SCIENTIFIC ABSTRACT IVANOV, V.V. - IVANOV, V.V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000619210005-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 10, 2001
• Sequence Number: 5
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

1. 1 V
OVO. IINNIKOV, A.M.; IVANOV, V.Vv; YAROTSKIY, L.A.
Origin of carbonated mineral waters. Sov. geol. I no. ItI45-149
Ja 158, 111-10
1. Mockovekly goologorazvedoohiV7 inetitut im. 34 Ordsihonikldze i
TSentral'W nanchno-iseledovatel'skiy institut latrortologii.
(Mineral waters) (Carbon dioxide)

IYANOV irqvich; OVCIIINIIIKOV, Alekaundr 149dwylottich;
_f2_1 ~A_ __
YAROTSKIY, Leon1d Ale6androvicb; Prinimla, ixchastiye TIYJWUOTA,
N.V. NWRAYXV, G.A., red.; IVANOTA, A.G., tekhn.red.
(Map of underground mineral waters of the U.S.S.R. with a scale
of 1:7,500.000; explanatory notes] Karta podzemiykIl mineralInykh
vod SSSR masshtaba 1:7,500,000; poiannitel'noin mapiska. Moskva.
Goa.nauchno-tekhn.izd-vo lit-ry po gool. I okhrane nodr, 196o.
59 P. (KIRA 13:12)
1. Gidrogeologicheskoye otdeleniye Gocudarstvannogo nauchno-isele-
dovatel'skogo instituta Imrortologii i fizioterapii Ifiaiaterstva
zdravookhraneniya SSSFL (for Ivanov, Ovehinnikov, Yarotskiy).
(Mineral waters--Maps)

Lvanov, V. V. S07/7-58-5-9/15
AUT40R: r -1
TITLE: The Chief Stages of the Hydrothermal Action of Lhe Volcanoes
of the Kamchatka an,' KUld-le Islands and the Types of Ther_,,al
Waters Connected With Tnem (Osnovny.7e st;;,dii C.,idrotermal'ncy
deyatellnosti vulkanov Kamchatki i Kurillskikh ostrovov _J
svyazannyye s nimi tipy ter-,rallriykh vod)
PERIODICAL: Geokhimiya, 1958, Nr 5, PP 473 - 485 (u,")SR)
ABSTRACT: The type and the intensity of the hydrothermal. activity of
active volcanoes is not only determined by the activity of the
deep magma centers but just as well by the thermodynamic ard,
hydrogeological conditions prevailing in the upper horizonis
of volcanic massifs. The volcanic gases nay well be separated
into the two groups known: fumarolic gases are exhalations of
high temperature, solfataric gases have a comji_-:,:Itive1y low
temperature and have been "filteredt" by iwbtavranean watf~rs.
Table 1 gives the division and the qualitative investi,:-,atiorl
of these. In table 2 the measuring results obtained are given.
In the Kuril-Kamchatka volcanic zone there arn four stages
Card 1/3 of hydrothermal activity to be diStinf3llil3hed: 1) The strong

The Chief Stages of the Hydrothermal Action of the SOV/1'-58-5-9/15
Volcanoes of the Kamchatka ane Kurdle Islands and the Types of Thermal Waters
Connected With Them
exhalation of chloric, sulfuric and carboxylic acid gases of
high temperature, and the formation of ultra acid thermal springs
containing free sulfuric and hydrochloric acid. 2) The hydro6;en
sulfide carboxylic acid gases of only low temptrature ccme to
the surface; acid sulfate thermal springs are formed in the
near-the-surface zones. 3) Only hydrogen sulfide carboxylic
acid gases are separated and only n.cid sulfate thermal sprinq-:s
are formed. 4) An exhalation of steam without any considerable
admixtures of gases; this is produced by highly overheated
underground waters. The dif-'erent types of thermal springs
are dealt with and explained by means of analyses- acid sulfate
thermal springs (Table 3), acid chloride or sulfate chloric
thermal springs (Table 4), alkali ohloride thermal springs
(Table 6). In table 5 the acid the:7mal springs are compared to
one another, in table 7 the alkali chloride th-ermal springs
are compared with those of similar areas. The alkali chloride
springs were formed by the thermal action of t1ne active vole-Inic.
centers; they are highly overheated, and they u!~iually have a
Card 2/3 low mineralization and a low gau factor (c0 'A"'j. The borl-,
2' ,

'~011
The Chief Stages of the Hydrothermal Action of the .) /7-58-5-9/15
Volcanoes of the Kamchatka antlUrlle Islands and the Types of ThermalWaters
Connected With Them
and silicic acid content are considerably increased. These thermal
springs may be used for the production of power. The following
scientists assisted by carryina out analyses:I-S.Krasnikovaq
S.S.Krapivina, Ye.F.Prokoflyeva, Ya.P.Ryabichkiiia. There are 7
tables and 19 references, 14 of which are Soviet.
ASSOCIATION: Laboratoriya vulkanolog:Li All SSSR, Moskva (Idoscow,Laboratory
for Volcanology,AS USSR)
SUBMITTED: March 27, 1958
Card 3/3

IVANOV, V.V.
Formation and distribution of thermal watero in Kanchatlui.. Trudy.
Lab.vulk. no.13:186-2111 '58. (MIRL 12:3)
(Kamchatka-Springs)

VLODAVETS, V.I., red.; DERGIMOV, I.D., red. [doceased]; IVAINOV, V.V.,
red.; MAKARMO, P.A., red.; KNITAROV, U.I.,
L.V., red.izd-va; GUS3VA, I.N., tekhn.red.
[Problems in geothermy and. practical utilization of the earth's
heat; transactions of the First All-UnLon Conference on Geo-
thermic Research, Karch 19561 ProblevXy gootermii i praktichaskorgo
ispollzovaniia tepla zemli; trudy Pervogo Veenaiuznol,,o soveshcha-
niia po geotermicheskim issledovaniiam, mart 1956 g. Hoekva.
Izd-vo Akad.nauk SSSR. Vol.l. 1959. 254 p. (MIRA 12:10)
1. Laboratoriya -,nilkanologii AN SSS~ (for Vlodavets). 2. Institut
fiziki Zemli AN SSSR im. O.Yu.Shmidta Uor Derg=ov [deceased]).
(Earth temperature-Congreases)

IVANOV, V.V.
Origin and claseification of thermal waters of the prei;eut. Geolchimiia
no-5:443-450 160. (Min 13:6)
1. Iaboratory of Volcanology, Academy of Scionaes, IJvBo-S&R*, Moscowo
(Water, Underground)
P I

VWDAVETS, V.I., red.; DERGUNMT, I.D., red. [deceased],-. I"VANOV-, V.V., red.;
MAKARENKOp F.A # red.; FMITAROV, N.I,q red.; BARABANOVI L.F.p red.;
SHMMAN, V..S., red. izd-va; YEGOROVA, N.F., teldin. red.
[Problems in geothermy and the practical utilization of the
earth's heat; transactions] Froblemy geotermii i prakticbeskogo is-
poltzovaniia tepla Zeml-1; trudy. Moskva, lzd-vo Akad. nauk 33-1E.
Vol.2. 1961. 304 p. OMU 34 t 8)
1. Vsesoyuznoys soveshchaniye po eotermichaeki:% isaledovaniyam.
(Heating) fWater, 'Underground)
j il J.

IVANOVV
Gooeblamistry of cadmium in d6ponits of the De~~utatvkoye group,
(;eokt&mlia no.2:150-153 161, (MIRA 14:3)
1. Institut mineralogiit geolaiivdl i kristallvkhimii redkikh
elementov AN SMp Moskwa.
(Yakutia--Cadmiun)'; (loomorphiam)

IVANOV, V.V~
Basic geological conditiono aryl geochemical procwwes of the
formation of thermal waters in the regionu of recont volounism.
Trudy DAb,vulk,. no.19:53-68 161. (14IRA 14:9)
(Volcanoea) Oc-Isers)

TV N-.: V,V,,
!A~-ht sc,itterinny in a clang? layer, -~--tron,,-zhur, .', I no - 1
A:fl.ronorjL,-h(!-FL,;,yfi olmorvatoriyet t
urd w rs, I tx "a.

GIZHITSKIY, Aleksandr Karianovich; SHIBA.NOV,F.A., redaktor; PORUNKOVA,G.G.,
redaktor; IYAROV V.V, tekhnicheskiy redaktor
[Manual for the determination of aotronamical points) Posobis
po opredeleniiu astronomichaskikh putktov. [Leningrad] Izd-vo
Laningradskogo univ., 1955. 165 p. NWA 9:3
(Astronomy, Spherical and practical) (GeogTaphica.1
positions)
.1 P I

S/019/60/000/023/098/116
A154/AO27
AUTHORS: Mak.simov, N.I., Leleykin, M.N., Ivanov, V.V.
TITLE: A Stand for the Group Machining and Testing for Curvature and Tvist-
ing of Long Aircraft Stringers
PERIODICALt Byulleten' izobreteniy, 1960, No. 23, p, 62
TEXT: Class 62b, 5W No. 134139 (64036o/27 of September 28, 1959). This
stand for the group machining and testing for curvature and twisting of long
aircraft stringers is distinguished by the fact that,-in order to make it V/
versatile and reduce labor consumption and production coats, it is made in
the form of a sectional girder, mounted on a concrete base and having hori-
zontally installed guide bars along which a carriage moves horizontally.
This carriaire bears a vertically fixed sleeve along which it is moved vertic-
ally and fixed at a given height on a column which has brackets for the at-
tachment of lofting boards (plazovyye shablony) in its upper part. The
column is also provided with transverse base holes so that it can be mounted
Card 1/2

S/019/60/000/023/098/116
A154/AO27
A Etand for the Group Machining and Testing for Curvature and Twisting of Z
Long Aircraft Stringers
at various heights.
Card 2/2
1 ! 11 1. 1; 1 ! ; 11 1 j. .: 3
II , , I, FfT -i;,rl

S/019/601UH?023/077/116
A154/AO27
AUTHORS: Ivanov,,..-V.V., Ignatlyev, K.S., Senatorov, V.A.
TITLEt A Bearing Alloy
PERIODICAL; Byulleten' izobreteniy, 1960, Ho. 23, P- 52
TEXT: Class 47b, 9. No- 1340e6 (655778/25 of February 23, 1960). This
bearing alloy is distinguished by the fact that, in order to ensure efficient
operation of aliding bearings lubricated with low-c2ncentration sulfuric or
phosphoric acid at a specific pressure of 3-4 kg/cm , the alloy consists of
30% bismuth and 70% lead.
Card 1/1

AUTHOR: Ivanov, V.V. SOV/19-58-6-5Bl/685
TITLE: A Centrifugal Self-Suction Pump
(Samovsasyvayushchiy tsentrobezhnyy nai~o3)
PERIODICAL; Byulleten' izobreteniy, 1958, Nr 6, p 126 (USSR)
ABSTRACT: Class 59b, 2. Nr 113936 (579084 of 17 Jun 57).. Submitted to
the Committee for Inventions and Discoveries at the Ministers
Council of USSR. A centrifugal self-suction pump with an
annular ejector, switching off automatically, for removing
air from the suction pipe during starting; the ejector is
formed by the bevelled mouthpiece of the suction pipe and
the neck of the work wheel which moves in an axial direction
together with the shaft against the pressure of a spring after
the pump housing fills with liquid and the liquid pressure
rises; the design includes seal packing on the bevelled shaft
portion.
Card 1/1
~61

L,
AUTHORS: Ivanov, V.V. and Formgkiy, S.A,, '07/19-58-6-21/685
TITLE: A Turbo-Vibrator for Core Drilling (Turbovibrator
dlya kolonkovogo bureniya)
PERIODICAL: Byulleten' izobreteniy, 1958, Nr 6, p 9 (USSR)
ABSTRACT: Class 5a, 19. Nr 113501 (575523/443-55 of 29 June
1955). Submitted to the Ministry of Coal Industry
of the USSR. A turbo-vibrator for drilling in
cleft rocks. The vibrator is placed in the drill-
ing column on a ohaft coaxial vith the column, and
connecied through an elaotic couplin,- tuo a hydraul-
ic turbine. The design givos trz.~nsve_ro,%~ vibrations
to the drillina tool.
Card 1/1
I ?I,j ILI'

04"b`11abod on the basid of y y.ar.,:f,:tudy that by
mans, of Larol. of negative polarity 1, 11 sible to
V"se the Resistance of tb~, oranism to the effect of-such
at-- factor as oxygon d-ficiency. acute lose or blood,
Lslctozlnm.swA allerga= responsible for ansphylactic
=
4bo4k. Negative asrolons increase the roalszance of the or-
-triLl-Ins. The au.
flamism to cooling sod to tbip effect or &&
thor thinks that this affect is &a"--P1Izhad rim the
(Zlow) In. bla rc-port 'On the Ma"nim
S.N RM
of the Act;z " nizatUm" advanced his idea that core-
&OWIF represent a sul-geocrLa physiological stimulator which
9 It:ieff"tivia sk1b vszoptcrz. T-1- rtf~lex mechanism
-T * -- -
fFf V 44 on a,. -.4 Is cz.-~-,kted by dUrt-rent rssp=.Aax
%WM stiMmUtion; of various *kln notamerest The author also
Obo". Mat V32der the effect of Ions a cmauctLon current
crigIrAtes In the tissues; the author soceeaded In offactirg
6100trOPhareels by mans of sa-claw. A.M. Bkorobogat-ova
POPArted the Important role of u7per in
the, mobmim or action or the Ionised air. The author de-
ManstratedL that aerclons &rrect the prot:ih composition of
4 the blood only 'after a prolonged course r action (after 40
0*0z"3); the, principal Charges take place in the bota-910-
buUn fraction. and there is a distinct difference In the of-
coat or positive and negative Ions.
R.A. X%SEEa9yjrA (Tashkent) reported cc the affect of
b7drosereLonization an the oxidation-raductic,= proce3mos.
Go the basis of experimatal investigations of the gas con-
'k4at In the blood and the residual mount of oxygen In the
bleed and urins,- the spaskar arrived at the conclusion that
b7droasmLoalzation In a darlmito dosage increases the OxL-
datical-reduction Wocesses. In another report Katsonovich
showed that UrAer the effect of hydroaaroicalzation there Is
IL ab"O Zaklng Place In the pbagocytary activity of the leu-
Goortea and the Indexes of Lao cutaneous &no.-gle test with
-Ww streptocoocus, allergen. I.S. YPva"Ta Moningrad) as-
tAblL4h*4 tbAt negative Ions retard the process or dying
an acute hemorrhage " have an effect = the subsequent
x4vuloatLon of the -iftsl. YU.S. Vayl, and V.V. avanov
(UnIngrad) reported on the poslt!T- ff .,I"-
tdaft or the unlpolar or bipolar 1~2.ad :*Irt.' In tb:4p=!."nM
a op
or these authors, positive and negative iota may a
ravorablo effect on various ranctional eysteras.
- . Tho exparlmutal studies of O.P. Sbtambo= showed
thef efreect of hydroscrolonization on nsFr-laseoret ion and
the FO:Ance or roflaz neebazda= of th Motion. A.Yo. ql
.3 __g&1
-Und DanIlUGhk-1- elicited by Means or experimental,
.7-
2.2
An ALI-Mloo Coftfarvncs on Avr- and P.3dro-
.rotoni.ation took place In T-sbk~t 25-28
PbT 1%0.
30t 7"rovy &L-or"lorli. 7171it~jp,jl I Lechib-
It= YWJ- 1961;
JMv 10011. 31 A%*!u1t 1961, Uhelassifial

I IVANCIV y V.V.; SHPj~jj;y,Aj,;, TEIA""ON"TYAN, N.S.
.... - - -, -
Molecular weight dist.-ibution of palymEmi in Lbl: cas-~.- of the
chain transfer and termination. Dokl. AN SSSR 161. no..'1:154-155
Mm 165. (MlF,-A 18:3)
1. Institut. khlmicheukoy fizllnoo For the solutions
of (1) and (2) holds n
X T, Pk xk1l -A. 0 if n ---~>co
k-o

Doklady Akad.Nauk 110. 15-16 (1956) CA-RD 2/2 PG - 530
This theorem is applied for the consideration of the singular integral
equation Kx - A(t 0)X(t0)+ B(to) f ,(t)dt +-A fT(t,to)x(t)dt - y(to).
Ir i T t-to )f
Here Y is the unit circlej V,A,B,T satisfy on in mll variables the Hdlder
condition with the exponents tA (0 < 1 on holds A2-B2 ~ 0.
INSTITUTIONt Novogerkasek.
i i.
F", 77" -- 7,

A
An approximate solution of singular integral equations when
the integral to taken along an open curve. Dokl.AN SSSR 111
no.5:933-936 D '56. (MIRA 10:2)
1. Moskovskiy gosudarstvanWy universitat Im. N.Y. Lomonosova.
Predstavlano akadenikom M.&. Lavrentlevyn.
(Integral equations)

AUTHOR IWOV. V. V. 20-5-8/60
TIM _-N-e-_U~136; of the Method of Moments and the OMixedll Kethod
for an Approximate Solution of SingulaT Integral
Equations.
(0 primenenit metoda momentov i "smeshannogo "metoda k
priblizhennomu resheniyu singulyarnykh lifttegral'afth
ure.vzeniy.- Russian)
PERIODICAL Doklady Akademii Hauk SSSR 1957, Vol 114, Nr 5,
PP 945-948 (USSR)
ABSTRACT The author here describes the bases of these two methods.
Only the so-called "charaoteristio" equation is accurately
investigated here. It is possible to go over to the case
of the general singular equation without any special
difficulties by means of a scheme "orked out by L.V,
KANTOROVICH (Usp. matem. nauk, Vol 3, 6(29) (1946))-
The equation
G9 - A(t )9(t.)+ 31to) j(tjdt - f(t toer (1)
0 0 Xi t - t
is assumed as given. Here a denotes the oircle of unit
radius with the center in the coordinate source. Further
CARD 1/3 A,Bgf 6. R, is true, i.e. they are steady on Z in the

20~5-,~/60
The Use of -the Method of llom,qnts an! that "Mized" Method
for an Approximate Solution of Singular Integral
Equations.
2_ 0 on a,,
sense of GELIDER: A 3 for the indsx
0 applies.
Further, A + I - I is assumed here, which does not
restrict the general character of the investigations.
The method of Moments:.The equation (1) is investigated
here as a linear equation in HILBERT'S space L2. The
approximate solution yX. is here set up in the form
(1) n k_ .6
T ak t ak.
At certain assumptions an algebraic system of equations
with respect to the unknown L c(k~ is obtained. Next,
two lemmata are given and proved. A thoorem is given for
the general singular equation'
G4? + T(t, t.)9(t)dt - f (to), to
CARD 2/3 The mixed method: On the amount of the functions 969

20-5-8/60
The Use of the Method of Moments and the "Mixed" Method
for an Approximate Solution of Singular Integral
Equations.
a norm according to the rule 11 9max 19,1 + MaX19-1
tEr
is here introduced. The closed oharsoter of H in the
sense of the introduce& metric Is denoted here as W1.
Here too a theorem on the.uniqueness of the solution Is
given.
(No Illustrations)
ABSOCIATION.: Mosoow'Statetniversity'"M.V. LOMONOSOV"
(Moakovskiy gosudar'stvennyy univetaitat im. M.V.
Lomonosova.- Russian) I
PREVOND BY: LAVRENTIYEV M.A.j member of-the.Aoademyl.29,12.1956
OU3VITTED: 28.12.1956
AV11LABLE: Library of~Congreps.
CARD 3/3
ti !P

88849
/6-4160 S/04Y60/000/007/003/058
X.2400 C1110222
AUTHOR: Ivanov, V.V.
TITM Approximate calculation of Singular IntegTals
PERIODICAL: Referativnyy zhurnal.Matematika, no-7, 1960, 57-
Abstract no-7461. Nauchn.tr.Novocherk.politekn.in-t, 1958,
67 (81), 75-86
TEXT: The author investigateB two methods for the approximate calculation
of singular integrals. In the first method the author applies the
deve-lopment in a uniformly convergent series in terms of Faber polynomials
corresponding to the continuum L, of the integral
1 f f(t)dt
t-t
L 0
taken along a smooth closed curve L and understood as a function of the
point t0E L. The series coefficients are expressed by integrals over L
which contain the functions f(t) and ~(t). Here W = ~(is) is a function
which conformally maps the simply connected region D containing the
infinitely far point and being bounded by L, onto the circle 1w1--,
Card 1/4

Approximate calculation...
iLza
80849
S/044/60/000/007/003/058
C111/0222
lim
. 1. (As it is well-known, the Faber polynomials are algo
Z-3k.00z
defined by (b(z)). In the theorems 1.1 and 2.1 it is assumed that t4e
P-th derivative f(p)(t) satisfies the Older condition, f(p)(tyrz11(_-A),
0 < XA1, and it is stated that the n-th remainder of the mentioned
series is not greater than const where L> 0 is arbitrarily small
nP+N- E 1
(in theorem 1-.1 it holds p = 0, i.e. the function f(t)~6 H(X )). No
explicit expileusion for const. is given in this estimation, Purtheriore
the author considers integrals over a smooth arc L with the.ands a and
f(t)dt i,
ri 7t_,)r(t_t (2)
1
1 1 % 0) a a or c - b.
ab
Developments of this integral in more complicated series are given with
the aid of Faber polynomials. it is remarked that special cases of t4e
proved theorems are of practical interest (L-oirclee; ab-interval of~t4e
real axis, then-the Faber polyfiomials are identical with the Chebylhqv'
Card 2/4

88849
S/044/60/000/007/003/058
Approximate calculation.,. C111/C222
polynomials which deviate least from zero). The second method of the
approximate calculation consists in the followingi in a special mannqr
the are L is subdivided into n partial arcs. For a SGPILration of the
singularity the integral (1) is transformed (result: in the numerator of
the integrand there appears f(t)-f(t 0) instead of f(t)) and approximately
replaced by an integral sum (as in the quadrature formula of rectangles)
in which those terms are omitted which correspond to the ares neighboring
to the point t0 . The error - under the assumption f(t)(-H(X is not
greater than 8Hf(ln n + where H is the H81der constant, L is
n f
the length of the are, the constant M is determined by the Torm of the
arc. In the case where f(P)(t)G:H(X ), the author proposes another more
exact and more complicated formula (the values of the derivatives up to
the order -p of the function f(t) in the intermediate points axe used).
Finally, b;r a transformation of variables, the integral (2) is reduced to
the case where ab is identical with the interval (-1,+1) of the real axis,
The author investigates (under the assumption that f(X)C H(&.)) on
ana'-Iogous quadralure formula the error of which naturally increases for
an approximation of x 0 to the endpoint C of the interval (Cw-l or C-+I).
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88849
Approximate calculation...
3/044/60/000/007/003/058
C111/C222
It is remarked that the formulas contained in the paper peradt to solve
numerically the Riemannian boundary value problem-and some inverse
boundary, value problems. There are misprinte: on P-77 (line 2) an inexapt
series developmenti on p.82 in the definition of the function Q P(t,to)
the factor t-t 0 is missing-in one of the terms, on P-83, line 4 the
factor H. Is missing.
[Abstracter's notes The above text is a full translation of the original
Soviet abstract.]
Card 4/4

AUTHOR: Ivanov, V,V S6~/140-58-4-10/30
TITLE3 Some Properties of 3ingular Integrals (Nekoloryys avoystva
I osobykh integralo-v)
PERIODICAL: Izvestiya vysslt!:-,',2Lchebnykh zavedeniy.Matematika, 1958, Nr 4,
PP 89-95 (USSR)
ABSTPJ,CT: Let L be a closed Lyapunov curve in the complex plane, where the
origin lies in the interior of L. Let H(p+ 0~,L) be the class of
functions defined on L, the p.-th deriyative of which satisfies the
Hblder condition with the exponent u_ Lot If n be the set of
polynomials 0( tk and
2~ k
n
~n( f,L) - inf sup )f(t) - Prlml"
Pne 'r-1 t 9- L
As it is well-known, the singular integral sf = -1 f f(t)dt
Ki t-t
to%~~_L, _~~:,iuprehended in the sense of the Cauchy principal value,
for 0 -_ , belongs to H(p+ o(, L) together vri th f.
Let f(t)';_:Z~p~, tC--L denote that
f(p) . f~pl [t (94h.)_1 + f(p) '
Card 1/2 2 Lt(.9-03- 2f~P)[t(s)]. 0(h).

T!, -,Vv
Some Properties of Singular Integrals SOV/1,40-56-4-10/30
Theorem,~ f C. Z(p) on L together with, sf , P-1
Theorem.-, From f C-2,(p) on L there fol'Lo*s,-, ~,(f,L) - 0(n'"
Theorem 7 If for every n> 0, 1? f,L) - O'n"P"" then f r-- Z(p) on L.
n
Theorew If for wiery integial In. ;~O holds ~:,(f,L) - 0(n
then 12 (sf,L) - 0(n-9-") and xeversely~ O(n-P-) implies
~n
3n ( f , L) = 0 (n'
There are 8 references, of whArh a-re Oloviet, and I American.
ASSOCIATION,F'ostovskiy inatitut sel-lokokhozyaystyennogo mashinostroyeniya
(Ros~ov institute for Agricultural Machine Construation)
SUBMITTEDs January 27., 1958
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AUTHOR- --lyanov., V-Y,
TITO't Some Properties of Singular Integrals of the Cauchy Type and
Their Applications (NakotoriLre evoystva Dsobykh integralov
tipa Koshi i ikh prilozheniya)
PERIODICAM Doklady Akademii nauk MR, 1956, Vol121,Nr 5t PP 193-794 (USSR)
ABSTRACT: Let L be a closed simple Lyapunov curve. Lot the origin of the
complex plane lie in L., Lot the function f(t) be defined on L,
lot Sf - 1 f(t)dt 9 t C-L, be improper in the sense of the
1-11ci f t-t
L
Cauchy prin4,ipal value. Let Z(p,L) denote the olasi3 of those
N
funations defAned on L for which f(p)[t(.,h)j.f(P)jt(.-h)] -
-2f(P)[t(a)j - O(h), where a means the abscissa of axe of the
point t(s)-CL. Let Sn( fqL) - sup inf If(')'-Pn(t)l' where H.
P rz H t 6 L
is the set of all polynomials k
Z Y -
.n
Card 1/2 Theorem% Prom f SZ(p,L) thire follows Sf E Z (p, L) a:na conversely,

Some Properties of Singular Integrals of the Cauchy Type mnd SOV/20-121-5-6/50
Their Applications
Theorem% From f4EZ(p,L) there follows 3n (f,L) - 0(n-*P-l
and ecwr&"a3X.
Theorems If f is continuous on L, then exp(Sf)C-L 0 p'> 0.
P-x p
Theoremx From 3 (f,L) - 0(n" ) there folloiro 5,,(Sf,L)
. 0(n'-p tz ) , 0 0 N --:;.'a)
Card 3/4 then beginning with a certain N it holds

0; :!! I U1 ;1 i It II If 111
Approximate Search of all Solutions of a Given 1;0',r/2C-- 126- 6- 5/67
Linear Equation in a Banacb Space
PH K X n C K nit C'-- 0
ThEre are 6 references, 4 of which are Soviet, I Polish,
and 1 American.
ASSOCIATION- VychislitelInyy tsentr AN USSR (computing Center AS Ukrain.
SSR)
PRE3EITTED: February 16, 1959, by 14.11. Bogolyubov, Acade;mician
3UBMITTED: February 12, 1959
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