SCIENTIFIC ABSTRACT RYBIN, N.G. - RYBIN, S.N.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001446410007-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: January 3, 2017
• Document Release Date: June 21, 2000
• Sequence Number: 7
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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TSTSI, P.N.; KAIXSNIK. S.V.; SOKOLOV, 11.1%; CHOCHIA, II.S.; PROTOPOPOV, A.P.;
ZABELIN, I.M.; GVOZIMTSKIY, N.A.; YEMMOV, Tu.L-, KARA-MOSKO, A.S.;
KOZLOV, I.V.: SOLNTSEV, N.A.; ISACEMITKO, A.G.; ARMAND, D.L.;
MIROSHITICE[EITKO, V.P.: PETROV, T-M.; KAZAKOVL, O.Y.; YILUYLOV, N.I.;
PARMUZIN, Yu.P.; GERENCRUK, K.I.; MILIEDV. F.N.; TAIRASOV, F.V.;
NIKOLAYEV, V.N.; SOBOIEV, L.N.; RYBIN, N.N.; DUMIN, B.Ya.; IGNATIYEV,
G.R.; ~MLIKHEYEV, M.N.; SANEBLIBGZE, U. S.; VASILIYEVA, I.V.;
PEREVALOV, V.A.; RASALIKAS, A.B.
Discussion at the conference on studying land forms. Nauk. zap. Llviv.
un,,4o:2 1-267 '57. (MIRA 11:6)
1. vovagy gosudarstvennyy universitet (for TSys', Gerencliuk, Dumin).
2.Laboratoriya aerometodov AN SSSR, Leningrad (for Sokolov,
Miroshnichenko, Petrov)..3.Institut geografii A14 SSSR, Mskva (for
Armand, Sobolev). 4.Gosudarstvennyy universitet, Voronezh (for Millkov,
Tarasov). 5.Leningradakiy gosudarstvennyy universitet (for Chochia,
Isachenko, Kazakova). 6.Komissiya okhrany prirody AN SSSR, Moskva (for
Protopopov). 7.Gosudarstvennyy universitet, Chernovtsy (for Rybin).
8.Gosudarstvennyy universitet, Irkutsk (for Melfk-heyev) ' 9.Go-
sudarstvennyy pedagogicheakiy institut im. V.I. Lenina, Moskva (for
Vasillyeva). 10.Bollshaya Sovetskaya Zntsiklopediya (for Zabelin).
ll.Gosudarstvennyy universitet, Tbilisi (for Saneblidze). 12.Moskovskiy,
gosudarstvenny3r universitet (for Gvozdetskiy, Solntsev, Mikhaylov,
Parmuzin, Nikolayev, Ignatlyev). 13.Torgovo-ekonomicheskiy institut,
Lfvnv (for Perevalov). 14.Gosudarstvannyy institut im. Kapsukasa,,
VilInyus (for Basalikas). 15.Muzey zemlevedeniya Moskovskogo go-
sudarstvennogo universiteta (for Tefremov, Kozlov). 16.Sreduyaya shkola
No-13, Kiyev (for Kara-Mosko). (Physical geography)

Y F,
AUTHOR% Rybin, P.P.
-----------
TITLE i On the Convergence of Series Obtained in Solving Non-Linear
integral Equations (0 ekbodImstj ryadav, poluchaysmykh pri
reshenii nelineynykh intograllnykh uravnoniy)
PERIODICAL& Doklady Akademii Nauk SSSR, 19571 Volt 115, Nr 3# Pp. 458 461
(USSR)
ABSTRAM This paper examines the nonlinear integral equation
(X) K(x, y. 99(y), A )dy. The function K(x9 YIY 1A
be continuous with regard to'all variables as well as analytical
with regard to and The representation
K(X1 Ys ?:0 A A, (x, Y) 9),1 withlItj(x, y)j< Bj~
ZT.
shall be valid and the functions A (x, Y) shall be oontinuous.
00
The aerieISIB(I ).-,7 B ij A' . shall converge at
ever A (XY Y) w 0shall apply. The
Card 1/3 author giv a general principles on the convergence ofthe,

2Q.A*
9/59
On the Convergence of Series Obtained in Solving Won-Linear Integral Equations
2
formal solutions (X) (X) + A of the
4 2 (X) +
equation P (X) K(xg y, (y)9 )dy. A camplicatlon
occurs only when the number I is an sigenvalue of the linear,
4
integral operator A103?(x)
I (XI 7) P (y)dy. The corre-
'
Imination of the fuzations
sponding equation for the dete (X)
has the fo rm, i 'A 10 (XIy) ?i (y) dy + N, (Z ty 9(Y) I
I(y))dy. When the condition of orthogonality is
;a 'fied, the ith equation
of the just given form has a solu-
tion 8f the form 91i(x) ~- 10(x) + cip(x). In this connection
is a known function n P(X) is the eigenfunction, cor-
relghding to the sigenvalue It of the nucleus A, (x,y). The
two theorems here given stato.the followinge A foo 1 selutio
rma n
(x) of the initially written integral equation be possible
the form.of th; series T(x) 11y, (x) +A2 T2(x) . .....
and the process o the definition of 1h@ functions Ti(x) shall
stabilize it lf Then th series uniformly converges with re-
g&Td to where is a cer-
x 6710t oil I / A 1< I
Card 2/3 tain positive numfeir, This aefies is then the actual solution

17
16(1) 06316
AUTHCa.-- Rybin,P.P. SOV/140-59-6-17/29
TITLE: On a Formula in.the Method of Nekrasov-Nazarov
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy. Matematika,,1959,
Nr 6, pp 131-137 (USSR)
ABSTRACT: According to the Academicians A.I.Nekrasov and N.N.Nazarov,the
solution.of the non-linear integral equation
1
U(X) (x,s)u(s)d s+ (x,s)ds Ai~(xps)v iuj(s)ds'
+01 + 10 +1 i+j), 2-
0 0 0
where v is a small parameter, A (X,3) are continuous functions,
can be obtained by the series arrangement
(4) UW viui(x).
But if 1 is an eigenvalue of A then the determination of the
01
functions u.(x) raiqes difficulties which partially are put
Card 1/2

c6316
On a Formula in the Method of Nekrasov-Nazarov SOV140-59-6-17/29
aside by V.V.Pokornyy Z Ref 3-7. Here it is essentialto obtain
an effective system for the determination of the constants of
integration. Such a system was already given by the author
L Ref 4__,7. The present paper contains a general result for this
problem.
There are 6 references, 5 of which are Soviet, and 1 German.
ASSOCIATION:Irkutskiy gorno-metallurgicheskiy institut (Irkutsk Mining-
Metallurgical Institute)
SUBMITTED: June 13, 1958
~Card 2/2

84756
S/042/60/015/004/014/017XX
/4,-2100 C111/C222
AUTHORS: Pokornyy, V.V., and.Rybin, P.P.
TITLE-, On the Stabilization of-the Process-of Finding Formal-!~Lplicit
FU action
PERIODICAL: Uspekhi triatematiche8kikh nauk, 1960, Vol-15, No-4, pp.169-172
TEXT: Let the function ac. OL(X) be defined by the equation
k 1
F(ce-p Tkl!' 0.
k+l~/l
Substituting 00 k
(2) (e 0e, 0-Ir (s. >11)
k-m I
in (1) 4e
P T -W- k 22
k1 ~~, ~ Z
k+l;0 1 n-1
then "Yk and s can be determined from the conditions
(3) P o.
n
Card 1/3

84756
W042/60/015/004/014/017XX
C111[C222
On the Stabilization of the Process.of..Finding Formal Implicit Functions
For a successive determination of the-coeffIcients ock from the system (3)
it was observed-that, beginning with a certain number no, all. equations. (3)
are linear with respect to c4, and at ca- they have the same coefficient
n n
different from zero. M.A,Krasnosellskiy.denoted this phenomenon as
stabilization"..The.authors-prove that this phenomenon always appears.
for the mentioned process, namely.at the latest if in the sequence iT 01
there Iappears the first coefficient different from zero.
-Let A kl (x,y) be continuous, small parameter.
Theorem 3:~For the equation.
(6) (x) fA (X Y) LP (Y) dy+~L c,y)dy+ Ak, (X, Y f'P (y)]
10 JA010 I
0 0 0
the determination of the coefficients %,Ok(x) of the solution arrangement
Card 2/3

22834
S/199/61/002/001/005/008
B1 1 2/B21 8
AUTHOR: Rybin, P. P.
TITLE, Construction of solutions of nonlinear integral equations in
the form of a Laurent series
PERIODICAL: Sibirskiy matematicheskiy zhurnal, v. 2, no. 1, 196-1, 127-128
TEXT' Integral equations of.the form T(x) I~kjA (X'S) T1(s) ds-
I i I j>0 ij
0
Wi+h f IA. (x,S)Ids< oo and continuous kernels A have small solutions for
0 ~ ij
a small X, which vanish for X --3~ 0 , and great solutions which tend to o0for
X ---~ 0. According to V. V.,Pokornyy, the small.solutions can be expanded inX
series of the form:
00
X,X) X /s if the number is not at all, or at,
T( - k( )X
k=o
least a single eigenvalue of the kernel A (x,s). Of the great solutionst
10
it is known that in their expansion in,a series of X also a finite number
Card 1/3

22834
S/199/61/002/001/005/008
Construction of ... B112/B218
of negative powers may occur,and that therefore the point X = 0 may be an
algebraic branch point or a pole.of finite order. M. A. Krasnosellskiy has
raised the questionvbether the point X = 0 may also be an essentially
singular point of the solutions In the present paper, the author prove's
that this question must be answered in the affirmative. For this proof he
uses the following nonlinear integral equation:
z(x) T(s)y (s) z(s) ds
2 n(s
+ A T(S)1111 (S)dS + 'Yi rdn (s)z )d where a n (s) bn (s)/n!p n5
k for k