Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.     

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     

Magnetic resonance study of (GdxY1−x)Co2 compounds

The results of magnetic resonance studies on ferrimagnetic (Gd_xY_1?x)Co₂ compounds, both below and above the Curie points, are presented. The ferrimagnetic resonance measurements show that the effective g values can be described by using the Wangsness relation. The spectroscopic splitting factors of cobalt atoms are not composition dependent. In the paramagnetic range the thermal variation of the linewidth is not linear and the g values are a function of temperature. This behavior is analyzed in correlation with the magnetic data.     

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     

The interaction between TEOS and some polyols

Hybrid organic-inorganic materials, silica – polyols (ethylene-glycol – EG; 1,2 propane diol – 1,2PG; 1,3 propane diol – 1,3PG and glycerol – GL), were prepared by a sol-gel process starting from tetraethylorthosilicate (TEOS) and polyols, in acid catalysis. The resulting materials were studied by thermal analysis (in air and nitrogen), FTIR and solid state ²⁹Si-NMR spectroscopy. These techniques evidenced the presence of polyols in the silica matrix both hydrogen bounded and chemically bounded in the silica network. The thermal analysis proves to be the most appropriate technique to evidence the organic chains linked in the matrix network and to follow the thermal evolution of the gels to the SiO₂ matrix.     

A kinetic method for <Emphasis Type="Italic">para</Emphasis>-nitrophenol determination based on its inhibitory effect on the catalatic reaction of catalase

The inhibitory effect of para-nitrophenol on the catalytic reaction of catalase was investigated. Michaelis-Menten kinetic parameters were determined from Lineweaver-Burk plots obtained in the absence or in the presence of the inhibitor. The inhibitor pattern, revealed by the Lineweaver-Burk plots, suggested a fully mixed inhibition mechanism. Spectrophotometric monitoring of the indicator reaction: in conjunction with initial rate measurements was employed for the kinetic determination of the inhibitor. Calibration plots of initial rate vs. para-nitrophenol concentration were linear in the concentration range 0.9·10⁻⁵–2.5·10⁻⁵ mol/L and the detection limit was 3·10⁻⁶ mol/L (417 μg/L) para-nitrophenol. Interferences from other phenolic compounds like orto-cresole, meta-and orto-nitrophenol were observed.     

Composition and thermal stability of SiO2-based hybrid materials TEOS-MTEOS system

Hybrid materials with different amounts of organics permanently bound on the inorganic network obtained in the TEOS-MTEOS (tetraethoxysilan-methyltriethoxysilan) system are used for obtaining coatings with different optical and mechanical properties. To study the thermal stability of the mentioned materials, compositions with different molar ratios of the precursors were prepared. The influence of the solvent and water amounts on the gelation process was also investigated. The gels obtained were characterised by IR spectrometry and their decomposition temperatures were determined by DTA/TG. Thermal stability of the gels is rather influenced by their composition than the conditions of the gelation process. This revised version was published online in July 2006 with corrections to the Cover Date.