SCIENTIFIC ABSTRACT YERSHOVA, YE.S. - YERUGIN, N.P.

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001962910015-7
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• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 15, 2001
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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

YERSHOVA, YE. S.
35331. Vliyanie.Dispersnosti Ulinozezna Na Spekanie Norwidovogo Ch re ka Trudy
Ynsk. Xhim.-Tekhnol. in-Ta Im. I'lendeleeva,VTYP. 16 1949, S. 59-782.2ibliogri
7Nazv.
SO- Latoois'Zhurnalinykh Statey, Vol. 34, I-',Oskva, 1949

ABM/,OVA, N.A., nauchn. sotr.; VOYEVODSKIY, A.S., nauchn. sotr.;
GIIIZBU.IG, O.F., doktor khim. nauk; YERSHOVA, Ye.TS., kand.
-:..f VSK
so "IF. 'Irl -~3 v
khim. nauk YOUCHEV, V.B., naucba J. I YAN EA,
K.Yu.,, nauchn. sotr.; MAZELI, R.L., nauchn. sotr.;
MELINIKOVA, N.S., nauchn. sotr.; PLATUNOVA, N.B., nauchn.
sotr.; RE21,0ZOV, A.L., !;and., khim. nauk; UTOGEK121, V.V.;
nauchn. sotr.; KHAVIN, Z.Ya., kand. khim. nauk; EFROS) L.S.,
doktor khim. nauk; NINOLISKrY, B.P., glav. rod.; RABINOVICH,
V.A.p kand. khim. nauk, zam. glav. red.; GRIGOROV, O.N.,
doktor khim. nauk, red.; POZIN, K.Ye.j doktor tekhn. nauk,
red.; PORAY-KOSHITS, B.A., doktor khim. naukj, red.;
RACHINSKIY, F.Yu.., kand.khim. nauk, red.; ROMANKOV, P.G.,
doktor tekhn. neuk, red.; FRIDRIKHSBERG, D.A., kand. khim.
nauk, red.; ZONIS, S.A., red.;.LMII, S.S., tekhn. red.;
EiUKH, Ye.7a.,, tekhn, red.
(Handbook of chemistry] Spravochnik khimika. 2. izd,, perer.
i dop. Leningrad.. Gookhimlzdat. Vol,2. [Basic properties of
inorganic and organic compounds] Oanovnye avoistva neorgani-
cheskikh i organicheskikh soedinenii. 1963. 1167 p.
(MIRA 17:3)
1, Chlon-korroapondont All 38SA (for llikollokiy).

GVERD-ISITMI, I. G.; YERSHOVA: Z. B.; GULIANOV, Yu. D.
"Thermoelectrical generator with isotopic heat source."
re-port submitted for 3rd Intl CorLf) Peaceful Uses of Atomic Energy, Geneva,
'31 Aug-9 sep 64.

YERSHOVA, Z.P.- OLOSHMKIT, Ya.l.
Equilibrivm of immiscible liquids In systems of the type
M672-MeO-SO2 [Vith summary In Znglish]. Gookbimlia
uo.3:214-221 '57. (MT-RA 10:7)
1. Institut geologii rudnvkh mestorozhdeniy, petrografti, minera-
logii i geokhimii AN SSSR, Moskva.
(Systems (Chemisti7))

TERSHOVA, Z.P.
RquilibrIum of Immiscible liquids in R700ms Of thff MO~P - A1201 - SIO2
type. Geokbimila no.4:296-303 '57. OCRA 1215)
1. Institute of Goolog7 of Ore Deposits, Petrograpby, Mineralogy and Goa-
chemistry, Academy of Sciencesl U.S.S,R.. Moscow.
(Systems (Chemistry)) (Chemical equilibrium)

YERSHOVA, Z. P,, Cand Geol-,Uin Sci - (dies) "Study of the t equilibria of
immiscible 212 liquida in Mov, 1958. 17 PP
with drawings (Acad Sci USSR, Inst. of Geology of Ora Deposits, Petrography,
Minemlogy, and Geochemistry), 125 " copies (KL, 18-,58, 96)
-26-

OVA. Z.P.; OWSHAVSKIY. Ya.l. Cdeceaoedl
Equilibrium of two liquid phases In fluort'do-milicate systems
containing alkali metals (with summaz7 in English]. GookhImlin
no.2:144-154 '58. (MIRA 12:4)
1. Institute of the Geolog7 of Ore Deposits, PetrogreThy, Mineral-
og7 and Geochemistry, Academy of Sciences V-S-S-R-, Moscow.
.(Phase rule and equlllbri=5

:1 1HIM 1131 If I11M, t I
V'^-j
SHUOT, V.N.; MIKMA,-.N.N.; YMSHOVA' Z.P.
Fusion method for approximating the chemical composition of Cenozo
igneous rocks In South Sakhnlln. Dokl. AN SSSR 119 no.2:326-129 Mr
158, (MIRA 11:5)
1. Sakhalinskiy komplekanyy nauchno-issledovatellskly institut AN
SSSR. Predstavleno akedemikom D.S. KorzbInskim.
(Sakhalin--Rocks, Igneous)

TSVIETKOV, A.I.; TERSHOVA, Z.P.; MT'VETI-Xt , N.A.
Synthesis of chromium silicate similar to olivine. Izv.
An SISSR.Ser. geol. 29 no. 20-15 F '64. (14 17, - 5 /1
1. Institut goologii ruenykh mestorozhdonly, petrografli,
mineralogii i geokhimii AN SSSR, Moskva.

. . 1 11 MH R . 11REHMAIJIM11111 I I j
I . -11-1 151 A i"l il : ~ I
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YERSHOVAt
In memor7 of Fr6dgric Joliot-Curia. Ked.rad. 3 no.6:62-65
I-D 058. (OBITUAR13SO (MIRA 22.*1)
Tollot-Curie, Frederic (Rue))

21(4)
AUTHORS: Yershova, Z. V., Vladfmiro-ja; M. V.
TITLE: The Effect Produced by a--Radiat-lor. 'Jj.--cn Aqueous Solutionj
of Acids (Deystviye a-izli_,cheniya na vodn3,ye raqtvory kiFiot)
PERIODICAL: Atomnaya ener~i
0 ya, 1950, Vol ~~ Nr 5-V PP 546 -1145 (USSR)
ABSTRACT: The effect produced by the a-radia~,ion of polonium
(0,09 --- 1,5 mC/131) upon a 0...8 n aqueo-Lis aulfuric acid w-.s
investigated.
The polonium Yas precipitated from a n1tr--c a._-id solution
on copper powder, after which tt was dist!Jled .1n. a Vacuum.
The diatillate wat) (11-inolved in a 6nnitric ar-iii. 11,1,ia
solution wan used as initia-l product for the experiments to
be carried out. A certain part of this solution was dried
by evaporation in -a quartz leovill, the reesidue3 viare di--
solved in freshly prepared 0,8 n oulfur--c acid -and stored
in a glas- vessel (Pyrex glass). The radiaticn- .-chemical
yie-'d of hydro-en peroxide is considoxed an critarion for
the purity of the poloniurn sulfqte aoliruion.
The laiter i3 determined by the rumber of lkydrogen per~,xide
Card 1/3 molecule2 whi-,-h are libeiated in the unit voluimo by 100 eV

SOV/89 -5-5 -6/27
The Effect Produced by a-Radiaticn, Upon Aqueous Solutions of A,,,ids
absorbed energy. The average quadratic error conmitted when
determining the yield amounted to + 10 T"'.
Tho hydrogen peroxide was determined by means of the apparatus
~3 K-14 according to the photocolorimatric method. Tho
average quadratic error in this case -amounted to +
Tile energy E in oV/ml absorbed during the tiT, TT.1n hou:-3)
- 7t06 10 I.A.T,
wan determinod from the relation E where
A donotea fulio ackivity of tho fjolittion In nC/,ml, rflil.rh wrlu
measui-ed by neana of a scintillation counter.
It was found by experiment that within the ranae -if nalonium
concentrations of from 0,09to 1,5'mc/ril the radiation-chemi-
cal yield of hydro-en peroxide is at first equally hi,,,h,
viz. 1;20 + 0,12 Moloculea per 100 eV absoi,bed energy. The
hydrogen peroxide concentration tends towards a limitinO~
value. The limiting equilibrium cai(aYmibai of hydro--q --)Cr-
oxide in 0,8 n sulfuric acid amounts to -5 -- 8-10 -.iole-
cules/ml. There are 3 ficuies.. '! table-, and 2 referennes,
2 of which are Soviet.
Card 213

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V9 A.,
if
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V"DIMUIVA. N.V.: MSH()VA, Z.V.
Action of ulphot radiation from polonjum = coarentriLtod evlfyjrl,,-
acid nolutiona. HadlokhWia 2 no.4095-4" .46o. (PURA 13sq)
(Polonium) (sulfuric acid) (Alpba rays)

U/844/62/000/000/026/129
D244/D307
AUTHORS: Vladimirovaq ki. V. and Yershovag Ze V.
TITLE: Radiolysi8 of aqueous sulphuric acid oolutions under, the
action of c( radiation
SOURCE: Trudy II Vsesoyuznogo. soveBhclianiya' po radiatsionnoy khi-
mii. Ed. by L. 6. Polak. Moscow, Izd-vo j~N SSSI~, 1962,
162-166
TEXT: The object oi~ the present work was to investigate tile evolu-
tion of ga8es resulting from rA irradiation of aqueoua H 2so 4 solu-
tions of various concentrations and the influence.of certain accep-
tors (glucose, methylene blue, H 2) on *the initial yields.of 1121 02
and H202* Po 210 dissolved in the solutions was uued as the source
-of(:~ rays. The dosage varied from*2 x 1014 to 2 x 10 16 ev/mi.sec.
It was found that the yield of H2 increases somewhat with the in-
Creasing If SO concentratiqn (0.4 to 4.0 M) and the yields of 0
2 4 2
card 112

5/84 62/000/000/026/12:~;
Radiolysis of aqueous 1)244YD307
become lower. The initial'y'ield of H in 0.4 1-1 H SO remains con-
2 2 4 " '18
atant for a wide _ran,..;e of absorbed energy (5 to 400 x 10 ev/mi),
and concentration of Po 210' (from 1 to 100 mouries/ml). Glucose
(0-005 1-1) and methylene blue (7 x 10-5 111) begin to interact with OH
in the 'track' region as su--ested by -the increased initial yieldU
of H202 and H 2' In the pre s'el nc e o f H2(0.1 M) the yield of H201, in-
creaues. The reactive capacity of the various acceptors with OH ra-
dicals decreases in the order methylene blue, Tl+, 91LICoz3e, H2,
There are 1 figure and 4 tables.

I=
VIADIMIROVA9 N.V.; YERSHOVA; Zj.
Effect ofo( -radiation on sulfuric acid oolutions of metbylene
blue. Mechanism ofo(-radiolysis. Radiokbimila 5 no.4:479-445
163. (HIM 16tio)
(Methylene blue, Effect of radiation on)

YERSHOVA-YAMY,AK, 1-1. V.
"Changes in the blood wyatem In ulcerous disease." First Uningard Medical
Inst, imeni Academician I. P. Pairlov. Leningrad,, 1956# (DISSMTATION For
the Degree of Candidate in MEDICAL SCIENCE.)
&Uziffiqu leltopial,
No 33, 1956,-f~s-cow

11 ]i [,1l 11111 '-fl[ I hill I il III !I I I I
1!11 11N1111 NH

i I qi 0 li~o- if: 1111: 111 It! Hill I UPOR I!jwF, IlifiIIIIIII 11,011:1 I'm 4"1 1 VIN i I I j.,
113,11IN 1-11151111111filitil
T 1

POKROVSKIYO A.A,; YERTANOV, I.D. (Mc~cow)
Susceptibility of dietary protoins to proteolytic enzywf: irt
vitro. Vop.pit. 24 no.3:38-" My-Je 165,
(MIRA 18:12)
1. Laboratoriya klinicheskoy enzimologii (zav. - prof. A.A.
Pokrovskiy) Instituta. pitaniya AMN SSSR, Moskva. Submitted
November 21+,, 1964.
rife: Ll
4W
Ii lill; ]HIM
in -Iff ID 11 -7
11 k [111111111011111111 ill! +~" II i 77

YERTANOV, 1. D.
Phyniological and nygt-ji.Lo evaluatJ rn of a foo," ration deve' --pw~
.1 A ., I
by the Central Scientific Research Institute of the Canned FQod
and Vegetable Industry. Vop. pit. 21 no.5.-71-75 S-0 162.
(MIRA 1'7: 5)
1. Iz laboratorli izuchenlya npetsittl1nogo pitanlya (zav. P.p.
Ivanov) Instituta pitan-4ya AM S-13-SR, Moskva.

Lit. prolzv, 0
11`1~ 111,11,1111 dill 11 1111:1 11 i11111 11 1
lit 111111

SOV/68-58-2-10/20
AUTHORS: X~, ~, ~,~olkov, Yu.m. and Lange, A.A.
TITIE: Purification of Raw Benzole Fraction by Catalytic
Hydrogenation Under Pressure of Ofte-aveat G" COchistka
fraktaiy syrogo benzola metodon kataliticheakogo
gidrirovaniya pod davleniyem koksovogo gaza)
PERIODICAL: Koks i Khimiya, 1959, Nr 29 PP 35 - 38 (USSR)
ABSTRACT: An investigation of the purification of raw benzole
fraction by hydrogenation over tungsten-aickel aulphide
and molybdenum cobalt oxides on alumina catalysts is
described. Preliminary experiments ivere carried out on
a high-pressure dropping apparatus (dropwise feed oof
raw benzole into the reactor (Figure 1). At 340 C
and 40 atm, the sulphide catalyst was found to be too
active as hydrogenation of benzene hydrocarbons was
taking place. Oxide catalyst was found to be more
suitable as a product containing oalY 0.005% of thiolJzne
could be obtained at 390 0 and contact time of 12 see
at 40 atm and 1G seconds at 60 atm. The sulphur balance
of the process is shown in Table 1. Further experiments
were carried out in a continuous small-scale plant
(Figure 3)- It was found in the initial experiments
Cardl/2 that the reaction temperature could be redlaced to 350 OC.

SOV/68-58-2-10/20
Purification of Raw Benzole Fraction by Catalytic Hydrogenation Under
Pressure of Coke-oven Gas
Further tests were carried out at 350 0C, 40 atum, and
volume velocity of 0.5 vol/vol/h. The experimental
results obtained are given in Table 6. It was found
that the hydrogenation process under these conditions
was satisfactory but in order to obtain pure benzole
a higher efficiency rectification column is necessary.
There are 3 figures, 2 tables and 3 references, 2 of
which are German and 1 Soviet.
ASSOCIATION: UKhIV
Card 2/2

. - 1 1. '. i;.1-11-2- t 11 ";~Ij' ;'TI';:I ill!;- IM 1 4941111111 H RIM 111 Illig! I ! i 1: ~ AM i ED r I
YERU, I.I., LAIM, A.A., TIMOSHMO, V.A.
Cj~talytlc Isomerization of meta-jyleno in the presence of coke-oven,
"gai-urder pressure. Koks i khim. no.3:51-53 160. (MIRA 13:6)
16 Ukralaskiy inglakhtmicheskiy Institute
(tylene) (Coke-oven gas)

... ........... ..... .... . .............I........ . ..........
~L ~Tll im
~I-I-' LANGE, A.A.
Catal7tic hydrofining of the fraction of cru4io benteame under tha
pressure of coke-oven gas. Koko i kIdm. no.807-41 16o.
(MIRA 13:8)
1. KharIkovskiy nauchno-iosledovatellakiy uglekhimicheski.7 institut.
(Benzene) (Coke-oven gas)

YERU, I.I.; LAME, A.A.; TDIOSHMO, V.A.; KIFIYANOVA, Ye.T.
Hydrogenation of naphthalene and naphthalene-cortaining oils.
Koko i khim. no. 5144,46 161. (14W 14 14)
1. Ukrainskiy uglekhimicheakiy inatitut.
(Vaphthalene) (Hydrogenatiop)
1
. ll.~; kilt
1 :,,I ", -, i ~ ! II t-, 11,111 11
H
A

YERU, I.I.; PODOROZIIANSKIYO M.M.
Results of the destructive hydrogenation of condensatilan prodjcti5 of
toluene with dichloroethane. Koks i khim. no.8:47-49 '61.
(MIRA 15:1)
1. Ukrainskiy uglekbimicheskiy institut.
(Condensation products) (Hydrogenation) (Toluene) (Ethane)

YERU, I.I.; LANGE,, A.A.; MARIICH, L.I.; SOKOLOV, V.Z.; YMELIYANDVA, L.P.
Purification of the fractions of crude benzene by catalytic hydro-
genation in coke-chemical plants of the Soviet East. Roks i kbim.
no.11:41-43 '61. (MIRA 15-1)
1. Ukrainskiy uglekhimicheskiy institut (for Yeru, Lange, Mariich).
2. Vostochnyy uglekhimicheskiy institut (for Sokolov, Yemel'yanova).
(Soviet Far East--Benzene)

s/o68/62/000/003/00_2/003
E071/E435
AUTHORS. Nosalevich, I,M, ,
I - I - - Ya s tr zh emb ~ Ra ya 0 V.
Andreyeva, V.S.
TITLE4 The production of lightly coloured and ]Lghi- tesistan~
indine-coumarone resins by the method of' ~atalvtl_
hydrogenation
PERIODICAL4 Koks i khimiya, no-3, 1962, 44_46
TEXT- The work was carried out in order to determine the
possibility of production of light coloured, stable and light-,
resistant indine-coumarone resins. similar to g#ood qual-ity resIns
produced in other countries, The' following tv
,pes of ~atal),6t
were tested: an industrial tungsten nickel. sulphide on alumin,-.1
(tablets), molybdenum trisulphide (powder) and ni-kel cl)romlum
oxide (tablets). The hydrogenation was done in two type_~ of
autoclaves: a) with a stirrer, 350 rpm, b) by r3tating about the
horizontal axis at 75 rPm~ As a starting material in IrIdUmtrLdi
product of catalysis containing 44 to 48% resin anfl abou'. 0,2j')'0
sulphur was used. Catalysts were added in the forin of a f i n,~
powder in an amount of 10 wt %, The hydrogenation ptoduct wris
Card 1/3

S/068/62/000/003/002/003
The production of lightly coloured E071/E435
filtered and steam distilled. The c-olour of indust-Irial
is usually determined by the iodine scale but the ~,olour of he
hydrogenated product was so much improved that. the iodinL --ale
could not be used and instead the chromate scale was applieci,
In addition, the iodine numbers of the starting i5q to 56) and the
finished product (25 to 30) were determined, irhe
light was determined by irradiation for 6 hours with
lights It was found that with the sulphide 'Y-;t-' a
25CC, the initial hydrogen pressure .--ould be r1~dU,,t!d
40 atm without noticeable effect on the ..,olour Of thr~
product. The colour of the s,arting prodn:., 35 kinits of the
iodine scale. finished produ~~t - 0,,5 un.,T-. of !he chroma-t
A decrease of the (Itiration of beating fiom 60 ~c) '30 mili ftl~- holfi
no influente on the quality of the pi odu..-. tr U-1. ~ 1) -i~ t' I I (-. . 1 -'3 -
10 minutes brings about a noti.-eable deterkcra~icri. Ref'Ad
of hydrogen by coke-oven gas brings about s-_mie-
toloration of the resins. Experiment.3 at~' ' ~d i rL 9.
autoclave gave somewhat results fcr b1,01. arld i_-*_'-;
oven gas, this is expl_ained by the
Card 2/3
"11111110:11 1H111- 11 "HiI ii':
Ii, I I

5/068/62/000/001/00a/003
The production of lightly coloured E071/E435
thin layer, For experiments with the oxide -~atal~it a fLrj~t-hed
industrial res:ln was dissolved in sulphur free borjzole "a 3510,
solution) which reduced the sulphur content of' tho hyd%-og*znafn--,7.
material to 0,190'., The colour of the hydrogenated pxorlu;.~.
reduced to 0.3 units. Specimens of tmported r-euin~i had a
of 0.6 units and were less resi&tant to the actJoin of ullravioiet
lights In addition to better colour and higher t~,
light, the hydrogenated resins had a lower ash content '0,07%
(against 0.48) in the initial state), and a higher ~ampatabLli--y
with vegetable oils, No data on the re,,iltstan-,o to light air.,
quoted, The production of hydrogenated resin,3 i..,~4 plann~-d at thia
Kadiyevskiy koksolchimicheskiy za-vod (Kadiyevlra Coal.. tor Cbc-miral
Works), There are 2 tables,
ASSOCIATION: UKhIN
L
Card 3/3

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-XPRpj,jq1.;~ WICEP A.A.; ZEYDLITS,, Ye.M.; SMOLINIKOVA, V.P.
CatalyLic liydrogomtion of quinoline for tli-~ production of the "Kyusol"
ropoUent. Koko i khim..no-10:46-49 162. (KIRA 16:9)
1. Ukrainskiy ugleldiimicheakiy institut,
(Kyusol) (Coke industry6.-By-products)

YERU, 1.1.1 LANGEp A.A.; MAR11CHp L.I.
Catalytic hydrofining of the BTX fractione of saw c*ke plants.
Koks i khim. no.7:48-50 t63- (MIRA 16:8d)
1. Ukrainakly uglekbimichookiy institut.
(Coke induntry-W-produoto) (honnuno)

I.I.; KARICH, L.I.; LANGE, A.AQ
Preparation of high purity cyclohexane from a narraj benzne fraction
of crude benzene. Khim. prom. no-8:576-579 Ag 163.
(MIRA 16:12)
1, Ukrainskiy uglekh W cheskiy inatituts

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'fF,RU,-- R.-- L~-
USSR/Medicine-Ultraviolet Rays Jan/Feb 50
. Radiation Effects
nExposure ofa Scarlet Fever Ward to Ultraviolet Radiation," Prof M. L. loshkin,
Docent, F. M. Moselevskiy, R. I. Eru, Chair of Gen Hygiene, Chair of Children's
Infections, Kharlkov Med Inst
O-Pediatriya" No 1, pp 30-38
Tests effect of subject radiation on bacterial confiamination of the air and various
objects in a scarlet fever ward and effect of radiation on patients. Finds radi-
ation reduces number of bacteria, especially streptacocei. Observes no harmful
roatilto in patients of subject ward. Wfinite dacreaso In coitiplinotionn in app-
arent. Includes five tables. Chief Chair of Gen Hygienes Prof M. L. Koshkin.
Chief, Chair of Children's Infections: Docent A. L Pevzner.
PA 163T32

YERUGIN, A.
Stud7ing the function -10) =j P~S) k ma .3, - Biu:L.S110 IDU
no.1:20-34 15A. (MIRA 13:6)
(Integrala)

WT(j)/M(M)/EWp(4)/T/pWP(t)/eTj~ JjP(c) GGAIH/b
0226A---0-7E
A&MM264 SOMS com ua/C*67/60/06/007/131511310
(#A%~, none
TMA: DialectriA gropertles of some SnEktals in the isillimater wavelengtk range
SOURM Zhurnal tokknicheskay limiki, Y, 36j no, 70 1315-233.6
TOPIC TAGS: Dielectric constant, dielectric loss* extrese high frequency, quartz,,
ruby, andalusite, single crystal
tric conAtents I a
ABSTRAM The duthor has n9s4ed the m-on temperature dlelel~' W
tangents at 10 HS of quartz,\"ondslusite, and synthetic rubyNainTle cEXatals%siz
the standing' wave ratio and standing wave pattern shift techniques of S,Roberts and
A&Hippel (J# Appl* Physe 17, 610# 1946). The values found for the dielectric constan
(lose tangent) of andalusite, ruby and qurArts are 8 (0.02, 9 (0.01), and 5 (0.01),
respectively* The loss tangents given above'for nndolusits and ruby were measured with
the electric field In the waveguide parallel to the optic iuris of the crystal (as
determined f rorm electron paraniagnetic resenance measuremento); *thezo long tangents were--
approximately twice as large when the electric field;was perpendicular to the optic
axis. The relative dielectric losses of the crystals were also measured at temper-
atures from 300 to 4*20 9 by observing the effect of the presence of Re specimen on
the reflection coefficient of a resonator. The dielectric lose at 10 HZ of all three
1/2

L 02264-67
-k~C-Wk,-AJ~6025264
crystals decroased by mora then two powers of ton as tho teaperature was deereased
from 300 to 4,20 x, Origo art, bast I figure and I table.
SUB CODE: 20 SU13M DATRz 09Aug65 ORIG,REFs 002 OrH REF:- 006

yntwu, A A - --~-
0 .
"
Structure of an explicit solution for an equatiou of the
integrals of clarves of an autonomous 8"tsm in the case
of a focus. Dokl. AN BSSR 2 no.11:441-" D 158.
(MM 12:8)
l.Predstavleno akademikom AN BSSR V.I. Txylovym.
(Differential equations)

.-MUGIN, A.M.
Structure of an explicit solution to the eqlAtIon of Integral
curves for one class of systems of two differential equations
with nonholomorphic right parts, Vestsi AN MR.Sordia.-
tekh,nave no,4:2 -32 158, (HIU 12:4)
iDifforeatial equations)

4 - - . c6Loi
16(l) SO'1/170-59-2-19,123
AUTHOR; A.N.
TME-. The Structure of the Explicit Solution of the Equation of Integral Curves
in the System of Two Differential Equationa for the Case of Two Equal Root's
of the Characteristic Equation
PERIODICAM Inzhenerno-fizicheskly;zhiirnal., 1959,, Nr 29 pp 121-128 (USSR)
ABSTRAM There Is a system of two differential equations.
dx dy
dt, x (X,Y); dt x 4- y + (x, y) 2 2 2
where ~P (x,y) and IP (x,y) are series which novirerge at x + Y r
Dividing the second equations by the first one obtains the equaAVAon Re-
noted by (4) in the text of the paper. The solution of Equation 4 In the
neighborhood of the alngOar point (0,0) qualitatively is a degenerated
node: all integral curves adher,~ to the origin and tire tai%,~nt:a b) Ulf,
y-axis. The problem set in this paper consists in- the clarification Of
the analytical structuare of the solution of Equation 4 in the infinitely
Card 1/2 small vicinity of the origin. The author states and then proveo that this

06401
SOV/170-59-2-19/23
The Structure of the Explicit Solution of the Equation of Integral Curves in the System
of Two Differential Ecpaations for the Case of Two Equal Roots of the Characteristic
Equation
solution can be presented by an expression of y baking a function of x,
Formula 6, in which the constant coeffloients are given by Formulae 31 and
the terms ')I K (x) have the properties def Ined bv ForrmAlae 7 in the text of
the paper.
ASSOCIATION: Otdeleniye Matematicheakogo Instituta AN SSSR (Branch of the Mathematicitl
Institute of the AS USSR), Leningrad.
Card 2/2

,/62/000/006/010/127
S/044
AUTHOR. Yerugin, A. N.
TITLE: Recurrence formulas for aaymptotio oxpanciona of integral
curves near the focus
PERIODICAL: Referativnyy zhurnal. Matematika, no, 6, 1962, 49, rbatract
6B214 (Izv. All BSSR. Ser. fiz.-tekh:n. n., no. 2, 1960, 16-28).
TMT~ This paper concludes a series of papers of the author (RZhMat, 1960,
2935, 2973 5242, 13791), which deals with the expabsion of a solution
r .. f(q, Gj (where r is the radius vector, kfthe polar angle, a an arbitr=7
constant) of a set of differential equations dx/d-t - X(x, y), dy/dt ..Y(X,Y)
in a series on the assumption that the focus be the coordinate origin and
that the series representing the solution converges for all )fj>)IT (where M
is an arbitrary number). In the present paperp new recurrence forr.-.ulas
are set up for the expansion coefficients. [Abstraoter's notes Complete
translation.
Card 1/1

YERUGIN, A.H.
Features of salutions of a s7stem of two di"ereirtial equations im
the case of a focus and in certain other cases. Testai AN BSSR.
Ser.fiz.-tekh.nav. no.3,-17-20 160. (HMA 13:9)
(Differential equatione) (Aayliptotlo Ommsionfl)

Asymptotic expansion of a solution for a. class of 'systev of two
differential, equations with holomorphic vight-halmd side. Test9i
AN BSSR.Ser.fis.-tskh,uav. no.1:27-42 160. (HIU 11:6)
(Differential equations) (Asymptotic expannions)

I-JMG1ff, A.M.
Structure of a set of values of an aLrbitrary constant In the case
of a focus. Dokl.Aff B&M 4 no.7:273-275 JI 960,,
WRL 13:8)
I. Natematicheekiy Institut AM SSS14 Predstavlexio akad. AN BSSR
V. L Krylovym.
(Aggregates)

YE-FILUGIN. ; A. N. , Cand. PI-Ijrs-MP~tn- - 90i -(diss)
Analytical Structure and Pro-pertles of Schit"'Is Of
Inter"'ral CLIIVOS of One Class of Systems of Two Dlffirentlai Enua-
tions ;:ith Holo:~,Lorphlc Ilight Parts In ~Casa of Vocue." 1-CL)
2 pp (Com','-Ined SocLentuific Council of Institute~i of Iliath e:,if, tic 51,
Physics, and Metallic PhYsics, Acad. of Scl. U,'!:i,SSR) 20r copies
(KL Supp 12-61,2550).
fl

VRUG.IN..A,N, [&mhins A.N.]
Approxjmat~e'computation and order of omallness of an improper inte-gral
(1.1). Vesti AN BSSR Ser, fiz.-tekh. nav. no. 1:37-41 161.
.(Integralej, Definite) (HIRA 14:4)
;H - h:~ ` IlHihi! i~l.i",,i'~i;iillllliilllllllllllii,illillilI liltA.,

INT
22827
S/17o/M/004/005/0-13/015
B111/11214
AUTHOR: ye.rugin A. N.
TITLE;: Approximate solution of a nonlinear equation
PERIODICAL: Inzhenerno-fizicheakiy zhurnal.p ya 4t,1104 5, 1961p 111-114
TM: The equation z" + P(x)z - q(x) t f(x,z) iii given, where'p(x), q(x),
f(XIZ) are integrable funotions, for xfX, m6ZV g(,x) it holds jT(x,z)1!sg(X),
where q(x) is dn integrable function. It further holdo:,,,Z(x Y(X) + T (XI
Y, ~ pkx)y f(]Ctz(x))* 1"lle funot ft ~X~ is e atimated
on'e-obtaina ln'd+(4'~'.) 'The formulae
f IF (X)I-' 70 + f (x. z (z)) F (x) dt
ire.
(3)
~(X) "P P (X)
dX1.
Card 1/4
I + g (!)F(X)d; (4)
- ----- --- --

'I I
'28 7
S11 74, 004100510131015
Approximate solution B111 "214 -
2) 4 X; 'ZIZ2 a Z; 21 -4~;fj.
kA
T4FXL-G"* To 'c 0, To -ff" XeX Z(A N(X)ez
Pf W I IF Wj I,?$ I + If (x, (x)) F(x) dX (5)
A-1.2 map ... ma @am-- go-R44-10
1)./(X, 2)>O(Xtx, -G'Z);
2) f (xzj) (x, 4) (-go X; 11, ?1 o Z-. z, > zj)
(fe > 0, *0 OF; XQX'-.Z~(X)' Y(X)GZ
(X)
flp(x)17 t(X. 9(X)) F(X)dx (6
Its
Card 2/4
MR-MR.".1.1
"flil,ii Hii

2,R927
3/170/61/004/00,c/013/015
Approximate solution B111/B214
allow to introduce a method of successive appiroximakions, where the first
-approximation is: 3;
+f, f(x,.V.(X))F(x)dx,'. If the
Z'(X) Y(X) + ~,(X); TI(x:Y- IF
first approximation zj(x) is substituted for z(x)-in (3) one obtains
z Y(X) + Generally the following equation holds:
2(x) q2(x)
z Z, (X) IF X - r,,
n1
X
+ (x) F (x) dx ... dx
S j
XO Jr.
g (x) F (z) dx ... dx +jF(xj const, (16)
3/4.
H III Mutt M

2,,1827
5/170/61/004/005/013/015
Approximate soluiion Bill/B214
it is see n from (15) that for certain m .6nd x6x (.16) holds and z(x) tends
to ZW as n tends to infinity. If ('15) and (16) are satisfied,, s,(x) may
be replaced.by f(xjy(x)). Therc- is I non-Boviet-bloo.reference.
-APSOCIATIOIT: Lening7radskoyq otdeleniye matematicheekogo inatituta AN SSSR
im. V. A. Stelcloval g. Leningrad (Leningrad Department of the
Institute of Hathematics, AS USSR'imeni V. A, Steklov,
Leningrad)
SUBMITTED: November.28,'1960
Card 4/4

TERUGIN A.N.
Analytical structure of an explicit oolution of wi equation of integrFA
curves ok certain systems of differential equatiow. rjOkI*ANWSR
5 noo5-.191-193 VV 161, WIR~ 14.-5)
1, Institut, matematiki AN SSSR. Predstavleno akademikom All BSSR
V. I. Kry:Lovym*
(Differential equatiow

-,W00
S/044/62/000/004/018/099
C111/C444
AUTHORs Yerugin, A. N.
TITLEt The analytic structure of the solution of the equation
of the integral curves of a system of two differential
equations with non-holomorphic right hands
PERIODICAL: Referativnyy zhurnal, Matematika, no. 4, 1962, 26,
abstrac-t 4B131. (Dokl. ANBSSR, 1961, 1, 110- 7, 284-265)
TEXT: Formal representations are given of the molution of the
equation 00
dr
R (G)r + T R,(G)rl+*n
In.T
and it is pointed out that sometimes (e. s-. ---f oLn-cc- n) the 4or-
responding series surely converges. Some time ago the author (RZhMat,
1962, 1B182) considered the case R 0(0) a 0.
[Abstracter's note: Complete translation.3
Card 1/1

-3110 0
AUTHOR:
TITLEt
PERIODICAL:
25179
Yerugin, A. N.
S/041/61/013/002/007/007
B112/B203
Analytical structure of the solution of the equation for
integral curves of a system of two differential equations
in certain cases
Ukrainskiy matematicheskiy zhurnal, v. 13, no. 2, 19611
224 - 226
TEXT: The author studies the integral curves of the systemi
i = Y + X, k - Y,
where X and Y are certain holomorphic functions of x and y, whose
leading terms are of second order at least. He defines two functions,
f(x) andT (x):
f (x) - Y(x,y(x)) a ax'L.:,+.
W - fLx + a-Y , a bx~ +
kb x 3Y)i y
Card 1/3

i. ~ I i1 I ff II I
1001 ;1 ;W , ~~ I - ~+
B/OW6i/0-13/002/007/007
Analytical structure of the solution... B112/B203
where Y(X) - I Aix i satisfies the equation3 y + X a 0. Tho author
1-2
consid:ers two cases; 1)OC - 2n - 1, a/,0, q,,(x) contains only terms of
an order higher than (V, + 1)/2: After introducing new variables, r and
instead of x.and y, the author obtains the following solution for the
equation of the integral curves of (1),
00
r = C +z Ui(10,%)C"
1-2
where C is an arbitrary constant, and u iM are certain functions with
the period 2 ti i: (1_)IF In + 1 which can be determined by an
(ti = 'V;nF 2n ~ -2n
infinite pyatem. of differential equations. 2)/J odd,ol, - 2~ + 1 -
2n - 1, b2 + 4( + I)a< Ot This case can be re&,,ced to case (1) by a
suitable transformation of variables. A. M. Lyapunov is mentioned.
Card 2/3

25179 13/041/61/013/002/007/007
Analytical structure of the solution.. 11112/B203
There are 4 Soviet-bloc references.
SUBMITTEDt December 21, 1960
Card 3/3

9
1" ~5"'V S/044 2 00/007/016/1C0
C 11 1,YC333
AUTHORi Yerugin, A. N.
TITLE; Th*__pzoper_tie&-of---the -asymp to tic expansions of the explicit
solution of the equation of the trajectories of some
differential equation systems
PMODICALs Referativnyy zhurnal, Matematika, no. 7, 1962, 36,
abstract 7i176. ("Dokl. All BSSR, 1961, 5t tic. 10, 421-423)
TEXT; Considered are differential equations
00
z 0
z +
0 qn(o ) z 0 Q(z.
9
n-1
n(G ) are functions which can be expanded into Fourier series,
Here 0.
.where the'series of the Fourier coefficients of ihese functions converge
absolutely; go "-- 0' L"/n - nci/- , .I- - const > 0. The series Q(Z' G) conver-
ges absolutely and uniformly for z --,:: z 01 zo M const > 0. One asserts
that (1) possesses solutions of the form
Card 1/2 z 1 +

S/044/62/COO/007/016/!%C0
The properties of the asymptotic ... C111/C333
where T-90T -.10 and where for tharo is -givon an asympto-
tic expansion in terms of the powers of The form of this expanuion
depends on the relation between or, and The proof of the assertion
is no'. given. 0
LAbstracter's notes Complete translation.]
Card 2/2

4~1132 5 U;;~~i ".1.1114111111h 11111HUM19 I 1111WILA 11M 111!~! gwj~ 1.mj ..i.'
jE_WSa& A.N.
Properties of asymptotic expansions of the explicit solution of an
equation of integral curves of some systems of differential equa-
tions. Dokl. AN BSSR 5 no.10:421-423 0 '61. (MIRA 15:3)
1. Institut matematiki AN SSSR. Predstavleno akademikom AN BSSR
V.I.Krylovym. (Differential equations)

k ].T I III
IT

-- - - - --- - I ---- I--,-,- - 4 :- ---- - ~L-- -, .:--,--.----'--4!`1 - - 41::- `-1 1 1! " . L, P ;I
, k - I , , ; ;
I i . ; j ~ ~. 0~ !: - 1 111
! I : : !~ !!- ; I I
s i I I ~ 1 1, ; I ! ~ .11 l" JII t ; I
~ 1 i ; r I
, - ! ; ! !., I ~ ; 1 .011111111, 111111,1111111111114 ~!Nlfl',11111111 ill 11111111:11., -1, d I I . Ii I .;: i I I

YERUGIN.. A.N.
Analytic structure of the solution to an equation (2.1).
Dif. urav. 1 no. 12:1606-1619 D 165. MRA 18:12)
1. Matematicheakiy institut imeni Staklovap Leningradskoyo
otdeleniye. Sutinitted July 21) 1965.

Yplwr~ I ti
ArlillYti2 s#,rt-,cture a,
-9c"llf-'On
nc.7g896-902'
JI '65. 1 -8
lo Leningradikop, ot,ejcnjyp Inq
V.A. Stoklovil,

Eff W. T-TP(e')
nP6014169 SOURCE CODEt UR70-37076-5 76- -5746- (04-f6
AUTHO14. Yeraidn
ORG: jAningrad Section, Mathematical Institute im. V. A. v (Leniniprailskoye
otdalonlye, Matematichesidy institut)
TITLE: The an*do structure of the solution of Equation (2.1)
SOURCEt DifferentsialInm uravuenlys, Y. 1, no. 12, 39659 1606-1619
TOPIC TAGS: 4ftrentW equi.& golution, mathematle an*sis, fVVM0A.)
00A.'Pegaefir
ABSTRACT: The author investigates the analytic structuare of the solution to the equation of
integml curves of a system of two differential equations -with nonholomorphic. right-hand sidesI
which In the case of the focus has the form
where Qn and 4n belong to specially defined K and T ihixtions. Q. - gn + _Qn; 9, a are
constants; and the series Q(z,, 0 ) Is absolutely and unifoi7aly convergent for sign(-06~>E)0,
and x 1 z':-P const. The paper presents the preliminary ioNostiption of the eVmtlon, aW
0

Ij
then discusses five particular cases. The basic properties of the asymptotic soluff ons of
Eq. (2.1) will be given in a separate paper. OzIg. art. has: 43 formulas.
SUB CODE: 12/ SUBM DATE: 21Jul65/ ORIG REF: 007

YERUGIN,--,A-N.
EotimtJono. Inzh,-fiz. zhur, nooll:109-11.1 R 164.
0411'A 181"')
1. 14atematicheskiy institut imeni V.A. Steklova, Leningrad.
.''j U.f,,

%= T v I D
A-UG~": N. K.
N "Sur la Substituttion Exposente Four Que2ques Systemes Irreguliers, "
Matem. Sb. (Mathemtical collection) 1935, 42:6~ pp. T45-753-
;IIJI! I

Poleazatellnaya Podstanovka iriegulyarnoy alstemy Uneynylch diffei-entsial1ryrt, ftVe~47-
Dan, 17 (1937), 235-236. 0 funktsionallno-inva-riAnykh resheniYakh. Dan, 42 K944,,
385-386. Privodimyye sisteny. Trudy mate=. in-ta Im. Steklova, 13 (1946)
SO: Mathematics in the USSRj 1917-194X
edited by Kurosh, A.G.,
Markushavich, A.I.,
Raahevskiy, P.K.
Moscow-Taningrad,, 1948

YERUGIN,, H. P.
"On Enmential Substitution in the System of Linear Differentlal Equations,
Poincarals Problem," Mstem. 6b. (HELthemtical C011"tiOU) 1938, 3 (45) PP. 509-526.

MUM, H.P.
"On Riwan's fflle==7 Problem for the System of Gauss)" Uohen. tap. Leningr.
W. in-ta (Scientific Transactions of the TAningred MaSogical Institute),
1939, 26p PP. 293-3o4.

Y&RWIN" N. F.
"Note to the Article of L. H. Shifter," Izv. AN. ser. ustem. (19m of the A
Acadewl of Sciences, Mathematical Series) 19 1,, 5, -PP. 377-W

YERWINP R. F.
"On Functioml-luvarient Solutions," DANg 1944y 49:9 VP. 385-386.

YERMINj N. P.
,,Reduced Systempn !!Uc~M MMR. UN (Scientific Bulletin of the Ioeniwad
State Universityt) 1945, 2, p. 5-6.

I fem; jLLI-

=WIN. 11. P.
P=ttonal 11blutions. Uch. zap. TAU ne.96-.101-134 148.
(Differential equations, Partial) MEL 10:8)

IS-' L FT1,14-fl;

YXMIN, N.P.
_g ~, ~,
aw
- -qlal;mcer
Functional invariant solutions of equations of the ascond order
with two Independent variables. Uch., sap. TAU no.1.11:142-166 110.
(Differential squAtions, Paxtial) (MLRA 10:8)

USSR/Mathematice Boundary-Value WwIAO~ 50
Problem
"Closed Sn1ution nf thA Nrahml4e-u-nlary N(jhho-
mogeneous Problem," N. P. Yerugin, bmimg~-ad,' 3 PP
"krlh~Lad Matewat L f4erh" Vo.L Xiv, ho r-
Considers partial differential equation, ut :;uyy
w1th the boundary conditions:
IL -onstant for y = 00 t >~ a
U 0 for y = L, t;;- (I
U 0 for 0 < y.< L, t
General solution by usual methods cannot be used
,fith given conditions, but another form of general
.solution-is found to be more adiptAble. Subajitte&
17 Jan 50.

1!11111 ilk! Illifilli:illll.~lilil~~iflilill~iiiiii~,,,Illlii;.,:;::il.I 11.11

YMI I NO P*
it
"Close Solution of a Parabolic Contiguous Hateropmous Problmj," M , 195o~
14:2 s pp. 215-217.

I U. 'I., U-1
LL I I 1117~ InLi'l-Ji
Hi I! I

USSR/Mathematics - Stabl~Uty Sep/Oct 50
Bonlinear Uechanics
Serrav
ft.stability of Motion, and the Qualitativa Theox-7
of Differential Equations as a Whole," N. P.
Yerugin, Leningrad
"Priklad Mattemat i Mekh" Vol XIV,- No 5., PP 459-
Solves proble= in M. A. Ayzermanla "Stability
th-- c?f D_vn=ie Systems" (UsDekb Mute-
Haukr Vol IV, r~o 4, 1-949), namely, --Tem-.
aaitrate or refute the f-olloving aasertion:
There exists at the orim_-,4n stable equilibrium
Ric
168T50
USSR/Mathe=mtics - Stability Sep/Ott 50
(Contd)'
4n& its region of attraction.encompasses all
pbase spaces of linear dIfferenti-al equations"
Work is in two parts: bebavloi of int Iegral curves.
and Ayzerman's problem. Submitted 23 HaY 50.
168T30
P:
fly
N

-ATE
-TIM

d. ~ 114
-A I A -1111 11 11 1

'll'I'T, TINIJ Ht

- ... I I I... I It 11 1 . .
I I ~ I .- -- I . f ~ - - ~ , - I - . . I . . ~ - , . - - " - I ~, ~ 1-1 - ~, P 11 . P,," t 4 ~
m '. " ,
"T"MAMME - - -Lul ~. I f -LJ'. - ~ - - '! !- t :-,, i .- _; ::~- - .1--ii - , -, J q p I, I I ; 1 1. : -, ~l
d=-4 Ll- ~~, I - 1 -1 . f, I I . I . . . I . . ;LLifli'll
I- , ~ "Y , . , ; - ~, , .:I. !I
fl. pf I !I
.1 1 . , . F, ~2 , in 1 i I

X,
PHASE x TREASURE ISLAND BIBLIOGRAPHICAL REPORT AID 669 - x
BOOK :call no.: AP648837
Author: YERUGIN,-N. P.
Full Title: ON A PROBLEM OF THE THEORY a? STABILITY CF SYSTEMS OF-
AUTOMATIC CONTROL (Photostat copy)
Transliterated Title: Ob odnoy zadache teoril witoychivosti sistem
avtomatioheokogo regulirovaniVa
PUBLISHING DATA
originating Agenoyi Academy of Sciencess Mechanics Institute U S S.R.
"Prikladnaya Matematika i MekhanikEt", 1952,,. Tom XVI, 620-626
(Applied Mathematics and Mechanios)
.Publishing House:' Not given
Date: 1952 No. pp.: 9 No. of copies: Not given
Editorial Staff: Not given
PURPOSE AND EVALUATION: A critical review of the 4ipplication by 1. 0.
Malkin (see: Applied Mathematics and Mechanics, 1952, is8ue 3) of
the method of Lyapunov's function to prove the stability of equili-
brium, made by the author at the request of the editors of this
periodical.
TEXT DATA:
Coverage: Theauthor states 1. 0. Ma.;kin-analysed the following problem:

Ob odnoy zadache i;eorii ustoychivosti AID 669 - x
distem avtomaticheskogo regullrovaniya
given a system of two differential equations
dx f(x) dy is bm + cy W
dt dt
where a, b and c are constants and.f(x)'is under the condi ione that
x Ef(x) + ex) ;e 0 f(O) ts 0 2~
x Cef(x) - *b=j > 0 (z ~. 0) 3)
Malkin assumed (as did.M. A. Ayzerman, who offered this problem In
"Uspekhi matematicheskikh nauk", 1949, v. iv, issue 4) that system (1)
satisfies the condition of the theorem of uniqueness for all the
values of x, y. It remained to be proved that the state of equili-
.brium x = 0, y = 0 of system (1) is asymptotically stab,;e for any
original perturbation. Further, Malkin constructed an integral
equation (4) to prove his assumption and finally obtained
Cf(x) + ex]. Cc:f(x) - abx]. 40
and concluded that the stability will be asymptotic even though V is
not a function of definite but of permanent sign.
The author develops Malkin's brief reasoning because it proves only
V(t) decreases when t--* 64, and also because the curves V - const.
2/5

Ob odnoy zadache teorii ustoychivosti AID 669 - x
sistem avtomaticheskogo regullrovaniya
may be open curves. The author introducea'Bendixon',s theorem for
this purpose. He also proves the faat~6f isymptotlo stability by
making the aecumption that the funot1&j..f(x)k,is cont1nuoua. In
analysing the decreasing function V(t).j-he adaumes that
2
V(t) ki 0"
and states that a value ti can be found, when V(tl) will have a pre-
deterinihed value and be reduced to any small domain kl . Let
V(-.,J) x k,2+, P0 whe" 9> 0 iv arbitrarily mn3l-
A is a domain bounded by closed curves:
V k12, and V . k?
At is part of the circle corresponding to
< x tj
dttains thd. curve, af-t2r. which ifeither enters inside the domain
bounded by-this ourve*,.*-,-
'ft Ally enciroles this curve, because V(t)
is decreasihg.. In further scussi6n he Introduces integral equations
and integral,curves and refers to his work on "Stability of Motion
V5

Ob odnoy zadache teorii ustoychivostj AID 669 - x
sistem avtomaticheskogo regulirovaniya
and the Qualitative Theory of Differential Equations" (Prikladnaya
matematika I mekhanika, 1950, v. XXV, issue 5). He uses two theorems
frorr, this work, 10.1 and 26.1; the first In full, but only the reason-
ing employed in the second, which has been oalled Incorrect., by N. 11.
Krasovskiy (Ibid., 1952, v. XV1, issue 5). 11lie auUiur
the domain oT -asymptotic stability includes the entire plano even
when D --_1 oo .
Mal"I n, according to the author, analysed also the system of differen-
tial equations: dx ax + f(y), -a- 4 = bx #- cy.,
H dt 1%
when a + c 4 0 y acy-bf(y)]>O and a function was deduced
2V = 2 Y (acy-' bf(y)dy) + (bx-ay)2 for.which we have
k
(a + c) (acy - bf(y)y < 0
dt
The author suggests the incorporation of his reasoning as given above
and his theorem (1) mentioned in his work "Theorems of Instability"
(Ibid., 1952, v. XVI, issue 3).
Concluding, the author says that Lyapunov's method, analyzed In this
article, does not allow presenting the whole multiform qualitative
4/5

Ob odnoy zadache teorii ustoychivosti AID 669 - x
sistem avtomaticheskogo regulirovanlya
picture of the discussed system of differential equations and defining
the role of parameters of this system, when the process is quickly
damping. For this reason, In the case of the existence of isolated
domains close to the origin of coordinates, the fact cannot be estab-
lished that the entire mass of solutions, when f(x) is a holomorphic
function, would be reached by non-holomorphic Poincare' series, and
that the boundary of these zones would correspond to a single holo-
morphic solution at the point (0.0) of the solution of equation
bx
dr.
(in the case when f(x) is not holomorphic, the analytic character of
the solution representing the boundaries of these isolated sectors,
is not clear).
Table of Contents: None
No. of References: 8, all Russian (1941-1952).
Facilities: None given.
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