SCIENTIFIC ABSTRACT ILLN, V.A. - ILIN, V.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000618510002-8
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: April 3, 2001
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

V.A. (Pockva)
---------Rrinciple8 for the designing of contELctlOSO Nltvta-ilontrol
a78 te cm equipped with exponential convertors twitb aunmrr in
Snglishl. Avtom. I tales. 20 no.4!Vj8-472 Ap '59.
NIRA 12:5)
(Remote control)

all a
I all
v .,I :Pit p I IIN tpp 5f
J4
14
0-1 i 1
3 t jig
u lit,

I WIN, V.A.----
[Concerning the methodology for tranmitting, Iriforiiation am tba
structure of remote control Pystema of 4ispirued objibcts) 0
metodakh peredachi informatsii i struktxwe diisteir. telemokhandki
dlia raearedotochennykh ob"ektor. Moskyap 1960. 3.0 Po (International
Federation of Automatic Conirol, Ist International Congroest Mocow,
1960. Dokladyp no.46) (Remote control) QIIRA 3-4: 8)

PWZ X BOOK M(FL4DXTATXON WOOD
Illin, Viktor Aleksandrovich
SistecWtelemekhanlki dlys, raseredotochennykh Wyektov- (Renote-Control Systma
for Dispersed Objects) Moscow, Goesnergoizdat, 1960. 110 p. 13~000 copies
~rinteC , (Series; Biblioteim po 0tonatike, "p. 15)
Editorial Board: I.V. Antik, S.Io Veshenevsklyt VoS, Kulabakln, A.D. Smirnov,
B-So Sotskovo Y~oP. Stefeni, and NoN, Shmllmkly; Edo: 10A. Kuzaetsov; Tech.
Ed*.- G.Ye. lAxionow.
XWOU: This book is intended for students in advanced c*urses and teabn1cal
poreannel concerned with the automation and remote control of manufacturIng
processes*
COVEMOR., The book exemines the structure and the principles of Usign of re-
note-control systems In vhIch the objects of remote control am lispersed
over a given area or along lines and participate In a single mmiafe-turing
process (oL1 and pa Industries, pipelines, quarries %n4 mines, railrind wA

28 (1) 9/o3o 6o/ooD/oi/o60/067
AUTHORS: Illin, V. A.9 Doctor of Technical B01 5X01 1
sclencedi NzZTkonovL-A. 0.1 Candidate of Technical Scien,-~as

TITLE: Position and Prospects in the Development of Ulomechanicio
PERIODICAL: Vestnik Akademii nauk SSSR# 1960v Nr 12 pp 110 - 113 (USS11)
ABSTRACT: The authors describe the course of the saliantllli~-technicALI
conference on telemechaniom hold in
to 21, 1959. The Conference had been convened by the Akademiy~&
nauk SSSR (Academy of Sciences of the USSR) and. the 03sudarst-
vennyy nauohno-tekhnioheskiy komitet Sovela Min;hotrov SS31
(State scientific-technioal Committee of 1,he Catimail. of
Ministers of the USSR), and was attended by deleirates of the
industry, scientific research institutes,, deslAn offices,, and
universities. The numerous and miscelltneous lectures shoired
the important progress made by scientifto rosearah in the fie:W
of telemeahanice and its praotical application iii the laut
years. Unlike former timesp when power economy wits regarded aii
the chief field of application, the facilities offered by tele-
mechanics today are introduced to an ever greater extent In the
Card 1/2 petroleum and gas industry, the railroad transportation, large

ILOIN, II.A. (Xoskys)
Reliability of switching circuits In dispermod ryotems.
Aytom.i toles, 21 no#4:330-532 Ap 160o
(XIRA 13 t 6)
(Switching theory)

N? ,69
S/ 10 3/60/02 1 /00 13/00 91014.
Bm./Bo63
AUTHOR: Win, V. 1.,(Moscow)
TITLE: Remote Control of Spread Objects
PERIODICAL: Avtomatika i telemakhanikag 1960, Vol,, 21t No# 8,
Pp- 1173-1160
TEXT: The present paper describes now, very reliable circuits for the
remote control of spread objects, using a code of two frequencisos Theo*
circuits were developed at the Institut aytomatiki i Islemolkhaniki Alt SSSA
(Institute of Automation and Telemechanics of the AS USSR). A, disturbance
of any element of these circuits cannot lead to an erroneoum selection
or command, but only to protective non-operation. Such a ci-rouit diagram
is shjwn in Fig. 1. It needs no local feeding sourcem. Two cubsequent
osoillatio.as of two frequencies, f I and f , are sent from the dispatcher
point* A dividing transformer lowers the influence of the line on the re-
sonant cir.,uita LIC Iand L 2C2* The circuit diagram is briefly described.
The same r9sonant circuits may also be used to select anothler object. In
Card 1/3

112 1,6y
Remote Control of Spread Objects S/lo 60/021/008/009/014
BO 12Y13064
this caset the oscillations are tranazitted In the iniftrao order of
frequencits (first f 21 and then fi). Such a circuit wam uetd for a slaton
developed by IAT AS USSR. The capacitor C in the oirouit d1agran shown
in Fig. 1 is charged at the expense of the energ;r of ths ftrat airoult.
In order to eliminate this drawback, an amplifier is 1,ionneotfed to tho
output of the first cirouit. Such a circuit diagram 141 reproduced in Pig. 2.
It is shown that it is neoessary for many telemechanii:i freqn,onoy sylittas
to reach a reasonable compromise between a singlo oirouit and compliolLted
filters with many inductances and capacitances. Two-cIrcuil irilt*rs used
in radiotechnical circuits are offered as a suitable oolutiom for tela-
mechanic systems with spread objects. LC resonant tw~y be replao*4
by two-cirouit filters without any appreciable chango of the mode of Opera-
tion of the circuit. Adjuatment and calculation are uivoomplioatod (R*t, 7)-
Fig. 3 shows the circuit diagram of a two-circuit MLer, by which rsaonan.t (/i
circuits way be replaced. The selective properties of resoAojit circuits are
compared with those of two-cirou-L't filtoraq and the advantages of the lat-
ter are diagrammatically illustrated in Fig. 6. It in finally noted ihat
the effici-ency of utilizing the channel of communication own be improved
Card 2/3

1'12 769
Remote Control of Spread Objects 3/103/60/021/008/09/01-t
B012/BO65
by the use of two-cirouit filtere. There are 6 figure* and 7 Soviet I
references. I /
- I
SUBMITTED: March 11, 1960
Card 3/3

WIN. Y.A.; SHISMA.MV6 I.A.
Uniform evaluations in a closed domain for s4wifunctions of an
olliptic operator and their derivatives. Izw , MI SSSR, Bar.
mat. 24 no. 6:883-896 JI-D 060. (.K]:RA 1411)
1. Predstavleno akademikom S.L. Sobolevym.
(ligenfunotions)

,/60/132/02/2-t/o67
S/020
BOD I 4/B 007
AUTHOR: 111in, V.I.
I
TITLE: The Generating of Pulse Oscillations of Stabko Proquency
PZRIODII%IOAL: Moklady Akademii nauk SSSR, 1960, Vol. 132, No. 21 PP- 323-325
TEXT: For the purpose of warranting a higher frequenoy stoLbility of generators
for sinusoidal vc1tages and pulse voltages, the use of
suggested. L diode is connected into the diagonal of the Vvidge, This kin(I of
generator is a further development of the exponential converter (Refs. 1'.0
suggested by the author in earlier papers. The circuit diagram. of this glallerator
with an eleotromagnetio relay is shown in Fig. 1, On the 'Im-sin of the volta4;0-
and current diagrams given, the mode of operation of the jj;tnerutOr is disiiuSsed.
Derivation of the formula for the calculation of the oscitlat'Aon period frou
the circuit elements is carried out without taking account of the internal
resistance of the current source and the Inductivity of t.he rol.a:f. Fig.. 2
shows the circuit diagram of such a generator which is comj-)solil of contactloss
elements (tubes, transistors etc.)# and Fig. 3 shown two :I'ully transistorLzed
Card 1/2

T1.e Generating of Pulse Oscillations of
Stable Frequency
81020160,1132102121106',r
1101 Vboo~
cirouits of this generator. In circuit A (Fig. 3) a frequomoy dhange of 0.0021~
occurs with a change of voltage of 1%, The author points out the general usability
of these generators. There are 4 figures and 2 Soviet referencesi,
PRESENTED: January 18, 1960, by L.I. Berg, Acaaemialan
SUBMITTED: Jenuary 16, 1960
Ozl
Card 2/2

WIN, V.A.; SIUSIOMBY. I.A.
Some problems for the Lu"div Cp(x)grad u1--q(x)u. operator with
discontinuous coefficients. Dokl- As 83SR 1,135 n0-41773-778 '60-
(KIRA 13~-11)
1. Moskovskiy gosudaretyaniWy univeraltat im. X.Mononosom
Predstayleno aka4ecdkom I.CV.Petrovskin.
(operators (Mathematics))

~L.IINp.V.A.,, red.; KOLBANOVSKIY, V-14.1 rod.1 KOLIMAN, S., rj4,;vjxTonGyA,V.,
red,; CIUMMM, 1, p mladshly roda; MOBKVIIIAp 8. p tok:hn. red.
[Philosophical problems an cybernetics] Filosof'sIde roprosy kibeme-
tiki. Moskvap zd-vo sotsiallno-ekon. lit-ryt 1961. ')91 P.
64IRA 1.4 16)
(Cybermetica)

/C44/62/0(:,0/G04/'N;7/099
C1 1 1/C222
.,.uTdoli: Jilin. V.
Som4~: q:aest4ons on the scicnee: of contro. v.,stam:~
FZ= '!CfCf~LtiVn~',; J~',atQ Zia tjjr 1 2, 6,
("Filoa. voprooy
1~61, 213,-261)
"'ZXT; The aaerk;e-vic s true' of control :,;ystem~~ -Ij
a, o' viier -Y izj in ~L curtrol L3~ ,; to~-, by f aodin - oz;all
Systems vrf.th fccd-b4ck
re.,,;uiators - .-re -Iescribed. Discuose-C, f-rc Self-adaptina
z,aci-inas, z.~, vioil a-- the reL~li,--;~.tion of -)rocessoa t-4A 1--1'3 an4Llcj;ouz to
Z, cOIIIk..--.Qn4l re"ley. Th, Cu~Iktiti-tivu~ CharactoriLticil L~-~ Who br4-in 4-nd
of 'U*,!~ 171OLiUrl'I ..-."ch-4nu:j ~-ro com ~zrcd, such aLi the ul)L-od of 9~-jrna'- t~rana-
t"e TOL~(;tioll ti:.-,L; O~,
C-:111. and the nu,-,,*.~or of cella. Of t he ~, a
only the numbor of cells of the brain is L~,rC;ev -,"-,~n that
of .-ZLLc,-,J-nLs. analooy is drawn bctwean t'ne div-fa--'Oli of
CGY,tr~).- fu--.Ctions of the lauau' 'z;nd soinal cor(.' and th-~ of
f~-.:.Ctions 0, -2,G "he industrial revolution, -xh4
A-.. 1. lc 'I
rU*-)IL,ccd lubor with i~; com,.Lired to t~o tend,:~ncy to
Cz.rd 1/2

S~Qal,~ cues tions or. -le sc.L~;ncc 0.
tho tiresome job of controllin- tho
4 toelf. Tho desiGrLtion lltliinkinj machinull
conv,~niunt one.
(Absti-axter's note: Complete tranolation.]
S/04,;/ 6 210,, ".')/'CC, 4/05 7/,D99
Cl 1 1/C222
ricchaniEjm "Vo tho r-ch`ile,
is defendell (w 1611iv .-,Oot
Card 2/2

S/044/62/000/007/064/100
C111/C333
AUTHOR: Illinp-,V.- A.---
TITLE; 'Teleautomaties and cybernetic
PERIODICAL: Referativnyy zhurnal, Matematika, no- 7, 1962, 42,
abstract 7V180- ("Kibornatiku-na sluzhbu 1kommunizzu. T.1".
M.-L., Gosenergoizdat, 1961, 262-272)
TEXT: For the modern automatic control a qualitivo leap is
characteristict this is the transition to complex Hill, Toma $10 control and
telemechunisation, to the union of the work-benches &nd -L)14j aggreples
in only one industrial procev-. in connection with this thore arises tha
necessitj of solving now proble.- which are connec-;cd with the opt~-mal
improvem,ant of the industrial processes with respe6t to numerous pal-a .
meters; there arise specific problems of the tranamiasion of informuti-
one by means of teleautomatics. According to the author taleautoma ties
investigates systnms possessing as well charaoteriatics of the
telemechanical systems as characteristics of the controll-oyste-As. The
author considers the characteristic properties of tolemechanics
and Jeleautomatics as Well &S specific characteristics ot the trans-
Card 1/2

Teleautomitics and oybern6tic C11I/C333
mission of informations in these systems. At the end the author discuss-
es the next tasks of teleautomatics and the chances Tor t.he applica-
tion of cybernetic to the solution of those quostion4i whi,::h are
connected with the degree of effect of the atuoring of talcautomatical V
systems.
FAbstracter's note; Complete translation.]
Card 2/2

3
S/103/62/023/006/007/012
D286/1)3DB
AUTHOR: -111int V.A. Moscow) N
TITL-:: Determining the efficiency of transufl.eision of tele-
mechanical information
-tvtomatika i telemelchanika, v. 23, no. 6, 1962,
778-735
T E" ~ T The author suggests a comparison of all signalling,
0
remote control and telemetering systems based on the., criterion oi
transmission speed in bandwidth F: RF = R/F - ('1092TIOF where T
time interval required -11or a single message and log.n. - number of
mossages (n . number of possible different combinaflions) all counted
ill li)iaary uni-ts. 5 methods are considered: ,Augle-channel time meth-
od; sinrrle frequency method; two-frequency method vrith simultaneous
transmission; two-frequency method with consecutive transmission;
binary time code. Formulas are given for RI? ia tellim of releNiant
parameters. The results are compared in a taVL(! and plotted. They
indicate the superiority of the binary code syt3tems for largo- values
C a r d (1'/ 2)

S/103/62/023,/006/007/012
Determining the efficiency ... D288/D308
of n, and of the simplest single -frequency system for n . 2-13.
Ilractical limitation of transmission ST)eeds is due Nattily to filter
t-.iethods are
bar-dwidths. For telemetery applications the followfilg
co-nsidered: E-1, pulse wl.dth modulation, pulse position modula-
tion and pulse code modulation; expressions for RI? iti terms of pulse
and modulation characteristics are compared. For cases of short
relative pulse duration P.41.1 and PIPM appear to be most efficient; in
cases demanding the error factor 6 . 1/2n to be undar 5%, PGM is
,.u-.)erior. 'Yor short distance hauls simple A,j nymtems provide a sat-
isfactory operation. i~ graphical representation of 11-F Vs & in
is given. There are 3 figures and 1 table.
SUBMITTM: December 14, 1961
Card 2/2

BERG A.I., gl,,,v. red.; V.A., glnv. 1"Ic Is., ~'J~.y
mml Clav. rcd.; A.Yr-., doktor tc-'Jn.
zar. F-Iiv. red.; AVIII, 0.1., red.; AGEY11311, D.I., rod., kanI.
tekhn. nauk# dots.p red.; AYZERI-M, M.A.# red.1 VEIIII(OV, V.A.,
doktor teklu.. imule, pror., md.; VOR01:011, A.A.t (Iolt-tor tokhr.
nauk, p~-of.y red.; GATUMV, M.A.2 eolctAn tal-hri, nnuir, prof.,
red.; 7TTOV, D.V., red:;. ILIIII, II.A., dok-tor tekhn. naW,~,
prof., red.; HIM, A.1 rc,d.- b.Y-~"
cloktor tokhn. imukj red.; KOSTOUSOV, A.I.P K;~'111171:411T.
N.A., kand. fiz.-mt. nauk red.;
LOZIFSKIY, X.G.2 doktor telchn. naWcy rc-(I..-
red.; VAKISAREV, Yu.Yo., rod.; WtSIAN A.A. dotdi . rod. I PU6 A.A., rod.
HAKOVOMY, N.Ye.t rod.j -OZ11111111,G, L.D., doittor tolifit.m",
prof., red.; SOT.:~E(,V, 1).S.p.red.; TIMOOMVI P.V.,
USIUKOV, V.b., doktor tol-hn. nauk, red.j F1,111AU1.1, A.A.p
doktor teklui. riauk$ prof., rod.; IT.'OLOV, V.S., redo;
rURKEVICII, A.A., red.; MU11,10Y, A.V.,, lvirA. Uikhn. muk$ rod..1
TSYMM, Ya.Z.., Ooktor takhn. naul., prof., rcxl.; CIIEUIUSTKII.,
A.B., kand* tekhn. nnuk-p red.; SHRETDER, Yu.A.j k'I.-nd. fiz.-
mat. nauk, doto., red.; 130CIIAROVA, 14.D.0 kand. t,ekIm.rmwq:v
r,tar.g!iiy nauchnyy rc-d.; DELORE, N.11,j, in-zh.~ wwchtn, red.;
BARMOV, V.I.p naucluiri red.; PAVLOVA ,7.1.P Lellm. red.
(Continucd on next oa-i'd)

BUIG) A.I.- (continued). Card 2.
(Industrial electronics wyl automation of pr&luction procer-
seslAvtomatizataiia proizvodstva 1. prorWnbleywittia (A.Oftronika.
Glav. red. A.I.Berg i V.A.Trapeznikov. Yoskvao Goaowiuchn.
izd-vo "Sovetakda gntsiklopedlia." Vol.l. A . 1. 1~ 62- 521,
(WOU 1 5110)
1. Chlen-korrespondent Akademii naWc MR (for rotl!l-,vv,
Kharkevich, Zernorv, Timofeyev,, Popkov).
(Automatic control) (Electronic conturol)

'Trw
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-n,f;

-_3 'Z_
L 1992-6-63
ACCESSION 1171: ,%?30048Z6 S/0103163/0Z41008/11,47/11154
AUTHOR: Win, V. A.. ElIdarov, E. A. (M'oscow)
TITLE: Signal transmission over power -distribution Aetwo~-" (4 review)'
SOURCE: Avtomatika i telemakhanika, v. 24, no..P_,
1jt:j:"
io pow
TOPIC TAGS: remote control, telematering, signal transnat A or-,
distribution network
ABSTRACT: Use of power distribution networks as connectIng litsks for remote*-
control, telernetering, and supervidory-control equipment la varlotis countries to
briefly reviewed. Two transmission classes are distinguished: (1~ circular
remote control (house meter switching) at 175-3,000 cps; and (2) two-way signal
transmissionti at 10-100 kc. H-v transmission lines are.uOed for ijignal tratts"
mission at 50-300 kc and sometimes up to 1,000 kc; they %re equipped with.wavi-'-
traps and coupling capacitors. Attenuation per kM-ii-tabulated I oe-ri -ciontact
C~4 -, I /Z

L 1992.6-63
ACCESSION MR: AP3004826
lines, mine networks, and cables, for 10-150 kc. Data meaonre4 on 380-v Ou~A
6-kv oilfield n,!tworks Ir reported, including the effects of agenerator, ~ trans-
former, or a spur line connected to the signal-tranamiselon link. ?rench.
German, and Swiss systems of frequency-divisiton and pulse-time citntralized
romote control are described in some detail. Soviet superv9sor-f-control
systems (descriptions published elsewhere) for mining power netwoxks'
electrified rr-s and industrial 0,4-6-kv networks are briefly described. A1190,
some USA supervisory sys-:ems are mentioned. Orig. art. has: 9 figures and
I t'able.
ASSOCIATION: none
SUBMITTED- z5oct6z DATE ACQ: Z6Aug63
SUB CODt: 'CO
C.c.rd Z/Z
NO REF SOY: 109
EXCL-. 00,
OTHIML: 006

ILIIN, IT.A. (Moskva)
Frequency stable pulse generators. Avtome i tdo3em. 21, no.6-
808414 Je 163* (MIRA 16:7)
(ClecMators, Transistor)
(Pulse tecImiques (Electronics))

WIN, V:.~ktorl Aleksandrovich; YURASOV, A.11.0 red.; MJ1,'1,'YAYEV,,
JT.A.p "khn. red.
[Telemetering and remote control *80 die tz-lWta4 objecto'l
,relekontroll i teleupravlenie raseradotochonnyud. ob"ok4smi.
Moskva, Gosenergoizdat, 1963. 311 P. (,MIRA .17: 3)

ILOIN, V.A... dektor tekhn.nauk
Modern trend of telsmechani?,,s; All-Union Conferfmce I..-i Moscow.
VeBt. AN SSSR 34 no. 1:105-101 Ja 164. 0411A 17; 5)
.1
4
..'0"

- -I -- ~i of - ~;,v -,
I .- I I-..--"-..-
, ol' r--m-3te ! - : : , . , ~ I ;.
!.~ IG/.. 1. 1 !",., . ,.7-. "-, I..

AVEN, O.A.; DVORETSKIY, V.M.; DOMANITAIY, S.M.; ZALMANZON, L.A.;
KRASSOV, I.M.; KRUG, Ye.K.; TALI, A.A.; KHOX111X)V, V.A.;
BULGAKOV, A.A.; DEMIDENKO, Ye.D.; BPRNS11TEY11, S.I.; YTWLIYANOV,
S.V.1 LERNFR, A.Ya.; MEYEROV, H.V.; PERELIMAN, LI., FITSDER,
L.N.; CHELY71STKIN, A.B.; ZIOZIIIKASHVILI, V.A.; ILIP V A
AGEYKIN, D.I.; GUSHCHIN, Yu.V.; KATYS, G.P.; MR
PARKHOMENKO, P.P.; MHAYLOV, H.N.; FITSNER, L,11,; PARKHOWNW,
P.P.; ROZENBLAT, M.A.; SOTSKOV, B.S.; VASIL'YEVA, N.P.; PRANGISFIV1LI,
I.V.; POLONNIKOV, D.Ye.; VOROBIYEVA, T.M.; DRYABRUP1, I.Ye.
Work on the development of syatems and principloq of automatic
control at the Institute of Automatic and Remote Control
during 1939-1964. Avtom. i telem. 25 no. 6007-851 JI) 164.
(MITUL 17M

KHRAMDY, A.V. I'FYEII()V, II.Y.; AY"T'MAN, II.A.; (J."LUkVir, G.M.j
TSYPKIN, Ya.Z.; F-ELIF-BATIM, A.A.; IZIRIIER, A.fa..; NJOACIFI, V.3.;
ILIIN, V.A.; GAVRILOV, M.A.
Work of the Institute of Automatic aril Romoto tontlrol
on the development of tho theory of autortiatic contra-I during
1939-1964. Avtom. I telem. 25 no. 600-~X)'? 3a 164.,
(MInA 170)

ILIIIN, V.A. (Moskva)
Stabilization of time parameters. Avtom. i telem. 25 no.6:
991-996 je 164. (KIRA 17 s 7)

WIN , 'I.A... doktor teklu-i.rjauk
Improving the stAbility of pulse systemr. *Ievi, JUI -w.4 no.9168-
70 S 164. (MIRA :1'~O.O~
1. Inatitut avtorint1k] I tolomokhanihi (teUmichaskay kl1wrmet.11d]
Gosudarstvaniwgo kr~jilte&A po priboroBtrayarilyu.0 aredii'van avtclr4Ltl-
!!atsJ.i i sistf-~mm Lj)ravlariya p-l rk):)plano SU. t A)w,-:imJJ nauk ISSRo

_JLIIN,.~iktor Aleksandrovich; KUTIFERSINIT, Ya.A., rail.
(Pulne devices vith brIdge circuit components] IMPIO.'snyo
ustroistva s mostovymi olementami. Moskva, Evergifta,
1965. 70 P. (Biblioteka po avtomatikop no.1.30)
(1-1 III.A 18: ~5)

lat.,
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:,o -J.roy onli 1p1, mrade tMl 147'1 -;;I:ln lill 11
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it v Il,r ll;r!l 1.
IL
VIM.: R V Ir ""ril I ftoo-im

!"I'll Ii - 1, 1,%(:, i; Ili:! I
A ) , t .
I, '. p ,, -.. ( ~,~ (A is ~ 1:11,114.11, ~:x K!
. . . I . M
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ili
11111131,11111, 1
I w I 101T

,%CC NRi AT6022311 SOURCE CODE: UR/I:)000/66j'000/000/1)065/0071
~AUTHOR: Win, V. A. (Doctor of technical sciences, Professor)
I
;ORG: none
I
;TITLE: Selecting the structure of complex remote control spitems
!SOURCE: Vscsoyuznaya nauchnaya sessiya, poavyashchennays Dnyu radio. 22d, 1966.
!Sektsiya telemekhaniki. Doklady. Hoscow, 1966, 65-71
i 0
'TOPIC TAGS: remote control system, automatic control theory, teletiketry system,
,optimal.automatic control
;ABSTRACT: Wit.1 an increase in the size of automatic control systelms and the number of,
I
!scattered obje:ts it is practical, under certain conditions, to adopt control hierarchy
:which is one of the basic principles of cybernetics. In this cast bi)th the reliability
land the high cost of transmission channels require a large amtonomy of controlled ob-
ijects at their locations. As a result of this the application of the control hierarchy
;becomes necessary for relatively simple telemetriC 6YSt0MS. A hierarchic structure ioi
defined quantizatively at each control step by hierarchy coeff 'icie-ato Ki and the numbel!_
!of control steps m. The quantity Ki is the number of men, %mits, or objects sub-
~ordinate directly at each given control step. The choice of the structure of a
!hierarchy system is in effect reduced to the choice of coefficiento.Ki at each control
:Card i I-)

* , I 1,~, , ,i. ~ .
Cri -I ru--- , ' niz t r a I -c utf; Cf th.43 f ':If' ~-,l !0
W *,Wfn3r. ok, i; ' v nFi r ',.rn ll.,ur i_ rb~ I I I.-, ,,
4, ", 1- -,,,ioj'
, ./1?
f*t,?,~ld. y Z h.6 Olmfn D.. .

~, ! k,, !- -
I z , , . 1, .
.- . .C-
Suauimb'Jity oil Foarier 5erlej in elyr.~,nfuni::U(ms of a bar,iA7e
OPi",ator by Caparo, RISO, hrld Iii,eragm). [I.uh AN
SSSF A60 F 165. (VIR.' 18:2)
t, - sudarstvennyy "tvitted O'lly 9,
L. Mcs.ovekiy go,
19b4.

r o- t r-

T --I
F-

.-,/- I !~ !-.
I l I /In, ';. A. -- ~'Dif f ractlon of 'e:loc' r 11 - SvJ'-:-n' --', tt'rO-
. - - th Scl, Moscow Str-tc lip Mam-~-"Jll 195:1
i-enri ti es. "CrLnd ?4, -14,
(Rt-.ferE.tivnr.f Zhurnal-Fizika, Jjlr-'!R~7 5L)
so: sm 16.";, 22 Jul-.,r 1954

114IN; V. A
SUBMT USSR/MATHEUTICS/Pouriar series CARD -1/2 PO - 354
WTHOR IWIN V.A.
TITLE The decomposition of the fanctions with orie singularity inte
a series in terms of eigenfunotione. The kornelo of brokon, arder,
?ERIODICAL Doklady JLkad. Hauk jS.5.&. 18-21 (11955)
reviewed 10/1956
Let. a function possess the singularity r~' ( C-40 or Xn the two-dimenoio-
nal case for a apecial function of this kind the authoir givos a direct com-
putation of th6 Pouri6r ooeffialents for the decomposition with respect to the
system of vJgenfunctionq of the equationAu * 'A u os 0 in aa a,rbitrary region 0.
A formula J4 derived which determines the Fourier coqiff'Aoit!~nts of thla fWketion
A
-up to the terms of order -n/21+5/4 (n - arbitrary integer),, A function In
K
constructel which possesses the mentioned singulatity and which at tho same
time eyerynbere else is sufficiently smooth. The res-dIts irbich have sketched
proofs for the two-dimensional casev are extended to mrbitrary dimensions
(withont proof) and are formialated in the following thooreas Every ALnotion
of 11 varlable6 which in one point possesses a singul.axity irl' (f_-)--O) and
which everywheru else satisfies the condition of diooc(m~posa:bJ.l1tj, con. be de-
composed Into an absolutely convergent series in terms of eigonfunctiona
inside of an arbitrary N-dimensional region. Here the convej.,gence or every
inner sub:.-egion GI of G is uniform.

f4,i
SUBJECT USSR/ltATHEI,'ATIC,':3Thc-r3r-- nf tllnuth)77il: 111A
AUTHOR ILJIN V.A.
TITLE Sufficient conditions fOr LL decomposition into ar. abj-Aut;c 1~
and uniformly convergent series In terms of
PERIODICAL Doklady Akad. Nauk j.25S. 210-213 (1955)
reviewed 7/1956
The author given an essentially wetikening of the knoion imiffLatent corditioas
for the devolopment of a function in an absolutely and w',iforady collyargent.
soriea in Le,rms of eigenfunctions of the equation
AU +'Au - 0
in an arbitrary region G with a homogeneous boundary cunditiin of arbitrary
kind. The strong continuity of the derivatives is suporfluouis. The first
derivatives can have jumps of first kind on arbitrary objecti:.q not higher
than of firtit dimension. Generally: The k-th derivatiwes can have Jumpa of
first kind on arbitrary objects not higher than of (2k-1)-th dimensiou.
INSTITUTIONt Lomonossov University Moscow.

WIN, V. A., Doc Phys-gail Sol -- (dim.@) "Comosernivig; tho Cont-
i," E4-, kn'
vergena* of Expanalon5___ i-ttt-46" 410 Felp4nal Poncticons of a
Laplace Opprator." Moe, 1957. 23 PP* (MoO StAts Thiv Im LOIuO-
nosov), 120 copies. BiblioPTS pp 22-23 (30 tittlemil- M, 7-58.
108)
- I -

ILI IN, 7.A.
-
The foundation of rourier's method for the wave equation. Usp.
imat.nauk 12 no.4:289-296 JI-Ig '57. (MrRA 10.10)
(calculus)

I , 1 7
T , -, -- / --
IL I IN, V.A. (Moskya)
The kernel of fra,:tlonal order. lfht.sbor. 41(83) no.41459-460
Ap 157. OKMA 10: 7)
(Fourier's series) (Xigenfutwtioms) (IntsKral equations)

PT HOR Il I in, V. A. 2o-n4_4_6/G3
TITLEj
'x An
j
on the Uniform Convergence of E ions in Characteristic
:dimosti r&zlozheniy po
Incresoing Numbers (0 raynomerno.;h

'
sobstvannym funkt i am pri summirovanii Y poryadk~vozrastamiya
sobst,rennykh ohis:
,~
PRRIODICA13 Daklady Akadsaii Nauk SSSHI 1957, Vol. 114g 113.* C pp. 698-
-701 (USSR)
ABSTRACTs The present paper studies the problem of tho wdform oonvex-
genoe of developments aacording to the eigeatunotions of the
equations A u +I u a 0 in any domain g wi th &tq number N of
dimensions. A homogeneous boundary condition of the first, so-
cond or third kind is assumed hem The oonaitions for further
development can be made easier if the demand fnr absolute coa-
Yergence is dropped and only the uniforn convergence of Fou-
rierlo series is studied wh*n su=&rAzing in '.he order of the
increasing eigennumbers.
This expectation in also confirmed. The author found an adequate
result for any domain with any anount of dimensions and, be-
Card 113 sides, was able to prove the follovingi Let lie g assumed to be

.On the Uniform Convergence of the Expansion Acoordimg 20-4-4/6o
, to the Eigenfunctions
of Domains with an Odd Number of Dim4insiove
ASSOCIATIONs Moscow State University
(Moskovskiy goeudarstvennyy univorsitot)
PRESENTED: March 7, 1957, by S.L. Sobolev,. Acado.Aicia-n
SUBMITTED: February 19, 1957
AVAILABL3s Library of Congress
Card 3/3

AVTHGR~ 111in- V.A. (Moscow) flOV/39-46-1-4/6
TITLEs Sufficiewt Conditions for ~he Expansibi,1Jty-of a Function Into
an Abeol-atel-y and Uniformly Convergent Rerieii in Tems of 3igen-
futetiane (Dostatochnyye unloiriya rnzIomMmotiti funktail v ab-
solyutn(% i ravnomerne akhodyashchAynya w1rad pa sobstven:nym
funktsiyam)
PER10DICA.Ls Matematicheakiy- abornik,1958;Vol 46,11r '1,,pp :$.,26 (USSR)
LBSTRAM The paper consists of two chapterse In 'the r1rat chapter the
following theorem is proved.
Thvoremt The function f(Q) of N variables in assumed to be de-
fined in an N-dimensional domain g with. Lyapariov boundary aM
to posaess in the interior point P of 6- a al:ngularity of the
type re (E > 0) or r2m In r
PQ PQ PQ (M-0129s*s) p ioee it ia
assumed to be representable in the form
6
rPq + v M
cor 2m
Card !A f(Q) rp, . In rp, 4, V M

Oufftcient Conditions for the Expansibility of a SOV139-46-1-116
Function Into an Absolutely and Uniformly Convergent Serieft in Terms of
Eigenfun,,tions
wheres 1) v r__ w (g) 2.) v is iso that the
2
&kf '[!1/4] for the first,
functions f, 6f; (k
and k 14 21 for the second and third boundary value
problem) satisfy the cor:responling homolSvnwove boundary con-
dition in the genexalized. sense (see (:Ref 2 1 , Ch 2) a Then
f(Q) can be expanded in g into an abmolutely and uniformly
convergent series in terms of the sigonfunatlions of AXt+.\n v 0.
By an Giample then It is whown that for ftnotions with thio min-
gularitioa lin r or r E (P, -e-0) at most conditionally con-
PQ Pq
verg,ent Fouriet expanslong are to be impecte,1(in blef 31 Wbero
this ccnjecture is alread7 proved). Dvside4i It is directed to
an error of Courant and Hilbext (Methods of' Vath.Physics
Vol .)f The series
Card 2/1

Suffici-ent Cordl~tione for the RzPansibility of a :';07/39, 46-1-1,//6
Function Into at Absolutely and Uniformly Conlrergeml; Sol-ins in Terms Of
Eigenfu:.actions
00 00 Sint mx. 9inZny,sjn3rmO".sinTn.%
ab _~: 2 2
M-1 'n., n
2 1
a b
denoted there as absolutely and unifo:rmly -convergent in the
rectangle in reality above absolute &1vergorice in the whole
rectangle.
The seccmd cha-pter gives a generalization of the classical
theorem of Hilbert-,Schmidt for kernols of fractional ordor
which are connected with tho *igenftrations of the Laplace
operators Among others it is proved t If t(Q) is continuous
in a clc3ed two dim9nsional domain g,, if it posseasos pioee-
via* continuous firvt derivativss ana squaro-integrable second
derivatives in g; and if it satiefien the ci)rrespo-nding
Card 3,14 boundary oondition, then it can be mupandod in g in toms of

Suff!~J*nt Conditions for the Expansibility of a SOV139-46,-~--IJ6
1~unsticn Into an Absolutely and Uniformly Converge:nt Se.ries in Torma of
Eigenfunctions
the eigenfunctions of this domain into an Misolutely an4 uni.-
for-mly convergent series. Here the piecewi-adi continalty to
understood in a somewhat restricted sense.
There are ? references, 6 of whiob mra Svriot; and I German.
SUBMITTEDs December 22.1, '956
Card 4/4

On the Expansion of Functions With Singularities into 38-22-1-3/6
Conditionally Convergent Series in Terms of Eigenfunctions
fies the usual conditions for the series d,x,pansion, the
Fc~urier series of this function uniformly converges in the
interior of g (after separation of tbe singular point), if
it is summed in the order of increasing eigen values. For
the proof the author applies a well-known antymptotic forimla
(see [Ref 213t4]) which he newly provais and as it appears
with an important method. There are 12 rofnrences, 9 of
which are Soviet, I Jugoslav, I German, ana 1 Poliah.
PRESENTEDs by 3.L. Sobolev, Academician
AVAILABIMI Library of Co W ess
1. lunctions-Analysts
Card 2/2

AliTHORt Illin, V-A-.(Y-gs or) 39-45-M/7
TITLE; '-Z~A~orm convergence of the Expansiouss in Terms of Thgen-
functions in the Whoto Closed Domain (0 skhodismosti
razlozheniy po sobstyennym funktaiyall, y,~ 1,1)e), o4z:Pputoy ablosil)
PERIODICALz Matematicheskiy sbornik, 1958, Vol 45, Nr 2, PP '195-232 (VSSR)
ABSTRACT: Let g be an X-dimensional domain, r- bowxdary of g, V- normal
of r. In g the withor considers expansionts in terms of eiif;en-
functions of the equation 4 u +'Pu a 0 for bo?a4dary coAditions
Ir - -~-u I r - 0 or i2' + 11 (1$) ul I r'w
(i.e. for u 0 or ~v H $1 01 where
h(S),?* 0). He investigates the convergenoo of Lhasa expmnoions in
the closed domaii: g.
In the chapter I the convergence of the series
2
00 U. M
-A Oc
i
is considered. In order to guarantee the uniform convorgenoe in
the closed domain, on r certain additional oijaumptiono havorto
be satisfied. The author proves the inl.areal.,iiag results if ris, a
Card 1/3 surface of the type of Lyapunov and if ~i,(P) are the tigenfunctions
or

Qn the Uniform Convergence of the Expansiorw in Terma of ZLJ,-On- 39-45-2-5/7
functions in the Whole Closed Domain
series and for giving a uniform estimation of the remain4or
series. For arbitrary smooth functions f the author givom thm
order for the vanishing of the Fourier remainder. Numerous
conclusions of these principal resuLts a:ro giYen.
There are 15 references, 13 of which are Soviet and 2 German.
SUBMITTEls December 22, 1956
1. Topology 2. Functions--Applications 3. Fourler series-4hoory
Card 3/3

16(1)
AUTHORSt L! CY/20-126-6-6/0
TITLEs On the Connection Between the Claenical and The Generalizod
Solution of the Dirichlet Problem and of the'Problem of
Eigen Values
PERIODICALs Doklady AkademAnauk 335R,1959OVol 61
pp 1176 - 117c~j (USSR)
ABSTRACT: It is proved that the classical and the generalized solutions
of the Diriohlet problem
Lu a - f in G u Ir 0
where r is the boundary of G, are almost everywhere identical
in 0 , if certain conditions are satitifted gparanteeing the
existence of the classical solution.
A similar result for the eigen value problem
Lv + Av - 0 in G v1r 0-1
is obtained.
Five theorems and lemmata are given.
Card 1/2

On the Connection Between the Classical anl the ;--;(17/20-126-6- 6/67
Generalized Solution of the Dirichlet Prob1om and of tho Problem ol
Eigen-Values
There are 8 roferoncess 4 Of Which are Sovilett, 2 German,
1 American, and I French.
ASSOCIATION: Moakovekiy gosudaratvennyy univeraitet Imemi. 114.7~Lomonosoya
(Moscow state University imani M,V. Lomonomov)
PRESENTEDs March 17, 1959, by S.L. Sobolev, Acadartici(in
SUBMITTEDt February 24, 1959
Card 2/2

16(1)
AUTKOR: Illin, 7.A. SCIV/2~- 127-1- 5/65
TITLEt Solvability of the Mixed T'roblem for m Ryperbalic and a Para-
bolic Equation in an Arbitrary Normal C~linder
PERIODICLL: Doklady Akademii nauk SSSR,1959,vol 12T, Ur 1,,pp 23-26 (US.13R)
AB3TRACT: The author considers the mixed boundary value problemt for
the Ityperbolic equation
Lu - utt f(x,t) in the cylinder OX 10< t 411.1
u(x'O) q(x) ut(X,O) -TOC) IXI[- - 0
2. for the parabolic equation
Lu - ut f(x,t) in the cylinder jQ
U(X,O) 1-f(X) , III,- - 0 -
g is an arbitrary H-dimenZ4nnal domain bound.ed by
x - (X1 '...'X if ) is a point from g; if (,r) and, Y (x) are
functions defined in g; L is a selfadjoint dAfferential operator
Card 1/3

.Solvability of the Mixed Problem for a Hyperbolic 30V/20-127-1-5/65
and a Parabolic Equation in an Arbitrary Normal Cylinder
H
LU -Z u! c(x)u
;x aij(x) ~xa
i9j-1 i I JJ
of elliptic type defined in CZDa&Ji
h
2 comat>O ; C(x) -~,O in C
i9j=1 ij 'J iml
The author shows that the problems (1) and (2) are solvable
in the classical sense, if 57Z Iis narauil, I.e. if the Dirich-
let problem for the Laplace equation im solvablo in g for
every continuous boundary function. Altog,ether there are Oiven
4 lonr~ar theorems.
The author mentions O.A. Ladyzhenskayap O.A., Oleynik, A.Y.
Tikhonov, I.A. Shishmarov and S.L6 Sobolav,,
Card 2/3

Solvability of the Mixed Problem for a Hyperbolic ;1~0/20-127-1-5/65
and a Farabolic Al"quation in an Arbitrary Normal Cylinder
There are 17 references, 15 of which are Soviet, 1 German,
and 1 American.
ASSOCIATIONt Yoskovakiy gosudarstvennyy univorsitet imeiii 11.7.Lomonoaava
(1,108cow State University ineni M.7. Limonoijov)
PRESENTED: March 17,1959,by S.L. Sobolev, Academician
SUBMITTED: Pebruary 24, 1959
Card 3/3

3452
.35-o o S/044/6 0/000/0 10/0 16/051
C 1 111 /C222
AUTHORt
TITLEt On the question of the foundation of the Fcmrier method for
hyperbolic equations
PERIODICALs Referativnyy shurnal. Matematika, no. 1D, 1961, 42,
abstract 10 B 183. ("Tr. Vass. soveshchaniya, po
differentsialln. uravneniyam, 1958"- Yorevan, AN Arm SSR.
1960, 88-9'r)
TEM In the N-dimensional region g which is bounded by the surface r
the author considers the mixed problem for the linear hyperbolic equation
Lv - v tt f(x,t), R, - g X
*~ v
vit-o - If(X) , ~-t Lo 0 Y(x) , v IF 0
where L is the selfadjoint, differential operator
Card l/If

A52
S/04#0/000/010/016/051
On the question of the foundation C111/C222
Ly 2 a (x) v C(X)V
7- -:7 -X, I Ij -T-Xj
iti i
of elliptic type, c(x).>, 0. As a clasuical solution *f tho mixed probletu
(1) the author denotes a function v(x,t) defined in the aylinder
I-LI M 9 XLO~St!:Ll] which satisfies the conditiona t
1) v(x,t) is continuous in the closed cylinder fL and has continuous
derivatives of first and second order in the interdir of SI 1 - 2) 4 v/*alt
is continuous in the closed cylinder rl 1 ; 3) in overy litner point of
fL 1 , v(x,t) satisfies the equation L. - v tt , - f(x,t) ; 4) in wrery
point x of the closed region g, v(x,t) satiefios the inifl.pil con4itions
D v
V(X,O) - If(X) (x,O) - T(x) 5) for every 't E j'0'.l] , V(-.,t)
satisfies the boundary condition vir 0 ; 6) the firmt derivatives
of v(x,t) are integrable in the square in SZ
Card 2/4

S/04 61/000/010/016/051
On the question of the foundation ... CIIIYC222
The author proves the theorem t The classical solution of the problem (1)
in represented for an arbitrary W-dimensional regiom g bounded by a aur-
face F of the Lyapunov type and for an arbitr^~.-y imterval of time
OtEtt!~l by the series
CID T
v(x,t) Un(x) ncos fTn - n
n
+Z U, A(X) fn sin FX n(t_ dI
n=1 A
(Un(x) eigenfunctionef fn 1 Yn and rn(t) Youriex coefficients
of tf(x) y (x) and f(x,t) with respect to the system u11 (t)) if the
followiz;g conditions are satisfied 1 1) %fe W2 ( [ST, 3) (g) and besides
2 1W+4 ~j
L , L L 7r~ satisfy the boundary valme conditions of' firist
Card 3/4

32~j52
S104 6-1/000/0111/016/051
On the question of the foundation C111YC222
kind in the( Ii d sense
_gan ra,
[ e+ ze It# 2
2) kk 6 W2 (g) and besides L Y L2 L V
the homogeneous boundary condition of first kind in -the gpneralized senve;
N+2
~12! 1+ 2 ..r
1. 2 1. 1
3) f6 W2 (ft 1) and besides f, Lf, L fq..*L f satisfy the
homogeneous boundary condition of first kind in the (:InneroAlized senso
4) in the closed region g the coefficients aij (X) halir'e contInuous
derivatives up to the order ( [2] + 2 c(i) up to the order 4, 1)
2
[Abstracter's note : Complete translation-I
Card 4/4

S/042/60./Ol 5/02/01 /,eee/18
AUTHORt Illin, V.A.
- 1. ~.,
TITLEt On Solvdbility of Mixed Problems for Hyperbolic and Parabolic
Eguations \1\0
PERIODICALi Uspekhi matematichookikh nauk, 1960, Vol 15,No. 2, PP. 97.154-
TEM The author considers the classical solvability of the mixed problem
for the hyperbolic equation
u - u
L tt f(x,t) in SI, a g X 10 < t 11
U(X,0) -,f(x), ut(X,O) =-~(X), Ul., - 0
~
and the solvability with the Fourier method of the mizod problem for the
parabolic equation
Lu - U.; - -f(x,t) in
(2) fu(X,0) -,f(x), uIxer 0.
Here g is an N-dimensional domain with the boundary
f (x) and y(x) are functions given in g, f (x, t) is a function given in i2l
Card 1/3

693.01
On Solvability of Mixed Problems for Hyperbolic S/O,f2/60/'Ol 5/02/01/Oge-/.18
and Farabolic Equations
L is the selfadjoint operator
O(x)u
(3) Lu a (X) -7y u
i,j=1 i I ij
of elliptic type; c(x)30.
The principal aim of the present paper is the determimation of the minimsl
conditions which have to be satisfied by r in order that (1) has a classical
solution or on (2) the Fourier method can be applied.
The principal result is the statement that (1) and (2) are aolvable
classically or with the Fourier method in an arbitrary normal. cylinder
if %f,Wf and the coefficients of L satisfy certain oanditions of stooth-
ness (A. is denoted to be normal if in g the Dirichlet problem is solvable
for the Lapalace equation for every continuous limit function). These results
are already announced by the author in a shortened forin (Rot.289 32). Here
they are founded in detail. The author gives a survey or tho papers about
the mixed problem. The paper contains 6 chapters with 19 paragraphs.
Card 2/3

2
OVA
On Solvability of Mixed Problems for Hyperbolic 3/042/60/015/02/01/We/18
and larabolic Equations
The author mentions S.L.Sbbolev, O.A.Oleynik# A-N.Tikhonov, U.V.K*ldVeh,
S.G.Mikhlin, O.A.Ladyzhenekaya, I.A.Shishmarov, V.I.Stuirnow, I.G.Potrovs-
kiy, V.A.Steklov, A.I.Barabanov, N.M-~Gyunter, D.M.Volkov, Xh,L,$no1itakty-j
G.1,Petrashent, and B.M.Budak.
There are 37 references, 33 Soviet, 1 Garment 2 Amorioan, and I French.
SUBMITTED: April 8, 1959
T
Card 3/3

1,12225
.0~50 0
S/03SJ60/024/04/01/001
C1 1 I/C222
AUTHORSs Illin, V.A.t and Shiebmarev, I.A.
TITLEt On the Connection Between the Generalized and Classical Solutiots
of.-the-Dirichlat Problem 1~
PERIODICAM Izvestlys Akademii nauk SSSRp Seriya matermtiob*0taya, 1960,
Val 24, No. 4, PP. 521 - 530
TEXTs In the arbitrary N-dirensional domain g with the boundary r the
authors consider the Dirichletproblem
(1) Lu w - f in g , u Ir M 0
where L in sit elliptic selfadjoined differential operator
(2) L U CWU
Lu X, [aij(x) Tx-~
,, 0 . A function u(x) which is continuous in (g + two times
where c(x) >
Card 1/2

S/038/(,0/024/005/004/004
C1 11/014,!2 2
AUTHORS-. 111tn V.A. and Shishmarev, I.A.
TITM On the Equivalence of Systems of Generalized amd. Classical Bigon-
functions
PERIODICAL: Izvestiya Akademit nauk S3SRO Sertys. matomattehoskays., 1960,
Vol. 241 No- 59 PF- 757 - 774
TEM In the N - 'dimensional domain g with the boundsty r ibe author oorl-
sidors the aigenvalue problem
Lu + A a m 0 (in g)
ulxer- 0
(2) Lu
Card 1/ 4

8h 7106
On the Equivalence of Systems of Generalized
and Cleasical Bigenfuncitons
3/038/$G/024/005/004/004
Gill/om
is-& Itusar-selfadjoint operator of elliptic type and. c-(x) >,,, 0.
Under-these-conditions theorem I aswertst.-Lot g be a nox.*alAomain (ie.
lot the Diriohlet-problen for the Laplace equatloh for- every,continuous
boundary function be solvable in g, cf. (Ref- 4)) and lot it lie together
with f- in an open domain G. Let the coefficients of L belong tn the
classes
(5) 9,j(x) G. a(Z) G C(01/0 (/_ > 0) -
Then-there-exiote a complete orthogonally normed systen of the classioal
eigenfunction of (1).
An a-generalized eigenfunction of (1) the author denotes 4 ftzetion u(X)
not equivalent to zero which belongs to the-elass B(,S) (D(.g') to the
olosure with respect to the nors of the *(')(a) of the get of functions
continnonsl;r differentiable in g whieh vanish in a certain boundary strip
of.the-do".-kn, g) and which satisfies the identity
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8bT46
On tho Equivalenoe of Systems of Generalized 3/03SJ60/024/005/004/004
and Clativical Eigenfunotions alit/0222
N
u + u4,] dx . 0
U
(4) F01-i ij rxi x
0
for-each function *(x) C- D (g)
thworeys I are saftsf leii-,, ther-Ahe ortha-
gan,sL.U7-_mv"ted-- systems of the generalized and the elaselLeal eigenfunotions
of Ahe~prablex (1) ao well as the corresponAing systems. of the sigenvalmea
are Idantical.
if g-ts not,only rmroal but bounded by a surface r" of %be Ljrapunoy typ*v
then it is nufficient-whan the a (z) and o(x) satisfy the conlitions in
(g + r ) formulated-in theorem I'4nd 2.
The proof of the theorems bass* on the inrestigation of the (Droan's
function of the problem Lu. - - f , u I xr= r 0 0. The erigitend4i of the Groett a
funcrtion--K(-X,Y follows from (Ref. 6). Then- the author proveAt that in go
X(x,y) - IE(y,x~ , K(x,y) > 0, K(x,y) is continuous eTarywbirre in g + r
with-the-exception of x -- y. Then the existence and continuity of the first
and second d-grivatives of K an well as of the regular part of 11 are proved
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MT46
Ott the Equivalence of Systems of Generalited
rivenftmeAlons
doxivatives, a" estimated (10001068 1
2 Are-,pravvd-with the aid of the Green's function
The author mentions B.G. Mikhlin. Thore are 9
and -3- Ane'rican.
PRESENTEDs by S.L. Soboley, Academician
SUBIaTTEDs April 91 1959
S/038/60/024/005/004/004
C I 11 /C:?22
4),. Than,,the ihoo"as, I and
and its propOrtles.
roferencems 6 Soviet, I Oorman
CA.rd 4/4

3/03 601024-1006100-11'004
C1 1 ly-0333
AUTHORS% Illin, V.A., Shishmarev, I.A.
TITLEs Uniform Estimations in the Closed Domain of the Eigenfunctions
of an Elliptic Operator and of Their Derivatlyes
PERIODICALs Izvestiya Akademii nauk SSSR, Seriya -zai;wm&tiohe*k&y&,.1q60,,
Vol. 24, No. 6, PP. 883 - 896
TEXTs Let the linear self-adjoint differential operator
(1) Lu W ? U C(x)u
7
iPj-I YX i ij TZ iI -
be given in the open N-dimensional domain C1 assume that it it elliptlc,r"~
i.&. lot N
(2) a ijW aji(x) and aij ~i gj >' a , (rX cons t > 0)
.1 ~ 2
for-all x (x19 x2f ... PXN)4E C for arbitrary real let
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C1 1170-533
Uniform Es-.imaticns in the Closed Domain of the Migetfunctions of an
Elliptic Operator and of Their Derivatives
(3) aij(:,,)d C("/J'L-), I(I)CC(O"'A) , /I > 0 , C(X) ;;'P 0
be in C. Assume that g is an arbitrary open normal domain raich lion In C
together with its boundary F (g is normal, if in g the Dirichlot problem
for the Laplace equation is solvable for every continxious boundary fuMotioft)t""'-
The authors consider the eigenvalue problem
(4) Lu + AU . 0 (in g)
I U I r- . 0
in g. Aa it is well-known (4) possesses complete orthogon&lly normed aystems
of classical and generalized eigenfunations, where thmme syeteme are
identical according to (Ref. 3). All the eigenfunctions co:rrespond to
positive eigenvalues.
At first the authors prove the following formula for the eiglonfunctions
of problem (4) 1
3/05M ?60/024/006/001/004
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5/03" /60/0~4/006/001/004
ci 117033
Uniform Estimations in the Closed Domain of the MigenTunotious of an
Ellipti.: Operator and of Their Derivatives
D u ~u
u2(y) 2
(16) H(X,y) 2 A u 2 a n n X)j dx
n n(r) ij X. + au'(
n 9
,
+ u2(x)LH dx
n
where y in an arbitrary fixed interior point of g
2
(12) H(x,y) AL (y)(z -Y )(X2-Y
AM 4.1 r a
(N- 2)011 y I r,s re r
A(y) - dot Ila re (y) 11 , A r9 (y) the ratio of the algobrmic conplement of
the element ars (y) to the determinant A(y)
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S/038/60/024/00 6/001/004
C1 11.1033
Uniform Estimations in the Closed Domain of the Eigenfunctions of an
Elliptic Operator and of Their Derivatives
Then the authors show i The estimation
u 4
(7) n(x)l 2 n
holds uniformly in an arbitrary closed domain (g + rY
A closed domain in said to belong to the class A(k#/*,) , ilt the
as:quation
of the boundary surface in local coordinates belongs to the al C (k,/-)
(i.e. if its k-th derivatives satisfy the H61der condition with the at-
L,,) . k 9 A)
onent Theorem 2 1 If the domain (g +f-) belongs to it and if the
5aij(x)
'a Xk O(x) belong to the class C(k-l,/I)(k >/2) in the closed domain
(g + r), then the eigenfunctions of (4) belong to C(k,r) An the closed
domain (g + F).
Theorem 3 1 For all C(k,~') in (g + r) there hold uniformly the
u(x)r
estimations
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C111Y0333
Uniform Istimations in the Cloaed Domain of the Zigenfunctions of an
Elliptic Operator and of Their Derivatives
1 k+ " 1
(37) u T+7~ U V+_r + u
1 0 ( Uk 0
0 ( I�L4, k-1 (1+/",)) 1 4k
(38) 'u1, U k+/,,, uk+r+ u R_
k Ot- 0 0
where R is the diameter of g, uI the sum of the maxima. of thei absolute
values of a.11 I-th derivatives of u(z) in (g + r), u,,,- the sum of the
Hider coefficients of these derivatives for the exponent,?,, where u 0
r-nd u091" ere the maxima of the absolute value and the H61der coefficient
of the function u(x) in (g + r).
Theorem 2 In deduced from theorem I (theorem of Schauder and Caccioppoli
Theorem 3 and a further theorem 4 contain well-known a-riori-estimations
P
3/03 60/02,1/006/001/004
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S/038/60/024/006/001/004
C111/033
Uniform Estimations in the Closed Domain of the Sigenfixnctioits of an
Elliptic Operator and of Their Derivatives
of Schauder and Caccioppoli (theorim I and the estimations of theorem 3
and 4 are oontained in (Ref- 4))-
From the atitimations of the theorems 1-4 the authors obtain tht follo*itg
results t
1. For the derivatives of the eigonfunctions of (4) it holds uniformI3, in
(g + S N + k
F A /2
(9) U(",) (X) C A
11 4 n
2. for the H61der coefficient uk,/& of the k-th derivative of the eigen-
function i,; holds s
N + k + jk
(10) uk, C5 A /4 /2 /2
C4 P C5 depend on &I t is the Hdlder exponent.
Kh.L. Smol:ttskiy, D.M. Eydue and L.N. Slobodetskiy ar* mentioned.
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C1111C333
Uniform Estimations in the Closed Domain of the Eigenfunctions of an
Elliptic Operator and of Their Derivatives
There are 10 references : 7 Soviet, 2 American and 1 French.
[Lbstracter's note i (Ref- 3) is a paper of the authors iii Izvestiya
Akademii nauk SSSRI Seriya matematicheskaya# 1960, 2.11 75T-774 I Ref44)
is the book of Miranda s Partial Differential Equations ol'.91liptic
Type]
PRESENTEDs by S.L. Sobolev, Academician
SUBMITTEDs April 9, 1959
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5/020J60/135/004/003/037
A.
AUTHORS: Illin, V.A., and Shishmarev, I.A.
TITLEs Some Problems for the Lu - diy[]p(x)grad u]-cL(x)u Operator With
Discontinuous Coefficients
PERIODICAL: Doklady Akedemli nauk SSSR, 1960, Vol-135, NO-4, PP-775-778
TEXTt Let g be an N-dimensional open region with tht boundlaryr; lot 0
be an (N-I)-dimensional region in g being homeomorphic to the sphere and
dividing q Into gI and g2- Let T be an open region containimg (g+r). In
(g+r) the author considers the following Diriohlet pro~lemi
L1u - div[p,(x)grad u]-qIWu - f 1(1) in g 1
L2u - div [P2 (x)grAd u3-q2(x)u ' f2(x" in 92
4n 'X(x)
ujr - 'Xx)1 lu-Ii. - YWI
where - I '? u u n is the
lul I C u I C-0 , I C+0 I [ pi-A a 0 P I nC-O-P21) n low
outer normal of g1 and the symbols C-0 and G+O mean that the boundary
values are taken from the inner and outer side, respsetively, of C (With
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S/020/60/135/004/003/037
Ciii/cm
Some Prob:.ems for the Lu - div[p(%)grad u]-q(x)u Operator With Discoa-
tinuoue Coefficients
res;ect to g,).
Definition 1; A function u(x) which satisfies the following conditiots LO
called a ..-lassical solution of the problem 0): 1) U~x~ belongs to the
class C(O" in (g 1+C) and ~g,+C+V)j u(x) belongs to 0 In. (g,+C) and
(92+0); u(x) belongs to C~27 in I and 92; 2) u(x) smtiefleiv the problem
(1) in the classical sense. (,(ni... C( n~n) are defin.ad an in (Ref.1)).
The following five conditions (A) are formulated3
1) C belongs to the Lyapunov class, r is regular.
2) pI(x)C-C(l,/A) in (g I+C ) 1 P2 (x) F- C( I ' '**) in (T-gl)l
ql(x)E:C(01/"*') in (g,+C); q2(x)6-C(O"") in (T-gj)j
fl(x)e.c(O,A-) in g 1; f2(x)C-.C(O*lx) in g2; beaida,si
fj(x)~'.C(O) in (gl+C); f2(x)r--C(O) In (92+C:r)
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S/020J60/135/004/003/037
C111/C222
Some Problemn for the Lut- div[p(x)grad u]-q(%)u Operator 'With
Discontinuous Coeffioien a
3) pi(%)> 0, qi(x)~~O (1-1,2) everywhere in the regioi;e of definition of
them,
4) W(x) is defined and continuous on r.
5) q(x) X are de fined on C; )4 G C (1 PIA) I -K,
Theorem 1-., If the first and third condition A is vntWied thon It Uisto
only one clasai.;al 3olution of (1).
Theorem 2: If all conditions A are satiafied then there e%-.!*ts a unique
solution (if (1). where it telont,-9 to the clais GO in oach of tho
regions (~'1+C) and (92+C)'
If (.- 0 then the clainical solution is simultaneously the
generalized solution in the sen3e of (1-Ref-4,5).
The Green's function K(x,y) of (1) is symmetrical, continmous in (XPY)
everywhero in (g+r) (Inclusively C!) for x and J.n (E;+1') it satisfies
the estim&tionq
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C1111C222
Some Problems for the Lut; div(pWiurad +q(x)u Operator With
Discontinuous Coefficien
I Y-(X'Y)1 A~ c1 +c2in for N - 2
(2) jK(x,y)!!~0 r2-N XY for R > 2
3 xy
Then the authors consider
LIu 4- Au - 0 in g,
(3) L2u +-~Lu - 0 in 92
uIr - 0, lull, - 0, UPI-fll. - 0'
where L and L are the same as in (Ref.1).
1 2
Definition 2t The classioal eigenfunction of (3) is in funotton u(x)*O
which 1) satisfies the condition 1) of the definition 1, *M 2) for a
certain k satisfies (3) in the classical sense.
Theorem 31 If the first three conditions of A are ssAiefiod then there
exists a complete system of classical sigenfunctions of (~) orthogonally
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C111/0222
Some Problems for the Lu a div[p(x)grad u]-q(x)u Operator With
Discontinuous Coefficients
normed in the L2(9)1 where besides each of them* sieentunctione belongs to
the clano each of the regions (6,+C), (62+0).
Theorem ift The complete system of classical &ISonfunotions of (3) to
identical with the complete eystom of generalized oilronfMijetions, of (3).
Theorem !51 Under the assumptions of theorem 4 there stisto a constu-t c
so that uniformly in (g+P) it holds
(5) U 11/4
(here u (x) in an arbitrary oigenfunotion of (3) corresponding to the
eigonvalue h.).
The authors mention D.X.Eydus and O.A.Oleynikj they thank A.S.Tikhonoy
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CM 0 22C 2
Some Problems for the Lut; div[p(x)gred u3-q(x)u operator Ilith
Discontinuous Coafficien
for advices. There are 8 referencess 6 Soviet, I German and 1 Aaerican.
[A,bstraoter-a note: (Ref.1) concerns Miranda, Partial Difforential
Equations of Elliptic Type. (R:f,:) concerns Courant Azd Hilberto Methods
of Mathematical Physics, 2, Ch P r 7.1
ASSOCI)TION: Moskovskiy gosudaretyennyy universitst imsni I.V.Lomonomova
(Moscow State University imeni X.V.Lontomosov)
PRESENTEDs June 20, 1960, by I.C.Petrovskiy, Acadoai*i&u
SUBMITTEDs June 189 1960
Card 6/6--

22832
S/199J61/002/001/003/008
BI 1 2/B2 18
AUTHORS: Win, V. A., Shishmarev, 1. A.
TITLE: Method of potentials of the Dirichlet-,11eum=n problem in the
case of equations with discontinuous ooefficients
PERIODICLL: Sibirekiy matematicheskiy zhurnal, v. 2, na~ 1, 1901, 46-58
TEXT: The authors' study is based on an N-dimensional open domain g with a
boundary manifold r. The domain g divides an (N-1).dimansional surface C
which is homeomorphic to the sphere, into two subdoinains g, and 92 . The
authors deal with the following Dirichlet problem:
Lku - div [,Pk(x) grad u1 qk(x) u
02u 'pk au q (in
[Pk(:c) ax2 axi ax il k(x) u fk(x)
F aul
uIr lul I C LF-8-ni I C
They assume that C belonis to Lyapunov class of eurface1j, that r is rigular,
Card 1.,2

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Method of ...
8/199/6 1 /002/1)01 /C)03/0t)B
and that -,he functions pi(x) , qi(x) , fi(x) X belong to certain clus-
see of functions which are more general than the clumses of functions
corresponding to the classical Dirichlet problem. 0. A. Oloynik has proved
existence theorems for a similar but more special Divichlet problem, The
authors of the present paper prove the existence and uniquertese of &
classical solution of the Dirichlet problem formulated abois. Their
existence is proved by the method of potentials; explicit ;solutions are not
given, Fc.llowing this, they disiuss the Neumann prob1mm:
LIU - fl(x) in g,, L2u - f,(X) in g2'
au Ir t aull
(P2 8n2 + hu) 1) X 9 where h is a function given on.
I C - Y, [
Also for this boundary problem, the authors prove the oxistence and uni-
queness of a classical solution. Finally, they solve the Dirichlet prob-
lem in a general way and study its rel4tion to the clussical solution. An
appendix gives the explicit form of some theorems that were implicitly
used or derived in the paper. The authors thank A. N.. Tikhonov for dis-
cusaions of the results obtained. There are 6 Soviet-bloc references.,
SUBMITTED: July 2, 1960
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~'J~A'$-SHISMAARSV., I.A.
"bigenhin dam *6blem for the operator IA44iT1:P(X)lP-ad ul-g(x).u
iOavi*,dftftnti=uU boafficionts. Sib. ntkt. ukjur. ~! moo41520-
.536 n * z 161. (Eiger,&wtiona) (NEIRA U.: 9)

20313
C11-11C222
AUTHORt Illin, V.A.
TITLEs The solvability of the problems of Diriehlet and Neumann for
a linear elliptic operator with disoontinuoui; coefficients
PERIODICALs Akademii nauk SSSR. Doklady, v. 137, no,. 1,11)61, 28-30
TEXT: Let the (N-1)-dimensional surface 0 homeomorphic to the sphere lit
in the o;en N-dimensional region g with the boundary r , and let it divide
g into the,aubregions g 1(in C) and 92 . Let the open region T contain
g + F ir. the interior. In g + r- the author !considers tht. Dirichlet
problem N 2 N D
L U 457 a 0 u + b(1) c (x)u-f(1)(x) in g,
1 ik i
? xi~ xk 11
N (2) 2u (2) u (2) (2)
L U a + b c (X)U-f (x) in g. (1)
2 ik W x )x,l W -Z.
i i
ujr ju] 0 . '\k , I u
Card 1/4 11-9
S/OP-OJ61/137/001/003/021