Janus Face All-cis 1,2,4,5-tetrakis(trifluoromethyl)- and All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)- Cyclohexanes

We report the synthesis of all-cis 1,2,4,5-tetrakis (trifluoromethyl)- and all-cis 1,2,3,4,5,6-hexakis (trifluoromethyl)- cyclohexanes by direct hydrogenation of precursor tetrakis- or hexakis- (trifluoromethyl)benzenes. The resultant cyclohexanes have a stereochemistry such that all the CF₃ groups are on the same face of the cyclohexyl ring. All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane is the most sterically demanding of the all-cis hexakis substituted cyclohexanes prepared to date, with a barrier (ΔG) to ring inversion calculated at 27 kcal mol⁻¹. The X-ray structure of all-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane displays a flattened chair conformation and the electrostatic profile of this compound reveals a large diffuse negative density on the fluorine face and a focused positive density on the hydrogen face. The electropositive hydrogen face can co-ordinate chloride (K≈10³) and to a lesser extent fluoride and iodide ions. Dehydrofluorination promoted decomposition occurs with fluoride ion acting as a base.     

Homotopy Theories of Algebras over Operads

Homotopy theories of algebras over operads, including operads over “little n-cubes,” are defined. Spectral sequences are constructed and the corresponding homotopy groups are calculated.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 278–285.Original Russian Text Copyright © 2005 by V. A. Smirnov.     

A class of periodic groups

We deal with periodic groups saturated with dihedral groups. In particular, it is proved that periodic groups of bounded period, and also periodic Shunkov groups, saturated with dihedral groups, are locally finite.Supported by RFBR grant No. 03-01-00356 and by the Krasnoyarsk Science Foundation, project 11F0202C.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 114–125, January–February, 2005.     

Quantum group invariant fermionic gases: GLp,q(2) and SUp/q(2) invariances

We first investigate the high-temperature behavior of a two-parameter deformed quantum group fermionic gas with GL_p,q(2) symmetry, where (p,q)C×C. We then discuss both the structural and thermodynamical differences between GL_p,q(2)- and SU_r(2)-fermions with r=p/q where (p,q)R×R.     

On Reflection Subgroups of Finite Coxeter Groups

Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.     

具有不同渗透的涨缩管道内微极性流动的同伦分析解

分析了壁面具有不同渗透的涨缩管道内微极性流体的流动．对于壁面的胀缩,考虑常系数和时间函数的膨胀率两种情况．对于第1种情况,应用同伦分析方法得到该问题的速度和微旋转角度的表达式．并且画图分析了各个不同参数,特别是膨胀系数和不同的渗透率对流体的动力特征的影响．可以得到第1个重要的结论:壁面的膨胀率和不同的渗透对流体的动力特征有重要的影响．根据Xu的模型,考虑了第2种也是更具有一般性的情况,假设壁面的膨胀率随时间的变化而变化．在这样的假设下,控制方程被转化成非线性偏微分方程,并且同样也可以应用HAM方法进行求解．应用代数和指数的模型来描述膨胀率从初始状态到最终状态的演变过程．然而,结果表明包含有时间的解很快地趋向于稳态的解．这样可以得到第2个重要的结论,时间在壁面的膨胀收缩中扮演着次要的角色,可以忽略不计．