Entropy and escape of mass for SL<Subscript>3</Subscript>(ℤ)\ SL<Subscript>3</Subscript>(ℝ)

We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices.     

Quinazolines X. Synthesis of 6,6'-methylenebisdeoxyvasicinone and its homologs

Summary 6,6-Methylenebisdeoxyvacisinone and its homologs have been synthesized by the reaction of methylenebisanthranilic acid with lactams (-butyrolactam, -valerolactam, -caprolactam, and -chloro- and ,-dichloro--caprolactams). The condensation of anthranilic acid and its derivatives (4-nitro-, 5-bromo-, 5-iodo-, and 5-nitroanthranilic acids) with ,-dichloro--caprolactam has given seven-membered analogs of deoxyvasicinone containing two chlorine atoms in the polymethylene ring.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 544–547, July–August, 1977.     

Addition of tetrahydrofuran to unsaturated acids

The corresponding tetrahydrofurancarboxylic acids were obtained in yields of 25 to 33% by the addition of tetrahydrofuran to acrylic, methacrylic, allylacetic, and undecylenic acids in the presence of tert-butyl peroxide at 200–300 deg C under pressure.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 147–149, February, 1971.