Isometers in the Cartesian product ofn unit open Hilbert balls with a hyperbolic metric

Summary In this paper we give a characterization of isometries in the Cartesian Products of n unit Hilbert balls with hyperbolic metrics and of their fixed point sets.     

Coumarin-naphthohydrazone ligand with a rare coordination mode to form Mn(II) and Co(II) 1-D coordination polymers: synthesis,characterization, and crystal structure

The hydrazone (E)-3-hydroxy-N’-(1-(2-oxo-2H-chromen-3-yl)ethylidene)-2-naphthohydrazide (H₂L) was synthesized from the reaction of 3-acetylcoumarin and 3-hydroxy-2-naphthoic hydrazide in methanol. Compounds [Mn(H₂L)(NO₃)₂(CH₃OH)]·CH₃OH (1a), [Mn(HL)(NO₃)(CH₃OH)]_n (1b), [Co(HL)(NO₃)(CH₃OH)]_n (2), and [Cu(HL)(NO₃)] (3) were obtained by reaction of an equimolar amount of H₂L with nitrate salts of Mn(II), Co(II), or Cu(II) in methanol. The reaction of ligand and Mn(NO₃)₂·4H₂O was also carried out in the presence of sodium azide which led to the 1-D coordination polymer, [Mn(HL)(N₃)(CH₃OH)]_n (4). All of the synthesized compounds were characterized by elemental analyses and spectroscopic methods. Single-crystal X-ray analysis of 1–4 indicated that H₂L is neutral (in 1a) or mononegative ligand (in 1b, 2, 3 and 4). In 1b, 2 and 4 the 1-D polymeric chain is found by a rare coordination mode of this kind of hydrazone ligand since the naphtholic oxygen is coordinated to the neighboring metal ions while the NH moiety of hydrazone remains intact, also confirmed by FT-IR spectroscopic studies. The thermal stability of 2 and 4 were also studied from 30–1000 °C.     

Control of Luminescence by Tuning of Crystal Symmetry and Local Structure in Mn4+‐Activated Narrow Band Fluoride Phosphors

Mn⁴⁺‐doped fluoride phosphors have been widely used in wide‐gamut backlighting devices because of their extremely narrow emission band. Solid solutions of Na₂(Si_xGe_1?x)F₆:Mn⁴⁺ and Na₂(Ge_yTi_1?y)F₆:Mn⁴⁺ were successfully synthesized to elucidate the behavior of the zero‐phonon line (ZPL) in different structures. The ratio between ZPL and the highest emission intensity υ₆ phonon sideband exhibits a strong relationship with luminescent decay rate. First‐principles calculations are conducted to model the variation in the structural and electronic properties of the prepared solid solutions as a function of the composition. To compensate for the limitations of the Rietveld refinement, electron paramagnetic resonance and high‐resolution steady‐state emission spectra are used to confirm the diverse local environment for Mn⁴⁺ in the structure. Finally, the spectral luminous efficacy of radiation (LER) is used to reveal the important role of ZPL in practical applications.     

Symmetric functions in the Kontsevich-Witten intersection theory of the moduli space of curves

We show that symmetric functions introduced by Di Francesco and co-workers, to prove Kontsevich's formula and Witten's conjecture in the intersection theory of the moduli space of curves are, up to sign, SchurQ-functions.On leave from Institute of Mathematics, Polish Academy of Sciences, Toru, Poland     

Weighted Banzhaf values

The family of weighted Banzhaf values for cooperativen-person TU-games is studied. First we introduce the weighted Banzhaf value for an exogenously given vector of positive weights of the players. Then we give an axiomatic characterization of the class of all possible weighted Banzhaf values.     

Synthesis and fluorescence behaviour of crown and azacrown ethers carrying the dansyl fluorophore as a pendant in acetonitrile solution

The influence of Li⁺, Na⁺, K⁺, Cs⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Pb²⁺ and Al³⁺ ions on the spectroscopic properties of the dansyl group covalently linked to crown ether or diazacrown ethers was investigated by means of absorption and emission spectrophotometry. Interaction of the alkali metal ions with all fluoroionophores studied is weak, while alkaline earth metal ions interact strongly causing about 50% quenching of dansyl fluorescence of A21C5-Dns and A₂18C6-Dns. The Cu²⁺, Pb²⁺ and Al³⁺ cations interact very strongly with dansyl chromophore regardless the crown ether type, causing a major change in absorption spectrum of the chromophore and forming non-fluorescent complexes. The Co²⁺, Ni²⁺, Zn², Mg²⁺ and Ag⁺ cations interact moderately with all fluoroionophores studied causing about 20% of fluorescence quenching of dansyl, except for a strong dansyl fluorescence quenching of 15C5-Dns by Co²⁺ ion. The quenching efficiency of didansylated fluoroionophores by the alkali metal ions and alkaline earth metal ions is weaker than monodansylated ones.     

Structure of zone-cast HBC-C12H25 films

The structure of a thin zone-cast film of the hexa-n-dodecyl-substituted hexa-peri-benzocoronene (HBC) has been investigated using grazing incidence X-ray diffraction. A model with an orthorhombic unit cell containing two molecules accounts well for the observations. The molecules are arranged in a "herringbone" structure resembling the packing observed for unsubstituted HBC. The molecular disk planes are oriented perpendicularly to the substrate, rotated by approximately 39 degrees about the film normal. The relatively long side chains of dodecyl were found to be in an ordered interdigitated state. The aliphatic side chains and the aromatic HBC-cores segregate to form regular vertical domains spanning the film thickness. For in-plane rocking scans a discrete orientation distribution is observed with peaks at regular angle intervals. We interpret this as a grain boundary effect induced by alkyl chain stacking faults.     

Elektrochemisch initiierte Pfropfung von Vinylmonomeren auf Viskosefasern

Zusammenfassung Im Vergleich zu anderen Methoden bietet die elektrochemische Initiierung bessere Möglichkeiten zur praktischen Verwendung.Sie gestattet eine direkte Einflußnahme auf den Prozeßverlauf und die Zusammensetzung der Pfropfpolymere. Unter den Bedingungen des Ausschlusses der Homopolymerisation ist die Pfropfung entsprechend den geforderten Eigenschaften der Fasern als ausreichend zu betrachten. Der Start der Pfropfreaktion erfolgt unter Bildung von Wasserstoffradikalen, so daß sich direkte Abhängigkeiten von Stromdichte und der Zeitdauer ergeben. Auch bei unterbrochenem Stromfluß schreitet der Prozeß weiter fort.Das Maximum des Pfropfgrades hat vorwiegend die Ausbildung kurzer Seitenketten zur Folge.Im Gegensatz zu den Seitenketten weist das durch Nebenreaktionen gebildete Homopolymere ein 10fach kleineres Molekulargewicht auf.Der Gesamtablauf der Reaktion zeigt radikalischen Charakter. Dafür sprechen der Einfluß der Temperatur und von Inhibitoren.Über die Bestimmung des Glasumwandlungspunktes konnte die Pfropfung als eine Reaktion auf molekularem Niveau determiniert werden.Analogieschlüsse zum Verhalten radikalisch-chemisch gestarteter Polymerisationsreaktionen erlauben, den Einfluß der Abbruchsreaktionen auf das gebildete Molekulargewicht zu erklären.

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Electrochemically initiated grafting of vinyl monomers onto viscose fibres

A study was made of the feasibility of electrochemical initiation of grafting vinyl monomers onto viscose fibres, the influence of basic parameters of the process on the number and molecular weight of grafted chains, and of the mechanism of the grafting process.It was found that an increase in current density led to an increase in the amount of grafted poly-(methylmethacrylate) up to a maximum value, accompanied by a decrease in the molecular weight of the side-chains. Still higher current densities resulted in a decrease in the degree of grafting without change of the molecular weight.The molecular weight of growing homopolymer was a tenth of that of grafted chains. Studies of the effect of inhibitors and temperature showed the grafting to be a radical process.Studies of the glass temperature enabled the course of the grafting to be defined on the molecular level.

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Mit 7 Abbildungen     

Ligation of alkoxymethylimidazoles towards cadmium(II) and zinc(II). X-ray,spectroscopic, thermal and potentiometric investigation

The stability constants and structure of the complexes of Cd^II and Zn^II with 1-ethoxymethylimidazole (ExMeIm), 1-propoxymethylimidazole (PxMeIm), 1-ethoxymethyl-2-methylimidazole (ExMe-2-MeIm) and 1-propoxymethyl-2-methylimidazole (PxMe-2-MeIm) in aqueous solution have been determined by potentiometric methods. Zn^II form both tetrahedral and octahedral species with the cited ligands according to the configurational equilibrium type: octahedron tetrahedron, but Cd^II prefers octahedral coordination of alkoxymethylimidazole complexes in aqueous solution. Retention of the six-coordination form of Cd^II has also been confirmed by the data obtained for two novel compounds which have been synthesized in the solid state. The crystal and molecular structure of [Cd(ExMeIm)₄(NO₃)₂] (1) has been determined by X-ray diffraction. The coordination geometry around the Cd^II ion can be considered as slightly distorted tetragonal bipyramidal (CdN₄O₂). Additionally, another six-coordinate Cd^II compound with ethoxymethyl-2-methylimidazole [Cd(ExMe-2-MeIm)₄(H₂O)](NO₃)₂ (2) has been characterized by spectroscopic (i.r., far i.r., Raman) ES–MS and t.g.a. methods.