SCIENTIFIC ABSTRACT BRUDNO, A. L. - BRUDZ, V. C.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000307110008-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 9, 2000
• Sequence Number: 8
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

ACCESSION NR: AP4013321
~,Atomic Ensrgy); Institut elektronnykb upraveyayusbobikh zashin (In-
,.;stitute of Electronic Control Machinery); Tsentrallnyoy nnucbno-
.issledovatellskiy institut komplekanoy automatizataii (Central Sci-
entifio Research Institute for Complex Automation)
SUBMITTED: OSJU163 DATE ACQ: 26Pbb64 ENCL: 00
SUB COM: CGO MN NR REF'SOV: 000 OMMR: 000
Card 2/2

BRUDNOP A.L.
Programmingl-n supporting notations. Dokl. AN SSSR 154
no.2:279-282 J064. (MIRA 17:2)
1. Institut elektronnykh upravlyayushchikh mashin.
Predstavleno akademikom P.S. Novikovym.

ADELISON-VELISKIY,, G.M.; BRUDNOJ. A.L.; KRONROD, A.S.; REZNIKOVSKIY, P.T.
System of commands for a three-address machine without address
register. Dokl. AN SSSR 154 no. 3:545-548 Ja 164.
(MIRA 17-5)
1. Institut teoreticheskoy i eksrorimentallnoy fiziki Gosudar-
stvannogo komitata po ispollzovshiyu atomnoy energii, lnstitut,
elektronny" upravlyayushchikh mashin i TSentrallnyy nauchno-
issledovatellskiy institut komplekinoy avtomatizatsii.

BPRIDNIO) AlcksanJr LIvovi.cl,i; GORYACHAYA, M.M., red.
[Introduction to programming in symbols according to
ccntent] Vvedenie v programmirovanie v soderzliatell-
nykh oboznachenilakh. Moskva, Nauka, 1965. 147 p.
(MIJA 18:11)

MWDMO, I.
Rml and iuaginary. IzobrA rats. no-7:42-43 JTl 160.
(MIRA 13:8)
1. Zaveduyushchly priyamnoy TSentrallnogo soveta
Vaesoyuznogo obshchestva, izobretateley i ratsionalizatorov.
(Technological innovations)

---- BRUDNO, I,; POLUSHKINP V.
" Approve but do not introduce". Izobr. i rats. no.7:5 J2 162.
(MIRA 14:6)
(Motor vebic:Les-&gines-Technological innovations)

BRUDN.0 L
Vivifying ions. Sov.shakht. 10 no.6:36-37 Je 161. (MIRA 14:9)
1. TSentrallnyy sovet Vsesoyuznogo obshchestva izobretateley
i ratsicnalizatorov.
(JUx, Ionized--Therapeutic use)
(coal miners--Diseases and hygiene)
wk

ERUDNO., I.
Unoultivated virgin land. Izobr. i rats. no.1:26--27 Ja t62.
O~MRA 34:12)
I* Starshiy instruktor TSentrallnogo soveta Vsasoyamogo
obahchestva izobretateley i rationalizatorov.
(Agriculture--.Technological innovations)

BRIJDVO, I., starshiy instruktor
Contribution of inventors and innovators. Okhr. truda i sots.
strakh. 5 no.5:14 My 162. (MDU 15-5)
1. TSentraltnyy sovet Vaesoyuznogo obshchestva izobretateley
i ratsionalizatorov.
(Technological innovations)

ZELENIN, Yevganly Vladimirovich; LAVKO, A.F., red.; RYVXIN, A,Z,.,
red.; ~LRUDN'Dj -L
, JL _
(Elementary manual on mechanical drawing] Elemantarnyi.
spravochnik po charchenii.u. Moskva, Fizmatgiz, 1963. 254 p.
(MIRA 16slO)
(Mechanical drawing)

BRUDNOY, G. (Voronezh)
With Initiative. HTO no-3:16 Ur '59. (HIRk 12:6)
1. Predsodatel' noveta pervichnoy organizatsti nauchno-
tokhnicheakogo nbahchnstv^ zavoda "Tyazhmekhpreos."
(Voronezh-Power presseB)

SERGETU, A.V.; MARKOV, 4.G.; BRUDNDT, G.A., inzhenar.
Cutting tool witb no-slot cbip breakers. Vast. mash. 36 no.6:
36-38 Ja 156. OMLRA 9:10)
(Cutting tools)

BRUDNDY,A.A~
Attachment for cutting rack-teetb on gear-shaping machines.
Vest. mash. 36 no.S.-68-69 956. (MIMA 9:10)
1. Syzranskiy gidroturbinrWy zavod.
(Sear cutting)

BRUDVOY, G.A.
Presses manufactured at the Vorokmzh Plant of Heavy Power Presses.
Biul.-'.ekh.-okon.inform.Gos.nauch.-isel.inst.nauch. i tekh.inform. no.7:
27-32 162. (MM 15--7)
(Voronezh-Power Presses)

_-B-WPNOY, G. A.
Automatic lines for stawning ball-bearing 37ings. Biul.' tekh.-
ek(M. inform. Gos. nauch.-isal. inst. naudh. i-te)(hi-AU--orme
no.12:32-34 162. (MIRA
(Machinery, Automatic)
(Bearing industry)

0, 9 tt 1) /\/ V ~' ~ 1P -
USSR/Human and Animal Physiology. Digestion. Salivary Glands. T-7
AbB Jour: Ref Zhur-Diol., No 12, 1958, 55697-
Author Drudnyy, A.
Inst
Title The Discharge of Radioactive Phosphorus Isotopes in
Processes of Chordal Secretion.
Orig Pub: Sov. zdravookhr. Kirgizii, 1957, No 5, 30-31-
Abstract: N3 p3~0 4 (with radioactivity of 15-500/ACurie/kg)
was iDtravenously injected into dogs-1 Subsequently,
the 113' salivary discharge curves of the submaxillary
gland (SG) were detemined for a period of 3-7 hours.
The saliva secretion was provoked by interrAttent
electric irritations of the chorda (10 second irrita-
tion time followed by an interval of 5-20 minutes).
These P32 discharge curves proved to be relatively
Card 1/2

USSR/Human and Animal Physiology - Nervous System. V-12
Ab s Jour : Ref Zhur ~- Biolip No lp 1958, 45011
Author : AaAi Brudnyy
Inst : KirGiz Medical Institute.
Title : On the Problem of the Unity of Two Signalling Systems.
Orig Pub : Trudy Kirg. med. in-t.. 1956, 8, lo5-lo8
Abstract : No abstract.
Card 1/1

BRUDNYYj A. L.
sClinics of Hypo- and AvitaninosiB of Upper RespiratorY Tract and OrPr'B of Hearing.0
Sb. Nauch Trudovp Vol. 4m pp. 156-62t 1949.
Kirgiz State Ned. Inst.

BRUDNTY, A.L.
Control of anginas and ecute catarrhal affections of the upper res-
piratory passages is the most Important task In lowering the inci-
dence of disease. Sov.zdrav.Klr. no.2:27-31 Mr-AP '58. (MIRA 12:12)
1. 1z kafedry bolezney ukha, gorla I nosa (zav. - zasluzhennyy deya-
tell nauki, prof. A.L. Bruanyy) Kirgizskogo goemedinstituta.
(RESPIWORY ORGANS-- DISFASES)

0 q u -D ~'~ Y, '~ p 137-1958-3-4632
Translation from: Referativnyy zhurnal, Metallurgiya, 1958, Nr 3, p 24 (USSR)
AUTHORS: Brudnyy, B. P., Kagan, N. B., Fel'dman, 1. A.
TITLE: Automation of Electrical Induction Furnaces (Avtomatizatsiya
induktsionnykh elektricheskikh pechey)
PERIODICAL: V sb. : Raboty M-va elektrotekhn. prom-sti SSSR po mekhaniz.
i avtomatiz. nar. kh-va. Vol 1. Moscow, 1956, pp 155-158
ABSTRACT: At the present time induction-type smelting furnaces are
operated manually. Attempts made in 1947 to control automati-
cally the voltage of the generator which supplied current to the
furnace were not successful and were, therefore, abandoned in
1951. The basic parameter, requiring automatic regulation in
induction furnaces. is Cos f . Complete automatization of the
electrical regimei automatic control of the power
factor (PF), the voltage, and the generator current. In 1955, a
special bureauof the "Elektropechl 11 ("Electrofurnace") trust
began work on the development of a PF (cos 29 ) regulator for
an induction furnace. The following design w s developed: A
special gage measures the PF of the apparatus and transmits a
Card 1/2 control impulse to a device which adds or partially removes

137-1958-3-4632
Automation of Electrical Induction Furnaces
condensers according to the nature of the impulse. During the
switching process the regulator derives voltage from the supply
generator. Positive operational results were obtained in the
first tests of the given regulator, operating in conjunction with a
regulator controlling the voltage of the generator. The number
of experimental smeltings of Nr 55 steel increased by 7-10 per-
cent; an average of 70,000 kw-hr may be saved annually, and an
operator is no longer needed to run the furnace. The annual
savings on electrical energy and wages are estimated at 30,000
to 40,000 rubles.
N. 0.
Card 2/2

POLISHCHUK, Ya.A., ifizh.; BRUDNYY, B.P., inzh.
- Automatic power regulator for charge resistance furnaces. Biul.
TSNIICHK no-7:7-11 158. WRA il:6)
(Electric furnaces) (Governors (Machinery))

MAU I =1 EXPL41-ATICr 507/"l I
? primi-only. diskrqtnykb owtonatichookIkI, miston,
No--. 191,8
Toorlys, I priwotmile -sk"-.nfkh sruo,stith-k4kh sixte,s; truiy konfor-toli
(Theory eat Application or Discrete A14toomatic Sy3teas; Transaoticna of the
cocr.~.~ Moscow, AX !"It. IcX4. 172 P. 5,000 .;.is. printed.
Acen AWzijs mck 5=. Witsionsl'nyy kc.Its- S:U* pa avtonati-
1_tttut ..t-ttki I
Zdlt~~-I B .. d, M.A. Doctor or Si.-,3, Tv.Y.
Doctar or V.A. Kate' '.k4,. C.V-14.w of
A.U. L.=-, D-L- of Sli.no. , I.S. Moroj"~ (Scloctiflo Sacrst4ry),
G.S. ftsp..'~, Do.-..r of *-bloal A.A. ?Wd~-, r4awr of T.-We.1
sol.anc-, A.T. Khraza.y. ralld.t. of T-1--lo.1 rki.zo." LA U... Uy-pltla'
D~tl? of Tach-2-1 PLe.p. Lt., 7.4. T.ypki., D..t.r of T-b.14.1
541mac..j Xd. of NhI1.h.Ig House, K.L. P~dgy.t.klyj 'moh. LI., S.G. Mrkvixh.
PMI~=g T~:Ato tr~sac%4c$ are intended for the zsmb~rv of the conferoac,o ad
oth.- I. ..,Lonatlc .~-trcl.
Confer--- .% -.h. rmbl... cf
.b'c~ on-I Applicstiia of Discrotm,
!uto'satid ZJrstas' tz'.'k P!A.'% in Xclcm ff~,o SioptoztAr Z2 -a 26, 191,9. It was
.be fL'-'- " d-A-1 1- dlallu~i*n, of the LWuS of tz. theory
of dimcr-" autc,ngt.4 my,-&= "I to PI-4-S for fut-~* develop-
*eat. perex di-sj4j a- t~.* coo~rersale tAv* beer. Ji'-dol Into four ;rvps.
1" Lb" "r3- gr"P oPti~"".'On "tt'hit; Ci'C%Its &r& di--4 an 1,11 a, *#Lbld3
of ml.7 Yet.-, Lt Particular Plant lag -anrol SYS.413 In whinh are
r--I-'z-d an to qlick ... p-.. -h- -'-d gmlp or ;.per. In
darted` " t-* -Irais " vfut*;ssis of Pulse sYsta= eallable par-tor.,
of Pula* sYst-s vIth -r-' ;r4!36 -tdtt..t., to the tW4 or
Pb'-~ LA c_--'14'~ Aa4 t1 tio. 111h"'. of
P,102. yrob~.. 'r ;-11'. 'Y'%- ~f cf a-.
P43. :or-".! ... r.- Z..A :h. 'Mr! cr:.p f -. with
t
d &I F-'o .1 "sing I-. d:,;-. t-.ta1;- _j djr-L't
fcr Lim- ~&:L-, flallj of I.e., ;,,or .2,j-
tetr-~C' -tc., or. 4-sc-.,4. Probleas
of 'lc. .r,. .. well .. '-robl- of J.-lopind
1~-.14"j 41-rtor. have b'ja '"IL~I-k: ta this V'Ap. no f-rth
P.;-j th%cr4t-=%1 -'-vats &~j cortsg pretizal opplic&..,cnj
of the tjp.~ .:I ~ctr.j y,t-,,
o-.-4
or. d.-J~Plj me pa.' V..j d_1gjtsj 46,iC.j. a,.. ... .1_ I
PAF*rx of !_rr*3tig&tjzg it-.11 at.-.*
cPtL=liz!AC -Ts~~3, rist"15 zf 3t-~ijrlz! the q!foctj _f rtriao factori on -he
; rwo . .. =: ., . ~ .a 31 a= Izg~, --A of . ~a . t..g p I.!=. Its inx "~ C-1
sYvt~. :w- of the =.r* ztvrsst!.zj c-Jestiors mc~j =ti dqr-
~stla of the srl- conference ;.per. ~.,. .1- in
I_ the ~Zra~ss^tl-v. Pora-11t!*3 and r*ferenc*3 acc=;w=y met of the Papers.
Tortano, - - I '- 7- -. 717---~-
tyb- - t -f-t- Control YAaia. for % Blc,-~~ -41'. 221
ribes a prnrramz~j control aac~,In# b*iol d"Ql0po4 for trA
AutOm,m-c c=trol or ral"te s,111 processes. Ther. or. no re,
A.T. v.:t.I_' A C=p.x
for tn. 1_07MC--ton C_TFoc--'i-
37st- vita D.Ct.1 Control yackto..
The 4~ttalo Oescrlboz scoo, =,_i2 or a blgb_sp.., discra# 2U
cort.
putor. 'k*m Is I Sceiat r.:or.cc.. rolling co,
C---",- lawmatiatj= ad Dme.jo~' of CO.P.A.Ato
7)1. utho' in DI-9-tal Pr.g.~_.j Ccatml
F,o,r-..4 :ucc CmParm' Ive so~dy of control eye,.-- umi-c dirltall
h .5 P..itlo. ."teoLs with 'n'j.
-4 with binsry c":. -1 "t.r, sY-t-., with dIsorm-. and with
4cnti-- AtIm-11 and with fricti.nal L~L*Crator
4 S.11.1, (I=IUzg I and. I English, - rhers arm 5 references,
of Oftw.rtar. of . Cc.%inwou, q,..ti_
f
convertors. TkAr. are 14

I L TT
PDLISIXIIIIIII YA.111.9 "-L-, inSh.~ _KALD._.', in--',-.;
~ B"MXF . e.
~ P., inzh.
Autolul.tic control of high-frequency sineltj
7 _r4f., devices. Vest. elcictro-
prao. 3:1 no.12.-54-57 D f60, (IMIPLA 14-'.2)
(Automatic control) furolaces)

s/lio/6o/ooo/ol2/O03/oo4
Eo4l/E421
AUTHORS Polishchuk. Ya.A,, Engineer, Treyzon. Z.L.. Engineer,
Kalinin, A.V,, Engineer and Engineer
TITLE: Automatic Controller for the Operation of a High
Frequency Melting Furnace
PERIODICAL: Vestnik elektropromyshlennostm, 1960, No~12, PP.54-57
TEXT~ The fundamental parameter to be regulated is the power
factor, The natural power factor is inductive and equal to 0,1 to
O~2. To obtain the best output from the generator, a capacitive
power factor of the order of 0,9 in preferred The correction of
the power factor is achieved by a battery of capacitors, Switching
in the capacitors has a significant effect on the voltage of the
system. e.g. increasing the capacitance by 3% increases the
generator voltage by as much as 12%- It is therefore necessary to
control the excitation current of the generator, The overall
sclieme has three separate regulators: a power factor regulator,
a voltage regulator with current limit and a circuit for
automatically changing over the electrical connections to the
generator, The capacitors are arranged in 5 sets, the value of
each set being twice that of the preceding one, It is thus
Card 1/2

s/110/60/000/012/003/004
E041/E421
Automatic Controller for the Operation of a High Frequency Melting
Furnace
possible to select 31 different capacitance vallies. The solectioii
is accomplished by an ordinary telephone stepping selector, The
third regulator is intended for setting automatically the optimum
value of the melter current by switching invarious values of
inductor, The overall effect of the system described has been an
increase in productivity of 19%, a reduction in power consumption
of 17% and a reduction in the number of servicing personnel, The
annual saving on a 100 kW installation working 3 shifts is of the
order of 50000 roubles, There are 3 figures,
SUBMITTED: May 23, ig6o
Card 2/2

Y4 049 6
AUTHORS.
27979
S/194/61/000/004/011/052
q.)/ 113 ~j i-_3 P D249/D302
Kagan, B.M., Dolkart, VJI., Voitelev, A.I. and
Brudny
~y~ B,P~
TITLE_~ A complex digital computer installation for investi-
gating processes occurring in control systems with
digital control machines
PERIODICAL-~ Referativnyy zhurnal. Avtomatika i radioclektronika,
L
no. 4, 1961, 21, abstract 4 B160 (V sb, Teoriya `
primeneniye diskretn, avtomat. sistem, M,, AN' SSSRI
1960, 288-295)
TEXT- A description is given of a complex computer installation
co,mprising the general purpose computer type 11-3, general purpose
electronic computer type MPI-WIN-8), and a two-way data converter
for the analog and digital forms of information, The installation
is intended for simulating complex automatic systems, consisting
of a controlled object (analog part) and a controlling dif~itai m,~t-
Card 1/4

27979
S/194,/61/000/004/011/052
A complex digital computer... D249/D302
chine,, In an exploratory system comprising a closed circuit, the
object and the digital machine are tied together by means of the
digital-analog and analog-digital converters. In this system the
task of the digital machine is to process the object's output mea-
sured at some instant of time, and to prepare the instructions which
are then sent to the object via converters. It is assumed that
after having received the data from the object, the digital machine
continues to process the data for a certain defined time interval
after which, it suddenly changes its output control instructions.
Then begins the "control cycle", at the end of which a new reading
is taken from the object a-Lid a new computing cycle is initiated by
the digital machine,, In the present complex installation the ob-
ject is simulated by the installation MN-8 and the function of the
calculating machine is performed by the installation M-3. It may
be noted that in general there exist three different operating con-
ditions for the kind of installation considered, If the digital
computer has the same speed of functioning as the analog computer,
the operation is carried out in the real time scale. If the speed
0 -A 9 /4

27979
S/194/61/000/004/011/052
A complex digital computer... D249/D302
instruction is given together with the address of the cell to which
the converted number should be sent, or from which a number to be
converted should be taken. By using this instruction the control
is effected of not only the converter, but also of channel switch-
ing and the corresponding switching in the computer itself. The
combined analog-digital computing installation can be put to the
dual purpose of solving mathematical problems and producing synthe-
sis of the optimum conditions for adjustment and control systems.
1 reference, Z7.Abstracter's note: Complete translation_7
Card 4/4

BARANOVA, E.G.v BRUDI-M, B.P., Inzh.; VARTANOV, Z.B., inzho
Sp;Cial Machine for regidating the charging or a b2ast. furnace.
M.f.ktrotekbnika 36 no.3L22-25 Mr 10-55.
(MIRA 18%6)

87232.
S/035/60/000/011/007/0 io
!Ft 7 0 AOOl/AOOl
Translation from: Referativnyy zhurnal, Astronomiya i Geodeziya, 1960, No. 11,
P. 52, # 11295
AUTHORS: Brudnyy, L.G., Bibarsov, R.Sh., Isamutdinov, Sh.O., Kolmakov, V.M.,
Tl=. Radar Observations of Meteors at the Stallnnbrv] Astronomical Ob-
servatory During June - December 1957
PERIODICAL: Byul. In-ta astrofiz. AN TadzhSSR, 1958, No. 24, Pp,-15-21
TEXT- In correspondence with the IGY program, radar determinations of
meteor numbers were conducted at Stalinabad from June 1, 1957. Instrument para-
meters are as follows: frequency, 72.98 Me/see; receiver sensitivity, 0.6xio-12w.
Antenna of the "radiating guide" type, consists of an oscillator, a reflector and
seven directors. It is mounted at a height of 11 m above the ground, its beam
slope is 220 to the horizon. Its directivity poefficient is 24. The width of
directivity diagram in horizontal plane is + 2_30. In the vertical plane ) lobes
are used with radiation maxima at the angles to the horizon being 22'~', and
Card 1/2

87232'
S/035/60/000/0 11/007/0 10
AOO I/AOO 1
Radar Observations of Meteors at the Stalinabad Astronomical Observatory During
June - December 1957
41030'. 'rhe graphs of monthly meteor activity are presented from June to December
1957, as well as monthly means of hourly numbers of meteors during daily and
nightly hours, which varied from 0.62 to 5.32. A number of active meteor streams
are noted.
V.N. Lebedinets
Translator's note- This is the full translation of the original Russian abstract.
Card 2/2

ISAMUTDINOV, Sh.O.; BRUDNYY, L.G.
Using radar observations in determininp radiants of meteor showers.
Biul.Inst.astrofiz.An Tadzh.SSR no.30:62-66 161. (HIRA 15:3)
(Meteors) (Radar in astronomy)

BIBARSQVP R.Sh.; BRUDIMP L.G.; KOLMAKOV, V.14.
Radar observations of meteors in Dushanbe in 1958-1959.
Biul. Inst, astrofiz. AN Tadzh. SSR no.32:32-37 162.
i (MIRA 17:1-1)

KESELIBRENER, Ye.G.; BDKSHA, V.G.; BOGUTSKIY, B.V.; BRUDNYY, O.Ye.;
K-4SATK1N, V.N. "PC ...... --.1--w ~,- z-0
Use of cybernetics in climatic therapy. Vop. kur., fizioter.
i lech. fiz. kul't. 28 no.5:404-410 M 163.
(MA 17:9)
1. Iz bazovogo sanatoriya imeni V.V. Kuybysheva, Yalta i
Instituta meditsinskoy klimatologii J. klimatoterapii imeni
Sechenova.

a it a 41 a U
A 1A a
aw 4 0
a TU lKi T(Ii-IT-1 I ~16 0 POICCISUt AMID P.00t*1191 Oil

areilmitioi method at sing
w 1"0
L farmstri
d
4 Ik
u
.
o
)
taft). A. G. Domin au
-The' 4 lion awthod of
22-4
9~10
N
-00
.
o.
.
Inctures Is SU11*1 to OPPM. the as
Loaking t we*
the "UKMtIM PKthW. It gives Unctur" with sliAlly
lower d., much lower ask content (UM64) Wit! Mitler no.

0 frons 2.5 to about 21% ID el think in mactralim thIrturis.
3 Alkaloid content may be as - as 30% lo e In bella-
"g
d
kkb GO&
gow -
"b
111ol
doomatinclure. Tnbuklt4 data show Y
tin of vakdan and belladonna doclums Mile fly the two see

"
rucibmIG. s"Illb Z
809

see

ae 0
CLAWK0011
lso., l1l.sviv. -

- 180424 -wif ov 444

1
W U IS 411M L
S -a
An a Cm 0 a w -1 W 2 v
"
T I
all 0 -a
10,
90 0 111 so**

BRUDNYY, Yu.A.
----------- . ......
The maximum modulus of a quasi-smooth function.
12 no.4:273-275 J1-Ag 157.
Usp.mat.nauk
(MIRA 10:10)
(Functions)

,AUTHORt BRUDNYYoYU.A.9 GOPENCAUZ,I.E. PA - 2903
TITLEt -Un-a-7-roW I`WR by X.N.LUZIN. (0b odnom Toprose N.H.LUZINA, Russian)
PERIODICALt Doklady Akademli Nauk SSSR, 1957, Vol 113, Nr 1, pp 12 - 15
. (U.S.S.R.)
. Received' 5 / 1957 Reviewedt 6 / 1957
ABSTRACTs In his paper on "An Integral and Trigonometrical Series" (1951)
N.N.LUZIN raised the following problems f(x) denotes a continuous
function; f (x) denotes its n-th approximation. At certain points

this approxiiation is very close and in other points it is only
remote. The problem &risen whether the measure of the point set of
the latter type of points equals zero. Everything;-,lof course, depends
in this case on the laws of the approximation. Tri~gonometric or
TSCHFABYSCHEFF's approximations are the most interesting.
The problen may also be put to foolows: Is there a measure of the not
M
for any ftfiotion f(x) which in continuous in Ca,bj , which in
ft
equal t~ zero In the case of all sufficiently great n? In the case
of the class of functions which are continuous in a half-open inter-
val the answer must be negative. A.F.TIMAN, in his lectures at the
University of Djnepropetrowakp su posed the answer to be negative
also in the case of functions f(x3 which are continuous in a closed
interval. On this occasion the measure of the set M tends towards
Card 1/2 zero, if n --p cu. The results obtained from the present paper confirm

On a Problem by N.N.LUZIN. PA - 2903
this assumption. Further, three theorems are given and proveds
Theorem It There exists a function F(z) continuous in -a,b] and
an infinite series of natural numbers nk(k - 0910-91 n 0 Ri so*)
in such a way that the inequality meoUnk (F) )0 holds for arbitrary
k. Here f(x) denotes a function continuous in [a,b], r n(f;X) the
polynomical with an 6rder (n which deviates as little as possible
from f(x) in this section, X n(f) the set of such points of the
given section where E n(f) - jf(X) - Pn (flx)l ap~~.lies. In addition
max lf(x) - P (fix)l holds good.
3n(f) -&4x,,,b A
Theorem 2t There exists a function FW continuous in [0,2%] and an
infinite series of numbers nk(k a' 0, 1 21 oo; 4 ... ) in
*6 " "14 "2
such & way that the inequality me*M(F)holds for arbitrary k. The
nk
Card 2/2, quantities ocourring In this theorem are defined.
Finally a third theorem and three conclusions re=l.ting therefrom
ASSOCIATIONt State University of Djnef rogretovsk are given.
PREBLITED BYtA.R.ZOLMOGOROV, Member 0 t e Academy
SUBMITTEDs 25-5-1956
A.VAILLBLEs Library of Congress

.1
BIZ'IDI,,IYY, Yn. A., Oand Phyn- lath Sci (d,-ss) " Stiidy ,X co,!structive
nro-,)crtics of functiom t*q= on fllo~~ of ~-. temilnl segr:~elit
and on 1 semiamis." f6propetrovsk, 1950. pp (!,in of IIJCher ;du-
cation USSR. Dnepropetrovsk 9tato V im 300th -',nniversary of tbs
lpy'nific,.-tion of the Ukraine AtiAh i~ussia). 1150 copier. -uiblioCrnphy
at end of text (11 titles-) (1:1,03-59, 113)

AUTHORt .--Bru SOV/38-23-4-6/8
TITLE: Approximation by Entire Functions on the Exterior of a Segment
and of the Semiaxis
PERIODICAL: Izvestiya Akademii nauk SSSR,Seriya matematicheskaya,1959,
Vol 23,Nr 4,pp 5105-612 (USSR)
ABSTRACT: Let Ea,b denote the set (- oo,al U [b,oo) , a 0 there exists an entire function Ga~f-'X)
of at most 6-th degree, so that for x C- E a,b it holds
:~ C + + '
1f(x)-G,7(f~x"- r (5, x _ a+b X _ a+b T2)
1 2 1 2
Card 1/3 where Cr does not depend on x and

Approximation by Entire Functions on the Exterior SOV138-23-4-618
of a Segment and of the Semiaxis
Theorem 5 : If for a certain modulus of continuity Q(~) and
for every 6' > 0 there exists an entire function G (x) of at
116,
most e-th degree to a function f(x) defined on E_ 1,1 so that
f (x) G,,(x) 0 (1zi , -L ~
61 jxj 0,2 )
then it exi sts a constant C independent of h, so that it holds
f h) 4C C h 21U1 du 0 < h -< -1 -
u2 2
Theorem 7 : Let f(x) possess r unifoTmly continuous and bounded
derivatives on [ 0, co ) , let j (f r ; h) Z LD(h) . Then for
every 6' > 0 there exists an entire function G6,(f ; x) of at
most T-th half degree (see Bernshteyn Z-Ref 1-7 ), so that for
x 6 EO,oo) it holds
Card 2/3

,A.pproximation by Entire Functions on the Exterior SOV/38-23-4-6/8
of a Segment and of the Semiaxia
f (x) - G G- (f ; x) C X r,, ( Lx: 1
, ( F -
T a,2 6' 012
Theorem I is a special case of theorem 2 for a 1
b - + 1 . The theorems 3 and 4 contain inequalities which are
needed for the proof of the following results. Theorem 6 is
the inversion of theorem 1. Theorem 8 concludes an estimation
.L
for lfl(x)j from theestimation for lf(x)l . The theorems 9
and 10 contain for the case E - LOPOO) the analogous state-
ments to the statements of the theorems 5 and 6 ~
The author mentions S.N. Bernsbteynt V.K. Dzyadyy a-nA N.I.
Akhiyezer. He thanks A.F. Timan for the subject.
There are 6 Soviet references.
PRESENTEDs by I.N. Vekuag Academician
SUBMITTED% June 12, 1958
Card 3/3

16(1)
AU TH DR: Brudnyy,fu.A. SOV/20-124-4-2/ 67
TITLE: Approximation by Entire Functions :)n the Exterior of an Interval
and on the Semiaxis(PriblizHeniye tselymi funktaiyami na
vneshnosti otrezka i po2uosi)
PERIODICAL: Doklady Akademii nauk SSSR,1959,Vol 1?4,'Jr 4,2p 739-742 (USSR)
ABSTRACT: Theorem: Let f(x) be defired or. tlie exterior E of the interval
(-1,1) and let it have thore r uniformly continuous and bounded
derivatives, where (f(r);Q (h). Then there exists a seque.1rice
of entirq. functions G (x), 0 co, of t:ie order and a
constant 0 not de~endiag on x on,- so that evqrywhere on the
exterior of (-1,1 it holJs:
X 2-1 X2_
M f(x)-G (x) C -- + + -2
X x
Theorem: Let f(x) be defined on E, let (h) be the modulus'of
continuity. If there exists a sequence G (x) so that
X2_1
f(x)-G (X) for x E
Card 1/3 x

Approximation by Entire Functions on the Exterior BOV/20-124-4-2/67
of an Interval and on the Semiaxis
then'there exists a constant,C not depending on h, so that
2
(f,h) Ch (u) du , 0 h 1
2 2
h u
Theorem : Lot f(x) be defined on E, lot (h) satisfy the
1
condition --Cul du oo. If there exists a sequence G (x)
u
0
satisfying (1) with C=1, then f(x) has r uniformly continuous,
bounded derivatives on E and
h h
(f(r) ;h) 0 h -(u) clu + (u) du , 0 h
-2 u2 0 u 2
Card 2/3

Approximation by Entire Functions on the Exterior SOV/20-124-4-2/67
of an Interval and on the Semiaxis
Similar theorems are valid if E is a semiaxis. Seven theorems
and auxiliary theorems are given altogether. The author thanks
A. F. Timan 4or stating the problem and" for'his help.
There are 4 Soviet references.
ASSOCIATION: Dnepropetrovskiy sell skokhozya3strennyy - institut (Dnepropetrovsk
Agricultural Institute)
PPESENTED: September 30, 1958, by S.N.Pernshteyn, Academician
SUBMITTED: September 25, 1958
Card 3/3

5
16(1)
AUTHORS: Brudnyy, Yu,A., Timan, A.F. SOV/20-126-5-~/69
TITLE: Constructional Characteristics of Compact Sets in Banach
Spaces and & - Entropy
PERIODICAL: Doklady Akademii nauk OSSR,1950,,Vol 1269Nr 5,-t)P 927-930 (USSR)
ABSTRACT: Let F be an infinite-dimensional separable Banach space;
X {xk ~ be a linear independent system closed in F. There al-
ways exist elements x, for which the best approximations
X n
E (X) = inf 11x c x tend arbitrarily slowly to
k k
c E;~o
zero, so that sup EX (x) where -1v is a bounded set in F,
n
YCW
-does not need tend to zero. If, however, this is- the case,
then W consists of elements for which the an-_~roximation -v-
locity of the beat approximations to zero posvesses a common
characteristic 6 X (Iff) - 811T) E"~ (N) . Let 6 be
n -- P.
Card 1/ 2 X C_ "I

Constructional Characteristics of Compact iota
in Banach Spaces and e - Entropy
the inverse function of the entropy of W. Theorem
X_ I (IV)