On square roots of the Haar state on compact quantum groups

The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context of compact quantum groups. We provide a simple characterisation for compact quantum groups which admit no non-trivial square roots of the Haar state in terms of their corepresentation theory. In particular it is shown that such compact quantum groups are necessarily of Kac type and their subalgebras generated by the coefficients of a fixed two-dimensional irreducible corepresentation are isomorphic (as finite quantum groups) to the algebra of functions on the group of unit quaternions. An example of a quantum group whose Haar state admits no nontrivial square root and which is neither commutative nor cocommutative is given.     

Gold nanoparticles located at the interface of anatase/rutile TiO2 particles as active plasmonic photocatalysts for aerobic oxidation

Visible-light irradiation (λ > 450 nm) of gold nanoparticles loaded on a mixture of anatase/rutile TiO(2) particles (Degussa, P25) promotes efficient aerobic oxidation at room temperature. The photocatalytic activity critically depends on the catalyst architecture: Au particles with <5 nm diameter located at the interface of anatase/rutile TiO(2) particles behave as the active sites for reaction. This photocatalysis is promoted via plasmon activation of the Au particles by visible light followed by consecutive electron transfer in the Au/rutile/anatase contact site. The activated Au particles transfer their conduction electrons to rutile and then to adjacent anatase TiO(2). This catalyzes the oxidation of substrates by the positively charged Au particles along with reduction of O(2) by the conduction band electrons on the surface of anatase TiO(2). This plasmonic photocatalysis is successfully promoted by sunlight exposure and enables efficient and selective aerobic oxidation of alcohols at ambient temperature.     

Magnetic phase transitions in transition-metal complexes with triazole derivatives

Three divalent transition-metal (Co, Ni and Cu) complexes with the organic anion, 1,2,4-triazolato (tr), as a ligand molecule were prepared by means of hydrothermal syntheses and their magnetic properties were investigated by SQUID magnetometry. The Co(tr)₂ and Cu(tr)₂ complexes exhibit long range ordering below 8 and 30 K, respectively, while the Ni(tr)₂ complex does not show any magnetic phase transition down to 1.8 K. The magnetization isotherms of Co(tr)₂ and Cu(tr)₂ measured at 2.0 K show hysteresis loops with the coercive fields of 0.5 and 4.7 kOe, respectively. At temperatures higher than about 50 K, the temperature dependence of the magnetic susceptibility of Co(tr)₂, Ni(tr)₂ and Cu(tr)₂ follows the Curie-Weiss law with the Curie constants of 2.95, 0.945 and 0.420 emu K mol⁻¹ and the Weiss temperatures of −62, −74 and −97 K, respectively. These results suggest that the magnetically ordered phases observed in Co(tr)₂ and Cu(tr)₂ at low temperatures come from antiferromagnetic interactions resulting in canted arrangements of magnetic moments of the transition-metal cations. We discuss here the magnetic interactions in these transition-metal complexes by referring the results of the magnetization measurements.     

Boundedness of integral operators on generalized Morrey spaces and its application to Schrödinger operators

In this paper, we study boundedness of integral operators on generalized Morrey spaces and its application to estimates in Morrey spaces for the Schrödinger operator with nonnegative (reverse Hölder class) and small perturbed potentials .

     

Local Theory of Primitive Theta Functions

We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U(1)).     

Approximate innerness and central triviality of endomorphisms

We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by Kawahigashi-Sutherland-Takesaki in automorphism case.     

On a stress function method of a thermoelastic problem expressed in cylindrical coordinates in a multiply-connected region exhibiting temperature-dependent material properties

Summary This paper is concerned with the formulation of a plane thermoelastic problem in a multiplyconnected region exhibiting temperature-dependent material properties in terms of a stress function by deriving the integral conditions necessary for the assurance of the single-valuedness of the rotation and displacements, i.e., new Michell's conditions and the finite difference representation of the resulting fundamental equations.The method of solution for the thermoelastic problem in the multiply-connected region is applied to a transient plane-strain thermal stress problem in a hollow circular cylinder having temperature-dependent material properties subjected to an asymmetrical heating by a high-temperature fluid on the inner surface of the cylinder.

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Zur Methode der Spannungsfunktion bei thermoelastischen Problemen mit mehrfach zusammenhängendem Gebiet und temperaturabhängigen Materialeigenschaften

Übersicht In dieser Untersuchung wird ein thermoelastisches Problem mit mehrfach zusammenhängendem Gebiet und temperaturabhängigen Materialeigenschaften mit Hilfe einer Spannungsfunktion behandelt. Die Bedingungen für Eindeutigkeit von Rotation und Verschiebung werden hergeleitet. Die Grundgleichungen des Problems werden mit der Methode der finiten Differenzen gelöst.Als Anwendungsbeispiel wird ein hohler Kreiszylinder mit temperaturabhängigen Werkstoffeigenschaften betrachtet. Der Zylinder wird dabei durch eine Flüssigkeit mit hoher Temperatur in seinem Innern einer symmetrischen Erwärmung unterworfen.

     

Carbon sources of natural cyanamide in Vicia villosa subsp. varia

The 13C labels of [13C]carbon dioxide and D-[13C?]glucose were incorporated into cyanamide (NH?CN) when they were administered to Vicia villosa subsp. varia shoots. In contrast, the administration of sodium [2,3-13C?]pyruvate did not affect the relative area of the [M + 1]+ ion of cyanamide in the gas chromatography-mass spectrometry analysis. [2,3-13C?]pyruvate was incorporated into organic acids that are part of the citric acid cycle, such as succinate and fumarate, confirming that the shoots absorbed and metabolised it. These observations demonstrated that the carbon atom of cyanamide is derived from any of the carbohydrates that are present upstream of pyruvate in the metabolic pathway.