Approximations of relations by continuous functions

Let X be a Tychonoff space, C(X) be the space of all continuous real-valued functions defined on X and CL(X×R) be the hyperspace of all nonempty closed subsets of X×R. We prove the following result. Let X be a countably paracompact normal space. The following are equivalent: (a) dimX=0; (b) the closure of C(X) in CL(X×R) with the Vietoris topology consists of all F∈CL(X×R) such that F(x)≠∅ for every x∈X and F maps isolated points into singletons; (c) each usco map which maps isolated points into singletons can be approximated by continuous functions in CL(X×R) with the locally finite topology. From the mentioned result we can also obtain the answer to Problem 5.5 in [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173-2182] and to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies, Quad. Mat. 3 (1998) 243-258] in the realm of normal, countably paracompact, strongly zero-dimensional spaces. Generalizations of some results from [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173-2182] are also given.     

Sorption of radionuclides on inorganic sorbents

Inorganic sorbents are often used in separation of metals and radionuclides in radioanalytical application and they were also used in technological scale for separation of radionuclides in cleanup of Three Mile Island NPP. Inorganic sorbents become popular in the last years because no problem with organic contamination, there are stable against radiation, sorption efficiency can be tailor made for selective separation of chosen metal. Contrary to the organic sorbents they have usually lower capacity and chemical stability is limited to narrower pH. Nevertheless of some problems, many good properties of inorganic sorbents make them very attractive for sorption study.     

The relationship between the structures of Cu(II) complexes and their chemical transformations: VII

The thermal decompositions of Cu(en)₂(NCS)X. where X^–=Cl^–, Br^–, NO ₃ ^– , BF ₄ ^– and ClO ₄ ^– , have been studied in comparison with the courses of Cu(en)₂(SCN)₂ and Cu(en)₂X₂ decomposition. It is shown that the presence of the thiocyanate group in the complexes Cu(en)₂(NCS)X is the most important factor in the decomposition course, in agreement with the fact that the anions X^– are not coordinated. or are only semicoordinated. Significant differences were found in the courses of thermal decomposition of two forms of Cu(en)₂(NCS)(BF₄) differing in the structure of their coordination polyhedra.

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Zusammenfassung Die thermische Zersetzung von Cu(en)₂(NCS)X (X=Cl Br, NO₃, BF₄ und ClO₄) wurde untersucht und mit der von Cu(en₂(SCN)₂ und Cu(en)₂X₂ verglichem. Der den Verlauf der Zersetzung entscheidend bestimmende Faktor isi die Anw esenheit der Thiocyanat-Gruppe in den Cu(en)₂(NCS)X-Komplexen, was in Übereinstimmung damit steht,. daß die Anionen X nicht oder nur teilweise koordiniert sind. Es wurden signifikante Unterschiedeim Verlauf der thermischen Zersetzung von zwei sich in der Struktur ihrer Kordinationspolyeder unter-, heidenden Formen von Cu(en)₂(NCS)(BF₄) gefunden.

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Cu(en)₂(NCS)X (X^–=Cl^–, Br^–, NO ₄ ^– , NO ₃ ^– , BF₄ ClO₄, Cu(en)₂(SCN)₂ Cu(en)₂(X)₂. , Cu(en)₂(NCS)X X Cu(en) (NCS)BF₄ i .

     

Photochemistry of condensed isoxazolines

Summary The condensed bridged isoxazolines4 are rearranged on irradiation with a low-pressure mercury lamp exclusively into condensed derivatives of tetrahydropyridine5. The selectivity of the rearrangement is due to a stabilization of the biradical8 by the overlap of the radical-electrons with -electrons of the C=C double bond and the heterocyclic ring. Quantum yields of the photorearrangement, established from the consumption of the starting materials4, were determined.

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Photochemie kondensierter Isoxazoline

Zusammenfassung Die kondensierten überbrückten Isoxazoline4 werden durch Bestrahlen mit einer Niederdruckquecksilberlampe ausschließlich zu kondensierten Tetrahydropyridinderivaten (5) umgelagert. Die Selektivität der Umlagerung beruht auf der Stabilisierung des Diradikals8 durch Überlappung der ungepaarten Elektronen mit -Elektronen der C=C-Doppelbindung und des Heterocyclus. Aus dem Verbrauch an Ausgangsmaterial (4) wurden Quantenausbeuten der Photoumlagerung bestimmt.

     

Preconcentration of platinum group metals on modified silicagel and their determination by inductively coupled plasma atomic emission spectrometry and inductively coupled plasma mass spectrometry in airborne particulates

Modified silicagel (C18) was studied for separation and preconcentration of platinum group metals (Ru, Rh, Pd, Os, Ir and Pt) as ion associates of their chlorocomplexes with cation of onium salt N(1-carbaethoxypentadecyl)-trimethyl ammonium bromide. Sample containing HCl and the onium salt was pumped through the column. After elution with ethanol the eluate was evaporated in the presence of HCl. Resulting aqueous solutions were analysed with inductively coupled plasma atomic emission spectrometry (ICP-AES) and inductively coupled plasma mass spectrometry (ICP-MS). Recovery values of 1-20 mug Pt and Pd from 50 ml of synthetic pure solution were 100+/-3 and 100+/-1%, respectively, however, they diminished with increasing sample volume and in the presence of the real sample matrix or nitrate ions. Samples of engine soot (NIES No. 8), decomposed by low pressure oxygen high-frequency plasma, and airborne particulates from dust filters of meteorological stations, leached with HNO(3) and H(2)O(2), were analysed. A reasonable agreement was found between ICP-MS and ICP-AES results for airborne dust samples and the values comparable with those in literature were determined in NIES No. 8.     

Diels-Alder reaction of fulvenes with N-(3,5-dichlorophenyl)-maleimide

Summary N-(3,5-Dichlorophenyl)-maleimide reacts smoothly with a variety of substituted fulvenes (1) to give onlyendo adducts (3) independent of the nature of fulvene substituent,Lewis acid catalyst, and reaction solvent and temperature. The structure of theDiels-Alder adduct3f was determined by X-ray crystallography. Semi-empirical quantum methods (AM1) were used to rationalize theendo stereoselectivity.Dedicated to Professor Fritz Sauter on the occasion of his 65^th birthday     

Effect of degradation of montmorillonite by vibration grinding on the dTA curves in the range 20–1500°C

The effect of vibration grinding on the DTA curves of montmorillonite isolated from the most important locality of bentonite in the Slovak Republic (Jel?ovy potok, Middle Slovakia) was studied in the temperature range 20–1500°C. Interpretation is offered for 6 endothermic and 3 exothermic peaks. vibration grinding modified the course of dehydration of the mineral, suppresses the “dehydroxylation’ peak at 700°C, enables the crystallization of high-temperature quartz, cristobalite and cordierite at lower temperatures in comparison with unground natural montmorillonite. Vibration griding slows down the crystallization of mullite which—unlike quartz, cristobalite and cordierite—does not belong to high-temperature phases of Cheto-montmorillonite. The order in which these high-temperature phases occur is not influenced by vibration grinding.     

Normality and paracompactness of the Fell topology

Let be a Hausdorff topological space and the hyperspace of all closed nonempty subsets of . We show that the Fell topology on is normal if and only if the space is Lindelöf and locally compact. For the Fell topology normality, paracompactness and Lindelöfness are equivalent.

     

Calcination of SiO2-aerogel in Oxidizing Atmosphere

Differences in mass loss occurring in the course of dynamic and isothermal heating of SiO₂-aerogel and changes of specific surface and hydrophylicity during calcination were studied by thermal analysis. SiO₂-aerogel was prepared from tetramethoxysilane (TMOS) hydrolyzed by ammonia solution at 0°C with molar ratio TMOS: H₂O:NH₄OH 4:1:0.01. Differences are caused mainly by oxidation of organic matter and by diffusion of products of the oxidation. Heat transfer has none or little effect on the differences. Samples calcined at temperatures about 300°C reach maximum hydrophilicity though they still contain small amounts of residual organic matter. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of Copper from the Kuprikol 50 Fungicide on Colorado Potato Beetle Adults Studied by Radionuclide X-Ray Fluorescence Analysis

The influence of copper on adults of the Colorado potato beetle (Leptinotarsa decemlineata Say) was studied. The adults were treated by the contact fungicide Kuprikol 50, which is used to control down powder mildew (Phytophtora infestans de Bary). Copper content was determined by radio-nuclide X-ray fluorescence analysis using a ²³⁸Pu exciting source. The obtained results contribute to the control measures against the Colorado potato beetle and to the question of the resistance of Colorado potato beetle towards pyrethroide insecticides.