SCIENTIFIC ABSTRACT KATS, I.S. (ODESSA) - KATS, M.E.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000721120016-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 13, 2000
• Sequence Number: 16
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

"BATS, I.S. (Odessa)
Behavior of the solutions to a linear second-order differential
equation (with reference to a paper by E.Hille). Mat. sbor. 62
no.4:476-495 D 63. (141RA 17W

KATS? I.S. -
Corrections to I.S.Katz paper "multiplicity of the spectrum of a
second-order differential operator and expansions in eigenfunctions."
Izv. AN SSSR. Ser. mat. 28 no. 4:951-952 Jl-A~ 164. (M1RA 17:9)

KATS, I.S.
Behavior of spectral functions of differential systems with
baundary cmditions at a singular end point. Dokl. AN SSSR
157 no.It 34-37 JI 164 (MIRA 17:8)
1. Predstavleno akademikom I.G. Petrovskim.

K A 7.-) 1 1 1 F) -.
Use of the method of variable directions in tlie tihilrd
bounlary value probl-em, Elop. AN URSR no.90,117-1120 165. (MIR-4 18:9)
1. Inatitut ki1xmetiki AN UkrSSR.

T~v% T.F. (fveFz~!: )
.-f - -P , SIS t-~Mm
-rd. ~'wlnot~gcmp -f go-rie-r-alized
t,~,a jij 741, bciindary cr,nd!tacno at tlt- srig-ollar ends
4 .
I,TAt. otwr. 68 r n .2 a 2,7xi- 227 1 165,,
(IdRA, 1&10)

HATS
E-I II.S.
Some cases of Lhe uniquenens of solutien to the inversc~ problem of
strings with a boundary conditiLn at the singular end. Dokl. AN
SSSR 164 no.5z975-978 0 165, (MIRA 18:10)
1. Odeuskly tekhnologichaskiy In6titut im. 14,V.Lomonosova.
Submitted March 11~ 1965.

L 16156 W(d), IJP(c)
SOUACE GODE: UlVO021/65/o,)o/oo~i/ili7,/'~l,)o
ACC NRs AP5024777 I A
AUTHORs Kats,
WG. Cybornetics Institute, AN U&SR (Institut kibernetiki AN U11SA)
TITLIS: Solution of mnim yj4 ro ariable
1b.2-tbird in S_by the methoa of v.
j y&_p b1
directions V
SOLRCS: AN UkrIISR. Dopovidip no. 9, 1965, 1117-1-120
MrIG TA:!S: boundary value problem, calculation, variational nothoi, -illiptic
differential equation
ABSMACT; The methoi of variable directions developed by Jo Dou-,,las (Numer.: I-LAth.,
4, 41, 1962) ani'A. Samarskiy anI B. Anlreav (Journal of math-pbysic co-mFutations)
3, IOD6 1963) was extended to the case of thi third boun4ary value problem for a
self-adjoint elliptical e(iuation with var4Rble coefficipints. With this method the
requirad accuracy was attained in 0 [ln(-L iterat-ions. Orig. art has: 12
formulas.
Gard 1/2

L 16156-66
AGG NR: AP5024777

KA'1118? M,.D. M_3,1
149thod of indIne, 2aroas of anjilytic finctions. Dop. 0 IJPSR
nc).r- -150'3-.* 5'~5 (ml,riit 3,9:1)
1. Tnstifut klix-mictiki. AN UkrSSR. Submitted Denember 23, 1964#

L 47160-66 - EWT(d) IJP(c)--
AUTHOR- Kats! I. Ya
- ------------
TITLE: Asymptotic stability as a whole for stochastic differential equations
SOURCE: Ref. sh..Mekhanika, Abs. 0AQr
REF SOURCE: Tr. Mezhvuz. konferentsii po prikl. teorii ustoychivoeti dvizheniya i
analit. mekhan., 1962. Kazan', 19649 91-92
TOPIC TAGS1 stability oriteriont stochastic process, differential equation
4W
'I,
'n,onor,e_
ABSTRACT: The stability problem is considered for the total probability of stochastic
systems and the stability criterion is givenj based on utilizing two Lyapunov func-
tions. A theorem is given on the stability of the total probability analogous to the,
theorem of ordinary differential equation stability, proved by Ye. A. Barbashin and
No N. Krasovskiy. So V. Kalinin anslation of abstract7
SUB CODE: 20p 12
Card

KATS, I.Ya.
Stability on a first approximation of systems with random
parameters. Mat.zap.Ural.mat.ob-va UrGu 3 no.2:30-37 162.
(F,I"Rk 19:1)

KAM , I. Ya.
"Asymptotic stability of stochastic differential equations~"
Report presented at the Conference on Applied Stability-of-Motion Theory and
Analytical Mechanics, Kazan Aviation Institute, 6-8 December 1962

ACCF-SSION NR: AP4027596 S/0040/64/0-'-'8/W,-/0366/0372
ATJTHORt Kats, 1. Ya. (Sverdlovsk)
&ITLFo Stability in the large of stochastic systems
SOURCE3 Prikladnaya matematika. i mekhanikap ve 28s no, 2p 1964s 366-372
TOPIC TAGS: stability in the larges stoohastic'system, stability in probability.,
Lyapanov function., perturbed motion, Lipschitz condition, Y=kov random process.,
asymptotic stability., Wiener processo Gaussian process
ABSMAICT: The author defines the concepts,of stability in probabilitys and
:asymptotic stabiLity in the large, of the solution x 0 of
dx I di M)
:where x is an n-dimensi~ii~l vector of phase coordinates of the systems. the vector- I
function f o.tfjj9*9,vfn~ is continuous in all variables in the region
j rd < + 0, Vey
Card 1/2

ACCLSSION NR:l AP4027596
satisfies Lipschitz conditions in this region in the variables x p y and is bounied
for all E Y in each finite region HX (IIXH -MIX Oxil
x. The function y(t) is "sumed to be 4 Markov random process which is
also assumed to be either purely discoahtinuous or continuous, The author proves a
:theorem giving sufficient conditions for the unperturbed motion x - 0 of system (1):
to be asymptotically stable in the large in probability. "The author thanks N. N,
Krasovskiy, who proposed the subject and offered many very valuable commentse"
Orig. art. has: 40 formulas,
AS=IATIONs none
SUBK=N)s Caeo63 DATE AGQt 28Apr64 ZNGL: 00
SUB GODSs FA ~O REF SOVI:' MI OTHERs 002
Card 2/2

Al. S10401601024100510041028
C111/C222
AUTHORS: Kats, I.YA. and Krasovskiy, N,N, (Sverdlovsk)
TITLE: On the Stability of Systems With Random Parameters
PERIODICAL: Prikladnaya inatematika 1 mekhanika, 1960, Vol,24, 140.5
pp.809-823
TEXT: The authors consider the equations of the disturbed motion
(1.1) dx/dt = f(x,t,y(t)),
where x =4'x,, ... 9X 9 f f19-tf the fi are continuous with.
%, n1 nj
respect to all arguments, and in
(1-3) vto,
where x I[= max (I x111-11xn") it holds;
(1.2) ifi(x,,,tty,(t))-fi(x,gtgy(t))I,---L 1,1:0-xiti
Here y(t) is a homogeneous Markov chain with a finite number of states,
i.e. in every moment,y(t) can assume one of the values y i out of a
), where the probability p (o".t'- of the
finite set of values Y(Y?Y---iyr 1j
Card 1/7

S/04 60/024/005/004/028
C1 1 !YC222
On the Stability of Systems With Random Parameters
change yi--,-yi in the time At satisfies the condition
(1-4) Pij(/-tt) -C~.ijAt+o(-e--t) (i/j) (r/,,j - const),
where o(A t) is infinitely small of higher order than 1,tt, It is
assumed that yi - 1 (1-1,2 .... r) and that
(1-5) f 1 (0, ta (t) 0 (Ycy, t~O).
A random vector function ~,X(x 't gy ;t),Y(tovy ;W the realizations
C 0 0 0 0 1%
(~(P)(x 't NY ;t),y (p)(t NY ;t)" of which satisfy (1.1) is called a
0 0 0 0 0
solution of (1.1).
The authors investigate the probability stability (cf,(Ref-5)) and
the asymptotic probability stability of the solution x = 0 of (1~1).
The conditions of stability are given in terms of Lyapuncv functions~
A function V(X,t,y) is ca'.1.1ed positive definite if v(xty)7~w(x) for
all y (-' Y, t~,,,t where w(x) is positive definite in the sense of
Card 2/7 O~ 1.

06-505/004/028
3104 60/b
C1 11 YC222
On the Stability of Systems With Random Parameters
Lyapunov; v(X,ty) is said to be of constant sign if in (1.3) it
cannot assume values of a distinct sign. A function v(X,t,y) admits
an infinitely small least upper bound if there exists a continuous
W(x) so that v(x,t,y) ,,- W(x), W(O) = 0 for fix;~