19F NMR study of relative polarities and reactivities of N-H,N-Hg,and N-Au bonds in 2-(4-fluorophenyl)benzimidazole and its PhHg and Ph3PAu derivatives in intermolecular exchange

It has been shown by the¹⁹F NMR method that the relative polarities of nitrogenelement bonds in 2-(4-fluorophenyl)benzimidazole and its PhHg and PPh₃Au derivatives increase in the order N-H19F NMR. It has been found that these reactions occur by a bimolecular associative mechanism and that the N-H bond is substantially less reactive than the N-Hg and N-Au bonds, which have identical reactivities within the limits of sensitivity of the method used.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1574–1580, August, 1995.This work was carried out with financial support from the Russian Foundation for Basic Research (Project No. 93-03-5528).     

矩阵方程（A^TXA，B^TXB=（C，D）的反对称解及其最佳逼近

本利用矩阵对的标准相关分解，得到了矩阵方程(A^TXB，B^TXB)=(C，D)反对称解存在的充分必要条件及通解表达式，同时给出了解关于已知矩阵的最佳逼近．     

布尔“复合函数”的Walsh循环谱和自相关函数

本文利用布尔随机变量联合分布的分解式给出了布尔“复合函数”和某布尔函数符合率的分解算式,由此求得了布尔“复合函数”的 Walsh循环谱和自相关函数的计算公式,公式清楚地表明了“复合”所得布尔函数的 Walsh循环谱与起“复合”作用的函数和被“复合”的各函数所有线性组合的 Walsh循环谱之间的关系、“复合”所得布尔函数的自相关函数与起“复合”作用的函数谱和被“复合”的各函数的谱及相关函数之间的关系,这两个公式在布尔函数的密码学性质研究中会有广泛的应用.     

ROBUSTNESS OF AN UPWIND FINITE DIFFERENCE SCHEME FOR SEMILINEAR CONVECTION-DIFFUSION PROBLEMS WITH BOUNDARY TURNING POINTS

We consider a singularly perturbed semilinear convection-diffusion problem with a boundary layer of attractive turning-point type. It is shown that its solution can be decomposed into a regular solution component and a layer component. This decomposi-tion is used to analyse the convergence of an upwinded finite difference scheme on Shishkin meshes.     

Calorimetric study of methane interaction with supported Pd catalysts

As supported palladium oxide catalysts present the best performances in methane combustion in lean conditions, microcalorimetric studies of the interaction between methane and palladium oxide or metallic palladium supported on Al₂O₃, ZrO₂ and BN have been performed at 673 K. At this temperature methane reduced the palladium oxide, and the heat of reduction of palladium oxide was shown to depend on the dispersion and on the support. The lowest heats of reduction corresponded to the highest rates of methane combustion. Moreover methane reforming occurred on metallic palladium, producing hydrogen, and again methane decomposition was shown to depend on the support. This revised version was published online in July 2006 with corrections to the Cover Date.     

The synthesis mechanism of Ca3Al2O6 from soft mechanochemically activated precursors studied by time-resolved neutron diffraction up to 1000°C

The reaction pathway for the Ca₃Al₂O₆ formation up to 1300°C, from mechanochemically treated mixtures of amorphous aluminum hydroxide and CaCO₃, was studied in situ by differential thermal analysis, constant heating rate dilatometry and time-resolved neutron powder diffraction. The experiment was carried out, in an open system, on a sample with the nominal Ca₃Al₂O₆ stoichiometry. The results obtained by neutron diffractometry and thermal analysis were in good agreement with the data obtained by scanning electron microscopy and X-ray diffraction on heat-treated and-quenched samples. The synthesis path implied the formation of cryptocrystalline Al₂O₃, crystalline CaO, CaAl₂O₄ and Ca₁₂Al₁₄O₃₃ as transitory phases. Finally the nucleation and growth of the single phase Ca₃Al₂O₆ took place at 1300°C and exhibited porous structure due to CO₂ and H₂O release.     

Structure theorem for tournaments omitting N5

A finite tournament T is tight if the class of finite tournaments omitting T is well‐quasi‐ordered. We show here that a certain tournament N₅ on five vertices is tight. This is one of the main steps in an exact classification of the tight tournaments, as explained in [10]; the third and final step is carried out in [11]. The proof involves an encoding of the indecomposable tournaments omitting N₅ by a finite alphabet, followed by an application of Kruskal's Tree Theorem. This problem arises in model theory and in computational complexity in a more general form, which remains open: the problem is to give an effective criterion for a finite set {T₁,…,T_k} of finite tournaments to be tight in the sense that the class of all finite tournaments omitting each of T₁,…,T_k is well‐quasi‐ordered. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 165–192, 2003     

Construction of best Bregman approximations in reflexive Banach spaces

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.