Critical groups of graphs with reflective symmetry

The critical group of a graph is a finite Abelian group whose order is the number of spanning forests of the graph. For a graph G with a certain reflective symmetry, we generalize a result of Ciucu–Yan–Zhang factorizing the spanning tree number of G by interpreting this as a result about the critical group of G. Our result takes the form of an exact sequence, and explicit connections to bicycle spaces are made.     

Blue fluorescent dye-protein complexes based on fluorogenic cyanine dyes and single chain antibody fragments

Fluoromodules are complexes formed upon the noncovalent binding of a fluorogenic dye to its cognate biomolecular partner, which significantly enhances the fluorescence quantum yield of the dye. Previously, several single-chain, variable fragment (scFv) antibodies were selected from a yeast cell surface-displayed library that activated fluorescence from a family of unsymmetrical cyanine dyes covering much of the visible and near-IR spectrum. The current work expands our repertoire of genetically encodable scFv-dye pairs by selecting and characterizing a group of scFvs that activate fluorogenic violet-absorbing, blue-fluorescing cyanine dyes, based on oxazole and thiazole heterocycles. The dye binds to both yeast cell surface-displayed and soluble scFvs with low nanomolar K(d) values. These dye-protein fluoromodules exhibit high quantum yields, approaching unity for the brightest system. The promiscuity of these scFvs with other fluorogenic cyanine dyes was also examined. Fluorescence microscopy demonstrates that the yeast cell surface-displayed scFvs can be used for multicolor imaging. The prevalence of 405 nm lasers on confocal imaging and flow cytometry systems make these new reagents potentially valuable for cell biological studies.     

Catalysis by titanocene-functionalized polymer-supported dendrimers

A series of variously-functionalized first-, second-, and third-generation dendrimers have been prepared and linked via a biphenyl core to a bis-styryl moiety suitable for use as a crosslinker in polymerization. Attachment of titanocene moieties to the first-generation system and copolymerization with styrene affords polymeric disks that exhibit catalytic properties superior to comparable solution-phase systems in a multicomponent coupling of chlorosilanes with Grignards to give bis-allylic silanes.     

Preconditioned iterative methods for coupled discretizations of fluid flow problems

Computational fluid dynamics, where simulations require largecomputation times, is one of the areas of application of highperformance computing. Schemes such as the SIMPLE (semi-implicitmethod for pressure-linked equations) algorithm are often usedto solve the discrete Navier-Stokes equations. Generally theseschemes take a short time per iteration but require a largenumber of iterations. For simple geometries (or coarser grids)the overall CPU time is small. However, for finer grids or morecomplex geometries the increase in the number of iterationsmay be a drawback and the decoupling of the differential equationsinvolved implies a slow convergence of rotationally dominatedproblems that can be very time consuming for realistic applications.So we analyze here another approach, DIRECTO, that solves theequations in a coupled way. With recent advances in hardwaretechnology and software design, it became possible to solvecoupled Navier-Stokes systems, which are more robust but implyincreasing computational requirements (both in terms of memoryand CPU time). Two approaches are described here (band blockLU factorization and preconditioned GMRES) for the linear solverrequired by the DIRECTO algorithm that solves the fluid flowequations as a coupled system. Comparisons of the effectivenessof incomplete factorization preconditioners applied to the GMRES(generalized minimum residual) method are shown. Some numericalresults are presented showing that it is possible to minimizeconsiderably the CPU time of the coupled approach so that itcan be faster than the decoupled one.     

Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.