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.     

Disintegration and perfectness of measure spaces

For every finite measure space (X,A,P) we find a unique representation P=Q₁+Q₂+Q₃ such that Q₁ is compact, Q₂ is perfect and purely noncompact and Q₃ is purely nonperfect. We show that every Pachl-_O-disintegrable probability space is Ramachandran-_O-disintegrable and therefore perfect and under a certain condition we prove the equivalence between compactness and Ramachandran-_O-disintegrability.     

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let ( _t ) _t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent ₀ is the Haar measure on some compact subgroupK. Then all the measures ₁ are supported by theK-contraction groupC _K() of the topological automorphism ofG. We prove here the structure theoremC _K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.     

Unprecedented intermolecular aldol-type condensation involving CH-acid and the nitro group

The first evidence that α-acylnitrone is an intermediate in the base-promoted reaction of 4-nitro-N,N-diethylaniline with aceptophenome to give an enaminoketone was obtained. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1645–1647, August, 1998.     

N-Amino Derivatives of Condensed Imidazole Systems

The previously unknown 1-amino- and 3-aminonaphtho[1,2-d]imidazoles, 1-aminonaphtho[2,3-d]imidazole, 1-aminophenanthro[9,10-d]imidazole and the N-amino-N'-methylimidazolium picrates corresponding to them have been obtained by direct amination of a series of condensed imidazoles with O-picrylhydroxylamine. An X-ray structural investigation of 1-amino-3-methylnaphtho[1,2-d]imidazolium picrate showed that, in difference to 1-aminobenzimidazolium salts, a conformation exists in it in which the hydrogen atoms of the N-NH₂ group are directed to the side of the meso carbon atom.     

Production of submicron-size monodisperse polymer particles having aldehyde groups by seeded aldol condensation polymerization

Submicron-size monodisperse polystyrene/polyglutaraldehyde composite particles having aldehyde groups at the surfaces were produced by seeded aldol condensation polymerization of glutaraldehyde in the presence of polystyrene particles prepared by emulsifier-free emulsion polymerization. This technique is expected to be useful for the production of size-controlled polymer particles having aldehyde groups.Part CXXXVI of the series Studies on Suspension and Emulsion     

Excess enthalpies of aqueous ternary solutions of urea and polyols at 25°C

The heats of dilution of nine ternary solutions of urea and polyols have been determined at 25°C. Excess enthalpies and their virial coefficients h _xy have been evaluated and compared with the data reported in the literature for mono- and polyfunctional alcohols and other oxygenated nonelectrolytes. The group additivity approach of Savage and Wood was applied and the contributions to the enthalpy coefficients, due to the water mediated interactions between urea and the functional groups –CH₂–, –OH, and –O– were determined. On the other hand, by using empirical combination rules among the cross- and self-enthalpic interaction coefficients it is possible to emphasize the large differences in the behavior (even in the presence of urea) of the polyols (and in particular of cyclitols) and of saccharides.     

Preparation of polysiloxane stationary phases for capillary column chromatography: A New methoxyphenyl phase

Contemporary methods for the synthesis of alkyl- and arylsubstituted polysiloxane stationary phases are reviewed. A new, moderately polar phase containing the 3-(4-methoxyphenyl)-propyl group is reported.     

含二氧杂环异黄酮的合成

本文报道含有3', 4'-亚甲二氧基, 3', 4'-亚乙二氧基, 3, 4'-三亚甲二氧基的异黄酮类化合物的合成, 所得25个新化合物的结构经元素分析、^1H NMR谱确证; 紫外光谱表明有异黄酮特征吸收。文中并对反应机理进行了探讨。