Separately harmonic and subharmonic functions

Let u(x, y) be defined in B ₁×B ₂ where B ₁ ^m and B ₂ ⁿ , and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C ² for each y then u is subharmonic in B ₁×B ₂ in both variables jointly.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

Electronic structure of octacyanides of molybdenum IV and V according to the SCCC MO method

The SCCC MO method has been used to calculate the electronic structure and spectrum of Mo(CN) ₈ ^4– and Mo(CN) ₈ ^3– ions of a D _4d symmetry. All metal-ligand and ligand-ligand interactions and all overlap integrals (over products of HF atomic orbitals) have been included within the SCCC MO scheme. Basing on these calculations a new assignment of some absorption bands is proposed. The overall agreement between the calculated and observed electronic spectrum is satisfactory.

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Zusammenfassung Elektronenstruktur und Spektrum der [Mo(CN)₈]^–4- und [Mo(CN)₈]^–3-Ionen in D _4d -Symmetrie wurden mit der SCCC-MO-Methode berechnet. Alle Metall-Ligand- und Ligand-Ligand-Wechsel-wirkungen und Überlappungsintegrale wurden berücksichtigt. Die Bandenzuordnung wurde neu vorgenommen. Die Übereinstimmung der berechneten und gemessenen Spektren ist befriedigend.

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Résumé Application à Mo(CN) ₈ ^4– et Mo(CN) ₈ ^3– de la méthode SCCC MO basée sur des orbitales atomiques HF approchées, en tenant compte du recouvrement et de toutes les interactions ligand-ligand. Dans la partie I on discute le cas de la symétrie D _4d . L'accord global avec l'expérience est satisfaisant en ce qui concerne les spectres. On montre aussi que toutes les attributions antérieures basées sur la théorie du champ cristallin semblent inadéquates.

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The authors are grateful to Prof. W. Jakób, Dr. Z. Stasicka and Dr. A. Samotus for many interesting discussions, to Prof. J. Chojnacki for providing us with new X-ray results before publication and to Dr. A. J. Sadlej for a help in dealing with the computer.     

Thermal decomposition of Cr(III) dithiocarbamates

The thermal stability of chromium(III) complexes with dithiocarbamate acid derivatives was studied. The general formula of these complexes is (RCS₂)₃Cr where: The thermal stability of these complexes was found to depend on the kind ofR and the decomposition occur in several stages.The final product of the decomposition of the complexes in the 20–600 temperature range investigated is chromium sulphide, Cr₂S₃ or with incomplete combusted sulfur atoms.

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Zusammenfassung Die Thermostabilität von Chrom(III)-Komplexen mit sauren Derivaten von Dithiocarbamat wurde untersucht. Die allgemeine Formel dieser Komplexe ist (RCS₂)₃Cr. Es wurde festgestellt, da\ die Thermostabilität dieser Komplexe von der Art von R abhängt und die Zersetzung in mehreren Stufen verläuft.Das Endprodukt der Zersetzung der Komplexe im untersuchten Temperaturbereich von 20 bis 600 ist Chromsulfid, Cr₂S₃, oder solches mit überschüssigem Schwefel.

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Résumé On a étudié la stabilité thermique des complexes du chrome(III) avec les dérivés de l'acide dithiocarbamique. La formule générale de ces complexes est (RCS₂)₃Cr où: On a trouvé que la stabilité thermique de ces complexes dépendait de la nature du radical et que la décomposition se déroulait en plusieurs étapes.Dans l'intervalle de température étudié, de 20 à 600, le produit final de la décomposition des complexes est le sulfure de chrome, Cr₂S₃, éventuellement accompagné de soufre résultant d'une combustion incomplÊte.

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(III) - . — (RCS₂)₃ Cr, , R . 20–600 Cr₂S₃ .

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The autors would like to thank Doc. dr h. J. F. Biernat for valuable discussions.     

Sensitive spectrophotometric determination of tin with Pyrogallol Red and cetyldimethylbenzylammonium ions

Summary Tin(IV), in the presence of cetyldimethylbenzylammonium chloride (CDBA), forms with Pyrogallol Red (PR) a complex SnPR-CDBA. This complex floates at the interface between hexane and aqueous medium. It dissolves in acetone and can be advantageously used for the determination of tin. The molar absorptivity is 6.5×10⁴ l·mole^–1·cm^–1 at 480 nm. The method is selective when citric acid is used as masking agent. Phosphate, fluoride, EDTA, nitrite and sulphide interfere.

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Zusammenfassung Zinn(IV) bildet mit Pyrogallolrot (PR) in Gegenwart von Cetyldimethylbenzylammoniumchlorid (CDBA) einen Komplex. Dieser wird flotiert, in Aceton gelöst und zur Bestimmung von Zinn verwendet. Der molare Absorptionskoeffizient bei =480 nm beträgt =6,5·10⁴ l·mol^–1 cm^–1. Die Methode ist selektiv, wenn Zitrate zur Maskierung verwendet werden. Es stören Phosphat, Fluorid, ÄDTA, Nitrit und Sulfid.

     

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.     

Controlled Rate Thermal Analysis of Hydrated Borates

Quasi-isothermal-isobaric analysis was applied as a main method for investigation of thermal decomposition of borates. The structural mechanism of the dehydration and dehydroxylation of selected borates is considered. It has been found that they consist of two independent stages: formation of gaseous water molecules localized into the structural framework and their release. The internal pressure of gaseous water molecules is the factor influencing the course of these processes. The strengths of the chemical bonds of the components and the freedom of their displacement also determine thermal stability of hydrated borates. This revised version was published online in July 2006 with corrections to the Cover Date.     

Studies of surface properties of Na- and La-montmorillonites

This paper presents possible applications of thermal analysis, sorptometry and porosimetry to study physico-chemical properties of Na- and La-montmorillonite samples, especially for determination of total surface heterogeneity. The quasi-isothermal thermogravimetric (Q-TG) mass loss and its first derivative (Q-DTG) curves with respect to temperature and time obtained during programmed liquid thermodesorption under quasi-isothermal conditions have been used to study adsorbed layers and heterogeneous properties of the Na- and La-montmorillonites. Calculations of the desorption energy distribution functions by analytical procedure using mass loss Q-TG and differential mass loss Q-DTG curves of thermodesorption under quasi-isothermal conditions of polar and non-polar liquid vapours preadsorbed on a material surface are presented. Parameters relating to porosity of samples were determined by sorptometry, mercury porosimetry and atomic force microscopy (AFM). From nitrogen sorption isotherms from sorptometry and porosimetry methods, the fractal dimensions of montmorillonites have been calculated. Moreover, a new approach is proposed to calculate fractal dimensions of materials obtained from Q-TG curve; this is compared with values obtained by the above methods. The total heterogeneous properties (energy distribution function and pore-size distribution functions) of samples studied were estimated. The radius and pore volume of the tested samples calculated on the basis of thermogravimetry, sorptometry and porosimetry techniques were compared and good correlations obtained.     

Exchange interactions in copper(II) complexes with tridentate Schiff bases: EPR and magnetic studies

The influence of the nature of ligands upon the magnetic and EPR properties was investigated for the series of polynuclear Cu(II) complexes with tridentate Schiff bases. A similar tendency of changes in the |J| and D parameters was found for binuclear Cu(II) complexes with ligands derived from condensation of 3-amino-1-propanol with 2-hydroxyaldehydes and acetylacetone as well as for Cu(II) complexes with condensation products of o-aminophenol and β-diketones. The Cu(II) complex with Schiff base of 1-amino-2-propanol and acetylacetone exhibits ferromagnetic behaviour suggesting tetrameric structure.     

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.