The Cut Loci, Conjugate Loci and Poles in a Complete Riemannian Manifold

Let M be a complete Riemannian manifold. We first prove that there exist at least two geodesics connecting p and every point in M if the tangent cut locus of ${p \in M}$ is not empty and does not meet its tangent conjugate locus. It follows from this that if M admits a pole and ${p \in M}$ is not a pole, then the tangent conjugate and tangent cut loci of p have a point in common. Here we say that a point q in M is a pole if the exponential map from the tangent space T _q M at q onto M is a diffeomorphism. Using this result, we estimate the size of the set of all poles in M having a pole whose sectional curvature is pinched by those of two von Mangoldt surfaces of revolution, meaning that their Gaussian curvatures are monotone and nonincreasing with respect to the distances to their vertices.     

Pyrrole-Based π-System–PtII Complexes: Chiroptical Properties and Excited-State Dynamics with Microsecond Triplet Lifetimes

Heteroleptic Pt^II complexes comprising π-extended dipyrrins and 2-phenylquinoline were prepared. Single-crystal X-ray analysis disclosed the stepped conformations of two ligand moieties in these Pt^II complexes. The enantiomers could be separated by HPLC and their configurations were determined from CD spectroscopy results and TD-DFT calculations. Transient absorption measurements revealed excited-state dynamics characterized by fast intersystem crossing and microsecond-order triplet-state lifetimes.     

Improvements of goodness-of-fit statistics for sparse multinomials based on normalizing transformations

We consider multinomial goodness-of-fit tests for a specified simple hypothesis under the assumption of sparseness. It is shown that the asymptotic normality of the PearsonX ² statistic (X _k ² ) and the log-likelihood ratio statistic (G _k ² ) assuming sparseness. In this paper, we improve the asymptotic normality ofX _k ² andG _k ² statistics based on two kinds of normalizing transformation. The performance of the transformed statistics is numerically investigated.     

Studies on pyrazines. 12 . N-oxidation of aminopyrazines with m-chloroperbenzoic acid

N-Oxidation reactions of 2-aminopyrazines, substituted by methyl or phenyl groups at C-3 or C-5, with m-chloroperbenzoic acid were undertaken to obtain the 2-aminopyrazine 1-oxides.     

Dynamic Interconversion between Boroxine Cages Based on Pyridine Ligation

Dynamic interconversion between large covalent organic cages was achieved simply by heating or acid/base treatment. A mixture of the boroxine cages 12‐mer and 15‐mer was cleanly converted into a pyridine adduct of the 9‐mer boroxine cage upon treatment with pyridine, and the geometry of N‐coordinated boron atoms changed from trigonal to tetrahedral. The reverse reaction was achieved by heating or acid treatment. In this process, the larger boroxine cages 12‐mer and 15‐mer were found to be entropically favored owing to the release of free pyridine molecules from 9‐mer ?6 Py.     

A new chiral 2-sulfonylamino-2′-phosphino-1,1′-binaphthyl ligand for highly enantioselective copper-catalyzed conjugate addition of diethylzinc to benzylideneacetones

A new axially chiral phosphine-sulfonamide ligand was prepared via a chiral component (R)-2-amino-2′-diphenylphosphinyl-1,1′-binaphthyl, which was conveniently synthesized through a new route involving hydrolysis of (R)-2-cyano-2′-phosphinyl-1,1′-binaphthyl followed by Hofmann rearrangement of the amide group. The new ligand was found to be very efficient in copper-catalyzed enantioselective conjugate addition of diethylzinc to acyclic enones such as benzylideneacetones, providing very high enantioselectivity up to 99% ee.     

Photoreactivating Enzyme for (6–4) Photoproducts in Cultured Goldfish Cells

We previously reported that when cultured goldfish cells are illuminated with fluorescent light, photorepair ability for both cyclobutane pyrimidine dimers and (6–4) photoproducts increased. In the present study, it was found that the duration of the induced photorepair ability for cyclobutane pyrimidine dimers was longer than that for (6–4) photoproducts, suggesting the presence of different photolyases for repair of these two major forms of DNA damage. A gel shift assay was then performed to show the presence of protein(s) binding to (6–4) photoproducts and its dissociation from (6–4) photoproducts under fluorescent light illumination. In addition, at 8 h after fluorescent light illumination of the cell, the binding of pro-tein(s) to (6–4) photoproducts increased. The restriction enzymes that have recognition sites containing TT or TC sequences failed to digest the UV-irradiated DNA pho-toreactivated by using Escherichia coli photolyase for cyclobutane pyrimidine dimers, indicating that restriction enzymes could not function because (6–4) photoproducts remained in recognition sites. But, when UV-irradiated DNA depleted of cyclobutane pyrimidine dimers was incubated with extract of cultured goldfish cells under fluorescent light illumination, it was digested with those restriction enzymes. These results suggested the presence of (6–4) photolyase in cultured goldfish cells as in Dro-sophila, Xenopus and Crotalus.     

Quantum-chemical investigation of the electroabsorption spectra of directly meso-meso-linked porphyrin arrays: essential role of charge-transfer excited states accidentally overlapping with soret bands

The electroabsorption (EA) spectra of directly meso-meso-linked porphyrin arrays (Zn, n = 1-3) have been investigated by means of the sum-over-states (SOS) approach at the INDO/S-SCI level theory. The experimental EA spectra of Zn (n > or = 2) exhibit an unusual second-derivative line shape at the exciton split low-energy B(x) band in contrast to the first-derivative spectrum of Z1, which is readily ascribed to a quadratic Stark shift of the B (Soret) band. Although the second-derivative line shape is usually attributed to a difference in the permanent dipole moment (Deltamu) between the ground and excited states, it should be vanishing for Zn due to their essentially D(2)(d) or D(2)(h) symmetry. As pointed out in our previous studies, the interporphyrinic charge-transfer (CT) excited states are accidentally overlapping with the excitonic B bands and the present calculations reveal that the B(x) state is strongly coupled via a transition dipole moment with two such CT states. These situations give rise to a quadratic Stark effect on the B(x) band that is intermediate between Stark shift (first derivative) and Stark broadening (second derivative), and play a central role in establishing the anomalous second derivative nature of the EA spectrum. Moreover, based on the comparison between the theoretical and experimental spectra, there must be an additional factor that further enhances the second derivative nature of the EA spectrum of porphyrin arrays. Discussions on this issue including the preliminary investigations on the role of solvent (PMMA)-induced asymmetry are also presented.