A comparative molecular field analysis (CoMFA) study using semiempirical, density functional, ab initio methods and pharmacophore derivation using DISCOtech on sigma 1 ligands

The Comparative Molecular Field Analysis (CoMFA) was developed to investigate a three-dimensional quantitative structure activity relationship (3D-QSAR) model of ligands for the sigma 1 receptor. The starting geometry of sigma-1 receptor ligands was obtained from the Tripos force field minimizations and conformations were decided from DISCOtech using the SYBYL 6.8. program. The structures of 48 molecules were fully optimized at the ab initio HF/3-21G* and semiempirical AM1 calculations using GAUSSIAN 98. The electrostatic charges were calculated using several methods such as semiempirical AM1, density functional B3LYP/3-21G*, and ab initio HF/3-21G*, MP2/3-21G* calculations within GAUSSIAN 98. Using the optimized geometries, the CoMFA results derived from the HF/3-21G method were better than those from AM1. The best CoMFA was obtained from HF/3-21G* optimized geometry and charges (R2 = 0.977). Using the optimized geometries, the CoMFA results derived from the HF/3-21G methods were better than those from AM1 calculations. The training set of 43 molecules gave higher R2 (0.989-0.977) from HF/3-21G* optimized geometries than R2 (0.966-0.911) values from AM1 optimized geometries. The test set of five molecules also suggested that HF/3-21G* optimized geometries produced good CoMFA models to predict bioactivity of sigma 1 receptor ligands but AM1 optimized geometries failed to predict reasonable bioactivity of sigma 1 receptor ligands using different calculations for atomic charges.     

Entrapment and release of sodium polystyrene sulfonate (SPS) from calcium alginate gel beads

The release of sodium polystyrene sulfonate (SPS) from calcium alginate hydrogel beads has been studied. It has been shown that the structure of the cross-linked calcium alginate network is of primary importance in the retention and/or release of the SPS. This has been evidenced by studying the influence of Ca²⁺ concentration, molar masses (M_n) and the ratio of mannuronic acid/guluronic acid components. A minimum in the SPS release is observed in relation with the organization of the network structure. Conditions inducing the organization of a strong gel (e.g. high Ca²⁺ concentration for example) are not always related to a low release. A good control of release is found when a compromise between a well-structured hydrogel and sterical consideration of SPS is reached.     

Electrochemical Determination of Ascorbic Acid at γ-MnO<Subscript>2</Subscript> Modified Carbon Black Microelectrodes

A carbon black microelectrode modified by -MnO₂ has been prepared. The electrocatalytical oxidation of ascorbic acid (AA) at this microelectrode was investigated. The 2nd-order linear scan voltammograms of AA are recorded from –0.5 to 0.5V (vs. SCE). The relationship between the oxidation peak current of AA and its concentration in the range of 1.0×10^–64.0×10^–3molL^–1 is linear. The detection limit (3) was found to be 6.0×10^–7molL^–1. Also, the determination of AA in samples is evaluated, and the results are satisfactory.     

Vibrational studies in aqueous solutions: Part II. The acid oxalate ion and oxalic acid

Assignments for oxalic acid in solution are re-examined. A detailed assignment of the IR and Raman spectra of the acid oxalate ion is presented for the first time. Raman spectroscopy is used to study the first ionization of oxalic acid.     

Numerical application of Euler's series transformation and its generalizations

Summary A nonlinear generalizationÊ _z of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE _z and a twoparametric methodE . It is shown how to applyE orE _, to compute the valuef(z_o) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE andE _, are superior toÊ _z . A compact recursive algorithm is given for computingE andE _,.     

Die mehrstellenformeln für den Laplaceoperator

Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called Mehrstellenformeln or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order.

     

Numerische Ermittlung quasikonformer Abbildungen mit finiten Elementen

Summary In this note we consider so called p-analytic mappings of simply or doubly connected domains on rectangles or circular rings. Real and imaginary parts of the mappings can be described by minimal-principles. By minimizing the corresponding functionals in a class of linear or bilinear finite elements we obtain an approximation of the mapping and also upper and lower bounds for the p-module of a domain with polygonal boundary. Error bounds are given for smooth and for piecewise constant functionsp. We present numerical experiments.

     

Produktintegration mit nicht-äquidistanten Stützstellen

Summary For the numerical evaluation of , 0<<1 andx smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.

     

A generalization of regula falsi

Summary The method of nondiscrete mathematical induction is applied to a multistep variant of the secant method. Optimal conditions for convergence as well as error estimates, sharp in every step, are obtained.     

Concerning the solution set ofAx=b whereP≦A≦Q andp≦b≦q

Summary LetPQ ben×n real matrices so that ifPAQ for some matrixA, thenA is nonsingular. Letp andq ben-dimensional real column vectors. This paper determines the set of all solutionsx to the equationAx=b for allA andb so thatPAQ andpbq.