Crossing the phantom divide in extended Dvali–Gabadadze–Porrati gravity

We propose a phantom crossing Dvali–Gabadadze–Porrati (DGP) model. In our model, the effective equation of state of the DGP gravity crosses the phantom divide line. We demonstrate crossing of the phantom divide does not occur within the framework of the original DGP model or the DGP model developed by Dvali and Turner. By extending their model, we construct a model that realizes crossing of the phantom divide. We find that the smaller the value of the new introduced parameter β is, the older epoch crossing of the phantom divide occurs in. Our model can account for late-time acceleration of the universe without dark energy. We investigate and show the property of Phantom crossing DGP model.     

Baouendi–Trèves approximation theorem for CR functions with values in a complex Fréchet space

We study CR functions with values in a complex Fréchet space X. We prove a vector valued analog to a result by Baouendi and Trèves (Ann Math 113:387–421, 1981), i.e. any X-valued CR function of Teodorescu class B ¹ may be locally approximated by X-valued holomorphic functions on ${{\mathbb C}^n}$ . We show that any CR function ${u \in C^\omega (M, X)}$ on a real analytic CR hypersurface ${M \subset {\mathbb {C}}^n}$ admits a unique holomorphic extension ${f \in {\mathcal {O}}(\Omega, X)}$ to some open neighborhood ${\Omega \supset M}$ .     

Critical metrics of the Schouten functional

Given a Riemannian metric on a compact smooth manifold, we consider its Schouten tensor, which is a tensor field of type (0, 2) arising in the remainder of the Weyl part in the standard decomposition of the curvature tensor of the metric. We study extremal properties of the Schouten functional, defined to be the scaling-invariant L ²-norm of the Schouten tensor. It is proved, for instance, that space form metrics are characterized as critical points of the Schouten functional among conformally flat metrics.     

One-pot multistep synthesis of 4-acetoxy-2-amino-3-arylbenzofurans from 1-aryl-2-nitroethylenes and cyclohexane-1,3-diones

[reaction: see text] A novel method for synthesizing 4-acetoxy-2-amino-3-arylbenzofurans (4) from 1-aryl-2-nitroethylenes (1) and cyclohexane-1,3-diones (2) is described. The method features one-pot operation of a solution of 1 and 2 in THF with catalytic Et3N (rt, 12 h) followed with Ac2O, Et3N, and DMAP (rt, 5 h), although the process consists of 13 elementary reactions.     

Binary and ternary complexes involving manganese(II), 2,2’-bipyridine and halide or thiocyanate ions inN,N-dimethylformamide

Ternary complexation involving the manganese(II) ion, 2,2’-bipyridine (bipy), and halide (chloride, bromide) or pseudohalide (thiocyanate) ions has been studied by precise titration calorimetry inN,N -dimethylformamide (DMF) at 298K. All the titration curves are explained well in terms of formation of mononuclear complexes of the type [MnX_m(bipy)_n](^2-m) + (X = CI, Br or SCN), and the formation of [MnCl(bipy)]⁺, [MnCl₂(bipy)], [MnCl(bipy)₂]⁺ and [MnCl₂(bipy)₂] has been established in the chloride system, [MnBr(bipy)]⁺, [MnBr₂(bipy)], [MnBr(bipy)₂]⁺ in the bromide system, and [Mn(NCS)(bipy)]⁺, [Mn(NCS)₂(bipy)], [Mn(NCS)₃(bipy)]^-, [Mn(NCS)(bipy)₂]⁺, and [Mn(NCS)₂(bipy)₂] in the thiocyanate system. The data were analyzed on the basis of the thermodynamic parameters for the binary Mn^lIbipy and Mn^II-X (X = Cl, Br and SCN) systems, the latter being determined in previous work. The formation constants, reaction enthalpies, and entropies of the ternary complexes were extracted. The thermodynamic parameters thus obtained are discussed in comparison with those of the corresponding systems of other transition metal(II) ions.     

Aerobic ruthenium-catalyzed oxidative cyanation of tertiary amines with sodium cyanide

RuCl3-catalyzed oxidative cyanation of tertiary amines with sodium cyanide under molecular oxygen (1 atm) at 60 degrees C gives the corresponding alpha-aminonitriles, which are versatile synthetic intermediates of various compounds such as amino acids and unsymmetrical 1,2-diamines, in excellent yields. This reaction is clean and should be an environmentally benign and useful process.     

Hanasanagin: a new antioxidative pseudo-di-peptide, 3,4-diguanidinobutanoyl-DOPA, from the mushroom, Isaria japonica

The ‘Hanasanagitake’ mushroom, Isaria japonica, is a folk medicine and a traditional health food. Fractionation of the 60% ethanol extract of the mushroom, guided by the antioxidant activity test, led to the isolation of a new pseudo-di-peptide, and it was called ‘hanasanagin’. Spectral analysis and chemical transformation determined the structure of hanasanagin as 3,4-diguanidinobutanoyl-DOPA.     

Highly Fluorescent Flavins: Rational Molecular Design for Quenching Protection Based on Repulsive and Attractive Control of Molecular Alignment

Unprecedented intense fluorescent emission was observed for a variety of flavin compounds bearing a perpendicular cyclic imide moiety at the C7 position of an isoalloxazine platform. A series of alloxan‐substituted flavins was prepared selectively by reduction of the corresponding N‐aryl‐2‐nitro‐5‐alkoxyanilines with zinc dust and subsequent reaction with alloxan monohydrate in the presence of boric acid. Analogues bearing oxazolidine‐2,4‐dione functionality were obtained on methylation of the alloxan‐substituted flavins with methyl iodide and subsequent rearrangement in the presence of an inorganic base. The flavin compounds exhibit intense white‐green fluorescent emission in the solution state under UV excitation at 298 K, with emission efficiencies Φ_{298 K} greater than 0.55 in CH₃CN, which are higher than the values for all reported flavin compounds under similar conditions. The highest Φ_{298 K} value of 0.70 was obtained in CH₃CN for isoalloxazine bearing C7‐alloxan and N10‐2,6‐diisopropylphenyl groups. The temperature dependence of the emission intensities indicates that the pronounced emission properties at 298 K are attributable to the highly heat resistant properties towards emission decay with increasing temperature. Mechanistic studies, including X‐ray diffraction analysis, revealed that the good emission properties and high heat resistance of the alloxan‐substituted flavins are due to a synergetic effect of the associative nature of the C7‐alloxan unit and the repulsive nature of the perpendicular bulky substituents at the C7 and N10 positions.     

Chemical Synthesis of O‐Glycosylated Human Interleukin‐2 by the Reverse Polarity Protection Strategy

The chemical synthesis of human interleukin‐2 (IL‐2) , having a core 1 sugar, by a ligation method is reported. Although IL‐2 is a globular glycoprotein, its C‐terminal region, in particular (99‐133), is extremely insoluble when synthesized by solid‐phase method. To overcome this problem, the side‐chain carboxylic acid of the Glu residues was protected by a picolyl ester, thus reversing its polarity from negative to positive. This reverse polarity protection significantly increased the isoelectric point of the peptide segment and made it positive under acidic conditions and facilitated the purification. An efficient method to prepare the prolyl peptide thioester required for the synthesis of the (28‐65) segment was also developed. These efforts resulted in the total synthesis of the glycosylated IL‐2 having full biological activity.     

Lewis acid-catalyzed nucleophilic substitutions of propargylic and allylic silyl ethers with enol silyl ethers

Nucleophilic reactions of various enol silyl ethers with carbocation species generated from propargyl silyl ethers by the action of a Lewis acid have been developed. The present method is highly useful for the introduction of allenic or enyne functionalities into the alpha-position of substituted ketones. [reaction--see text]