Facile Carbon–Fluorine Bond Activation and Subsequent Functionalisation of 1,1‐Difluoroethylene and Tetrafluoroethylene Promoted by Adjacent Metal Centres

The bridging fluoroolefin ligands in the complexes [Ir₂(CH₃)(CO)₂(μ‐olefin)(dppm)₂][OTf] (olefin=tetrafluoroethylene, 1,1‐difluoroethylene; dppm=μ‐Ph₂PCH₂PPh₂; OTf^?=CF₃SO₃^?) are susceptible to facile fluoride ion abstraction. Both fluoroolefin complexes react with trimethylsilyltriflate (Me₃SiOTf) to give the corresponding fluorovinyl products by abstraction of a single fluoride ion. Although the trifluorovinyl ligand is bound to one metal, the monofluorovinyl group is bridging, bound to one metal through carbon and to the other metal through a dative bond from fluorine. Addition of two equivalents of Me₃SiOTf to the tetrafluoroethylene‐bridged species gives the difluorovinylidene‐bridged product [Ir₂(CH₃)(OTf)(CO)₂(μ‐OTf)(μ‐C?CF₂)(dppm)₂][OTf]. The 1,1‐difluoroethylene species is exceedingly reactive, reacting with water to give 2‐fluoropropene and [Ir₂(CO)₂(μ‐OH)(dppm)₂][OTf] and with carbon monoxide to give [Ir₂(CO)₃(μ‐κ¹:η²‐C?CCH₃)(dppm)₂][OTf] together with two equivalents of HF. The trifluorovinyl product [Ir₂(κ¹‐C₂F₃)(OTf)(CO)₂(μ‐H)(μ‐CH₂)(dppm)₂][OTf], obtained through single C? F bond activation of the tetrafluoroethylene‐bridged complex, reacts with H₂ to form trifluoroethylene, allowing the facile replacement of one fluorine in C₂F₄ with hydrogen.     

Three dimensional homogeneous Finsler manifolds

In this paper we study three dimensional homogeneous Finsler manifolds. We first obtain a complete list of the three‐dimensional homogeneous manifolds which admit invariant Finsler metrics. Then we consider invariant Randers metrics and present the classification of three dimensional homogeneous Randers spaces under isometrics.     

烟气脱硫活性炭微波再生特性的实验研究

研究了烟气脱硫活性炭的微波再生特性。通过扫描电镜、N₂吸附、元素分析、Boehm滴定表征微波再生对活性炭孔隙结构和表面化学性质的影响,分析微波再生对活性炭吸附烟气中SO₂的影响规律。结果表明,微波再生功率越高,SO₂再生曲线越窄,峰值浓度越高,有利于载硫活性炭的解吸和高浓度再生气的获取。微波再生对活性炭起到了活化作用,使活性炭的孔结构变狭长。随着微波再生功率的提高,活性炭的微孔比表面积、微孔孔容增加,酸性官能团含量上升,碱性官能团含量下降。100 W再生后,活性炭再生不完全,残留的H₂SO₄影响了活性炭的吸附,活性炭的SO₂吸附性能下降。200、300、400 W工况下,活性炭的SO₂吸附容量均得到提高,且随着再生功率的提高,活性炭的碱性官能团含量上升,微孔比表面积、微孔孔容增加,SO₂吸附性能逐渐增强。     

SO2和NO对ACF低温脱除模拟燃煤烟气中VOC的影响

采用H₂O₂浸渍的方法对活性炭纤维(ACF)进行改性,并利用氮吸附等温线和XPS(X-ray photoelectron spectroscopy)的方法对ACF样品进行表征。通过实验测定改性前后ACF脱除VOC(甲苯作为VOC的代表物)的效果,同时考察二氧化硫(SO₂)和一氧化氮(NO)对ACF脱除甲苯的影响。研究发现,双氧水浸渍改性对ACF的BET表面积和孔容没有影响,但使得ACF样品表面的含氧官能团含量大量增加。实验数据也表明,SO₂和NO对VOC在ACF上的吸附具有抑制作用,且随着两者浓度的增加,抑制作用也增强。 研究还发现,SO₂和NO同时存在比单一的SO₂或NO对VOC在ACF上吸附的抑制作用更为明显。     

临界群与二阶差分方程解的多重性

研究了一类二阶非线性差分方程两点边值问题解的多重性.当该问题的非线性项在无穷远点具有特殊的渐近线性性质时,利用变分方法,结合临界群与Morse理论,同时考虑正、负能量泛函的临界点,不论该问题是否发生共振,均证明了它至少存在两个非零解.     

Reduction of continuous symmetries of chaotic flows by the method of slices

We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a ‘slice’ defined by minimizing the distance to a single generic ‘template’ intersects the group orbit of every point in the full state space. Global symmetry reduction by a single slice is, however, not natural for a chaotic/ turbulent flow; it is better to cover the reduced state space by a set of slices, one for each dynamically prominent unstable pattern. Judiciously chosen, such tessellation eliminates the singular traversals of the inflection hyperplane that comes along with each slice, an artifact of using the templates local group linearization globally. We compute the jump in the reduced state space induced by crossing the inflection hyperplane. As an illustration of the method, we reduce the SO (2) symmetry of the complex Lorenz equations.     

Groups with the same order and degree pattern

The degree pattern of a finite group has been introduced in [18].A group M is called k-fold OD- characterizable if there exist exactly k non-isomorphic finite groups having the same order and degree pattern as M .In particular,a 1-fold OD-characterizable group is simply called OD-characterizable.It is shown that the alternating groups A m and A m+1 ,for m = 27,35,51,57,65,77,87,93 and 95,are OD-characterizable,while their automorphism groups are 3-fold OD-characterizable.It is also shown that the symmetric groups S m+2 ,for m = 7,13,19,23,31,37,43,47,53,61,67,73,79,83,89 and 97,are 3-fold OD-characterizable.From this,the following theorem is derived.Let m be a natural number such that m 100.Then one of the following holds: (a) if m = 10,then the alternating groups A m are OD-characterizable,while the symmetric groups S m are OD- characterizable or 3-fold OD-characterizable;(b) the alternating group A 10 is 2-fold OD-characterizable;(c) the symmetric group S 10 is 8-fold OD-characterizable.This theorem completes the study of OD-characterizability of the alternating and symmetric groups A m and S m of degree m 100.     

Reducibility of finite reflection groups

A finite (pseudo-)reflection group G naturally gives rise to a hyperplane arrangement,i.e.,its reflection arrangement.We show that G is reducible if and only if its reflection arrangement is reducible.     

Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties

A shallow water model on a rotating attracting sphere is proposed to describe large-scale motions of the gas in planetary atmospheres and of the liquid in the world ocean. The equations of the model coincide with the equations of gas-dynamic of a polytropic gas in the case of spherical gas motions on the surface of a rotating sphere. The range of applicability of the model is discussed, and the conservation of potential vorticity along the trajectories is proved. The equations of stationary shallow water motions are presented in the form of Bernoulli and potential vorticity integrals, which relate the liquid depth to the stream function. The simplest stationary solutions that describe the equilibrium state differing from the spherically symmetric state and the zonal flows along the parallels are found. It is demonstrated that the stationary equations of the model admit the infinitely dimensional Lie group of equivalence. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 24–36, March–April, 2009.