SCIENTIFIC ABSTRACT SOBOLEV, S.I. - SOBOLEV, S.L.

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• Collection: Scientific Abstracts
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• Document Creation Date: November 2, 2016
• Document Release Date: August 26, 2000
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

.-A -a volnovo in-ta Lm..
-i:.''tsi o: ial c) i-nvariaA'n,-l.*e recnc go a. Trudy
Stchlova, 5 2 -@-29P.
, -5,
S6: lWaLLI,emntics t'.e USSR, 47
edited by Kuro-jh, A.

3OD"I EY '3%. 1 .
K voprnsu @b ana-I itiche skikh resh-e-niyakh sistemy uravneniy v chas'unykh proizvodnykE s
d,.-x.qya nezavisimy-u pere@iermy-rd. Trudy fiz. - matem. in-ta i@rl. St"eklova, 5 (1934),
265-2P-2.
SO: i4pthematics in the U77R, 1917-1947
edited by Kurosh, A.G.,
ClarRushevich, @- I. ,
Rashavskiy, P.K.
5C,014-Teningm-1, 1948

3 c;,-, L - --@L -
,a 1:11 vtorc,,go por,;,
(.11, , a v
ldva C'n"
SC.- l.'a-L"liernatics i@l the U"S-R, 1?1:?-1947
1 -
ed-ited b7l Kul r 0, s h
1'ashevski:r, F. K.

3091,10,1, L;.
11-1 "', If
f. .; R@AL- Ln Pv:l-:;--,@r)@-T,t-nt,, Si4amol( '. FrorO, N.ulki i
Lic. 5/0', jtp. 68-72. @@l

9js',icha,r '-eo,*-''.,a c"c"nalftsi-I vol!; --,,I iz. iatev@ :,-,a
a L -L_
SC,: i@atjjematics in tk,@ie 'U-3SR, 1?2:@-I@47
edited by Kurosh,
T.,
Rashc-vsL-..i-J--,

Sc3CLE'll, J.
Sobolev, S., an-' '@iidhlin, S. ;3. ll?ltnle@-- in -111--@ Usr-ekhi
@ @- 0
228
r,@ L, -, a 4 -- i @, h @- 3 lr-@ i I h"Tlz@ul-, vo-l. -,, p---. -256.

3. L.
SC: ',@at'.ieriaticz3 L. the 1': 1-7 -1'-, 47
edited hurosh, A. G.,
:.,- 'llcushovich, A. I.,
Loscow-Le.aint-y-ad, 1')48

ns
10 7-rObl6lie
SO.: 2-:atheriatic5 the USS.',, i-,)17-1,?4*7
edited by E.-,ixosh, A. C-.
Earl-Lislievich, A. I.
-shevsk-!:,-,
J"

S 03- `-, LL 7
-@Icorjirii Sl-martusa -,,- 41--orill ur-rii-:0-sti. 4 (!`@-3`) 2'35-@`
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eclited A. G.
i@-rllalshevich, -z. i.
.osco-@,-Len-!r.,,-r-,d, 1948

".:la7--ze t@z,,f .11 Ul ien-
-la:., ser. .,-@te. -15-550.
SO: ti-,e !J33,11,
cditcd b,:., -',,rr)sh,
osc,

Clu
rnv:
SO: i-iatllcn@l tics i'- ' the UJJP, 1917-1947
ed-i ted b. .II Yiuxosh, A.

1-57.
.--od. of s, - 'Y -
o s

-jioj,;j
N, 1,. (1 rof.)
113everal Proble:-.-ts in th-@ Dheornr of the Proya-ation of 7ibrations," 1937.
-1
Mosccvr Order Lenin State Univ. im. M. V. Loraonosov, 1941.

LL
Ob I@ja5z-e es":
ser. "1 0,
e,- -.z,. -. !- -; n-!- e 1S -in47
so: :zat; cs usjH -;17
edited 0:,r Hurosh,
A. I.
7@ a0zievol-i.-

3. -.-1
Ob od-o-- kn@,rcwo.- :@a@ ac'-,c dl-.-,-. 7iata-
-V
nmik., 4 (193' -275-277.
'lie U:3SR,
edited by Kw-osh, G. ,

'J. L. (,rof.)
I
"On the 'i@ err - of flon-linear Hyrerbo-lic &iuations with I ar!lial Deriva@ives,ll
193 9 .
loscow Order Lenin 3tate Univ. ira. 14. V. Lomonosov.

S. 1'.
"On th- ie"viluarioll of liev.--r.-al, Sums for the Giv-n Functirms on a System,"
Dokl. AN. 25, "o. '1) 1.0139-

1. S. L.
2. USSR (0-00)
"Discussion of the '.,Io--ks of G. V. 3richipanov,"
Iz. AN 33Si, Otdel. Tekn. Nauk, 1110. 4, 1940.
9.-@ Re-ort U-1530, 25 Oct 1951.

32 (1-:141)
fmidacift dlya v
j-" the
editodlby Kurossh, G.,

y ;. -,
- - 1) 1 -
11' I I I I I L
,on@ern-in@ tite --ro'blem of @he 7t-.bilit-.- of 3olu'ions ',D -he- LL71-te' '--obl--m
`h - Q -4
t'or @-ua'i@,ns wiL. .-ar+-ial Deriwiliv-3s of 'he H-,,yer-olic -Dokl. IUM No. 7, IQ 1.

30 P '-, L 6',/ 1j. T .
I' ',,)n,,ornin- 3ev,.-ral Grolis of Trans formations in n-Dim,@@nsional 3race,"
Dokl.. AN, -12, No. 6, 1941.
Acad. of 3ci.

ti
ia*.ivne---",' v cha,-k-
'lu Wt,
'155-903.
sb.
zthe!ratics t- u t,
edited by ilurosll,
Has".
I-evski

1. 31 -). i-
2a. U. -3. S. iZ. (600)
Tbr. , je,@ t. T h-sico-Mathematical Sci. , Arad. 3ci (1944)
- . , 1 1
4. Mathe:aatics
7. "I"Ind'efloribal Froblems in the field of Mathe@aa tics and 3cirmce," Vest. AIN.
33.3A, No. 11-1,1, 1944.
9. @3A-52059019

SQboleff, S. L. Sur la presque p4riodicitd des solutions

-
2
D
kl
d
Ac
d
d
C a -for the or-dinary- I p. ly-unde r the altcrnate@ 7@
La I ician simp
-
a
.
es. L
o
a
dd
4
equation des on
. It. (
y) certain
O with
boundary conditions ujg@-O
or . clu/ors I s =
Sci.URSS(N.S.)48,542-545(1945). CMFI@@
53 .
.
smoothiitfss-rLquirej)icji6
the boundary and differentia-
o
n
,
,
,
,
Soboleff,, S. L. Sur lit presque pgriodlcit6 des s on
solut'"s bility - conditions on u(x; I). @ He obtain this cbnclusi
de 116quation des ondes, 11. . C. R.-( Do cad.
k6dy). A
M@
by-utilizing. in addition- to. the Ifamiliar energyint@gral
Sci. URSS (N.S.) 48, 618-620 (1945). [MF
Q] f(r(au1JX41+u1)d2,-which hadbc6-thc only one " used
Soboleff, S. L. Sur lit presque Iigrlodit;IM des solutions a al
before,- i new* type of energy integr, I which involves parti
do 116quation des ondes. IIL C@ R,- (Doklady) Acad.

'
derivatives (it the second order and whose. constancy
per-
16638]
Sci. URSS (N.S.) 49,12-AS (1945). [MF mits die conclusion (partly "'bit results of W. Kovidra-
After a theorem of Muckenhoupt for n=t [J. Math. chov) that the lmi-tial derivatives of the first order in .x are
163-199 (1924)] it wis proved
Phys. Mass. Inst. Tech. 8, also compact. I t is unlikel

y that: the
integral has notbeen
by the reviewer [Acta Math. 62, 227-237 (1934)] that .
noticed Worc, but its usein this typeof problem seems to be
a solution u u(*,, X. -, f) of the wave - equation
novel.
if:compact as a function of t, is auto-
In note I the nutbor gencralizes,his conclusions froin the
matica!ly almost periodic in 1. The operator Av im this state-. -
Jnplacian in:rectilinea? coordinates to one in curvilinear

ment is a fairly general elliptic operator over a suitable

- - o
i i; the
x.) in a doma i
Ifilbert space of functions of (xi -111 he t in to the classical
Coordinates. In note re urns aga

l
2
,
,
"compactriess" and "almost periodicity" refer to the func- ;.however, he admits -
operator a
a/01
"

tion u(x: 1) as an abstract-valued function in 1-whosL values generalized
solutions of E]u=O.for which no partial de

elements of the Hilbert space. lit a paper by. the re-
are rivatives in x tical exist. Such generalized solutions-,are

defin6d by the adjoint equation (y, 00) =0, in which 0
-291
viewer and von Neumann [Ann. bf Math. (2) 36, 255
b0ongs
to a large class of differentiable functions. The
(1935)] this was generalized to solutions of morc:g@neral, ,
author proves again @ that'the boundary co dition U =0
n
equations which are linear in 1,
'"'arcs compactne-is and. thus @ almost
periodicity of-the
In the present notes the author is concerned in the case

: @
'trajectory.. The latter type of: "generalized" soluti6n
by
of equations (@) with drawing up assumptions under which
' ,
A1S'o
means of-adjoint equations has-.
bmn treatM in the
in order- to be
the prerequisite compactness will be verified
r* ,
.
meantime by the reviewer CAnn. of Math. (2) 47, 202-212
able to draw the conclusion that the rajectories are almost
t
(1946). theve Rev. 7 4463, S. Bochntr.
periodic (in the average). In note I he proves this compact-
Source: EatheTratical Reviews, - 'Vol 8. No. 2

i, J.
c, @:ocjjtj -)or4o@ij(,-jjtjo:jtj I-rsiloni
4-roll OVOCC ul .1e;.i. 1 Da.
SO: tics i,: "r-C

S. L
0 -OCjjtj rcshc!.-i:r vol,-jovogo U. Lan, (1945"
SO: 'I@athe.,,vatic,3 in the
edited by Oarosh, -'. G.,
@@arlaishevicl';, A. I.,
P. IF-

no -. L,
0 p-_Cilti -,@I-j:@djc@j ra volnovo-
..0 ura"r. j: T D,
SO:
edited b.- K-l"roSh, A.
1-7a-lnushevich, A. 1.,
-iu'- --, P. I"
i
Rashe r.i.
':oZcow-Lor,-ir,,Srad, jc)1@8

It.30L @V, _;. L.
?I L .11 : Jave 11,11
;,oricern-iril-, tu@le_ :'ear-l e-iocicit.,f of t;,e Sol'It-Ons Of' th
Dolkl. AN 48 , ilo. 9.1 1945.

J) I. L.
?1,;oncernin- of the 3@[e-mail] to t@--- TIJ 11
- .9
Dokl. AMI., 49, No-.1, 1945-
A:ad. o-* j@i.

f 7
Lat, 'or @ech-
-ni- --Jte:@ r@a 21, 440 -,-3, 1.4 finvairig,
-DD ri@Ael.

nkad.; FIKHTEILOLITS, G.M., prof.
Academician V.I. Smirnov. Vest. LGLJ 2 no.6:155-157 Je 147.
(MIRA 12:9)
(Smirnov, 171adimir Ivanovich, 1887-)

SODOLEV, S.L.
USW*thGWtIcs - Biography NOTA)OC 154T
*Vladizir Ivanovich SmIrnov," S. L. Sobo'lev), 2pp
"Uspekhi Hatematicheskikh Nauk" vol ii, No 6 (22)
Brief biography of V. I. ftIrnov written in honor of
his 60th birthday and the 35th anniversary of his
scientific endeavor. At present, professor at Imin-
grad State Universtty,. has written many articles,on
complex variables. On his 60th birthday is in excel-
lent health, axid can be expected to contribute wn
iLore productive years to the service of mathematics.
ID
5MO
FA 50T50

Sobolev, S.L.
USSRPM,Ith,.@ma ties - Calculations
Mathematics, ApPlied
PA@zl n-@-,i6
Jan 194 7
"The K-membered Tables, of Panctions of Three Variables, Shown as the Sum of the
Products of l'unctions of One VariLble," L Ya NoyshuL@r, 4 pp
"Pok A-Ic Yau.'@c SSSR" Vol LIT, No '@I
Submitted by S L Sobolev 27 Jul t(,. Mathematically -t@xpounds the statement that
calculated forrnilae (containing three factors) , are, mr-t in practicable calculations,
most frenixently shom as the sum of the -products of the function, @@Iach from one
variable, or the function from such a sum.

SOBOLEV) 3. L.
In a bibliography of USSR works on Autonatic aegulation and 3ervomechanisms
1917-1947, from Avtomatika i Telemekhanika, No, 5, 1948.

Uch. tap, IM no.96r5-14 1W. WLRA 10:'!)
(Giunter, Nikolat Maksimovich. 3871-194:@

T
*Sobolev, S. L. Nekotorye primeneniya funkcion4l"nogo
analiza v matematiZeskol fizike. [Some applications of
functional analysis in mathematical physics.] Izdat.
Leningrad. Gos. Univ., Leningrad, 1950. 255 pp. 16
rubles.
Chap. 1, Special questions of functional analysis: Intro-
duction; Fundamental properties of spaces L,; Linear func-
tionals in L,; Compactness of spaces; Generalized deriva-
tives; Propertiesof integralsof the typeof a potential;Spaces
L,M mid TVM; Embedding theorems; General methods of
norming IVW and consequences of 1111 elnhtddiog theorem;
Some consequences of embedding theorems; Complete con-
tinuity of the embedding operator (theorem of Kondrakv).
Chap. 11, Variational methods in mathematical physics-
Dirichlet's problem; Neumann's problem; Polyharmoinic
equation; Uniqueness of solution of a fundamental boundary
problem for the polyharmonic equation; Problem of chaac-
teristic values. Chap. I I I, Theory of hyperbolic differential
equations: Solution of the wave equation with smooth
initial conditions; Generalized Cauchy problem for the
wave equation; Linear equation of normal hyperbolic type
with variable coefficients (basic properties); Cauchy's pr6b-
lern for linear equations with smooth coefficients; Investiga-
tk;A of linear hyperbolic equations with variable coeffi-
cients; Quasi-linear equations. Tabk of contents.'
SO, "`.'atherqatical iteview Vol, 14, @Io. 6, PP 523-608, 1953.

r 3n"q" FIR ELI R"N I kl-@,., ;- 'lIll;;MRr - -@-A

MMIZ@k

SOPOLEV, S.L.
USSR/Mathematics - Partial Differential 21 D6c 51
Equations
"A New Problem for Systems of Partial Differential
Equations," Acad S. L. Sobolev, Math Inst imeni
Steklov, Acad Sci USSR
"Dok Ak Nauk SSSR" Vol LXXXI, No 6, PP 1007-1009
Indicates a system of partial differential eqx ,
which is not a system of Kovalevskaya, for which
not only Cauchy's problem but also the mixed prob-
lem in an arbitrary smooth region stays rational.
Submitted 31 Oct 51.
215T41

--0 L
USSIZ
Mathematics 3-3:3sion5
Jan/Feb 52
"A New Problem of Mathemati@-al Physics", Report at "Five Sessions of the Moscow
'-:athe(natical So--iety, Selt, and Oct. 191.U'l. Uspekh Hatemat Na Vo - 7, .1,
uk" I No
(47), rp 130-150.
9. PA 204T26

Wthmatioal Revia"
Vol. 14 No. 7
July - AUUpt@:-1953
Analysise
Myii4A. D. the sb46d bowWw pabless Sw
ised sydms of tabpqk oqmdnc Mat. Sbm& NS@
31(73), 53S-352 419S2). (Rumim) . I @'J
IISAftediad of separstim of variables was used by N. A.
BmAa [Doklady AW. Nauk.SftR (NA) M. 41..."
(19SO; these Rev. 12- 6573 to Ad@s hrmay in tam a a
sma of nomW modes Ow .P0301IMMIS VICtOr-MIStrig -A
qua&:-
telijapW e The
frt.&.%3 'OCir _,!,CFO In.
of UIVWW W=k
i
317-M
S@@S 3
U)
b
M
.
&
m 14,
); t
9(
.
(
511 an extensive r4p=w UPIRwimm.,
tbmy jus*@mg this
covering abo the inhomogedemm am. An impartsma cc!* is
&y4Avtk investigation by *0'PmSHsid sautions of
L %&Aev [Sam, appOmtiom of funcqwml amlysis
i
in mthem
kal physiM ImIst. LfnWgmd GdL Univ., 1950;
tbese Rew 14, S66] and by theeuncept of A "qum*aticaNy
'
continuoue
function. There am awnftvm tbeorems giving
conditionz on the initial data which ensure the convergence.
in mean or uniforWy. of the series wAution, and various Z@
degreem of anoothness ul the genemOsed or ontimary sol,-
tion.
The author propom,
as important unsolved probleam
.
the cases of variable coefficients, or of more
than two inde-
@
;
"
i; pendent variables. A V. Alk;msox (Ibadan). -
`

USSR /Mathematics - Cauchy's Problem 11 Jan 52
"Cauchy's Problem for the Partial Cases of Sys-
tems That Do Not Belong to the Kovalevskaya
Type," Acad S. L. Sobole-v, Math Inst imeni Stek-
lov, Acad Sci USSR
"Dok Ak Nauk SSSR" Vol LXXXII, No 2, pp 205-206
Considers the fundamental solns of the eq
L (0 = 0 (e. 9 - v-J (rtR-I)/R) which for in-
creasingtforam a system of waves, on the sur-
face of each sphere R=const. These waves aris-
ing on the equator move in the direction toward
the poles accumulating continuously in greater
202T74
USSR /Mathematics - Cauchy's Problem 11 Jan 52
(Contd)
and greater quantity on the surface of the
sphere. In this way large-scale waves gen-
erate from small-scale waves. Submitted
14 Nov 51.
202T74

USSR/Mathematics - Difference
Equation
11 Nov 52
"Uniqueness of Solution of Difference Equations
of the Elliptic Type," Acad S. L. Sobolev, Math
Inst imeni Steklov, Acad Sci USSR
"Dok Ak Nauk SSSR" Vol 87, No 2, PP 179-182
Considers the difference equation of the follow-
ing type.,
4Lum,n - Um4l,nj1 - Um-l,n-l - u,+I,i,-l - Um-l,nkl:
0 for all values of m4,n over the
245T74
xy-plane. Demonstrates that solution of this
equation increases to infinity*slover than
and tends to a constant. Submitted
24 Sep 52.
245T74

SOBOLOV, S. L. PA 245T78
USSR/Mathematics - Difference Equation 21 Dec 52
"A Difference EL',jUation," Acad S, L. Sobolov, Math Inst-
imeni Steklov, Acad Sci USSR
"Dok Ak Nauk SSSR" Vol 87, No 3j PP 341--44-
Considers the following difference equation.
wm-l,n-l - '*'mPl,n-l - Irm-l,ntl
- 4wm n (if or 0 (if m2+n2>0) for all
values"of m,n. Constructs the solution of this
equation Increasing to infin4ty as 1nf62+a2)5; also
woo.O. States that such a solution is uniq:ae accord-
ing to author's previous work ("Dok Ak Nauk SSSR"
No 2 (1952)), Submitted 24 Sep 52.
245T78

ai Lici - S-oc im /Fell) 53
'IFIve Sessions (2- Sep Ont srj,24etyll
Tisp vlat Na4., Vol 6, 110 _'(@53), PP 173-17.6
P. S. Aleksandrov, pi-es of -U@,e Society, urE;ed :-,embers to assist in iroblevis amoujice(i
at ',he 157,th Pal-ty @,Dn,@.reSs. --rie _followinf- reports were mde: K. A. S-itn-ikov
IlPossi',_dlity of Capture in t1he T--iree-ic-ody Problen.11 S. L. Sab,@@,r, "A Difference
E'cuation. "A. 11, KoL-io@;orov "Spec'ura of Dyna.@dc Systens on a Tionis.".L. V. Bitsadze,
"T'rB 1-:ixed-type E@:;uation uxx+sgriy.u@ --0 of 1-11. A. Lavrent'l ev." L. 111. Srete@iskiy,
IIT,@e T.Totion of the Gorfachev-ChapiA@Kn Gyroscope." 1. 111. Vekua, 'IS,-;. -stens of
Elliptic Ecuations."V. ',;T. JjerZrts1kiy, "Structure of t,,ie Spectrun. o'L lionlinear
Operat,or --cuations.11.- P. Yus!,-,1kc;vich, '111@athemiatics of Central A34 an Peoples in the
e t7y OnS
@Y-I@Ah @,eaturics.ll L. S. Sretenskiy vice zres of the Soci sub-@-,,eskled -el-Lcita'-J-
foZ ...emlber S. S. ayush,@ems L)a )iis 70th birthday.
P.@, 250T75'

PETROVSKIY, I.G.; VOVCHENKO, G.D.; SALISHCHEV, K.A.; SERGEYEV, E.M.;
MOSKVITIN, V.V.; SRETENSKIY, L.V.; GEWFOND, A.D.; GOLUBEV, V.V.;
,:d3KS.i.ND-ROV, P.S.; SOBOLFV, @S@@
- " . ; BAMALOV, S.B.; GGUBALOV, P.M.;
KREYNES, M.A.; KYASNIKOT, F.V.; ZHIDKOV, M.P.; GALIPERN, S.A.;
ZHEGALKINA-SLUDSKAYA, M.,&.
Veevolod Aleksandrovich Kudriavtsev; obituary. Vest.Mosk.un. 8
no.12:129 D '53. (MIRA 7:2)
(Kudriavteev, Vsevolod Aleksandrovich, 1885-1953)

KAMYRIN, L.I.; , akademik.
Applicability of the method of finite differences in solving equations for
thetmal conductivity. Part 2. Izv.AN SSSR. Ser.mat. 17 no.3:249-268 153.
(MLRA 6-5)
1. Al-ademiya Nauk SSSR (for Sobolev). (Differential equations, Partial)
(Heat--Conduction)

4.
7. -,;res@ntat`or- of func@ions of' @-,;o inde-endent varial-des, pcv;rittilng
derivati.ves in iriterpretatlon, and @,he @--ohlem of pri,.ni-!.l'vp-s.,
7 " 'Ll .1 @.- _j -
.1@. vek a. no. 5, l(6-4
9. Monthl List of Russian Accessions, Library of Congress, kPEIL 1953, Uncl.

,- , q -f:@ 9& -- ij '.., - L .
RUBINSRTSYN, L.I.; SOBOLEV, S.L., akademik.
Dynamics of the evaporation of ideal -polycom-ponent fluid mixtures. Dokl.
AN SSSR 90 no.6:987-990 Je 153. (MLR& 6:6)
1. Turkmenskiy filial Vsesoyuznogo nauchnc-isaledovatellskogo instituta
g. Nebit-Dag (Bnbinshteyn). 2. Akademiya hauk =R (for Sobolev).
(EvaDoration) (Fluids)

BRUDNO, A.L.; SOBOLIEV, S.1.., akademik.
Norms for Toeplitz fields. Dokl. AN SSSR 91 no.1:11-14 J1 '53.
(MLEA 6:6)
1. Akademiya nauk SS.SR (for Sobolev).
(Spaces, Generalized) (Matrixes)

ALITWDRIYSKIY, B.I.; SOBOLXVJ@S.L., akademik.
Theory of certain linear integro-differential systems. Dokl. AN SWR 91 no.
2:iBl-i84 ji 53. (91-RA 6:6)
1. Novosibirskiy inzhenerno-stroitellnyy institut im. V.V.&kvbysheva. 2. Aks-
demiya nauk SSSR (for Sobolev).
(Differential equations, Lin4ar) (Integral equations)

BRUDNO, A.L.; SOBOLEV, S.L.. akademik.
Relative norms fo?- Toepli - matrixes. Dc.'-I.Aff SSSR 91 no.2:197-200 J1 953.
MRA 6:6)
1. Akademiya nauk SSSR (for Sobolev). (Katrizes)

X.N. Ta.l.; SOBOLEV, S.L.. akademik.
One class of an integral equation of the first order with a singular ker-
nel. Dokl.AN SSSR 91 no.2:205-208 J1 '53. (MLRA 6:6)
1. Rostovskiy na Donu gosudarstvennyy pedagogicheskiy institut. 2. "-L-
demiya nauk SSSR (for Sobolev). (Integral equations)

E@ YJ L
RUBINSHTEYN, L.I.; SOBOLEV, S.L., akademik.
Dynamics of evaporation of polycomponent solutions with non-volatile
solvent. Dokl.AN SSSR 91 ao.4-.767-769 Ag '53. (MLRA 6:8)
1. Akademlya nauk SWR (for Soboley). 2. TurkmenBkiy filial VNII
g. Mebit-Dag.
(Yvaporation) (Solution (Chemistry))

ZIMMIL7,11, 0.; SOBOLEV, S.L., ukudemik.
M,i5ten--e @@'L solutions fcr inte!@ral-dilfferentibl erquatir)nz. , JIN SSSA 91
r.11a.6:'.261-12U"2 k, '53. (RU& 6:8)
1. Akarlemi,rn nauk SSSR (for Sobolev). 2. Gosudarstvengyy universitet L-i'l.
Kim Ir Sp r
.Ila KC)rO:rLj, Pkhenl.- an.
(Integral eq@mtions) (Differential equations)

VATOERG, M.M.; SOB0JJV, S.L. ,, akademik.
Structure of a certain operator. Dok1.AN SSSR 92 no.2:213-216 9 153.
(MI-RA 6:9)
1. Akademiya nauk SSSR (for Soboley).
(Operators (Mathematics)) (Functions of real variables)

VAYITBF,RG, akademik.
Solvability of certain operational equations. Dokl.AN SSSR 92 no-3:457-
460 8 153. (mLaA 6;9)
1. jika(lemiya nauk SSSR (for Sobolev).
(Operators (Mathematics)) (Spaces, Generalized)

BLINVA. Yo.g.; SOBOLEV. S.L., ukudemik.
Pressure determination at sea level. Dol-I.Ali =R 92 uo.3:V?-560 S 15).
( laaA 6: q )
1. Akademiya nauk SSSR (for Sobolev). 2. TSentrallnyy institut prognozov
(for Blinova). (Atmospheric pressure)

TAIDYKIN, A.T.; SOBOIJCV, S.L., akademik.
Existence of eigenvaluss and the completeness of systems of characteristic
elements of linear operators. Dokl.AN SSSR 92 no.6:1121-1124 0 153.
(MLHA 6:10)
1. Akademiya, nauk SSSR (for Sobolev). (Operators (MathematiciM

VISHIK, M.I.; SOBOLEV, S.L., akademik.
First boundary problem for elliptic equations, degenerate at the boundary of
the domain. Dokl.AN SSSR 93 no.1:9-12 N '53. (MLRA 6:10)
1. Akademiya nauk SSSR (for Sobolev). (Differential equations)

VISHIK, M.I.; SOBOLZV, S.L., akademik.
Bo,indar7 problems for elliptic equations degenerating at the limit of a
domain. Dokl.AN SSSR 93 no.2:225-228 N '53. (MMA 6:10)
1. Akademlya nauk SSSR (for Sobolev). (Differential equations)

BRODSKIY, M.L.; SOBOLEV, S.L., akademik.
itaymptotic estimates of errors in numerical integration of uystems of ordina
differential equations by methods of differences. Dokl.AN SSSR 93 no.4:599-
602 D '51. (MMA 6-:11)
1. Akademiya nauk SSSR (for Sobolev). (Differential equations)

BURDINA, V.I.; SOBOLRV, S.L., akademik.
-",- - @@ . I @ - @'. - -4
Boundedness of solutions of a system of differential eTaations. Dokl."
SSSR 93 no.IF:603-606 D '53. (M12A 6:11 )
1, Akademiya nau.1c SSSR (for Sobolev). (Differential equations)

L

[The
maternatiteskol fIzikL
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V*Sobolev, S- L,
Gosu-
3d ed 3
.
physics.]
athematical I
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;Y,&bo1eY,S.L. On anew problem of mathematical physics
-A-Mg.-Ana Nauk SSSR. Ser. Mat. is, 3-50 (1954)
(Russian)
ow.
The author solves the initial-value problem for the foll
ing system of partial differential equations:
av
M @---VXk+gradP=F, divV=g.
Here F is a given vector, g is a given function and k is a unit
vector in the z-direction. The vector V and the function p
are to be determined subject. to the initial condition at time
1=0 that Vequal a given vectorVa forall points in a region
R which may be the whole space or may be bounded by a
closed surface S. In the latter case a boundary condition,
such as p = 0 on S or the normal component of V= 0 on S,
must be satisfied. The author uses the method of orthogonal
projection in Hilbert space to show that (*) has a solution.
If R is the whole space, a fundamental solution of the system
is constructed and then by the use of generalized Green's
formula an explicit-solution of is obtained. Finally, the

AL

Al

author obtains an explicit solution of a'Au/(7t2+c11u/a;0=@
with the initial conditions: u = uo and clu/clt= ul at time 1=0.
B. Friedman (Berkeley, Calif.).

Sobolev, S. L. On a new problem of mathematical physics.
-
Re
Po
Romlne
An
Romino-Soviet
Acad
ub
Mat
.
.
.
.
.
p.
.
p
1(12), 5-5S (1955). (Romanian)
Fiz. (3) 9, no
1@32
anelation oi the paper reviewedabove.
@i Y-

f Z
e
44-1-9
TRANSLATION FRC14: Referativniy zhurnal, Matematika, 1957,, Nr 1, @t 1 (USSR)
Sobolev, S.L., Kitov, A.I., Lyapunov, A.A.
TITLE: The Principal Features of Cybernetits(OcnovaM cberty k1berm tiki)
PERIODICAL: Vopr. Filosofii, 1955, Nr 4, pp 136-148
ABSTRACT: The article represents the first attempt at a serious study of
the scientific content of cybernetics. Cybernetics is defined
as a new scientific trend, created by N. Wiener, thich is not,
however, a sufficiently wen-developed and complete scientific
discipline. The,main divisions of cybernetics, according to
the authors 1) are: (1) information theory; (2) theory of
computing mkchines, as a theory of self-organizing logical
processes similar to htum thinking; and (3) theory of
automatic control systems, which includes the studyfram the
functional point of view, of the working processes of the
nervous system, the sen&ory-organ* end other organs of living
organisms. Attention is given to the mathematicar-appamtus,
of cybernetics, in particular to the study of informstion,with
reference to the work of K. Shannon (collection of translations,
"Transmission of Electrical Signals in the Presence of
Intexference", Moscow, 1953) and A. Ya. Khinchin (Both., 1954,
3T71). The necessity of ccabating foreign reactionary
Card V2

20-1-14/54
IriibeddinK Thoorcias for Abstract Functions of Sets
point Q. The first of these theorems reads as follows:
t, andw(@ P) be continuous as functions of'
(E)
point in Then U(@) is a continuous abstract function of
point The cuncept of the derivation of an abstract function
of the sets is also introduced. The proof of the theorems E;iven
in this paper is based on the transition to "medium" (averaped?)
functions. There are 4 Slavic references, no figures.
ASSOCIATION: Mathematical Institute im. V. A. Steklov, AN SSSR
(Matematicheskiy instizut im. V.A. Steklova Akademii nauk SSSR)
SUBIMTEDt February 22t 1957
AVAILABLE-t Library of Congress
Card 2/2
20-114-6-9/54
kcademY
Sobolev 9 S. Member Of "he
AUTHORt at Bunction Spaces Connected With the
kb stra rostranstv abstraktnykh
,y,tensions Of gr 1 (Rasshireniya P
TITLE1 The F e a iyey integrala)
Theory Of the IrIt nyye s teor 0
funktsiy 9 svyazan jqaik SSSR,1957,VOI-114)Nr-6,pp.1170-1173(USSR)
nRIODICALI Doklady Pkademii of abstract functions is suitably constructed
The integration
ABSTRkCTt by limiting the integration operator
(p) dP of the graduated functions
is defined in the quantity 0 ace X. This hoperator is
(Wh* alues of the Banakh SP sumed by t e equation
T (Y) yith the v ons which are a 2,
thus defined for functi
(i
sipify certain elements of X and
ion the f- esgue measurable
In that connect I ense Of Leb
B - signify in the S
the 0
Card 1/2 uantities,

L;. L. anu LYi',-VUJl,)V, A. A.
i
Cybernetics ard lkatural Science," Vopros-y filosofii Zproblems oC Philojophy/)
1,',@158, I-I.o. 5, F@u;-es 127 - 138.

-I - ,
@S .
VISHIK, M-1-;,.SOROLFV, S.L., akaiemik.
@' ' -1 @ - @ I I 1 :-1;7 1, k-@@
Gens)ral formulation of certain boundary problems for
elliptical differential equations with partial derivatives.
Dokl. AN SSSR Ill no-3:521-523 N '56. (MLRA 10.-2)
(Differential nquations, Partial) (functional analysis)

so: Rf2C?:r 1 195@,57, mirlstry of
ar4 Scintific R*EoIsrch, ln`!"
36
1-litul..
-Tune I. by Prof. J. B. S H.Ihiwi, I.
1.di.. Ni.th ...... k.l S-6ty
I,"Th@ Nature el Sp.-" by D" X, S.
1955.
2. "rhe. Ext,-- d I- b, D,, G S @-t.pnl In
Deeemb-, 1956.
C411.1t4 S-kiy.
L "The Clc.u,. .1 1 a@ Apj,@,-
,.Iorn" by A-d--- S 1@@,l
I "Pre4iction The,ry and 4;MrAtinnal Anal
Y,, Pto:
W,c.,r, I. !A-n, 155,1
ludi- Ch-ii-l S-i.4y.
1. -L Mchtrtm- by P,.f R G C-. in J--@.
"Principal N
Motho@b; of Slotty of Ttrro,;rwi @4 S-i lroiect3
Dam ig ic,ultural Cnpa, Treeu and Snrutc. ' t,,- Ac-lonici-
D. Fxfo4na.ury, 1954.
3. "Recerit Ade:lnees in Phy,ics in the Scmice .)! C-inwry" by
P..(. S. S Aug%,s:. N@-
Z-1cigi-I Su,..y .1 1.dla@
-The Role .1 Ta;.I-.y In 1.d4", Moinch. 11@@
"On the Application of Nocitar Enerl;,v to Meci,-, Agricull,ire
and Industry, lt--h Reactors trid Science I.. III Apill,
29. VIGYAN SIANDIR
A %ch... for the t.Wre.-ent of Rur@l S-wifi, C-tire, k.I,..,
'V,gy,,, @londlm ., - sUM11 b) Ila, Minx-ry . Aog,,,t, lit,41,
..d w Ulq.,i,(-,i ..all m-Wk a., icing .,,C in
@lecte'@ in -r,nu, pci, f the T!, bW,t 1,e
"/Iain M-firs, is w @tircaw the @111.4,rs 1. t6' .1
the methocis of m-ce in their day-t-lay life.
Fourteen Vigy.o, M-dir,i h,Iee h-n at
K.N@her. (Dcih,). NU-.1, 1U P ), K,illopu, Cc,,mb.n-.@
(NUdir-). Pd., fum,,-p-rn (K,,.i@i P.,harigatij .,,.i
Surri-pur Seho,w 4 M 11 r, Sh.r., Ia-y). Vik4r-A-1

SOBOLEV, j. L. and I.YAI-UIOV, A. A.
Ubernetika i estestvoznaniye fCybernetics and Natural Scien,::J, Publishing
House of the Academy of Sciences USS-,@, 1957, 26 pa,ges. (1-1--teria-I for the
All-Union Gonference on Philosophical Problems of Natural Science).

LAVRKKT'YXV, N.A.; SOBOLIV, S.L.
Illia Nestorovich Vekus; on the ocansion of his 50th birthday.
Usp.mat.nauk 12 no.4:227-234 Jl-Ag '57. (KIRA lo:10)
(Vekna, Illin Nestorovich, 1907- )
I

SOBOLEV, S.L.
A. M. Liapunov's work in the theory of potential. Prikl.mat. i
mekh. 21 no-3:306-308 My@Je '57. (MIRA 10:10)
(Potential, Theory of)

(d)/FCC(w)/BDS AFFTC ljpk
12833-63- EWT
ACCESSION DR: AP3003216 S/0020/63/150/006/.1238/441
AUTHOR: -Sobolev, S. L. (Academician)'
TITIZ- Application of computation factor to formulas of mechanical volumes
SOURCE: All SSR Doklady, v. 150, no. 6, 1 1238-1241
90
TOPIC TAGS: computation factor, mechanical volume, Fourier representation,
Dirac function, degree of polynomial,
polynomial
ABSTRACI!- The problem*is to determine the coefficients of equation (1) of the
Enclosure such that the functional I(x), defined by equation (2) of the'
Enclosure vanishes oil ail polynomials of degree m-l. For a finite case, a
necessary'and sufficient condition that I(x) vanishes on all polynomials' of
degree m-lAs thatt its Fourier representation should have a root of order mat
the origin. An analogous theorem is given in the case of unbounded regions.
Orig. art. has: 6 formulas.
Association: Inst. of Mathematics with Comuter Cahter., Siberian Division.,
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SODOLEV, S. L. (Acad.) and LYAPUI4GV, A. A. (Prof.)
"Cybernetics and the Natural Sciences."
report presented at All-Union Conference on Philosophical Questions of the Natural
Sciences.t @`cientlfAs Club, 22 Oct c8

AUTHOR: Sobolev, S.L. (Academician) S 0 v / 2 0 - 12dfo h-
TITLE: Remarks on the Criterion of Petrovski-Y of t`ne Uniform
ness of Cauchy's Problem for Partial Differential Ewiaticr?
(Zameohaniya o kriterii Petrcvskogo ravnomernoy korrekt-.o,,-.'-
zadachi Koshi dlya uravrieriy v (-,hastnykh proizvodnykh)
PERIODICAL: Doklad-,.- Ahademii nauk SSSR,19@;9,Vol 121,Yr 4,PP @,)8-60! (U@SSR)
d I J
ABSTRACT: Lot the Cauchy problem
(1) U
Lu r- iLu + L A k
atp k cr' , where e+ it. In this case L is called an
0
operator of Petrovskiy. The operator
(4) Lu A u
is called an elementary oparator of Petrovskiy. If m is even
and I arg k+ 'A]l < 'U , then (4) is called strongly par,2-
2
bolic. If m is odd or
I arg 'Alj then (4) 48
called semihyperbolic.
Theorems The operator Lu n - B Jlp-) u is an operator
Card 2/4 atr, ?xp)

Remarks on the Criterion of Petrovskiy of the Uniform SOV20-121-4-7/54
Correctness of Cauchy's Problem for Partial Differential Equations
of Petrovskiy if and only if n = 2, p = 2m and if the factors
CB 9
are semihyperbolic operators of Petrovskiy.
Theorem : Every operator of Petrovskiy is representable as a
product of elementary operators of Petrovskiy
m
Lu A d u + L U
s m 2
s=1 Ox S )
where L2u contains the terms of lower order. By the expansion
of the root of (3) in terms of powers of 01,
1
A + A1 oc M- Ir + + AM +
Card 3/ 4

Remarks on the Criterion of Petrovskiy of the Uniform SOV20-121-4-T/54
'Correctness of Cauchy's Problem for Partial Differential Equations
and formation of symmetric functions from the conjugate roots
(i.e. from those which arise by the sustitution
1/s 1/s 20ii/s
OC -4.(/ . e the author obtains
certain canonical operatGrs of Petrovskiy. It is shown that
every operator of Petrovskiy differs only by unessential terms
from a product of canonical operators.
There is 1 Soviet reference.
SUBMITTED: April 19, 1958
Card 4/4

AUTHORS: Sobolev, S. L., Mukhina, G. V. SOV/89-5-2--15/36
TITLE: The Determination of Thermal Stresses in a Medium Containing
Cavities (Opredeleniye temicheskikh napryazheniy v srede s
pustotami)
PERIODICAL: Atomnaya energiya, 1958, Vol. 5, Nr 2, pp. 178-181 (USSR)
ABSTRACT: When calculating some types of fuel elements it is essential to
solve the following mathematical problems:
A body with a uniformly distributed heat emission Q with respect
to its entire volume exists. The body is subdivided by cylindrical
channels which have circular cross sections the axes of which are
parallel to one another. Heat removal takes place only by the sur-
face of the channels and the surface temperature is constant and
equal in all channels. The body is able to expand freely in all
directions. The demand is made to find the maximum ailatation-,
compression- and shearing stresses in the body under the following
conditions:
1.) No exterior forces act upon the body and it is influenced only
by the interior thermal stresses.
2.) The maximum drop in temperature in the body is not high and
Card 113- the material properties of the body do not change within this

The Determination of Thermal Stresses in a Medium SOV/89-5-2,-15/36
Containing Cavities
range of temper-ature.
3.) All stresses produced in the material of the body in no case
exceed the limits of the elastic deformations and the
properties of the material are isotropic in all directions,
The problem of calculating the elastic stresses is carried out by
means of the variation method according to Ritz.
By the introduction of the function according to "Eri" (Airy?) the
problem is reduced to the determination of a maximum of the
integral: ff [( L U) 2-2qU] dxdy.
When using this method the selection of the most suitable system
of the function on which the approximated solution is based is of
essential importance. It is shown that the function according to
"Eri!' is suitable for the solution of the problem in question.
A simple method is given for the determination of the approximated
Card 213 S,)lution. There are 5 figures.

AFTHOR. -.Jobolev, j.L. , Academician SOV/20-122-4-4/57
TITLE: On Mixed Problems for Partial Differential Equations With Two
Independent Variables (0 smeshannykh zadachakh dlya, uravneniy
v chastnykh proizvodnykh s dvumya nezavisimymi Deremennymi)
PERIODICAL: Doklady Akademii naDk @;SSR,1958,Vol 122,Nr 4,PP 555-558 (USSR)
ABSTRACT: The equation with constant coefficients
M @nu + 7 A Dk+1U f
@tn k