SCIENTIFIC ABSTRACT BORIS, A.V. - ARNOLD, Z.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000102120008-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 6, 2000
• Sequence Number: 8
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

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S/081/62/ooo/oo6/o65/117
B149/BlOB
AUTHORS: Markhilevich, K. I., Arnolld, To. S., Abritalin, V. L.
TITLEs Study of the treatment of highly senbitive panchromatic
aerial film. IV. The influence of hydrazine on the
developing proooso
PERIODICALt Referativnyy zhurnal. IChimiya, no. 6, 1962, 505,
abstract
6L450 (Tr. Voss. n-i kino-fotoin-ta, no. 35, 19609 126 - 136)
TEM The influence of various hydrazine derivatives added to metolo-
hydroquinone developer on the photographic properties of aerial
film has
been investigated. Some of these derivatives increase the speed of
development and the photosensitivity of the layer with a
simultaneous
increase in image granularity and fog density. It is possible to
select
such concentrations of hydrazine derivatives that the increase in
photo-
sensitivity is not followed by an increase in fog density or
granularity.
Report III, see RZhKhim, 4L429. [Abstracter's notes Complete
translation.._~
Card 1/1

ARNOLID., TS.
Simplified method of prooessing qolor negativeso
Sov.foto 22
no.5:38 My 162. (MIRA 15:5)
(Color photography)

ARNOLID, V.
Correotion to V. Arnolld's paper *Small denominators.*
Part 1.
Izv. AN SSSR. Ser. mat, 28 no.2.-479-480 *.-Ap 164.
(MIRA 170)
. 1, i.

ROUNTUL, M.A., professor; TASILOTAT, T.T., kand. nod. nauk;
SOMIN. A.Z.,
kand.ned.nauk: RAKHHMVA. N.V., nanchn.tatr.; PRCIRVICH,
L.T.,,. nucabla.
s'Otr.: ZUTKINA. A.R., muchn.sotr.; ARNOL'ib-I evrach; PIMMM
SKIY, S.I., vrach; PLAVIT, P.Ta,, vrach; VILIC N.V*, Trach-,
GLOBUS,
R.I., vrach-. MOISHMMG9 HoHogvrach; TUtWZOVA. A.I., -vTach
Results of treating syphilis according to the 1949-1951
prograxas Veste
van, i dam. no,lt22-25 ~&-? 155. (MM 8:4)
l.'Bollnitea In. Korolanko (for Arnolld, Petrushavskiy) 2. 1-Y
I 2-3e
kosbno-venerologichaskiye dispanser7 (for Plavit, Veliahko,
Globus,
Golldenberg, Tungukova) 3. Is otdala sifilidologii
(taveduyusheMy
professor H.A.Rosentul) TSentralinogo
kozhno-vanarologicheakogo insti-
tUtA6 (direktor - kandidat maditsinakikh nauk N.K.Turanov)
Kinisteretva
sdravookhranarlya BSSR.
BYPH LIS, therapy,
in Russia, pattern of ther.)

URTANYBREY, A.I.; ARNOLID. V.A.
---"dwdMML
[Cosmetic -08""eqrewMki~nosmeticheskil ukhod za
koshei. Kiev,
Goo. sod. iad-vo USSR, 1956. 156 p. (MLRA 10:4)
(3XIN-CiPA AND HTGIZHI)

KARTAMISHEV. A.I.; ARNO 1 .1, 1
.,-.a
[Cosmee-c care of the skln] Kosmetlchnyl dogliad
;,a shkiroiu.
Kyev, Dershmadv_vdav URSR, 1957. 147 P. (MIRA 12:1)
(COSMETICS) (SKIN--CARE AND ffGIFIW,)

KART&YSHEV, Anatolly loasafevich,, prof.; ABOLID Vera
Aleksandroyna doktor
(deceased]; ASTVATSATUROV, X.R.,
.9 tekhn.
red,
(Cosmetic care of the skin) Kosmaticheskii ukhod za
kozhei. 2.
ispr. i dop. izd. Kievp Goa, med.izd-vo USSRj 1961. 188
P6
(WRA 15:4)
(SKIN-CARE AND HYGIENE) (HAIR--CARE AND HYGIENE)

-1
- t . I -;-, - ul V- "- I.Al - -- ~V. - f - -- - - --. -- .
I -- I ,
r-- .1
rf 1 . .LjK t~ , , '17 ~ I . ~ , i I I . . ,

AIWOLID, V.j.(Mo8cow)
Visiting tile school club of mathematics at the Moscow
State
University. Mat. proo.no. 2:241-245 '57. (MIRA 11:7)
(Hoe cow-11athoms tics)

TANATAR, I.Ta. (Moscow); SKOPETS, Z.A.
(Taroslsv1Q;'ARUOL1.D...V,I.
(Moscow); DYNKIN, Ye.B. (Moscow); I4RDKIPAITIDZE,
B.G.(Livov);
rONSTAITTINOV, U.N. (Moscow); B IN, F.A.(Moscow)
Problems of elementary mathematics. Hat. pros. noo2:267-270
157.
(MIRA 11:7)
(Mathematics--Problems, exercises, ate.)
tIr

AIMOLID T $!'.. '.
IT, -.- 0 . ,
The possibility to r resent funotions of two variqbIes
in the
f orm X EIP(.X) t 'P (~) 7. Usp.ust.nauk 12
no.2(74):119-121
Mr,Ap 157. (MM 10:7)
(Funotions of severRl variables)

AUTHORs
Arnolld, V. I. 20-114-Jwl/63
TITLEs
On the Funotions of Three
Variables (0 funktoiyakh trekh

peremennykh)
PERIODICAM
Doklady
Akademii, #auk SSSR, 1957, Vol. 114, Nr 4, pp. 679-601

(USSR)
ABSTRLCTs
The present paper deals with a method of proving a
theorem

whioh makes the total solution of the thirteenth problem
set

up by Hilbert possible (in the sense of a refutation of
Hilbert's

hypothesis) i

Theorem Is ;Lny real steady funotion f
(xI,xj,x ) of three
L

be represented
variables.assumed on the unit hexahedron 9 a

in the form
t

f(xl,x29x3) a
h ijTij(xIPX2)1x~

jai

The functions of the two variables h and are
in this
l4
W

case real and steady. This theorem
a resu
of the exis~enee

ca of Kolmogorov's representation f(xj9X
9x
hi[Tj(xI,x2),z
)-A
]

2
3
,
3
Card 1/2
-

On the Functions of Three Variables
ASSOCIATIONs
PRESENTEN
SUBMITTED:
20-114-4-1/63
and of the following theorem 2s
with any family F of the real andequally graded steady func-
tions fa ) assumed on the Itreell "Wit is possible to realize
the"tree" in such 4 manner.in forl-of a subquantity X of the thr
dimensional oube Z2 that an fLjQOtiOn Of the family F can be
represented in the form t (I)-'T:fk(xk) . The points of the
" '4
"tree" ow-Ij have a small ramif iallion index &, 3-x-(xi Px2,x3)
is
an image J 6 E in the "tree" X; f (xk) are steady re'al functions
of a variable, where fk depends steadily on f(in the sense of
a uniform oonvorgeece). The author then gives several definit-
ions and proofs. There are 2 references, I of which is SOTiet.
Moscow State University imeni X. V. Lomonosoy(Moskovskiy
gosudarstyennyy universitet im. M. V. Lomonosova)
April lop 1957 by A. N. Kolmogorov, Member, Academy of Soienoes,
USSR
April 4P 1957
Card 2/2

ARNOLD, V. I. and KO1WGOROV, A. N.
"Some Questions of Approximation and Representation of
Functions."
Paper submitted at International Congress Mathematicians,
FAibburgh, 14-21 Aug
58-

AILTY)LID, V.1. (Moskva)
Repreannti functions of several variables ~y superposition of
functions of Fk smIler number of variables, Mat, pros, no.31
41-61 158. (MIRA 11:9)
(Functions of saveii4'1 -.-artables)

AMLID V.I. (%skva)
,~~Awk,4x
Visiting tho school club of matbomatics at the Moscow
State
Univernity (Conclusion). 14at. pros. no.3a.241-250 158.
(Moscow-14tthemat Ica ) - (14IRA 11:9)
i

GALOPERN, S.A. (Mnnkva); WPS11ITS, A.M. (Moskva):
BAIX, H.B. (Snolensk);
ZHAROV, V.A. (Yaroslavl'): BTJKIN. V.1. (L'yor);
AZWLID V.I.
(Moskva); KUTIN, I.Yu. (,Moskva); DUKIN, Y~.B.
vjb-fk---.
VOLOV, Y. (Moskva); ALUSANDROV, A.D. (laningrad);
VITUSHKIN, A,,Go
(Honk9a).
Problems of elementary mathematics. Hat. pros.
no.3:267-270 158.
Onthematics-Problems, exercises, etc.) (WRA lls9)

ZALGALLER, S-, (Leningrad); SKOPETS, Z.A. (Yaroslavl'); ROFX~BMTOV,
F.B.
(Kharli.v ); UNDIS, Ye.M. Noekva); IRVIN, V.I. (14ookra); STICHKID,
S.D. (14oakv&)-, LTAMOV, A.A. (Moskva)- ARIJOLID, V.I. (Moskva);
IAIPSHITS, A.R. (14oskva).
Problems of higher mathematics. Mat.proe. noo3:270-274 158.
(min 11: 9)
(Hath"mtice-Problems, exercises, ate.) - *

16(1)
AUTHOR: Arno ("Pw) SOV/39-48-1-- 7/5
TITLE: On the Representation of Continuous Functions of
Three VariabI6,1
by Superpositions of Continuous Functions of Two Variablev
(0 pred8tavlenii nepreryvnykh funktsiy trekh peremennykh
suporpozitsiyami nepreryviWkli fuyiktsiy dvukh peremennykh)
PERIODICAL: Matematicheakiy sbornik, 1959, Vol 48, Nr 1, PP
3--74 (USSR)
ABSTRACT: The paper contains the detailed proof of the
theorem announced
r in Z-Ref 1
by the autho _7s Every real continuous function of
the variable f(XJjx 2 'x3) defined on the unit cube E3
admit2 a
representation
3 3
f(xl,x2'X3 ;~r. Zh ij f.'f,,(x1,x2),x3]
i-1 J-1
where the functions of two variableB h ij and Tij are real
ani
continuous. The proof bases on 2 theorems and 23 lemmas
wh-~',rh
partly, in a somewhat other form, can be found already In the
paper of Kolmogorov f-Ref 2_7, where also the final result is
somewhat stre thened. In an appendix some constructions of
Card 1/2 A.S. Kronrod ?Ref 4-7 are collected. The author
thanks his

` -0 W
On the Representation of Continuous Functions of Three
SOV/39-48-1--1/5
Variables by Superpositions of Continuous Functions of
Two Variables
teachers A.G.Vitushkin, and A.N.Kolmogorov for ad7ices.
There are 27 figures, and 9 references, 5 of which are Soviet,
I Polisht 2 German, and 1 American.
SUBMITTED: December 25, 1958
Card 2/2

0. 1") 0 VO
778-14

SOV/4 2-15- 1 --211,/2-(
AUTHOM
Arnolld, V. I.,
Moshalkln, L. D.
TITLE t
A. N. Kolmogorov's Seminar on SelQcted
Problem8 in

Analysis (1958/1959)
PERIODICAL:
Uspelchi
matematiches)(11ch nati1c, 1960, Nr 2, 1) 2117-250

(USSR)
ABSTRACT:
The seminar was devoted to the following two groups of

problemst
I.Incorrectly posed problems in analysis and

mee-hanics, i.e.' ,
problems whose solutions depend d1s-

continuously on a
parameter.H.Mathematical models of

turbulent motion of an
incompressible viscous fluid.

The first group dealt mainly with
the boundary valtie

problem for the vibrating string, The papers
by N. 14.

Vakhaniya, B. V. Boyar3kiy, V. I. Arnolld arid A. N.

Kolmogorov presented a survey of this topic. In tYie

second group,
Kolmogorov pointed out two factzi (1)

In decreasing the viscosity
V the laminar solubion

of stationary problems becomes unstable, or
stable
Card 1/4
in a very small region, both of which are not;
ob3er,ied

A. N. Kulmogorov Is Seminar on Selected
Problems in Analysis (1958/1959)
'(78 1 It
SOV/42 -35 --1 -21/27
in reality; mass depeiids ot-ily on a typical velocity, and
a typical length, and is independent or V . Ile
proposed investigation of solutiori of' the following
probleml
Du ap
i)-t- = - w- + vAit + V sill Y,
Du (1p
gi = - - -l- V, v,
4914 0t, OY
where x oy
D- _ a + + v
Tit ~J-t
Y
A= + 02
G.,
Card 0/)t

A. N. KollnOgOrOv's SL
-minar on Selected
Problems in Analysis (1958/1959)
814
77
'-,OV/42-15-1-21/-!7
the solutions being periodic In 2a and 2 7r in x and y.
respectively) and satisfying
dy = o. 0)
_U
He stated the hypothesis that for small V turbulent;
solution should appear, (in the sense of nontrivial
invariant measure in the (u,v) space) and that
Thus far the hypothesis could
not be verified on any mathematical model. There are
25 references, 6 U.S., 12 Soviet, 3 French, 1 German,
2 Dutch, 1 Chinese. 5 Recent U.S. referencesi 14. Wasow,
Asymptottic Solution of the Differential Equation of
Hydrodynamic Stability in a Domain Containing a Transi-
tion Point, Ann. Math., 58 (1953) 222-252; W. Wasow,
One Small Disturbance of Plane Coutte Flow, Journ. Res.
Nat. Bur. Stand., 51 (1953) 195-202; E. Hopf, Statisti-
Card 3/4 cal Hydromechanics and Functional Calculus, Journ.
Rat.

WrIp VIVY- UF
It. N. Kolmogorov's Seminar on Selected 77814
Problems in Analysis (1958/1959) sov/42-15-1-21/2-7
Mech. Analysis, 1 Nr 1 (1952) 87-123; C. L. Siegel,
Iterations of Analytic Functions, Ann. of Math. 43, 4.,
(1942), 607; F. John, The Dirichlet Problem for a
Hyperbolic Equation, Amer. Journ. Math. 63, (1941),
i4l-154.
Card 4/4

GXLI,pA"t I.M. (Moskva); DyUDXNI, Nero. (SSU); KIRILLOV,
A.A. (Moskva);
FCDSYPANIN, V. (Tula); T3CR-MKRTACM. M. (Yerevan); XMIMIN,
Tu.I.
(Moskva): VXU', G. (SShA); ?AWZT3Vl D.K. (Leningrad);
ARHOLID,
14_L-(Moskva)-, IVAHOV, V.P. (San-Karloe, Kaliformiya, 09)
GRATNT, M.I. (Moskva); LIDIDEV, N.A. (Leningrad); LOPSHITS,
A.M.
(Moskva); ZHITOMIRSKIY, Th.I.-, MITYAGIN, B.S. (Moskva);
SMPXTS,
Z.A. (Taroslavll); PUANMR, A. (Pranteiya); GAVEL, V.V. (Brno,
Chekhoolovakip); SOLOWAK, M.Z. (Leningrad); LEVIN, V.I.
(Moskva);
BARM, M.B. (Tashkent); MDW. L.M. (Tulzi)
Aroblems. Mat, prose no*5:253-260 160. (MIRA 13:12)
(Mathematics-Problems, exercises, etc.)

ARNOLID, V. I.., Cand. Phys-Mvttlh. Sci. (di-18) "On Represen-
tntion of Continuous Functions of Three Variables b.-- Super.pr,,si-
tions of Continuous Pinotbons of Two Variables" Moscot-r, 1961.
3 pp (Moscow State Univ.. Mechanical-Math. Faculty) 000 copies
(KL Supp 12-61, 249).

ARNOLID,, V.I.
Remarks on numbers of rotation. Sib. mat. zhur. 2
no.6t8O7-813
N-D 161. (MIRA 15:7)
(Rotating bodies) (Dynamics)

ARNOLID1 V I -- -
Nmographic calculability with the aid of the rectilinear abacus
I '6f Decartes. Usp. mat. nauk 16 no.4:133-135 JI-Ag '61. (MIRA 14:8)
k1lomography) (Abacus)

6bc7e - --- - -
164140 S1038J611025100110021003
14.000 0111/0222
AUTHORa. Arnolid,.N.I.
TITM Small denoiiiators.I* On the mapping of the Circle onto
itself
PERIODICAM Akademii nauk 88BRo layestiya, Seriya
matematichaskeyap
v.25, no.1t 1961, 21-86
TEM The paper consists of two partst I* On analytic mappings
of the
circle onto itself, II. On the space of mappings of the circle
onto
itself.
In the first part it is shown that uder certain assumptions an
analytic
mapping of the circle into itself whidiis little different
from a
rotation ban'be changed in a rotation by an analytic
transformation of
variables, Lot F(z) be a function real on the real axis and
analytic in
its neighborhood, P(z+24r) - P(z) P1(z) ~-l for Im z - 0* Then
to the
mapping of the strip of the oompl;x plane z--:!p As az+F(s)
there corresponds
a homeomorphism B of the circular points w(z)-e is i w
-w(z)-p~w(Az) UBw
which preserves the orientation. In this sense, A is called an
analytic
mapping of the circle onto itself. Lot 2 Wt% be the rotation
number of A.
If /Ais irrational then there exists a continuous real
funotiony(s) of
the real z so that%f(z~21r) .-f(z)+21r and,
Card 1/6

88292
S/03 61/025/001/002/005
Sm&Vl denominatorzkoI. On the mapping... 0111YC222
Tho' aiithor~ 106nj.e*cturest'There exists aset M Qb,13 of
measure'l.iothat
for every Pke M the solutions of (1) are analytid with the rota
'tion
numbii~ 2-KIA for an arbitrarv.-ahalytio mapping 44 But he only
proves
Thedi,em 2t Given a family of'analytio mappings of the oircle
z --~ A(z. of, 4)1 z+2 'KtA+ AtF(Z,o E (2)
depending'on two parameters Lt At and suoh numbers R >0, E 1> 0,
K > 0, L0,
that .
I ~ F(z+2 it, E F(z, E
2 for m z - IM c- 0 it always holds Im F(ZI 0;
3 for Vm z1fcR, IF-I*L 0 it holds
IIP(zo E )I fzL Ifj
4) For an arbitrary integral m and no
the inequality
IIA_ K
n
Card 2/6 Inj
M-
the irrational number /A Satisfies
(4)

88292
B10361611025100110021003
Small denominatore.I. On the mapping... 0111/C222
Then there exist numbers f.1 and R', 04 EIg F_og 0 4R'f4Rp and
functions
A( E)l %f(zo t ) real for real f- and z and analytic for 1614, p.,
I Jim z I< R
so that
(A(z9 Cs A( E ))9 E ) -tf(zt E)+21C,*. (5)
The proof consists in the construction of the solution(of (1) by
the
solution of the auxiliary equation g(z+21[14)-g(z) - f z). For this
equation it in proved~_
Theorem Ii Lot f z I~Rf(z) be an analytic 21r-pariodio function,
lot
f (z) I -,c 0 for jIm . Lot rVe an irrational number, K>O#and
I/A - a 1;~ L. (9)
n n3
for arbitrary m and n**Oo Then g(z+27rlA)-g(z) - f(z) has an
analytic
solution g(z) - 'gjz) and for Jim z 14IR-2 & and an arbitrary qf<
1,
0 0
fi ld'Y(T) on the torus (i.e* suoh
suffioiently smallplr(x)14E for
whioh the system of differential
dx' I(x+).aw
Tt_
ohanges to dT
Rt
S/038/61/025/001/002/003
0111/0222
so that for every inalylLiq veator
one thatr(' whioh
Ilm '114 R, there exists a veotorl
equations
by an analytio transformation of variables*
in
for
Altogether the paper oontains 19 lemmas and 15 theorems.
The author
mentions A.N.Kolmogorovq V.A.Plies, A.A.Andronovp
L.S.Pontryagin, X.N.
Vakhaniyaq P.P.Mosoloy, B.L&Sobolov, R.A*Alekeandryan
and R#Denohev.
There are 11 figureag 24 Soviet-bloo and 19
non-Sovist-bloo referenoss.
The four most reoent referenoes to English-language
publioations read
as follows: P.John, The Dirichlet problem for a
hyperbolio equation,
Amer.J.Math.g63 (1941)9141-154; C.L.Siegelp Iterations
of analytio
Card 5/6

- - - ---- - 88292 - -
S103 61/025/001/002/003
Small denominatoresIs On the mapping##. 0111YC222
functionel Ann.of Math*, 43t no-4 (1942), 607-612; Anzai, Ergodic
skew
produot transformations on the torus, Osaca math.Journ., 3, nool
(1951),
83-99; A.Wintner, The linear differeno ions of first order for
angular variables, Duke Math.J., 12 (1;4;Iu,s`4t45-449-
SUBMITTEDs September 17, 1959
Card 616

20730
S/02 61/137/002/001/020
14 '3qOO 0111 YC222
AUTHORs Arnolld, V.I.
TITM The stability of the,equilibrium position of a
Hand-Itonian
system of ordinary differential equations in the genor*l
elliptic case
PERIODICALi Akademii nauk SSBR. Doklady, v*le137,no.2vIq6It
255-257
TEXT: Lot p - q 0 be a fixed point of the system
14 i -6 111 (1)
'? p -a q
where H(p,q#t) H(ppqpt+2,g) is analytic in p,q,t. The case
where
2 U -A
H --Iric 2.r +.00+0nr +H(p,q,t), (2)
where 2r - p2+q 2, '~ - o(rn+l) is analytic in pgqptp n*?.2
and at least one
03. (2.~-l O such that JI(t) - I(0)1