SCIENTIFIC ABSTRACT ZINGEL, I. YE. - ZINGER, N. M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R002065220004-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 16, 2001
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ZINOLI, Lys.
Protection of pipalinios and equipment against aorrouloao~
Sakh.prom. 34 no-3:41 Nr
(MM 13*
!0
1. XrasvV&uakiy sakhaimyy vA~od.'
(Sugar Industry!-Jquipment and supplies)
(Gorrosiop and anticorrosives)

I

~USSR/Chemical Technology Chemical.Products and Their 1-9
Applicationo Wood Chitmistry.Products4 HydrolyAs Industry
Abs Jour Ref Zhur - Kbimiya, 110 1, 1958,.267o
Author Zingell, M.A., Vasina, L.P.
inat
Title Production Uprovements at the Sukhonakiy Sulfite-Alcohol
Plant.
Orig Pab Gidroliwaya i lesokh;Lm. proza-st', 1957,ARO 5, 21
Abstract An enumeration ofthe Improvements (nzw technology of Ii-
quor withdrawing, fertmmtstion mithod with floa:ting C;apl
installation of a cyclone separator and high-delivery
centrifugal pumps, increased yields of vinasse by means
of hycro-traps).
"e-
Card 1/1

3-218
AbtHOR: Zinger A-
TIT The Independence (A Quasi-P61yaomial Stai~tis0i,zls:and. the
Analytical Properties of Distributions~(Neziv:Lsimesti,~~.
kvazipolinamiallny'kh statistik-i analitleheskiye svoy4tva
raspredeleniy)
PERIODICAL: Teoriya, veroyatnostey i yeye primeaeniYa,, ~1958, 01 3:f
Nr 3, pp 265-284 (11.3SR)
ABSTRACT: The various problems of any mathematical. bt,"atistics' aro,
based on the distribution of components,,of sati;styijif;
This work.
certain properties of the statistio SGET)
q
concerned with the ~,.'Letermination of the disti~ibution P~ the
random vector, when there are inde:pend6nt stati6tias.
The statistics S(8. il are called quasi--p
o4nomial if there;
exist a function ~p(, and 2 non-negative poilynomialai
r(S) and R(,P, (called lower and higher res ~piactively) so
Card 1/8

3-3-218
The Independence of Quasi-Polynomial S tati 9 t and'. ke Analjtic' 1.
tk
Properties of Distributions
(p (S R' The polynom:u
j a.1 P(X
that
is called llpermissl"Vlell for X if i-V c ontaifts,
11 j
where m - the step of P(Xl, I.Lie statisiticis
X2 X.J.
S(S) will be permissible for X ow'sr. polyl~iolm,iall'.
will include X In order that 2 sta'~t'istias, S a~nd
S were independe~nt, it Is necessary that for any loonttn-
2(8)
uous function of 2 7~triables, F(x,y) the sta'tistics,
F(S were equally distri-
1G), S2T)) an(' F("'31(3)v S2(0,'))::~~
buted (Lemma 3.). (Ifeetors P and P..' b
are Aistri uted
equally but independently). ~The quo stioril. of ~moments 'is con-
sidered for the independent linear and pD'Anoinial statistics
with the following t;heorems proved: 1) YAS31~ "! (X X2-:1 4n)
I I J) Ok
'S2
- random vector with independent componetI-Iss ~S andp
- 2 independent quasi-polynomial statistics, ~.Permi Boil) 10 for
X Q =. 1.2...n), then the expression (1.1) wi`l.-~ be true fdr,
X>O- d. 0i:
Card 218 every component of the vector I

-3-3-2/8,
The Independence of Quasi-Pol~momial Statistics and 'the, Anal tical
Properties of Distributions
constant). 2)For the above Oonditions the distribution of:
every component of the vector "P has p6sitiire viomen~.6,.
The, roof is based ion Lemma 2, stating ~that th.e~expr6,stiou~
(1.23 can be applied for eve'ry non-neg~~!ive va
Aue of ; X7
distributed as FW - P(X0 . can be ap-611ed tor a Iveryi non--~.
negeat ve value dist:rAbuted as. FW
i e 6 -ase may s~-is6
when one of the stat;istics is linear. T4en th,t charikoterl's-
tic function of the components distribution be ext'etnd4d
over the whole comp'.1A,eX plame R; Thereforelo' lh*'~ itmalyti6al pro-
perties of the dist-,Abui~ion of the vectoil t should b,~, de,"
termined. This has beett done by the author by proving.~thei
following two theorems: if ".'R (X1 7 X;~ Xn) random veo~or
with independent components, S quasi pclynomia-l~:
permissible over all components statistiel S
Card 3/8

52 -5-2/8
SOV/ -5:
The Independence of Quasi-Polynomial-statisties~and t~he Analytical,
Properties of Distributions
Gard 4/8
linear form then if~both statistics are 1ndej)endent, the
mathematicai expectations (2,1) and (2.21 exist for
-~11 21 ...n and 0 < (A;~l 4 ~e'onstant) (Theorem 3).
vec V,
The characteristic fimotion of the -to, 0'.3) satisify;,
ing the above conditions extends the whole co#,lex plane, aj~d
is defined as the fm .lotion of .finite order (Theo'rem Th,e
latter theorem provides iadications, ill some cases, of-the'
possibility of the normal distribution of,ithe'voctor 1Z
This can occur when the ftalction f is eXpressed as
Eq (3-1) for all I ~be trbjisf erred into:
camp ex V This can
Eq:(3.2) where F.(t) - polynoomial (Ref.18, p! 284).. Th~sl~~
applying the MarcLkiawicz lemma (Ref,l5)i,*the'zxorma1 dis-
Vribution of the component X of the veoor ~*R is obtained.
j
Therefore, a statement can be made that the component ot,the
vector P with the characteristie functi6ri- haTitg no zetos'.
are distributed normally (Theorem 5). However.,!~it. shoul4 '0.
noted that the indepeudent statistics k. 0 may ~.sometimes;
form the function equalling~O., Two exampl(~s ekn:be show#.

.............
SOY/52-34-3-2/8
The Independence of Quasi-Pdlynomial Statiaticsiand Phe Analy-tical
-Properties of Distributions'
First if the components -of' the vector 1 ard, distribiited
equally as.Eq.(3-3) a'rxd (b3~ I~b2-;.bff) i~popuiation hdi~~ing
property X X (i;j-1.,2. n) h0the:,'::, S'tati.6. tic (3.4) dan
i - J:
'Thusi- the
be formed which does not depend on fun8~ion:
f M will take the form showing~that 40 will~occur
on the complex plane.~ Two if (ZlItX And en6--
and 2 ep
::2
ent statistics, S ICZ S 3a6) are
~2 2 - Xi-
:(Y
given, then for the statistitas
1r2)
173
Sit y3 S7 3 3 '-are also indep6ndeiit. .(Xj_y,,43 :j ~2)
it
1 21 2 Y~
The characteristic fwLotion of: the componellts-.
ai
Card 5/8

-2
XV152' 373
~The Independence ot Quasi-Polynomial; Statistics"and the.Analytilickl:
Rooperties of Distributions
X; 7:
3 ity- 1*7 2
y dy
E [exp(it Y S e
A iff T
will have an infinite numboxf: of zeros (R6f io,. It C 'pal IN
shown that, in some ~,,aseg, the indepehdend6 air both~ th4
polynomial statistio, and itS~, linc-_%ar char-ftete:q aef ines; 4
zero characteristic funotion of the 4ist:kbution ~f t'
0 he
vector If. (X1711, 9 ~..Xn) - r=,dom -,rector ith4i
independent components and 'Che permissible po.1;7nomiaL ~tatis_
tic P(P,) and Y exe independent, theni~in Order thati,th'd
characteristic -Lunotion of the component. X .4ad a zero
point of the order m.(j - 1 27 soon) the v~:Iue
j
IT(ml, m2,...mn) should be eq:,aal to 0 (Lemma 4), (if Xk
transformed into m (M 1) ...(M., - kj,i:,_ 1)1. the pol omiAl
j yn
of (M will be 11(m ~in The conditions
Card 6/8 J? m2-mn) m2,,,,,f

POV/9,2 ll.3-3-2181
TheIndependence of Quasi-Pa-lynomialistatistirs'.*gind the AnalytUall
Properties of Distributidns~~,
of the component characteris'bir, funetio 'of the vec o:~i,.
t
r%
gd: J;f 16~
not being zero can tie expressedas foll'o,
(x randlom vectoi~ vrith indep'ndetit compon6its;;~
1 X2"-xn)
and the non-specific rmissible for all-arguagnts OV-I~
;PO Y_
nomial statistic FMI-ir and X X2 X~, are in(f4peri-
dent then for the vector to be norm~lj onp:of the'lollow-:
ing is sufficient: (a) the components of.the .~Aor are
divided into equally dist::~ib!
uted pairs,,,,~nd .b) e a c h the:
is represented as X -2F t Z11;
components of the vector
where Z~ and ZI! are independent and eqi.,Lally distributed
Card ?/8
r

.", 05-
i I
1 :
i .
i
i :
, , i
I
~j! -

."!t Tot
cfd
02ki/63/14" D2/023
-I'stribut.-Dii of polrnomial 3112/ BI 86
d I/r- + D/4 if NIX) io 1,L form of a
of N IT0
da6ree n + 1 > qrid SX. .
HE 5Irl E D I Octabor 10, 1962,
3 U 3 T T E, D SeDtember 29, 14."'1

ZINGERs A.A.

........ .......
:j: I
6n Mr:: 4F 110882'
Transactions of the, Third A111-unlon Mathematical ess, X (Cont
,,Jun-Jul .1,56, Trudy 15b, V.-I$ Se;t. Rpts., lzdatellstvo 0.1sr, Iddscov, 1951, ~37 pp
Khalilov, Z. I. (Baku). On the Discreteness Spectrwn Part
of Non-self-conjugate Operators of Unteal. 122
-Taitlanadze E. S. (Tbilisi),. On the Conditionali
Extremumo and the CorrespondIng Functional Equation
in Hilbert Space.
Theory of Probabilities Sectlon,
Reports by he following personalities are inolud6d:
Boroducliev, N. A. (Moscow). On the Structure.of Some
Probable Aggregates and Processes, Reflecting Conla;'riete;i
Production Processes.
.123;
There are 2 references, both of them LtSSR.
v
Linnik, Y V. (Leningrad), Zinizer. A.: A. (Leningrad).
Some New Data on Independeitf-M-R-stiez. 24:
Card 39/80

SUBJECT USSR/UAMILTICS/Thioory of probability CARD 1/1 PO 307
AUTHOR ZINGER A.At,L1NNIK'Ju.V.
TITLE -W-W-U-ititio generalizationlof the Cram6r theo:r*m and Lisa
appliaction.
PBRIODICAL Vestnik Leningradsk. Univ. 10, NO-11, 51-56 (1955)
reviewed 10/1956
The authors prove the following generalization of a well known theorem of
H. alrsm6r (Random variable:)aa&.probatility Ustributionsi C"tridge Tra6ts
3-6-L (1937)) s If fl(t)'f2( .. f,(t) are characteriati*,funclions,
a positive numbere and
I I a29 ... Pas
t-t
2
f 1(t)f W f 6(t)
2
to valid for -oo