SCIENTIFIC ABSTRACT STRATIYENKO, V.T. - STRATONOVICH, R.L.
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CIA-RDP86-00513R001653510002-8
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RIF
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S
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100
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Publication Date:
December 31, 1967
Content Type:
SCIENTIFIC ABSTRACT
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Diphenyl-chloro-phosphazo-sulfone Aryls S/079J60/030/05/33/074
13005/BO16
ASSOCIATION, Dnepropetrovskiy metallurgicheskiy institut (DnUEo
Institute of Metallurgy)
SUBMITTED: may 13, 1959
Card 3/3
B/079/60/030/006/024/033/XX
BOOI/B055
AUTHORS; She,,rchenko, V. I. and Stratiyenko, V. T.
TITLE: Diphenyl-alkoxy... and Diphenyl-aroxy-phosphazo-sulfonary1
Compounds
PERIODICAL: Zhurnal. obshchey khimii., 1960, Vol. 30, No.. 6,
PP. 1958 - 1960
TEXT: Diphc-nyl.,.,,-hlorc-phosphazo-.sulfonaryl compounds, as the acid
-T~hlorides of aryl-sulfonimido-diphenyl phosphiric acids2 react readily
with water,, alochols, amineE., and other compounds containing an active
hydrogen atom. They react still more easily with sodium alcoholates and
phenolates forming diphenyl-alkoxy-,phoaphazo-slilfonaryls (eaters of
aryl-sulfonimido-diphenyl phosphinic aoids)7(i,., R - alkyl) and diphenyl-
aroxy-phosphazo.-sulfonaryls (II~ R - TXT-1 respectively:
Ar' RONa (C H ) R0)P-NSO Ar.
(C6H 5)2C'p - NS02 - NaC1 6 5 2( 2
Card 1/2
SfTEVCHENKO, V.I., STRATIYENKO, V.T.
Reaction of ar-yl-phosphor-as chlorides with acid amides.
n
L 52794-65 E*T(m,/
ACCESSION NR: AP5016190 -UR/007?/64/034/012/3954/3955'
iAUTHOR: Shevchenko, V. I.; Stratilenko Pinchuk, A.M.
A-
TITLE:.Triphenylpho8phazosulfonylaryls
SOURCE; Zhurnal obahchey khimii, V-.34, no. 12, 19641 3954-3955
TOPIC TAGS: organic phosphorus compound, organic sulfur compoundt chloride, organic
amide
Abstract: -A Kirsahov reactl'on takei 01dee under'the action of triphonyl-J
11phosphorus dichloride on arenesulfamides o form tripheny;phosphazosul-
fonylaryls in 89-94% yield. The reactiot"rates of diphenylphospho rus
trichloride and triphenylphosphorus--dichloride :rith arenesulfamldeiiare..~
1approximately the same..-'Orig. aif#' has L-torauia-and 1 table.
ASSOCIATION: Institut organicheskoy khimii Akademii nauk Ukrainskoy SSR (Institute
,of Or
-ganic,%emistry Academy of Sciences,,, Ukrainian M)
SUBMITTED.' 305ep63 ENCL., 00 SUB COM., 00, GO
INO REF SOV.* 003 OTHM; 001
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L-2i833-66 EWP(j)IEWT(m) RM
ACC NR, AP6ol2652 SOURCE CODE: UR/0079/65/035/002/()363/0364
AUTHOR: Shevchenkoj V. I.; Stratiyqnkq,,,..X,. Pinchuk, A. M. 7
ORG: Institute of Organic chemistry, AN UkrSSR (Institu~ organicheskoy khim:Li AN
UkrSSR)-
TITLE: Phenyl-p-tolylchlorophosphazosulfonylarylsiI
SOURCE: Zhurnal obshchey khimii, V. 35, no. 2, 1965, 36.-;-364
TOPIC TAGS., amine,-alcohol,-hydrolysis, chemical rf bicn, organic sulfur compowidq
organic phosphorous compound, chlorinated organic cr-apound
ABSTRACT: Phenyl-p-tolylehlorophosphazosulfor7laryle reaat readily with,
aal-nes, alcoholap and other compounds containing an activo hydrogen atom.-
Cold water and moist air slowly hydrolyze these.arjla with the formation
of arenesulforqlw4d~s of phonyl-p-tolylphosphonic acid.. The reaction
s. ' Orig.'aM-.---h'a**s': 2 tables.
temperature is 125% and the reaction time is ur
[JPRS]
SUB CODE: 07 / SUBM DATE: 13Dec63 / ORIG W: 001 / GTH REF:' 001',
nat
_L 29286-66 EWP(j)/EVIT(m) RM
ACC NR! AP6019326 SOMACE COLE., UR/0079t'651'n35/008/1487/14,
AUTHOR% Shevchenko, V& I*#._.Stratiyenko, Ve T.; Pinchu1c, A~ Me c,-2-t:g_
ORGi Institute of Organic Chazdatry, ANU-~!~Instltut organicheskoy khixdi
AN U)CrSSR)
TITIEt Phemylbenzyletbylphosphazosulf2MLaMl
SOURCEt Zl=nal obahchey khlrdi, ve 35, no.'8, 1965, 1487-1488
TOPIC TAGS: sulfonia acid, organic azo compound, chlorinated organic compoundl
organic synthetic process, cyclic group.
ABSTRACT: Phenylbenzylethylphosphazosulfonylarvls (A) can be
prepared.by oxidative introduction of an ArSO 2N= group into phenyl-
benzylethylphosphine by means of Na salts of sulfonle acid chlo--
ramides or by means of sulfonic. acid azides:
ArSO2 NNaCl + P(Ph) (CH2 Ph)Et ., NoOl +. ArSO2 N=P(ph) (CH2 Ph)Et (A)
--Ai~,A~N3 + P(Ph)(CH2Ph)Et - N2 + A
.By using these reaotionsq compounds A with Ar = Php P-14eC041
o-MeCOO and d-CIOH 7 were prepared. They were crystalline sub-
stances melting at 107-80 102-309 125-60, and - io5-600 respo Orige arts
has: I formula, and 1 table. ~h
P_ ~Rf
suB cow-,: o7 sum DATE, 08jun64 / ORIG REF: 001 / OTH REF; 002
4-14-, . A er-e .1 a e
!JV, Ni,~c-] Ly Gtra-,-l.,..ov-j 0.; G I ~- IN 111"V, Gileindar H lzvanr~vich;
'TRLTIY-V, Valentin jv-inovich; ' ',T li", 'M.YA, G.'., red.
- -1 " - 1.
[Frequericy-type rumote clntrol. syntem for oil fielisj
Ghti-,totnaia rn-~Ipma telemekhan-lLatLii refteprcx,~-.-Iov.
Ufa, Jaslikirokoe Imizhnoe lzd-vo, 1962. 83 P.
(MRA
~KiL:T'KvK, T .
"Trade-Union Urganizations Fight for Economy of Electric Fower. 11
P. 40-0) of cover,
(LF.Kn Pitul-LISHLAillUd", Vol. 3, No. 2, 1954, Sofiya, Bul'garia)
SO: Monthlj List of East European Accessions, (Ea#-A.L), LC, Vol. 4
No. 5, May 1955, Uncl.
STRATKOV, T.
Ways for development of the rationalization and invention Movement. P. 33.
(Leka Promishlenost-i Vol. 5, no. 12, 1956, Wlgaria)
SO: Monthly List of East European Accessions (EEAL) LC, Vol. 6, no. 6, June 1957, Uncl.
- 3,TRATKOV, T.
STRATKOV9 T. For the introductim of traionalization suggestions In tho
light and food industry. P.11.
Vol. 6, no. 3, Mar. 1956 RATSIONALIZATSILA Sofiya, Bulgaria
SO: Monthly List of East European Accessicna, (EXAT), LC, Vol. 5, No. 10
Oct. 1956
'?i': C'~ '71CS
&CC-:Cl::, COU, C4 1
c r r c~ t~-Chl- C
4-ut
LIES( 1.( Gli
~~c - ;Last -~-xrc e,.ri Vol. "C'. -il
STRATKOV T.
I
I
"Yore active participatinn od women in th-:~ rationalizing movement."
p. 9 (Ratsionalizatsita) Vol. 7, no. 9. Sept. 1957
Sofiia, Fulgaria
SO: Monthly Index of East EuMpean Accessions (E7-,AI) W. V01. 7, no. 4,
April 11~-58
ST11ATKOV, Tralcho
Road wide open to new initiatives and rationalization
movement. Tekstilna prom 13 no. 4:15-18 164.
1. Chief of Section In the Central Committee of the Trade
Union of the Workers in the Light Industry and the Food
Industry.
AGULINIK, M.A., professor; KORNEYEV, I.P., dotsont; STRATONITASKATA, G.A.
Micreflera of pork brisket during the process of salting in 1954.
Vaterinariia 32 no-3:78-79 Mr 15-5. (KWRA 8: 4)
l.Moskovokly tekhnologicheskiy institut myasmov i molochney promr-
shlennesti.
(PORK--BACMIOLOGY)
. .11. . ,p ~',). , : - .
.1 1 .*--. i - . . 1 1 .. It .
Bee Culture - ~-*,iu'-m-eriL anal 1--es
1-.oldeA '-.;-vF- fr~.,mn ulanL fiber ril'-Ilcri~-ds. Pcir.elovorl 3 t I.- 3k , -No- 2,
9. Morithl List of Russian Accessions, Ltbrary of Congress, June 1953, Uncl.
ISTRA1100NOV. N.
USSR/Engineering Turbines, Stearr Repairs Jan 49
"Duration of Opearting Period of Steam Turbines Between Major Overhauls," B. F.
Dobkin, N. G. Stratonov, Engineers, 3 pp
"Eldk Stants" No 1
Operating Codebook calls for major overhauls annually without regard to operating
hours. Authors compiled 2-year data on repairs and Lreakdown of turbines to use
as basis for recommending changes in overhaul schedule. Lists data in tabular
form by operatind periods between overhauls, and analyzes causes of breakdown.
Recommend 10,000 - 12,000 hours operation between overhauls (gradual implementa-
tion), excluding new installations (one-year overhaul, initially).
PA 55A9T53
USSR/Engineering mar 49
Turbines
rI\
F~ Condensers
"An Eff!cient Condenser Arrangement for Therzifi-
cation Turbines, Jo( G. Stratmov, Engr, 1 p
nMek Stants" No 3
Discusses optimum choice of cooling surface for
condensers. Turbine type AP-29-1 has cooling
surface of 1,~00 sq m, which w--.rks well in winter,
but forces turbine to work at reduced vacuum in
sg=aer. Another type, AT-25-1, has 1,900-sq-m
beating surface, which secures sufficient vacuum
4M .718/49T37
USSR /z-ngineering (Contd) mar 49
in suramer, but is wasteful in winter. Saggeste
and tests crosspiece cormecting water chamber
of second flow of rear half with water chamber
of first flow of front half. fitted with valve for
operation in summer.
-Z.
"I /49T37
E-.
'
-
A fA-Jt-J,-A--I. A k f W- A
A4 0, M W tl
I
'.~fss* -h is. essollpf
.4
A
5116. DMUTION OF WCUM PMtIOV8 OF STIAM TURDTIM MWEIN TOTAL
OVIRRAULS. Dobkin, S.F. wW Stratonov, N.G. Mlektridwakle
Zi
I l stantall, Jan. 1949P vol. 20t
I
al I
is
0 as
see
A METALLURGICAL LITERAIL41F CLASILVOCAUCH
144.1 I;iv %*
"I aft all"VIC"t
I -
IIIALIV aK -1
v so Ls
N
cy a tv ON 49 it oc 4 IM 0 0 0 1 Ir Of I A 4 7 2
v
00,
0 0 000
00 00 0 000 00 0 00 0 00000004
1. STRAMNOV, q. G.
2. USSR (600)
-. Water ha=er
4. Kinetic energy of water hammer. Rab. energy. 3 No. 2, 1953-
9. Monthl List of Russian Accessions, Library of Congress, June 11053, Uncl.
STRATOVDV, N.G.
Utilization of waste steam. Xnergetik 4 no.4:38 Ap 156.
(Waste heat) (MLRA 9:7)
STRATONOV, N.G.
Cleaning the water level indicator glasses of condensers.
Inergetik 5 no.8:40 Ag '57. - (KIRA 10:10)
(TURBINES)
I-- , ~ - I
/ , -i
," I. ki": , - V C, V ~ I,,-;
STRATONOV. IT.G.
Scavenging the Shukhov-Berlin A-7 boiler. Inergetik 5 no.9:38
S '57. (KIRA 10:10)
(Boilers)
- , -;- ~, - 1 ~7 - -
'. . :1 . V - -11
STRATONOV, N.G.-
On wear in tube surfaces of boiler installations. Energetik 5
no-9:39 S 157. (MIRA 10:10)
(Boilers)
MARSHAK,Yu.L.-. ROMADIN, V.P.;,Z12AT.2 ~OVF ~G., inzh., red.; RADZTUKEVICH,
Te.I., red.izd-va; BORUNOV, N.I., tekhn.red.
[High-temperature wet-bottom furnaces designed by the All-Union
Rest Engineering Institute] Topki VTI a vyaokim shlakoulavlivaniom.
Moskva, Goo.energ.izd-vo, 1958. 95 P. (MIRA 12:2)
(Furnaces)
NOV, N. G.
. -
Utilizing the drainage system for heating. Energotik 6 no.11:37
11 158. (MIRA 11:11)
(Steam engineering)
STRi,TOITOV, 11. G. , lnzh.
Saving electric power in station auxiliaries of steam power
- 1 -6 Ap 160. (MIRA 13:8)
.Aants. Energetik 8 no.4:3
(Electric power plants)
STfdtTC)NOVI, N.G.
Concerning the tightening of pack-ing glaM compenBators.
amrgetik 9 no.2:36 F 161. (MIRA 16:7)
(Steampipes)
STRATONOV, Mj~
Yp,asures for inerpasing the operational reliability of heat and power
equipment, Energetik 13 no.314O Mr 165. (MIRA 18:?)
83385
Z//9 0 Z/037/60/000/005/026/0_~6
E192/E382
AUTHORS, Stratonov, Oleg and Jedlina, Mi.roslav
TIT L E Multi-.alkaline Photocathodes%.\
PERIODICAL.: Ceskoslovensky' c-asopis pro fysiku, 1960,
No. 5, pp. 425 .. 429
TEXT; The characteristics of multi.-alkaline photocathodes
were first described by Sommer (Ref. 0. Such cathodes were
produced and investigated at the Research Institute for Vacuum
Elei,,~-rotechnology in Czec-hoslovakia during th-e last three years.
Thtee methods of producing multi,--alkaline layers were investi.-.
gated. The first method is based on a simultaneous single-
stage e,-aporati-on of all. the alkalis (Sb--Na-.K--Cs). In the
se,7ond method the alkali;i ar:e evaporated su~,cessively (in three
stages), and the base layer is successively activated by
individual metals. The advantage of this method lies in the
fact that it is possible to control the quantity of the
evaporat c-.-d alkalls. The method of combined (two-stage)
evaporation is as follows.. the alkali metal Na is first
eflaporated on a basE- layer of Sb and then the two remaining
Card 1/5
63385
Z/037/60/000/005/026/056
E192/E382
Multi-alkaline Photocathodes
metals, K and Cs. are deposited. The majority of the cathodes
produced were oxidized before completing their processing,
since.. in this way, it was possible to increase their sensitivity.
The overall sensitiv:ity of the photocathodes so prepared was
200 4A/Lm. This is the sensitivity relative to the current
temperature.of a tungsten bulb of 2 250 0K. The spectral
sensitivity curves of the cathodes of the three types are given
in Fig. 1. It is seen that for all the curves the spectral-
sensitivity at 600 m~L is 30--5000 of the maximum sensitivity.
This effect is very important if the photocathodes are to be
employed in colour television or for colorimetric purposes.
Fig. 3 gives the spectral s-ensitivity and spectral transmittivity
of Sb-Cs and Sn,-.Na-K-Cs photocathodes which were chosen so that
the spectral tvansm�tt!-.r�ty �n the vicinity of 600 mtL was
approximately the same. It is seen that the relative emissivity
at 600 mu of the Sb-.Cs photocathode is approximately 1/2 that
of the multi-.alkaline photocathode at the same transmittivity.
From the in-est-igation it is concluded that though the
Card 2/1,
83385
Z/037/60/000/005/o26/ocO6
E192/E.382
Multi.-alkaline Photocathodes
preparation of a multi-allcali.ne photocathode 3,s complex and
difficult, the cathode is very efficient and can be successfully
employed In the photomultipliers for nuel.ear physics and in
certat-n tele-vision camera tubes. The authors express their
thanks to M. Dvo?'A and P. Vilfm for ad-ice and preparation of
the samples.
There are 3 figures and 7 references. 3 English. 2 Soviet
and 2 Cze(-h.
ASSOCIATION,. Vyzkumny U's+-av pro -akuorou elektrotechna-ku,
Praha (Research In3titute for Vacuum
Electrotechnology, PragueT_
Card j/3
Ql~. ~-Cwr~
-"I'i , T'j';,--'V-, ~7 ~*. A.. jti ~,U.
~t . I I
I A
.'hysical chara,Ae ris ties of forest soils -ind their chan-e under the Jnfliience of
fore3try wark- Goslestekhi7d,-It, 1935. 1-6 P. (54-469-'l)
SD)~- 7 - 38
,~* --~ ~l '1'1~ - - -
- , -1.,- ~ I ~ I . . . I .
,- - r, - -1 % -
2305 sost-) ad.ye I- Pers-ekli-.rr introluktsii hereskletov ~evan.-;:,iols) v sssr.
-r sh: is~:Iedovaniva r,,c, les. khr)z - vy. 1., l'ALF" ~ra o'-Il: 1. 1. f- -.
153-74
31.-: 31, 1) W,
M, - -- - . - ~
.- ; "fJ7 i - - ~ ~
I - ., - I .
Cultivat"On ~f tht- tr,!e in tile USSR f4oskva, 60sle3t3urnizdat, i~,s~,2. 118 ~ . rUicl.
(54-17615)
SB2~)l . DJE~32-
,S7 K 14 7- 0 A/*O V/ C q., 14,
STRATONOVICII, A.I.,
Establishing
no.2:134-144
laureat Stalinskoy promii.
fruit-bearing trees in forest stands. Geog.sbor.
'53. (MLRA 7:2)
(Forrestation) (Fruit culture)
STRATONOVICH, Arseniy Ivanovich
(Central Sci-Res Inst of Forestry), Academic degree of Doctor of
Agricultural Sciences, based on his defense, 24 March 1955, in the
Council of the Inst of Forestry, Acad Sci, USSR, of his dissertation
entitled: "Spindle trees of the USSR and their industrial significance."
(krlcu !~,- (-A I
Academic 8egree and/or title: Doctor of Sciences
SO: Decisions of VAK, List no. 18, 10 Sep 55, Byulletent MVO SSR, No. 17,
Sep 56, Moscow, pp 9-16, Uncl. JPRS/NY-435
STRATONOVICH, A.I.
Distribtition of the warty, spindle tree along the northern limit of
Its habitat and some theoretical conclusions. Geog. sbor. noo5:
5-15 '55- (Spindle tree) (KLRA 9:6)
KIIARITONOVICH, Fedor Nikolayevich. professor; &T4TO~QVIq!I, A.I ., radaktor;
OSOKINA, A.M., redaktor izdatelletva; SHITS. V.P., 'teiGf6heskiy
radaktor
[The European spindle tree and how to grow it) Beresklet evropeiakil
I agrotekhnika ago vyrashchi-,raniia. Moskva. Goslesbumizdat, 1956.
108 P. (MIRA 10:2)
(Spindle tree)
U-
USSM/F~n-1---, try cu It",-
J,--ur ~ur 21;195n, qTiS42
c f Z:, -~j
)f F:-..rc,3try.
01(l Dat
Titiu
0--.-i:. ?U-- Dyul- J11--ta lusl~-
1957, i:L, 4,, 34-43.
it
t c t rc;c-,nistructi.-)~--
cki -
r-Itat-i ~11 wit'
f c -z!r --7-1 w"ich t'.c Dv i
i t%c Gatc'-- i_ -.s' -iy Sivc-rsld3r
r:,-)t if tre~--s crc~Accl loy )r scali..~;.
Card 1/2
21, 95B"2
-Iul-
liof 7~
---CtiVL
J-,rc;
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S"Irfacc
jL
with
jay,~~
val tio-
t c. ". " I
.1. :, V-.c ti:c;c;~',
tl-.I Z~, - rs
-xrJ
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3
rAl-t:. ic 44) flia -,0-
_~Cr t--f~:l
car,!-- --I: crj,,rl 33c~ i ' - ..~ f,-r
a -,f C D,
i,3 citc
a:-A V.V,
2/2 22
STRATONOVICH, N.I.
Teaching epidemiology at a medical institute. Zhur. m1krobiol.,
epid. i imm. 41 no. 2:133-134 F 64. (WRA 17s9)
1. Smclenskiy meditsinskiy institut.
t! i z ra! c I on
k Lai n. C~ f,
S/262/62/000/01 OjO 17/024
10071[207
AUTHOR: Stratonovich, N.
TITLE: Field testing of new winter-type crankcase lubricants
PERIODICAL. Referativnyy zhurnal, otdei'nyy vypusk. 42. Silovyye ustanovki. no. 10, 1962, 68. abstract
42.10.387. "Doki. Nauchno-tekhn. konferent5ii molodykh 5petsiyalistov lesn. prozi-va
Sverdl. obl. po itogam rabot 1960 g." Sverdlovsk, 1961, 65-67
TEXT: The department for transportation and hauling machinery of the Ural'skii lesoteklinicheskii Institut
(Ural Forestry- Engineering Institute) tested new types of crankcase lubricants prepared from sulfur-containing
additive-type oil products. Three types of lube oils were tested on 18 tractors at temperatures down to 38'C.
As shown bv tests, these oils, in terms ofantiwear and starting properties during wii..er operation. are superior
io the best grades of standard lubricants, permitting tl-,: starting at a temperature as low as -4WC uithout
preheating the engine. The lube oil of tile An-8 (Dp-8) type prepared from sulfur-containing oil products of'
tile Eastern oil fiefds is recommended for large-scale production.
[Abstracter*s note: Complete translation.]
Card 1/1
Mar 52
C.Yliz-h-ieal Plaoxa.." R. L. Stratonovich,
`b,;~,t U1, ~Eot~r Fiz, Mat, i Yest Nauk, No 2,
Pp
Analyz,~s t.wc-dimerislonal longitudinal waves in plasma
bol.)P-d by sid- walls of a cylindrical discharge tube
of radius. Derives and solves eqs of waves,
usin-sz linear PInproximations sufficient for small am-
23 V"jl 51.
242T103
KUZNICTSOV, P.I.; STRATONOVICH. R.L.
- -,
Long heterogeneous lines. Radiotekhnika 8 no.6:14-22 N-D 153.
(Radio lines) (Radio, Shortwave) (mm 11:6)
ST_I',TQI;U~!TCII, 2L. L., TE 'HONOVI, V. I.. i-.UzI-,z;TS0V, P. I.
"Passa.e of Corta n Ranrxr, rune'tions Throu-Ii Lire-nr Syster,,,s",
Avto,-.a'uj_'-a 1 Teiemek'iailika, Vol 14, No 2, 1953, PP 144-163-
Discw3es linear systems in which the input anri output of a sL:nal
is connected intc--rally by vicans of the kernel (the trayv3fer 'Lunc-'L-*,I-n of
systo-m), dependii-C, on the time, and parw- ter.
DetermLies ~;cnaralizzel` correlative functions as coefficients of ex-
of -roba-
oansim. of char_~cteristic functions of nmultiple d-Aztributions
bilities aTy-', est-i'blishes the correlations, bindirv; the output correlative
fUjjCI,j !,~S 10 L110 j
I . ~ U input function-s. For the c:!se of st,-1tionar-,r output
sisnals 'U~e c !-.a rac "cris ties of proicki-ity of certain functi~-.ns of the density
of prdbabUity (sl-mrp attenuation and of one pezu"C) to me ~Cnsity
of baussian di3trj:bu~tion is discusSed.' Other results arlsInG from tran-
sient randoma si!,n--115 tIxou"h linear a.-,,stemis, may be found in in the works
of A. 11. KoJ_,:ioZ;orov (Jubilee Collection, Acad Sci US3H, 1947),
where analysis of -the case of stati-~mt-y distui-bances and constant
Urans-rdttinz function of the systezri is Lgiven; cf. V. S. PuCachav (Izvestlva
Seriya '-Iaterpti,~:a, 195), No 5, 1*1-4,20) and Zadeh (Froc,
J-R4L-, 1950, 41 38, No 11, 1342-1345). (RZhI:e? q ~Pkj ... Pk5
There follows an examination as to the manner in which the definition of the
local moments of itiomentum p on the occasion of the Cauk!,e transformation
4r-."--,
JMMM
2o-6-12/40
6tratonovicho R.L. aution Function
AUP110R, ;ation of the Diatril ychisleniYa
On a Liethod for the COMPOTheory (0b odnoM metode v
TITLEI Pertaining to the Quanturiledeleniya)
kvantovykh funktsiy ra9pr 1. 115, Nr 6, PP- 1097 - 1100 ('USSR)
PERIODICAL' Doklady All SSSR, 1957, VO for the distribution func-
i relations Its of
in a form which reminds Of the resu
ABSTRACT3 The present reprt aeducee author here con-
tions and it does it tion functions. The I -relativistic
the theory Of the propaga component non
generalization on other
self to the model of a one
fines him Boze). of course the tion (gamil'toni'an) is
Bose gas (gaz liamiltons' B tune
71) T
case,, is also possible g forms X1%
arranged in the followin i~2n
w) IV (X1 - X) q* (X) V (X) 3 d3c' dx G LF * Tlf+ I (x)~ anT*(%)
(x A abreviatiOns have been applied denotes the
lowing I - .
Here the fOl 2/2m -2 T (X X) tized wave
I T a 13 P he secondarily quan ies the
otential. 4' (') is twhich function satisf
interaction I ridimensional spa(le, 0,
function in t tionB1 LT 9 1 0, 14*,
Card 1/3 follwoing exchange rela
-71;1nuOUs Fourier trans-
---uced to the examination Of parotnicles
Ln an exterior
m -t vexiadmeianlesvatlhueesdeavniEdL he int fl"tuation field. Then the
f rO h tion conditioned bY the interacti
roduces functions for the de-
cription Of this deviation. Te each link of this function a
diaGram with i closed Curves and r not closed lines can be as-
Card 213 3icned. Then these graphs are described more in detail. In these
4-- -
20-6-12/10
On a Method for the Computation of the Dijtribution Function Pert-dnin.; to the
~tzantum fheory
diagrains several interaction lines can emnnate from one vertex.
There are 1 fi-ure, 5 references, 3 of which are Slavic.
ASSOCIATIONt I!o3coVI State Univeraity imeni I.I.Y. Lomonosov
(Moskovskciy ~aaudarstvennyy iu. M.V. Lomonosova-)
U
PRESMITEDs April 10, 1957~b~r 11.1T. Bo,3olyubov, Academician
SUBMIT,ZED: April 9, 1957
AVAILABLE: Library of Con.-ress
Card 3/3
AUTHOR
_
"
'
STRATONOVICH R
TI TLE 1
1
~Tlif;-Tnrc- tit of the QuanLuui Thoor~-
n tho S tal T ~1
(K atatint che8kc-Y )terpr-~%;0W k-varitavoy t~-nrll.-
PERIODICAL Zhurnal EYnperjm. i Teoret. Flziki 1957~ '101 ,12, Nr 6,
pp 1483-1495 (U.S.S.R.)
LBS TRAC T The principles for the clas5ificatlon of operators and
the partplayed by them in statistical interpretation:
,
These principles are here condidered to be the basis of
statistical interpretation. Various of such principles
of classification are discussed. The most simple principle
A,
of olassification skirs that in all products k
n
n
1 2
one of the operators always acts sooner or
here denote the
later than the other. (The A
v A
.,
.
2
operators). To the classifica ion princtiples disoussed
here there correspond certain distributions and charac-
teristic functionalist, whioh are here described by means
of an index in brackets.
.The case of linear oQuationa of motion: The author iu-
vestigates the distribution types corresponding to the
aforemeixtioned olassifioat4on principles on the basis
CARD 11A_
ajSTrjzUtjoh
iutrolluoed by SCHNINGER f"'t-he i;eneral case of
t~'e ex-"tFaOe Of exterior sources are n0thing but corre-
laticu fu-n'1'.t1-)n5- Several equat!,ons `30M'e~:tod herew4th
t~'Us fi-nd a trJvjai. explanatior,._
(lic 11-lustrat,
CARD 2/3-3
~C'
0
-H,
ation."
.e 'poise 7 ~'Iuence on an OS-2-T-1
i - . n.L
report pres'ent'ed at, the P-LI-Union Conference on S-tatistical Ra.,UO Physics,
Gorlkiy 1--,-18 October 1958- (.Izv. vyssh uchev zaved-RhjiotekJi., vol. "I,
Y ~
No. 1, pp 121-127) COMPLETE card under SDIOROV, "1. 1.)
AKO.PYAN. i.G.; bTRATUNOVIC!~,AiAw . ~ -
Nstablishment of synchronism in a self-oscillator in the presence of
of fluctuation noise. Nauch. dokl. v7s. ekol7; fiz.-mat. nauki no.l:
162-166 '58. VIRA 12;3)
l.Moskovski5r gosudarstvenny7 universitet im. M .V. lononosova.
k0scillators, Xlectron-tube)
AKOIIYAN, I.G.; STRATONOVICIT, R.L.
I
Establishment of amplitude In a synchronized solf-oocillator in the
presence of fluctuation noise. Nauch. dokl. vye. skolr; fiz.-mat.
nauki no.l:lb?-172 '58- (MIRA 12:3)
I.Moskovskiy gosudarstvennvy universitat im. M.V. Lomonosova.
(Osc4llators, Electron-tube)
17, ~L971 S/044/61/000/008/018/039
C111/C333
AUTHORS: Stratonovich, R. L., Romanovskiy, Yu. M.
TITLE: Parametric influence of a random force on linear and non-
linear oscillation systems
PERIODICAL: Referativnyy zhurnal, Matematika, no. 8, 1961, 53,
abstract OB224. ("Nauchn, dokl, vyssh. shkoly, Fiz-
matem., n,,", 1956, no. 3, 221-224)
TEXT., The authors consider the behavior of oscillation systens,
in the equations of which the coefficient, deteri;iininC tile eigerfrequen-
cy, is 3ubject to fluctuations. The uuthors solve the problem on the
busis of thc: results of Stratonovich (R Zh Mat, 196o, 14227) and of
the easymptatic methods of Krylov-Bogolyubov. Linear systems
2 + CO2 El + ~ (t) y = o,
are con~_;idered, wh(,re i(t) is a random function, tind the non-linear
Sys tem
Ps 4 2
y + 2 2 y + J El + t) 0,
Card 1/2 0
S1044161100010061016107)9
Parametric influence of a random . . . Ciillc~~33
where A0 is the amplitude of the stationary o-se-J"llations As the re-
sult of the inv,~-sti&~tion an inequality is obtained which characterizes
the conc~ition~; for the excitation of oscillations in, system N under
the in.F'luence of a Darametric random force. Furthermore, the influence
f
thc- nonlineL~rit,-- in (2) on the Crowth of the rezonance amplitude is
investi;ated
U
'bstracterl.; note: Complete tran~:lation
Card 2/2
60V-10-1-3-4-5/28
AUTHOR: onovi~ch, R. L.
TITLE: Synchronisation of an Oscillator in the Presence of Noise
(Sink-hronizatsiya avtogeneratora pri nalichii pomekh)
--~Z_!"RIODIjAL: Radiotelchnika i Elektronika, 1953, Vol 3, Nr 4,
P-p 4"-)7-506 (USSR)
ABSTRAC'12: The presence of noise in a synclLronised oscillator leads
to: (1) continuous fluctuation of the phase, (2) spurious
chan.-7es of the phase of the order of Tr12 and, (3) spurious
junps of the phase over a ntLTber of periods. The word is
mainly concerned with the investigation of the last two
effects and the problem is solved by using the Einstein-
Fock.er equation. It is assumed that, if the synchronising
voltace is absolutely stable, the o3Deration of the synchron-
ised oscillator can be described by Eq.(l), where C(t) is
-the fluctuation noise, and z , B and ~ are of the same
order, For a tuned-grid oscillator, synchronised by a
voltar-e E' (2)
the system equation T, can be written as Eq.
in which the anode current i a a(U9) + iam consists of
G-1 c'i 1/4
Synchj-onisa~iori of an Oscillator in the Presence of J101sp-
where ~W and ~ltt) are two similar random functions,
h,,lvin- a correlation function 2X-1b(T) where 1A is
expressed by Eo.(13). Derivation of Eqs.(12) from Eqs.(.7)
is done in the appendix on P 504. If Eqs.(12) fulfil the
condition expressed by Eqs.(14), tile steady state amplitude
distribution of the system can be described by Eq.(15),
vihere 14 (P is a normalised multiplier. Eq.(14) can approxi-
nately be written as Eo.(16). If the system fulfils also
the condition exDressed by Eq.(17), the phase variation can
be described by ~q.(18), from which the steady state phase
distribution can be expressed by Eq.(21),lwhere D = ie&
and D. = Xa-A c . The solution of Eq.( ) is in the form
of Eq,(22), where the inte-ration constant N is defined
cj
by Eq.(23) or (24). The average frequency deviation of the
system can be expressed by Eq.~26). This is used to analyse
a nuriber of particular cetses, suc~i O's Dc A46 c
2 2 _V5
and 4/A - 1:,>,D :~ . In the last case the average fre--
quenc,y deviation is represented by Eq.(32). The results are
Synclaronisat-'.on -of an Oscil-la--~-or In the __,-presence o.*L' _',ioise
the re-ular co-,_.v')onent i (U and the noise cojaDonent i
'~J - a aw
the --rid characteristic of the system is expressed by a
I -
polynomial: i 2 YU3
ia(U9 + (XU,. + PU'7 Ea.(2) can be
transformed into a system off equations representing the
0
amplitude A and the phase variation ~p of the oscillator.
These are expressed by Eqs.(7), in which the various para-
meters are defined by Eqs.(3), (4), (5) and (6) and vi~ere
((02 w2)/2wwo - w and S, and is the sum of
0 S2
sines and cosines of the multiple angles, having coefficients.
depending on A and (p Eqs.(?) can be transformed into
5 A2)A + wE COS (P + l +-
7 -7 NA
a (12)
sin ~n +
A_ A
7
~-,ynch-roni sat i on of an Oscillator in the Presence of -Noise
indicated in normalised co-ordinates in Fiiss.2 and It
is also sAowl that the t)hase deviation of tiLe srste-m, ta.:ei
over a time interval t I can be ext.-ressed by Eq.(37).
L~ Soviet references and an Ap,
There are 3 fi--ures, pendix.
0
A6JOCIATIOit': Fizicl-ieskiy fallail'tet ',Ioskovsl-:or-,-o -osudzirstverino:7o
universiteta im. M. V. Lomonosova (Physics Department of the
.Zoscola State University, ira N1. V. Lumonosov)
SUBMITTED: February 21, 195?.
1. Oscillators-Synchronizatioii 2. Oscillators-Propertuies
3. Mathematics-Applications
4/4
i 6(4) 1 ~' 6 1 0 0
AUTHORS: StratoDovieh, R.L., Romanovskiy, Yu.M. SOV/155-58-4-27/34
TITLEt X-Sir"taxamous Parametric Influence of an Harmonic and of a
RaD-i . Force on Oscillation Systems (Odnovremennoye Parametri-
cheskoye vozdeystviye garmonicheakoy i slur-aynoy sily n&
kolebatellnyye sistemy)
PERIODICALt Nauchnyye doklady vysshey shkoIX. Fiziko-matematicheakiye
nauki, 1958, Nr 4, pp 161 - 170'0=10'
ABSTRACT% Enlarging the systems considered by the authors in Z-Ref 1-7
they investigate the systems
Y + 2E ~ + w 2 [1 + h ain 9t +-r~(t)I y M 0
.where g (t) is a stationary random function with mean value
zero, while h and :P are constants. Amplitude and phase are
sought in the form
y(t) A(t) Cos t + LP (t)
2
It is assumed that A and change slowly which imposes
restrictions of the intensity of I,: (t) (as in CR-ef 1-7
Card 1/ 3 The simplest case, where (t) c6ntains no components of
28
A Simultaneous Parametric Influence of an Harmonic and SOV/155-58-4-27/34
of a Random Force on Oscillation 5yetems
lower frequencies, is explioitly considered. Then for
u = 1n A and one obtains i
u M + cos 2 P + 51
4
4 hia
7 T sin 2 T + q2
where the intensities of 1~, and ~2 are equal to
2
K Wj ( 2 w)
(-dt(20) is half the spectral density for the frequency 2 0
2
2 c~) kZ- a0- ( 2 u)) .
, m 1 - 8
Then conditions for parametric excitation are obtained and
the boundaries of the domain of instability depending on
Card 2/3 the parameters of the system are determined. e
A Simultaneous Parametric Influence of an Harmonic and SOV/155-58-4-27/34
of a Random Force on Oscillation Systems
The authors thank Professor S.P.
for their assistance.
There are 2 figures, and 3 Soviet
Strelkov and D.P. Koatdmarov
references.
ASSOCIATION: Moskovskiy gosudarstvennyy universitet imeni M.V.
(Moscow state University imeni M.V. Lomonosov)
SUBMITTEDs February 21, 1956
L'3monosova
k-~
Card 3/3
C6333
SOV/141-2-1-5/19
AUTHQP-: Stratonovich, R.L. and Landa, P.S.
TITLE: The t~ffect of lioise on an Oscillator with Hard Excitation
P1~11'IdDi(~AL: Izvestiya vysshikh uchebnykh zavedeniy, Radiofizika,
19501, Vol 21 jNr 1, pp ~? - 44 (USSR)
ABSTRACT: The growth process in an oscillator with soft excitation
~,as already been studied (Fefs 1, 2); a linear approxi-
-tation valid at small amplitudes,
7. was used. With hard
excitaulon the situation is more complex since the presence
of noise may either encourage or inhibit oscillations and
a raore sophisticated approach is needed. The problem is
of interest in closed-loop control systems (which are
iDotential oscillators) and the case examined here is such
a second-order circuit. In the presence of noise and an
external harmonic signal, it is described by 3q (1). If
it may be assumed that the correlation time of the noise
is mu,~h less than the relaxation time of the system -
if Eq (1) is convei-ted into phase-plane coordinates and
tlie noise has zero mean spectral density then the corres-
ponding Fokker-Plank equation is Ea (4). Introducing the
potential function at 6he top of D_ 0
39, allowing for the
06
S 41-2-1-5/10
The Effect of Noise on an Oscillator with ffa Excitation'
order of smallness of noise and external si,-,nal, there
are 2 regions of greatest probability in the phase-plane
correspondinc~; to 2 st;able s-5ates of the oscillator:
unexcited and excited. Between these 2 regions lies allother,
of low probability, representing an unstable condition.
Fi6ure i shows the pha.-,e plane, the shaded area S1 is
for the 'unexcited' and S- for the 'excited' states. The
ex-Dressions for the curves rl and r2 are at the foot
of p 39 and head of p 40, respectively. The probabilities
of the unexcited and excited states are Eqs (8) and (9),
respectively. These can be found as time functions by
solvin,,, - the Fokker-Plank e.~iuation. In an oscillator with
hand excitation, the presence of noise means that both
6rowth and decay Drocesses exist simultaneously. The
probability of the state-point being at any particular place
is conveniently thou.,ht oi as the result of two counter-
flows of probability between the re6ions. The probability
Card2/3 ttiat the oscillator will remain unexcited if originally so
C6333
SOII/141-2-1-5/19
The 7ft'-.a,:!t of 11oi-s-e on an Oscillator with Hard Excitation
is Eq (20) and the probability that oscillations will
cease is Eq (21). These expressions evidently depend
(:) n k10 and k20 1 as defined in Eqs (24) and (25), when
there is no external signal and Eqs (26) and (27) when
there is. In the former case, the potential function is
Y.18ure 2. Figures 3 and 4 show the uean frequency of
chanL~e of state as a result of noise. The oscillator
is more often excited than ot;herwise. S.P. Strelkov is
thanked for assistance.
There are 4 figures and 4 Soviet references.
ASSOCIATION: Nioskovskiy Sosudarstvennyy universitet (Moscow
State University
SUBMITTiO: May 2L~ . 19 58
Card 3/,-,
80126
6,?000 S/141/59AWWO07/024
AUTHOR: -Stratongvj-,~-.h. R.L. 9192/9382
TITLE: Optimum, Non-linear Systems Permitting the Separation of
the _Li1jal" Having Constant Parameters from.Noiseo
PERIODICAL. Izvestlya vysshikh uchebnykh zavedeniy, Radiofizika,
1959, Vol 2, Nr 6, pp 892 - 901 (USSR)
ABSTRACT,, The mathemati,,.s of the Markov processes are c-imployed to
determi.ne the a posteriori distribution of the parameters
of the usc~ful signal when the signal is received together
with non.-Gaussian noise. The following procedure is adopted.
A probability functional W'U(t)l of a random process ~(t)
i-:, an expression depeudi=g on t(t) which, with an accuracy
up to a constant multiplier, characterizes the probability''
of a given realization of the process. The probability
functional can be obtained by a simultaneous consideration
of the distribution of the random quantities t(t 1), ...
~(tN) . If 4(t) Is the delta-correlated normal noise
whose correlation function is given by:
Cardl/4 4M~(tf) = K6(t - tt) M
80126
S/141/59/002/06/007/024
EIR2/�382
Optimum Non-linear Systems Permitting e eparation of the Signal
Having Constant Parameters from Noise
its probability functional is expressed by Eq (5), where
T is the chosen time inter~val. For the case of a noise
n(t) which is in the form of a Markov process such that
it satisfies Eq (6), where ~(t) is the normal noise, the
probability density distribution obeys Eq (7). For small
intervals A the probability density can be expressed
by Eq (8). The probability functional is in the form of:
W[n(t)l = exp [U(nT) + U (n.)j
K
T T (21)
2 2 1
n +,f (n dt - - fl(n)dt
2K 2
0 0
If the form of the received signal is known, it is possible
Card2/4 by employing the expression for the probability functional
Lr
a) 126
S/141/59/002/o6/oO7/024
EjRj/�j82
Optimum (Von-linear Systems Permitting paration of the Signal
Having Constant Parameters from Noise
to determine the a posteriori distribution of the parameters
of the signal. For this purpose it is necessary to employ
the principle of inverse probability. It is shown that
the conditional. or the a posteriori distribution of the
parameters.is expressed by Eq (25), where the constant C
;.s independent of xl, *.*, x m . In order to obtain the
equal.lon for optimum filtration it is necessary to investi-
gate the change of the a posteriori distribution when the
ob5ervation time is increased. It is shown that if the
cb5ei-wation time T is Increased by dT the change in the
a posteriori density distribution can be found from Eq (27).
By introducing the notation defined by Eq (28), it is
possible to write Eq (27) in the form of Eq (29). The
above differential equation for the optimum filtration is
employed to investigate the case when the useful signal
is represented by an unknown constant value. During a
time T a signal r(t) = s + AM is received; n(t)
Card3/11 represents a generalized MarkoV process. On the basis of
80126
s/141/59/002/o6/007/024
EJR2
e/gJ82
Optimum Non-Ifnear Systems Permitting paration of the Signal
Having Constant Parameters from Noise
Eqs (28) and (21), the following expression is obtained:
F(r - s) C~ - f(r - s 2 f I (r -- s) (36).
2K 2
The expression for the optimum filtration is in the form
of Eqs (37). It is seen that Eqs (37) are non-linear. In
a particular case when f(n) is a linear function,
Eqs (37) b~acome linear. If it is assumed that f(n) = P-n
Eqs (37) can be written as Eqs (41). There are
7 referexices, 2 of which a:re English and 5 Sovieti 2 of
the Soviet references are translated from English.
ASSOCIATION: Moskovskiy gosudarstvennyy unfversitet (Moscow
State University
SUBMITTED: December 29, 1958
Card 4/4
P3937
S/'188/60/000/004/014/014
9 BOC;;/BO60
AUTHOR: St,ratonovA_c
TITLE: The Paradox in the Theory of Thermal Fluctuations of
Nonlinear Resisters
PERIODICAL: Vestnik Moskovskogo universiteta. Seriya 3, fizika,
astronomiya, 1960, No. 4, pp. 99-!02
TEXT: Internal thermal fluctuations giving rise to constant,
nonvanishing mean values of potentials and currents apparently arise in
nonlinear resistors with asymmetric conductivity. This phenomenon would
contradict the second principle of thermodynamics. The author of the
pre8ent paper bases on the analysis of a dynamic model cf a nonlinear
resistor to prove that there occurs a shift in the characteristics of the
nonlinear element, and that the probability distribution for the
potential at the capacitance coincides with the distribution
corresponding in the case of a linear resistor. When it is assumed that
every electron of a nonlinear resistor moves abciut in a given potential
Card I
P3937
The Paradox in the Theory of Thermal S/188/60/000/004/014/014
Fluctuations of Nonlinear Resistors B305/BO60
field independently of other electrons, alLd tha- there is a Boltzmann
distribution of electrons in the metal, the follcwing equation results
for the mean current strengths from left to right (f',) and from right to
Y-. - en exu(-eV /kT), where e denotes the elementary
charge and V. is the electrode potential. If there is a potential
difference V between ther(nistor contacts, the following holds for the
individual partial current strengths; I = en exp(..eV,/kT);
+ 0 i
en0exp(-.F,.V2/kT) (1). Here, V, and Ir2 are the differences between
the extreme potential values of the potential barrier between the
electrodes, which the electrons have to surmoun-,, and the electrcde
potentials. The paradox which arises in connection with thermal
fluctuation is eliminated by taking acccunt of the fact that the
ootential. difference V does not remain constant during the motion of an
Pler.tron, however short its duration. The author deri~fed the kinetic
equation for the probability densityg which describes the fluctuation
process in the model considered. The steady-state solution of this
Card 2
The Paradox in the Theory of Thermal S1188YMA00100410141014
Fluctuations of Nonlinear Resistors B005/-B060
equation shown here indicates the probability distribution w(v):
w(V) = (C/21EkT) 112. exp(.-CV2 /2kT) (C being the capacity). ThLs result
fits the distribution in the case of a linear resistor. The author shows
that it is not enough to know the characteristic f(V) = T~ for
setting up the said kinetic equation nor for a complete statistical
interpretation of the process, but that also the individual components
f'+(V) arid !--(V) as well as the value of the elementary jump e/C must be
Icrkown. For the special case of the nonlinear characteristic being
symmetrical, the given kinet4 equation atisumes a simpler form which Is
likewise shown and which the author had previously obtained by another
way for the case of symmetrical mechanical nonlirear friction. This
equation has, therefore, in this context a geneval validity for
physical Markov processes. The author finally thanks V. 1.
Shma-llgauzen~ who helped solvinj the paradox with his su&;escions.
Gratitude is further expressed to the heads ef the seminars and their
participants, Professor S. P. Strelkov. Professor S. D. Gvczdover,
Professor V. V.. Migulin, and A. Marek for their useful discussions.
There are 4 non-Soviet references.
Card
KUZNETSOV, P.I.;.STRATONOVICH. R.L.; T11HONOV, V-L (Moskva)
Quasi-moment functions In the theory of random processess. Teor.
veroit.t. I ee prim. 14 no.1:84-102 160. (MIRA 13:10)
(Probabilities)
STRATONOVICH, R.L. (Hoecow)
Conditional Markov -Drocesses. Teor. verciat. i ee prim. 5
no.2:172-195 16o. (MIRA 13:9)
(Probabilities)
68!53
S/109/60/005/011/001/014
lLo /00 n4o/E485
AUTHOR:
TITLE': _of Markov Processes Applied to Optimal
Signal Filtering--
N-RIODICAL: Itadioteklinika i clel-tronika, 1960, Vol-5, No.11.
pp-1751-1763
TEXT: For Gaussian signal and noise and a criterion of minimum
mean-square error, the optimal detector is linear and can be
calculated by the Kolmogorov-I-Jicner theory (Ref.1,2). V,ith non-
Gaussian signal or noise the optimal tran_~;formation is nonlinear.
A special case has been solved by V:oodward and Davies (Ref.3)
insing the method of inverse probability. For complicated cases
this method encounters substantial computational difficulty. in
such cases the theory of' Markov processes has been applied by the
author (Ref 5) -
Markov processes can be continuous or
discontinuous, unicomponent or ritulticoryiponent, correspond to
continuous time or discrete sequences. Ifere the author
investigates the detection of a signal with time-variable parameters
in non-Gaussian noise, which is assumed to be delta-correlated.
Ca r d I / Ij
38153
S/109/60/005/011/001/014
E,1110/1,1185
The Theory of '-Izkrl,.ov Processes Applied to Optimal Signal Filtering
To point up the advantages of the method over that of Woodward and
Davies, the aiahor first considers the case of the useful signal
constituting a rectangular pulse of known amplitude and duration,
-hose time is to be determined. The noise is assumed to be white
noise . The formula derived by the method of inverse probabilities
leads to certain difficulties where the pulse positions in different
repetition periods are a priori independent or when the successive
pus i tions are correlated but the rate of change of position is very
processes are useful
high. 'Then the properties of the Markov
for determining the a posteriori probability density. For the
pulso positions to form a Markov chain, it is necessary that the
conditional distribution for xj~ + 1. depend only on Xk and not
Oil Xk-1, Xk-2,--- If the latter dependencies are also taken into
account a complex Narkov process is obtained, which can also be
handled by the method presented in the article, In general, a real
process can be represented as constituting a multi-dimensional
~Iarkov process to any prescribed precision. The complexity of the
process increases with increase of precision. Forther, the
author considers only the simple Markov process. The author
Card 2/4
I I, -~' t
S/109~60/005/011/001/014
E14o/E485
The Theory of Markov Processes Applied to Optimal Signal Filtering
derives easily
Eq.
(8) Wk-~-l (4+1) C C.X11 V
k7*
Y (1) so (I - A'T - x,,,) dA WT (Xk+t - -Tk) X
1
(8)
where t is the current, T is the length of period, x is the
coordinate and w the probability density. A computer to realize
the transformations given in Eq.(8) will be an optimal nonlinear
detector of the input signal y(t), It can be realized by the
system given in the figure, where BB is the Woodward-Davies unit,
G,Y is a muitiplier unit. 4Y.' is an amplifier, 62 iL a
delay unit, 90 is a unit for realizing convolution. Further,
the author considers a system for detecting the phase of a narrow-
band signal in white noise. Examining, the differential equations
of optimal filtration, the author shows that the theory leads to an
Card 3/4
s/iog/60/005/011/001/014
E14O/E483
The Theory of Markov Processes Applied to Optimal Signal Filtering
infinite system of equations, i.e. a system which
realizable. An analysis is given of the effects
first few equations and breaking off the system at
Finally, the question of a Gaussian approximation
process is conqidered. There are I figure and 6
4 Soviet and 2 non-Soviet.
is
of
a
to
reCerences:
not physically
modelling the
given point.
a non-Gaussian
ASSOCIATION: Fizicheskiy fakul'tet Moskovskogo gosudarstvennogo
universiteta im. M.V.Lomonosova (Physics Division,
Moscow State University imeni M.V.Lomonosov)
Fig.
SUBMITTED: December 24, 1959
Card 4/4
URATONOVICH, R.L.
Paradox in the theory of thermal fluctuations in nonlinear resistances.
Vest.Mosk.un.Ser-3:riz.,aetron. 15 no.4:99-102 Jl-Ag 160.
(MMA 13:9)
1. Dfedra obshche7 fiziki d1ya mekhmats. Hookobskogo universiteta.
(Zlectric resi store --Therml properties)
STRATONOVICH, R.L.
Theory of nonequilibrium statistical processes, Zbur.eksp.i
teor.fiz. 38 no-3:825-833 Mr 160. (MM 13:7)
1. Moskovskiy goeudaretvennyy universitat.
(Probabilities) (Motion)