Correction to the paper “on the curvature of a generalization of a contact metric manifolds”

We considered in Example 3.1 of the paper [1] an S-structure on R^2n+s . We concluded that when s > 1 this manifold cannot be of constant φ-sectional curvature. Unfortunately this result is wrong. In fact, essentially due to a sign mistake in defining the φ-structure and a consequent transposition of the elements of the φ-basis (3.2), some of the Christoffel’s symbols were incorrect. In the present rectification, using a more slendler tecnique, we prove that our manifold is of constant φ-sectional curvature −3s and then it is η-Einstein.     

Damping of giant monopole resonances within a linearized Landau-Vlasov dynamics

Isoscalar monopole vibrations in spherical nuclei are studied within the Landau-Vlasov dynamics. Energy and strength of the giant monopole resonance (GMR) are well reproduced. The Landau damping of the monopole vibrations is analyzed. It is found that the local Fermi surface corresponding to the GMR is deformed. The collision integral is included within the relaxation time approximation. The found total width is too small to explain the observed one in heavy nuclei. Because the Landau damping is sensitive to the effective nuclear force the missing part of the width can be connected to certain properties of the latter.     

Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction–diffusion equations

We consider some reaction–diffusion equations perturbed by white noise and prove Schauder estimates for the elliptic problem associated with the generator of the corresponding transition semigroup, defined in the Banach space of continuous functions. This requires the proof of some new interpolation result.     

Full C1,α-regularity for free and constrained local minimizers of elliptic variational integrals¶with nearly linear growth

We consider local minimizers of elliptic variational integrals with integrand f of nearly linear growth. In the scalar case N= 1 a side condition of the type u≥Φ may be incorporated, for N > 1 u is an unconstrained minimizer and f is required just to depend on the modulus of Du. We show in both cases that u has H?lder continuous first derivatives in the interior of the domain Ω.     

Rosenbluth-sampled nonequilibrium work method for calculation of free energies in molecular simulation

We present methods that introduce concepts from Rosenbluth sampling [M. N. Rosenbluth and A. W. Rosenbluth, J. Chem. Phys. 23, 356 (1955)] into the Jarzynski nonequilibrium work (NEW) free-energy calculation technique [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)]. The proposed hybrid modifies the way steps are taken in the NEW process. With it, each step is selected from a range of alternatives, with bias given to steps that contribute the least work. The definition of the work average is modified to account for the bias. We introduce two variants of this method, lambda-bias sampling and configuration-bias sampling, respectively; a combined lambda- and configuration-bias method is also considered. By reducing the likelihood that large nonequilibrated work values enter the ensemble average, the Rosenbluth sampling aids in remedying problems of inaccuracy of the calculation. We demonstrate the performance of the proposed methods through a model system of N independent harmonic oscillators. This model captures the difficulties involved in calculating free energies in real systems while retaining many tractable features that are helpful to the study. We examine four variants of this model that differ qualitatively in the nature of their phase-space overlap. Results indicate that the lambda-bias sampling method is most useful for systems with entropic sampling barriers, while the configuration-bias methods are best for systems with energetic sampling barriers. The Rosenbluth-sampling schemes yield much more accurate results than the unbiased nonequilibrium work method. Typically the accuracy can be improved by about an order of magnitude for a given amount of sampling; this improvement translates into two or more orders of magnitude less sampling required to obtain a given level of accuracy, owing to the generally slow convergence of the NEW calculation when the inaccuracy is large.     

Cis-and Trans-Coordination Assembly of Nitrogen Heterocycle with Copper(II) and Silver(I)

After the preparation of 1,4-bis(4,5-dihydro-1H-imidazol-2-yl)benzene(bdib),a nitrogen heterocycle with potential coordination manners of both cis-and tram-configuration forms,three complexes,including successfully self-assembled.Complexes 1 and 2 crystallized in the monoclinic system with P21/n space group and complex 3 in the triclinic system with P1 space group.     

Mononuclear heterocyclic rearrangement. Note I. Kinetic study of the rearrangement of the phenylhydrazone of 3-benzoyl-5-phenyl-1,2,4-oxadiazole into 2,5-diphenyl-4-benzoylamino-1,2,3-triazole

The rates of the mononuclear heterocyclic rearrangement of the phenylhydrazone of 3-benzoyl-5-phenyl-1,2,4-oxadiazole (1) into 2,5-diphenyl-4-benzoylamino-1,2,3-triazole (II) have heen measured in dioxane/water (50:50, v:v) in the range of pS⁺ 3.8–12.2 at various temperatures and the activation parameters determined. On the basis of the results obtained, we present evidence for the occurrence of two different types of reaction: the first, base-catalyzed; the second, pS⁺ -independent. In the base-catalyzed range the catalysis is of the general type.     

Phosphite-oxazole/imidazole ligands in asymmetric intermolecular Heck reaction

We describe the application of a new class of ligands--the phosphite-oxazole/imidazole (L1-L5a-g)--in asymmetric intermolecular Pd-catalyzed Heck reactions under thermal and microwave conditions. These ligands combine the advantages of the oxazole/imidazole moiety with those of the phosphite moiety: they are more stable than their oxazoline counterparts, less sensitive to air and other oxidizing agents than phosphines and phosphinites, and easy to synthesize from readily available alcohols. The results indicate that activities, regio- and enantioselectivities, are highly influenced by the type of nitrogen donor group (oxazole or imidazole), the oxazole and biaryl-phosphite substituents and the axial chirality of the biaryl moiety of the ligand. By carefully selecting the ligand components, we achieved high activities, regio- (up to 99%) and enantioselectivities (up to 99%) using several triflate sources. Under microwave-irradiation conditions, reaction times were considerably shorter (from 24 h to 30 min) and regio- and enantioselectivities were still excellent.     

高效液相色谱溶剂系统四面体优化法

改进了Ｇｌａｊｃｈ的三角形法,建立了适合于高效液相色谱（ＨＰＬＣ）的四面体优化法。将７个溶剂系统的实验结果输入计算机,由计算机模拟２３１个溶剂系统的色谱行为,优选出最佳溶剂系统。将此法用于１２种磺胺药物的分离,得到了满意的结果。