On concepts of directional differentiability

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of -directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.     

四（五氟化苯基）卟啉氯化铁选择催化氧化超临界丙烷的反应机理

 以BHT为自由基捕捉剂，研究了四（五氟化苯基）卟啉氯化铁（Ⅲ）将超临界丙烷高选择性催化氧化为丙醇的反应机理．通过GC－MS分析发现，反应产物中有PBHT，故可认为在超临界丙烷氧化反应过程中有丙基自由基存在，初步推断反应涉及自由基机理．同时发现高浓度BHT抑制反应，低浓度BHT促进反应的现象，而以戊烷为底物时没有促进作用．这是由于BHT的位阻效应所致．并对BHT存在时超临界丙烷氧化反应机理进行了初步的推断．     

Composition catalysts of ethylbenzene oxidation based on bis(acetylacetonato)nickel(ii) and phase transfer catalysts as ligands 1. Macrocyclic polyethers

The addition of the macrocyclic polyether 18-Crown-6 (18C6) increases the selectivity of oxidation of ethylbenzene to -phenylethylhydroperoxide (PEH) in the presence of Ni(acac)₂. The initial oxidation rate, selectivity and degree of conversion of ethylbenzene to PEH are greater than those catalyzed by Ni(acac)₂ only. The efficiency of the macrocyclic ligand as an activator of Ni(acac)₂ exceeds that of monodentate donor ligands. The high selectivity of the process is due to both the primary Ni(acac)₂ · 18C6 complexes and the products of their transformation in the course of oxidation. The mechanism of ethylbenzene oxidation catalyzed by Ni(acac)₂ · 18C6 complexes is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1406–1411, August, 1994.     

Tree-gel and loop-gel conversions in nonlinear polymerization

Ａｓｉｓｗｅｌｌｋｎｏｗｎ,ｔｈｅｔｈｅｏｒｙｆｏｒｎｏｎｌｉｎｅａｒｐｏｌｙｍｅｒｉｚａｔｉｏｎｓｗａｓｉｎｉｔｉａｔｅｄｂｙＦｌｏｒｙａｎｄＳｔｏｃｋｍａｙｅｒ[1—3].ＭｉｌｌｅｒａｎｄＭａｃｏｓｋｏ[4—6]ｐｒｏｐｏｓｅｄａｒｅｃｕｒｓｉｖｅｍｅｔｈｏｄｆｏｒｄｅａｌｉｎｇｗｉｔｈｔｈｅｐｒｏｂｌｅｍｏｆｔｈｅｐｏｓｔｇｅｌｐｒｏｐｅｒｔｉｅｓｏｆｔｈｅｎｅｔｗｏｒｋｆｏｒｍｉｎｇｐｏｌｙｍｅｒｉｚａｔｉｏｎ.Ｓｔｅｐｔｏ[7]ｉｎｖｅｓｔｉｇａｔｅｄｔｈｅｇｅｌｇｅｌｒｅａｃｔｉｏｎｏｆＲＡｆｔ…     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

A density functional study on a biomimetic non-heme iron catalyst: insights into alkane hydroxylation by a formally HO-FeV=O oxidant

The reactivity of [HO-(tpa)Fe(V)=O] (TPA=tris(2-pyridylmethyl)amine), derived from O-O bond heterolysis of its [H(2)O-(tpa)Fe(III)-OOH] precursor, was explored by means of hybrid density functional theory. The mechanism for alkane hydroxylation by the high-valent iron-oxo species invoked as an intermediate in Fe(tpa)/H(2)O(2) catalysis was investigated. Hydroxylation of methane and propane by HO-Fe(V)=O was studied by following the rebound mechanism associated with the heme center of cytochrome P450, and it is demonstrated that this species is capable of stereospecific alkane hydroxylation. The mechanism proposed for alkane hydroxylation by HO-Fe(V)=O accounts for the experimentally observed incorporation of solvent water into the products. An investigation of the possible hydroxylation of acetonitrile (i.e., the solvent used in the experiments) shows that the activation energy for hydrogen-atom abstraction by HO-Fe(V)=O is rather high and, in fact, rather similar to that of methane, despite the similarity of the H-CH(2)CN bond strength to that of the secondary C-H bond in propane. This result indicates that the kinetics of hydrogen-atom abstraction are strongly affected by the cyano group and rationalizes the lack of experimental evidence for solvent hydroxylation in competition with that of substrates such as cyclohexane.     

A Novel Environmentally Benign Method for the Selective Oxidation of Alcohols to Aldehydes and Ketones

In the presence of [Ru(terpyridine)(2,6‐pyridinedicarboxylate)], aliphatic and benzylic alcohols are oxidized to the corresponding aldehydes or ketones with high selectivity by using hydrogen peroxide as the oxidant. There is no need for the addition of co‐catalysts or organic solvents. By applying an optimized reaction protocol, high catalyst productivity (turnover number>10 000) and activity (turnover frequency up to 14 800 h^?1) has been achieved.     

A simple direct enzyme immunoassay of antibodies based on the differences in diffusion rates in a gel of a synthetic antigen and of its complex with antibodies

A simple direct enzyme immunoassay for semiquantitative detec tion of antibodies is suggested. It is based on the difference in diffusion rates in a gel for a synthetic low-mol-wt antigen and of its complexes with antibodies to be detected. Sensitivity and specificity of the devel oped assay are equal to an ELISA method. The assay has been tested with antibodies against HIV protein gp41 in rabbit serum. Possible applications and limitations of the method are discussed.