A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

Neue stellungsisomere reineckesalzähnliche Verbindungen mit Toluidinen

Zusammenfassung Es wurden eine Reihe von Substitutionsreaktionen mit entwässertem K₃[Cr(NCS)₆] und aromatischen Aminen, ohne Verwendung von Lösungsmitteln, durchgeführt. Es wurde beobachtet, da die sehr schwachen Basen mit p_K-Werten 14–16, wie die isomeren Mono- und Dinitro-aniline, die Anthranil- und Sulfanilsäuren, für diese Substitutionsreaktionen ungeeignet sind. Die Alkyl-anilinderivate, wie daso-, m- undp-Toluidin (p_K=10–11) bilden dagegen leicht reineckesalzähnliche Verbindungen: Amin· H[Cr(Toluidin)₂(NCS)₄]. Die Zusammensetzung der neuen Komplexanionen wurde bei einer Reihe von doppelten Umsetzungsreaktionen mit den Chlorhydraten einiger heterocyclischen Aminen festgestellt.Für die Klärung einiger Strukturfragen wurden spektrophotometrische Untersuchungen im UV und IR durchgeführt und die thermische Stabilität bzw. der Mechanismus des Pyrolysenvorganges auf thermogravimetrischem Wege verfolgt.

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Substitution reactions of anhydrous K₃[Cr(NCS)₆] with aromatic amines without applying of solvents were studied.It was observed, that the very weak bases (pK-values 14–16, e.g. isomeric mono- and dinitro-anilines, the anthranilic and sulfanilic acids) are unsuitable for substitution reactions. The alkylaniline derivates e.g.o-, m- andp-toluidine (pK=10–11) form easily reineckesalt analogous compounds: Amin· ·H[Cr(toluidine)₂(NCS)₄]·The formula of the 3 new complex anions: [Cr(toluidine)₂ (NCS)₄]- was established by preparative methods, with a series of double decomposition reactions, using chlorohydrates of some heterocyclic amines for this purpose. From spectroscopical investigations (UV and IR) some structural problems are resolved and discussed.The thermal stability and the mechanism of pyrolysis of these salts was studied by thermogravimetric analysis.

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Mit 8 Abbildungen     

Thermal behaviour of the homopolynuclear glyoxylate complex combinations with Cu(II) and Cr(III)

Homopolynuclear complexes of Cu(II) respectively Cr(III) with the glyoxylate dianion, C₂H₂O₄ ^2-, have been studied in non-isothermal regime in air and nitrogen. The results of the non-isothermal analysis performed for the synthesised complexes, Cu(C₂H₂O₄)·0.5H₂O, respectively [Cr₂(OH)₂(C₂H₂O₄)₂(OH₂)₄]·2H₂O, correlated with the results of the IR and TG analysis of the compounds obtained by thermal treatment from the initial complexes and the results of the GLC and XR analysis have led to the establishment of the thermal decomposition mechanisms for the two studied complexes. The decomposition mechanisms confirm the stoichiometric and structural formulae proposed for the two synthesised homopolynuclear complexes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Isolated subgroups of finite abelian groups

Czechoslovak Mathematical Journal - We say that a subgroup H is isolated in a group G if for every x ∈ G we have either x ∈ H or 〈x〉 ∩ H = 1. We describe the set of...     

Existence of rank 3 vector bundles with given chern classes on homogeneous rational 3-folds

One proves that any rank 3 topological vector bundle on a homogeneous rational 3-fold has an algebraic structure. The proof uses extensions of ideals by rank 2 vector bundles. The paper also contains a construction of rank 3 vector bundles on 3-folds using extensions of ideals by rank 2 reflexive sheaves.     

Improved sample preparation method for environmental plutonium analysis by ICP-SFMS and alpha-spectrometry

A rapid and simple sample preparation method for plutonium determination in environmental samples by inductively coupled plasma sector field mass spectrometry (ICP-SFMS) and alpha-spectrometry is described. The developed procedure involves a selective CaF₂ co-precipitation for preconcentration followed by extraction chromatographic separation. The proposed method effectively eliminates the possible interferences in mass spectrometric analysis and also removes interfering radionuclides that may disturb alpha-spectrometric measurement. For ²³⁹Pu, ²⁴⁰Pu and ²⁴¹Pu limits of detection of 9.0 fg·g⁻¹ (0.021 mBq), 1.7 fg·g⁻¹ (0.014 mBq) and 3.1 fg·g⁻¹ (11.9 mBq) were achieved by ICP-SFMS, respectively, and 0.02 mBq by alpha-spectrometry. Results of certified reference materials agreed well with the recommended values.     

Janus-type isopropyl groups revealed by 1H-NMR spectra of alkylpyridines with lanthanide shift reagents (LSR)

Two Isomeric pyridines were designed and prepared : 2-isopropyl-4,5,6-trimethyl-(3) and 2-isopropyl-3,4,6-trimethyl-pyridine (7); the latter, with a buttressed isopropyl, leads to much lower induced shifts by Eu(dpm)₃ and Pr(dpm)₃ than the former, owing to the conformation in which the Janus-type iPr group how to the LSR a t-butyl-like face.     

Sur les fibrés instables de rang 2 sur ℙ3 (ℂ)

Sans résumé