Generic cosmic-censorship violation in anti-de Sitter space

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.     

Conformally invariant powers of the Laplacian -- A complete nonexistence theorem

We show that on conformal manifolds of even dimension there is no conformally invariant natural differential operator between density bundles with leading part a power of the Laplacian for n/2$">. This shows that a large class of invariant operators on conformally flat manifolds do not generalise to arbitrarily curved manifolds and that the theorem of Graham, Jenne, Mason and Sparling, asserting the existence of curved version of for , is sharp.

     

New hierarchies of knot polynomials from topological Chern-Simons gauge theory

In this Letter, we report on a study of the expectation values of Wilson loops in D=3 topological Chern-Simons theory associated with the fundamental representation of the simple Lie algebras SO(n) and Sp(n). The skein relations satisfied by these expectation values are derived by conformal field-theory techniques. New hierarchies of invariant polynomials for knots in S ³ can be derived from these relations (at least) up to ten crossings. The N=3 Akutsu-Wadati polynomials are a special case with G=SO(3). The expectation value of the Wilson loops for a couple of simple unknotted circles is identified to the Weyl character.Work supported in part by U.S. National Science Foundation Grant PHY8706501.Work supported in party by Chinese National Science Foundation through Nankai University.     

An efficient and selective conversion of sorbitol in ionic liquids: Use of ion exchange resin as a solid acid catalyst

Sorbitol was readily converted by heating in hydrophobic ionic liquids by the presence of ion exchange resins. Chemoseletivity of the dehydration depended on the choice of ion exchange resin; Nafion selectively produced isosorbide while Amberlite gave 1,5-anhydrosorbitol along with unreacted sorbitol. Ionic liquids used in the reaction were readily recovered by simple extraction procedure. With these procedures, we succeeded to prepare isosorbide in pure form, not contaminated with either ionic liquids or acid catalyst, by simple experimental procedure.     

Determination of the rate constants of the reactions of NO3 radical with CF3I and I(2P3/2)

The rate constant of the reaction of NO₃ radical with CF₃I was determined by a relative rate method using a Fourier transform infrared (FTIR) spectrometer smog chamber with a long path length gas cell. As a result, the upper limit of the rate constant was determined to be <2.2 × 10^?18 cm³ molecule^?1 s^?1 in 100 Torr of total pressure at 298 K, which suggests that CF₃I emitted into the atmosphere accumulates during night. The rate constant of the reaction of NO₃ with I(²P_3/2) was also measured using time‐resolved cavity ring‐down spectroscopy. The rate constant showed no pressure dependence in the range of 100–500 Torr of total pressure at 298 K and was determined to be (3.9 ± 1.0) × 10^?11 cm³ molecule^?1 s^?1. The present result is different from the previous ones and is about half of that reported most recently. From this rate constant, it is likely that the reaction of NO₃ radical with I(²P_3/2) does not have a much influence on the loss of I(²P_3/2) and the formation cycle of IO radical in the atmosphere. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 649–660, 2012     

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases

Synthesis of plakevulin A and structure-activity relationships of its related compounds against DNA polymerases is described. We have achieved a total synthesis and revised the structure of plakevulin A. Several analogues including untenone A, manzamenone A, and optically active plakevulin A, were prepared and tested with an enzyme inhibition assay for mammalian DNA polymerases. The effect of the methyl ester moiety, and the substituents at the 1- and 4-positions of plakevulin A on DNA polymerase activities are discussed.     

A Near-Infrared Dye That Undergoes Multiple Interconversions through Acid–Base Equilibrium and Reversible Redox Processes

A near-infrared (NIR) polymethine dye ( 1 ), consisting of a cyclohepta[1,2-b;4,3-b′]dithiophene and two phenol moieties, was synthesized. This dye exhibited pH-responsive changes in its photophysical properties due to a two-step acid–base equilibrium that produced a protonated cation ( 1H⁺ ) and an anion ( 1⁻ ). While 1H⁺ showed an intense fluorescence in the red region of the visible spectrum, 1⁻ exhibited a strong absorption in the NIR region. The tropylium ion character in 1H⁺ induces high pK_a1 and pK_a2 values for 1 . Moreover, a stable radical ( 1^. ) was prepared, which showed a NIR absorption band with a maximum at circa 1600 nm. The cyclic voltammogram of 1^. revealed a two-step reversible redox process that produced 1⁻ and the cation 1⁺ , which is different from 1H⁺ . These redox processes accompany drastic electrochromic changes in the vis–NIR region. Overall, 1 is susceptible to multiple interconversions between five forms, due to the multifaceted character of the cycloheptadithiophene skeleton.     

Continuous orbit equivalence,flow equivalence of Markov shifts and circle actions on Cuntz–Krieger algebras

We will study circle actions on Cuntz–Krieger algebras trivially acting on its canonical maximal abelian \(C^*\)-subalgebras from the view points of continuous orbit equivalence of one-sided topological Markov shifts and flow equivalence of two-sided topological Markov shifts.