Optimisation of a flow injection system with electrochemical detection using the desirability function: Application to the determination of hydroquinone in cosmetics

A procedure is proposed in which the determination of hydroquinone using a flow injection system with electrochemical detection is described. Size and coefficient of variation of the signal are optimised by a desirability function and a central composite design. The robustness of the optimum reached in the optimisation step is evaluated by means a Plackett-Burman design. The optimised FIA system is able to determine hydroquinone with a minimum detectable net concentration of 10 μg l⁻¹ with a false positive probability of 0.05 and a false negative probability less than 0.05. In samples of bleaching cream, the proposed procedure has a recovery of 102.2% with standard deviation of 4.4% and a relative error of 6.2%.     

Application of Artificial Neural Network and Multiple Linear Regression Retention Models for Optimization of Separation in Ion Chromatography by Using Several Criteria Functions

This work focuses on problems regarding empirical retention modelling and optimization of separation in ion chromatography. Influences of eluent flow rate and concentration of eluent competing ion (OH^–) on separation of seven inorganic anions (fluoride, chloride, nitrite, sulphate, bromide, nitrate, and phosphate) were investigated. Artificial neural networks and multiple linear regression retention models in combination with several criteria functions were used and compared in global optimization process. It can be seen that general recommendations for optimization of separation in ion chromatography is application of chromatography exponential function criterion in combination with artificial neural networks retention model.     

The W algorithm and the D transformation for the numerical evaluation of three‐center nuclear attraction integrals

Three‐center nuclear attraction integrals over exponential‐type functions are required for ab initio molecular structure calculations and density functional theory (DFT). These integrals occur in many millions of terms, even for small molecules, and they require rapid and accurate numerical evaluation. The use of a basis set of B functions to represent atomic orbitals, combined with the Fourier transform method, led to the development of analytic expressions for these molecular integrals. Unfortunately, the numerical evaluation of the analytic expressions obtained turned out to be extremely difficult due to the presence of two‐dimensional integral representations, involving spherical Bessel integral functions. % The present work concerns the development of an extremely accurate and rapid algorithm for the numerical evaluation of these spherical Bessel integrals. This algorithm, which is based on the nonlinear D transformation and the W algorithm of Sidi, can be computed recursively, allowing the control of the degree of accuracy. Numerical analysis tests were performed to further improve the efficiency of our algorithm. The numerical results section demonstrates the efficiency of this new algorithm for the numerical evaluation of three‐center nuclear attraction integrals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

新型有序结构分子聚集体的构筑

本文概述了近年来我们在新型有序结构分子聚集体构筑方面取得的一些主要成绩，并展望了今后进一步的研究和发展方向。     

Thermodynamic excess properties of alkanol + amine mixtures and application of the ERAS model

New experimental data of the molar excess volume V ^E of the mixtures ethanol/n-butylamine, heptanol/n-butylamine, n-propanol/dibutylamine have been obtained using the technique of the vibrating tube densitometer. Together with the data for the molar excess enthalpy H ^E from the literature, the V ^E data have been used for testing the applicability of the socalled ERAS model which accounts for hydrogen bonding effects as well as for free volume effects in associating mixtures. The results obtained by adjusting the model parameters reveal a strong cross association between the unlike molecules in the mixture resulting from strong negative values for the hydrogen bonding energy and the hydrogen bonding volume.Communicated at the Festsymposium celebrating Dr. Henry V. Kehiaian's 60^th birthday, Clermont-Ferrand, France, 17–18 May 1990.     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.