Chiral copper-bipyridine complexes: Synthesis, characterization and mechanistic studies on asymmetric cyclopropanation

Chiral bipyridine ligands of different steric properties when reacted with CuCl₂ formed orange, yellow or green solids of new copper(II) complexes, [Cu(L)Cl₂] (L = L2-6), in good yield. Together with [Cu(L1)Cl₂], these complexes were characterized in solution by UV-Vis spectroscopy and cyclic voltammetry. The complexes give d-d transitions between 860 and 970 nm, and exhibit one quasi-reversible Cu(II)/Cu(I) couple between +0.405 V and +0.516 V versus NHE. Two of the copper(II) complexes, [Cu(L5)Cl₂] and [Cu(L6)Cl₂], and a copper(I) complex of L1, [Cu(L1)Cl], were characterized by X-ray crystallography. The triflate derivatives of both the Cu(I) and Cu(II) complexes are active catalysts towards the cyclopropanation of ethyl diazoacetate with styrene. The asymmetric induction suffers when the size difference between the alkyl and alkoxyl groups was minimized. The mechanism of the cyclopropanation was studied with kinetic and competition experiments. The rate is first order in catalyst and ethyl diazoacetate, inverse order with styrene and is strongly affected by the counterion.     

An efficient palladium-benzimidazolyl phosphine complex for the Suzuki-Miyaura coupling of aryl mesylates: facile ligand synthesis and metal complex characterization

A new class of easily accessible hemilabile benzimidazolyl phosphine ligands has been developed. The ligand skeleton is prepared from commercially available and inexpensive o-phenylenediamine and 2-bromobenzoic acid. With catalyst loading down to 0.5 mol% palladium, excellent catalytic activity towards the Suzuki-Miyaura coupling of aryl mesylates is still observed. This represents the lowest catalyst loading achieved so far for this reaction in general. X-Ray crystallography shows that new ligand L2 is coordinated with Pd in a κ(2)-P,N fashion.     

On product-cordial index sets and friendly index sets of 2-regular graphs and generalized wheels

A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.     

Synthesis of Biomorphic ZrO2-CeO2 Nanostructures by Silkworm Silk Template

以桑蚕丝为模板制备多级生物形态结构ZrO₂-CeO₂. 整个合成过程是由桑蚕丝模板的导向作用决定的. 分析结果表明ZrO₂-CeO₂结晶良好,呈多级网络中空纤维结构,直径为16～28μm,800 oC煅烧后ZrO₂-CeO₂晶粒尺寸约为14 nm.     

Synthesis of Biomorphic ZrO2-CeO2 Nanostructures by Silkworm Silk Template

A simple and green technique has been developed to prepare hierarchical biomorphic ZrO₂-CeO₂, using silkworm silk as the template. Different from traditional immersion technics, the whole synthesis process depends more on the restriction or direction functions of the silkwormsilk template. The analytic results showed that ZrO₂-CeO₂ exhibited a well-crystallized hierarchically interwoven hollow fiber structure with 16-28 μm in diameter. The grain size of the sample calcined at 800 oC was about 14 nm. Consequently, the interwoven meshwork at three dimensions is formed due to the direction of biotemplate. The action mechanism is summarily discussed here. It may bring the biomorphic ZrO₂-CeO₂ nanomaterials with hierarchical interwoven structures to more applications, such as catalysts.     

Inequalities for Taylor series involving the divisor function

Czechoslovak Mathematical Journal - Let $$T(q) = \sum\limits_{k = 1}^\infty {d(k){q^k},\,\,\,\,\left| q \right| < 1,} $$ where d(k) denotes the number of positive divisors of the natural...     

The Brown–York Mass of Revolution Surfaces in Asymptotically Schwarzschild Manifolds

In this paper, we will show that the limit of the Brown–York mass of a family of convex revolution surfaces in an asymptotically Schwarzschild manifold is the ADM mass.     

An optimization model for software component selection under multiple applications development

Component based software development (CBSD) is well acknowledged as a methodology which establishes reusability of software and reduce development cost effectively. While developing enterprise application using component based software engineering (CBSE) methods, software component selection plays a very important role in the process of component retrieval, adaptation and assembly. However, most of current researches focus on technical aspects from domain engineering and application engineering to improve reusability and system efficiency rather than application of optimization methods in CBSD management, especially application in component selection. Moreover, few existing researches have concerned about the situation where a software developer or enterprise develops multi-applications at the same time. By introducing the concept of reusability and a new formulation of compatibility matrix, an optimization model is proposed to solve component selection problem considering reusability and compatibility simultaneously. The model can be used to assist software developers in selecting software components when multi-applications are undertaken concurrently. Four experiments are conducted with the purpose to provide some insights in management perspective.