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.

     

Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction

The uniqueness and the global Markov property for the regular Gibbs measure corresponding to the interaction $$U_\Lambda (\varphi ): = \lambda \int\limits_\Lambda {d_2 x\int {d\varrho (\alpha ):e^{\alpha \varphi } :_0 (x)} } $$ [forλ>0,d?(α) a probability measure with support in \(( - 2\sqrt {\pi ,} 2\sqrt \pi )\) ] is proved.     

Sr and stable strontium in bones of wild, herbivorous animals from Poland

Activity concentration of ⁹⁰ Sr and stable strontium concentration was analysed in 42 samples of animal (deer, roe-deer, elk and boar) bones, which mostly originated from north-eastern Poland. Strontium separation was performed by extraction chromatography. Determination of chemical yield was controlled by means of stable Sr determination using atomic spectrometry at the beginning and at the end of the separation procedure. Equilibrated ⁹⁰ Sr and ⁹⁰ Y activity was measured using a liquid scintillator spectrometer. Stable strontium range was from 55.4±1.7 ppm to 91.8±4.5 ppm, the mean was 71.84 ppm with a standard deviation (SD) of 9.31 ppm. The mean recovery of strontium was 26.7% with SD = 16.1%. The maximum activity of ⁹⁰ Sr, equal to 629±13 Bq/kg (ash) was found for a deer sample from Augustów Primeval Forest. In average, deer show the highest radiostrontium level, followed by roe-deer, elk and the lowest level were observed for boar. Differences between boar and deer or roe-deer are significant in terms of Kruskal-Wallis statistical test. Animal bones from north-eastern Poland showed about twice the mean concentration of ⁹⁰ Sr, compared to those of south-central Poland, but the difference was found not significant. Activities observed in roe-deer bones suggest the deposition of a concentration of 1.9 to 3.5 kBq/m² in the average of Chernobyl-origin ⁹⁰ Sr in 1986 in north-eastern Poland.     

Interaction of oxygen with preadsorbed hydrogen on magnesium oxide studied by temperature-Programmed desorption method

The interaction of oxygen with preadsorbed hydrogen on thermally activated magnesium oxide has been studied by temperature-programmed desorption (TPD) method. It was found that oxygen at 450 K reacts with preadsorbed hydrogen and the resulting hydroxylation suppresses the adsorptive capacity of magnesia with respect to oxygen.

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. , 450 K , .

     

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.     

High precision measurements of the hyperfine structure of seven metastable atomic states of57Fe by laser-Rf double-resonance

The hyperfine structure of the metastable atomic states (3d ⁷4s)⁵ F _2,3,4,5 and (3d ⁷ 4s)³ F _2,3,4 of⁵⁷Fe has been measured using theABMR- LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence). From these measurements the following hfs constantsA of the magnetic dipole interaction have been obtained (corrected for second order effects):A(⁵ F ₂)=55.994(7) MHzA(⁵ F ₃)=69.632(5) MHzA(⁵ F ₄)=78.435(4) MHzA(⁵ F ₅)=87.246(3) MHzA(³ F ₂)=143.328(4) MHzA(³ F ₃)=50.602(10) MHzA(³ F ₄)=13.456(5) MHz     

Magnetic equation of state for thin films

The magnetization fluctuations are considered in thin films treated as a set of monoatomic layers parallel to the film surfaces. The correlation functions have been determined and their forms are discussed. The influence of inhomogeneity of magnetization on the equation of state for a magnetic system described by Valenta's model is studied. The behaviour of the spontaneous magnetization as well as the magnetic susceptibility near the Curie point is described.This work is partially supported by the Institute of Physics of the P.A.S.     

Triplet losses in dye lasers

The expression for losses due to triplet states in dye laser considered as a six-level system is given. It is shown that triplet losses depend on pumping parameters and photon number. Depending on molecular and cavity parameters two different behaviours of dye lasers are expected. Physical conditions are discussed in which triplet losses as well as photon number undergo a jump at the threshold.