Entire regularizations of strongly continuous groups and products of analytic generators

Using entire regularizations of groups, we give a characterization of their analytic generators which we apply to the study of products of such generators.

     

Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals

We analyze the radially symmetric solution corresponding to the vortex defect (the so-called melting hedgehog) in the Landau–de Gennes theory for nematic liquid crystals. We prove the existence, uniqueness and stability results of the melting hedgehog.     

Kinetics of thermoinitiated oligomerization of 3,3′-(2,4,6-triethyl-1,3-phenylene)bis(5-methyl-1,2,4-oxadiazole)

The crystal structure of 3,3′-(2,4,6-triethyl-1,3-phenylene)bis(5-methyl-1,2,4-oxadiazole), which models the cross-linking fragment of polynitriles by benzodinitrile oxides, was determined by X-ray diffraction analysis. The kinetic regularities of its thermoinitiated oligomerization were studied by isothermal calorimetry and spectrophotometry. The process proceeds with self-acceleration, and the Arrhenius dependences of the initial and maximum reaction rates were determined. The reaction accelaration is determined by an increase in the viscosity of the reaction medium. Possible mechanisms were proposed for oligomerization.     

A dynamic model of spherical perturbations in the Friedmann Universe. II. Retarded solutions to an ultrarelativistic equation of state

The exact linear retarded spherically symmetrical solutions to the Einstein equations linearized around the Friedmann background are derived and examined for an ultrarelativistic equation of state. The uniqueness of the solutions in class C¹ is proved. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 69–76, July, 2008.     

Isomerization of silicenium and germenium ions in the systems C<Subscript>4</Subscript>H<Subscript>11</Subscript>M<Superscript>+</Superscript> (M = Si,Ge)

Equilibrium structures of the isomers and transition states of their interconversion in the system C₄H₁₁M⁺ (M = Si, Ge) have been obtained at theB3LYP level of theory using the cc-pVTZ basis set. The structures of these stationary points are close for Si and Ge; the most stable isomer in both systems is the tertiary cation (C₂H₅)(CH₃)₂M⁺, the second in energy is complex with ethylene [(CH₃)₂HM·C₂H₄]⁺. The secondary cation (C₂H₅)₂HM⁺ is third in energy isomer, the height of the barrier of interconversion for these three cations being practically independent on M. However, for M = Ge a substantial decrease in the energy of isomeric forms corresponding to complexes with alkanes is observed. As a result, in the system C₄H₁₁Ge⁺ the fourth in energy is isomer [(C₂H₅)Ge·C₂H₆]⁺ rather than [(C₂H₅)H₂Ge·C₂H₄]⁺ as for M = Si. Nevertheless, the height of the barriers for transition into these structures, although decreasing from M = Si to Ge, remain rather high, and the most favorable route of decomposition in both systems is the elimination of ethylene.     

Protein–Inorganic Array Construction: Design and Synthesis of the Building Blocks

Herein we describe the design and synthesis of the first series of di‐functional ligands for the directed construction of inorganic‐protein frameworks. The synthesized ligands are composed of a metal‐ion binding moiety (terpyridine‐based) conjugated to an epoxysuccinyl peptide, known to covalently bind active cysteine proteases through the active‐site cysteine. We explore and optimize two different conjugation chemistries between the di‐functionalized metal‐ion ligand and the epoxysuccinyl‐containing peptide moiety: peptide‐bond formation (with limited success) and Cu^I‐catalysed click chemistry (with good results). Further, the complexation of the synthesized ligands with Fe^II and Ni^II ions is investigated: the di‐functional ligands are confirmed to behave similarly to the parent terpyridine. As designed, the peptidic moiety does not interfere with the complexation reaction, in spite of the presence of two triazole rings that result from the click reaction. ES‐MS together with NMR and UV/Vis studies establish the structure, the stoichiometry of the complexation reactions, as well as the conditions under which chemically sensitive peptide‐containing polypyridine ligands can undergo the self‐assembly process. These results establish the versatility of our approach and open the way to the synthesis of di‐functional ligands containing more elaborated polypyridine ligands as well as affinity labels for different enzyme families. As such, this paper is the first step towards the construction of robust supramolecular species that cover a size‐regime and organization level previously unexplored.     

X-ray powder diffraction study of polytetrafluoroethylene

Samples of polytetrafluoroethylene were studied by X-ray diffraction. A quantitative X-ray powder diffraction analysis of three components of the polymer was performed for the first time. All samples of polytetrafluoroethylene were found to be three-phase and consist of one crystalline and two amorphous phases. One of the amorphous phases is composed of low-molecular-weight products. The structure of the latter phase was established for the first time by X-ray diffraction methods and computer simulation.     

Family constraining of iterative algorithms

In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.