Local rotundity structure of generalized Orlicz–Lorentz sequence spaces

We give some criteria for extreme points and strong U-points in generalized Orlicz–Lorentz sequence spaces, which were introduced in [P. Foralewski, H. Hudzik, L. Szymaszkiewicz, On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces, Math. Nachr. (in press)] (cf. [G.G. Lorentz, An inequality for rearrangements, Amer. Math. Monthly 60 (1953) 176–179; M. Nawrocki, The Mackey topology of some F-spaces, Ph.D. Dissertation, Adam Mickiewicz University, Poznań, 1984 (in Polish)]). Some examples show that in these spaces the notion of the strong U-point is essentially stronger than the notion of the extreme point. This paper is related to the results from [A. Kamińska, Extreme points in Orlicz–Lorentz spaces, Arch. Math. 55 (1990) 173–180] (see Remark 1).     

On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces

Generalized Orlicz–Lorentz sequence spaces λ_φ generated by Musielak‐Orlicz functions φ satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition δ^λ ₂ for φ is defined in such a way that it guarantees many positive topological and geometric properties of λ_φ. The problems of the Fatou property, the order continuity and the Kadec–Klee property with respect to the uniform convergence of the space λ_φ are considered. Moreover, some embeddings between λ_φ and their two subspaces are established and strict monotonicity as well as lower and upper local uniform monotonicities are characterized. Finally, necessary and sufficient conditions for rotundity of λ_φ, their subspaces of order continuous elements and finite dimensional subspaces are presented. This paper generalizes the results from [19], [4] and [17]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

“Push-pull” 2-ferrocenyl-4-hydroxythiazoles: A novel method of the construction of the thiazole ring

The title compounds were obtained by cyclization of ferrocenyl thioimidates in the presence of sodium ethoxide. They were transformed into the corresponding 4-acetoxy-derivatives in reaction with acetic anhydride/pyridine. The structure of 4-acetoxy-5-(ethoxycarbonyl)-2-ferrocenylthiazole was determined by X-ray diffraction. The EFISH measurements revealed significant second-order nonlinear properties of 4-acetoxy-2-ferrocenyl-5-(4-nitrophenyl)ferrocenylthiazole (μβ = 250 × 10⁻⁴⁸ esu at 1907 nm).     

Analytical assessment of some characteristic ratios for <Emphasis Type="Italic">s</Emphasis>-wave superconductors

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ? T_c are discussed using the method of successive approximations. The equation for the ratio R₁, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R₂, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-T_c superconductors. The prospect of application of the presented model in studies of high-T_c superconductors and other superconducting systems of the new generation is also discussed.     

Elastic, quasielastic, and inelastic neutron-scattering studies on the charge-transfer hexamethylbenzene-tetracyanoquinodimethane complex

The 1:1 hexamethylbenzene (HMB)-tetracyanoquinodimethane (TCNQ) complex shows a first-order phase transition at 230/218 K (heating/cooling) with no change of the space group. The neutron-diffraction studies reveal that this transition is related to a freezing of the rotation of methyl groups. The results for 100 K enabled precise determination of configuration of HMB.TCNQ complexes. The planes of HMB and TCNQ molecules from small angle (6 degrees) so that the dicyanomethylene group approaches the HMB molecule to a distance of 3.34 angstroms. The conformation of methyl groups was exactly determined. The quasielastic neutron-scattering spectra can be interpreted in terms of 120 degrees jumps with different activation barrier in low- and high-temperature phases, equal to 3.7 and 1.8 kJ/mol, respectively. These values are lower than that for neat HMB (6 kJ/mol). The conclusion can be drawn that the methyl groups can reorient more freely in the complex. This conclusion is in agreement with the results of inelastic neutron-scattering studies of low-frequency modes assigned to torsional vibrations of methyl groups. These frequencies are lower than those for neat HMB. The analyzed increase of frequencies of these modes as compared with free molecules can be interpreted as due to formation of unconventional C-H...Y hydrogen bonds which are more pronounced in crystals of neat HMB than in those of HMB.TCNQ. The low-frequency librational modes can be treated as a sensitive measure of unconventional hydrogen bonds formed by the CH3 groups.     

Modification of MCM-48-, SBA-15-, MCF-, and MSU-type mesoporous silicas with transition metal oxides using the molecular designed dispersion method

Four various mesoporous silicas (MCM-48, SBA-15, MCF, and MSU) were modified by the molecular designed dispersion method using Fe(acac)3, Cr(acac)3, and Cu(acac)2 complexes. The deposition was performed at the same concentration of the metal acetylacetonate (acac) complex in a toluene solution. All as-synthesized samples were investigated by diffuse reflectance infrared Fourier transform spectroscopy, Fourier transform infrared photoacoustic spectroscopy, and thermogravimetric analysis. The calcined materials were studied with respect to their textural properties (Brunauer-Emmett-Teller adsorption isotherm) and chemical composition (electron microprobe analysis). It allowed elucidation of the mechanism of interaction between the acac complex and the silanol groups. For the MCM-48, SBA-15, and MCF materials, the formation of hydrogen bonding was found for the chromium- and copper-modified samples, whereas the Fe-containing materials showed the ligand exchange mechanism. The strong interaction of the MSU support and the different acetylacetonate complexes, resulting in a loss of at least one acac ligand, was observed. The mesoporous silicas modified with transition metal oxides were studied by UV-vis-DR spectroscopy. The different metal dispersions were found for the samples containing various transition metal oxides.     

Polarization behaviour of fibre waveguide couplers

In this paper a new analytic method is presented to determine the coupling parameters of single mode, fibre waveguide couplers for sensor applications. The method is based on the analysis of a coupling matrix whose elements represent the parameters which define a coupler configuration.On leave from Instytut Fizyki, Politechnika Warszawska, Warszawa, ul. Koszykowa 75, Poland.     

Methoxide ion mediated reactions of methyl azidoacetate with 4-and 2-cyanobenzaldehyde. An unexpected cyclization of the ortho isomer to a 2(1H)-benzazepine derivative

A condensation reaction of 4-cyanobenzaldehyde ( 1 ) with methyl azidoacetate ( 2 ) in the presence of sodium methoxide produces a mixture of geometrical isomers of azidocinnamates 3 which undergoes thermolysis to give an indole 4 . By contrast, the treatment of 2-cyanobenzaldehyde ( 5 ) with 2 in the presence of sodium methoxide and followed by the usual workup furnishes an azepine derivative 6 .     

Syntheses, structure, and properties of a manganese-calcium cluster containing a Mn4Ca2 core

We describe here a novel, simple, efficient self-assembly method for the in situ generation of [Mn4Cl4(micro-OCH2CH2OMe)4(EtOH)4] and [Mn4(micro-Cl)Cl3(micro-OCH2CH2OMe)4(HOCH2CH2OMe)3]2 cubane-type compounds which react readily with calcium species to form cluster [Mn4Ca2Cl4(micro-OCH2CH2OMe)8], the calcium atoms attached to the Mn4 unit of flatten out the cubane inducing significant conformational changes.