Photocatalytic activity of R3MO7 and R2Ti2O7 (R=Y, Gd, La; M=Nb, Ta) for water splitting into H2 and O2

The photocatalytic activities of R3MO7 and R2Ti2O7 (R=Y, Gd, La; M=Nb, Ta) strongly depended on the crystal structure. Overall, photocatalytic water splitting into H2 and O2 proceeded over La3TaO7 and La3NbO7, which have an orthorhombic weberite structure, Y2Ti2O7 and Gd2Ti2O7, which have a cubic pyrochlore structure, and La2Ti2O7, which has a monoclinic perovskite structure. All of these materials are composed of a network of corner-shared octahedral units of metal cations (TaO6, NbO6, or TiO6); materials without such a network were inactive. The octahedral network certainly increased the mobility of electrons and holes, thereby enhancing photocatalytic activity.     

Parabolic quasi‐concavity for solutions to parabolic problems in convex rings

We investigate some geometric properties of level sets of the solutions of parabolic problems in convex rings. We introduce the notion of parabolic quasi‐concavity, which involves time and space jointly and is a stronger property than the spatial quasi‐concavity, and study the convexity of superlevel sets of the solutions (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sequential pericyclic reaction of ene-diallenes: an efficient approach to the steroid skeleton

[reaction: see text] The one-pot construction of polycyclic aromatic systems from acyclic ene-bis(propargyl alcohols) was achieved through a tandem dual [2,3]-sigmatropic rearrangement/6pi-electrocyclic reaction/intramolecular [4 + 2] cycloaddition sequence. A steroidal compound was conveniently synthesized using the present method.     

Rate enhancement of Diels-Alder reactions in aqueous perfluorinated emulsions

A marked acceleration property for the Diels-Alder reaction was observed in an aqueous micellar system composed of perfluorohexane and lithium perfluorooctanesulfonate. The reaction rate increased with the concentration of the equimolar mixture of PFH and LiFOS, and the rate in 500 mM PFH and 500 mM LiFOS was about 100-fold greater than that in water without the fluorous field. After completion of the reaction, the products were simply extracted from the aqueous reaction mixture using n-hexane. [reaction: see text].     

Crosscap numbers of pretzel knots

The crosscap number of a knot in the 3-sphere is defined as the minimal first Betti number of non-orientable surfaces bounded by the knot. In this paper, we determine the crosscap numbers of a large class of pretzel knots. The key ingredient to obtain the result is the algorithm of enumerating all essential surfaces for Montesinos knots developed by Hatcher and Oertel.     

Mordell–Tornheim multiple zeta values at non-positive integers

We study the Mordell–Tornheim multiple zeta function with all the same parameters. Its values at non-positive integers are evaluated explicitly.     

Mechanism of the shape memory effect in martensitic alloys: an assessment

The (one-way) shape memory effect is a phenomenon that when a martensitic alloy is deformed in a martensitic state it recovers its original shape upon heating to the parent phase. This is a universal effect for certain martensitic alloys. We will assess the mechanism of the effect critically and select the essential factors which govern the effect. We try to understand it from a unified view, invoking the group–subgroup symmetry relation between the parent and martensite phase, along with analysis of reversible twinning modes in martensite. By such an assessment, we will show why typical shape memory alloys, such as Ti–Ni, Cu–Al–Ni etc., exhibit good shape memory characteristics, while others, such as ferrous alloys, do not. Thus, we will show that most of the shape memory characteristics of various martensitic alloys can be understood consistently from such an approach.