SCIENTIFIC ABSTRACT LOZINSKIY, M.O. - LOZINSKIY, M.O.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000930630004-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 23, 2000
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ACC NRs AP7005397
sults show only slight differences in the red hardness of dispersion-hardened alloys
as determined from hardness measurements in the cold state after heating to 700-7500C
(2-3 HRC units). At the same time, the alloys differ considerably with respect to hot,
hardness: for instance V27K25 and V2OM7K25 show a hardness of 400-430 HV at 7500C
while V27K25G4 and V27K25N3 alloys show a hardness at this same temperature of only
170-190 kg/mm?. A direct relationship was observed between the hot hardness and the
cutting properties of the alloys. Machining tests using tools made from the various ai_
loys for continuous turning of lKhl8NqT steel at a speed of 33 mm/min and a feed rate
of 0.3 mm/rev taking a cut of 1 mm gave stabilities of 18, 20, 5, 3 and 3 minutes for
V27K25, V2OM7K25, V27K25N3'and V27K25G4 alloys and R18 high-speed steel respectively.
With continuous turning of 3OKhlOG10 steel, the stabiiity of V2OM7K25 and V27K25 alloyE
was 20 times higher than that of V27K25G4 and V27K25N3 alloys and R18 steel. The dis-
crepancies between hardness and cutting properties indicate that the temperature for
beginning of the a-y-transformation in V2TK25 and V2OM7K25 alloys is 920-9100C, while
the corresponding temperature for V27K25G4 and VZTK25N3 is 750-770*C. This conclusion
is confirmed by measurements of resistivity and;coercive force. Orig. art. has., 2
figures, 2 tables..
SUB CODE: 11/ SUBM DATE: l8Feb66/, ORIG REF:. 03
Card 2/2
n

OJ=GINDM, G.M. (deceased]; LOZIUSKIY, M.O.,
Thioindigoid dvps from athylbenzens, isopropylbenzens, and tert-
butylbenzone. ukr.khim.shur. 25 no.1:95-98 159.
(MIRA 12:4)
1. Nauchno-isoledovatellskiy institut poluproduktov i krasitelev
im. K.Ye. Toroshilova. filial v g. Rubezhnoys.
(Dyos) (Benzene)

LOZINSIElf, M.O.; PILIZIS, P-3.
1,5-Diaril-3-haloformazans-e Part It Synthesis of moza- and dihalo-
substituted derivatives of 1,5-41phanyl-3-chloroformaxan. Zhure ob.
khim.- 30 no-12:4002-4005 D 160. (MUA 13:12)
1. Institut organicheakoy khtmii Akademii Bank Ukrainekoy SSRe
(Pormazan)

IDZINSKIYP I
m.o. rLozynalkyi, M.0.1$- PELIKIS, P.S.
On the synthesis of arylazochlora~cetic acids. Dop.All URSR
no.4:508-510 t6l. (MIRA-14:6)
1. Institut organicheskoy khimii AN USSR. Predstavleno akaderrtikom
AN USSR A.I. Kiprianovym. (Acetic acid)

LOZINSKIY, M.O.; PELIKIS, P.S.
Synkbesis of same symetrical derivatives of 1,5-diphenyl-3-chl-
oroformazan. Ukr.khim.zhur. 27 no.5:667-669 161. (MIRAL 14:9)
1. Institut organicheskoy khimi-* AN USSR.
(Formazan)

LOZINSKIY, M.O.; FELIKIS, P.S.
1,, 5-Diaryl-3-haloformazan series. Part 2: Synthesis of arylazo-
chloracetic acids. Zhw.ob.khime .11 no-5..16,-)l-1624 my 161.
(MIRA 14:5)
1. Institut organicheskoy khImli Akademii nauk Ukrainskoy SSR.
(Acetic acid) (Formazans)

LOZINSKIYJ M.G.; PELIKIS, P.S.
1-5-Diaryl-3-haloformazan serieB. Part 3: Reaction of
arylazoehloroacetic acids with rrucleophilic agents. Zhur.
ob.khim. 32 no.2:526-531 F 162. (MIRA 15:2)
1. Institut organicheskoy khimii AN Ukrainskoy SSR.
(Acetic acid)
(Ammonia)

LOZINSKIY, M.O.; FELIKISY P.S.
'"now-
Asy=etric substituted 1,5-diphenyl-3-chloroformazan and
their reaction witb ammonia and morpholine. Ukr. kh1m. zimr.
29 no.4:414-418 163. (MIRA 16:6)
1. Institut orfanicheskoy khimii AN UkrSSR.
k ormazan) (Ammonia) (Morpholine)

LOZINSKIY, M. 0,1 PELIKIS) P. S.
105.Diary.1-3-halo;o=azans. Part 4: Reaction of vubstituted
1,,5-diphenyl-3-ohloroformazan with nuoleophille agento
Zhur. ob. khim.'33 no.i:n3-il8 163. (MIRA 16:11
1. Institut organicheskoy khimii AN UkrSSR.
(Formaxan) (Subistitution(Chemistry))

LOZINSKIYO M.O.; FELIKISO P.S.; SANOVA, S.N.
Condensation and cyclization of aryl azo chloroacetic acids.
Part I.- 4-Phenyl-substituted i~ 1,3,4-~xadiazolin-5-ones.
Zhur.ob.khim. 33 no.7:2231-2235 Jl 163. NIRA 16:8)
1. Institut organicheakoy khimii AN UkrSSR.
f%Oxadiazolinone)

WZINSKIY M.O.~ FELIKIS, F.S.-, SANOVA, S.N.
P__ &ration of arylazochloroa~e4ic a,~ids and 4-phenyl_autxit~lltuted
4P!1,3,4 -1.3,4-oxadiazolin-5-one. Ukr. khim. zhur. 30
no.1:68-72 464. (MIRA 17:6)
1. Institut organicheskoy khImij AN UkrxSSR.
i-Ae
YN-_

LOZI."ISKIY, M.O.; SANOVA, S.N.; PELIKIS, P.S.
1,5-Diary-1-3-(arylsulfonyl) formazans. Zhur.org.khi-n-. 1 no.2:314-
318 F 165. (MIRA 18:4)
1. Institut organicheekoy khimii AN UkrSSR.
-Ii

914 J-~6 6 S /00 iOuu 0 9
Lozinskiy, M. Q.; ~3.
I'LE. Syrthasl-s of
A ?Q6 7?C
Zhurval organicheskoy khimii, v. 1, nv~ 19-55,
TOPIC TkGS.- organic eynthesis, amiae, acellic acid
in studying the reaction of a-r-
i t w a-- fo imd tha t -n Ii t~- t, ti I a: I-In a ri-i*.r~:-
i.-, a.~-, arc~mar,-c nuc`e~us) witir
2x
Lrmwd by spectroscopic tnvesstlFasti-,:~..,
-Zl ~-, i,
.-aLl~a-
11/2
S,

L 52550-65
ACCESSION fa-.- Ap5ou194
rkvl)-l.hdihydro-1,2,415-tetrazine forms cherry-brawn crptals, with a yield of
T. he melting, point 15 166-16%'-' . t1lia f-or-rada GILH-, oi60~. 1, -di (21 -Ma nX7
U th
~forn,3 gray-oreen a
Tile Meltine
on, -E
inatitut organiche3koy khinii, zk,~adeuU nauk, Ukrainstcoy S&R
sc
of Grganic Chamisti-1, Acadeau of -iences, Ukralnian S.SR)

JB~l INSKTY
Condensation and cyclizatt-n r-riactArinto (it itryin?.r,
so ',is. Part 2j lsoth.loryanates and s-elenoccyanat(-a ot'
obloroacetic acids and their reactLon-- witr, arornatic ewries,
Zhur. org. kh-tm, kg
1:, InstWit nrganichemx,~y AN Ulh-311-;?,

LOZINSKIY, M.O.; PELIKIS, P.S.
Reactions of condensation and cyclization of arylazochloroacetic
acids. Part 5: Chlorides, arylamides, and acyl hydrazides of
arylazochloroadetic acids. Zhur. org. khim. 1 no.11:1970-1981
N 165. (MIRA 18:12)
1, Inatitut organicheskoy khimii AN UkrSSR. Submitted December 11,
1964.

wzii,*SXIY, 14. Ya., Engineer-14achinist
"Computing Form Tools" Stanki I Instnment, 17, Vo. 9, 1946
BR-52G59019

DYMARSKIY, Y~kov Semenovich; ILZINSKIT, Nikol#y ko4yevich;
MAKUSHKIN, Aleks dr1T.MMzWyWvx
Vladimir Yakovlevich; ERGLIS, Vladimir Rudollfovich;
OGANESYAN, L.A., kand. tekhn. nauk, retaenzent;
GINZBURGp R.I., kand. tekhn. nauk; BUMV, V.N., nauchn.
red.; CHICHKANOVA, V.S.-, red.; KONTOROVICH, A.L., tekhn.
red.
(Programmer's manual] Spravochnik programmista. (By] IA.S.
Dymarskii i dr. Leningrad, Sudpromgiz. Vol.l. 1963. 627 p.
(MIRA 16:9)
(Programming (Electronic computers))-Handbooks, manuals, etc.)
'4t

TOPIC TAGS: digieal computer, control computer
ABSTRACT: A tentative statistical appr9ach to the proble . of selecting
da mental parameters of a control-type digital corppqLa 'ICs described. The
compriPes: externall and tnternal stnrages. an ar,.1hr-netic lir~l, a
control unit, analog-digital input converters, and digit;--I -analog outpuL
converters. Storage capacities and time of operation are sought. Statis, -s are
used for analyzing the factual material accumulated in the course of desigiiing
C"r"

L 34154-65
ACCESSION NR: AT50036ZO
control computers and for processing this material by the Monte-Carlo method.
The analysis is divided into 3 stages: (1) Evaluation o~ the program capacity for
a specified count pattern; (Z) Evaluation of the program length for each of N
problems; (3) Estimation of the prograrn length and time required to solve all N
problems. The speed of operation is determined for these 3 types of problems.
(a) continuous, (b) single, and (c) episodic (incidental). Orig. art. has-
4 figures, 9 formulas, and 2 tables.
1-_-A45OCIATLON: , none ----- -
SUBMITTED: 08Ju164 ENCL: 00 SUB CODE: DP
NO REF SOV: 002 OTHER: 002
!Card -2

BAZILEVICH, Vsevolod Llvovich; BAZILEVICH, Leonid Vsevolodovich;
MUMMY; inzh., retsenzent; HOZENBMG, V.Ya.,
11, KITIFA, K.I., red.
(Gommand system and programming for the BESMI-2 computer]
Sistema komand i programmirovanie dlia BES111-2. Leningrad,
lzd-vo "Sudostroitellstvo..' 1964. 341 p. (MIRA 17:8)
"wZRJAHMu-

i.n -.h, ROZENBEPup V.Iu., An-(~it, k;ifAtaTi 3--go ranga
Metlir~ds o" otating algorithms and 'he AIIGOI-60 language.
Mar. s*bor. 47 no,.5,413-52 My 164. (MM 18:6)

L. 1599Z-66
ACC NR: AP6005012 ------- SOURCE CODE UR/O .1 20 8/6 6/00-6/001/01DOOM'
',AUTHOR: Vasillyevq V. A. (Leningrad); Lozinskiy, N, N. (Leningrad)
:ORG: none
TITLE: Automatic check on recording of algorithms in ALGOL-60
'SOURCE: Zhurnal vychislitellnoy matematiki i matematicheskoy fiziki, v. 6, no. 1,
f1966, 130-143
JOPIC TAGS: computer programming, electronic checkout, algorithmic language/ALGOL
ialgorithmic language
!ABSTRACT: A semantic method for checking:the accuracy of ALGOL algebraic problems
is proposed, The content and organization of the semantic program are discussed as~
iwell. as various additional problems associated with freeing the information from
,err i
ors. The proposed method verifies theprogram w th respect to the following
points: 1. the rulesestablished for description ofthe programs should be observ
;e
id; 2. the quantities appearing in the:program should be used in positions corre-
Isponding to their "nature"; 4. the aetual-parameters of the procedure operator and
UDC:-, 681 142.2

TIT

:C_NRi---Ap6Ql7989 SOURCE CODE: UR/0413/66/ooo/olo/oogo/oogo
INVENTOR: Basalayev, G. V.; Lozinskiy, 0. Yu.; Frenkell, P. G.
'ORG: None
I
TITLE: A method for measuring and registering the temperature in plasma electric
heating units. Class 42, No. 181845 (announced by the All-Union Scientific Research
Institute of Electric Heating Equipment (Vsesoyuznyy nauchno-isaledovatellskiy in-
stitut elektrotermicheskogo oborudovaniya))
SOURCE: Izobreteniya, promyshlennyye obraztsy, tovarnyye znaki, no. 10, 1966, go
TOPIC TAGS: temperature measurement, plasma heating, electronic measurement
ABSTRACTz This Author's Certificate introduces a method for measuring and register-
ing the temperature in plasma electric heating units based on the generalized method
of spectrum reversal. The procedure is designed for improved measurement accuracy
as well as for obtaining more detailed information on temperature field distribution.
The optical system of the pickup is mechanically oscillated with respect to the zone
being monitored 'with am amplitude greater than the dimensions of this zone and in a
direction normal to the optical axis of the pickup. Working signals are received-
when the optical axis of the pickup is passing through the zone being monitored,
while calibration signals are received when the optical axis Pf the pickup passes
Card 1/2
uDc; 536.5-OBT;533.9

ACC NRi Ap6ol7989
beyond the limits of this zone. A special device is used for scaling the signals on
the basis of the generalized method of spectrum reversal with statistical averaging
into a continuous signal proportional to the temperature of the obj.ect.
SUB CODE; 13, 09,.20/ SUBM DATE: 18Sep64

ZHURkVISVA, Z.D.; DCBROIMAVOV, F.N.; WZINSKIT, R.B.
Use of bydrocyclones at the Novo-Troitak Factory. Saldi.prome
34 no.2:14-20 7 160. (mm 13:5)
1. Moskovskiy takhnologichookiy institut pishchevoy pramy~-
ahlennosti (for Zhuravlffva). 2. Novo-Troitakly sakharnyy zavod
(for Dobronravov, Latinakiy).
(Novo-Troitsk (K Irgh iz Is tan) --Sugar machinery)
(Separators (Machines))
V A,

PESTRIY N.V.p inz-h.; KHIRIN, N.D., lnzh.,- LOZINSKIY, R.P., inzh,,
VESELOV, V.T,,, inzh.
Studying the model of a wet ash collector with a gas overfeed
system. Teploenergetika 9 no.1:11-14 Ja 162. (MA 14.12)
1. Yuzhnoye otdeleniye Gosudarntvennogo tresta po organizataii
i ratsionalizatsii elektrootantsiy.
(Gases--Purification)
(Electric power plants-Equipment and suppli.ee)
2~

VESELOV, V.T., inzh.; DAROVSKIY, Ye.T.,, inzb.;,, Zjj~aKl
jg j, R.P., inzh.;
KHIRIR, N.D.., inzh.
Adjustment and'-Eesting of type MP-VTL &+ collectors with a
4500 mm.diameter. Teploenergetika 9 no.11:42-45 N 162. (MW 25:10)
1, Yuzhnoye otdeleniye Gosudari3tvapnogo treats po organizataii i
ratsionalizatsii rayonnykh, elektrostantsiy i setey.
(Fly ash)

ticoncnming Vhn Process of Fe4erls Interpolation,"
SO: Dok. AN$ 24, ITO. 4, 1939. inst. of Mech., Univ. of Lenirimmi, c1939-.
--- 85- -A.N
iz

ItCn t.--- Stronp Converrene7e of' ~Iip- Pro--sFes of Internolation."
90:28 No. 3, 1940- Univ. of lening. Inst. of I-lath. c!040-.
. . . .. ....
i W~,

Mn the Converging Strength of t". Proce-11,,res of Interpolation."
SO: Dok. AN, 30, No. 5, 1941. Int. of Math. Acad. of 3ci. cl941-.

LOZINZ15M, S. ".
"On an Analogy Between t~,e S=. ation -f Fourier Seriel and teat of
Interpolation Trigono-etric PolynorJals," ,
SO: Dok. AN, 39, No. 3, 1q43. c19,'.3-.

LOZTNSKTY, . M.
0 subgarmonicheskikh funktsiyakh i ikh prilozheniyakh v teopii poverkhnostey.
IAN, ser. Matem., 8(1944), 175-194.
0 formulakh mekhanicheskikh kvadratur. IAN, ser. Matem., 4(1940), 113-126.
0 trigonometricheskoy interpolyataii. IAN, SER. Mateml, 4(1940), 229-248.
0 sillnoy skhodimosti interpolyatsiohnykh protessov. DAN, 28(1040), 20P-205.
Ueber singula"re Integrale. Matem. SB,, 7(49)~ (1940), 32(-'-364.
Ueber interpolation. Matem. SB., 8(5 ), (1940), 57-6s.
0 si-11noy skhodimosti interpolyatsionnykh prot8essov. DAN, 30 (1941), 334-398.
Ob analogii mezhdu summirovaniyem ryadon furle i summirovanlyem interpoly-
atsionnykh triconometricheskikh polinomov. DAN, 39 (1943), 79-84.
On convergense and smmnability of fourier series and interpolation processes.
Matem. SB., 14(56), (1944), 175-258.
Obobshcheniye teoremy S.~,. Bernshteyna o proizvodnoy triconometricheskogo
polinoma. DAN, 55(1947), 01-12.
SO: Mathematics in the USSR, 191791947
edited by Kurosh, A.G
Markushevich, A.I.
Rashevskly, P.K.
Moscow-Lenin.-rad, 1948

REP
AOU-
ON4
iN

- - ------- -
Tl~
--o
ff- art m

Wr-111. 5paces C.,, and Cw, and +Ie Converpence of Interpolation Proce--3es in Then."
SO: Dok. AN, 59, 1.11o. 8, 1948
Z~M

Vol 10.

finn ~T-e Sharp Converr- nce r~, 11-ter7olatlor. Frocesses,
50: Dok) AN, 60 No. 6, 1948.

LOZL~TS,Crf, S. If ?' '!A,?'f5o
4-1.

7T,
J2
'Zi

4.1 S kj 1.
The following result is zvpl,:.,! ;f
Let w(T4) !,ee cont!n.,,O~5

Uk"

~ . -.- , I -11V 51 ~-`
- AF
-/-
t
I
- I "1W ~ .. ..

S. 1,11. On cbe con;rl-rgtace cit in
vroce3ges for flar;c1liozs of two ~ariabjfes.
ae

MathemEttiral -RIVic"M
Vol. 15 No. 2
Feb. 1954
AncL I yn -1. S
Lo;ri.-r:kiY, S, 'M&. On the rapidi ty -of -convergence of -a
m scquf-n-"~ . o, iwear operations. Doklady Akad. Nauk'
89, 609-612 (1953). (Russian)
zijl?,!.:~ 51. On the rapidity of convergence of w
seqiie~..:- lin ear trign ii o metric polynomial operations.;
Dokladv Akad. Nauk SSSR (N.S.) 89, 785-787 (195:1).
(Russian)
'i iw author cootitiu,.; his announcements without pro3fs':
of complicated therinnis concerning linear operators oW
variotisclassesof futictiouson r0, 2r]. [See Lozinskil,same
Dokfad% KS (4, 453-456 (1949); these Rev. 10, 529 and;
(lie literature there cited.] E. He7vitt. -

1,
USSR/Mathematics - Convergence Speed 1.1 Arlr 53
"The Speed of Convergence of Sequence of Linear Trigonometric Polynomial
Operations,," S. M. Lozinsldy
SSS; Vol 89, No 5, pp 785-787
DAd -
Continuation of author's previous work (66d&% 89, No 4 (1953))~ in which he
considers functionals of the form o-T(f) E o'T(f,x) n 1 /.f(t)T(x-t)dt.,
where T is inTand f in Presented by Acad V. I. Smirnov 24 Jan 53.

L0ZINSXIYj, S. V.
USSIR/Plathematics Approximations 11 Sep 53
"Evaluation of the Error in the Approximate Solution
to a System of Ordinary Differential Equations,"
S. M. Lozinskiy
DAN SSSR, Vol 92$ No 2, pp 225-228
Considers the system of differential ey yi= f(tal,
... lyn) (i- 1,...,nl, its vector soln yi(t), the
approk Vector soln Y(t), and the vector residual
X~t)-Fw-xt). Establishes 4.theorems that de-
~termine the upper bounds of the residual error in
terms of the soln of a linear matrix (vector) system
269T77
el.z A(t)e&+ t(t), where A(t) is a matrix //aik//.
'Presented by Acad V. 1. Smirnov 8 Jul 53.

llili'4w

I ~A
N S

a

The a "a 1 u
A. S. H-v-cAcl":f-

V4

Call Nr: AF 11088-5
Transactions of the Third All-union Mathematical Congress ont.)MO
(C scow,
Jun-Jul 156, Trudy '56, V. 1, Sect. Rpts., Izdatellstvo AN SSSR, Moscow, 1956, 237 PP.
Kuahmar, M. I. (Tashkent). On some Theorems of Existence and
Uniqueness for a Non-linear Integral Equation of a General Type. 1;6-57
Landis, Ye. M. (Moscow). On Some Properties of Solutions of
Elliptic Equation. 57-58
11ozinskiyj S. K. (Leningrad). Error Bounds of the Solution
of__OFHnafy_ Differential Equations Solved by Approximate
Methods. 58-59
Lopatihskiy, Ya. B. (Llvov). On One Method of Solution of
a Basic Problem of the Theory of Elasticity. 59
Markosyan, S. A. (Leninakan). Application of "a Geometrical
Method" to the Investigations of Some Problems of Dynamic
Systems in a Plane. 59-60
Meyman, N. N. (Moscow). Some Applications of the Method
of Finite Difference to Differential Equations. 6o-6i
Card 18/8o

I
In-mrse-T=t
W th stimmry
, iri~pliait functions, and solution of - - -'~ !One
Vast. LGU 12 no-7:131-142 '5' ;"*
.1 1 ~
(Functions) ( ,, 7 ~. ,1 n,: 6)

GAKHOY, F.D.; LOZI14SKIY, S.M.;TU14ARkIN, L.A.
[Program in mathematical analysis for physicomathematics, and
mechanics and mathematics faculties of state universities. Majors:
mathematics and mechanics] ProgrBmma po matematicheakomu analizu dlia
fiziko-matematicheskikh i makhaniko-matematichookikh fakul'tetoy
gosudarstvennykh univerettetoy. Spetsiallnosti: Matemattka i
mekhaniks. Minsk, Izd-vo Golgosuniv., 1958. 6 p. (MIRA 11:3)
1. Russia (1923- U.S.S.R.) Hinisterstvo vyeahego obrazovanlya.
(Haihematice-Study and teaching)

AUTHORs Lozimaluiz,_ S-M.-DA"Ingrad) SOY/140-58-5-6/14
TITLEz Estimation of the Error in the Numerical Integration of Ordinary
Differential Eqvations I (Otsenka pogresh-nosti chislennogo in-
tegrirovaniya obyknovennykh differentsiallnykh uravneniy I)
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy. Matematika, 1958, Nr 5.
PP 52- 90 (USSR)
ABSTRACTs The present paper is the first part of a paper on error estiaa-.
tions in the numerical integration of Cauchy's problems for
ordinary differential equations. The extensive investigation
deals with rigorous estimations of the errors w1tch arise after
the performance of k steps. The present part consists of a
longer introduction, of a chapter with preparing notations and
of a number of lemmata and of a chapter with error estimations.
For a wide class of numerical integration methods the author
gives an apriori and an aposteriori estimation of the error.
In accordance with the difficulty of the problem the estimations
depend on a great number of conditions which involve and com-
plete each other in a characL'eristic way. In spite of the un-
questionable theoretical value of the investigation one is in-
clined to call in question whether the large expenditure is
Card 1/2 paid, considering the practical uselessness of the results.

Estimation of the Error in the Numerical Integration SOV/140-58-5-6/14
of Ordinary Differential Equations I
There are 21 references, 12 of which are Soviet, 4 American.,
3 German, 1 English, and 1 Polish.
ASSOCIATION: Leningradskaya voyenno-vozdushnaya Akademiya imeni A.F.
Mozhayskogo ~Leningrad Air Force Academy imeni A.F.Mozhayskiy)
SUBMITTED: December 6, 1957 (Date of Lecture)Leningrad)
Card 2/2

V)
LUTHORt LOZINSalylS.M. 43-7-9/18
TITLE: -- -dn ~theBanaci Indicatrix (0b indikatrise Banakha)
PERIODICAL: Vestnik Leningradskogo Universiteta, Seriya Matematiki,Mekhaniki
i Astronomiiq 1958, Nr.7 (2), PP 70-87 (USSR)
ABSTRACT. The paper contains the proofs for the theorems announced ten
years ago LRef.3] . Let the function X - X(t) be real and
bounded on 0 Let T11 (X) denote the complete variation
_ X
t
_
of X(t) on [0,11 - Let V be the set of functions X for which
T1
(X)< +oo. Let C be the set of the X(t) being continuous on
.
t 0
10,11 and U1 be the set of those X(t) which have only dis-
continuities of first kind. Lot x CEO,13 and XE U The following
cases may appear; 1) x - X(t) i 2) x Q [min~X(t-),X(tl3i
max~X(t-),X~~Jand x / X(t); 3) x e- [minfx(t),x(t+) i fmaxEx(t),x(t+)),
and x / X~t). Let t be no root of X(t) - x if there appears
neither I nor 2) nor 3). Let t be a simple root if there
appears only one of the cases. Let t be a double root if there
Card 1/3 appear two of the cases. Let N(x,X) denote the number of roots t
V
M

On the Banach Indicatrix
43-7-9/18
of the equation X(t) . x, -co-ex