SCIENTIFIC ABSTRACT YEFIMOV, N. V. - YEFIMOV, S.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001962410003-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 19, 2001
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

16(1)
AUTHORS: Yefimov,N.Y.,, and Stechkin,S.B. SOV/20-127-2-5/70
TITLE: 1-irome Supporting Properties of Sots in Banaoh Spaces and
Chebyshev~- Sets
PERIODICAL: Doklady Akademii nauk SSSR,1959,Vol 127,Nr 2,pp 254-257 (USSR)
ABSTRACT: A set M of the metric apace R is called a Chebyshev set if to
every xE R there exists only one y 9-M such that S(xy) e,(x,M),
where .9 denotes the distance. Let X be a Banach apace, lot E a be
a sphere of radius a. The a-closure of the set MCX is the inter-
section of the complements of all open E a which do not intersect
M. M is called a-convex if it is identical with its a-closure. It
is proved that every bounded compact Chebyshev set of a uniformly
convex and smooth Banach space is convex. The properties of a-
closures and a-sets are used essentially for the proof.4 theorems
and 2 lemmas are given altogether. The authors mention Shmullyan.
There are 14 references, 3 of which are Soviet, 2 American,
1 Dutch, I Polish, 4 Italian, and 3 Danish.
ASSOCIATIOX:Moskovskiy gosudarstvennyy universitet imeni M.V.Lomonosova
(Moscow state University imeni M.V.Lomonosov)
PRESENTED: March 20, 1959, by ~.S.Aleksandrov, Academician
SUBMITTED: March 17t 1959
Card 1/1

UJIMOY.~,,$I-kplay_-,~indimirovieli-,_ SOLODKOYt'Y,-A~-i~ rod. TUKARKINA: N.A..
tekhn.red.
[Short course of analytical geometry] ]Eratkii kure analiticheBkoi
&-oomstrii. Izd.5., stereotipnoo. Moskva, Gos.izd-vo fiziko-
matem.lit-ryo 1960. 256 p. (MIRA 13:7)
(Geometry, Analytic)
q44R"; AP-
Qw,
wt;
-VA R-F

YMIMOV, N.V.
ffstudying the possibility of imbedding -negative cm-yature surfaces
into three dimensional space" by II.V. Zfimov and E.Heinz. Hat.
pros. no-5:243-246 160. (MIRA 13:12)
(surfaces of constant curvature)
ag ig
z -R"Me 9-71~1 if~ V:
K
NN
A

Y]WIY.GV, N.V. (Moskva)
NFundamentals of vector Analysis,* part 1: Vector algebra. Zlements
of vector analysis, b7 IA.B.Dabnov. Reviewed by N-IT. Efimov. Mat.
pros. no.5:293-302 160. ('KIRA 13:12)
(Vector analysis) (Dubnov, U.S.)

YEFIMOV, Nikolay Vladimirovicb; KOPYLOVA, A.P., red.; POLOVINKIN, S.M.,
red.
(Higher geometry] Vy~F~aia geometriia. lzd.4., ispr. I dop. Mo-
skvaq Gos. izd-vo fiziko-matem. lit-rY9 1961. 580 p. (MIRA 14:9)
(Geometry)
4M
R

YEFIMOV., N.V.
Validity of Hilbert's theorem on ourfaces of constant negative
curvature. Dokl. AN SSSR 136 no.6:1283-1286 F 161. (MM 14:3)
1. Moskovskiy gosudarstvennyy universitat im. M.- V. Lomonosova.
Predotavleno akademiXom P. S. Aleksandrovym.
(Surfaces)

YEFIMOV .N.V POZNYA.K, B.G.
Some transformations of the basic equations in the theory of
surfaces. Dokl. All SSSR 137 no.lr25-27 Mr-Ap 161. (Ml .14:2)
1. Moskovskiy gosudarstvenn~7 universitet, im. M.V.Lomonosova.
Predstavleno akademik= I.G.Petrovskim.
pl,
(surfaces)
1 li"R

YEFD(UVq N.V.1 POWEAK, E.G.
Generalization of the Hilbert tbeorem concerning surfaces of constant
negative curvature. DAL AN SSSR 137 no-32509-512 Mr 161*
IRA i
(m 14*1)
1. Moskovakiy, goaudarstvennyy universitet im.M.V.Lomonosova. Pred-
atavleno, akademikom P.S.Aleksandrovym.
(Surfaces)
MOM

28723
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0111/C222
AUTHORSt -Yefimovi -,I.V. , and Stechkint S. B.
TITLE: Approximate compactness and ChebyBeV Bets
PERIODICALs Akademiya nauk SSSR. Dokladyp v. 140, no. 3, 1961,
522-524
TEXTs The present paper is a continuation of earlier publications of
the authors (Ref. 1, DAN 118~ no. 1, 17, 1958; Ref. 2, DAN 121, no. 4,
562, 19581 Ref- 3, DAN 1271 no. 2f 2541 1959). The authors give necessa-,
ry and sufficient condition3 for the convexity of a Chebyshev set
lying in a uniformly convex and smooth Banach space. The result is
applied to the investigation of the approximate properties of the set
of rational fractions with given straight lines of-numerator and
denominator in the spaces L (p > I).
p
E M (n- 1
Let X be a-real Banach space, M -- subset of X. If x G X, y 2,
n
and lim 8 (x,y n (x,M) then the'sequence j ynI is called
n -+ oD
minimizing for x in M. Definition: The set M G X is called approximately
compact if for every x E X every minimizing sequence of elements
Card 1/*

28723
S/020/61/140/003/001/020
Approximate compactness and Chebysev ... 0111/C222
Yn 6 M is compact in M.
The set M~G: X is called sequentially weakly closed if every point being
a weak limit value of a certain sequence of elements yn G M belongs
to M.
Lemma 1: Let X be a uniformly convex Banach space. If the set M!~-_ X is
sequentially weakly closed-then it is approximately compact.
In lemma 2 the authors transfer a property proved by them in an earlier
paper for boundedly compact sets to approximately compact-sets.
Lemma 3s Let X -- uniformly convex Banach space, M -- its approximately
compact subset. Then for every a > 0 the closed a-extension M of the
set M is approximately compact. a
(A closed a-extension M of M is the set of all x 6 X for which
The set MC_ X is called a Chebyshev set if for every x 0C= X there exists
a single point y 0G X for which 5(x 0 M) - S(Xpy). The set M C X is
Card 2/~

28723
S/020/61/140/003/001/020
Approximate compactness and Chebysev... C111/0222
called a sun in X if it is an existence set (i.e.s for every x G X the
lower boundary inf S(x,y) is reached on a y0G M) and if it has the
YGM
following property: let x be an arbitrary point not belonging to M, and
let y G M be so that 9(x,M) = 9(x,y); for an arbitrary point z of a
ray originating from y and going through x then it holds:.9(z,M)-S(z,y).
Given MrX and a > 0; the intersection of the complements of all open
spheres Ea with the radius a which do not intersect M is called the
a-closure of M. The set M C X is called a-convex if i~ is Identical
with-its-a-closurs.
Theorem 1: In a uniformly convex space X, the-property of an approxima-
tely compact set to be. a sun in X is equivalent to'-the Chebyshev proper-
ty.
Theorem 21 An approximately compaot-set in a uniformly convex space has
the Chebyshev property-then and-only then if each of-its closed b-ex-
tensions is a;..oonvex for every a > 0.
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Approximate-compactness'and Chebysev... C111/C222
Theorem 3 (basic): Let X be a uniformly convex and smooth Banach space.
In order that a Chebyshev set M C X is convex it is necessary and
sufficient that~it~is approximately compact.
Lot Rmfn be tne set of all rational fractions belonging to the space
LPLot1j, p > 1, the numerator of which has the degree m and the
denominator of which has the degree n. From-theorem 3 it follows: for
~arbitrary m >
1 , Rm, nis an existence set in L p(p 1 but no
0, n >
Chebyshev set.
There are 4 Soviet-bloc references.
ASSOCIATION: Matematicheskiy inatitut imeni V.A.Steklova Akademii nauk
SSSR (Mathematical Institute imeni V.A-.Steklov of the
Academy of Sciences USSR) Moskovskiy gosudarstvennyy
universitet imeni M.V.Lomonosova-(Moscow State University
imeni M.V. Lomonosov)
PRESENTFDs~ April 7, 1961, by J.-M. Vinogradov, Academician
SUBMITTEDt January 12v 1961
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YEFIMOV, N. V.
"Surfaces of negative Gaussian curvature"
report submitted at the Intl Conf of Mathematics, Stockholm, Sweden,
15-22 Aug 62
R
A

YEFIMOV, N. V., and STECKHIN, S. B.
"Chebyshev sets in Banach spaces"
report submitted at the Intl Conf of Mathematics, Stockholm, Sweden,
15-22 Aug 62
A -4-:

YEFIMOV, Niko VI imirovich; CUR.YSFXVA, L.Yu., rGd.; BRUDITO,
.C---
. ... tekhn. red.
(Quadratic forms and m4trices]Kvadratichnye formy i ratritsy
Moskvaj Fizmatgiz, 1962. 159 P. (MM 15:10)
(Formss Quadratic) (Matrices)

YEFIMOV, Nikolay Vladimirovich-ICHERNYSHZVA, L.Yu.., red.; BRUDNO, K.F.,
(Brief course in.ana2ytic (gOftetx7]KratkU kure analiftcheskoi
geometrii. W.6., nerer.-i'sokrashchennioie. Moskva, Fizmat-
[7EF~I (Geometry, Analytic)
giz# 1962o A27 p. I (MIRA 15:11)

YEFIMOV, N.V.; ZALGALLER, V.A.; POGOREIDV, A.V.
Alsksandr Danilovich Alelmandran, on hiB 50th birthday. Usp.
miAt.nauk 17 no.6sl72-194 N-D 162*- (MIRA 16d)
(Aleksandrov, Alsksandr Danilovicht 1912-)
!-C~W -1
~ IfA

7EFIKOVI N.V.
Impossibility of isometric imbedding of certain manifolds with a
negative Gaussian curvature into three-dimensional Euclidean
space. Dokl. AN SSSR 146 no.2:296-299 S 162. (MIRA 15:9)
1. Moskovskiy gosudarstvennyy universitet im. M.V. Lomonosova.
Predstavleno akademikom P.S. Aleksandrovym.
(Topology)
-i 7
P 'j6.
p

YEFIMOV, N.V.
Impossibility for three-dimensional Euclidean space to contain a
complete regular surface of Gaussian curvature with a negative
upper bound. Dokl. AN SSSR 150 no.611206-1209 Je 163.
(MIRA 16:8)
1. Moskovskiy gosudarstvennyy universitet im. Lomonosova.
Predstavleno akademikom I.G.Petrovskim.
(Curves of surfaces)
M MIM I

~~ccmioN NR, APOW437 S/0039/64/064/002/0286/o32o
iAUMORI Yefimov, N, V, (Moscow)
;TITLEt Arising of singularities on surfaces of negative curvature
i SOURM Matematicheskiy*sbornik, v,. 64(106)p no* 2., 1964# 286-320
:i
TOPIO TAGS t singularity, negative curvature surface, Wl regular surf ace, constart
negative curvature, cuspidal edge., Gaussian curvature
ABSTRACT t The basic result of this paper is the theoremt In E3 on every full
regular surfacep the upper bound of Gaussian curvature is not less than zero, The
author gives a detailed proof and also investigates some mapping problems which
are used in the proof and which have other applications. Orig. art. hasi 32
;'formulas and 3 figurese
ASSOCIATIONs none
SU131-11TTED t o5Nov63 DATE ACQs 2hjun64 EPTCL 1 00
021DEt MA NO REF SOV: OTHEP: 000
FB 015
m

YEFIMOV, N.V., (Moskva)
Formation of singularities on surfaces of negative curvature.
Mat. sbor. 64 no.2t286-320 Je 064. (MIRA 170)
REM
-A,
3
.4

KLUTNIK, David ViAtorovic1q, YEF1,110-VI _1 V.y. red.; 1,101MUN"
I.Ye., red.
,f] Obomik za~,~.ch po anaJiLA.-
(Problems in analytic Ucometr-
cheoltoi georactrii. Vo!7kvpj 1,,,,d-vo "Nalika," 254 p,
(1,1111A 18-3)

r-V: %M 0V
"
.2M ~ILKYNV, V.S.; SOKOLINSKIY, Ye.A.
POSTNOV, G.A.; UFIMOL.2~hi,
Observations of Mare in 1930. Biul,VAGO no.12:12-15 133.
(KIRA 7:3)
1. Moskovskoye otdeleniye VAGO. otdal planet i luny.
(Mars (Planet))

33303
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j, (W72b06) D299/D302
I. ZLI 5 0
AUTHORS: Yefremov, A. I., Podomoshenskiyq A. L.,
Yefimov, 0. N., and Lebedev, A. A.
TITLE; Study of short-wave radiation of the sun
SOURCE: Akademiya nauk SSSR. Iskusetvennyye sputniki
Zemli. no. 10. Moscowo 1961, 3-11
TEXT; The apparatus was installed in the 2nd Soviet sputnik.
Depending on the orientation of the space-ship, the various
photon-counter units were switched on and off. The "zero" (i.e*9
the reading when the entrance window was covered by an aluminum
film 1 mm thick) was basically determined by radiation penetrat-
ing the photon-counter unit through the gaps between the entrance
window and the discs with filters. Owing to the little sensiti-
vity of the apparatus to hard X-rayso no significant increase in
the "zero"-level was observed in the polar regiona. The effect
Gard- 1/04

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Study of short-wave... D299/D302
of charged-particle flow on the readings was accounted for by
means of a special tungsten-plate in front of one of the entrance
windows; this effect was found to be negligible. Sample-readings
(taken on August 19, 1960) for a photon-counter with a BeO
photo-cathode are shown in a figure; another figure shows the
readings for a SrF 2 photo-cathode. Each iigure has 3 parts
indicating the readings for various positions of the disc with
filters. The area and thickness of the Cu, Be, A10 (")n -
filters are also indicated. The figures show the variations in
the readings due to the rotation of the space-ship. A comparison
of the curves corresponding to the SiO 2, LiF and CaF2 -filters
with,thoee for Al, (OH) n, Be and Ou -filters permitted ascer-
taining the X-ray level registered. The results of data process-
ing led to the following conclusions: (1) The radiation in the
44 - 110 range (CH) n- filter) was constant to an accitracy of
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Study of short-wave...
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+ 8%, corresponding to 1.5 -10 7 counts- cm-2. see.- 1. (2) The
radiation in the 8 - 21 R range (Al-filter) was constant
(6,,2- 104 counts- cm-2. seco-1) except for the time between 15 hr.
45 min. and 15 hr. 54 min.9 when it increased by a factor of
3.2, and also between 14 hr. 24 min. and 14 hr. 28 min., when
it increased by 63~G. (3) In the region below 8 R (Be-filter),
the radiation was very zreak and often could not be distinguished
from the background radiation of non-solar origin. (4) During
increased solar activity, the radiation in the 5 - 10 range
Be-filter) increased eleven"fold. (5) In the 1.4 - 3 range
-filter), only background radiation of non-solar origin was
M
recorded. In order to determine the energy flux from the re-
corded data, it was assumed that the spectral distribution of
the radiation follows the law of black-body radiation (Planck's
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Study of short-wave...
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D299YI)302
Law). A figure shows the dependence of output signals on sun
temperature for a receiver with BeO-photocathode and Cu, Beg A19
and (011)n-filters. Another figureshows the spectral distribu.-
tion of the short-wave radiation. It was found that the radia-
tion fluctuations are constant for wavelengths shorter than
20 R and in particular for those shorter than 10 R. The tempera-
ture of the quiescent corona was found to be almost double the
value obtained by American investigators (Ref. 3: H. Friedman,
Trans,, Intern Astr. Un., 10, 706, 1960, Cambridge Univ. Press.).
The observed flare, too, corresponds to a higher temperature
6.5- 10 6 oK as compared to (4 + 2)- 1.6 oK), There are 7 fi-.
and 3 references : 2 Soviet-bloc and 1 non-Soviet-bloc. The
reference to the English-language publication reads as follows:
H. Priedman, Trans. Intern. Astr. Un., 10, 706, 1960, Cambridge
Univ. Press.
SUBMITTEDt April 10, 1961
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a/ r0 6? Iro Y 7, 2-)
J s/169/62/oOO/008/072/090
E032/E114
AUTHORS: -Yefremov, A.I., Podmoshenskiy, A.L., I,~anov,,
Nikiforov, V.N., Yefimov, O.N.
TITLE: Filteririg apparatus for the study of short-wave
solar radiation
PERIObICAL: Referativnyy zhurnal, Geofizika,*no.8, 1962, 17,
abstract 8 G 128. (In the Symposium: 'Iskusetv.
sputniki Zemlil ('Artificial Earth Satellites')
.no.10, M., AN SSSR,.iq6i,.48-54)
TEXT: A brief description is given of the method a4d'apparatus
used on a satellite to study the'intensity of shdrt-wave solar
radiation by isolating different spectral regions with the aid of
filters. The spectral sensitivity of the pulse counting radiation 'A
detectors, the secondary electron multipliers of the open type with
BeO and SrF2 photocathodes, and also the spectral sensitivity of
the apparatus with the various filters C(Cu, Be, Al, (CH)n, LiF1
are described. The advantages of this method as compared with the
counter method are emphasised; it is possible to use an extensive
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Filtering apparatua for the study... s/169/62/000/008/072/090
E032/EI14
selection of filters with a single sensitive element capable of
covering a wide spectral region (from X-rays to the ultraviolet),
the lower sensitivity to the cosmic ray background, and the very
wide range of the counting rates which can be recorded. Provision
was made for regular zero checks and also checks of the overall
sensitivity. A photograph and a block diagram of the apparatu-t are
given, the electronic circuits (partly transistorised) are
described, and the operation of a two-lens oDtical probe of the
automatic switcl~, -which operates when solar radiation enters the
device, are described. The instrument is capable of recording
the short-wave emission of solar flares from a satellite.
8 references.
[Abstractor's note; Complete translation.]
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-,BE Mal

110881
8/101/62/004/009/012/045
B108/B186
AUTHORSi Yelietratov, A. M.s and Yefimov, 0. N.
TITLEi The influence of periodicity disturbances on the effect of
the abnormal passage of X-rays. Integral characteristics
for the abnormal passage of X-rays
PERIODICAL: Fizika tverdogo telaig v. 4, no, 9, 1962, 2397 - 2410
TEXTt The passage of X-rays through n-type Ge single crystals was in-
vestigated using a double crystal spectrometer with Bragg reflection (220)
and the crystal position (2,-2). Thick specimensiin the range,
5.14