From the Solution of the Tsarev System to the Solution of the Whitham Equations

We study the Cauchy problem for the Whitham modulation equations for increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, ... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so-called hodograph transformation introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each g>0, we construct the unique solution of the Tsarev system, which matches the genus g+1 and g–1 solutions on the transition boundaries.     

Solid-Phase Synthesis and Encoding Strategies for Olefin Polymerization Catalyst Libraries

Active polymerization catalysts , novel resin-bound diimine complexes of nickel(II ) and palladium(II ) are obtained by combinatorial synthesis and combined in a catalyst library. By tagging with fluorescent markers, the catalysts can be coded. Therefore, after cleavage of the tag from the polymer-coated resin, HPLC can be used to determine the pathway along which the products were formed.     

Exploiting Incommensurate Symmetry Numbers: Rational Design and Assembly of M2M3′L6 Supramolecular Clusters with C3h Symmetry

Mixed-metal mesocates [M₂Pd₃Br₆L₆]⁴⁻ (M=Ti^IV, Sn^IV; L=4-diphenylphosphanyl-catecholate) have been synthesized, in which the two incommensurate symmetry elements generated by the different metal ions are linked by a rigid, bifunctional ligand to generate a C_3h-symmetrical cluster (see picture).     

Initial value problem of the Whitham equations for the Camassa-Holm equation

We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham solution matches the Burgers solution, which exists outside the cusp.     

Tissue-specific and neural activity-regulated expression of human BDNF gene in BAC transgenic mice

Background  

Brain-derived neurotrophic factor (BDNF) is a small secreted protein that has important roles in the developing and adult nervous system. Altered expression or changes in the regulation of the BDNF gene have been implicated in a variety of human nervous system disorders. Although regulation of the rodent BDNF gene has been extensively investigated, in vivo studies regarding the human BDNF gene are largely limited to postmortem analysis. Bacterial artificial chromosome (BAC) transgenic mice harboring the human BDNF gene and its regulatory flanking sequences constitute a useful tool for studying human BDNF gene regulation and for identification of therapeutic compounds modulating BDNF expression.     

Luminescence of ruthenium halide complexes containing a hemilabile phosphine pyrenyl ether ligand

A series of Ru(II) complexes, tcc-RuX2(POC4Pyr-P,O)2 (X = Cl (3), Br (4), I (5)), containing the hemilabile phosphine pyrenyl ether ligand 4-{2-(diphenylphosphino)phenoxy}butylpyrene (POC4Pyr (1)) are reported. The synthesis and spectroscopic properties of both the ligand, POC4pyr (1), and ligand oxide, P(=O)OC4pyr 2, and the solid-state structure of 1 are reported. Complexes 3-5 react rapidly with CO to give complexes ttt-RuX2(CO)2(POC4pyr-P)2 (X = Cl (6), Br (7), I (8)). No pyrene excimer emission is detected from 3-5; however, different intensities of excimer emission are observed for 6-8. The intensity of excimer emission decreases through the series, with 6 showing the most intense response. The emission is solely due to intramolecular pyrene excimers at low concentrations (< or =10(-4) M). Comparison of the UV-vis and steady-state fluorescence spectra shows overlap between the low energy d-d absorption of 7 and 8 with excimer emission (480 nm), suggesting nonradiative energy transfer may be occurring. Once excess CO is removed, complexes 6-8 isomerize to cis-dicarbonyl complexes cct-RuX2(CO)2(POC4Pyr-P)2 (X = Cl (9), Br (10), I (11)). The intensity of excimer emission from 9-11 increases with respect to the excimer emission observed for 6-8, with 9 showing a significant increase in excimer intensity.     

Mono(dinitrogen) and carbon monoxide adducts of bis(cyclopentadienyl) titanium sandwiches

The silyl-substituted titanocene complex, (eta5-C5Me4SiMe2Ph)2Ti, coordinates dinitrogen upon cooling to -35 degrees C to yield an unprecedented example of a mono(dinitrogen) complex of a substituted bis(cyclopentadienyl) titanium compound, (eta5-C5Me4SiMe2Ph)2Ti(N2). Analogous monocarbonyl derivatives, (eta5-C5Me4R)2Ti(CO) (R = SiMe3, SiMe2Ph, CHMe2), have been prepared by mixing the dicarbonyl compounds with the corresponding sandwiches. Both (eta5-C5Me4SiMe2Ph)2Ti(N2) and (eta5-C5Me4SiMe2Ph)2Ti(CO) have been characterized by X-ray diffraction, and mixed N2-CO titanocene complexes have also been observed by in situ IR spectroscopy.     

Anion separation by selective crystallization of metal-organic frameworks

A novel approach for the separation of anions from aqueous mixtures was demonstrated, which involves their selective crystallization with metal-organic frameworks (MOFs) containing urea functional groups. Self-assembly of Zn2+ with the N,N'-bis(m-pyridyl)urea (BPU) linker results in the formation of one-dimensional MOFs including various anions for charge balance, which interact to different extents with the zinc nodes and the urea hydrogen-bonding groups, depending on their coordinating abilities. Thus, Cl-, Br-, I-, and SO4(2-), in the presence of BPU and Zn2+, form MOFs from water, in which the anions coordinate the zinc and are hydrogen-bonded to the urea groups, whereas NO3- and ClO4- anions either do not form MOFs or form water-soluble discrete coordination complexes under the same conditions. X-ray diffraction, FTIR, and elemental analysis of the coordination polymers precipitated from aqueous mixtures containing equivalent amounts of these anions indicated total exclusion of the oxoanions and selective crystallization of the halides in the form of solid solutions with the general composition ZnCl(x)Br(y)I(z).BPU (x + y + z = 2), with an anti-Hofmeister selectivity. The concomitant inclusion of the halides in the same structural frameworks facilitates the rationalization of the observed selectivity on the basis of the diminishing interactions with the zinc and urea acidic centers in the MOFs when going from Cl- to I-, which correlates with decreasing anionic charge density in the same order. The overall crystal packing efficiency of the coordination frameworks, which ultimately determines their solubility, also plays an important role in the anion crystallization selectivity under thermodynamic equilibration.