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.     

1,4-dioxane as a solvent in spectroscopy and photochemistry

Commercially available 1,4-dioxane, even of spectroscopic grade, contains various impurities that arise mostly from reaction of the solvent with oxygen. Aspects relevant to the spectroscopy and photochemistry of the dioxane/oxygen system are discussed. Methods of purification and storage of the solvent are presented.     

Generation and reactions of substituted phenide anions in an electrospray triple quadrupole mass spectrometer

Substituted benzoic acid anions undergo decarboxylation in the medium-pressure region of an electrospray ion source yielding in most cases the correspondingly substituted phenide anions in high yield. The location of the anionic center is specified by the position of the carboxylic group. The only exceptions are compounds with substituents containing acidic hydrogen atoms, like OH and NH(2) groups. For such compounds, either an intra- or an intermolecular (mediated by the molecules of methanol or water) proton transfer from the more acidic position to the benzene ring is observed. The generated anions can be selected using the first quadrupole for studying their ion-molecule chemistry in the second quadrupole of a triple quadrupole mass spectrometer. Their reactions with CO(2), O(2), CH(3)COCH(3) and CCl(4) may serve as typical examples. The general applicability of this method for the generation of phenide anions has been confirmed on three different mass spectrometers. Experiments performed using carboxylic acids other then benzoic acid and its derivatives show that this method is not limited to phenide anions and can be used for the generation of a much wider range of carbanions in the gas phase.     

Properties and analytical application of chlorpromazine picrate

In neutral medium, picric acid (PA) reacts with chlorpromazine (CPM) hydrochloride with the formation of an orange compound, sparingly soluble in water, of molar ratio PA:CPM = 1:1. The compound is thermally stable up to a temperature of about 200 degrees C. The m.p. (178 degrees C) can be used for identification of picric acid as well as of chlorpromazine hydrochloride. Chlorpromazine picrate is extracted quantitatively with benzene, and the extract can be used for colorimetric determination of chlorpromazine hydrochloride. Beer's law is obeyed in the CPM concentration range 10-60 mug/ml.     

High-Temperature Adsorption of n-Octane, Benzene, and Chloroform onto Silica Gel Surface

A model for the steady laminar flow of an incompressible fluid through a deformable gel-coated channel with slowly varying tapered shape is presented. Previous work has shown that the flow rate through such a channel is less than that which would be expected from the Hagen-Poiseuille equation (1973, J. Lahav, N. Eliezer, and A. Silberberg, Biorheology 10, 595; 1979, P. Krindel and A. Silberberg, J. Colloid Interface Sci. 71, 39). Krindel and Silberberg also observed the onset of turbulent flow at lower rates than would normally be expected; they attributed these phenomena to a turbulent boundary layer near the channel walls. Our analysis shows that the rate reduction is in fact due to kinetic energy effects related to the converging flowlines. A model to describe this rate reduction is presented and is shown to agree well with experimental results, successfully predicting the observed flow rate reduction over Reynolds numbers ranging from 1 to 1000. Copyright 2000 Academic Press.     

Isotope exchange between U/III/ and U/IV/ in the HCl-TBP extraction system

The measurement of the isotope-exchange reaction between U/IV/ in the organic phase and U/III/ in the aqueous phase in the extraction systems: 7-8M HCl—5–40% TBP /aromatic diluent or CCL₄/ were made. The high rate of exchange with the rate constant >10²M^–1min^–1 was observed.     

Application of Discrete Wavelet Transform in the Analysis of Nonlinear Chemical System

Oscillations of species concentration are phenomena accompanying several types of electrochemical and purely chemical processes. Importance of analyzing of such processes results from both scientific and practical reasons. In the paper the authors deal with investigation of time dependent spectra of various stages of Belousov-Zhabotinsky type chemical oscillations. As the analytical tool the discrete wavelet transform is proposed.     

Note on vertex degrees of planar graphs

In this note the second moment of the vertex degree sequence of planar graphs is considered. We prove that

• 1 If G is an outerplanar graph of order n ? 3 then

• 2 If G is a planar graph of order n ? 4 then

where d₁,…,d_n is the vertex degree sequence of G. We exhibit all graphs for which these upper bounds are attained.     

Application of the ellipsoid method in an interactive procedure for multicriteria linear programming

The research reported in this paper is concerned with an application of the ellipsoid algorithm in the interactive multicriteria linear programming step method (STEM) byBenayoun et al. [1971]. Due to this application we eliminate some drawbacks of the original version of STEM and, moreover, we avoid extra computations connected with sensitivity analysis in every iteration. Specifically, we use the ellipsoid algorithm to minimize the Euclidean norm in the criterion space instead of the Chebyshev norm, which ensures that every solution submitted to the decision maker is efficient. As follows from a computational experiment, in comparison with the application of the simplex method, the proposed modification of STEM shows a smaller increase of the computational effort when the number of criteria increases. However, the absolute computation time becomes worse for problems of larger size.

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Zusammenfassung In dieser Arbeit wird über eine Anwendungsmöglichkeit der Khachiyan-Shor-Algorithmus (Ellipsoid-Algorithmus) im Rahmen des STEM-Verfahrens zur interaktiven Lösung linearer Vektoroptimierungsmodelle berichtet. Auf diese Weise können einige spezifische Nachteile des STEM-Verfahrens in seiner Originalversion vermieden werden. Durch die Verwendung der Euklidischen Norm anstelle der beim STEM-Verfahren üblichen Tschebyscheff-Norm wird garantiert, daß dem Entscheidungsträger nur effiziente Lösungen vorgeschlagen werden. Die numerischen Erfahrungen zeigen, daß der Lösungsaufwand der hier vorgeschlagenen Modifikation des STEM-Verfahrens mit steigender Anzahl von Zielfunktionen weniger stark zunimmt als bei der üblichen Version. Dies gilt jedoch nicht hinsichtlich der allgemeinen Problemgröße.

     

13C Chemical shifts of some azaindolizines versus electron charge distribution

Azaindolizines, which contain all possible combinations of nitrogen atoms within the five-membered ring moiety, are used as models for the investigation of a relationship between electron charge distribution and ¹³C shifts. A linear correlation is observed between the shifts and total rather than π-charge densities as calculated by the INDO-MO method. The average excitation energy (AEE) approximation in the theory of nuclear screening is shown to hold separately for the CH moieties and the carbon atoms at the ring junction in indolizines. An empirical correlation with charge densities is obtained from the AEE method, as a result of the compensation of effects within the local paramagnetic term and the prevailing contribution to the latter of the effective nuclear charge.¹³C shifts afford a reasonable measure of the total net charges at the carbon atoms of indolizines. The INDO calculations indicate that the π-charges follow the pattern suggested by simple resonance structures but the overall charge density depends heavily on σ-core polarization effects.