Elliptic and parabolic equations for measures

Bogachev VI, Krylov NV, Röckner M. Elliptic and parabolic equations for measures. Russian Mathematical Surveys . 2009;64(6):973-1078.This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semi-groups associated with second-order elliptic operators acting in L-p-spaces with respect to infinitesimally invariant measures are investigated

Pleiotropic effects of hemagglutinin amino acid substitutions of H5 influenza escape mutants

AbstractIn the present study we assessed pleiotropic characteristics of the antibody-selected mutations. We examined pH optimum of fusion, temperatures of HA heat inactivation, and in vitro and in vivo replication kinetics of the previously obtained influenza H5 escape mutants. Our results showed that HA1 N142K mutation significantly lowered the pH of fusion optimum. Mutations of the escape mutants located in the HA lateral loop significantly affected H5 HA thermostability (P<0.05). HA changes at positions 131, 144, 145, and 156 and substitutions at positions 131, 142, 145, and 156 affected the replicative ability of H5 escape mutants in vitro and in vivo, respectively. Overall, a co-variation between antigenic specificity and different HA phenotypic properties has been demonstrated. We believe that the monitoring of pleiotropic effects of the HA mutations found in H5 escape mutants is essential for accurate prediction of mutants with pandemic potential

A Challenge toward Novel Quaternary Sulfides SrLnCuS3 (Ln = La, Nd, Tm): Unraveling Synthetic Pathways, Structures and Properties

We report on the novel heterometallic quaternary sulfides SrLnCuS3 (Ln = La, Nd, Tm), obtained as both single crystals and powdered samples. The structures of both the single crystal and powdered samples of SrLaCuS3 and SrNdCuS3 belong to the orthorhombic space group Pnma but are of different structural types, while both samples of SrTmCuS3 crystallize in the orthorhombic space group Cmcm with the structural type KZrCuS3. Three-dimensional crystal structures of SrLaCuS3 and SrNdCuS3 are formed from the (Sr/Ln)S7 capped trigonal prisms and CuS4 tetrahedra. In SrLaCuS3, alternating 2D layers are stacked, while the main backbone of the structure of SrNdCuS3 is a polymeric 3D framework [(Sr/Ln)S7]n, strengthened by 1D polymeric chains (CuS4)n with 1D channels, filled by the other Sr2+/Ln3+ cations, which, in turn, form 1D dimeric ribbons. A 3D crystal structure of SrTmCuS3 is constructed from the SrS6 trigonal prisms, TmS6 octahedra and CuS4 tetrahedra. The latter two polyhedra are packed together into 2D layers, which are separated by 1D chains (SrS6)n and 1D free channels. In both crystal structures of SrLaCuS3 obtained in this work, the crystallographic positions of strontium and lanthanum were partially mixed, while only in the structure of SrNdCuS3, solved from the powder X-ray diffraction data, were the crystallographic positions of strontium and neodymium partially mixed. Band gaps of SrLnCuS3 (Ln = La, Nd, Tm) were found to be 1.86, 1.94 and 2.57 eV, respectively. Both SrNdCuS3 and SrTmCuS3 were found to be paramagnetic at 20&ndash;300 K, with the experimental magnetic characteristics being in good agreement with the corresponding calculated parameters

Robotic optical telescopes global network MASTER II. Equipment, structure, algorithms

Presented paper describes the basic principles and features of the implementation of a robotic network of optical telescopes MASTER, designed to study the prompt (simultaneous with gamma radiation) optical emission of gamma-ray bursts and to perform the sky survey to detect unknown objects and transient phenomena. With joint efforts of Sternberg astronomical institute, High altitude astronomical station of the Pulkovo observatory, Ural state university, Irkutsk state university, Blagoveshchensk pedagogical university, the robotic telescopes MASTER II near Kislovodsk, Yekaterinburg, Irkutsk and Blagoveshchensk were installed and tested. The network spread over the longitudes is greater than 6 h. A further expansion of the network is considered. © 2011 Springer Science+Business Media B.V