SCIENTIFIC ABSTRACT SHIROKHOV, M.F. - SHIROKOV, A.P.
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SCIENTIFIC ABSTRACT
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11,06oo S/043/60/019/004/010/015XX
C 111/ C 333
AUTHOR: Shirokhov, M. F.
TITLE: The Application of the Functions of the Decompositions to
the Theory of Semiordered Space~ %~
PERIODICAL: Vestnik Leningradskogo universiteta, Seriya matematiki,
mekhaniki i astronomii, 1960, Vol-19, No-4, pp.29-36
TEXT: The author uses notions and notations from (Ref.1) of L. V.
Kantorovich, B, Z. Vulikh and A. G. Pinsker and proposes a new
direct method for defining the continuous functions fo a
decomposition (the method renders possible a generalization to
certain discontinuous functions. )
Let E be a complete Boolean algebra, e 6 Let ~L(e) be the set
of all decompositions w ( X) of e, Letd,Lbe the set of all decompo-
sitions(,j(A) at all. It is putWl;k !,J OW2 F- JI(e),
if from it follows w 1((") Z W2?A)-' W1 and W 2 are
called equivalent, if W 1 f~j 2 0 Simulta eously.
and - W 1 h lds n
Lu 2 4~
Theorem 1.SL(e) is a complete structure (proof in (Ref.1)).
Definition 2: Let F( u,v) be a real continuous function defined
in the whole plane, Lj - r),
Card 114 1 ' Lj 2 ~j . Let the decomposition
M907
S/043/60/019/004/010/015XX
C 111/ C 333
The Application of the Functions of the Decompositions to the
Theory of Semiordered Spaces
W 3 F( W if1i 2) be defined by W 3 l.u..b. (b) -(41(a)]
/~'E 2(d) W 2(c)j~ , where l.u,b. is carried out over all
sebments 1a,b; c, d] for which It is
a, b; c,d e- (F(u,v) 4
(u'v).
Theorem 2%. Definition 2 gives a decomposition, i. e.
G) ~jj'-' ) satisfies the usual definition (Ref..1).
3 - 2
Theorem 5: Let F(U'V) and 4 (U.V) be real continuous functions
defined in the whole plane. Then: 1.) If F(u'v) - '~(u,v) every-
where exnept the set E which has zero weight relative to the
decompositions (,U,, W 2 , then it is F(W 1s Uj 2) - 0((.l?'-j2);
?. ) if F( r-IJ I GJ2) = P W I, W 2), then it is F(u,v) = 0 (u,v)
everywhere except the se t E which has zero weight relative to
W1 and Cj 2'
Card 2/4
84907
3/043 60/019/CO4/0'0/015XX
C 111~ C 333
The Application of the Functions of the bccompositions to the
Theory of Semiordered Spaces
Theorem 4: Let F lk(u,v), F2k(u,v) (k - 1,2, m),
4 (u,v)' (~2(u. v) be real, continuous, defined in -the whole plane.
If from F (u,v) = F (u'v) (k = 1,2,...,m) it follows that
Ik 21-
':~I(uiv) ':~2(u'v)"Where u, v are real numbers, then from
F I k (w 12) F ( WiYU)") k = 1,2,...,m) it follows that
( S'J'W
'~'2 2 1 ' `2
Theorem 5: The setAof the partitions of the unit of the algebra
with introduced partial order and linearization is a K-space,.
(Proof see (Ref.1)),
Theorem 6: The K-spaced% of the partitions of the unit Df the
algebra contains the unit and its basis is isomorphic to the
initial Boolean algebra (proof see (Ref.1)).
Let X be a K--space -vith unit, E (X) - its basis - a complete
Boolean algebra. 2L.(X) = K the space of the partitions of the
unit of E (X), To every x E: X there corresponds its characteristic
Card 3/4
8007
3/043/60/019/004/010/015XX
C ill/ C 333
The Application of the Functions of the Decompositions to the
Thee-.ry of Semiordered Spaces
x "'~ (X) consisting-
I L M . wiie re c-iA e 'A The subset of
of all charac teris tics is called JV ,
Theorem 7: Every K-space with uni.t is isomorphic to the normal
subspace 1 W, where ~~' is complete inil (X).
There are 2 Soviet references.
Card 4/d
IOGIN, M.I.; SHROEVISKIYt DA.
Nolselezs vibratory c3nveyer. HashinostrAtel' no.11-8 11 '61.
(MIRA 14:11)
(Conveying machinery)
b.
01.
4247. S-;,*LiOKIY, B. -- U direktivakh kh s"yezda kompartii ChakhoslovELkii no sostav-
laniyu n1ana razuitiyu rLarodno--o kliozyaystva n& 1933 God i o kratkosrochnom
Plane znachitel'noco uvelicheniya sel'skokhozyhystuennO.-O Droizvodstua v
blizhavshie 2-3 goda. Doklad na X slyezde kompartii Chekhoelovakii. M.
uosnolitizdat, 1954. 56 c. 21 cm. 100.000 ekz. (1-25 tys.)
60k. -- (54-58029)
SU: Knizhxittyu Letopsis', Vol. 1, 1955
BUIRANKOV, G.D.; SHIROXIT, D.K.
Slactronic device for the automatic control of batching apparatus
Avtomatyka no.2:104-106 157. (KM 10:8)
1.Kiivskiy ordena. Lenina politakhnichniy institut.
(Automatic control)
KOMAROV, Gannadiy Pavlovich, insh.; CHEKHOVOY, Yurly Nikolayevichp
lnzh.; SHIROKIY D K kand. tekhn. nauk, retaenzent;
SAVCHENO, L.Ta',; ini-iA., red. izd-va; MATUSEVICH, S.M., tekhn.
red.
(Automation of industrial processes in a thermal electric
power plant)Avtomatizatsiia proizvodstvennykh protsessov teplo-
voi elektrostantsii. Kiev, Gostekhizdat, USSR, 1962. 116 p.
(MIRA 16:2)
(Electric power plants) (Automatic control)
SOV/ 137-58- 9 -20Z19
Tranilation froin: Reterativrivy zhurnal, Metallurgiya, 1958, Nr 9, p 299(USSR)
AU'moits Yakobton. 1.I., Shirokiv, P.L., Khil'ko, N.L. Chubarov, L.B.
'r rr L E 'rec hn:cal Quality Control With Gamma Rays From Radioactive
Cobalt C060 (Tekhnicheskiv kontrol' garnma-lucharni radso-
aKtivnogo kobal'ta C060)
PERIODICAL~ Sb. nauchn. tr. Tashkentsk. in-t inzh. zh.-d. transp., 1q57,
INr 7. pp 131-14Z
ABSTRACT De", r-bed are -y-ray emitters, apparatus for flaw dete(tion
with -y-rays, methods for plotting gamma-diagrams, and the
sensitiv:tv of the method of flaw detection with ~ -ravs. The
i7nethod it, developed for the utilization of the GUP-Co-0.5-1
installation for ~, -ray examination of steel 10-170 mm thick.
For small thicknesses of steel ( - 10 mm) it is considered
feasible to use C060 provided that the focal di9tance is
increased to 40-50 cm and that Pb electrons Telectrodes?
Trans]. Notej are used. I. Steel-IncPecti.cr. 2. Ga=;', Z,;- 47-p cr-:,,
Gan:rr. _-,V anaIys,_'.3--EquID.7en' 4. CobP.It i ootopt!n T. R.
L U
(HPd ' c= r! tve)
Card 1/1 1 . Anc e
SHIROKIT, P.L.
Casting shot-blasting turbine parts from high-manganese steel.
Lit. proizv. no.1:48 A 159. (MIRA 12:1)
(Founding)
SHIRGKIY, P.L.
Introduce new technical methods and equipment In diesel locomotive
repair plants. Elek. I tepl. tiaga 5 no.30-7 Mr 161. (MIRA 24:6)
1. flachallnik Tashkentskogo proyektno-konatruktorskogo byuro
Glavnogo upravleniya lokomotivoremontnymi I vagonoremontnymi
zavodami, PO romontu teplovoeov.
(Diesel locomotiveo-Repairing)
- SHIROKIYI V.
Attention, readers.
Energetik 9 no.5:40 MY 161.
1. Zaveduyusbchiy otdelom spetsvidov tekhnicheskoy 3-iteratury-
Gosudarstvennoy publichnoy nauchno-tekhnicbeskoy bib)ioteki
SSSR.
(Technical Libraries)
Yarel [ZIvny, Krim!]; - SIIII-IOKIYJ.V.A. [-txanslatori; VAYSFELID)
I.N., red. (deceauedjj XHIMOVA, N.A., takhn. red.
jElectric heating of trainsj Maktrichaskoe, otoplenie zhelezno-
dorozhnykh sostavov. Yoskva,, Voes. izdatellsko-poligr. ob"odine-
rde 14-va soobabcbeniiap 1961. 54 p. (HIM 15:2)
(Czechoslovakia-Railroads--Cars--Natir-g and ventilation)
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5111ROKI V. F.
"Thic-ory of Ncri-linear Helations and the Quality of Irritation."
Rep~rt presented at the Pharmccology Conference, Ryazan, 17 1'9 June l.;'154
SHEKKIY. V.V., otv.red.; ANCKHIN, F.K., red. (Moskva); DVOYNINA, A.P..
red.: LABUTIN. I.I., red.; LIXVIKOV, G.S., red.; ROBINS(W.
V.Te.. red.; SAKWOVA, O.S., red.; FROLOV, Tu.P., red. (Koskva)
(Abstracts of reports of the Scientific Conference in Honor of
the 110th Anniversary of Ivan Petrovich Pavlov's Birth, 19591
Tesisy dokladov Nauchnoi konferenteii, pooviashchannol 110-i
godovahchine so dnia rozhdeniia Ivana Petroviche Pavlovs. Rlazan',
1959. 224 p. (MIRA 14:2)
1. Unuchnsyn konferentsiya, poevyashchennaya 110-y godovahchine
so dnya rozhdaniye Ivans Petrovicha Pavlova. 1959. 2. Kafedra
fiziologii Ryazanskogo maditsinskogo institute imani skedemika
I.P.Pavlove (for Shirokly). 3. lafedra nornallnoy f12iOlOgii
Rytizanskogo maditsinskogo institute imeni Bkodemiks I.P.Pavlova
(for Dvoynina). 4. Kafedra fiziologii zhivotnykh Ryazenskogo
sellskokhozyaystvanncgo institute imeni P.A.Kostychava (for Labutin).
5. Dom-mussy akademike I.F.Favlovs, Ryazan' (for Linnikov). 6. Ka-
fedre anstomii i fiziologii Ry82anskogo pedagogichookogo institute
(for Robinson). 7. Kafedra normallnoy fixiologii Ryasanskogo me-
ditsinskogo Institute imeni skademika I.P.Pavlova (for Sakharova).
(=VMS STS-im)
SHIROKIY, Y.F., prof.; SAKHAROTA, O.S.. dotsent. red.; SMIRMOY. N.I.,
_ta.1chn-.red.
[Now data In the development of I.P.Pavloy's teaching an the
circuit-closing function of the brain and the problem of
Inhibition: speech to the anaanbly, October 20, 19391 Novys
dannye v rnzvitil uchanii I.P.Pavlova o zar7ki-tallnoi funktaii
golovnogo mozge I problemn tornozhaniia; ektovais rech' 20
oktiabrio 1959 goda. Riazan', Riazanskii mad. in-t im. akB-
demikti I.P.Pavloyn. 1959. 41 p. (MIRA 14:5)
(INHIBITION) (PAYWY, IYAN PETROVICH, 1849-1936) OMAIN)
- Sill "-.OKl-Y. j V.F.
Problem of functional changes in the spinal cord of frogs during
stimulation of the optic thalami,with sodium and magnesium salts.
Fiziol.zhur. 47 no.5:575-581 My 160.' (HM 14:5)
I
1. From the Department of Physiology, I.P.Pavlov Medical Institute,
Riazan.
(SPINAL CORD) (SMIUM CHLORIDE"PHYSIOLOGICAL EFFECT)
(OPTIC THLIJUMS) (MAGIIESiWIL-PUSIOLDGICAL EFFECT)
.i
z
Organllzatlon, taskii and results of a prcfcund atudy
Influence of working condit!cns on the organism of
workers of the Ryazan Ccmbine of Ar!--ificlal Fitmrs.
trudv Riaz.med.Jni;t. 23-3-9 163.
CHIm.~11, r,..P.; Vd.; K.UIkSiM-VICH,.V.I.
N,sw siipplf-.mentary oFeratlng program for the Al-100-1 pulse height
analyzer. izv. All 33S.R. 35r. fiz. 29 no.7sl23.1,1235 J1 165. (PIRA 18g7)
n z7 0 r; r. OIL. "ov.
o-, Acces-.-ions, 1,,;, Nj.
SHIROKOGOROV, M.M. - -- - --- --- - - - - --
Gelatin from whale sinews. Patent U.S.S.R. 77,281, Dec.31, 1949.
(CA 47 no.19:10262 '53)
. ------ -. -
jjT'.()*.C,LOA,V, O.G. (Yani:-u-.~,h)
fLnctj'.o-.-.. :~it. v ahkolc no. ':-D lk-~O.
I (Fklrc.*.i-o.,.., --'.qjc'.'c:;tiRl) 14.:-),'
3 ': '~ TL - 7 ,T- V .
b1l; I ~ulD, 11. V. -- "Lit,dt Laws of Calculation for Heterogeneous 1-';arkov Chains
'-~.'Jth Two Conditions." Sub 2c, Jun 52, I%oscow City Pedagopical InBt Irkni
V. P. PotevJln. (Dissertation for the Degrep of I;andidate in Physicom-the-
matical :~clences)-
SO: Vecherna-,,a i-:oskva January-Decerler 191"2
ALrokorad, B. V. On the applicability of the central limit
theorem to MarkoT Chains. lzvestiya Akad. Nauk
SSSR. Ser. Mat. 18, 95-104 1,1954). (Russian)
Let j. be the sum of the first n variables of a Nlarkov
chain with the two states 0, 1 and mth transition ma-
trix [.P,jl, where Pit-am-, pqj-bm-#, O