On the 2-norm distance from a normal matrix to the set of matrices with a multiple zero eigenvalue

An elementary proof of a formula for the 2-norm distance from a normal matrix A to the set of matrices with a multiple zero eigenvalue is given. Earlier, the authors obtained this formula as an implication of a nontrivial result due to A. N. Malyshev. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 50–56.     

Structure of the new monoterpenoid liganolide

The structure of the new ester liganolide C₂₇H₃₈O₈, isolated from the roots ofLigularia thomsonii has been established by x-ray structural analysis. Liganolide is a monoterpenoid including a six-membered ring with substitutents at C(2), C(3), and C(4), and an epoxy group at C(1) and C(6).     

ESR determination of the rate constant for the addition of CpW(CO)3 to spin traps

Conclusions The reaction of [CpW(CO)₃]₂ with PhCH₂Cl and the decomposition of CpW(CO)₃Me were studied by ESR spectroscopy using 2,4,6-tri-tert-butyinitrobenzene (BNB) and -phenyl-N-tert-butylnitrone (PNB) as spin traps. The rate constants for the addition of CpW(CO)₃ radicals to the spin traps at 20°C were determined by identification of the intermediate radicals in these reactions: k _ad ^BNB =6.7·10⁵-7.0·10⁵ and k _ad ^PNB =5.8·10⁴-6.1·10⁴ liters/mole · sec.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2631–2633, November, 1984.     

The structure of the xylan from cotton-plant stems

Summary The results of a study of the products of the hydrolysis and oxidative cleavage according to Barry of cotton-plant-stem xylan has shown that its main chain consists of 14--L-anhydroxylopyranose units. Each elementary link of the xylan contains 6–7 xylopyranose units and has two side chains formed by residues of D-glucose and D-glucuronic acid, which are attached in position 2 or 3 of the xylose units of the main chain.V. I. Lenin Tashkent State University. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 305–308, May–June, 1973.     

Electronic structure and absorption spectra of dicarbonium ions containing bridging groups

The electronic structure and spectral characteristics of polymethines with the general formulas [CH₃-M-C₆H₄-(CH)_n-C₆H₄]⁺ X^– (C) and [R-C₆H₄-(CH)_n-C₆H₄-M-C₆H₄-(CH)_n-C₆H₄-R]²⁺ 2X^– (D) were investigated. The absorption spectra of the dicarbonium ions were treated in terms of the theory of intramolecular interaction of the chromophores. By analysis of the experimental data and calculated data, obtained by the PPP method, it was established that the long-wave splitting in compounds of type D increases in the series M= (CH₂)₂ CH₂, O, S, NCH₃, does not depend on the electronic symmetry of the parent compounds (C), decreases with increase in the length of the polymethine chain (n), and decreases with increase in the electrondonating characteristics of the substituents (R). The energy of intramolecular interaction of the chromophores is separated into dipole-dipole, resonance, and exchange components, a method is proposed for their quantitative assessment, and the effect of various structural factors on them is discussed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 4, pp. 419–427, July–August, 1988.     

Anatolii Dem'yanovich Kuntsevich (to his 60th birthday)

Anatolii Dem'yanovich Kuntsevich (to his 60th birthday)