On the connected stability of the large-scale systems of dynamical equations on the time scale in critical cases

The connected stability of a large-scale system of dynamical equations on the time scale is investigated. The case where the trivial zero solution of the system is non-asymptotically stable in the linear approximation is considered. The sufficient conditions for the connected asymptotic stability of the zero solution of the system are obtained on the basis of the Lyapunov direct method.     

To the question on the almost everywhere convergence of the Riesz means of double orthogonal series

Sufficient conditions of the classical type ensuring the almost everywhere (a.e.) convergence of the nonnegative-order Riesz means of double orthogonal series are indicated. Analogies of the onedimensional results of Kolmogoroff [7] and Kaczmarz?CZygmund [5, 12] have been obtained for the Cesaro means and those of Zygmund [13] for the Riesz means. These analogies establish the a.e. equiconvergence of the lacunary subsequences of rectangular partial sums and of the entire sequence of Riesz means, generalize the corresponding results of Moricz [9] for the Cesaro a.e. summability by (C, 1, 1), (C, 1, 0), and (C, 0, 1) methods of double orthogonal series, and were announced earlier without proofs in the author??s work [3].     

ODMR Study of Zn1−x Mn x Se/Zn1−y Be y Se and (Cd1−x ,Mn)Te/Cd1−y Mg y Te Diluted Magnetic Semiconductor Quantum Wells

The effects of microwave pumping with a frequency of 60 GHz on the magneto-optical properties of diluted magnetic semiconductors (DMSs) are studied in (Zn,Mn)Se/(Zn,Be)Se and (Cd,Mn)Te/(Cd,Mg)Te quantum wells. Resonant heating of the Mn²⁺ ions in the electron spin resonance conditions leads to an increase in the Mn-spin temperature, which exceeds the bath temperature by up to 5.2 K, as detected by the shift of exciton emission line and decrease of its integral intensity. Nonresonant heating mediated by free carriers is also observed through variation of the polarization degree of emission. Direct measurements of spin–lattice relaxation times for both materials using time-resolved optically detected magnetic resonance (ODMR) technique have been performed. The mechanisms of ODMR in nanostructures of DMSs are discussed.     

Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

A multi-color study of the variability of the magnetic cataclysmic variable BY Cam is presented. The observations were obtained at the Korean 1.8 m and Ukrainian 2.6 m, 1.2 m and 38 cm telescopes in 2003–2005, 56 observational runs cover 189 hours. The variations of the mean brightness in different colors are correlated with a slope dR/dV = 1:29(4), where the number in brackets denotes the error estimates in the last digits. For individual runs, this slope is much smaller ranging from 0.98(3) to 1.24(3), with a mean value of 1.11(1). Near the maximum, the slope becomes smaller for some nights, indicating more “blue” spectral energy distribution, whereas the night-to-night variability has an “infrared” character. For the simultaneous UBVRI photometry, the slopes increase with wavelength from dU/dR = 0:23(1) to dI/dR = 1:18(1). Such wavelength dependence is the opposite of that observed in non-magnetic cataclysmic variables, in agreement with the model of cyclotron emission. The principal component analysis shows two components of variablitity with different spectral energy distributions (with a third at the limit of detection), which possibly correspond to different regions of emission. The highest peak in the scalegram analysis corresponds to the 200 min spin variability, its quarter and to the 30 min and 8 min QPOs. The amplitudes of these components are dependent on wavelength and luminosity state. The light curves were fitted by a statistically optimal trigonometrical polynomial (up to 4th order) to take into account a 4-hump structure. The dependences of these parameters on the phase of the beat period and on mean brightness are discussed. The amplitude of spin variations increases with an increasing wavelength and with decreasing brightness. The linear ephemeris based on 46 mean minima for 2003–2005 is HJD 2453213:010(3) + 0:137123(3)E: The extensive tables of the original observations and of results of analysis are published in an electronic form. The nearby star GSC 4081–1562 was found to be an eclipsing red variable.      

Limit theorems for number of diffusion processes, which did not absorb by boundaries

We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞. This research was partially supported by the Ministry of Education and Science of Ukraine, project 01.07/103 and University of Salerno, Italy.     

Quantum-Chemical Investigation of the Electronic and Spatial Structure of 1-Vinyltetrazoles

Calculations have been carried out of the total Mulliken charges on carbon and nitrogen atoms, the relative stability, and equilibrium populations of the s-cis(R) and s-trans(R) conformers of a series of 1-vinyl-5R-tetrazoles (R = H, Me, n-Bu, tert-Bu, Ph, NH₂, I, CF₃, NO₂) by the ab initio MP2/6-31G** method. Out-of-plane structures correspond to the stable s-cis(R) conformer, and the deviation from planarity grows regularly with an increase in the bulk of the substituent. The proportion of s-trans(R) conformation increases in the same series and reaches 100% for R = tert-C₄H₉. The data of quantum-chemical calculations are in agreement with the results of investigations of the spatial structure of 1-vinyl-5R-tetrazoles by ¹H and ¹³C NMR methods. Values of the total energies of the corresponding homodesmotic reactions were calculated to assess the effect of the nature of the substituent in position 5 of the tetrazole ring on the size of the conjugation energy in planar s-trans(R) conformations of the compounds investigated. The quantum-chemical calculations carried out show that the conjugation energy decreases regularly according to the increase in electron-withdrawing properties of the substituent in position 5 of the ring.__________Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 537–548, April, 2005.     

Maximum Noble‐Metal Efficiency in Catalytic Materials: Atomically Dispersed Surface Platinum

Platinum is the most versatile element in catalysis, but it is rare and its high price limits large‐scale applications, for example in fuel‐cell technology. Still, conventional catalysts use only a small fraction of the Pt content, that is, those atoms located at the catalyst’s surface. To maximize the noble‐metal efficiency, the precious metal should be atomically dispersed and exclusively located within the outermost surface layer of the material. Such atomically dispersed Pt surface species can indeed be prepared with exceptionally high stability. Using DFT calculations we identify a specific structural element, a ceria “nanopocket”, which binds Pt²⁺ so strongly that it withstands sintering and bulk diffusion. On model catalysts we experimentally confirm the theoretically predicted stability, and on real Pt‐CeO₂ nanocomposites showing high Pt efficiency in fuel‐cell catalysis we also identify these anchoring sites.     

Inversion of the local Pompeiu transformation on Riemannian symmetric spaces of rank one

We study the problem of inversion of the local Pompeiu transform on Riemannian symmetric spaces of rank one. The explicit formula for the reconstruction of a function by its averages over balls and spheres with a single fixed radius is obtained.     

Isomorphic Schauder decompositions in certain Banach spaces

We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ?_ψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and M-cotype of a Banach space and study the properties of unconditional Schauder decompositions in Banach spaces possessing certain geometric structure.