Factorization of univalent analytic functions on compact Riemann surfaces with boundary

The paper is devoted to the theory of factorization of univalent analytic functions on a compact Riemann surface with boundary. The main component of the theory is a new method for the removal of the periods of certain functions (the natural analogues of the Schwarz integral and Blaschke products) along the boundary curves and bundle sections.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 285–313, 1989.     

Cationic polyelectrolytes. III. Nitrile-group reaction of macromolecular compounds with N,N-dialkylaminoalkylamines

The chemical reaction in aqueous medium of polyacrylonitrile and acrylonitrile–vinyl acetate co-polymer using asymmetrical diamines of H₂N? (CH₂)_m? NR₂ (m = 2,3) structure was studied. It was found that the nitrile group is modified to an dialkylaminoalkylacrylamide group; also determined were the reaction conditions required to obtain the highest degree of chemical transformation of the nitrile groups. All modified compounds were characterized by analytical spectroscopy (IR and ¹H NMR) and by rheological methods. It was also established that glutaronitrile can be used as a low-molecular-weight model to study the chemical transformation of nitrile groups in polyacrylonitrile and related polymers.     

Cationic polyelectrolytes. II. Amination of chloromethylated polystyrene with hydroxyalkylic secondary amines

The reaction of chloromethylated polystyrene with methyl(2- hydroxyethyl)amine and butyle (2-hydroxyethyl)amine was studied kinetically. The reaction of benzyl chloride with these amines was also investigated for comparison. N,N-dimethylformamide and dioxane were used as solvents. The reactions of benzyl chloride with the two amines in these solvents took place according to normal kinetics of the second order. Reaction kinetics depend on the nature of the amine and solvent in Chloromethylated polystyrene reactions. In dioxane the self-accelerating effect of the reaction for β ? 0.5 is apparent. Steric hindrance of the reaction, beginning with a conversion degree of about 75%, wss observed for butyl(2-hydroxyethyl)amine in N,N-dimethylformamide. This self-accelerating effect is observed in dioxane at the same reaction degree. The activation energies and frequency factors were calculated for the amination of benzyl chloride and chloromethylated polystyrene with the two amines in N,N-dimethylformamide and dioxane.     

Etude sur le comportement thermique de quelques polymeres ignifugeants contenant du phosphore et des halogenes

The thermal behaviour a series of polyphosphonates was studied by thermogravimetry (TG) and differential thermal analysis (DTA). The obtained data permitted the calculation of activation energies and reaction orders on decomposition zones by the Coats — Redfern method.     

PageRank model of opinion formation on social networks

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of the Universities of Cambridge and Oxford, LiveJournal, and Twitter. In this model, the opinion formation of linked electors is weighted with their PageRank probability. Such a probability is used by the Google search engine for ranking of web pages. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion on a significant fraction of the society. However, for a homogeneous distribution of two opinions, there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that the LiveJournal and Twitter networks have a stronger tendency to a totalitarian opinion formation than the university networks. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.     

Time evolution of Wikipedia network ranking

X-ray circular magnetic dichroism, polarized neutron diffraction, ac susceptibility, and Seebeck effect have been measured for several members of the RCo₂ series (R = Ho, Tm, Er) as a function of temperature and applied magnetic field. The experimental results show robust parimagnetism (a general behaviour along the RCo₂ series with R being a heavy rare earth ion) and two reversal temperatures in some systems, which is an unexpected result. Polarised neutron diffraction show differences between results obtained on single crystals or polycrystalline ingots. We propose an interpretation of parimagnetic RCo₂ as a Griffiths phase of the high temperature, magnetically ordered, amorphous RCo₂ phase.     

Protein–ligand docking using FFT based sampling: D3R case study

Fast Fourier transform (FFT) based approaches have been successful in application to modeling of relatively rigid protein–protein complexes. Recently, we have been able to adapt the FFT methodology to treatment of flexible protein–peptide interactions. Here, we report our latest attempt to expand the capabilities of the FFT approach to treatment of flexible protein–ligand interactions in application to the D3R PL-2016-1 challenge. Based on the D3R assessment, our FFT approach in conjunction with Monte Carlo minimization off-grid refinement was among the top performing methods in the challenge. The potential advantage of our method is its ability to globally sample the protein–ligand interaction landscape, which will be explored in further applications.     

Effect of electron irradiation on the crystalline structure of hgte and hgl-xcdxte thin films

The influence of 8 MeV electrons on the crystalline structure of HgTe and Hg1-xCdxTe thin films was studied. HgTe and Hg1-xCdxTe layers were obtained by thermal evaporation and condensation in vacuum on optically flat silica glass substrates heated at different temperatures.

One finds that the results of irradiation of HgTe and Hg_1-xCd_xTe thin films with 8 MeV electrons depend on the preparation conditions of the samples, and therefore on the level of perfection of the crystalline structure and the quantity of nonstoichiometric atoms.