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1957, Volume 113, Number 1  


MATHEMATICS
On the problem of periodical solutions of non-linear systems with a small parameter
I. Berstein
9
On a problem raised by N. N. Lusin
Yu. A. Brudnyi, I. E. Gopengauz
12
The matrix elements of irreducible unitary representations of the group of real orthogonal matrices and group of Euclidean $(n-1)$-dimensional space motions
N. Ya. Vilenkin
16
Systems of singular integral convolution equations
R. Kh. Zaripov
20
Solution of a certain class of singular integral equations with line integrals
E. I. Kim
24
Conditions for a complete continuity of the resolvent of a differential operator
V. B. Lidskii
28
Some Tauberian theorems for generalized Fourier transformations
Yu. I. Lyubich
32
On sets of points where the derivative is $+\infty$ or $-\infty$ correspondingly
V. M. Tsodyks
36
On equivalency and transformations of program schemes
Yu. I. Yanov
39

MECHANICS
On a mechanical transformer
I. I. Artobolevsky
43
Some problems of dynamics of Moon flight
V. A. Yegorov
46
On the solution of Veriguin's problem
L. I. Rubinshtein
50
On a generalization of the deflection accumulation theory and its use for determining autooscillations in generators
G. M. Ulanov
54

FLUID MECHANICS
On the periodicity of a jet coming out of a symmetrical nozzle under rated conditions
G. A. Dombrovskii
58

ASTRONOMY
On the origin of meteoritic chondrules
B. Yu. Levin, G. L. Slonimskii
62

PHYSICS
Angular and energy distribution of fast photoprotons from $\mathrm{Ni}$ and $\mathrm{Al}$
E. B. Bazhanov, Yu. M. Volkov, A. P. Komar, L. A. Kulchitskii, V. P. Chizhov
65
The Fermi fields and spinors of a space of an infinite number of dimensions
Yu. A. Gol'fand
68
On the division of the cathode spot of an electric arc
I. G. Kesaev
71
The triple division of uranium on fast particles
N. A. Perfilov, V. P. Shamov, O. V. Lozhkin
75
The examination of the domain structure of a ferromagnetic by means of photoelectrons
G. V. Spivak, T. N. Dombrovskaya, N. N. Sedov
78

GEOPHYSICS
On certain factors influencing the rate of propagation of elastic vibrations in rocks
V. B. Sollogub, P. Ya. Galushko, A. A. Vopilkin, A. M. Patiokha
82
On extension of the theory of steady currents in a shallow sea to the case where the coefficient of vertical exchange is a variable
A. I. Felzenbaum
86

CHEMISTRY
Investigation of organic derivatives of selenic acid and telluric acid, as analytical reagents
I. P. Alimarin, V. S. Sotnikov
105
Electrolysis of $\mathrm{CaO}$$\mathrm{Al}_2\mathrm{O}_3$$\mathrm{SiO}_2$ melts
O. A. Esin, V. A. Chechulin
109
Reduction dimerization of derivatives of $\alpha$, $\beta$-unsaturated acids
I. L. Knuniants, N. S. Vyazankin
112
The interaction of benzylpyridinium chloride with cyclopentadienyllithium
D. N. Kursanov, N. K. Baranetskaya, V. N. Setkina
116
Thermal telomerization of trichlorosilane with ethylene
A. N. Nesmeyanov, R. Kh. Freidlina, E. Ts. Chukovskaya
120

PHYSICAL CHEMISTRY
The polymerization of 2,3-dimethylbutene-2, 2,3-dimethylbutene-1 and 3,3-dimethylbutene-1 at pressures up to 4000 atm
M. G. Gonikberg, V. M. Zhulin, V. T. Aleksanyan, Kh. E. Sterin
123
Surface tension of ternary metal solutions $\mathrm{Hg}$$\mathrm{Cd}$$\mathrm{K}$ at $22^\circ$
P. P. Pugaehevich, V. B. Lazarev
127
On the diffusion of active centres in the volume when there is a quadratic rupture of chains
Yu. S. Sayasov, N. S. Enikolopyan
130
Development of crystallization structures in tricalcium aluminate suspensions
E. E. Segalova, E. S. Solov'eva, P. A. Rebinder
134
Regularities in the capture of copper, antimony, lead, cobalt, iron and zinc admixtures by a cathode deposit of tin
V. L. Kheifets, E. S. Kozich, O. M. Danilovich
138

Поправки к статье В. С. Кирпичникова, А. Н. Световидова, А. С. Трошина, “Мечение карпа радиоактивными изотопами фосфора и кальция” (ДАН, т. 111, № 1, 1956 г.)
Поправки к статье “Упругое рассеяние $\gamma$-квантов с энергией до 120 Мэв протонами” (ДАН, т. 111, № 5, 1956 г.)
B. B. Govorkov, V. I. Gol'danskiĭ, O. A. Karpukhin, A. V. Kutsenko, V. V. Pavlovskaya
Поправки к статье “Зависимость сечений фотообразования $\pi^0$-мезонов от массовых чисел ядер” (ДАН, т. 112, № 1, 1957 г.)
B. B. Govorkov, V. I. Gol'danskiĭ, O. A. Karpukhin, V. V. Pavlovskaya, A. V. Kutsenko
 
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