Pinching of the first eigenvalue of the Laplacian and almost-Einstein hypersurfaces of the Euclidean space

In this article, we prove new pinching theorems for the first eigenvalue λ₁(M) of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound for λ₁(M) in terms of higher order mean curvatures H _k . We show that under a suitable pinching condition, the hypersurface is diffeomorpic and almost-isometric to a standard sphere. Moreover, as a corollary, we show that a hypersurface of the Euclidean space which is almost-Einstein is diffeomorpic and almost-isometric to a standard sphere.      

The deacylation mechanism of AmpC beta-lactamase at ultrahigh resolution

Beta-lactamases confer bacterial resistance to beta-lactam antibiotics, such as penicillins. The characteristic class C beta-lactamase AmpC catalyzes the reaction with several key residues including Ser64, Tyr150, and Lys67. Here, we describe a 1.07 A X-ray crystallographic structure of AmpC beta-lactamase in complex with a boronic acid deacylation transition-state analogue. The high quality of the electron density map allows the determination of many proton positions. The proton on the Tyr150 hydroxyl group is clearly visible and is donated to the boronic oxygen mimicking the deacylation water. Meanwhile, Lys67 hydrogen bonds with Ser64Ogamma, Asn152Odelta1, and the backbone oxygen of Ala220. This suggests that this residue is positively charged and has relinquished the hydrogen bond with Tyr150 observed in acyl-enzyme complex structures. Together with previous biochemical and NMR studies, these observations indicate that Tyr150 is protonated throughout the reaction coordinate, disfavoring mechanisms that involve a stable tyrosinate as the general base for deacylation. Rather, the hydroxyl of Tyr150 appears to be well positioned to electrostatically stabilize the negative charge buildup in the tetrahedral high-energy intermediate. This structure, in itself, appears consistent with a mechanism involving either Tyr150 acting as a transient catalytic base in conjunction with a neutral Lys67 or the lactam nitrogen as the general base. Whereas mutagenesis studies suggest that Lys67 may be replaced by an arginine, disfavoring the conjugate base mechanism, distinguishing between these two hypotheses may ultimately depend on direct determination of the pK(a) of Lys67 along the reaction coordinate.     

Coordination chemistry of the solvated silver(I) ion in the oxygen donor solvents water, dimethyl sulfoxide, and N,N'-dimethylpropyleneurea

The hydrated and dimethyl sulfoxide and N,N'-dimethylpropyleneurea solvated silver(I) ions have been characterized structurally in solution by means of extended X-ray absorption fine structure (EXAFS) and large-angle X-ray scattering (LAXS). The coordination chemistry of the hydrated and dimethyl sulfoxide solvated silver(I) ions has been reevaluated because of different results from the EXAFS and LAXS methods reported previously. Consistent results are obtained with a linearly distorted tetrahedral model with two short and approximately two long Ag-O bond distances: mean Ag-O bond lengths of 2.32(1) and 2.54(1) A for the hydrate, 2.31(1) and 2.48(2) A for the dimethyl sulfoxide solvate, and 2.31(1) and 2.54(2) A for the N,N'-dimethylpropyleneurea solvate, in solution.     

Some quantum chemical aspects on outer-sphere electron-transfer reactions: the U(V)/Fe(III)-U(VI)/Fe(II) system

The activation energy and rate constant of U(V)-Fe(III) to U(VI)-Fe(II) outer-sphere electron-transfer reaction was studied using Marcus model. Experimental values were used for Gibbs energy change of the reaction, and energy surfaces were calculated by quantum chemical methods. The calculated rate constant was in reasonable accord with experimental value.     

mu-GISAXS experiment and simulation of a highly ordered model monolayer of PMMA-beads

Uniform sized PMMA-beads were deposited as a monolayer on silicon substrates using dip-coating techniques. High-resolution grazing incidence X-ray small angle scattering experiments were performed using a micrometer sized beam (mu-GISAXS) to determine the structure of a highly ordered monolayer with two-dimensional hexagonal arrays. A clear and strong interference pattern coming from the reflection and refraction effects of particles on flat surfaces with small uncorrelated roughnesses is shown. The quantitative analysis and simulations of the X-ray scattering pattern have been performed, and a detailed explanation of the analysis is reported. The results were directly compared and verified with atomic force microscopy (AFM) measurements and their resulting FFT spectra.