Asymmetric reduction of acetophenone and propiophenone by NaAl(IPTOLate)H2 combined with enantiomeric enrichment of the reaction product as an inclusion complex with IPTOL

An improved procedure was developed for asymmetric reduction of acetophenone and propiophenone by the chiral reagent NaAl(IPTOLate)H₂. This procedure is based on isolation of the chiral alcohol that formed as a crystalline host—guest complex with the IPTOL ligand. The enantiomeric enrichment of the product was as high as 97% ee. The ability of IPTOL and its analogs to form host—guest complexes with a number of ether-type solvents, 1-phenylethanol, and 1-phenylpropan-1-ol as well as thermal stabilities of IPTOL-containing complexes with these alcohols were studied.     

Synthesis of trialkylaluminum derivatives by the reaction of non-solvated aluminum hydride with α-olefins

Hydroalumination of -olefins by non-solvated polymeric aluminum hydride (AlH₃) _n occurs at 120—140 °C. Mechanochemical activation accelerates this reaction. The addition of catalytic amounts of the prepared R₃Al forms to the reaction system decreases the temperature of the process to 90—100 °C. The greatest initiation effect is observed when ate-complexes of the MAlR₄ type (M = Li, Na) are used: the reaction occurs with a higher rate already at 60—90 °C affording R₃Al free of admixtures of carbalumination products and dimers of -olefins.     

Oxiranyl β-Aminovinyl Ketones. 7. Synthesis of 5-Hydroxy-3-(1-oxo-2,3-epoxyalkyl)benzofurans

5-Hydroxy-3-(1-oxo-2,3-epoxyalkyl)benzofurans were obtained with yields of up to 81% by the reaction of p-benzoquinone with oxiranyl -dimethylaminovinyl ketones in acetic acid.     

Calculation of Families of Stationary Filtration Convection Regimes in a Narrow Container

A plane Darcy filtration convection problem for rectangular containers elongated in the vertical direction is considered. By the spectraldifference method, which preserved cosymmetry of the initial problem, evolution of families of stationary regimes from the onset of instability on the primary family till the collision of the families is studied.     

Uniform Continuity of a Family of Weakly Regular Set Functions on Topological Spaces

Conditions for the uniform continuity of a family of weakly regular set functions defined on an algebra of subsets of a -topological space (T,) and taking values in an arbitrary topological space are found.     

On Fučik Spectra and Periodic Solutions

In this paper, we continue extending the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand side. To this end, we construct a new version of the method of shifts along trajectories. We compare the results obtained by the new approach and those obtained by the method of Fuik spectra.     

On Cesàro Means of Double Trigonometric Fourier Series

Zhizhiashvili studied questions associated with the approximation properties of Cesàro means of trigonometric Fourier series for functions of two variables in the spaces H. It is proved here that the corresponding estimate cannot be improved for p = 1 or p = .     

Iterated monoidal categories

We develop a notion of an n-fold monoidal category and show that it corresponds in a precise way to the notion of an n-fold loop space. Specifically, the group completion of the nerve of such a category is an n-fold loop space, and free n-fold monoidal categories give rise to a finite simplicial operad of the same homotopy type as the classical little cubes operad used to parametrize the higher H-space structure of an n-fold loop space. We also show directly that this operad has the same homotopy type as the n-th Smith filtration of the Barratt-Eccles operad and the n-th filtration of Berger's complete graph operad. Moreover, this operad contains an equivalent preoperad which gives rise to Milgram's small model for when n=2 and is very closely related to Milgram's model of for n>2.     

Completion of Linearly Ordered Metabelian Groups

We prove a theorem saying that in finitely generated linearly ordered metabelian groups there exists a finite system of normal convex subgroups satisfying orderability conditions for groups, and an embedding theorem for linearly ordered metabelian groups whose initial linear orders extend to -divisible linearly ordered metabelian ones. As a consequence, it is stated that orderable metabelian groups are embedded, with extension of all their linear orders, in -divisible orderable metabelian groups.