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 MATHEMATICS A mixed problem for equation $\psi_{\sigma\sigma}-K(\sigma)\psi_{\theta\theta}=0$ with Cauchy data given on curve $\theta=s(\sigma)$R. G. Barantsev 919 Some estimates from the tabulation theoryA. G. Vitushkin 923 On the closest uniform approximation of polynomialsE. V. Voronovskaya 927 Approximation of certain classes of continuous functions by Fourier sums and Fejer meansA. V. Efimov 930 Solution by the Fourier method of non-self-adjoint mixed problems for hyperbolic systems on a planeV. F. Zhdanovich 934 Imbedding theorems for a space having its metric degenerating at a finite number of internal points within a bounded domainV. K. Zakharov 938 An investigation of the stability problem for systems of equation with homogeneous righthand membersV. I. Zubov 942 The use of the method of moments and the “mixed” method for an approximate solution of singular integral equationsV. V. Ivanov 945 On the asymptotic behaviour of solutions of linear difference equations and linear differential equationsP. I. Koval' 949 On the representation of continuous functions of many variables by superposition of continuous functions of one variable and additionA. N. Kolmogorov 953 Degeneration on passing from a discrete spectrum to a continuous one and transition from quantum mechanics to classical mechanicsV. P. Maslov 957 On a class of continuous mappings of some $\infty$-dimensional setsS. S. Ryshkov 961 HYDRAULICS Percolation of water in peat, studied by means of radioactive isotopesM. P. Volarovich, N. V. Churaev, B. Ya. Minkov 964 THEORY OF ELASTICITY On the non-linear theory of thin platesN. F. Morozov 968 PHYSICS An experimental investigation of highly elastic polymere specimens for relation between the rate of their rupture process and rate of deformationV. E. Gul', G. P. Krutetskaya 973 Zinc borate phosphors and their luminescent propertiesYu. S. Leonov 976 The dependence of the emission frequency of shower particles on the atomic number of the split nucleusZh. S. Takibaev 980 On the pulsation of plasma in a cylinderA. G. Kulikovskii 984 The oscillations of an infinite self-gravitating gas cylinder in the presence of a magnetic fieldI. M. Yavorskaya 988 CHEMISTRY The synthesis of polyorganoaluminium siloxanes. Exchange decomposition reaction between sodium salts of alkylsilantriols and aluminium chlorideK. A. Andrianov, A. A. Zhdanov 1005 The principles of the chemistry of enzymes and antimetabolites from the standpoint of the theory of catalysisA. A. Balandin 1008 On the precipitation of halite in Karabogaz-GolYa. B. Blyumberg 1012 On the antituberculous activity of thiosulphonic acid ethersB. G. Boldyrev, T. S. Ginzburg, R. O. Drabkina 1014 Cleavage of pyridine bases, mechanism of reactionA. F. Vompe, N. F. Turitsyna 1017 Association states of selenium in the gas phaseV. V. Illarionov, L. M. Lapina 1021 The action of inogranic acid chlorides on arylsulphonic acids. A general method for the production of anhydrides from a reaction of arylsulphonic acids with $\mathrm{P}_2\mathrm{O}_5$V. O. Lukashevich 1025 The synthesis of geranylacetone, 3-methylgeranylacetone pseudoionone and pseudoironeI. N. Nazarov, L. A. Yanovskaya, B. P. Gusev, S. M. Makin, I. I. Nazarova 1029 New halogen containing organoaluminiumsilicic compounds of the $\mathrm{R}_3\mathrm{SiOAl}\mathrm{X}_2$ typeN. F. Orlov 1033 The synthesis of pyrroles, pyrrolines and pyrrolidines from $\gamma$-ketoalcoholsA. P. Terent'ev, M. A. Volodina, N. L. Podlesova, N. E. Golubeva 1036 Convertion of levoglucosan into aromatic compoundsN. N. Shorygina, G. V. Perfilova 1040 PHYSICAL CHEMISTRY Absorption spectra of certain dyes in mixed solventsKh. L. Arvan, N. V. Ivanova 1043 The investigation of the process of exchange $\mathrm{Zn}\rightleftarrows\mathrm{Zn}^{++}$ on the facets of a zinc monocrystall by the method of radioactive indicatorsB. N. Bushmanov, G. S. Vozdvizhenskiii 1046 Use of labelled atoms in studying the mechanism of the anodic liberation of oxygenM. A. Gerovich, R. I. Kaganovich, V. A. Vergelesov, L. N. Gorokhov 1049 The behaviour of thermosetting plasticsI. F. Kanavets, L. G. Batalova 1053 The mechanism and isotopic effect of the primary act in the thermal decomposition of chloroformA. E. Shilov, R. D. Sabirova 1058 Ïîïðàâêè ê ñòàòüå “Øòàìï, ëåæàùèé íà óïðóãîì ïîëóïðîñòðàíñòâå, ìîäóëü óïðóãîñòè êîòîðîãî ÿâëÿåòñÿ ñòåïåííîé ôóíêöèåé ãëóáèíû” (ÄÀÍ. ò. 112, № 5, 1957 ã.)B. G. Korenev