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.     

Quantum Interference, Quantum Theory of Measurement, and (In)completeness of Quantum Mechanics

The new techniques and ideas in quantum interferometry with neutrons, photons, atoms, electrons, and Bose condensates that fluorished in the last two decades have influenced in a decisive way the thinking and the research in the foundations and interpretation of quantum mechanics. The controversies existing among different schools on the reality of matter waves of quantum theory, the postulates of quantum measurement theory, and the (in)completeness of quantum mechanics have to be approached now in a new way. Our argumentation follows the spirit of the Paris school.     

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.     

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.     

On Properties of Rectangular Hyperbolas

This paper improves an old theorem about a rectangular hyperbola : its centre lies on the pedal circle of any point on with respect to any triangle inscribed in . We also prove that an analogous result holds for Cevian circles. These results are used to obtain new characterisations of the Feuerbach, Jarabek, and Kiepert hyperbolas of a triangle.     

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.