SCIENTIFIC ABSTRACT KUKLA, S. - KUKLEV. YU. I.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000927310010-8
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 10
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

The problem of c1naring of tht improved pent lands. n. 137.
r Warszf
WSPODO-K& 1,40DNA. -,vm) Poland. Vol. 18, no. 3, 1958.
Monthly Idst of East Huropasn Accessions, LC, Vol, 9, no. 2, Feb. 1960.
Uncl.

, li~~h-.
------.
Oils and fats industry of the Moldavian S. S. R. 1--fasl.-zhir.
prom. 27 no.11:8-9 N 161. (MIRA 15:1)
(Mold&v--',a-Oil industries)

EXCERPTA MFI)ICA sec 8 Vol 12/8 Neurology Aug 59
3627. DISORDERS OF THE SKIN TEMPERATURE OF PARALYSED LIMBS IN
PATIENTS WITH TUMOURS AND TRAUMAS OF THE SPINAL MEDULLA -
Zaburzenia cleploty sk6rnej kodczy,.-i poratonych u chorych z gumami i
urazatnt rd7.cnia krqgowego - Kukla W . and Ro a te k J . Klin. Neuro-
chir. A. M. Poznah - NE _E_
URO . NEI)"ROCIIIII. PSYCH IAT. 1956, 7/suppl.4
(618-620) .
The results of skin temperature measurements are reprcisented as coefficicnts ex-
pressing temperature differences between the trunk and the finger. The clinical
material comprised 21 patients with tumours of the spinal cord, and 25 casualties
with fractures rf the vertebral column. One consequence of an acute trauma of the
spinal cord iti paralysis of the va:somotor activity In the distal parts of the limbs.
This paralyflis leads to an increase In the skin temperature of the limbs relative to
that of the trunk. Contrariwise, patients with prolonged apinal cord disturbances,
even -in the stage of complete paralysis, presented no observable differenc7 be-
tween trunk and limb temperatures. Paralysis of vasomotor activity is proportion-
ally slighter. the shorter the duration of the paralysis, Decrease in the temperature
of the distal limbs to observed simultaneously with the symptoms of returning
activity in the spinal cord or often even earlier. In casualties exhibiting a complete
clinical breakdown of spinal activity, the Iradomotor paralysis has no tendenc:' to
improv,e,

KUK12t, Wieslaw
Trauma in the Poznan and Zielona Gora region in 1962 and 1963.
Zdrow. publiczne 7/8:265-271 Jl-Ag 165.
1. Z Kliniki Neurochh-urgicznej AM w Poznaniu (Kierownik: doc.
dr. med. H. Powiertowski).
V
Rr
R7
, ~4 I,
kY-W-
.ll~r
. . . . . . . . . .
XIF

KUKLANOV, I.N.P inzh.; KHLISTUN, V.I.; SHCHERBAKOV) M.I.
Analysis of the designs of blastproof inertial mine locomotives
with hydraulic drives. Vop. rud. transp. no.61251-269 162.
(MIRA, 15:8)
1. Toretskiy mashinostroitellnyy zavod.
(Mine railroads)

-76-32-2-19/~8
AUTHORS: Panchenkov, G. M. Gorshkov, V. I. , ~Q~uklanova, M. V.
- ----------------
TITLE: The Effect of the Addition of Organic Solvents on the Ion
Exchange Equilibrium (Vliyaniye dobavok organicheskikh rast-
voriteley na ravnovesiye ionnogo obmena) I. The Effect of
Alcohols on the Equilibrium of Alkaline Ion Exchange on
Sulfo-Resins (I. V'liyaniye spirtov na ravnovesiye obmena
ionoV 3hchelochnyk.h metallov na sullfosmolakh)
PERIODICAL: Zhurnal Fizicheskoy Khimii, 195a, Vol. 32, I.Tr 2, Pp. 361-367
(U.SSR)
ABSTRACT: The authors mainly investigated the effect of mathylalcohol
on the equilibrium constant of alkaline ion exchange in the
sulfo resins of Inland origin CAB-3, C6C and espatite-1.
The kind of dependence of the equilibrium constant on the
composition of the mixed solvent and its dielectric constant
was checked. The effect of alcohol on various sulfo resins
in the exchange process wag compared for the purpose of ex-
plaining the part played by the carbon skeleton in resin.
Card 1/3 Finally the offoct of alcohol on tho exchange of various
U

76-32-2-19/38
The Effect of the Addition of Organic Solvents on the Ion Exchange Equili-
brium. I. The Effect of Alcohola on the Equilibrium of Alkaline Ion Ex-
change on Sulfo-Resins
cations was compared and the part played by the salt-anion
in the salts of one and the same metal +was explained. - The
ion exchange of the alkaline metals Li , Na , and K with
the H+ ion was mainly investiCated with chlorides. It is
shown that the logarithm of the exchange constant in all in-
vestigated ions linearly depends on the quantity l/D (up to
the values of about;~'0,02) of the solvent. (D denotes the di-
electric constant of the solvent). This shows that on these
conditions the basic r6le is played by the change of the
electrostatic interaction of ions and not by the change of
solvation. It is further shown that an addition of alcohol
increases the exchange constants of all three cations,that
ofLiC1 changing least and that of KC1, most. Within the range
of the used concentrations of water-alcohol solutions (UD
to 60 'j'O Cli OH) a linear dependence of the logarithm of the
exchange c8nstant on l/D was obtained. It is shoym that
with an increase of the,concentration these exchange constants
in alcohol become greater which can be used for improvin-n,
the chromatographic separation of alkaline elements. it is
Card 2/3 shown that the exchange constants with the 11aJ solution

76-32-2-19/38
The Effect of the Addition of Org;:wic Solvents on the Ion ExchanS Equi-
librium. I. The Effect of Alcohols on the Equilibrium of Alkaline Ion Ex-
change on Sulfo-Resins
almost cdncider'with the corresponding exchange constants Trith
the NaCl solution. This means that in the case of similar
salts the nature of the anion has little effect on the mag-
nitude of the exchange constant in water as well as on the
change of the constant with alcohol addition. On the other
hand, however, if a weakly dissociated ion was formed In
con,-equence of the reaction, this influence is a great one.
There are 5 figures, 7 tables, and 10 references, 8 of which
are Soviet.
ASSOCIATION: Gosudarstvennyy universitet im. IS. V. Lomonosova (loscow
State Universitz-,,imeni 14. V. Lomonosov)
SUBMITTED: November 3, 1956
1. Ion exchange resins--Properties 2. Methanol--Exchange reactions
Card 3. Organic solvents--Dielectric properties

AUTHORS: Panchankov# G. M., Gorshikov, V. 1., 76-32-3-18/43
Kuklanova, M. V.
TITLE: The Influence of Organic Solvents Upon the Ionic Exchange
Equilibrium (Vliyaniye organicheskikh rastvoriteley na
ravnovesiye ionnogo obmena),
II. The Influence of Acetone Upon the Ionic Exchange
Equilibrium of Alkali Metals on Sulfo Resins
(II. Vliyaniye atsetona na ravnovesiye ionnogo obmena
shchelochnykh metallov na sullfosmolakh)
PERIODICAL: Zhurnal Fizicheskoy Khimii, 1958, Vol. 32, Nr 3,
pp.- W-619 (uss"i)
ABSTRACT: Kressman and Kit~-hener (ref 1) obtained equilibrium
constants of the ionic exchange of K+ in water *-acetone
mixtures, but did not explain the obtained results.
Bafna (ref 2) doen not give any confirmation of his
assumptions either, whereas the investigations by Materova,
Vert and Grinberg (ref 3) did not yield positive results,
perbaps because.of knowledge inexact
of the activity coefficients in water-acetone solutions.
Card 1/3 Thus, there exists almost no satisfactory explanation on

The Influenoe of Organic Solvents Upon the Ionic 76-32-3-18/43
Exchange Equilibrium.
II. The Influence of Acetone Upon the Ionic Exchange
Equilibrium of Alkali Metals on Sulfo Resins
the influence of acetone upon the ionic exchange
equilibrium. The present paper investigates the ionic
exchange equilibrium --)f the alkali metals Li+, Na+ and
K+ on the domestic sulfo resins SBS, espatite-1 and the
resin SM-12 (the latter contains sulfo and carboxyl
groups), where the H-form of the resins was used and work
was done in water-acetone solutions. The method of the
taking of isothermal lines was described in an ea:7lier
paper. From the experimental results follows that acetone
exerts a stronger influence on the equilibrium constant than
methanol, - The chkWbf -the corist~ftt with con-
ceiitration, ii simileCrfbr allmdno. The prebeilee bt-12-M&MOday
dissociated -COOH groups,in the resin SM-12 apparently.
does not play any part. The increaso in the ionio exohangs
by the influence of acetone according to its strength aotc
bike in water i.e. most on K+ and least on Li+.*In the
investigations of the Li-form of the resin with N&+ ions
Card 2/3 it was determined that the values for lgK yield a linear

The Influence of Organic Solvents Upon -,he Ionic 76-32-3-18/43
Exchange Equilibrium.
II. The Influence of Acetone UDon the Ionic Exchange
Equilibrium of Alkali Metals on Sulfo Resins
function of 1/D which indicates' that no interaction of
the ions with the molecules of the solvent takes place,
but that the electrostatic ionic interaction is decisive.
When a Mo+ - H"t* exchange is performed,,the
linear function is not attainedt which is explained~by the
fact that in this case an influence of the H+ ions upon the
molecules of the solvent probably takes place.
There are 3 figures, 3 tables, and 4 references, 2 of which
are Soviet
ASSOCIATION: Mosko,rskiy gosudarstvennyy universitet im. M. V. Lomonosova
(Moscow state University imeni,M. V. Lomonosov)
SUBMITTED: November 13, 1956
Card 3/3

LUT, F. A. - KUVANKO, A. P.
,-~- ~
Clover and its mixtures in field crop rotations. Zemledelie 6
no.ii:66-67 N 138. (MIRA 11:11)
(Clover (Rotation of crops)

rot,~, C)
112-2-3423
Translation from: Pleferativnyy 21urnal, Elektrotekhnika, 1957, Nr 2, p. 130 (USSR)
AVROR: Kuklenkov, I. P.
TI=-. Wye-Delta Switcbover Starting Circuit for Electric Motors (Suggested
by I. P. Kuklenkov and I. B. Osinskiy) (9khema puska- elektrodvigateley
perek-1yucheniyem. so If 7ve%dy" na "treugollnik") ( Predlozheniye 1. P.
Kuklenkova, I. B. Osimskogo)
PERIODICAL% Sb rate. predlozh. M-vo Blektrotekhach. prom-sti SSSR, 1955, Nr 49,
pp: 22-P-3'v-
f,
ABS-TRACT: The operation of a system for switching stator windin8iI f vye to
delta utilizing a minimum number of contactors is proposed and'des-
cribed in details The system is intended to reduce the starting
current of induction squirrel-cage motors. Mlee "1~nearn and "delta"
contactors have two contact groups,, and the "wye" contactor has one.
The contactors are actuated by three push buttons. The "delta" and
1twye push buttons have two contacts each and the "stop" push button has
one. Pushing the Nye" button starts the mator and when it has begun
Card 1/2 to turn, the "delta" contactor button is pres6ed and the motor 4indings

10,
112-2-3423
Wye-Delta Switchover Starting Circuit for Electric bbtors (cont. )
are switched over to "delta". A great number of installations \
which have been set up according to this plan axe simple and reliable
in operation.
A. I. F.
I
Card 2/2

KTJKLES. I. S.
0 t8entrakh i fokusakh. Dg.', 19 (1.933), 459-461.
0 neobl,.hodinWkh i dostatochnykh usloviyakh sushchestvovaniya tsentra.
DAN, 42 (1944), 164-3L67.
0 nakotorykJ1 sluchiftyakh otlichlya fok.usa ot tsentra. DAN, 42 (1944), 212-215.
SO: Mathematics in the USSR, 1917-1947
Edited by Kurosh, A. G.
Markusevich, A. I.
Rashevskly, P. K.
Moscow-Ianingrad, 1948

j.1,! rows J(oc ibe DiAWmtWJ E4
ds*mimlits tbo Cu"tkNu at RaW =
-IdIrr"v* US. F6& Val.
49, #49- 0- PP 2WOP W

I.S., prof., doktor fiz.-mt. nauk.
problems in the methodology of mechanics. Trady UzGU no,53-.
Some
3-53 155. (MM 10:12)
(Mechanics)
'M WIM&A
40- VON
L IN

KUKLES,
Pfaff's equations with linear coefficients. Tm-dy UzGu no-59:97-104
'55. (MIR& 10t12)
(Differential equations)

AUTHORt KUKLES'I.S. 20-3-3/52
TITLE: -;"-On the Frommer Me7thod for the Investigation of a Singular Point
(0 me.tode.Frommera insledovaniya osoboy tochki)
PERIODICAM Doklady .1kademii Nauk 890$ 1957., Vol. 117, Nr. -3, PP. 367-37o (usm)
ABSTRACTt Given the differential equation
dy Yn(x-ty) + r(xfY
dx -
xn(I-PY) + X(X,Y)
where In and Yn are homogeneous polynomials of n-th degree,
while X and Y are imulytio,funations with terms of higher
order. For the invostigation of the question how many
characteristics go through the coordinate origin with a given
tangent, if the equation xYn-yxn = 0 has real roots, the author
uses the method of Frommer [Yef.1,7 with the introduction of the
order of curvature and the measure of curvature. The author
gives seven theorems with sketched proofs and a great number
of further single results.
Card 1/2 Theie is one figuro and 2 Soviet and 2 foreign references.

On the Frommer Method for the Investigation of a Singular Point 20-3-3/52
ASSOOIATIONt Uzbek St&te Uhivewsi%r im.AlisbAwa Navoi (Uzbekptwj 1~)
gosudaretvannyy universitet im. Alichera Ravo,
PRESENTEDi By I.R.Kolmogorov, Academiaian, 10 APril 1957
SUBMITTEDi 3 January 195.7
AVAILABLEt Library of Congress

Characteristics which Intersect the origin with zero and infinite
orders or measures of curvature. IzT. AN Us. SSP. Sor. fiz.-mato*
nar.k. -io.1:15-27 158.' (MBA 1116)
IGeomgtry, Algebraic)
(Diffex*ntial ev&' tions)

v-UMS9 I*S*; GRUZ# D~H*
Number of operations connected with the use of -Prommer method.
Izv. AN Uz. S2. Ser. ftz.-mat, nauk no.1:29-45 158. (MIRA 11:6)
(Geometrys Algebraic)
(Differential equations)

AUTHOR: Kukles, I.S. SOV/140-58-3-1 5/34
TITLEs On the Behavior of the Characteristics of the Eauation of
Rukukhara in the Neighborhood of the Origin (0 povedenii
kharakteristik U3.,avneniya Gukukhary v okrestnosti nachala)
PERIODICAL: Izvestiya vysshil:h uchebnykh zavedeniy. Fateniatika, 1958,
Nr 3, PP Ill - IZ2
.(USSR)
ABSTRACT: Hukukhara [Ref 1-
.1 showed that in many cases the behavior of
the characteristics of
-qZ YLX.Ly). results from the behavior
dx x x ~Y7
F
of the characteristics of
x dy - Ay k + B(x)
dx
Lot now be Bl'(x) = BW [A (k - 1)1 k-1
In (n) X = 11n In ... In x
..............................
n times
Card 1/3

On the Behavior of the Characteristics of the Equation SOVj-'140-58-3-15-34
of Hukukhara in the Neighborhood of the Origin
k '[In (2)x In (3) x ... In In) 2
(x)--! B (x)kx-'(- in x) x] -
?n 2 1
1 j.Z[jn(2)" 1n(3) x.... In (n) xj2 + In (3) x In (4) x ... In In) 2+
~ k I X]
+ [ln(4),...ln In) x]2+ ...+ lin(n-l)x In (n) X]2 + [In(n) X12 + 1~
Theorems If for sufficiently small x >0 one of the functions
fn(x) is 1:~O, then (1) possesses characteristics which run
into the origin irk the first quadrant. If there exists a
'fn(x) which for arbitrarily small positive x is larger than
an arbitrary positive number h, then such characteristics do
not exist in the first quadrant.
There are 3 references, i of which is Soviet, 1 Japanese, and
1 Italian.
ASSOCIATION: Uzbekskiy gosudarstvennyy universitet imeni A.Navoi (Uzbek
State University imeni A. Navoi)
Card 2/3

On the Behavior of the Characteristics of the Equation SOV/140-58-3-15/34
of Hukukhara in the Neighborhood of the Origin
SUBMITTED: January 20, 1958
Card 3/3

KUKLES, I.S.
Differentiation problems for Frommer's normal domains. Izv.
AN UxASR.Ser.fis.-mt.nauk no.5:69-78 '58- (KM 11:12)
1. Institnt matematiki i me"aniki im. V.I.Romafiovskogo AN UzSM-
(Differe~tiai equations)

Kunns , I
Behavior of the characteristics of Gukuharals ea 'uations in the
vicinity of the beginning. Dokl. All Uz.SSR no.7:5-10 158.
(,41BA 11:10)
1. Inatitut matematiki i mekhaniki imeni V.I. Romanovrkogo AN
UzSSR. Predstavleno akELdsmikom AN UzSSR T.A. Sarymsak-ovym.
(Diffartintial equations)

KUKIM, I.S., ORUZ, D.M.
One analogy of the Hukuhim equation. Trudy UzGU no-78:43-
52 158. (MIRA 13:6)
(Differential equations)

16(1)
AUTHOR: Kukles, I.S.
-
- SOV/166-59-1-11/11
TITLEi & -t-h-e
ii
stinguishing Probleme of Frommer (
K,problemam
razlicheniya Frommera) -
PERIODICAM Izvestiya Akademii nauk Uzbekskoy SSR, Sertya fiziko-
matematioheskikh nauk, '1959, Nr 1, PP 91-104 (USSP)
ABSTRACT: Given the equatiG-i
Y
(xpy) + Y(Xfy)
n
dy
-
'
dx
Xn(xfy) + X
FX'7y
where X
, Y
are homogeneous polynomials of n-th degree, while
n
n
X, Y in the neighborhood of the origin are continuous, satis
the Lipschitz conditions and l4m X = lim X- = 0, r. X 2 +Y
n
r -,*o r n
r
In polar coordinates (1) changes into r F('P)+f(r,y.)
dr G(
Fr
)+
7
k g
f
IT1
Theoremt If lim f(r, IF) L-ln r]k-1 . 0 for u [-ln ri k-1
r->o I
and every fixed u, then the characteri stic of (1) is unique in
Card 1/2

On the Distinguishing Problems of Frommer SOV/166-59-1-11/11
the first and second problem of Frommer.
Two further similar theorems for other special cased; and seven
examples are given. The author mentions N.B.Khaimov, V.E.
Vinograd, and D.MoGrobmane
There are 8 figures and 9 references, 6 of which are Soviet,
1 Swedish, 1 American, and 1 Italian.
ASSOCIATION:Institut matematiki i mekhaniki All Uz SSR (Institute of
Mathematics and MechanicsAS Uz SSR)
SUBMITTED: April 30, 1958
Card 2/2

_Lu.k S011/1 40-5/9-2-10 !30
AUTHOR: le-9, 1. 1.
TITLE.~ On the Pirst and Second Distinction Problem of Frommer (0 pervoy
i vtoroy problenakh razlicheniya Fro-mmera)
PERIODICAL-, Izvestiya vysshikh uchebnykh zavedeniy, Matematika., ig5g,
Nr 2, pp 101-1-i'1' (USSR)
ABSTRAXT. Given the equation
d k
N dx I:-! y P(Y) + f(x,y),
where k is even,, P(O) = 1, P(y) is analybic or Sali~,Z;'468 11,C_
Lipschitz condition, f(-X,Y) satisfies the Lipschitz condition ir.
y and tends to zero with x~
Theoremt If the:re exists a u,',--O so that for all lul >u 0 it hoid~-,
..k I --k i-k
u r(xu) (1-u + U)'X'u)11 >h
k 1 k
and besides for all % -oo< ) r(x,y>~, thor.
iio characteristic o f ~11 endirg in tho cri-gin, Bu~ if i~(X'U)05go
in an arbitrarily small interval (-F-,+E) or r(x,u):,-O J-ri
while for at least one value outside of the interval rfxoi 0,
Card 1/ 3 then there exist infinitely mary charac teris -lies ending J'In tl'z~

On the First and Second Distinction Problem of VomMer SOI-1/140-59-2-00/30
k-1
origin. Here tj(:C,U) = f(x,y)(-lnx)
Given
(2) x 1Z 1 kP(-Y) + f(X,Y)
d x y
k
and let lim f(x,O)(-Inx) k-1 = 0, k odd.
X-po
Theorems If for all Jul-->u 01
u1--k q(x,u) - 1_,,+ul-k) - d~x,u)u 1-k > h >0,
k--1 k
X,U) = W(X,U) and besides q(x,u),>h *--0 foz
where 0(-( 1
."':L ,then only one characteristic> &nds in the origin,. Bu-~ if
a
~ uy
q(x,ii)< 0 for then there exist infinitely many
characteriBUCB ending in the origin.
k
Theorem 3 and 4 consider the case where f(x,O)-(-ln-.t) k-1 has a
Card 2/3

On the First and Second Distinction Probl-,m of Frommer S0111140-59-2-10130
finite licit value 0 and a special case.
The author mentions N.B,Knaimov.. V,E,Vinograd, D.M.Grobran, and
A.F.Andreyev.
There are 6 figures and 13 rofer,~n,-'~fi, 8 of
2 German, 1 Japanese, 1 AmerJ-~;an, and
ASSOCIATION: Uzbekskiy gosudarstvennyy univ-3rsitet Jmi~ni Alishel7a Nia*-r0i.
(Uzbek - ;~State University lme.-J Al.issho_-- ~.'avci
SUBMITTED: October 14, 1958
Card 3/3

67130
-44k4-~- 16, 3 q0 0 SOV/166-59-6-3/11
A'UTHOR- Kukles, I.S.
TITLE- On a Special Case of the First Classification Problem
PERIODICALs Izvestiya Akademii nauk Uzbekskoy SSR, Seriya fiziko-mate-
maticheskikh nauk., 1959, Nr 6) PP 14 .. 26 (usa)
ABSTRACT- Let the.-~_gj~ ~io n _ V 'j,
dy, k
(1) x -~- Ay + y "r (X) I B(X)
x 1 1
be considered, where p(x), B(x) is continuous,kf(0)=B(O)-0.
/k-1
By the transformation y, = y [A(k.-I).I' one obtains
(2) x ~U 1 k + y Y(x) + A k(x) with A k(x)
dir, k -- 1 y
B(x)l A(k - 1:)j 1'/k-. I- Let donote
Card 1/4

67130
On a Special Case of the First Classification SOV/166-59-6-3/11
Problem
(2) (n)
(3) Yn (x) y(x)ln x: in X... In X - k-1 11 + In X +
(n) (n-1) (n) (n-1) (2)
+ In x In x + ... + In X In x: In X1
(4) X n(X) = A (X) I - In x In (2) x ... In(n)X 1/k-1
where In (2) X W Injin xj , ..., In (n) x - In Iln (n-1)Xj
The author investigates the behavior of the integral curves of
(1) in the right half plane. If there exists only one character-
istic running into the origin, then it is spoken of situation a,
if there are infinitely many, then it is spoken of situation b.
Theorem 1 % If there exists a number n (n = 1,2,...) for which
it is
(5) lim (X) ;-, 0
X-) + 0
Card 2/ 4

On a Special Case of the First Classification
Problem
67130
SOV/166-59-6-3/11
while %fn (x)< - h4O is for small positive x, then the
situation a takes place. If, however, (5) is satisfied and
LPn (x)> h> 0 , then one has situation b .
Theorem 2 : If there exist positive numbers xo and h so that
(7) (x) (k-1 )If (x) 1h x+ I I h
%k-1
k A (x) in x
holds in 0 u 0
it holds u-kr(x,u):,-h while for all other u it holds r(x,u)>h,
Card 2/3

Three Discrimination Problems SOV/20-128-2-5/59
then the charactEoristics of (8) have the situation b. But if
there exist the values u 1' U2' so that r(x,ul);~,h and r(x, U2)e -h,
while r(x,O)!~,O, then the characteristics have the situation a.
Further three theorems relate to the first problem and one
theorem relates to the third problem.
The author mentions Frommer, N.B. Khaimov, V.E.Vinograd, D.M.
Grobman, and A.F..Andreyev.
There are 14 references, 10 of which are Soviet, 1 German,
I Japanese, 1 Argentinian, and 1 American.
ASSOCIATION:Institut matematiki i mekhr-niki imeni V.I.Romanovskogo Akademii
nauk Uz SSR (Institute of Mathematics and Mechanics imeni V.I.
Romanovskiy,AS Uz SSR)
PRESENTED: April 27, 1959, by I.G.Petrovskiy, Academician
SUBMUTTEDs April 23, 1959
Card 3/3

-d
31 41
'Ad i-
i Po
g i g
all-'a
-VI
-d A!
a
Sj
et

KUKLES, IoS.; SUTARSHAYBY, A.M.
Generalized method of Frommer. Izv. vys. ucheb. zav., mat. no. -.11:173-
187 16o. I
(MMA 13 -.12'
1. Uzbekskiy gosudarei;vennyy universitet imcni Alishera Navoi i
Institut matematiki 11 led Romanovekogo AN UzSSR.
(Differential equations)

S/166/60/000/004/001/008
C111 0222
AUTHORS: -- L-1PA-, TAS., Corresponding Member of the AcadenV of Sciences
UZ.SSR , and Suyarshayev, A.M.
TITLE: Generalization of the, Method of Frommer for Equations With
Semianalytic Right Sides
PERIODICALs Izvestiya AkademJ.i nauk Uzbekskoy S3R. Seriya fiziko.-
matematicheskikh nauk, 1960, No-4, pp.11-24..
TEXTs The paper joins the eurlier investigations of Kuklos (Ref.2,3,4)
on the problem of Frommer. The authors consider an equation in normal
form (compare (Ref.4))
(5) 4;(X) 4Z - a Y n + T, (X)v n,+,,2(,)Yn2+"'+'P2(x)y+ )~,(x)+R(x,u),
dx 0
where
(4) n>n I> n2 > ne 0,
(49 lim. %Pj(x) 0 i=1,2,...'8
'Pi-1TX7
X->+o
-k
and the remainder R(X~Y) consists of terms oCk(x)y' '. where to every k
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S-/166/60/000/004/001/008
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Generalization of the Method of Frommer for Equations With Semianalytic
Right Sides
there exists at least one i so that
(4") O'k (x)Y n-k
, (Y
i _)Yni
1
with x and. y--_D. The authors investigate the question whether for x >0
there exist trajectories which end in (0,0) and if there exist such
trajectories, whether their siat:is finite or infinite. By :Lntrodu(3ing of
so-called characteristic functions which are small of difffirent order,
the problem of Frommer is generalized to the considered ca3G. Three
lemmns on the orders of the introduced characteristic functions are proved.
No final result with respect to the initial problem is given.
There are 4 Soviet references,.
[Abstracter's note: The comprehension of the paper is very difficult by
very confused and incompletely explained notations and by ~Drobable
misprints or mistakes owing to inadvertence].
ASSOCIATION: Institut matematiki im. V.I.Romanovskogo AN Ut SSR
(Institute of Mathematics im.V.I.Romanovskiy AS Uz SSR)
SUBMITTEDs January 14, 1960
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AUTHORa
Kukles, I. S.
8/044/61/000/005/007/0t--jc
C111/C444
TITLEt On some problems of nonlinear oscillations
PERIODICALa Referativnyy zhurnal, Matew4s'lka~ nG. 5, 1961t 2'6',
abstract 5B134.(Vses. MezhoiR. Konferentsiya po teorii
i metodam, ruscheta nelineyn. elektr. tseuey, no. 7~ Tash-
kent, 1960, 13 - 24) 11
TEXTa A survey, representing the main results of I. S. Kukles
and his discipless N. B. Khaimov, P. L. Khalmova, D. M , Gruz, A.
Suyartayev, N. Abdulayev, on some questions of the theory of nonli---,_t-
near oscillationsl e. g. methods for establishing the beha.viour-of the
integral curves of the system
AA - x (x, Y) Y(Xfy)
dt dt
if the right hands are non-analytic functions of the kind
0,,n + OLI (X) yn- I+ 0-C - 2., t oc~'(X)
2(x)y,
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one some problems of nonlinear ... 8/044/61/000/005/007/023
0111/0444
where o~4 are continuous f-anotions. There are also given rasults oil
the isochronoue problemv obtained by the author together with S. P.
Abdulayev,
(Abstracter's notei Complete translation.)
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r-Mill"S ) I . S .-
"Gii Luo problem of nonlinear oscill,ations thoorj."
report aubWtted for the Intl. S~Woaiiua on Nonlinear VibrationG, 1UPPA,
Kiev SeDt 12-18) 3.961.
'Uzbek State Univ. Smarkend 'USSR

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AUTHORSs Kukles, I.S. a
_, nd lluyarshayev, A.M.
TITLE3 Frommer's Generalized Method
PERIODICAL: Doklady AkademiJ. nauk SSSR, 1961, Vol. 136, No. l,pp.29-32
TEXT: The authors consider
dy ocoym+ a,(X)Y,-'+ -.62(x)y,-2+. + OCM(x)
dx n n-2
3 Y + el(x)y,- + B, y n
0 '~(X) (X)
where oe 8 are constants, -~ 2 + a 2 j 0 ; Vi(x)f Si(x) differentiable
0 0 0 0
for small x> 0 and of a constant sign, ai(O) = Bi(O) = 0, i = 1,m and
i 1,n , respectively. If all '~4 i(x) Z; 0, i = 1,m then let at least one
8 X-) )+- 0
Putting y uG>(x), where G)J:x) is differentiable for small x>O then
one obtains
~2 du P(X,U)
ar)d 1/ 6 dx (Xju)

88559
Frommer's Generalized Method 8/020/61/136/001/004/037
C111/C222
where
M-1 m-2 Cal
(3) P(X,U) - umw'- (.to - 13 + u (-c +
0 00
+ U(Oc 13 + m
m- M-i
and
W) Q(x,u) - 8 0um-1 to .U- 1+ 81(x)u m-2 to m-2 + 82uM-3U)m-3+...+ Bm-l(x)
Here m = n + 1, that gives no loss of generality.
Let y(x), x> 0, be continuous. If lim Y-Lxl - A , where O< JAI -~ oo
15T 7X
then it is said that y(x) has the same order of smallness than 0 (x) and
has the measure of smallness A.
Let - 1 1
tj -j1j-1
00(i I Q it' Wip - Wpi
ij - I i
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Frommer's Generalized Method
88559
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C1 1 1YC222
1
i-j at
x I Ot dx] exp dx
0
0 0
Let '-i_ i to '- j-1 (or rp JBiLO m-J-2 (a lie at the right side of
~~, = OqLjm_'_1 (or Til = 13 1 , m- i-2W 1) if j> i ; let r,, lie at the,
right side of k'i -F6rtherm6res: let (4) ik lie at the right side of 63 ij if
k>j ; let LOW lie at the right side of Wik etc-
Let k, (or be the utmost loft element r ~ 0. Considering the
functions 0 0 im (or t3it 'i+I
(j j f P tJ 4 1
O(W)' ~ ti+2 'Jilm) then that one of them is called the
first characteristic function which has the least order of smallness.
if ij (or cJi,j,) is the first characteristic function then the functiow
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Frommer's Generalized Method S70 6;/136/001/004/037
C111/c 2
62 G) j,j+l La jm are considered. That one of
them which has the least order of smallness is called the second character-
istic function etc . The functions w k1 1 4? k1l , and 0 k11' are called
ordinary, the function EO kk' is called singular.
The total number of characteristic functions is i~~m . The order of small-
ness of the i-th characteristic function is greater than that of the
(i-1)-st.
Theorem I s Every solution y(:c) of (1) defined in the right halfplane
and vanishing in the origin, has the order of smallness of a character-
istic function.
If the characteristic function c0 is ordinary then (2) has the form
(4) ftu N(u) + & (x'u~
dx k(u)[N, (u)+ C I (x"u)
where N(U) H1(u) are polynomials 6(%,u) , f;,(x,u) , k(x) are
continuous functions vanishing with x, and dx 00
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Frommer's Generalized Method S/020/61/136/001/004/037
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Theorem 2 1 If the order of smallness of the solution y(x) of (1)
L, -18
identical with the order of an ordinary characteristic function CO then
the measure of smallness of this solution equals one of the real roots of
the equation N(u) = 0 which aria different from zero.
If Z is a singular characteriatic function then (2) has the form
W) du N2(u) + C (x,~.)
7x 1 X (u) INl(u)+
where N., , N1are polynomials, 6(x,u) El(x,u) are continuous,functions
vanishing with x ; X(m) is continuous for small x >0 but for x - 0 it may
have a jump.
Theorem 3 : If (Okk' is a singular characteristic function then three
cases are possible : 1) -x, (x) and B (x) have different signs; 2)1)4,(x)
k k k
and 0 k( x) have equal signs, where dx
(5)
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Frommer's Generalized Method S10201611136100110041037
C111/C222
diverges; 3) 0/-k(x) and 8 k(:c) have equal signs where (5) converges.
In the case 1) (1) has no solutions with the order of smallness of W kkl
in the right halfplane. In the case 2) there exist such solutions only then
if their measures of smallness are equal to the real roots of N 2(u) - 0
which are different from zero. In the case 3) there exist infinitely many
solutions with the order of smallness of W kk1 , and every solution has its
own measure of smallness (singular case).
There are 4 referencest 3 Soviet and 1 German.
Abstracter's note : There are several misprints in the formulas]
E
ASSOCIATT ONs Uzbekskiy gosudarstvennyy universitet imeni Alishera Navoi
(Uzbekskaya State University imeni Alisher Navoi)
PRESENTEDt July 8, 1960, by I.G. Petrovskiy, Academician
SUBMITTED: June 21, 1960
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KUKI-%'), T.S. ('~amavktwd);
Distinct-lon b--twpen a center and a lf=us. v-ys. u,::heb. zav.;
mnt. no.6:fM-."O8 163 (AINOA 37:9)

= 9"ILITNRI AP5017236 uR/o14o/64/boo/bo6/iooS8/cK)97
SjUmarkan
AUIMOR d) N. Sanwrkand)
7 -stribution of sing-alax poLnto of a firot a-:. ~j~- ona &rcup
SOURCE. 21UZ. MaLe=t-lka. no. 6. 1964t W-9?
?-I P 1 -1 differential equabtontNiztribution theory
"his 98"r is a study of -$- listrib-,H-in -,-f tbe s-izular points of
equatLon
dY
dx -.r? 1 11 ~ V3
(pi and qi are constant in the finite protion of the pione. This
p--oble-- !-~a3 been studied hy various natliemaL,'zians. The early, partly erroneous
rP--tjIt,1 n-I W, BTJ(,'IiEL (1904) and M, FROMIFP (1034) the Soviet
mathematicians N. A. SAKHAPAIROV, N. A. LUKASHEIV, A. N. BERLINSKIY, Kh. R.
LATIFOV, and 1. 1. SHIR(Yi, ;:. P. LAT-'J'.KOV, in particular, demonstrated the
Ipossibility of the coexistence of-a-I.,entpr oi-id focus for Equation (1) and
studied the behavior of the curves o1! this equation on Poincarcf's sphere for
:_Card. 1/6

1 L
ACCESSION 11R. AP5017236
the case in which the origin is at i:he center, A, N, RF',RLPN.~KIY ha!; developed
aa-eraL geaaral thevrema conceralng -he Sirgldlat ',)OL"LS UL EqUULJLU" ~0;
';&i;C approach has been to intro~~.uce an af L:i';e 'L r a ii E:2 -1 -1 _n , wh ch :-Lgu it a
tt-if, numtrator and denominator of the right-hand mem.-_r of ~'l '; beLng, re,_Iclved
Into a product ckf linear factors. OT, this boats, one .,ith 'he help oi~ Poincare's
e(4 0!. L
y of Lrdices, he derionstrated tInt il a queidrnnKl,~ ~he
ne ;iio_ ointq
is convex, then 'LwQ cpposiLe !j~n,,u~ar P
r W I P_ OnTisadllf 0
e ~.uadrangie *,a concave, tnen ea~,,er an D)Int wii I-e a
and th,are will be three external poLnzi, or tie extecnal
-;ill be saddle points, al point, an antiiaddle p(~.!~!. in
and the intern
-is t -f sing I 1~ie
e 3.,icTwed ti the number ullar potnts of o nd
focL) does not exceed twc.
.'a-_LDov!q proof of this theorem, intended to replace
Coml, i ex one, is Arld to t~E~
I. is Lia0e r Inc , uci-!; r!li- a L~
Imp., id rigoroun, ago does 11'JL za- ocing the nLtnerator
~Z:1(~ Ge;i'011"Ifltor in the right-hand meaber of (1), points yj),
a'd M'(x3. Y3'
are tout- a ngu I or po in ~ !3 equn
Cord 216

substitution

0
(XI Y- xy. y (y2x -7-K -
X
e4~uat ~r~ ~ I ) becomes
dy ax(x-l + f v(v-) rxv
dx alx(x-l) 4 + Qjry
for which, Lt is shown that point 0 reTning at the origin, point A' is shifted
to Point A Q 0) , and point B' Ls shift-d t o point B90, 1).
-Ccom-_~
X2 ic 4. b( 2 _Y)
y
__ . + exy
x ,
a (x x F" (Y' -- " )_ICIXY
Thc disr~rimlnant of the iiecular equattor. --a, 2
'
~Io L o rto the first group of Doir"'S a 0
.-a L~'e

MR _M OF -M-0-0- ~__
7
L 573743-65
ACOMSION FR-. 050172-Yu
second (thnt is$ it becomes a center -of a focue). Vith D Ov. the c-rigin- T411
e a degenerate nods, provided the characteriaL(: deLe,.;at7aW P( C. For
t A 0) the. d tact iminant of' the .3ecul, r equs, - r.. n
--a. -b)2 while for .1 it i B D (c a b) h. ,c -I
Wl-th- the ands_ -ftj - I-Ir Ltte~
2 + 4(v + k lid, Da V2 + 4b (u + k 1), Setting
inant becomes DA a u
RA n-81 the authors Obtain the parnbalaa,
U2 -4(v 4. k b (3)
V2 er _jtb. (U + k -1) (4)
'A
-bt- it'
4rk 4 _-, L
Cr. -he`that~ by. _-p
h6urdz& I -C
wfthin then A belongs to the tecond group; and if Lt falls outuide c< A#
1 Card 4/6
MM W ^~A M WM$
Mb
con
W,- -:V-,~ U R 4K _W90

-------------
L 53743-65
AMMION H99 AP5M7236
similarly, Lf Wit. V) ~3118 withino(
it belongs to the fit-at. potnt 3 belongfi~
t~~ aTc~~nd group; -and if it Calla outside CY R , it bp-long3 to the first group.
n !,~e bound6ry of i Ti d thp-11 A ~s a dege-erate node.
A
1) and (4) intersect a F, i point Im is wLtiii;i :A c_~ A sild
(yuadrati~le Cl~_Mi),
it is shown that-H is a sOgUtar-node.if and anly Lf t: = 0 and c (if the
origin is also a aingular nade~) G&BM is convex, points 11 and W.
are points, and lines AR: AM, OR and CX4 consist of curves in -:his ca 'Be;
the d~4~pr-ii KB is an L3ocline -f infLiiit)(, snd tfte diagonal OA cons.sts of
curve and is also an isocline of infinity. Painta A-and B are sL ~,iiar nodea
ic c. and z = 2 or if C~ = 4 = I ( C>- (1--c I)/(I---cc I ) , ~j - (1--c)/
thi- coordinates of point i,). In all case3, it t3 oniv ipiosite
poi-tits uhtch Q-:Otheva are-
the au4drnngla being convex and its sides consisting of curves.
that if A and f are irrur.,iti, Znci, then M, i ii-in the first
.1 ni-4avq a saddle Doint. IL -36 1
a "add
e r, il h a n z e r-, OVIA"n, La A ~;ju. i;. -I e "ad a ~'l
.is Orig. &rt. han ftg=ss and 22 forau~Lw.
C.,d 5/6

L 53743-,-,
ACC~S-Ijori N 12: AM17236
-0 C a , ~
none
S 93',a WE DO&JU,164
~Ua Want la
RET 010
W3
IL-card

~HA411.,VAY i,.L.
';,mlying the behavior of surfaces deterrined by the Pfaff equation
near a point at infinity. Trud~ Sam. Gos. un. no.144t.1.9-62 164.
(MIRA 180)

KUKLE;S, I.
Snformuttion on the Samarkand Sympor)Lum. Dif. ura--.r. I no-4-56G-563
Ap 165.. (MIRA 18:5)

KUKLES, I.S.; SHAKHOVA, L.V.
Limiting cycles of the differential equation
2 bij xivi
5-
dy i-+j -= o
dx 2
_5- aijxi7i
t j = 0
Izv. AN Uz.SSR. Ser. fiz.-mat. nank 9 no.5:24-29 165.
(MIRA 181ll)
1. Samarkandskeye otdeleniye Instituta matematiki imeni
Romanovokogo AN UzSSR. Submitted December 22, 1964.

I
- -EVIT --y
--L -P591&o66 - Vd)- - - lip(c
a -
[ACTC,NRi 96o16676 II.-
c
,kU OR., Kukles, I...~ 6A, h I~ho,,
!9 ~.a:l _
IN ~

- 7----.-,L 25918- 66 -- --- -- - - 7. -1 -- ---- - - - - - - -.-- - --- - -
I
I :.

WOMM
.1, U 5 iq,5_ L!"'! k.rj) ijp( CJ,
i ACC NR. AP70007-50-
SOU:,CZ CODE: U;Z/0140/66/000/003/0073/0033
KUKLES, 1.-S.', and AKCHVRINA, R. Yu., ~amarkand)
1 ."Discrimination Problums for Characteristics in a Three-Dimensional Space"
Moscow, Izvestiya-VUZ -- Matematika', No. 3 (52), 1966, pp'73-83
ABSTRACT% -The articio considers the three differential equatio-as
ft (x - YZ) + FI (X. Y, Z),
dii
-F, Y11 ('r' YI Z) i_ [.72 (-V1 Y, Z),I
it I
ih!
-~k (-v*w J1, Z) + F.3 (X, V, z),
where fk(xl Y, Z),