Limit distributions arising in branching random walks on integer lattices

The paper completes the investigation of limit distribution of the number of particles at the source of branching in the model of critical catalytic branching random walk on ^dd N {{mathbb Z}^d};d in {mathbb N} . Limit theorems of such kind were established only for d = 1, 2, 3, 4 under the assumption that, at the initial moment, there is a single particle at the source of branching. We prove their analog for d geqslant 5 d geqslant 5 . Moreover, in any dimension, we generalize the previous results by permitting the initial particle to start at an arbitrary point of the lattice.     

New quasi-Newton method for solving systems of nonlinear equations

We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n ²) arithmetic operations per iteration in contrast with the Newton method, which requires O(n ³) operations per iteration. Computational experiments confirm the high efficiency of the new method.     

Modeling of spectral features in the dynamic spectra of neutron stars

Modeling of atomic and cyclotron lines in the emergent spectra of rotating neutron stars with various distributions of temperature over the star surface is carried out. General and special relativity effects are taken into account in the radiation transfer calculations. A novel method of analysis based on the Fourier series expansion of the observed spectra over rotation frequencies is proposed. It is shown that the mutual influence of the gravitational bending of light rays and rotation of the star leads to the formation of strong features (sometimes several features at once) in the Fourier-harmonic spectrum, whereas these features remain almost invisible in both the integrated and dynamic spectra. Possible application of the obtained results to the interpretation of absorption features in the spectrum of the single neutron star 1E 1207.4 − 5209 is discussed.     

Untersuchung von Obstkonserven

Ohne Zusammenfassung     

Ion Mobility Spectrometry of Imidazole and Possibilities of Its Determination

Journal of Analytical Chemistry - The drift time and ion mobility of imidazole are determined and a procedure for the mathematical processing of spectra is developed. The specific features of...     

SnS and SnS2 thin films deposited using a spin‐coating technique from intramolecularly coordinated organotin sulfides

Synthesis and applications of organotin(II) sulfide ({2,6‐(Me₂NCH₂)₂C₆H₃}Sn)₂(μ‐S) ( 1 ), organotin(II) thiophenolate {2,6‐(Me₂NCH₂)₂C₆H₃}Sn(SPh) ( 2 ) and organotin(IV) heptasulfide {2,6‐(Me₂NCH₂)₂C₆H₃}₂Sn₂S₇ ( 3 ) as potential single‐source precursors (SSPs) for the deposition of SnS or SnS₂ thin films using a spin‐coating method are reported. Compounds 1 , 2 and 3 differ either by tin oxidation state or by Sn:S ratio (Sn:S = 2:1 in 1 , 1:1 in 2 and 2:7 in 3 ). It is shown that compound 1 is not a suitable SSP for thin‐film fabrication using the spin‐coating process because of its incomplete decomposition at annealing temperature. However, compounds 2 and 3 seem to be promising SSPs for spin‐coating of amorphous semiconducting thin films of SnS and SnS₂, respectively. Copyright © 2015 John Wiley & Sons, Ltd.