Regioselective Arene Functionalization: Simple Substitution of Carboxylate by Alkyl Groups

Arenes with various alkyl side‐chains were synthesized in high yields and excellent regioselectivities. Starting from toluic and naphthoic acids, the carboxylate group was conveniently substituted by alkyl halides by Birch reduction and subsequent decarbonylation. The method is characterized by inexpensive starting materials and reagents, and methylation of arenes was realized. Besides simple alkyl substituents, the scope of arene functionalization was extended by benzyl, fluoro, amino, and ester groups. We were able to control the alkylation of 1‐naphthoic acid during Birch reduction by the addition of tert‐butanol. This allowed the regioselective synthesis of mono and bis‐substituted naphthalenes from the same starting material.     

Photochemical Reduction of Aromatic Imines by 2-Phenyl-N, N-dimethylbenzimidazoline

Reduction of C=N double bonds has been recognized as an important reaction both in organic chemistry and bio-chemistry1. Hantzsch 1,4-dihydropyridine (HEH, one of NADH model compounds) has been reported as a reductive reagent for imines2. However, application of dihydropyridines as practical reducing reagents in organic synthesis is limited because of their instability3. Like NADH models, 2-phenyl-N, N-dimethylbenzimidazoline (PDMBI) is an efficient electron and hydrogen donor (Eox = 0…     

Gröbner bases, H-bases and interpolation

The paper is concerned with a construction for H-bases of polynomial ideals without relying on term orders. The main ingredient is a homogeneous reduction algorithm which orthogonalizes leading terms instead of completely canceling them. This allows for an extension of Buchberger's algorithm to construct these H-bases algorithmically. In addition, the close connection of this approach to minimal degree interpolation, and in particular to the least interpolation scheme due to de Boor and Ron, is pointed out.

     

人造金刚石生长中的温度控制

 本文讨论了与腔体组装方法、温度梯度和边界条件等有关的温度控制问题及其对金刚石生长的影响。     

Geometric Condition Measures and Smoothness Condition Measures for Closed Convex Sets and Linear Regularity of Infinitely Many Closed Convex Sets

In this paper, we study geometric condition measures and smoothness condition measures of closed convex sets, bounded linear regularity, and linear regularity. We show that, under certain conditions, the constant for the linear regularity of infinitely many closed convex sets can be characterized by the geometric condition measure of the intersection or by the smoothness condition measure of the intersection. We study also the bounded linear regularity and present some interesting properties of the general linear regularity problem.The author is grateful to the referees for valuable and constructive suggestions. In particular, she thanks a referee for drawing her attention to Corollary 5.14 of Ref. 3, which inspired her to derive Theorem 4.2 and Corollary 4.2 in the revision of this paper.     

Generalizing Mutational Equations for Uniqueness of Some Nonlocal 1st-Order Geometric Evolutions

The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order geometric evolutions, however, the topological boundary need not be continuous in the sense of Painlevé–Kuratowski. So this paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional analysis beyond the traditional border of vector spaces: Distribution-like solutions are introduced in a set just supplied with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of ℝ ^N evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions for the uniqueness of these solutions.      

Generation of turbulent inflow and initial conditions based on multi‐correlated random fields

Direct or large eddy simulation of a turbulent flow field is strongly influenced by its initial or inflow boundary condition. This paper presents a new stochastic approach to generate an artificial turbulent velocity field for initial or inflow boundary condition based on digital filtering. Each velocity component of the artificial turbulent velocity field is generated by linear combination of individual uncorrelated random fields. These uncorrelated random fields are obtained by filtering random white‐noise fields. Using common elements in these linear combinations results in multi‐correlation among different velocity components. The generated velocity field reproduces locally desired Reynolds stress components and integral length scales including cross‐integral length scales. The method appears to be simple, flexible and more accurate in comparison with previously developed methods. The accuracy and performance of the method are demonstrated by numerical simulation of a homogeneous turbulent shear flow with high and low shear rates. To assess the accuracy and performance of the method, simulation results are compared with a reference simulation. Copyright © 2007 John Wiley & Sons, Ltd.     

Reactions of 2,5-di(2-thienyl)pyrroles

We have studied the possible modification of 2,5-di(thienyl)pyrroles with the aim of preparing compounds which can serve as precursors of polymers and monomers showing electrical conductivity and specific photochemical properties. Dedicated to Boris Aleksandrovich Trofimov on his 70^th jubilee. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1356–1365, September, 2008.     

A(∞)TH上的辫子Monoidal范畴

Let A and H be Hopf algebra,T-smash product A (∞)T H generalizes twisted smash product A*H.This paper shows a necessary and sufficient condition for T-smash product module category A(∞)T H M to be braided monoidal category.