Synthesis of derivatives of 4,5-dihydrofuran,furan, and hexahydrobenzofuran from conjugated alkenynes

The regiochemistry of the reaction of 1,2- and 1-substituted derivatives of 1-buten-3-yne and its 4- and 2,4-substituted derivatives of the isoprenoid type with acetoacetic ester and acetylacetone in the presence of the manganese(III) acetate-copper(II) acetate oxidative system was studied. Derivatives of 4,5-dihydrofuran, furan, and hexahydrobenzofuran were obtained.Communication 137 from the series Reactions of unsaturated compounds. See [1] for communication 136.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 24, No. 3, pp. 317–323, March, 1988.     

On Coverings of Tori with Cubes

Doklady Mathematics - We obtain new bounds and exact values of the minimum number of cubes with side length $$\varepsilon \in (0,\;1)$$ covering the torus...     

Rearranged series by Haar system

For the orthonormal Haar system {X _n} the paper proves that for each 0 < ? < 1 there exist a measurable set E ? [0, 1] with measure | E | > 1 ? ? and a series of the form Σ _n=1 ^∞ a _n X _n with a _i ↘ 0, such that for every function f ∈ L ¹(0, 1) one can find a function \(\tilde f\) ∈ L ¹(0, 1) coinciding with f on E, and a series of the form

$\sum\limits_{i = 1}^\infty {\delta _i a_i \chi _i } where \delta _i = 0 or 1$

, that would converge to \(\tilde f\) in L ¹(0, 1).

     

Boundedness and stability criteria for linear ordinary differential equations of the second order

We establish some correlations for solutions of ordinary differential equations and the imaginary part of the complex solution of the corresponding Riccati equation. On the basis of these correlations and the I. M. Sobol’ theorem we prove some new stability and boundedness criteria for linear equations of the second order.     

On compact quantum semigroup QS red

We study some properties of a reduced semigroup C*-algebra of a semigroup S. For the semigroup C*-algebra generated by the deformation of the algebra of continuous functions on a compact abelian group we obtain a structure of a compact quantum semigroup. We also consider morphisms of constructed compact quantum semigroups.     

Optical transmission spectra of a silicate glass containing nanocrystallites of cadmium sulphoselenide

The optical transmission spectra of CdSe _x S_1-x doped low viscosity silicate glass are experimentally studied. Glass samples were subjected to one- or multi-step heat treatment for different lengths of time. We have followed the modification of the absorption spectra after each heat treatment. The red shift of the absorption edge and the accompanying change of coloration from orange to red are explained by size-quantization effects in the energy spectrum of electrons and holes in semiconductor nanoparticles thermally developed in low viscosity glass matrix. X-ray diffraction data show no stoichiometry changes during the heat treatment processes. Crystallites composition ( ) defined from the diffraction peaks was very close to the value estimated from the position of absorption edge.Received: 14 March 2003, Published online: 9 September 2003PACS: 79.60.Jv Interfaces; heterostructures; nanostructures - 78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity) - 78.40.Fy Semiconductors     

The near infrared (0.8−2.6µm) absorption spectrum of a dense sodium vapor and possible mechanisms of the spectrum formation

The absorption coefficient of a dense sodium vapor (N₀ ～ 10¹⁷–10¹⁸ cm^{? 3}) in the near infrared spectral range (0.8–2.6 µm) was measured in a homogeneously heated isolated cell. In the range of parameters studied, the sample exhibits significant absorption. Neither the observed spectral features nor the measured absorption coefficients can be explained using the existing notions of the possible absorption mechanisms (absorption due to a forbidden intercombination transition, collision-induced processes, the trimer vapor component, and many-particle effects) and the available data.     

Hydrocarbalkoxylation of cyclohexene and carbalkoxylation of cyclohexanol with formic esters

Conclusions Mixtures of the esters of the 1-methylcyclopentanecarboxylic and cyclohexanecarboxylic acids were obtained in a 48 ratio by the hydrocarbalkoxylation of cyclohexene and the carbalkoxylation of cyclohexanol with alkyl formates at atmospheric pressures and temperatures of 10–30° in the presence of acids.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 704–705, March, 1973.