Some alternating sums of Lucas numbers

We consider alternating sums of squares of odd and even terms of the Lucas sequence and alternating sums of their products. These alternating sums have nice representations as products of appropriate Fibonacci and Lucas numbers.     

On the computation of scaling coefficients of Daubechies' wavelets

In the present paper, Daubechies' wavelets and the computation of their scaling coefficients are briefly reviewed. Then a new method of computation is proposed. This method is based on the work [7] concerning a new orthonormality condition and relations among scaling moments, respectively. For filter lengths up to 16, the arising system can be explicitly solved with algebraic methods like Gröbner bases. Its simple structure allows one to find quickly all possible solutions.     

Stereoselectivity of (−)-(1<Emphasis Type="Italic">R</Emphasis>,2<Emphasis Type="Italic">S</Emphasis>)-2-methylamino-1-phenylpropan-1-ol preparation

Stereoselectivity of reductive amination of (R)-1-hydroxy-1-phenylpropan-2-one by methylamine was studied. From the four isomers possible, only two are produced by this reaction. These are marked as (−)-(1R,2S)-ephedrine (desired product) and (+)-(1S,2R)-ephedrine. The reaction stereoselectivity depends both on the type of the catalyst and reaction conditions. The most suitable type is the supported platinum. However, this catalyst rapidly deactivates. With a decreasing activity of Pt catalyst, the stereoselectivity decreases. It is also decreased during the production of the second liquid phase (water) in the reaction mixture.     

Evolution of femtosecond laser-induced damage in doped GaN thin films

Mg- and Si-doped GaN layers deposited by metalorganic chemical vapor deposition method were irradiated with femtosecond pulse duration laser of three different wavelengths 1,030, 515 and 343 nm. Both single and multiple shot laser induced damage thresholds of doped GaN layers were evaluated and discussed. The scanning electron microscopy employed with electron beam induced current and energy dispersive X-ray techniques were used to study laser damage morphology. It was observed that ablated area and laser-induced damage increased with irradiation fluence. The mechanism of damage generation by Gaussian beam profile laser was considered.     

Structural diversity of isothiocyanato Cd(II) and Zn(II) Girard’s T hydrazone complexes in solution and solid state: effect of H-bonding on coordination number and supramolecular assembly of Cd(II) complex in solid state

The isothiocyanato Zn(II) complex (1) and mixed isothiocyanato/thiocyanato Cd(II) complex (2) with the condensation product of 2-acetylpyridine and trimethylammoniumacetohydrazide chloride (Girard’s T reagent) (HLCl) were investigated both experimentally and theoretically. The crystal structures of both complexes showed tridentate N₂O coordination of hydrazine ligand. In complex 1 square-pyramidal coordination surrounding of Zn(II) consists of deprotonated hydrazone ligand and two isothiocyanato ligands, while in octahedral Cd(II) complex ligand is coordinated without deprotonation as a positively charged species and coordination geometry is completed with two N-coordinated and one S-coordinated NCS^? anions. NMR spectroscopy and molar conductivity results for Cd(II) and Zn(II) complexes indicated their instability in solution. DFT calculations were performed to explain coordination preference and stability of complexes 1 and 2 in solid state and in solution. The obtained Cd(II) complex is the first reported mononuclear pseudohalide/halide Cd(II) complex with quinoline-/pyridine-based hydrazone ligands possessing octahedral geometry in solid state. In this complex, H-bonding has significant impact on coordination number and supramolecular assembly in solid state.     

Note on nonuniform estimate for compound poisson approximations to 2-runs

We obtain nonuniform estimates depending on the interval length for Poisson and compound Poisson approximations to 2-runs. We calculate exact constants for the estimates in the Wasserstein metric.     

On Hadamard Inequality for Log-Concave Functions

Some improvements and generalizations of Finks results about Hadamards inequality for log-concave functions are given.AMS Subject Classification: 26D07, 26D15, 26A51.     

DSC study of stabilizing effect of antioxidant mixtures in styrene-butadiene rubber

The type of cooperation between antioxidants in the binary mixtures of four substituted diphenylamines and phenotiazine in the stabilization of styrene-butadiene rubber has been tested. Thermooxidation of the samples has been studied by differential scanning calorimetry under non-isothermal conditions. The protection factors of the individual stabilizers and their mixtures were determined. The synergy factors were applied to asses the type of cooperation of antioxidants in the mixtures. From their values it can be concluded that the type of cooperation depends on temperature. The highest synergistic effect has been observed for the mixture of phenotiazine and [4-(1-methyl-1-phenyl-ethyl)-phenyl]-phenylamine.