SCIENTIFIC ABSTRACT SARMAI, E. - SARMANOVA, YE.S.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001447210017-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 31, 2001
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

lumania
CITEOCRY
ABS, MR., i Rmadap 0 Nq*.~ ~z !959 SO*
:.Macovsc ii An armsmioti C-
1-4umanian'Acadmy, of Sciences:~
TS V ~4 J Modifications of the Bertrand and Bierri Method6.,

thei Glucose d: Contan t
for.,the-Deter
mina Ion o

MOO PU% ltm'Acad

No
Stud erce' ari'B o

ABSTRA
UT
d h, icatioh o t he. aVov
e
The.,main., rawback, inA, appl
indicat ed,- iatuvds r6r,. ~he. detsrmi-nati6n of tfie,
er'6tofor~P.-. has'
con h deft n. need.
t f
for tile, atilizaiiion of
.-pr h of, the, c(i oric ide!
o~edure'js 'for A e :reparation
-Allich, is formed., .'Them authors propo6e'a modifica.~-
-onsists it 1~-he~
~tion 6f I above ~ met!2od,whi:ch,;,-
addItion: bf' sodl UM b1carbo te. P411
ne, ehl ng
e a. r~Lti'00, which-permits ~Ih~-
OQI,Ut on b r nit
-filtration~to,ba ma'de.xith, standArd La:~~eF. y~~per

Y) 'dy -
P(X)

whem F(x, y) is a symmetrical distri~tion (unctinn for the
variables (x, y) and I)Cr; is the prior distrbution furictirm
nf i F)e main f-cm0itsirm i- thm such a w4ution. i0lich is
c i,rq p, -irl n.- tn

S&fManoq, C). V 3eneT"Aljr
,o )f 1 11 lIj tAe~!e= of Ih,.
FL:-Iaq, o eptvrjtrl~
,ulabies -,a%-Sry--g I-U,,!-!IjerXv:o -liticr
-Ie
i e.W t3 Of (-ajS tl.p-- "e.7, lViath. Pure$!
Appl. (9) 24. 249-318 N UP - P. 4 53

1 0
1 ft
b . I I I.
R
w
I .

~)r ;he rPctilCa'T0n Of CIr 08tlo~
F~ TT
KM; -i K 58. '45 .4
80.3. 106 1 - I O(A (1949). 60, ~45 -.48 (1948) , thespe Rev
10, 45, 9 442. iM
a t ho R--V i ev 3
I C

M

X I k.*
DI!, 1. ~,
-put III 1Q,
U1.1 16.
JO
otp
um 1,
Ut
P11-
SO;
pul.
L%
JO
1 oj !I- to u0jjrj.l III,
1:1-'A k
IU(, UM4.1
I P.11i .3ip ul Awl
jumoti mn amn, fp~

Tj;3Iuuj,kq!ImI nj vljol I III, I
X,

1.1A I I I...

Iriv

Cl)
i

Sarmanov, 0. V. On the order of magnitude of Li. ," of
reiFe-s-siom DnkladN Akad. Nauk SSSR 59 '061-
C+ 1064 , I 94-h, , RusbiAn)
Let F(x. be the density of the chstributi,ii; ,i two
variabit" ~'I dei,-rrnmes a (otrelation III 11'e plane,
and satifit- !ht , otidition
IJ) ,L..
f J_ -P (I X) Pty)
Whrre 'ri i , iml Ply) are the marginal densities of t and y,
reispev(l%-~' (III dit- ba.ls of the restilts of an earlit-F paper
refervii, !n [fit- prt-ceding review] thu author proves the
I-,
fullou, g I, tict wren is. rhere. exists no sy mnictTical ct.,t I t-lation J
hit I, it ~miiri,m 1.) and whi(h is such hat the
~~t.s id 'PU) of V on x, SMISf-,' the -,)mfition
T
a >0, tur ix >A,while thesmne%l~
k here
'Ffx,y:l pivIdY
cor,elimon satisf, lig con-0.1f
dit hi, I s im [I that of regre-ssi,~ ,i
the lines r). Of
Y (11, V- satisfy the ('011ditions
0
y~l A ->0 >o >
> 0. y 1 >
00
-hlie Ifif lim ,,'i >0 t,~~
Whete 4,1(y) has j~ji analogous meanuig t. that Kiven for
oi x AbOve. -! folk-wiag results, are stated as _Ptoll
Th arie& L,
14 KW uty correlation which satisfies condition ( I I rile
0 ~egremion are polpictmials of positive degrm they mjjot~q
be i:nc.ti ii Llir linea of rt:g.e.-,.3I1un ~ky) ait- 41gebrait:I1.
cu rves of dcsrecs 6":l, 0. 6, > 0, then H
fl. P Thwo)"in (Anics owa).

Sarmanov, 0. V. On the order of magnitude of a line of
1. Doklady Akad. a*-u1-','S-S'TT-?N,-;T60,
545-548 (.1948). (Russian)
The following, tk,,o thc,.orems generaliz( previous rt~iulrs
of the author [F.;mw Doklady (N.S.) 59, 1061-1064 (1948);
these Rev. 9, 442]. There exists no symmetric correlation
-which -atisfies the condition (1) of the rc%iew of the earlier
paper, and which is such that the lines of
*7--Z -7f
-tot.
V
I- A > 0; T 'ere eMAh- no nonsymnie'ric tre,
~:A A>1,
lation safisf~ing the same condition (1) and which is tutch
that the lines of regression O(x), of y or. r, and J,(y). of
xony.satisfy theconditions 10(x)ji-tr(Ix ) for fxl-:-2!:A>O;
10(y)j for jyj 2-:,Y>O, p.,0, where Wxj)
is a monotone increasing, continuous coavzx function of
jxj sucli that r(0)-0, and 7-1(lyl) is its inver,-:e function.
H. 11. Thielman (Ames, Iowa).
Source: Hathernatical Reviexis, Vol No.

I~ngM ld.;~'Mining:-'Iiist
S 81SR "~~:.Vol IMIV "Vo 6 pp' 1135

3. ~

TI

'AUTHORt 4-
Sarrnanov', O.VS 1207 8/67

ITLE:
Maximum Correlatioii-,Co6ffi6ieiit~~(Sy~mm6tri~6~' (Maks ima
'Caae nyy.
korrelyats
koeffitslyepl ii ~-.(simjnetrichnyT, sluchay)
PERIODICAL: Doklady Aka ,clemii. 958,Vol.,) ~Q,ffr 4
ABSTRACT:
t
Let. F (i ii) (Y he:density~of-,the dis ribu ion de -
t rmining~lhe ~corieiation between':.the,random,*variables : -and
.y-
e ..x
in:tfte do6ain' :
La 41 Sb --Aet fu'rthermore
b"
X y

c
(j
Y)
Y)
,
.
(X)

and let K(' iie_g~abie 'iith ~:r'eipeic'tt d
x e*square~-ir o x an
'
&,that_-,th~e
in:a f ormer,:jpa~er A the iau~thor. sh8we
spebtrum~
'
'
1
.-.,_
as the'.
f6rM_
of the kei~nel, Vijy) h

0
if (i
~p
(X) (X)
o
vvhere I relat" c t
.,the.obr ion, oefficien
'
x ands
betwedn the eig6nfunctipns~;~,'(
),
Card 1/2

i
9

AUTHOR: Sarmanov~ O.V. SOIV/20-121.~i-'l
TITLE: The Maximal:Coofficient,oi,Correl~tioii (Asymmetric Case)
(Maksimal1niy`1koeffitsiYent korrel atsii (nes1mmetTichnYY sluchay
y

PERIODICAL: a ei zv~k 'SSSR9 1958 9"':- Vol 121, ffr.lv ~P'52-5
Poklady Ak d. ii, n 51~OSSR)
4
ABSTRAM Let F(x',I) be'~the_ density~of.,-distribution,~dete'rmining in
. [iL,6x ~,Qb; a' < y Q_ bA the.loorrelation between x and:7. Le t,
'b
x F X* y :F(xoy)dx
a.
-of x an 0
be the a priori-d6iiities d~yllet the ~iorn 1:::,:

ip(x~
vy
K

X7~ YTL~~
PT
be integrable~in,~,the,square';w th-respect~~to2:both"variables.~ Th
asymmetric density F ~'determines wo .~symmetrio -Ldensities
b

F(x If tgx By
y
Fj( Y) It,:_ LF '(joy) dt
Xt
p
~~7 J L
PM

Card 1/3 a a

'~On:t~e, Corre
lation.]Between-thiD.~kereen~age-Vaiia~I s SOV -M
20 126
5)6
Theorem 7., and z f
2 ,be:.indepehdentof eachother and o
the. other 'variable a., The.!'11 area assumed ~..to be positives

'lion -coel
The, correla ~ffbient R
i a the
0 2
correlation-coefficient-R vi R(X X wiwrespeot
o the
T: 2
~absolute value: and has the same~.sign.~ ~The Ooeffi i t
e a
(~ , . , -
R R(x x can only siima aneou
Sly
2
vanish

There are,3 'references,9 - h: is Soviet and 2are
1 of wh c
American.
ASSOCIATIM Matemati~h6siiy.:i siitit:imsni ~V.A'&~ Steklova AN SSSR
n
(kathematical'Instit-ute imeni.. V.A. ~:Steklov.,-AS USSR)
PRESENTED: Novemb

.
er.. 26 9 19 56, ht
S.& Berns eyn,
by Academician
S.UBMITTED.- .
November 2 1958.'
c
ard 2/9
f

16

AUTHORSx -lakh -2-6/59
Sarmanov 0 T and Mrovl' Y.Ke SOV/20 12,8
TITLE S~ectra of:Enlarged Stochastic~Matrices:~'.
PERIODICALi Doklady.Akademii.nauk-SSSR~ 1959.,-Vol:.128:.lTr 201~p~243-245.(USSAY ~J.`,`

ABSTRACT.,'
Lst: b6- -'tW6 Aep
A endent,fin i te seque no es-. of events with
a symmetric table'of,correla ion p. 2
(l p P (A. B~)

~Let
(2 0

and~l n.. -n

P;
.:(3)

J-1
A
l
a
The spec rum~,,.bf the s ocha tic.m trix
rp
j~

has, e:. form
th
Card 1/2
(5)
n-1

5
_VM/60/05?/O~~/001
GI 11 /.G222-

ea -ra: of,
M~asures of the Dependende-:Between.Ranaom Terms and'si +
Stocba'stic Kernel's and -Matrices
Theorem, For', the, independenoe.'.of Ahe:~.rAndom t e rms ~~x 'and Y it-Is

nd suffiol
necessary

n~ f
th 6" max mal:corre a,
i t
t Ibs t ion, coe ~fc on,
eq a s: zero..

~:A ~A pA
2 A! 44 i '~i p

i j

B
:B p3
1 0"

''M
2 k,l,

,
:
tie two 6omplete, s,er;_,~ -
"t]~~"Aei~iicleno6...~
s oi i~6ompatible.evenis.;~'Lei
'
'
"
~
between thesescheme s ~be:'give*:..by ~the~
Iar"-c.orrelatibn table.
eo+,a
r
p"
-.,where;,
9m)
tp =,P(A B
i
j j
m
~(0.3) -pi n.

ij,

M
Pi
I
1 no m

i=i:
j=
card 3/10
rr

87115

S 0
/03 60/05~/004/0
/

c 21
If
2
tw
Measures of the Dependence .e eeii,Ran'dom. S t
Terms, an,.., pec ra of
S to'chas ti cKernels 'and:.Matrices'..
Let bi,-sides
p.. (i,,J-l 2vo.. n,
(0-4) 1 ji p '2
i)j ja b

of: th
64a
y etricca. The. fir3t,eigennum ei r R . e
(S mm Be)
P41 j=1 2, on) ie:6ailled the maximal !correlation,
Pi
coefficient ~(d finifi6xi Here t66~:it
' holds,:,heorem.l. Jiv.-the
e '~nl~

i
unsymmetric casev Wh r
e
,val,

wo.:quadratic symmetke"
d
trices
ma
OY

'j=1
M)
1571 p
j
..are formed, where.
dard 4/10

87115
1039160/052106410611002~;,
cill/C222_

Measures.. of the Dependence
Between:Random. Te t f
rms and Spec ra,,o
Stochas C.Kerne s,"and Ma t ri c e s

two
Given dependent:finite

chemes of'
-incoipati~l
only~possible e ir
(1

vent (A A - A
`
1 1

nd (A
(2)
(2) ~wi
A th a:Symmetric.
.
~ n.
1'. 21 1 2
n
'Correlationlable
lp
ij -The: -symme r zable stochastic matrix,
~
p
,
'
'

7 1
n,
tp is
called given schemes..
the ma rix of. the
'
`40 M -
~A
s M
d
it
V A
A
..If two
events .6
o event .9. A, an t, =
ar un
e
e
d
.-then the correlationAable.~ changes acc ording o, the scheme
P1 iPiz
~Nn
PIL Pt3
Ps P22 P_ .

taA

=

&L .

3 33 3n
P P
P f

aX1d 7/16 P"
Pin P 3 P

'' - ~:~- . . -1 ~ - ~ I ~ .1 i~
',~ : ~ : , - , " ,
- -11 1 . - .1 1 :;a~ i ~4. , "-~v

so

e,
th
-z
hftvinis~~ Rel
20. 1: ~Uj on "dud
A ons~ Ultl eg6iPo Yh
d1tive rit
-moo
3SS3
KAM
'bion, ooeS
~hendklyi~
-Blagbveose
h
"Va~rian
-Small.,
h ti
t as
"22 Alr6dnovi td _0~ 00
rd
Vr semio OXN
23
11fix
Theory,,O,
3 V S
agayev-
N
g6B With .,Dis6~~t4 .~~V g:!
Fro6e6-
ota: om
IhV'.: 0
-0
stynnan

~Iliithiai~tio`t
ti
inte-irest'-W ICon', ildir'
tical' e_val'u:a'ti6i~ti~6
omation
Le'tali~ ditir

in sin zic arG i
e -a ove ebyShe
,thin.
fu`n- d'a' m-en
~k-66~wl it
t3~ams