Preparation,characterization and photocatalytic performance of noble metals (Ag,Pd, Pt,Rh) deposited on sponge-like ZnO microcuboids

Novel sponge-like ZnO microcuboids with a hierarchical structure were fabricated via an alcoholic thermal process. Then a series of noble metals (Ag, Pd, Pt, Rh) was loaded onto the microcuboids. The samples obtained were characterized by nitrogen physical adsorption, powder X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), UV-vis diffuse reflectance spectroscopy (DRS), and X-ray photoelectron spectroscopy (XPS). The results show that the ZnO microcuboids have a high surface area and a sponge-like hierarchical structure. Activity tests for the degradation of acid orange II dye showed that the noble metals enhanced the activity of ZnO to different extents. For loading of 0.5 wt.%, the activity enhancement decreased in the order Pd>Ag>Pt>Rh. Co-loading of Pd and Ag had a detrimental effect on activity compared to single loading. The enhanced photocatalytic performance can be attributed to an increase in the rate of separation of photogenerated e^–/h⁺ pairs induced by the noble metals.     

On the Yamabe constants of S2×R3 and S3×R2

We compare the isoperimetric profiles of $S^2\times {\mathbb{R}}^3$ and of $S^3\times {\mathbb{R}}^2$ with that of a round 5-sphere (of appropriate radius). Then we use this comparison to obtain lower bounds for the Yamabe constants of $S^2\times {\mathbb{R}}^3$ and $S^3\times {\mathbb{R}}^2$. Explicitly we show that $Y(S^3\times {\mathbb{R}}^2,[g_0^3+d{x}^2])>(3/4)Y(S^5)$ and $Y(S^2\times {\mathbb{R}}^3,[g_0^2+d{x}^2])>0.63Y(S^5)$. We also obtain explicit lower bounds in higher dimensions and for products of Euclidean space with a closed manifold of positive Ricci curvature. The techniques are a more general version of those used by the same authors in Petean and Ruiz (2011) [15] and the results are a complement to the work developed by B. Ammann, M. Dahl and E. Humbert to obtain explicit gap theorems for the Yamabe invariants in low dimensions.     

Generalized Borcea–Voisin Construction

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi–Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi–Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the mirror pairing is lost.     

Inside dynamics of pulled and pushed fronts

We investigate the inside structure of one-dimensional reaction–diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical diffusion and growth rates, we analyze the spreading properties of each component. In the monostable case, the fronts are classified as pulled or pushed ones, depending on the propagation speed. We prove that any localized component of a pulled front converges locally to 0 at large times in the moving frame of the front, while any component of a pushed front converges to a well determined positive proportion of the front in the moving frame. These results give a new and more complete interpretation of the pulled/pushed terminology which extends the previous definitions to the case of general transition waves. In particular, in the bistable and ignition cases, the fronts are proved to be pushed as they share the same inside structure as the pushed monostable critical fronts. Uniform convergence results and precise estimates of the left and right spreading speeds of the components of pulled and pushed fronts are also established.     

On nodal solutions of the Yamabe equation on products

Let (M,g), (N,h) be closed Riemannian manifolds of constant scalar curvature. We prove the existence of nodal solutions of the Yamabe equation on the Riemannian product which depend on only one of the factors. We do this by studying the second Yamabe invariant introduced by Ammann and Humbert. We work out the case when M=S¹ explicitly showing the existence of an infinite number of solutions.     

On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted?

The aim of this work was to study the diffusion-related signal attenuation curves (signal-vs.-b curves) measured perpendicular and parallel to the neuronal fibers of the corticospinal tract in vivo and to determine whether effects of restricted diffusion could be observed when varying the diffusion time (T_D). A biexponential model and a two-compartment model including exchange according to the Kärger formalism were employed to analyze the signal-vs.-b curves. To validate the two-compartment model, restricted diffusion with exchange was simulated for uniformly sized cylinders, using different diameters and exchange times. The model was shown to retrieve the simulated parameters well, also when the short gradient pulse approximation was not met. The in vivo measurements performed perpendicular to the tracts, using b values up to 28000 s/mm² and T_D values between 64 and 256 ms, did not show the effects of restricted diffusion as expected from previous ex vivo studies. The applied two-compartment model yielded an average axonal diameter of about 4 μm and an intracellular exchange time of about 300 ms, but did not fit statistically well to the data. In conclusion, this study indicates that if the diffusion is modeled as two compartments, of which one is restricted, exchange must be included in the model.     

Novel synthesis of 2,2-dialkyl-3-dialkylamino-2,3-dihydro-1H-naphtho[2,1-b]pyrans

2,2-Dialkyl-3-dialkylamino-2,3-dihydro-1H-naphtho[2,1-b]pyrans were prepared from 2-naphthol, a secondary amine, and 3-hydroxy-2,2-dialkylpropanal in the presence of a catalytic amount of p-toluenesulfonic acid. This one-pot reaction involves retro-aldol disintegration of 3-hydroxy-2,2-dialkylpropanal followed by formation of a Mannich base intermediate from 2-naphthol, a secondary amine, and formaldehyde (retro-aldol product). This Mannich base then disproportionates into a quinone methide intermediate and the secondary amine is regenerated. It then forms an enamine intermediate with 2,2-dialkylacetaldehyde (another retro-aldol product). Finally, the quinone methide intermediate undergoes electrocyclic ring closure with enamines to produce the title compounds.     

Investigations on mechanical properties of PI-PS multigraft copolymers

The stress-strain behaviour of multigraft copolymers consisting of a polyisoprene (PI) backbone and grafted polystyrene (PS) arms have been characterized by applying models of rubber elasticity such as Mooney-Rivlin, slip-tube and the extended non-affine tube model. Additionally, the range of low deformation has been investigated by relaxation tests for determining the stress relaxation. Multigraft copolymers show high strain at break and low residual strain caused by the large number of physical cross links resulting from several grafted PS side chains. From the model fits the material parameters and of the slip-tube model, representing the influence of chemical cross links and entanglements effects, respectively, and the n_e/T_e-value (n_e - number of statistical segments between two successive entanglements, T_e - Langley trapping factor) of the extended non-affine tube model, are used to describe the tensile behaviour of these thermoplastic elastomers. The PS content was considered as filler phase taking into account the effect of hydrodynamic amplification. The influence of functionality and the number of branch points per molecule on the strain at break and the tensile strength is explained by the model parameters describing the stress-strain curve at low to medium (?400%, slip-tube, Mooney-Rivlin) and low to high (?900%, extended non-affine tube) elongations. It was observed that for the material with a spherical morphology is increasing with the number of branch points β (each branch point consists of a PI backbone segment, depending on the functionality one, two or four grafted PS arms). For cylindrical and lamellar morphologies the was decreasing with increasing β, which could be reconfirmed by applying the extended non-affine tube model where the n_e/T_e-parameter is increasing with β.     

Badly approximable affine forms and Schmidt games

For any real number θ, the set of all real numbers x for which there exists a constant c(x)>0 such that for all q∈Z\{0} is a 1/8-winning set.