SCIENTIFIC ABSTRACT ZUBOV, V.G. - ZUBOV, V.I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R002065610004-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 1, 2001
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT


B/169/62/000/007/075,/149'
D228/D347
AUTHORS: Mizyuky L. Ya. and ~ubovq Vo Go
TITLE.6 Transistorized computing autocompeneator K(,P' Tj~
(KSR-Ti)
PERIODICAL: Referativnyy zhurnal, Geofizika,'!no. 71 1962,'~3#',ab-
fitract 7A217 (V sb. Razved. i pr6mysl. geofiz.i no.
42, M., 1961y 41-47)
TEXT: In the described KSR~-Tl transistor autocompeneator division
and multiplication operations are accomplished, by means of~a va-
riable instrument shunt. When there is such a otrc4it the convert-
ing unit is independent of the measuring limit and'allows the
equation Pk ~__ K(AU/I) to be solved in one stag ie. A~, n.egative ~,direc.t-
current feedback is employed to compensate temperature changes in
the device. This ensures the instrument's stable operation in the
temperature range from -20 to +6000. The principli of the deyiec's
circuit is given. ~_Abstracterls note: Complete translation.'7
Gard 1/1
L

Ei/651/62/000/006/004/010
E140/EI35
AUTHOR: V~.G.
TITLEi Numerical system with fractio'nal base
SOURCE: Akademiya nauk Ukrayinalkoyi RSR. . Instytut
mashynoznavatva i avtomatyky, L' viv. 1~vtom~at icheskiy
kontrol, i izitieriteltnaya tekhnika. noi.~6. 19621 93-97.
TEXT: The author proposes the base A11-0 ror'14ndi6ator typ e
instruments and analogue computers, in a llfloatiiig-pointrf
representation. The dial reading is a fraction~df unity, using
an auxiliary representation of the particular power of
A/-10 3. 16....
There is I table.
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0294~
s/65l/62?coo/oo6/oo5/oXo
E14o/EM
AUTHOR: Zubov. V.G.-
TITLEt Experimental study of residual paramoters, of a transistor
used as a small-signal switch
SOURCE: Akademiya nauk 11krayins1koyi IISR. Ihstyttut
mashynoznavstva i avtomatyky, LIviv. AvtoTa t iche 2kiy
kontroll i izmeritelInaya tekhnika~ no.6.~1962. 98_~104.
TEXT: The author has found discrepancies botween the
theoretical and the experimental behaviour of transistors use d a.z
small-signal switches (e.g.- in d.c.-amplifier choppers). Iqi
particular the drifts of the collector current in the cut-off state
and the saturation voltage with temperature are far less tha n
expected, so that such applications can in fact be.realised even
though it would appenr theoretically impossible~ Tbe author claims
to have found a slow process in cut-off transistors which renders
the a.c. and d.c. properties different hence t,he d.c. parameter4
have no significance in rapidly switched transistors.- The time
constant of the d. c. process. is about three miniu'tea'f or the Soviot
transistor (113A (P13A), during which the residual current' in the
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t~x

Experimental study of residual s/651/6,0/000/006/005/610,
E140/E135
cut-off transistor grows from a value 0f the order of 3 sLA to one
of the order of a few tens PA at 80 *C. The author, claims this is
is llcut-off'1,7 but
not a thermal phenomenon, since the transistor'
the value of collector voltage used in the experiment is not given.
However, the use of a mechanical chopper in th4 base -circuit ~at
50 - 400 c.p.s. appears to confirm the authorls, analysis, izi that
the residual cut-off current remains constant with time and does
not exceed 2 PA at 80 OC. No conjectures are advanced concernin'
the nature of the phenomenon observed.
There are 7 figures.
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- 1 ZU130V 7 a
i I o

4 P95
631/62/6b /006/iDW010
94006 E140/P,133
131azhkevich, Hi Ii and Zubov Vi'Q&
AUTILURS:
or
TlTLE: -New transistorized self -t)&, la,ticing- potentiometer.r
thermocouple measurements!
SvURCE: Akademiya nauk.Ukroyins I'koyk RSR6 U.
mashynoviavatva. i avtomatyky'l L!ViVs::. 'Ay~~bmatiche6kW'
kontroll i izmeritel'naya-'tekhnika#~
TEXr: The article describes, MrI NK" (XPAK)O,~
transistorized self-balancing ~potentiomete
0 to 800 *C,' with a4 error,not,exceedifi.g'04.5% 'of! fidl, 'stale
indication. This potent iom'cter'was! devoloped.;a~~'-6i :institut-
mashinovedeniya i avtomatilci AN Ussil .(jjj6titjjt6' 6f Sciencip of,.,
Machinery anti Automatics, A$ Ukr+SSn) Fig".1 the ~Principle-
of the device. rhere are-21figures.,
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Now
t 4tol."ZO(j
"ncfne
20 40 &J 40
ac. 00 7/01
)o
0/00
W-7
910
to
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r. (184P7-~7 Wnwot 41 T.TP1
ACC NRj XT60044 --d- SOURCE CODE: URI*660-6)661000/000/0122/0140
AUTRPR: Zubov, V. G. (L'vov)
ORG: none
TITLE: Microvolt transistor inverter with microthermostatic control
SOURCE: AN UkrSSR. Termostoykiye radiotelemetricheskiye' ~istemy.(Heat reoistailt
radiotelemetering systems). Kiev, Naukova dumka, 1966, 111-140
TQPIC TA~S: thermospt, thermal stability, thermal degradsitiont,
ABST A microthermostat for close temperature control~of atransistori,
Jed
inverter is described in detail. Special care was taken in circuit design'~And layout
to insure maximum thermal stability of the transistor and associa'ted compon6nts.' in
order that input signals on the order of microvolts could be rel:Lably handled. A
cross section of the microthermostat is shown in Fig. 1. With an Internal! ambient
control point of 70C, the circuit was found to operate satisfactorily over An outside
Card
1/2

L 08427-67
ACC NRI AT6034430
Fig. 1. Mlc~othermdl.stat
Aluminum cylinde,r with outside Jacque'r
2 ....... %nnaulatlon;2- NQIA'~,trlodo;: 3 - mlcnr~ta plate;
3 4 - lead connections; 5 thermistor;
4 6 - heating coil-, 7,1 9 - asbestos walls;
8 - heating coil tarininals; 10 - feed-thro;ugh
for leads; 11 - dateilts for mounting iaica.)rta
15 9 plate; 12 - asbestpajillor; 13 - micarta.rings;
14 - polyamide resi,n~ 15 dead air space;
.16 - diodei,
ambient range of 0-60C. Zero drift over this range -does'. not ezceed 210 yvp and
inverter operation is within specification limits for line*oltage changes up to
I I
110%. Thermostat dimensions are 105 x 150 x 50 mm, and its, 'weight is not over I kg.
Orig. art. has: 7 figures.
SUB CODE: 09/ SUBM DATE: 05Apr66/ ORIG REF: 004/ 0711 REP.- 0021 ATD PRESS: 5163
Card

L 07839-61 EWT(l) Ij~(.c)
ACC NR: AP600470 SOURCE ODDS.' UIV*O 65"
iAUTHOR; Govorova. re, Zubov V G.;-Firsov M, Hill;
14q
~ORG: scow State University im. V, H. Lamnosov Hookovskiy gosudarstv4n~
rosi
univorsitot)
:TITLE. Cortain features of acoustic wave intoractlon iri crystals
f
SOURCE! Kristallografiya, v. 3.11, no. 4v 1966, 62a-6)1
!TOPIC TAGS; acoustic wave, ultrasonic wave propagaitionlk~! mmo6ium,compnnot
!acoustic diffraction, single crystal* quarts crystal
-This in a continuation of earlior woi
;ABSTRACT; rk (Krisi~llogiiarlya V. 91;noo
*59 __ 465, 1964)o where the authors observed In a-quak' Ao"ic
~~t by:An ultra
ifract"n'mothod,-tho appoarance of longitudinaloscination modos accoMP6 pri n
Ltransvorse osoi3.lations.' The present article is dovotAd[, to a ~similar study W1
!singlo-crYAa AbPo in uhich thor6 am no.piosocooffioishts causing longitudiiial.
oscillationsp " In uhioh the elastic nonlinoarity is liuMerthan in quatts. T40 -
iresults have shown that the transverse mods is continuously adomptniod by a seciondl__.~.
+
;harmonic of a longitudinal made In the same direction. In the general case. bis
lCard 2/2 50 !539,.37-,
I J I 1 1!14;j III VIA I I 111 1 IM 1411 1 ill

L 07839-67
ACC NR: AP&2467o
longitudinal mode is weaker than the mode exciting iC 11)ut ukidor *ortaln,gaomotrloal
irosonanco conditions the dirfraotion mfixJ mA on the, longitudimal mode be'c6mo com- I
'parable in brightness with the original transverse mode,, The result is Ahom to
agree with a general formula derived for the Iropagatloh of Ain elastic Vivo in a
(nonlinoAr crystalline modium, uhoroby under certain cohdition'* the secondAarsonie
.1longitudinal oscillation can increase spo ntanOOU31,y and ~ivo r1so eventually ~ to a
first harmonic, which was not present hitherto. Th13 worgy transf or fr6a one har-
!monic to another is in good agreement with the results 4 E. Formit J. Past& and
IS. M. Ulam (Studies of Nonlinear Problemsg LA
-1940p OT3j' US Dopartment of, Com'=rc
Vashingtong D. C.)j who investigated dirootly the energy transitions in'tho ipeo~-
Itrum of a vibrating string with nonlinear parameters. 11~ pro$ivit ox*im'onts't like
I
Itho observations of Fervd ot al.j only permit obaervatioh of this pr;cossl,but still,"
!offer no theoretical explanation. The authors thank-Lji,-Rolls, Eminat., and
L-R_._~Z ~sev& for preparin the high grade ADP crystals, OrIg. ma-~LrQs
and 4 formulas.
SUBK DAM 0& OTH NW: 00).,
'SUB ODDS: 20/ P O~RIG- W; 004/
bo

r I _r-
ACC NRI .,T6008315 S_0'_U-fi"dE_-C-~-F-6ff
AUTHOR: Zubov, V. G. (Llvov) (Candidate of technical sciene
ORG; none
TITLE: A semi conductor.converte r of small d. c. voltatz a
SOURCE: AN UkrSSR. Elementy sistem otbora I peredacht Informataft (Elements',of systems
for selecting and transferring Information). Kiev, Naukova dumka, 1966, 61-66
TOPIC TAGS: voltage converter, elect-. ~fde circuit,: circuit deg~'iim, 440,0A
ABSTRACT: Although semiconductor voltage converters still bihibit humerous shortcomings,
the fast response and the almost infinite lifetime of such devic~$'Imake the continuous efforts
for the perfection of such devices meaningful. The author dl OCUsses In considerable detail
the theory and operation of the thermally compensated converter forming a bridge circuit.
The theoretical conclusions were tested on an experimental circuit, shown in Figure 1, ~
containing the heat-sensitive resistor Rt. Tests show that the olicult is. quite Insensitive to the
choice of triodes, the residual (false) signnIs at normal operatinIg teraj)eratures does not
exceed klO pV, and a temperature change of the order of 600 causes an additional zero drift
within the +10 pV limits. Orig. art. has: 8 formulas and 2 figures.

ACC NRt AT6008315
soil III
Ta
Figure 1. Small d. c. voltage semiconductot conyorter,
SUB CODE: 09/ SU13M DATE: 6Nov65/ ORIG, REF: 002/ OTH REP: 002
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77

T.,--AI5-6-01877 2
SOURCE CODE: UR/0070/66/0111003/0422/0424
;AUTHOR: Zubov, V..G.- Ivanov A. T.
;ORG: Moscow State University im. M. V. Lomonosov (Hoskovskiy*;gosudar,,r,:Cv~epy3yy'~ univIa-0-
sitet)
'TITLE: Dilatation of auartz caused by bombardment with fast n.
--outrions
ISOURICE: Kristallografiya, v. 11, no. 3, 1966, 422-424
ITOPIC TAGS: 'quartz crystal, neutron absorption, neutron flux, lattice defect ..c4sr
ABSTRACT: The dilatation of quartz exposed to fast neutrons Up'tegral fluk.den.sities
of 0 to 20 n/cm2) was studied. The analysis of the results'was'based on the fotmation
l
of submicroscopic amorphous regions and their effect on neighboring crystal',Iattice
sites; the number of amorphous sites was proportional to the increase in volume. Data
on the % volume expansion and % decrease in density as fun~tionsof integral, flux den-
sity of fast neutrons are presented. Theoretically, the number (dn) of amorphous re-
gions formed in a dose interval fTom ~ to 0do was proportional to the number of,un-
formed amorphous regions (N-n), i. e., dn=(cL+Bn) (N-n)do,,where ct and 0 are constants.
Integrating and letting E=lm be the relative volume expansion sothat E., =kN,
x
atm' [exp(b(p)-11
tmax + v,,.vp(b(p)
UDC: 5484
Cord 1/2

L 34t$16-66
ACC NRs AP6010772
0
where the new constants a--WO and b=Nom. rrom experimental ditto, a=0.272% and b=
=0.45-10 19 cm2/n for the results of Wittels (light envlro~nment) and a=0.898% a.,fd bm
-19 cn
=0.42-10 2/n for the results of Primak'(darkness); tMax in:all cases was equal to
17.65%. The above equations agreed well with the experimental,results and the amor-
phous region hypothesis, with the constants a and b adjusting for any rate changes in
amorphous quartz accumulation as a function of light exposure. Orig. art. has:~ 2
figures, 4 formulas., [14]
SUB CODE-. 20,11/ SUBM DATE: 1OApr64/ OTH REF: 005F ATD PRESS:
card 2/2

ZUBOV V 0 - GULINOT, V,P*; KUZMMOVA, Ta,D., teUkt r YWOVo V.A.,
~-----tor; MUKOTSFAYA, R.A., tolchdlchesk"~y

2MOV
V&W Gep divevich; SHLLINOV,'V W imir Petrovidh; MSOVA,
TO.B., red-akt-or; GAV~ILOV, S.S., tekhnicbeskiy rodAktoi-
EPAroblems in physice;'textbQok for solf-instructiblal Z~ditchi P'o
fizike; posobie dlia samoo~razov-aniia.'IicI-'I' pj Ispr. Moskva
Gos. i2d-vo tekh o 320.p..,
nik -teo
(Physics--Problems. ezarciaes, ate.)

ZUBOV, V.G.- SHICUBLID, TS.I.
Dielectric losses in tee near the melting temp6ratura,. Report
Ho.l. Yest.mook.un, Ssr*mat6,mekh,,nmtron.,fItb khit. 11
no.1:181-185 156. KLIA 10:12)
(Ice-Blectric properties)

2 G,:
USSR/Radiopbysics Generation ana ConvereLon,of RF Oseilla'tions
Abet Journals Referat ZhUr FixiMp No 12, 1956s ~~275
Zuboy
Authors V. Go
Institutions Moscov State Urdversity-
Titles On the Temperature Behavior of~the Elastic C6vataniwof Quartz,
Original
Periodicals Dokl. AN SSSRJP 1956, 107., 103..139e-;393
Abstracts Report on the results of a new.messurement of the temperature be-
havior of the natural frequencies of quartz:r'O'sonatoir's In the ~em-,Z
perature range from 20 to 5730, using the madod ox! cibser'ving ~tbe t
diffraction of light by ultrasonic waves. The quartz cubes, driemted
along the principal axeoj,vere excited by abialtermating field with a
freqgancy of 8-10 mc. Thi light source eVloyed was a mercux-j Isay
with -a green filter. The photograpbB of the ~ diffmatia Atu= Nero
used to calculate the velocity of the qu&si-lcngit-WJnaI acdlquasl-
transverse waves and the value's.of all the 9~effective elastic co4f-
ficients. The resultant experimental curves~.vake It poasibla:to
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------------- --------------- - -------------- --------- - ----- - ----------- --------

Category USSR/Sol Id State Fhyoi~.s - Wichanical, Fr6pdrUo"".0c E-9
Crystal a tnd Folycryotnllino Comrounds
tbs Jour Ref,Zhur Fizikr, No 3, 1957, tTo 6771
Author Zubov, V.G., Firsovn, M.M.
Inst I!dsbcw LIRM-reity, USSR
Titlo i Concerning the EInBtic Froportion of High Tonporature qu r r tz
Orig Fub Dokl, AN SSSR, 191,6, 109, No 3, 493-494
Abstract :,The Bergmen-Scherer method wftc used to study,the tenperature
behavior of the Kactic constcnts ofj9 quverti in fba
roraturo rengo fron 578 -- 635'. An tho tot,,.~,erattirrj is in-
crop.cad, CII, C r incronno monotoniaellyj C1111 ro-
meins conctent Uthi'n'4tc~cl'mrita of oxperimailtel orror. At
58C0 C - C33 end C12 reverses its si n. C(66);' C C
f I IA- 1~ !2
12 incro"Ases nonotonicel1v fro;-.1 50 x lo U to~"Il xilo 0 no cm
C12 incroacoo from 17 x lb'O dyne/cr. 2 at 5P960 to ~6,.x 1010
dyne/craZ at 615 -- 6200. The blesticity of quertz in-
creases with temperature.
Cr.rd t 1/1

.QU, Viktor Gennadiggy1cU. SHALINOT, Vladimir Petrovich; "XITSOVAt Ts.B
TWUM0270-MVIA13737, 3.8s, takhaicheekly redaktor
[Problems in physics-. &.manual, for self-education] Eadachi po~fisikq;
posoble dlia aamodbrazovaniis.,Izd.4-oe, ispro' Moskva Gossild-vo:
takhniko-tooratelit-ry, 1937. 320 P. (KLRA i0:9)
(Pbysico-ProblaIRS, oxer'ciess, etas)

SO~1-10_ .3-6-11/25-

AUTHORS: t
Zhdanov, G.S., 7,11hav, V-G.,_~vanov Firsova; M.M.
TITLE: On the Elastic Properties of Quartz~jlrra'diated byiNeultrons
(0b uprugikh svoystvakh kvartsa, obluche~wiogo neytronami)
PERIODICAL: Kristallografiya, 1958t Vol 3, Nr 61 pp 720-?25 (bSSR)
ABSTRACT-. The elastic constants of quartz, irkadiated in a reactor
by fast neutrons, have been measure(I by,the mthod'of~
Bergmann and Schaeffer. After irradiatioa by
19 2 i
2.10 neutrons/am increasing errors which lay in -the
limits of 0.9 to l.?% for a relative de6rease in,the
'
'-
!
timont
the
expe
density of quartz of 0.18% were foUhd in
for measuring the elastic constantsli Comparison~with
the temperature variation of the elestid constants s4owed
that the temperature and radiation ~,hangeiB in therelitstic
constants corresponding to the same~-,hatge in deabity
were sharply distinguished. The reiults agree qualitatively
'igon (J,. PhyB*Rad. 195?~
with the work of Mayer and G I
Vol 18, p 109) on the elastic moduli of irTadiated quartz.
Measurements were made on blocks ab6ut go x 20 x:4 xM
cut perpendicular to the crystallogj?aphic axes. :~ou_r'
aeries each of three plates were used, 6areful contr44)ls
being kept. The friquencies used wiare 8-10 Mc/s.~ Wittels
and Sherill (Phil.Mag., 1957, Vol 48, p',24) contrasted the
Cardl/2

SOV/P70-3-6-11/25
On the Elastic Properties of Quartz Irradiated, by Ifeutrons
changes in the elastic constants produced by thermal 'and
radiation-produced expansion of the,11crystal lattice.
Although qualitatively the anistropy is the same,t.he
actual values for it are quite differentO This is shown
experimentally. The structural meaning of the results
obtained is not discussed. Acknowledgments to .
Academician I.K. Kikoin and V.L. Kaipov.' There ar .e 4 tables.
There are 11 references, 3 of whiehare Soviet, 8 F-hglish.
ASSOCIATION: Moskovskiy gosudarstvennyy universitat ire.
M.V.,Lomonosou (Moscow State Uhiversityimenl,
M V. Lj~onj5g
SUBMITTED: June
Card 2/2

S/07o/62/007/002/007/02'i
E132/Ei6o
AUTHORS: Zubov. V.-G,, and Grishina, A.P.
TITLE: The dielectric susceptibility and refractive indices,
of quartz irradiated by fast neutr6ns
FERIODICAL: Kristallografiya, V-7, no.2, 1962j~~238-241
TEXT.- For comparison with measurements by ii. I)rimak
(Ref.2: Phys. Rev., v.110, no.6, 1958, 1240-1254) the d.c.0
density and refractive indices of quartz crysttils after
irradiation by,2 x.1019 neutrons/cm2 have been'studied. As~ihe,
density and refractive indices depend on the two effects of,.
irradiation - the general breaking up of the structure and the
distortion of the interatomic forces by defects - it is
ae7
concluded that the dielectric constant is a more sensitive ih x
by which to follow the irradiation6 The d.c. changes by ]~% ford
this dose while the density changen by 0.18%, the r.i. by abbut~
0.05~9 and the eiastic constants by about 1%. There are 5 tables.
ASSOCIAT16N: Moskovskiy gosudarstvennyy universitet im.
Card 1/1 M.V. Lomonosova
(Moscow State University imeni MaY. Lomonosov)
SUBMITTED: June 30, 1960

S/0701/62~0671~9,4~012/010!
EO~i/E435'
AUTHORS: Zubo G.,--Osipova, L.P.
TITLE., Intonality and width Iof lines of cowbi"tid~n
s6atteri~iga in synthetic quartz
PERIODICAL: Kristall'o~grafiya, ,v,7','no!4, 49~2,- 6~0-6314
TEXT: Low pressure mercury lamps with-a very low ba!ckground verei
ujped. This r ult d:in a considerable deerea3e,lbf,tbe parasitic
scattering: and ena led measurements on the-,lings(- iz$,. w6, ~6'6
357, 4661 696,'795-905, 1o61, l08l,and'll59-4,m-J!jA th4se-were
carried out on a AOC -4 (DFS-10 spectrometer,. T'heltint4ndity :of
the lines -206, 266, 357, 466 And 6 96 -- tm-l 1 on 1 -tho %~~spe C tx~ak - of
synthetic and natural7quartz agreed; the total intenaity of the
band loft-loft cm-1 was greater in synthetic thA'n in;natural
quartz. , The intensity of the doublet 795-805 0111-1 WiAll somewhat
less in synthetic than in natural quartz. The *ntensilty and'the!:
width of the line 128 cm-1 were both greater forlsynthotic than
for natural quartz. The synthetic quartz possemsed a layer
structure, which might explain the appearance 0f.4 wdalc line vith~
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44f
/604 0 14'
3/020/
/010/
B12 S108
AUTHORS. Zubov, V. 0. and Osipovaf LIP P.
qu Wed by fast houtrons
TITLE. The Haman scattPring in artz irr,a!i
PERIODICAL's Akademiy4 n1auk SSSR, Doklady, v. .14410 no.~4, 962, 7~3465
c
TEXTt The spectrum of the Rainan scattering on a qulArtzr piogle rys,tal :was
it n! dimi ishe"'i t~e
irmatigated. Irradiation of the crystal by fast r1ai. ro 0 n
3
density of the sample from 2.65; to'2-49 e/cm i :ThO namp1o' retainod a re-
sidual I-activity, turned ligiit-violet, and began to abmorb -,-50 %iof the
incident ligbt of 5600 - 4000 R& The,intense flu0i;6sc-bn-r,4 writh its makimum
at 5750 R decreaced monotoniailly. Owing to tho int4inse. bac ound~ ;Onlk the
brightest,peake of the apectruwcoul&be determinl3d with an OM-5`1 i(ISP-51)
spectrograph. The very reliable photoelectric method, ijoyiever, a the
gay
in of the Rqman ocatteri-n# cmII- (ng. I
whole (continuous) spectru up to 1500
Many of the penks are caused:by~:the very diffuse,l [)2e or no .' rrddiab~d
S~ the n-
quartz. New peaks at 540P 930P:1050o: 1350 cm-1 were foillid. The 4~ffuse
maxima of the irradiated quartz,spectra are 20 ~30 timbs' less int~-nsfj than.
-Card 1/y

T
-ZM,Y. Vikt -Gennadi;revic#LSHAL 'NOV, Vladimir Petroirichl KUMETSOVA,
re L
L.V., tekhn. red.---
(Problems In physics] Zadachi po fizikel poisobis dlia saw-
obrazovaniia. Izd.7. Yoakvat GosAzd-Yo fizi,ko-matemat. lit-
ry, 1963. 271 p. (1411k 16:10)
(Physics-Problems$ exercises, etc.)

;14567~!
lip 070 -3./661/001/020/024
E132/EA60!
AUTHORS: Zubov. V.Gk Firsova 4 11.~N, Molokova 11T.M.',
TITLr!,: The temperature dependence ofthe didiectrIc
permeability of crystalline and fuse6~~quart't
PERIODICAL: Kristallografiya,' v.8 noil 1963, 1
12 114
TEXT: In order to'61car up discrepancies in tha.~j aari'i~r
literature, measurements were made of the dlelect-Ac constants
el.1 and c of quartz at I Mc/s over the temperature range 20 to
0C. ?3
700 -and Z-cut plate* about 20 x 20 X 4 111iii! having
platinized surfaces were used. Fused quartz shooed hardly any~
riso in o with tomporaturo and for crystalline Q-qu~rtz the
change was slight until 500"C There in a aliglit discontinuity
.in ell at about.the a-P transition temperatura.of..57VC-
did not rise as rapidly as early workers Courid for :1 to 90 Kc/s.
e33 I I
To get the beat values Of 033 9POcimens of quarti' were claaaed tby
L.G.Chentsovals mathod of applying a constant pokentia;i of
2 kV/cm along the optic axis at 7000C- This hao'the'effect Pit
reducing 033 steadily with each treatment until it became
i;ijbstantially the same as ell. and also showed a, small disconti;~UAY
ign ions in the atructurib on 3
-L 5730C. The effect of fore
Ciord 1/2

MO 1 9/t 435
it,,, Zhdanov Zubov.-.. V.G. E o Ion I: uovni , YC V.
C, L . P. 1 e. x1la V
TITLE Radiation effects in m-quartm
P--,R:GDTCAL: Kristallogra.Ciya. v.8, no.2, 1963, 20-,1-212
k comparison of' the Raman i5pectrati of' beforil alid
a t! r exposure to noutcons i fi carri o d ou t: , '711e Fitt-k-cl:klral
cliaracteristicit are obtaLned by the Laue mothu-6 and *,he anoviaLous
S. 'Itterinz metho-J, (p I e s r I pt t. e 1 3.11 -1 1 a
I ia it -i r .31 r I I m r t) 41
V. A 0
cnar,.ku I r) :4 tt ri t y o ;.ua r ir r'.r v 11 It N F", C tr.
I a t jV11%, 11, l;m.,-)l.:y V) 1) 1 vl
r-I-
t r ii-, C U.. r!T It I
I W I I- ;I I a x I Twl !-oi~i v r o 5 04' rt
rina ifl v e r N S.Lni.l 1,h,- Cl I: hit 1-,g C 1. e- t I on

B
P,60A 4 5 1;
(juartz d) the intensity of scatterin$,, i.n the i.rradlatod quartz
depends on tile orientation of the crystal. Tlie X-ray analysis
shows that the third orcier sytrimetry C3 it; chart.f,(Iid to sA-ALh order
i: 6 t,y t lie irradiat ion and thore i % a s L!;n i l'i.can-t cnange Ln th e
djstrib~,Itlon of diffuse Acattering. Ag a 11,1!~_,4111J. of 11011tron
irradiati(,n, tile structure of (x-qu--4rtz is tho-~khk to CiW111gle In tile
followi-rig manner: 1) Initially, deCecttt devolop which lead tv a
weakening and breaking of the SJ.-O bond and honco to the
possibility of rearrangentent lit the SJ-0 totit-ahedri-mis. L) t a
definite stage of the axposure the a-quartz bcrcotw~ti unstable and
there is a transition to the more syniinetriCikl hip-
,h temperature
modification. This remains stable at room tmmporatixre.
3) There is a complete loits of orientation In parts of the cryatal.
There are 4 figures.
ASSOCIATION: Moskovskiy gosudars'-vennyy unive-ruitat -im.
M.V.Lomonosova (Moscow State Umiversity imeni
M.V.Lomonosov)
S U 1 P- i I T-1 '~,, Dittly 10, 1962
Card 2/2

-j. 06
02.
ACCESSIal NR: AP4036721 S/ W/a/1WOM/600/6
AUMOR: Zubov Vo 0. Osipova,, L# P0
TITIE:. Regularities in spectrum c,hiinges of,Ramn effect In &ISU-quartz caused by
irrawliation vith fast neutrons'
SOURm AN SSSR. Doklady*o 116 is" 19&s: 300,36;
V-1 5 no
TOPIC TAGS: fast neutron Irradiation, quartz Raman I "e4irum,, 40ha-quart2ij boeta, -
i- quartz, irradiated quartz Paman aWctr=, R-orsa spectrum
AMTRACT: The autbors bave recorded +ha Rams& Spectra 1u41Ph&,-qWLrtz irrv4iateil
d
by neutron fluxes of 4o5 and 7 X 10'Qcm`~jvreayectively~ It "a found that
irradiation causes a gradual decrease of maAma corresymAing U Raton liae s'of a
nonirradiatad quartz and an Increase of their vidths. '~ This waitiva an shute4
loan
Uward =a1JAr frequencies; the cout"Aw" ~rua to ingreasing. This RM
spectra of the specimen irradiated with 7 ;S1A0"1cm:e appioaches, tbAt
quartz. Heating has a slmiW effect. It sews that the
r0rult
irradiation is the creation of-regions of smorpWu qurU* Orlaw art*
figure and 1 tab]A
is,

,:ACC NR, AP6012940 sounip, Cont
.~AUTHOR: Zubov, V. G.; Govorovaj V0. Z.

ORG: Moscow State University im. M. V4 Lcmonosov (Moskovswl 408114,tatim
nnni, I
_~
unlvereitetT_
.
JITLE: Thijrd-order~:'anhampnicity effects in crystale
.SOURCE: Kristallo'graflya, 10, no. 1, 1 r/65, 5,6-~Q
D.

TOPIC TAGS:
phase tran8itionj, ultrasouics,
ABSTRACT: The conditions are formulated ror rbsiol~iAt Jute--61) Ldond~otviedn tvt~

Intersecting waves in a crystal. A num(~lrical rjolu~,ion I ~Iil
n
-
o t' ~ 6 at
n a e 9u
.
for the interaction between X3 and Y5 vmves in t.C -quartz. 4 h it; 16 16
:
.verified experimentally by the Dergmen4chefror ultrasonic dITW
.1 Un methojI4
Lpfiotographa at room temperature anrl nem, the phase travitiltiolli (501 0) are 6-4n
which support the numerical cAcuiation-s Orig'. art hae$ 2, tigurtmi and
mulas. (JPM3
10 fo

-SUB CODE: W3
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ZUBOV,.V.j,
A method of integrating differential oquatioAi~dascrlblxg the
vibrations of mechanical systems with distrili~ted pirameters.
Vast*Len*un*9 no#2:69-75 7 1540: (MM 9:7)
(Vibration) (Differential evations)

L-1 A. ; 1 .11.11 ~i 11 Iti
8 ptotie- WAlUk
MathemAtic 118yr 8
cam 1/1 Pub. 22 - 1/40
Authors j Zubovj V.I.
Title 1 Regarding the theory of, A.M. Lyapinovia second mothod.
Perloacal i Dok..AN SSSR 90,/),;341-344) Nov'P,1j 1954
Abetraot iA seconl Lyapunoy mlithad. for soiling systems d' M04;r~ntial tsa~t4 is
of the dxi - fi (xl, x2, Xro t) type wter~q i -t 11 2, *.** ro iis
At
analyzed. The obvious solution of the system, l.not, ze x:? w *so
has been called, after Lympunov, a 3olution of the siaMtotic e.04tbilll.ty.
Definitions and sufficient -anditions from tho lattew ims given, "
another Lyapunov's criterion (method), for tho maymptotit st4LUlLty,
is presented and dt3cussed by means of a seri*-j of theoms. Throo
Russian references (1946-1954).
Institute:
Presented-byt. Academician V.I.~Smirnov, September3:1954

I'l. I ,--I i-vr
i..' a fit). I a lll~
im Aet-t "Nnretm

2
c4m,, of t,.. n
f I lilt" i1, Nt I. . . . . .4 f -t h I Ti I itt e
of , I: f , , , - I. , I a I I ~ w I t tj am
-TI I - ' I - 11 -

Zubo t
V. T. Ort tLe It illarv of A. 11. rJailunWI; EPOI :~ld
RM, IV" 1

r__ V Uu V ) V - , ,
SUBJECT USSR/MATMUTICS/Differential equations CAM 1/1 PO - 568
AUTHOR ZUBOV Me
TITLE qualitative investigation of a system of ordinary'differential
equations.
PERIODICAL Doklady Akad.Nauk 899-901 (1956)
reviewed 2/1957
Let be given the system
dx dm
. f f
WT 1 (xt Y) I -dkt f2(xty) Wt 3(xpy'z)
where the functions fi (1-112,3) satisfy some conditions much that SM0,40,
others the system has a unique solution x a x(tx 01,YO)t iy - y(t,xotyo)#,r
Z - Z(tox py tz ) for t - Ot The author investigates tho asymptotic ate",
0 0 0
bility of the trivial solution in the large and with a sketchy proof ho'gives
six sufficient and one necessary and sufficient condition of stability.: then
under further assumptions the existence and number of boundary surfaces are-
investigated which separate the stable domain from the instable one. Further-
more it is established whenthe obtained qualitative image is stable at little
changes of the function fi (i-1t2t3)-- In a certain regard the obtained results
are more general than the well-known results of Erugin (Priklad.Xat.Mech~14.L 5,
(1950)),Krasovski (Priklad.Mat.Mech.17, 6, (1953)) and Plies (ibid, 17, 5-t(1953))-

SUBJECT TJSSR/MATHEMJLTICS/,Differential equations CM 1/2 PG - 499
AUTHOR ZUBOT V.I.
TITLE repr sentation of the solutions of tht sysbams of differential
equations in the neighborhood of a Sin lax point.
nRIODICAL Doklady Lkad.Mauk .1094 1095--40097 (1956f
reviewed 111957
The author considers the system
n n z
2p
Sul a i-1
k n
qji(t)zj + r i(t)xi + z (Xlp..O,x 'Zj9-1;Pzk0t)
n
It is assumed that X and Z admit series devalopmentp with respect t+o integral
S i
positive powers of xl,,...x n'z 19""lk%' where the coeffieieats of these series
are real, continuous and bounded functions of t for~t~->,Q. Also p
si(t)
and r (t) are real, continuous and bounded for t >0.kIt im stated that under
ij
a
certain assumptions there exists a group of tunotions zi (x1go.ox nott 11.0.co)
(J-1,...,,k) having the following propertyi Every z i:ctepende.on P cons tants,
in a region 1x'1 ~--. X0 M / 0' t C- rO,'+ooj it can be developed in a series and it

'Doklady Akad.ffauk j22.,. 1095-1097 (1956) COD 2/2 PO - 499
atisfies (1). If especially psiq qji and r are 064: tants and X are
ji
independent of t and analytic in a neighborhood of t~roj if furtherA
and ~Aj (1-1,,,.k) are the eigennumbero,i~of the matrices
P - lip K and Q -a Jq4jj1 , then the following theorem~ia valids If 1YRO )~O constant, and let 17~kyo conve"rge jlet the fur~ctioine
(M'm
P.i(z)t PS(z), P (z) be 4erim; d, real qontinuout
and bounded on z E(0913 be~ the charadteristio
4~ Let AO-1
numbers of
(2) n
Card 1/3 dt -Tpsi(e )Yi 5-1,siogn

Some Problems of Motion Stability SOY/59-46-2-3/9
e
Theoremt Let t-A,,>O for iii~l; lot (2) 11) ro4-ular. Then' (1),! has
a family of solutions depending on I 6onstatito and be-log
representable by series
M+ mijof
M M,
yo (Z)Z. al;
2-
m+m +,*+M
converging for lzllrz jc3jj,-c., who-to z and C :t~< where
0 0 0
Pis a sufficiently stall conotant, zo~>O con$ianto It
0?
(MRM poafml)
0(/
holds: I's (z)Z-.>O for Z-IoOp wh6rO o4>0 la:constant.
The author gives several.conclusions'llospedially for"Ahe C'ELse
where p si, p P are.conotants.
Chapter II: Investigation of,the stabilityjn some critical
cases. The author joins the papers of~A.M.Lyapunov, li.~P.Yorugin,
and A.A.Shestakov and considers. the qualitative imago ot the
) ;' the asym tonic
state of equilibrium for x' f (x11 ~-Ixn P
Card 2/3

SOV39-48-2-3/9
Some Problems of Motion Stability
stability of X1 fx(m)(tlx 9160tx I' ~V ~er~, the X(m).dre
a 1 n)
homogeneous forms of m-th;degree; the'analy~ia iapres4ntation or
0-curves of this syatem (compare Rem I.s.kiy fRef ~~ I the; case
of some pairs of purely imaginary roots. The paper containtl
25 theorems and numerous concluaionsp,lemmas, and remarka.'A
part of the results overlaps with knowA results, The author
thanks V.I.Smirnov, and VV.Ilemytskiy for the interest in this
paper.
There are 21 references, 15 of which are Soviet, 3 leraan,,and
3 French.
SUBMITTED: September2, 1957
Card 3/3
HN17 !["'d~ ~Ifl jI ,;7~
t4 '1111141MO H11 111 fli ii PN; 11 111'.

3/140J66/000/006/007/018
AUTHORs Zubay-1-1-
TITLEt On Periodic and Almost Periodic Forced 01,6~,cillations Ari.ping Under
the Influence of an External Force.
PERIODICALs Izveatiya, vysahikh uchabnykh zaved,0niy.,V&tem&tiki;19P,
-No. 6, ppo 93 109
TEXTs The author considers the system
dX
(1-1) dt F(X,l t)
where
X jx1y"xnj P
F(X1 t) f1(Xf t)"`~fn(X# t)j Let the f (Xq1t) be defined
real and continuous for all finite real values of,,. the argumeosu'let them
be almost periodic in t for arbitrary finite! fixed 'value 19 of, X ;' in every
finite region of the variables x 1J-01 xn let thim be un, f or mljr,,' continuous
in t ; let them in x,16061 X n natisfy,the,Lipachi-tz condition with a fixed
Card 1/ 6

-A
Sp4 60/000/006/007/0;18
C111 2P2
. YC
On Periodic and Almost Periodic Yoroed Oacillations;4rising Underlhe
Influence of an External Force
constant.
Definition 2 1 Let (1*1) have the property of conve rgenc'elf (1.1)!bss~&
unique almost periodic solution X = flt), where for every C 0 ixisto
a ~(e)> 0 so that from IX 0(t0) < ~9 (e) i: 4follovs IX(t,x:,to)
,,t 2. In every finite aamain of variation 'of
- 0(t)1< for t >
0
X f or t - t + 00 uniformly in to> cD it holds I 1X(t:1X ~t
:0 -
0 0
(t) 0
Theorem I t In order that (1.1) has the property.'ol,f convergence is"
necessary and sufficient thwt
1. every solution X(t,X 't ) of (1.1) is bounded,f or t,> t
0 0 0
2. to every r,**O and 6 > 0 there existis a r)>
0 80 tha~;If
1Xo- T ,r) in satisfied then it holds X t,X;lt 1(t x t
014 9( r
0 0 0
< 6 f or t:> t and X(tvX Y 0 oonverges uMf ormly
0 01to) X(to 0110
wit4 respect to t > oD for t t --31 + 00 IX01 0 so that the total derivative of V in which
Card 4/ 6

88181
S
NO
J60/000/006/007/018
C II I/C2~22
On Periodic and Almost Periodic Forced Oscillfitiohw~,Lrising Under The
Influence of an External Force
for dX the values (1.1) are substituted, in fXl> r satisfies the
dt
dVj
inequation dt < - oC const > 0
0) there exist such r > r > r, so that
3 2
inf V
V
> sup
(XI - r3 IXI - r2
t F (-CO , CC t e- (- OD ,00
2) The condition 2 of theorem 2 is satiefied'in IZI > 2 Th'on1(1.1) ha.0
the property of convergence*
Theorem 4 relates to systems (1-1) representable in the',form
(3-8) A(t)X + H(Xj t) + P(t)
Card 5/6

S/1-4oj6d/000/006/067/018
C11,I/CM' 1:
On Periodic and Almost Periodic Forced Oscillationp!:,Arising Under the
Influence of an External Force
and givos sufficient conditions that (3,8) has the property of
convergence*
There are 3 referenceg 1 2 Soviet and 1 C29cho-Slovi,klan.,
ASSOCIATIONt Leningradakiy gosudarstvennyy univermitet
(Leningrad State University)
SUBMITTEDs November 29, 1958
Card 616

80502
S/043/6O/OOO 1/008/014
/Op
a III/ C~$33
AUTHORs Zubov V.
TITLEs On almost periodic solutions of ayst"Ims oj differen'tial
equations
PERIODICAL; Leninprad. Univeraitet. Veatnik. Seriya mitomatiki,
mekhaniki i astronomii/i-rno. 11 1960?~:104-106
TEXTs The author considers
dX
F(X,t)
where
x (Xiv x
n
F(X,t) - ff,(X,09-09 f
Let the f (X,t) be defined for all finite real values of the
argumentsg real and continuous; almost periodio,f6r fixed Xin t;
uniformly continuous in t in every tinite domain:Pf th;6 x .... x
The f (X,t) satisfy a Lipschitz condition with affixed coAstan;.Yn
x X
n
Card 1/4

89502
S/043/60/Q00/00
il/008/014:
On almost periodic solutions . . . 3133
Definitions (1) is said to possess the property 6~1, convergence
if it has a unique almost periodic solution x O~(t) ~,n4 1.) to'
0 there exists a cr <
every (E) >, 0 so that from I X (t A,
O for t to~-4 + co uniformly-in t >-~oo VY
in every finite domain of X
0
Theorem Is In order that (1) possesses the property of convergence
it is necessary and sufficient that 1.) every solutilon~x(t,X , t ) i
0 0;
of (1) is bounded for t >,d t ; 2 to every r >: 0, F- > 0 there
f
exists a d(&,r)>-O so Thai from Ix -Y.1.4 J(f.,r) it follows..:
0
IX(t,x 't.) - X(t,y , t 1< for t >.'. t and jx(t,i t~) X(t,y itoy
0 0 0 0 :0 0 W
0 for t - t -*) + co uniformly in t > - ! I yo I
c0 0 Ix wC r, r.:
0 0 0
3.) For fixed x there exist 1 and T to every F- 0 fluch that ini'
every interval CX-+l) there exists at least one so that
C ar d 2/4

89502
B/043/60/000/001/008/014
on almost periodic solutions . . .
Ix (ttrv x vt X(t,X Vt ) 1-4 C for t t + V and', t~ +T V t + T
0 0 0 0 0 ii~ 0
Theorem 2s Assume that the following conditions are satiefieds 1-
There exists a function V (X,t) which is real and;rcontinuous for
1
all finite values of the arguments, uniformly bounded relative to
t are substituted.
total de ,,r, > 0 (in which the
dt
according to (1)). 2. There exists a function V(XY,Z,t) with them
properties a.) V is positive definite and admits B-n infinitel
y
small upper bound in every domain I ZI 49 ; b.) the futiotion
JV M-
n rgv.fi(X,t) + f
W(X,Y,Z,t) - 9 V + i+
at -a Y Jy, t) z
(f,(Z+Y,t) - fi(y,t)) is negative definite inZ in every finite'
domain JZ1 0 and every t - ehere exists an Le so tfiat in~ every inte rval
J
with the length Le there exists at least one t1t, so,that
f(t + V f(t)1 < f
Theorem I : Every recurrent function is I Ilounded and the!set of, such fu:nctions
forms a complete space on the whole real axis in,ttht? nenae of thel4nitorm
convergence*
Definition 2 t Let rx(t) be arbitrary real continuotis f4nGt I a na,
- ou < t 0 there exists a finite 'set
of real linear forms ple , 1:::Ske in r, ''rH(t) :and a 6'! > 0n0
that all compatible solutions of 'the syntem of inoqutitiond
(2) plt (t +1r) - ple (t)l < (mod 21r), 1.z~: k
for every fixed t satisfy the condition (1)
Theorem 2 asserts that to every f(t)G 1~ there exim;t at,most countdbly:
many linear forms of the mentioned kind,
Theorem 3 states that H N is a complet e linear space on~ the whole real axis
in the sense of the uniform convergence,
Theorem 4 If f(t)G H , then for every 6 > 0 there exists a trigonometric
IT
polynomial
k(t)
p6 ck e 00
k=1
Card 213

1 4`2
Ergodic Classes of Recurrent Motions 9/0?0/60/132/03/05/066
so that If(t) - p,, (t)1 (t) are finite lit-'.aar forms of tl-i~
k
functions p (t), P (t), of theorem 2.
1 2
Theorem 5 asserts that for every fSH or f C- 11 there exists the' mei7,n
value M (f(t)) - lim f(t)dt
t
T,>co
Theorem 6 1 Every f (-- H N has at most cojjzjtnj)jy mally ~Ourlor..exponentsl ftn4 8,
unique Fourier series
00 ip
- k(t)
f 2 X
0 e wh re 9
,t (I
k
k-1
Theorem 7 and 8 treat Feyer sums of fC-, ]I and the ropresenbation of ~f H
i. : rd
by functions periodic in the limit value.
The author mentions A.A. Markov, N.N. Bogolyubov, V.I. Stepanov and Mai,
Levitan. There are 7 references: 5 Soviet, 1 Swedish,,:and 1. filnglish..
PRESENTED: Januptry 26, 1960, by N.N. Bogolyubov, Academic:ian
SUBMITTED: Januar- 28, 1960
Card 3/3

28503~'
8/040/61/09.5/002/014/02~
D201/1)3!02
IUTHORt Zubovt V-I- (Leningrad)
TITIEt On the behayior of integral ourvevin a. neighborhoo4
of periodic notion
ya matematika i mekh ka' v..,25, no.
.eZRIODICALt Prikladna
303 - 31%
TEXTt The basic case is considered#
f
2(xt Y)
re the fi(xj are defined in some region 'G of: the xy pl,sne
and are realp continuous and twice differentiable 'With continuous
.i
derivatives. There are 2 continuously differentiable~real ~e~rir,6Ac
functions
X = CPJM =T2(t)
obtained by solving (1.1) with period 21rq whose gra''Ph M iie~s, -W 11th-
Card 1/7

8/040/6i~/025 021014~022i
On tho behavior of integral W-01/10 M
in G. (1.2) is said to be isolated if there exi~-.s a suffictlebt,14,
small 6-neighborhood S(M. 6) -_ G of the set M which does nom
.~
tain the graphs of the second solution of (1.1). Isolated peT_
solutions of (1.1) are called extreme cycles,,An extreme cycle -'s
i) at 'able if there exists a sufficiently small heighborhood S'Mb,'
G such that all -Integral curves of (1.1) lying ii S(Mr 6)
roach M without limi"t as c ----p oo . A.1-terna-uively., Lf
is the distance of (x, y) from Mo then for (x Y~ ?((X.,
ol~ 0
M) 0 as t + 00
x = X(t, x Y(.t, x
01 Yo 0 0
in a eolution of (1.1) passing through (X YJ f or',t 0 1 Ur~.-
stable if there exists a sufficientl small Vbighbo~~ood B(M10 6)
such that for (x OE S(MO 6)t XF Y)f M) 1" 6 as t
o Yo
V Semi-stable if there exists a sufficiently Mall'
neighborhood
8 M, 8) such that it is divided by M into 2 regions 81 and 829
Card 2/7

8104 1/025/002/014An
On the behavior of into ral D201%3609
.00
such that ((xo y)t X) --> 0 as t +oo (x ((X
0
es shows ~Ithat Lyap~nov
YO )tF- S2]. Examination of all possible cuxv
stability conditions apply in this.easeo The gen'eraI form of iho
equation of motion is
dv
1e (9) + fz* (0 - Sid1l (9) / di - %df, (8)
(2.6)
dit dV
+ + A (t),
dst dv
(9-7)
/2 01 + TI'. Zs' + (PI) - /2 W
dt
where or r (t) (2.1). lemmal H(z 22# t) defin'6d b~
H(zl,.z t) z f
2 1 1(t) + z2f2(t)P (fi(t) 7. 1 1
2(
; 1 (2-3)
is a solution of (2&7), Theoremi A periodic soluition of the system
(1.1) is stable in the Lyapunov s6neelf and only if the nulli so:
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28503
13104Y06'11025) 002/014/022
D
On the behavior of integral D201 D302
lution 0 Or 0 of
(alot+vI(I), a2*9 + (1), a*
dg 9+Ts!(;* h (01,~
(fit (9) + /s2 (f) - (ajOd1j (1) 1 d$ + a0dlt (1) / dt) t I
x
It, W /I (diog + (h. g1*9 + 93) + A (8) /1 (4394 + qh. all + 4NI
+ [a,xI 111) a,"
dt j
/I M
a,
AI M + 7? (1) 0*7 Ir(s) T /P (s)
dG/dt FQF ~t) I
are stable in the Lyapunov sensor where is de:rined~by
z f
I 2(t) z2fl(t)O z1fl(t) t z2f2(t;)!:
(Abstractorli,notat 0 not defined], If-the:right-*hand~-side oV (10,I)
is arialytiop then (2~15)9, (2,16) become
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28503 lk
.8/040 61~/025~002/014/~22,
On the behavior of integral 3)201%DI02
co
dj
= Yj bk (9)
dt
di
where the series converge: for'/Y/< Iri r 0. WAti
nV
2x
(13~. 3
.Gj b, (t) di 4- dt
J:
where all 41 (1). tpi(t))
b, (t) +
ax
2)'
In
2 at
it follows that for Gl< Ot (102) 1 a a stable e~trem4 4c,le and is
stable in the Lyapunov senset and for G 0 t (1.2) is an undtable
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6
2
S/040 1 025/0 2/014/02
On the behavior of integral ... D2ol D302
D
3
Y
extreme cycle, stable in the Lyapunov sense an t -~-41 -w Writing
E it exp bi (t) di (344)
ato (t) nk, dq bko (t) nk (3
2 k
+ +
+ 92(t)c gk(t)c
it follows that G for m 2. Theorem: It m f~ odd and
0 0,
then (IA) is a stable extreme clole. If L+ 1> i then it is sia-,
ble in the Lyapunov sense# and i t+ I < z it is,'unatable in the
Lyapunov sense i If a is odd and GM -;> 0. then (1. 2) is4n unstable
extreme cycle. If t+ 1~:-z it is stable in the Lyapuiiov sensed its
t -co t and if + I M it is unstable in the
sense.,
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L

28503
S/040/61/025~002/014/092
On the,behavior of integral D20l/D3O-2
If ais eveno then (1.2) is semi-stablea If J,+ X >-W. then (100
is conditionally stable in the Lyapunov sense in~the directions in
which the integral curves of (1.1) approach M. If t+ I v-- a the
conditions for stability do not occur. This theorem isnecessary
eat
and sufficient. There are 5 Soviet-bloc referenc
SUBMITTED: November 171, 1960
Card 7/7
SRZ F Mon But now 4 a W1W