A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is “rotating”—i.e., is such that the stationary Killing field is not everywhere normal to the horizon—must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, P. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.     

Nomura algebras of nonsymmetric Hadamard models

We show that the Nomura algebra of the nonsymmetric Hadamard model coincides with the Bose–Mesner algebra of the directed Hadamard graph.     

Highly efficient catalytic system for hydrosilylation of ketones with iron(II) acetate-thiophenecarboxylate

A combination of a catalyst derived from ferrous acetate and sodium thiophene-2-carboxylate efficiently promoted hydrosilylation of aromatic and aliphatic ketones to give the corresponding secondary alcohols in high yields with extremely high selectivity.     

New microscopic wave function of ��-condensation

We explain how to treat a microscopic wave function of ??-condensation taking a 3??-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuchi, R?pke, Schuck and the present author (Phys. Rev. Lett., 2001, 87: 192501). The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective internucleon forces and the Coulomb force, can play an important role in reproducing an ??-gas nature thanks to ??-condensation as an excited state of ??-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3??-condensation.     

A Characterization of Designs Related to an Extremal Doubly-Even Self-Dual Code of Length 48

The uniqueness of a binary doubly-even self-dual [48, 24, 12] code is used to prove that a self-orthogonal 5-(48, 12, 8) design, as well as some of its derived and residual designs, including a quasi-symmetric 2-(45, 9, 8) design, are all unique up to isomorphism.Received November 5, 2003     

Metallocene bis(perfluoroalkanesulfonate)s as air-stable cationic Lewis acids

Zirconocene and titanocene bis(perfluorooctanesulfonate)s were synthesized. In contrast to the corresponding triflates and perchlorates, these compounds are air- and water-stable. They were proved to be ionic on the basis of conductivity measurements and X-ray analysis, allowing these complexes to be stored for months. The strong Lewis acidity of these cationic metallocene species, which was proved by ESR study, enabled catalytic glycosylation.     

The effect of the N‐substituent s‐trans to the carbonyl group of N‐methylacrylamide derivatives on the stereospecificity of radical polymerizations

Radical polymerization of N‐methylacrylamide (NMAAm), N,N‐dimethylacrylamide (DMAAm), and N‐methyl‐N‐phenylacrylamide (MPhAAm) was investigated in toluene at low temperatures. Atactic, isotactic, and syndiotactic polymers were obtained by the polymerization of NMAAm, DMAAm, and MPhAAm, respectively, indicating that the stereospecificity of the radical polymerization of acrylamide derivatives depended on the N‐substituents of the monomer used. From the viewpoint of monomer structure, the origin of the stereospecificity of radical polymerization of NMAAm derivatives is discussed. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6534–6539, 2009