Carbon-13 NMR spectra of some epoxides derived from dicyclopentadiene

The ¹³C NMR spectra of a series of epoxides derived from endo- and exo-dicyclopentadiene and their partially hydrogenated compounds were determined to examine the substituent effects arising from the introduction of the oxirane ring in comparison with those found in other ring systems. The ¹³C signals of some epoxides were assigned by using lanthanide shift reagents. Characteristic substituent effects exerted by an oxirane ring were demonstrated. Marked steric γ-effects of ?8—13 ppm were observed at the bridge carbon signal in the bicyclo[2.2.1]heptane skeleton. Differences were found in the substituent effects between endo- and exo-dicyclopentadiene epoxides, and have been discussed in relation to the molecular geometry.     

Computer-generated holograms for producing fractal speckles

When a diffuser is illuminated by the coherent light with a negative power-law distribution, fractal speckles are produced in the far-field diffraction region. Fractal speckles have extremely long spatial correlation functions of the intensity distributions in comparison with ordinary speckles, which implies that they may extend measurement ranges in various metrological applications based on the spatial correlation of speckles. To have fractal speckles with satisfactory statistical properties, it is required to produce a power-law illumination profile with high quality. In this paper, we report on the computer-generated holograms for producing power-law intensities on the basis of the method of stationary phase, with the error-reduction algorithm combined with to suppress strong ringing of the intensity.     

Low-energy charge-density excitations in MgB2: Striking interplay between single-particle and collective behavior for large momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB2, displaying a remarkable cosinelike, periodic energy dispersion with momentum transfer (q) along the c* axis, has been observed for the first time by high-resolution nonresonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-q collective mode residing in the single-particle excitation gap of the B pi bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB2.     

Phosphonation of arenes with dialkyl phosphites catalyzed by Mn(II)/Co(II)/O2 redox couple

[reaction: see text]. Arylphosphonates were first synthesized through a catalytic phosphonation of various arenes with dialkyl phosphites under the influence of an Mn(OAc)2/Co(OAc)2/O2 redox couple. For instance, the reaction of benzene with diethyl phosphite in the presence of Mn(OAc)2 (5 mol %) and Co(OAc)2 (1 mol %) under a mixed gas of O2 (0.5 atm) and N2 (0.5 atm) at 45 degrees C led to diethyl phenylphosphonate in 81% selectivity at 62% conversion. This is the first successful phosphonation of benzene with dialkyl phosphites through a catalytic radical process.     

Finite Hilbert stability of (bi)canonical curves

We prove that a generic canonically or bicanonically embedded smooth curve has semistable mth Hilbert points for all m≥2. We also prove that a generic bicanonically embedded smooth curve has stable mth Hilbert points for all m≥3. In the canonical case, this is accomplished by proving finite Hilbert semistability of special singular curves with $\mathbb{G}_{m}$ -action, namely the canonically embedded balanced ribbon and the canonically embedded balanced double A _2k+1-curve. In the bicanonical case, we prove finite Hilbert stability of special hyperelliptic curves, namely Wiman curves. Finally, we give examples of canonically embedded smooth curves whose mth Hilbert points are non-semistable for low values of m, but become semistable past a definite threshold.     

Archimedean zeta integrals on GL n × GL m and SO2n+1 × GL m

In this paper, we evaluate archimedean zeta integrals for automorphic L-functions on GL _n × GL _n-1+? and on SO_2n+1 × GL _n+? , for ? = ?1, 0, and 1. In each of these cases, the zeta integrals in question may be expressed as Mellin transforms of products of class one Whittaker functions. Here, we obtain explicit expressions for these Mellin transforms in terms of Gamma functions and Barnes integrals. When ? = 0 or ? = 1, the archimedean zeta integrals amount to integrals over the full torus. We show that, as has been predicted by Bump for such domains of integration, these zeta integrals are equal to the corresponding local L-factors—which are simple rational combinations of Gamma functions. (In the cases of GL _n × GL _n-1 and GL _n × GL _n this has, in large part, been shown previously by the second author of the present work, though the results here are more general in that they do not require the assumption of trivial central characters. Our techniques here are also quite different. New formulas for GL(n, R) Whittaker functions, obtained recently by the authors of this work, allow for substantially simplified computations). In the case ? = ?1, we express our archimedean zeta integrals explicitly in terms of Gamma functions and certain Barnes-type integrals. These evaluations rely on new recursive formulas, derived herein, for GL(n, R) Whittaker functions. Finally, we indicate an approach to certain unramified calculations, on SO_2n+1 × GL _n and SO_2n+1 × GL _n+1, that parallels our method herein for the corresponding archimedean situation. While the unramified theory has already been treated using more direct methods, we hope that the connections evoked herein might facilitate future archimedean computations.     

Augmenting Outerplanar Graphs to Meet Diameter Requirements

Given an undirected graph and an integer , we consider the problem of augmenting G by a minimum set of new edges so that the diameter becomes at most D. It is known that no constant factor approximation algorithms to this problem with an arbitrary graph G can be obtained unless , while the problem with only a few graph classes such as forests is approximable within a constant factor. In this article, we give the first constant factor approximation algorithm to the problem with an outerplanar graph G. We also show that if the target diameter D is even, then the case where G is a partial 2‐tree is also approximable within a constant.     

Interaction of anti-aggregation agent dimethylethylammonium propane sulfonate with acidic fibroblast growth factor

Prevention of aggregation is critical for analyzing protein structure. Non-detergent sulfobetaines (NDSBs) are known to prevent protein aggregation, but the molecular mechanisms of their anti-aggregation effect are poorly understood. To elucidate the underlying mechanisms, we analyzed the effects of dimethylethylammonium propane sulfonate (NDSB-195) on acidic fibroblast growth factor (aFGF). NDSB-195 (0.5M) increased both aggregation and denaturation temperatures of aFGF by 4 degrees C. Chemical shift perturbation analyses indicated that many affected residues were located at the junction between a beta-strand (or 3(10)-helix) and a loop, irrespective of the chemical properties of the residue. The apparent dissociation constants of the interaction ranged from 0.04 to 3M, indicating weak interactions between NDSB and protein molecules.     

Luminescence properties and relaxation processes of strongly correlated organic radical TTTA crystals and molecules

Photoluminescence of strongly correlated organic radical 1,3,5-trithia-2,4,6-triazapentalenyl (TTTA) crystals was measured at room temperature in order to elucidate the relaxation process in the excited state, which is responsible for an initiation of the photoinduced magnetic phase transition in this material. The electronic structure and luminescence properties of TTTA molecule were also investigated to clarify the relaxation process. We found that a luminescence band lies at 1.8 eV in the high-temperature (HT) phase crystal having almost same characteristics as that in TTTA molecule, suggesting that the intramolecular lattice distortion plays an important role for the relaxation process. On the other hand, a broad luminescence band appears at 1.4 eV with a large Stokes shift in the low-temperature (LT) phase crystal. The large Stokes shift observed shows that rearrangement of the dimerized TTTA molecules toward the evenly spaced radicals takes place due to a large intermolecular lattice distortion. This molecular rearrangement in the excited state initiates the photoinduced magnetic phase transition from the LT to HT phases in this material.