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.     

Magnetic Properties of the cis-[CuCl2(DMSO)2] Complex

Theoretical and Experimental Chemistry - The magnetochemical behavior of the cis-[CuCl2(DMSO)2] complex was analyzed. cis-Complex crystals were found to be perfectly paramagnetic above 50 K and...     

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.     

Structural and magnetic properties of nanocrystalline bismuth manganite obtained by mechanochemical synthesis

We have studied the formation of BiMnO3 (BMO) nanocrystalline perovskite powder produced by high-energy milling of the constituent oxides. The crystal structure and the amount of crystalline and amorphous phases in the powder as a function of the milling time were determined with XRPD using Rietveld refinement. BMO perovskite formed directly from highly activated nano-sized constituent oxides after 240 min of milling and subsequently grew during prolonged milling. The morphology, structure, and chemical composition of the powder were investigated by SEM and TEM. A clear ferromagnetic transition was observed at T _C ~66 K for a sample milled for 240 min and increased with milling time. The magnetic hysteresis behavior is similar to that of a soft ferromagnet. The magnetic properties of the obtained BMO powders were found to change as a function of milling time in a manner consistent with variations in the nanocomposite microstructure.     

Magnetic properties of Mn-oxide nanoparticles dispersed in an amorphous SiO2 matrix

Samples of Mn-oxide nanoparticles dispersed in an amorphous SiO₂ matrix with manganese concentration 0.7 and 3 at% have been synthesized by a sol-gel method. Transmission electron microscopy analysis has shown that the samples contain agglomerates of amorphous silica particles 10-20 nm in size. In silica matrix two types of Mn-rich particles are dispersed, smaller nanoparticles with dimensions between 3 and 10 nm, and larger crystalline areas consisting of aggregates of the smaller nanoparticles. High-temperature magnetic susceptibility study reveals that dominant magnetic phase at higher temperatures is λ-MnO₂. At temperatures below T_C=43 K strong ferrimagnetism originating from the minor Mn₃O₄ phase masks the relatively weak magnetism of λ-MnO₂ with antiferromagnetic interactions. Magnetic field dependence of the maximum in the zero-field-cooled magnetization for both the samples in the vicinity of 40 K, and a frequency shift of the real component of the ac magnetic susceptibility in the sample with 3 at% Mn suggest that the magnetic moments of the smaller Mn₃O₄ nanoparticles with dimensions below 10 nm are exposed to thermally activated blocking process just below the Curie temperature T_C. Appearance of a maximum in the zero-field-cooled magnetization for both the samples below 10 K indicates possible spin glass freezing of the magnetic moments at low temperatures which might occur in the geometrically frustrated Mn sublattice of the λ-MnO₂ crystal structure.     

Anomalous thermal conductivity of single crystal Cu2Te2O5Cl2

A strong increase of the thermal conductivity is observed at the phase transition (T _c=18.2 K) in Cu₂Te₂O₅Cl₂ single crystal. This behavior is compared with that of the spin-Peierls system NaV₂O₅, where a similar experimental observation has been made, and the conventional spin-Peierls system CuGeO₃, where a modest kink in the thermal conductivity curve has been observed. The strong increase of the thermal conductivity atT _c in Cu₂Te₂O₅Cl₂ could be partially attributed to the opening of the energy gap in the magnetic excitation spectrum evident from the magnetic susceptibility measurements. However, the main reason for the anomaly of the thermal conductivity could be explained by a strong spin-lattice coupling in this system, which what is in agreement with the preliminary X-band electron spin resonance measurement.