Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations

We discuss the calculation of homotopy indices on closed convex sets in a Banach space and then use these ideas to prove the existence of multiple solutions of nonlinear elliptic equations. We obtain more information on the solutions than in earlier work. A key idea is to calculate the homotopy index of the stable and mountain pass solutions and the connections joining them. Dedicated to the memory of Jean Leray     

Stark structure of the Yb3+ ion levels in (YbxY1?x)2Ti2O7 and the crystal field in rare-earth titanates with a pyrochlore structure

The absorption spectra of Yb₂Ti₂O₇ single crystals and the luminescence and luminescence excitation spectra of Y₂Ti₂O₇: Yb (1%) polycrystals were studied in the temperature range 4.2–300 K. The spectra were analyzed in terms of the crystal-field theory and the exchange-charge model. Based on the set of crystal-field parameters found for Yb₂Ti₂O₇, analogous sets of parameters were determined for other rare-earth titanates and proved to be in reasonable agreement with all available experimental data. __________ Translated from Fizika Tverdogo Tela, Vol. 47, No. 8, 2005, pp. 1376–1380. Original Russian Text Copyright ? 2005 by Klimin, Popova, Chukalina, Malkin, Zakirov, Antic-Fidancev, Goldner, Aschehoug, Dhalenne.     

Measures of complexity for 3D image analysis of trabecular bone

Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.     

Macroscopic properties and self-organization in mixed solutions of surfactants

The directions of the studies of aqueous solutions containing two surfactants or surfactants and various additives performed by the authors and coworkers are discussed, with the focus being on systems in which mixing is accompanied by synergistic effects (a significant decrease in the critical micelle concentration, the growth of aggregates, an increase in the viscosity, changes in the topology of the solubility diagram, etc.). Experimental data and results of modeling with the use of molecular-thermodynamic approaches of various levels are presented.     

Dynamics of moving interacting atoms in a laser radiation field and optical size resonances

The forces acting on interacting moving atoms exposed to resonant laser radiation are calculated. It is shown that the forces acting on the atoms include the radiation pressure forces as well as the external and internal bias forces. The dependences of the forces on the atomic spacing, polarization, and laser radiation frequency are given. It is found that the internal bias force associated with the interaction of atomic dipoles via the reemitted field may play an important role in the dynamics of dense atomic ensembles in a light field. It is shown that optical size resonances appear in the system of interacting atoms at frequencies differing substantially from transition frequencies in the spectrum of atoms. It is noted that optical size resonances as well as the Doppler frequency shift in the spectrum of interacting atoms play a significant role in the processes of laser-radiation-controlled motion of the atoms.     

Determination of formic and acetic acids in air by piezoelectric microweighing

The quantitative and kinetic parameters of sorption of formic and acetic acids on thin films of various modifiers of piezoelectric quartz resonator electrodes are determined. Parameters of film formation on the electrodes (application procedure and thickness) are optimized. Methods for joint and separate determination of formic and acetic acids in air by piezoelectric microweighing with single- and double-sensor devices are developed.     

Ultraviolet photoemission spectroscopy of hydrogen complex deactivation on InP:Zn(1 0 0) surfaces

Ultraviolet photoemission spectroscopy is used to study the kinetics of the H-Zn complex deactivation in Zn doped InP(1 0 0). Hydrogen injected into the material electronically passivates the local carrier concentration. Reverse-biased anneals of the InP under ultra-high vacuum show a dramatic change in the work function of the material with increasing temperature. Spectral features are also shown to be sensitive to sample temperature. To our knowledge, we show the first view of hydrogen retrapping at the surface using photoemission spectroscopy. A simple photoelectron threshold energy analysis shows the state of charge compensation of the material.     

Liquid Chromatography-Mass Spectrometry Determination of Six 5-Nitroimidazoles in Animal Feedstuff

A liquid chromatography-mass spectrometry method for the determination of the coccidiostats metronidazole, ronidazole, dimetridazole, secnidazole, tinidazole and ipronidazole in feedstuff was developed. The 5-nitroimidazoles were extracted from animal feed with a pH 2 phosphate buffer solution followed by a solid phase extraction procedure based on HLB cartridges. The liquid chromatographic separation of the extracts was performed on a C₁₈ bonded silica column applying a gradient of elution with pH 4.3 ammonium acetate buffer solution and acetonitrile. Quantification for each 5-nitroimidazole was carried out monitoring its molecular ion [M + H]⁺ obtained by positive electrospray ionisation mode. A pool of feedstuffs was used to optimise and validate the method. Linearity, quantification limit, intra-day and inter-day reproducibility and accuracy were estimated using this pool of feedstuffs spiked with the drugs. For the confirmatory assay, several fragment ions from each 5-nitroimidazole were obtained and monitored. The method was applied successfully to determine 5-nitroimidazoles in feedstuff at level of 0.05 mg kg⁻¹.     

Influence of temperature on phosphorescence spectra of Pd-porphine in Shpol’skii matrices

We have studied the temperature dependence of the radiative deactivation of the Pd-porphine triplet states in Shpol’skii matrices in the temperature range 1.2–210 K. A substantial transformation of the phosphorescence spectra is observed as the temperature increases and is due to the inclusion of thermally activated Pd-porphine states in the radiative deactivation processes. The activation energy E_a of these Pd-porphine states is measured in matrices of n-octane and n-nonane. The splitting of the lowest quasidegenerate triplet state ΔE(T₂−T₁) is determined for planar and distorted conformations of the Pd-porphine macrocycle in the n-octane matrix as 40 and 57 cm⁻¹, respectively. The ability to use the temperature dependence of the phosphorescence properties of Pd-porphine to fabricate molecular thermometers for the low-temperature range is analyzed. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 4, pp. 460–464, July–August, 2007.