and validation subset partitioning. The obtained models are compared in terms of prediction performance by employing an independent set of samples not used for calibration or validation. The results of F-tests at 95% confidence level reveal that the proposed technique may be an advantageous alternative to the other three strategies.     

Quantitative determination of Malathion in pesticide by modified attenuated total reflectance-Fourier transform infrared spectrometry applying genetic algorithm wavelength selection method

A simple and environment friendly method was developed for determination of Malathion content of analytical and commercial insecticide samples with no special preparation. Attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectra were characterized and 1000-2000 cm⁻¹ region was selected for quantitative analysis utilizing partial least square (PLS) and two wavelength selection methods: (a) principal component regression (PCR) and (b) genetic algorithm (GA). Relative error of prediction (REP) was calculated in PLS, PCR-PLS and GA-PLS methods and was 3.536, 1.656 and 0.188, respectively. Proposed method is successfully applicable for quantification of Malathion in commercial grade samples and reliable results in comparison with known methods, confirms this idea.     

SPE – Microwave‐assisted extraction coupled system for the extraction of pesticides from water samples

SPE is a commonly applied technique for preconcentration of pesticides from water samples. Microwave‐assisted extraction (MAE) technique is the extraction applied for preconcentration of different compounds from solid samples. SPE coupled with MAE is capable of preconcentrating these compounds from water samples too. This investigation was aimed at improving the efficiency of atrazine, alachlor, and α‐cypermethrin pesticide extraction from the spiked water samples applying SPE followed by MAE. In this way, MAE served for elution of pesticides from C₁₈‐extraction disks with solvent heated by microwave energy. Various elution conditions were tested for their effects on the extraction efficiency of the SPE–MAE combined technique. Several parameters, such as elution solvent volume (mL), elution temperature (°C), and duration of elution (min), affect the extraction efficiency of the SPE–MAE coupled system and need to be optimized for the selected pesticides. In order to develop a mathematical model, 15 experiments were performed in the central composite design. The equation was then used to predict recoveries of the pesticides under specific experimental conditions. Optimization of microwave extraction was accomplished using the genetic algorithm approach. Best results were achieved using 20 mL of ethanol at 60°C. Optimal hold time was 5 min and 24 s. The SPE–MAE combination was also compared with the conventional SPE extraction technique with elution of a nonpolar or a moderately polar compound with nonpolar solvents.     

The Enhancement of Efficiency of High-order Harmonic in Intense Laser Field Based on Asymptotic Boundary Conditions and Symplectic Algorithm

Asymptotic boundary condition (ABC) of laser-atom interaction presented recently is applied to transform the initial value problem of the time-dependent Schrödinger equation (TDSE) in infinite space into the initial and boundary value problem in the finite space, and then the TDSE is discretized into linear canonical equations by substituting the symmetry difference quotient for the 2-order partial derivative. The canonical equation is solved by symplectic algorithm. The ground state and the equal weight coherent superposition of the ground state and the first excited state have been taken as the initial conditions, respectively, while we calculate the population of bound states, the evolution of average distance and the high-order harmonic generation (HHG). The conversion efficiency of HHG can be enhanced by initial coherent superposition state and moderate laser intensities     

Density functional calculations of large systems containing heavy elements by means of the regionalization algorithm

The compounds containing transition metals orother heavy elements play important roles in chemistry.They possess diverse properties which have been util-ized in numerous functional materials. Some of theseproperties are also involved in biological processes.However, it is very difficult to study these compoundsdeeply by means of quantum chemical methods, be-cause in these systems usually there are a large amountof electrons, the distribution of the frontier orbitals isdense, the correlation be…     

Computing the Kekulé structure count for alternant hydrocarbons

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. A simple method is presented for determining the Kekulé structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekulé structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 × N/2 matrix need be evaluated. The Kekulé structure count correlates with topological indices. The inclusion of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekulé structure count. This heat increments 349 kJ/mol each time the Kekulé structure count increases by one order of magnitude. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

On the automatic restricted-step rational-function-optimization method

The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states. Received: 18 June 1998 / Accepted: 17 September 1998 / Published online: 23 November 1998     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.