SCIENTIFIC ABSTRACT MERMAN, A. M. - MERONOV, V. F.

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• Collection: Scientific Abstracts
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• Document Creation Date: January 3, 2017
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• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

IORMaN. A.H.. kandidat meditsinskikh nauk (Moslcva); HIRONEUKO. I.S., glavnyy
Gastric sarcoma In a 15-year-old girl. Vest.rent.i rad. no-3:86-87 Ifq-Je
'53. NLRA 6:8)
1. Polikliatka imeni Dzerzhimakogo. (Stomach-Tumors)

MHRKM. A.M. kwAidat meditsinskikh nauk
Septic (metastatic) pneumonias following labor and abortions. Test.
rent. i rad. no.5:6&72 S-0 154. (KIRA 7:12)
1. Iz rentgenologichookogo kabineta (tav. kandidat meditainakikh
na*,A.M.Nerman) I septichaskogo otdeleniya (zav. dotsent S.B.
Rafalikes) rodillnogo dome, No.3 (glavny7 vrach V.K.Dashunina)
UMMONIA
metastatic, after labor abortion)
(ABORTWIT. complications
pneumonia, metastatici
(PUIRPZRMK. complications,
pneumonia, metastatic)

-W,RM9 A.M.9 kand.med.nauk.
-------
Leiomyosarcoma of the duodemm. Vest. rent. i rad. 35 no. 5:76-77
s-o l6o. (KM 13:12)
1. Iz Gorodskoy klinicheskoy bolinitsy No. 60 (glavnyy vrach
M.I. Kamnev).
(DUDODENUM-TUMORS)

WMN, A.M. (Moskva)
Close-focus I-ray therapy of'skir, tunors, Trudy TSentr. naucb.-
issl. inst. rentg. i rad. 11 no.1:252-259 164.
O%Ulbl 18:111,

IMMhli, G.A.
"New Class of Periodic Solutions in the Ldaited Hill Problem,"
Trudy In-ta teor. astr., No 1, 1952 (Works of bhe Inst. of Theoretical
Astronow).

1. VZWFUI~.-'N' G. A.
2. T713JR (6CO)
4. I'oon, Theory of
7. Convergence radius of I'lill's serica. L~iul. Inst. toor. ait-Dn. 5, 710. 41
1952.
9. Monthly List of Russian Accessions, Library of Congress, ~rlw -1953. Unclassified.

'USSR /Astronowi - Three-Body Problem 1 Aug 52
"A Criterion Governing the Realizability of
Hyperbolico-Elliptic Motion in the Three-Body
Problem' G.A. Merman, Inst of Theoretical Astr,
Aced Sci USSR
"Dok Ak Nauk SSSR" Vol 85, No 4, PP 727-730
Slaborates a criterion similar to the crite-
rion given in the works of G.F. Xhillmi in "Dok
Ak Nauk SSSRY Vol 78, No 4, 1951; "Problem of
A Bodies in Celestial Mechanics and Cosmogony,
1951, which criterion suggests a radial velo-
city so large that for a given total energy of
the system the relative motion of the masses
227T36
% and ml will be elliptical. Author states
he weakens somewhat some of limitations im-
posed on the radical velocity. Submitted by
Acad 0. Yu. Shmidt, 1 Apr 52,
227T36

G~ A-. 01a out 1, F. Wr "Ptlart-, M
k with c1 Se. 1 F/w.

approachm Akad. 1,,~ a
BYUIL

leg P& r. 4ubj~~t to -theic u I
kAven-three partk

Mcut,
hia we dilly- la wuro t--,ke-i: j-!acr aniang~ wo U.
11 the r-,tuaw-c
if (i)
whik~- the (Aer two
ank bounds ai%d NFI all mutual

'ar he ffi 'c ;z Mcrl~~ n c v -IS
t
s, - -ces be tween: t; imt~-~ pa~v Ir -s--i definit 1.
d
'
nlotioa). 0. CDOkladv Akad.
uk SSSR (N.S.) 53, ~ 213 1
1L!avc -th.- :fi~at
ekamtilc illugratins~ lite
h
a neral probtam ~ of tfim~, fiGd6' (agautntig thzt:t
An
h>0, 1, being tile wilstant )f C, r-rl"y.

..'a, IS the o:ictzlatiiig orbit of P, Vr,
Ith
to

"Chalw& from hyperbolic to elliptic whil14 the ori--, of the
it

9M

Werman,G.A. New criteria of hyperbolic and hyperbolic
--eMpffE-ffi a in the problem of three bodie kad
A
-339 (1953). (Russi .
Nauk SSSR. Astr. 2urnal 30 332 anj
J-
This paper is a continuation of an earlier paper by the
ad, Nauk SSSR (N.S.), 85 - 727-
same author [Doklady Ak.
730 (1952); these Rev. 14, 590]. New criteria of realizability

Mathe-matical Reviiiws
:and hyperbolic-elliptic motion in'the problem
of hyperbolic

'5 -~ go- 4 of three bodies are established. It is pointed out diat they
:~:-:AI)r* 1954, can be regarded is an improvement of the cri,~ria obtained

Astronomy- -Iii'mi
previously by the author. (loc. cit.) and G. F. I
, -s in mechanics and cosmogony, -it.
problem of is bodiL lzd,
Akad. Nauk SSSR, Moscow, 19S1] in the sense that the
velocities f,
restrictions imposed ill these papers on the radial
of the bodies
and their initial configuration are reinioved.:
'

ac red'that
InSte d it is mqui
the corresponding (Off VC10cities'.
be sufficiently large. The n~Nv criteria are too lengil y t t,-P--
reorodu~o herei They are applied to the example given by
'

:Na SS.1;R (N.S.) $3, 213-
0. Y uk
u. 9midt [Doklady Ak~d
216 (1947)] of illiiatrating the' ' ibilitv of a capture ill

t of thCW bodies.,
he problei~ Leimatg~!,,-.

r on c

17

ULM
u2m4 ~Tzbf ~'
WuTti
-6 1
A-4
'idt-r-ifie-t ot W11 a 1

of
f fiad p,-rticics P1 ard P,~
J. Cifm~ fAwl. SOL Nflm. :iop' (3 '19

dh~lc ill 01--gimcl 1, till "'e-hr"ly
V-130 (02-1,
'
.
-
of cw'l-gy) lvvp~-'~
- Q 111t.
nrobleni for h
bolic-dliptic filotio!l:; (fgle~ 0( the lFimc. mutual
rernains bmind-cd whiilc the other two di--'3r%CC.3 P;Cri~k'_SC L*I-
Al- 1- w w-A arkl~ d the -1-Zime of maggliltude
-IF 0-
-as t) or p~xabolic mfji i(m.'s (a .'rec nlutuai dismn';P_~~
7
crca~~ille m;telvast -Iicj areof '61 U$ t;

hyl, 1'. rl P. I.- -
lyff 1)0~'61DIII it d ara C, lc-,--i
c1liplic motio.m. are ImpvS~;1ble. YM-11 thiA it folluivs th-tit in
th'~ gezlerz-'! ptoblem for h=u-the probability of
apt 'CrO.
Sillck- rull flht~ Onf., ham!, fl-w r~'~;Lrictcj p"m'bolic probjeal of
thrce. brAiCs rfiv Iiwjtj'ng rji,5e oj flip threc-110fly

m f a Nvil-i one Hile, three 11111sici uppmachol
p
a thi~i fxic -Orl the okke"
zero, A capluv~ I
-
.7

'
hol"'t v
~c f 111,
,:sId-Lv
po W,fit: f-a

t he I OA 11 IVI-I lom ~h > 0) 0r a i C: Ii pse (A 0)

:11-proj" -,;-Zern. Tlv.st~ two limitin"j- CIsC5 '-hoi the possi-
v
,

UP t iv, -In~ltiu t
IC-An- th~,- nArited fabolic I
--k-,rm elal, U.
fwo-type:,'of n- m buinir UIMa-
IYO~L% )tA

--O)A I I
'i: p Yolk --if Ow if- Possible.
pal bodiL
.
it in-Okown in tile pkpcc tilIt AI dlc~ typ!-~ OE' 4rx"i'Al
me."'fic-ned "djove ill thio m~;trictedf parabolk problern arc!

1~, it' rertain
Ilich are too dt:t,-d!r-,d w bc re-

In many ft-ataj res il It III f~str

problein r ).1_7 .1 u- -it - 1 -y the at~,O---rr I
Bt
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5
~i
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Infp
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2
i
.-M

KWIAN, G. A.
New criterion of the 17-perbolic motion in the problem
of three bodies. Biul.Inst.teor.astron. 6 no.2:69-72
155. 04IRA 13:3)
(Problem of throe bodies)

MERMAN, G.A.
Hyperbolic approaching in the problem of three bodies.
Biul.Inst.toor.astron. 6 no-2:73-84 '55. (MIRA 13:3)
(Problem of three bodies)

MMAN. G.A.: KOCIIINA. N.G.
Applying the method of evaluations to O.IU.Shtaidt's
example. Blul.Inst.teor.astron. 6 no.2:85-111 155.
(14IIU. 13:3)
(Problem of three bodies)
777

124-1957-1-26
Translation from: Referativnyy zhurnal, Mekhanika, 1957, Nr 1, p 4 (USSR)
AUTHOR: Merman, G.A.
TITLE- On one of Birkhoff's Theorems (0b odnoy teoreme Birkgofa)
PERIODICAL: ByuJ. In-ta teor. astron. AN SSSR, 1956, Vol 6, Nr 4,
pp 232-239
ABSTRACT: It is shown that some of Birkhoff'7, theorems relating to
problems of the qualitative theory of motion of three bodies,
examined in his book "Dynamic Systems", must be stated more
specifically and require additional clarification. A detailed
proof is given of two of Birkhoff's theorems concerning the
problems of capture, and proof is offered for one corollary
derived from BirkhofPs theorems which is of value for the
qualitative theory of the problem,
G. N. Duboshin
1. Mathematics 2 Books--Revjew
Card 1/1

IRA
"Concerning one Method of Approxiration of the Solution of the
n Body Problem in Hatural Coordinates," by Yu. V. %landakurov,
by Ull. In-ta teor. astron. AN SSSR vol 6, No 4, 1956, pp 240-
243 (from Referativnyy /Zhurnal -- Mekbanika, No 1, Jan 57, Ab-
stract I-To 27, by G, A. Merman)
"Pro-ooses a method of approximate integration of equatior s of celes-
t1al mechanics under the condition that the solution of the two bodywcb-
lem is substituted into Dertubation functions and that only the firs.:
stage deviations of perturbed motion- from the unperturbed are considered.
The newness consists in the use of natural coordinates." (U)

RV
.
lirmjc

,
I
t
6
s
r.
fl
9~6) I

rdernum, G A Zu Arbeften voa~_ R - Vernie fiber' dip
'
~Rw
un
d -die ~ Oalo&schen L&fingaa
des
DiefUrperproblenis. 13vull. -Inst. __Teo~et,- ~.A_str.

IS.- (Rui~ia-n. German- sumn. a
(1956). 408A
'Verni6 , [Diskussion der Sundmans6en Usting -des
DreiUrperproblems,jugodav Ak-ad, Znan. Umid.,

'
-h
Il
Z
19S4
l
86
MR 16 867
ii
o
it
a
c
icorem
r,,,s O
c,
agr.
,:
. p.
1 c
;
,
-for the in t!
5) to have obtained tranusformations dependen

variable ich regulariU P~6ty e--, of collisions in_tlae ------- -
4
_p
ral 0 e author - show- -
that
_
WnuA6's Pra~,M de ective and that, whereas his theonom!
holds for rill binary collisions and far real triple collisions~_
-
-ill the
case 6fthe La&ang- inotions and in the base of.

A 6ther motions for-certain values of the masses-, it does not
hold for all r triple collisiOns,,and it,does not hold I'm-
e ollisiori.
Iry trip! c
ar'YZ
I
V

At r theorem of ~ Vernid fffrvathko Prirod. Drugtvo.
t
h
A
Galndk 114at -16
Fiz. AstT. Ser-.11. 8 (1953), 147-2.66- MR
her th
1811 or. the non-existence of periodic solutions at
-
I
n
th
the :Lagrangian solutions
o goneral three-body.

ro e ia also shown to be false-
-P bI m
'
The reviewer would like to point oul-that in the last

1, 1
differential p. 400 the factorl/k3-Is I ckringl
l
'a
l
=`o
ri F,,ht-band side, B.-Lehnanis,
in the first
e
Tth

V 4_1 4)

9_7_718j~'
S-OV/124-5
Translation from; Referativnyj zh:-Irnal, Mekhanika, L959, Nr 7, p 10 (USSR)
AUTHOR,, Merman, G.A.
Roam
T*1'MF,,, Qualitative Investigations in the Three-Body Problem
PERIODICAL! Byul. In-ta teor,'astron. AS USSR, 1958, Vol 6, Nr 10,
pp 6e~ - 712 (R~-s-FT-ench)
ABSTRACT., The final motions In the three-body problem are studied qualita-
tively for negative values of the constant energy, The conditions
are presented, which ensure the analyzing of the motion of three
bodies into two motions, which are nearly independent and --lose
to Kepler motion. The author shows that the mimiffrum dls*an--.e o_11'
the remote body does not change essentia-lly, so that further close
approaches of this body to the other two bodies are not possible,
which could sharply change the entire motion configuration, The
limits, withi-n which the velocity of the third body varies both
in magnitude and direction, are also near the elliptic Kepla, values,,
The distance between the two nearest bodies remains always limited,
Card 112 so that some kind of a partial Lagrange stability takes place, As

SOV/124-919-7-7186
qualitative Investigations in tne Three-Body Problem
an example of applying the criteria of denomposition of motion into two
approximate Kepler motions in the three-body problem, the author analyzes th,:-
%,V "'and
problem of r~o' Lryk Pluto (the author neglect, here
tions of the 1~61D.
~jerc
all the rest perturbationz from the other planets). The itithor ,;hows uiaf.
Mercury never will move away from the Sun farther than four astronomi-al units
and Pluto will never approach the Sun closer tnan 11,2 astronomi,zaL unv.~. -he
study represents a considerable supplement to the classical works of Shazi OrJ
the qualitative theory of the three-body problem
G,N. Duboshin
Card 2/2

80852
3L/9 U/ SOII/124-59-8-8383
Trarslation from; Referativnyy zhurnal, Mekhanika, 1959, Nr 8, p 8 (USSR)
AUTHOR - Merman, G.A.
TITLE. On the Presentation of the General Solution of the Three-Bcdy
Problem by Convergent Series
(Z~ 1~
P0110DICAL. Byul. In-ta teor. astron. AS USSR, 1958, Vol 6, Nr 10, Pp 713-
732 ~French. Res.)
AB&1'RACT-. It Is known that the general solution of the three-body problem
presented by Sundman (K.P. Sundman, Acta Math., 1913, Vol 36)
in the form of absolutely convergent infinite series can not. be
applied in practice, as it was shown by Belorlzky (M.D. Belorizky,
Recherches sur l1application protique des solutions gk6ral d'j
probleme des trois corps. J-0., 1933, Vol 16, Marseille) becau_~e
the series in que5tion converge extremely slow. Tho aut,hor deter-
mines in his study the possibility of presenting the g,~neral
solution of the three-body problem by convergent Seriez of poly-
nomials and, moreover, of quantitative rating thc- error -a-ased
Card 1/ 5 by the replacement of the rigorous solution by polynomials cf a

80852;
SOV/124-59-8-8383
On. the Presentation of the General Solution of the Three-Body Problem
certain fin.1tedegree. The author discusses at first some general I~heoremS
of the theory of differential equations, of which the most _Jmport&nt theorem
for applying to the three-body problem is the following Theorem Let a
system of m differential equations be given-,
dyi M)
dx -1 M
where Pi are polynomials of ki-th degree of m. variables with conztarl ~.o-
efficients: k.
Pi(yr Yr + ... f 1 0 X a (l Y~ Ir
s r + r
ir 5 r
Yr M).
s
aund the initial condisi?n~ are given
Yi - Yi 0 for 7-- 0 (1 - 1. M).
~-.'ard 2/ 5

80852
SOV/124-59-8-8383
On the Presentation of the General Solution of the Three-Body Problem
Let be known also that the solution of the given system
Yi(X), Y1(0) - yi (0) (1 - I, .... M)
exists and is limited for all real x by the same number C
Yi(X) :S c (i - 1, .." M)
Let x ----> 0 be an arbitrary real number, 0 be an arbitrary small number,
and n be a natural number satisfying the inequality
n ~> [e Li(s) -X - 1] -K
where [ (C &)k, + I mi
Mi(F_ Mi a C+ 6-1
L F-) L M k a (c. + 4 i
i i i I c + )e1
Card 3/ 5

80852
SOV/124-59-8-8383
On the Presentation of the General Solution of the Three-Body Problem
k m
i max
ai max a,( r rs
1r 1r 0
emikiai~ Ci - 1 1
I C - 1
Yi (n) Yi (n) (x yi (n) (y, y1 (0), YM (0) M)
are polynomials determined by the recurrent correlations
Y + y (0L + -2L p (y (00, y (0()
i n r rSi
Then the inequality is valid;
Card V 5
- 1, .-,, m
01 11 .-1 M 1)

80852
SOV/124-59-8-8383
on the Presentation of the General Solution of the Three-Body Problem
I Yi (n) (_X ) - Yi CK ) IF_ (I . 1, ...' M)
Proceeding thereupon to the three-body problem, the author reduces the equations
of this problem to a form suitable for applying Theorem 5. This is attained by
introducing certain new dependent variables and a new independent variable - the
Sundman-variable instead of time. Thereupon, the author formulates the basic
theorem, the proof of which Is reduced to the verification of falfilment of the
conditions of Theorem 5. Moreover, the author gives some critical remarks in
connection with the study of Vernich, which have polemic nature,
G.N. Duboshin
V~
Card 5/5

- -59-9-6850
"0v/35
Translation from: Referativn3rj zhurnal, Astronomiya i Geodeziya, i959, lor 9, pp 2 - ]l
(USSR)
AUTHOR: Merman, G.A.
TITLE: An Outline of the Mathematical Studies of Mikhail Fedorovich Subbotin
(on the 65th Anniversary of His Birthday)
PERIODICAL: Byul. in-ta teor. astron. AS USSR, 1959, Vol 7, Nr 3, pp 233 - 255
ABSTRACT: The field of scientific problems studied by M.F. Subbotin from 1916 was
very widelsuch as: algebra, differential equations, the theory of
probability, law, applied and calculational mathematics, astrometry, the
history of a.Rtronomy, the compilation of textbooks and popular articles.
There is a detailed account of the main mathematical works by M.F. Subbotin.
His early works "On the Form of Power Expansions of Algebraic Functions",
and "On Particular Singularities of Some Differential Equations" are de-
voted to the theory of functions; the first describes the criterion that
the function, represented by Taylor's series, is non-algebraic~ the second
is a criterion that the function given in the form of a differential
Card 1/2 equation is not holomorphic function. To these works is added the one

SOV/35-59-9-685o
An Outline of the Mathematical Studies of Mikhail Fedorovich Subbotin (on the 65th
Anniversary of His Birthday)
"On the Extremal Properties of Entire Functions of Finite Orders" (1930). In the work
"On the Law of the Distribution of Errors" a generalized law of the distribution of
errors is derived whose particular case is Gaussian normal law of distribution. The
new law of distribution was used in order to determine the period of the Sun's rotation
around"the axis from bservations of the sunspots in Greenwich during 1886 - 1909. From
D
works Which apply tNe-l-estial mechanics the works concerning the improvement of the
convergence of trigonometric series, are singled out, as well as the work on the' in-
troduction of a new anomaly, comprising as particular cases the eccentric, true and
tangential anomaly, as well as the work on a new form of Euler-Lambert equation. In
articles "On the Problem of Two Bodies With Variable Masses" and "on Certain Properties
of Motion in the Problem of 71 Bodies". 3ubbotin approaches the solution of the problem
by proceeding from problems of the qualitative celestial mechanics. A series of works has
a preeminently applied nature. They are dedicated to the calculation of secular in-
equalities, to the calculation of the coordinates of planets by the quadrature method, to
the determination of orbital elements by the method of the variation of geocentric distanc
the numerical integration of differential equations and others. A full bibliography of
the scientific studies of M.F. Subbotin is adjoined, which contains 74 titles,
Card 2/2 N.S. Yakhontova

30386
S/618/61/000/008/00 i/00 i
/go ?6, t1,3-2-1 /-1-2-7 AOOI/AIOI
2-- ~-
AU'PHOR~ Merman, G.A_
TITLE- Almost-periodic solutions and divergence of the Lindstedt. and Birk-
hoff series In the restricted three-body problem
SOURCE: Akademiya nauk SSSR, Institut teoreticneskoy astronomii, Trudy
no~ 3, 1961, 5 - 134
TUT,, The present work has two main purposes; first, to prove the exis-
ence of almost-periodic solutions in the plane restricted three-body problem,
and second, to demonstrate, for the same problem, the divergence of some formal
trigonometric series called by the author Lindstedt and Birkhoff series, The
solutions of both of these problems follow from the same circumstance; exist.-
ence of a compact set of periodic solutions with purely Imaginary characteristic
indices, whose periods are multiple of the periods of the known Schwarzschild
solutions.
In the introduction the author prouents tho cemitemporary dofinltiori of' an a1mcni
periodic function as given by Levitan (1953) and describes In some length the
history of development of the theory of almost-periodic func~Aons, mentioning Ln
Card 1/ 5

3C-386
S/618/6- 1/000/008/06- I/Oo
Almost-periodic solutions AOOI/AlOl
*.his :onne:tion the names of Poincar6, Krylov, Bogoly-ubov, Van der Pohl, Mallkl_!.,
e*c, He shows that the results obtained by the latter investigators in the
.,heory of non-linear oscillations are not valid for conservative systems, a par-
tl~ular case of which is the system of points mutually attracting each other a~_
I-ording to Newton's law. On the other hand, the theorem of Birkhoff (1941) on
the existence of almost-periodic solutions for a canonic system with one degree
.-f freedom, was proved by him with insufficient mathematical rigor and is r.-~- a!:-
plicabie generally for the problem in question, Some defects in his prc-of were
discovered already in 1956 by Siegel. Therefore, at the present time nc general
rigorous methods of constructing almost-periodic solutions for conservative sy~
-.ems, in particular for the three-body problem, exist. Then the autrior pre-se-~,.i
his definitions of Lindstedt and Birkhoff series and mentions t.hal t.he zliverwer~.
of Lindstedt series was shown by Poincar~ (1892-1899), although ccnsideraticn: o!
the latter do not hold for all cases, The author formulates the I-asic idea ander
lying the present Investigation in the Collowing, way Let some colllneatory
,ransformation be determined In a plane; let two invariant curves of -hl:- *.rana-
formation be given, which do not pass through invariant poinls, one cf whl~'-l i-:z
:.osed and the other is an asymptotic branch, Then these curves car. nc-~ in-~er-
zec-, since the intersection point must, on one hand, remain on the ciosed curvp
Cari 21' 5

30386
S/618/61/0