SCIENTIFIC ABSTRACT MARKOV, A.A. - MARKOV, A.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001032420014-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 19, 2001
• Sequence Number: 14
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

_
77 :-7.
Z

ili
I
t
l
a
iii
3479
RA
l
Ii
d
4

A

if
- s
v
2
on a re
ve
n
ve
,
mpL
s
copst
po
;aad. A- A MA%kXOV. Nn, I I
7-4, lekh. 1.
2071-

A RMC3 of IA4"Vaflans a
To

TA
foim and amplit tudi; of the patentiahicross a I~a NO

abe ~Lvrrenis. These. -l-,mvi duns nre shown to
-rot a Minlrar HC nalviA-0050 citcuil ii
:trply
77-
given. Ilic pvlent~ s cuminil for ~_\Vwjenllpl
curivit impuh--i and ciinvi ~iiv gi\vn %h-hing,
%.IlLiliou rl _-fnplitnda Ailli rcriv~mo for
f
f
j
j
orms o
IMS
&~. V.. V. ZAKYAROV
mvu

-- -V 71- il,,-
- - i V ~ 'j A ~, i ~, -, . I r) -t ~~
j, -~V 7.i -I

f
l
f th
Iff
t ;e
ann
e
me o
e
e
asurement o -s
.
m
-r~
kin
UU11sia-

MARIUN. A~.A.
Type GWI-4 pulse generntor. Sbor.kmlcb,rAb. XIFI no-9:135-144 155.
(KLAA 10:1)
(Pulse techniques (Illectronice))

I
II ~ 1 1 1 1 1~ 11 14 1 ;
GAYDAYKV. G.L.. KARKOV. A.A.; TSA7MCRODTSXV, M,11.
-
ftylee for recording out-of-phase (inhibited) coincidences.Sbar.
nauch.rab. HIPI no.9:lL6-154 055. (KW 10:1)
(Palse techniques (Blectronice))

EDZODAYEV. M.S.; TYAPKIN, A.A.; BATUKOV, Tu.D.; MARKOV, A.A.; PROKOSHKIN, Yu.D.
Production of neutral mesons by high-energy nucleons. Izv.AH 339R. Ser.
f12.19 no.5:589-603 3-0 155. (KLP-A 9:4)
I.Institut yadernykh problem Akademii nauk SSSR.
(Cosmic rays) (Nuclear physics)

EDZODAY3CV, M.S.; tA
&.j", TYAMTI, A.A.
Measuring 4r*-weson lifetime. Izv.AJI SSSR.Ser.fiz.19 ne.6:
715-719 N-D '55. (KLRA 9:4)
1.Institut radernykh problem Akademil nauk SSSR.
(Cosmic rays) (Nuclear phymice)

As oxcraD $TAT= 4w POLSOMI:

JL A. Mw~
-win*
umbsEff E-10

_iA

MUOV, A. A.
"Inversion of Comp.Ucated Systems of Functions."
report presented at All-Union Gonference in Problems in the rhe~~ry of Relay Dw_zv-_ces,
Inst. for Automation and i~emote Control AN USSR. 3-9 Oct 1957.
Vestnik AN SSSR, 1956, No. 1, v. 28, pp. 1)1-11-2. (author 0--tianu, V. M.)

";1 T
11 ILV IN , . . ~ .
F'r m rs i n ~~' i c I , ; i t * , T, s - , , I I .- a t ; t,;- :; ~ i i m., ": ~'i: 1, r , r, :: - ~ ' ne
"I L L . . I I . I
4th InternatiD!,al -'Iectrorics and liuclear i!.nerg.-; Fxhlb;tinn and ~'.-Nnforf~ncp 4r,
Rome, ijmU Italy, 24' jul 19~7
ti - I r. 1, 12 , ~ ~: ic t 5, 7

)f
1. Pulse counter5-Errors 2. Mathematical-Theory

AUTHOR.-):` A S)"'l-v 'Z.
Tl pr t~*
A.,
:3pri -7 njy u r J 1j;
PERIjDl,,AL: Ti -:,n h; :.T.
A133TRA~,T: A Li.; -iven for a )r
*
w r:, v; 1:11,, 1a , e ,-j i i:, I y -;,! r sT!
-.1 r-~ " I ril-I i L) iii.:i (Fi,,. I T
f i Lr-,
---!UB.I,IT.'ED: 3c; -t
Pulse generators--De, F _. i.
lard 1/1

SOV/ 120- 58-t'l-)-4/ 32
AUTHORS-.Bayukov. Yu D. Kozodayev 1A S-, Markov. A. A. Sina~ye-:
A~ N , Tyapkin A. A,
TITLE: A Mult2.channel Pair y-Spectrometer. I.. Calculation of thf~
Main CharacterisLics. of the y-Spectrometer (Mnogokanal ny-y
parn,yy gamma-spektrometr- I Raschet oanovnykh kharakleri
stik-gamma-spektrometra)
PERIODICAL, Pribory i teklinika eksperimenta, 1958, 14r 6
(USSR)
A.BSTRACT-
Card 1/6
In a padr -r-spect.-ometer tne energy of the quanta is dr---
termined by measuring the total energy of the components If
the elect:-on -)-~--tron pair foim,~.d -~n a thin conve:-ter Tne
first 2-cha-nnel pai: ~,pecTr(-,mRter was built by Dzhelepc-,!
(Ref Lat--- spectrometers -tuillt on this prin-r-ip.'-e we:-
widely used in. measuiing trLe sj)ectra of hard y-raye (R,--fs
to 8). The ele-tron and the posi~rozi leaving the :on-,-erte.-
were deflectpd by a maenetic field in different dir,~ction~;
;y they enter icni'--a'tion
a-nd for certain value,, cf their enerF
counters connected in coincidence, For a given intensity of
'the magnet"ir f1pld and a fixed position of th~? c-,3unters S'A;'
a spectrcmeter wil.1 r,~-cDTrl a fraction of the pairs produ,ed
by y-rays in a girt~n energy range, In a simple 21 --haane~
spectrometer in whi,-h one channel. reccrds the electror- and

-30V/ lc!O- 56-6-4/ 3.~
A Multichannel -Pair Y-s;:ec~2cmeter I Calculation of the Yaln
Chaxacteristi,:~s of the y--sp,:~-trcmeter
the other the pos4-trons, aii increase in the accuracy of
measuremenf is ass,-~ciated with a marked decrease in the
efficien,7-v- (--nerp;7 ,es~_,A~on and bigh eff4:-~en:-.-
only be in a s"Dt
_p~' b~ i -3 z:
meter- In lush a s tae effi;_--,enc,,, ms,~- -
by a fa,,tc.," w s -; f rt--, ~x o I u V iw a 2
n~ are -h- -or. an~
s ch a oer~y
at the sa-me ti-mz, A
meters ha.~e d4:7 and 8), T h -?c P'
of a a U, iT_str__r.F1-T' F
by its t-f-'z c 7
multichanxiel bjstem t is to takt; in-r-,
characteristics fcr the vari:)Ls pairs of channels of the
spectrum, In this connection, a discussion is given in the
present paper of the dependence of the efficien,-y and spe-
tral sensitivity of the separate pairs of channels oi. varicu
Card 2/6

,30V/120-58-6-4/~2
A Multichannel Pai-r y-spectrometer. 1, Calculation of the Ma,~--
Characteristics of the y-spectrometer
parameters of the spectrometer:
1) Spectral sensitivity: the basic diagram of a y-spectrc-
meter considered in this paper is shown in Fig.1, in
the meanings of the symbols employed are indicated, In view
of the finite width of the counters, the spectrometer recordE
y-quanta in a certain energy interval from E Y min to
E The corresponding spectral sensitivity curve is
Y max 01
then shown in Fig.2a and is of triangular form with a dis-
persion given by
1/6 k21 (r i- r )2 where is the widTh -,.f a
c 1 2 c
counter and r 1 and r 2 are the distances 1"rom the cor.-
verter to 41-11ie centres of the counters, respectively. The
effect of the width of the converter upon the spectral
sensitivity is examined and it is shown that a conver"~er of
a finite width introduces a spread into the spectral line
in the high energy region of y-quanta. As the angle (p
between the direction of motion of the y-quanta and the
Card 3/6 straight line connecting the centre of the converter with

SOV/120-58-6-4/31-f
A Multichannel Pair y-spectrometer. 1. Calculation of the Main
Characteristics of the y-spectrometer
the counter increases, the spread of the spectral line de-
creases. At (P = 900 the width of the spectral sensitiv-;_tv
curve is independent of the converter width. The effec- 0.'
the converter width gives a distributi3n of the forin
in Fig.2b, whicE has a dispersion given by:
4 4
2 t~ctg (P
CY2- 0 Vie effect of
laor 11 1112
scattering in trip ~ojaverter is estimated and exp;,-ez~
are derived fo.- this effect also. Finally, an r~st.--E-
given for the radiation loss experienced by the electron-
positron pair on traversing the converter.
2) Efficiency; in this section the Bethe-Heitler expressi_)n
for the probability of formation of a pair by a y-quantum cf
Card 4/6

SOV/120-58-6-4/32
A Multichannel Pair y-spectrometer, 1. Calcuiation of the _111-n4n
Characteristics of the y-spectrometer
energy E is used (Ref,13) with a modification descrIbed
b~ Bethe Yet al in Ref.,22.
3 Multichannel system: in a multichannel speci!rometer the
electrons and positrons formed by y-quanta of a giver energy
are recorded by a number of combination c-f paIrs of rounter.-~
The electronic circuit of such a spectrometer should record
coincidences between pulses from each electron counter with
pulses from any positron counter. Thus, any combination of
one electr6n coun+~er and one positron counter is, in fact. a
2-channel spectr_,,mt-.ter, For a given geometry a spectrometer
containing n channels re~aozds y-quanta in n-1 erter&v in-
tervals of different mean enerFy. In practice, one seeKs to
find the form of the spectrum and the absolute intens-it.-; in
dne of the energy intervals. To find the form of the spe,-
trum it is bufficient to know tlie relative effLciency of
recording fov the difl'erent energy intervals, and th-s is
given by Eq.(10). In order to obtain the absolute intensitv
in one of the energy intervals it is necessary to know t~.e
total absolute efficiency of recording of y.-qua-nta in ona
of the energy irtervals, This problem is not treated.
Card 5/6

A Multichannel Pair y-spectrometer. 1, Ca-Iculation of ttLe hlair~
Characteristics of the y-spectrometer
V~ V. Mel'niko~r is thanked for carrying out a number of
calculations. There are 2' figures and 2,2 referenceF cf
which 4 are Soviet, 1 German I Soviet translated frim
English and the rest are English-
ASSOCIATION: Ob6yedineri.~~y:~ .nL6C4-tut yaci~rnykh
(United Instdtut- -'-r 6i jdies~
SUBMITTED: December 2?
Card 6/6

SOV/120-58-6-5/32
AUTHORS:Bayukov, Yu. D., Kozodayev, M. S., Markov, A. A, Sinayev A
Tyapkin, A. A.
TITLE: A Multichannel Pair y-Spectrometer. II. Descriptdon of a
12-channel Spectrometer (Mnogokanal'nyy parnyy gamma-spek-
trometr. II. Opisaniye dvenadtsatikanal'nogo spektromet-ra)
PERIODICAL: Pribory i tekhnika eksperimenta, 1958, Nr 6. pp 30-40
(USSR)
A3STRACT: Application of a multichannel pair spectrometer in synchr
cyclotron work presents a number of specific requirements as
far as counters of the ionising particles and the electronic
system of the spectrometer are concerned. Since the beam
intensity is high and consists of short pulses of 200 to
300 ~is each at a repetition frequency of 40 to 80 pulses per
see, it follows that the apparatus must be very fast, It is
desirable that the input blocks should have resolving times
not greater than 1 4s. The large background intensity in
synchro-cyclotron work means that it is always necessary to
use a special selection system which records only electron-
positron pairs. For this reason, in the spectrometer each
component of a pair should be recorded by a number cf counte
in coincidence with sufficiently low resolving time- The
Card 1/? present paper describes a 12-channel y-spectrometer which ha

3OV/120-58-6-5/32
A Muitichannel Pair y-Spectrometer. II. Description of a 12-zharnel
Spectrometer
been used over a number of years in studying the spe,-tra of
hard y-rays and neutral W-meson decays (Refs.2'-6), Tnt-
first variant of the spectrometer was built in 194,,~,, .'% J91~
and 1954 the spectrometer was modified to improve itc- "p-rac
teristics, The spectrometer described here satisfiec~
pletely the above requirements and is based en t-',le dps c-:.
calculations given in the previous paper (Ref,I'l
issue.
1) MaFrnetic system and geometry of the instrumerl,
The magnetic field is produced by an SP-56 eI_ectrc;ma..-_
Fig,l shows the dispositi..)n of the counters for two
demountable pole pieces. Tne gap between the p,.,.--,;
and the maximum field in the ga,,-, is 18 000 oers~e_-
electromagnet current is stabiiised to 0.1%. in studies of
ray s5ectra in the energy region 20 to 200 MeV, 2Q = 1800
F-ig.lb and in the energy region 100 to 450 MeV, 2~p = _)OO
I
(Fig,la). In the former case semi-circular focussing of
Card 217

SOV/120-58-6-5/32
A Multichannel Pair y-Spectrometer. II. Description of a 12-chall-rel
Spectrometer
electrons and positrons was used', and this led to increased
efficiency (Ref.1) because it was possible to use wider and
thicker converters. For y-quqnta in the energy range 450-
600 MeVI 2(p = 900 but the counters were at a larger distance
from the converter. Copper converters were used (0,1, 0,3
and 0.5 mm, depending on the energy).
2) Resolving power and efficiency.
Fig.2 shows curves of the total spectral sensitivity for the
7th energy interval for various values of E YO and thick-
nesses T. of the copper converters. These curves are based
on the theoretical data given in the previous paper and are
obtained by a statistical combination of the partial distri-
butions due to a) width of the counters, b) width of the con-
verter, c) multiple scattering and d) radiation. As can be
seen, the form of the total spectral sensitivity curve is
Vacy nearly triangular, which means that the total spectral
sensitivity is governed mainly by the width of the channels
tc (see Fig.1 of previous paper, p 24, this issue).
Card 3/7

SOV/12J-58-6-5/32
A Multichannel Fair y-Spectrometer. II. Description of a 12-cha=el
Spectrometer
3) Counters and selection system. The counters used were
proportional counters having a cylindrical stainless steel
cathode, 10 mm in diameter and a molybdenum filament 0.1 mm
in diameter. They were filled with (CH2(OCH 3)2 ) at a
pressure of 160 to 200 mm. The working voltage was 1611-0 tc
2000 V. T" counters have an effective dead time not ex-
ceeding 10-1 sec. The efficiency of the counters for :~ar-
ticles with relativistic ionisation reaches 98% in a
cidence scheme with a resolving time of 5 x 10_7 se__ 7-LE;
delay of the pulses due to drift of electrons through tde
counter gas is less than 10-7. The counters give
cal pulses with amplitudes between 10-4 and 1 V. Th-
difference in the amplitudes requires the use of amplif -5
having a wide dynamic range and an amplification of a few
thousands. 6-fold coincidences were used and the number of
random coincidences in each 6-fold channel was 0,02 pulses
per sec. The number of electron-positron pairs recorded per
Card 4/7

SOV/120-58-6-5/32
A Multichannel Pair y-Spectrometer. II. Description f a 12-channel
Spectrometer
sec depended on the efficiency of the spectrometer with
respect to the y-quanta in the measured energy interval and
the form of the spectrum and was in the range 0.1 to 10 pair
per see.
4) Electronic scheme.
A block diagram of the electronic part of the spectrometer i
shown in Fig.3, The left-hand portion of this diagram shows
6 co-ordinate counters of the electron series (a 1 -a6 ), 6
co-ordinate counters of the positron series (5 1 -B6 ) and
4 selection counters (A', A"? TP and 'U"). Each of these
counters in practice consists of a group of counters whose
filaments are connected. A recorded electron or positron
should pass through 3 counters (1 co-ordinate and 2 selectic
counters). A pair is recorded if a 6-fold coincidence takeE
place. Negative-going pulses from each counter are ampli-
fied by a corresponding amplifier-converter (Fig,4). These
amplifiers have a rise time of 2 x 10-4 sec. Pulses from
all the 16 amplifier-converters are applied to the main blo(
which is at a distance of 1.5 M from the amplifier-convertei
Card 5/7 (Fig.5). Pulses from the selection counters are applied to

SO V112,)- 58-6- 5/32
A Multichnnnel Pair y-Spectrometer. II, Description of a 12-channel
Spectrometer
4-fold coincidence scheme while pulses from the co-ordinate
counters are applied to mixers and in addition th-rough delay
lines to a hodoscopic, system consisting of 2-fold coincidenc
circuits and output univibrators. The pulse at the output
of a mixer appears in the presence of a pulse in at least on
of the co-ordinate counters of a given series, Pulses from
both the mixers and also from the 4-foLd coincidenc-3 t-:,.eme
are applied to a 3-fold coincidence scheme which prod-uc;-~6 th
final output pulse. It follows that the latter pulse apyea-r
when a 6-fold coincidence takes place,i.e.when a particle
passes through at least one of the co-ordinate counterF In
the electron series, througn one of the co-ordinate '-':~,,s
of the positron series, and all the counters of the ~Ic
system. T~e resolving time of the above coincidence schemes
is 5 x 10- .
5) Method of measurement and treatment of results.
Fig.7 shows the experimental arrangement. In t7i's figure 1
is the proton trajectory, 2 is the target, 3 is the synchro-
cyclotron chamber, 4 is a concrete wall, 5 is a collimator,
Card 6/7

SOV/120-58-6-5/32
A Multichannel Pair y-Spectrometer. II. Description of a 12-channel
Spectrometer
6 is a diaphragm, 7 is a clearing magnet which removes
e-ectrors and positrons from the beam, 8 is an additional
screen', 9 is the convertor and 10 is the spectrometer
electro magnet. Fig.8 shows a typical result obtained for
the energy spectrum of y-quanta from neutral V-meson decays,
The mesons were produced by 660 MeV protons at a carbon targe
The spectra are measured at an angle of 180-00 to the direct-
ion of motion of the protons. G.P.Zorin, B.A.Krasnovidov,L.
A.Fadeyev and G.N.Stepanov are thanked for their assistance.
There are 8 figures, 4 tables and ? Soviet references,
ASSOCIATION: Ob"yedinezinyy institut yaderny1rh issledovaniy (United
111%titute for Nuclear Studies)
SUBMITTED: December 27, 195?.
Card 7/7

SOV/120-59-1-38/50
AUTHOR: Markov, A. A.
TITLE: A Method for the Meaouremont of the Ratio of PtiL!3,,- ii-,
(Metod izmereniya otnosheniya ainplitud iiapul'3oi)
PERIODICAL: Pribory i teklinika eksperimenta, 195--l", Nr 1, i 1~8 ("T R'
-33
ABSTRACT: In experimental nuclear physics it is
to measure the ra'6i.,) of i,,-ilse heiL.,Jits of coiric id-iuI
This problem, -~ay be solved b~ ,.ieans of t',le appa,,~it. u~ S'.
diagrammatically in Fi~; 1. Short .ulses wh)se '.,iei-,~ -S
ua and uT) are applied to the two inputs an(.' r-e
Ca and C-5 are charged to rour~hly the same valuos
the two diodes and then begin to discha-r-7e tnr)-i,,--, R an'.
C)
R Assuzmin- that R C and R C.6 are both
b C~ a a Z
RC and that the latter time cjn;3tant is much -,reate-~ -,:,an
pulse length one finds that the voltages acros-,
will fall off exponentiaiiy with a time consLar:u equal '.c.,
These voltages are applied to two palse lieight
with the same threshold E The voltages acro,-,s
sers will be equal to the threshold volta-e at IL-1-f-ren-
Card 1/3

SOV/120-59-1-38/50
A Method for the Measure,.-,ent of tLe Rjti,-) of hi,`--
t and t b so that
E = u - u6 exp
(- t
a e x-,) RC
This is illustrated in Fi- 2. The differencj 1),-,Uw,~er. 'u-c.,
0
times when the voltages are across the two con6ensers o:-.e
equal to the threshold of the discriminators is ~~-.t-n -,-ven by
ta - te = RC log(ua/ue) -
It follows that the lo--aritlim of the ratio of
U -
heights is proportional to the time difference t!,,-IS
be determined usin:] one of the well--,-nown t.-L,..e
analyzers. The method was su;-rested in 1956 ar.
Card 2/3

3OV/120-59-1-38/50
A Method for the Measurement of the Ratio of Plilse Hei--h~s
at the All-UnlDn Conference on Analyzers ir I--A57. T ". -al - ~:
2 fi-ures.
SUBLUTTED- Janupa,Y 31, i,45111.
Card 3/3

24 (4), 21 (8)
-AUTHORS: Vasil'yev, ~;. Ya., Usatiy, A. F., SCV/20-12~ -
Lazurk'n, Yu. :;., Markov, A. A.
TITLE: Measurement of the Luminescence and Darkening of Jlass Di~r,.njz
the Process of Their Irradiation in a Nuclear Regotor
(Izmereniye ly-uminestsentsii i potemneniya stekol v protsespA
ikh oblucheniya v yad-~rnom reak-ore)
PERIODICAL: Doklady Akademii nauk 3~;SR, 1q59, Vo' 125, Nr
pp 1?19-1222 (US."R)
ABSTRACT: The present paper is intended to work cut the constructicn of
device for the simultaneous measurement of the luminescence
and darkening of transparent materials in a nuclear reactcr
and to deql with the carrying out of experiments by means of
this apparstus, The uuefulness of parallel measurements of
the yield of the luminescence and of the darkening of the
sample may be seen from the close connection between these
phenomena during irradiation. The device consists of an
aluminlim tubg )f 5 m length and 6c) mm diameter, inside of
which tivo tubes of the darkening tract (polished inside) and
one polinhed tube of the luminericencp trnct wers~ fitted '
Card 1/3 Further detni's of the apparstus are described, Luminescence

Measurement of the Luminescence and Darkening of SCVj/20-!-~5---)--1/,-1
Glass During the Process of Their Irradintion in a Nuclear Reactor
and darkening were me8sured in the perpendicular, dry, ,Iqnn,-
of 65 mm (with external wqtpr-cooling) of the experimentRI
renctor VVR, In this rmnr~tor ordinary w,iter is uspd as
moderator and coolnnt The chrinnol wil.9 nnnr the active zone
of the reactor By vnrInti.on of the power of thp renct-r
various values nre obtriined fcr the differential dose in the
case of all experiments temperature remained below 35' The
samples consisted of 10 mm thick disks with q diameter r)f
20 mm~ The following qiiantities were mennured by remote contrc
a) the brightness of luminescence and its time dependence at
various differential dones. b) The darkening of the samples
and their time dependnrice at various differenti,il doses
c) Measurement of dnrkening after irrqdiation wRs stop7-d
Measurements were carried out on various types of quartz,
pyrex glass, cerium glass, polymethylmethnr~rylnte, -ind
polystyrene. In the chne of till juartz --amplen, tho r-plrtti,.n
B - t1P holds up to ~i differential dose of P - 2000 rni '/ser;,
where (!idenotes the specific brightneog coefficient of
luminescence. In the case of po1ymethylmPthacrylqte and
Card 2/3 polystyrene the brightness of' luminescence kc-ren.-es wiQ-, pr,,gm-win

Measurement of the Luminescence and Darkening of SOV/20-121:-1-1-11/61,
Glass During the Process of Their Irradiation in a Nuclear Reactor
time and increasing integral dose. The optical density D for
some dozens of minutes remains on the equilibrium level, the
amount of whioh depends on the differential dose, and changes
only little with an increase of the integral dose. The
measurements carried out in the course of this investigation
are only the first part'~f a series of measurements which
is planned. There are ~ figures and 2 Soviet references
PRESENTED, January 8, 1959, by A, P. Aleksandrov, Academician
SUBMITTED: September 23, 1958
Card 3/3

MARKOVI A. A., DYAKOV Yu. Ye., SAKALYANY K., and SHEBESHTENY B.
"Impulse Scaling Circuit Using new System with Muitipie E-quiiitjr',-11T.
States"
I
Joint Institute of Nuclear Reseach, Dubna, USSR.
report submitted for the IAEA conf. on Nuclear Electronics. Belgrade, Yagt-siavia
15-20 May 1961

6/12G/62/GOG/OOVU0,,/048
114
:,;ark-(-,v, A.A.
Differonce ii,easurements in niultichazinel spectrometers
Ilk ~A L r)ribory i te'dinika ck.-,pcri.,.;O-nta, no.3, 196 -50-35
X 7 1 a t
It is -,ointud out t! low-intensity photopeai~s at low
c e ],.- -;Cs 111:11), ijeco.,;L: Ljy tne Compton c;istr-butions belon,,,,.ing
to Such photopeaks can be separated by
~;,Ur k2aLU-6" ,
bubtractii-.-
_ fro:i- the overall spectrum the high-CnLrgy CoMponents.
T'le T)rOSL-.1-,t author ive-~, a general description of a procelure
,Ler~'~-y this :-.iay be clone (semi -au toma tically ) in practice. Thus
oi-.ce The ;,IAill r.LA:~s in the spectrum under investigation have been
ic,leritified, pure sources are introduced in place' of the specii.,,en
under investigation a;iL: their spectra subtracted from the original
spectrum. lzic;,.ground and statistical errors must be taken into
account in suc~i procudures and the author gives a general analy.'31.
of tile;-,I. The discussion is concerned both with amplitude analysers
and time selectors. :-,o experimental results are reported.
sLj~,ITTL~D: june 15, 1961
Card 1/1

5/120/62/000/006/019/029
E14o/E435
AUTHORS: Levin, G.L., Markov.-A A-., Plakhov, A.G.. Smolkin, G.Y
Sofiyev, G.N., Stepanov, G.N., Shapkin, V.V.
TITLE: Line and frame scanning generator for electron-optical
image intensifiers
PERIODICAL: Pribory i tekhnika eksperimenta, no.6. 1962, loo-io6
TEXT: The authors discuss the use of image-intensifier tubes for
the spectroscopic and space-geometric a .tudy oi pulsed gas
discharges in plasma studies (controlled thermonuclear synthesis).
The system permits spectral analys in of dynamic processes with
time resolution in the range 5 x 10-8 to 1.25 x 10-5 sec.
A five-stage intensifier is used. Free-running and triggered
versions are used, the latter to reduce background noise where
necessary. There are 6 figures.
ASSOCIATIONt Institut atomnoy energii AN SS*R
(Institute of Atomic Energy AS,USSR)
SUBMITTEDt January 25, 1962
Card 1/1

MARKOV, A.A.
Difference measurements in maltichannel spectrometers. Prib. i
tekh. eksp. 7 no.3:30-35 MY-Je '62. OURA 1b: 7)
(Optical measurements) (Spectrometer)

L 353h9-66 r-WT (m)
A_CC__NR-_1Y00l7791 SOURCE CODE:
AUTHOR: Markov, A. A.
TITLE: Coifteidences of arbitrary multiplicity
uR/oo58/66/ow/oo1/AO44/A04
SOURCE: Ref. zh. Fizika, Abs. IA397
REF SOURCE: Tr. 6-y Nauchno-tekhn. konferentsi ._2g
,.n,L_:L3. ~ __yA!~ern. radioelektron. 2. M.
Atomizdat, 1965, 42-51
TOPIC TAGS: coincidence circuit, nuclear radiation, radiation measurement
ABSTRACT: The author considers one case hat is frequently enco-antered 'n tire prac-
tice of measurement of nucleox 4 iden
radiat---- when it is necessary to reGister coinc-i
of arbitrary multiplicity from several (m) pickups. In this case all the s"Gnals
entering the m inputs must be divided into two groups: a) noncoinciding and b"
, coin
ciding, for at least two arbitrary inputs. Depending on the purpose of 1he syztem,
it is necessary to ensure in it measurement of either only such signals when arbitra
coincidence took place, or, to the contrary, signals which do not coincide. Several
practical examples of measurement of nuclear radiation are presented, in which it is
necessary to have such a coincidence registration system. Different metijods of con-
struction of such systems are analyzed. A method of constructing a system of this
type, which appears to be the simplest, is described. M. L. [Translation of abstra
SUB CODE: 18, 09

r
~4797_66
L
ACC NR- A 160 1720,-- SOURCE CODE: UR/0058/65/()()n/()12/AO,V~/AO~4
A(MION: Mnrkov, A. A.
TITLE: Crtlibration and stabilization of slope and shift of an amplitude character-
istir
00MCF: HPf. 711. F17,11ka, Abs. 12A3,15
W-T -101MCE: Tr. 6-y Nauchno-teklin. konferentsii po yadern. radioelektron. T. 1. M.,
Ai-mizdat, 190s, 61-89
TOPIC TAGII: coding, pulse amplitude, pulse amplifier, pulse height analyzer, auto-
mritic stabilization equipment
ABSTRACT: Methods are considered for calibrating and stabilizing the slope and shift
of the amplitude characteristic of converters of an Input guantity Into a unitnrjx i
codc.*11 Is noted that the gain calibration error of a proportional amplifier can
be derreased by determining the gain from the measured ratio of increments of the
input nnd output quantities. To stabilize the gain, it in proposed to apply to an
auxiliary control input of the amplifier an error-signal iroltage equal to the differ-;.
ence bctween the actual pulse amplitude and a standard signal converted from a pulse
Into a slowly varying voltage. In the case of a linear pulse-height discrim1nator
with a characteristic shifted relative to zero, the stabilization of the Ghift can
also be attained by means of a circuit that compares the output voltage pulse with
a reference voltage. The slope of the characteristic can be stabilized with a cir-
Card 1/2

L 34797-66
ACC NR, AR6o17202
cuit that compares the difference of two ouLput signals. Corresponding calculation
formulas are presented. G. K. [Translation of abstract]
SUB CODE: 09
12

;Ora' I
00
o*
0
00
-
Or tillniAlton h1pthmi 0o 111whimptry it? AW Viethiii AsIrip
stmittlital 4111)pslb.A k1allbill,I d, i t-J 40 .00
A-a.. .. I N A R I ft. it. 103t$ 1'"0024 AbitrAftj -00
IAI-w:ti" val"submts and a companmwin to the remalts III pnwinut,
twimarrivrn shrow thM extimt1cm vwthods alre the mmt suitable for nrawa ng
the brightness of the millry way, rftbt sky. and the like. and also far faint
vartAble atlims w"h rapitt fluctuatinvist. The tipparatuit nf Wawikvw fw*
Al"trart 4P" (1036)) is wim& and an-timle UN-tmil"I tal4m alvIvar 0
1- "4 fl.11111 I%Vt!iio 6101 itill-VA 11"414111#16114 ft. lit' 11VOWIFY011 lit '00
1
.1;'11416111 the nwashavi of.) - Is I.., - m
won -0 1 tellava -to (1.. 00
a mal. a j I q
age
'00
'els
INS*
DO 0
'no@
061411 NO Sit" III see
; v I : 1 00 Ile, go :0 a a 3 0 L-F,
906 0

NIA 11(kT Ail
Nevozmozhnost' nekotorykh algorifmov v teorii assotsiativnykh siste-. E)A~",
55 (1947), 597-590. Nevozrnzhnost'nekotorykh algorifrov v teoril assotsiativnykh
sistei., 11 DAIN, 58(3047), 353-256- 0 rredstavlenii re~-ursivnykh formul.
D,U#I, 58(1947), 1891-1892. On the rerresentatinn of relatively definite
functions. MateL. 5D. 4(46),(1'38). On the determinat on of the numicr of
roots of an alf,ebraic equation situated in ii givendomain. Mate . SF., T49-,
(194L)p 3-6. 0 svobodnykh topolori&ieskikh Prup-akb. DAIS, 110941), 2W-,~02.
SO: Mathematics in the USSh-, 1917-lq47
edited by Kurosh, A. G.
Markushevich, A. 1.
Rashevskiy, P. K.
Moscrw-LeninFrad, 1948

RARKOV3. A.k. Continued
0 sushchestvovanii periodicheskikh svyazny', h topo logic hesk i1, h 7rur- . Ian, sc, . matem,
8 (1944), 225-232
0 bezuslovno zamknutykh mnozhestvakh. Dan, 44 (1044), 1Q,-107.
Nekotoryye teoremy ob abelevykh mnozhestvakh. Dan, 1 (1036)p 200-302.
0 sushchestvovanil inteFrallnogo ivarianta. Dan, 17 (1937), 455-458.
On mean values and exterior densities. Vatem sb., 4 (46), (1038) 165--191.
0 svobodnykh topologicheskikh gruppakh. IAN, ser. ~iiteii., 9 (Y)54% 3-64.
Arifteticheskaya kharaktorizatsiya trigono-net-i-hes~-Ikh rol~no ov. L., Trudy Vtorogo
Vaesoyuzn. matem. S'lezda, T. 2 (1936), 202-201
Sur les mouvements presque perodiques. C-R. A;,d. 3ei. IFO (IQ28)p 712-795.
Sur une propriete generale des enserbles 'Tinll-aux ]e Birkhoff. C.R. Acad. Sci.. (1C'11)
823-825.
Stabilitat im Liapou,.off schen Sinne und Fr st periodizi'nt. Ma, h. 2., --6 (11 3-~), 71,~,8-718.
Pochti periodic 1r.ost I I Gara.onizuemost' . L., Trudy v-torwo Vesesoyuzn. Mqter.' S"r--A,
T. 2 (1936), 227-231.
0 sushchestvovanii integrallnogo invarianta.Dan, 17 (1017), 455-458.
Uber eine Minimwneigensehaft de Schrodinptorschen Well enFt-upren. L. f. Phys., 42
637-64o.
0b odioy zodriche na ekstremu,.. Novocherkassk, Izv. S(i-.-KAvk. Industr. in-ta, 1 (15),
(1935), 59-62.
Chto takoye g)adkaya poverkhno3t'. L., Uchai - zap. un-t- , sor. r~ater, 10 (1"40), 27-'~O.

MMOV, A. A.
Mbr. , ~ialheiwjtics Inst. im. V. A. Steklov, Dept. Physico-Math. *i., A.~.
"On Unconditionally Closed Sets," Dok. AN, 44, No. 5, 1944
"The Impossibility of >onw AlUorisms in the Theory of Associative Systemsj;j" 1610.1
Dok. AN, 5~j, No. 7, 1947
"Representation of 1,ecursive FurIrtions," Iz. Ak. Nauk SSSR, Ser. Matemat, 13, %o. 5,
1949

KAHOV, A.A.
.......
[Principles of the algebraic theory of braids] 09novy algebraiche-
skol teorli kos. Akademlia nauk SSSR, Moscow-Leningrad, 1945. 53 P.
(Geometry, Differential--Projective) (MLEU, 7:8)

7
theory of Pills-
%Markoff, A. A. VariAtion principlex In the
-7 tiri . Appl. Matli. Mech. [Akad. Nau SSSV--Ijrik-f
Mat. AIM11-3 11, 339-450 (194 7). (Russian. English
summary)
The author provc-9 coliclraing
the velecity field iii'an 111cornpre asible lierkIctly Platiiisnlid
which Obeys the stress-stritin reintion of von Mises. Tile
W
ettiriplest of thew principled is mcerned with the case where
the velocities are prescribed On the surface subject, of coum,
to 60 condition that,tIle illFfaCC illtVgf;ll Of the normal
velocity component vanishes. If the velocity s1rain is de-
no#,ed by eq. and if E the ininirnmr) principle in
-is foll,
question can be forinulateti . ows: aniong all velocity
distributhns which satisfy tile boundary:colldifinnsalld tile
equatioa of-incompressibility, the actiml distribution fur-
nishes the arrialkst valuelor-die volume in(egral Of the
inva 'Mint B. The author's ather mininium principles are
concerned with the Casea where (a) tile stresses are given
on the surface or (b) tile tangential str(w)(-sand the iiorrnil
velocity;: The minimum principles ire 11 41 to establish
uniqueness of the stresses in the interior (it) within an arbi-..
I constant hydrostatic author mssilme-
trar i)reg4tire). [The
tacitly that the boundary conditio'nslissum A1.41C Ix-luivior
throughout the body. In many practica'~ly importin -t cases
(e.g.' indentation problems) thisal%- unip6on is not justified.]
W. Pragry (Providence, R. 1.).
*qW41-0
Flathen"'Cal R'-Acl-rdt Vol 90 No- 2
A4

Markoff, A.- On the ImpossUlty of certain algorithms In
the theoty of nssoch
ative Gystems, C, R. .(Doklady)
Armd. Sci, URSS (IN,&) 55, 583-586 (1947).
Two theorems on recur.-ive unsolvabihty in associative
systems with a finit e set of generators and relations are
stated- and -roved in outline. Theoreem I asserts the un-
SolvaNlity ( tile word (identity) problem and is identical
with a`the6 ein of E. L. Post I
-we the precediniz review].
The met T.Itially ahnilar aking se
hGd of proof ia esi
-in ~earae
rresult,ol Post tamer. J.-Alath.0, 197-215(1943),
Aliese Rev. 4. 209] and Rosser's combinatoriall logic [Ann.
of Math. (2) 16,127-150 (1935)].-Theorem 2 states that
at' , e systein can be constructed in which the word
;oci
an a& v
Y- Ili- 1011
-go HbIe e,
is Iva tit e cri v ~is lilem is u so ab
i.el, the-qur-stion whether-XQ"-R-has-a -solution--in- the-
-in), kiven Q and R. Ut A be
system for -a finite alphabet
I -o
and Gj, G, y - 1, 21 in)-words in it such that the i;
----pro ado"we - -
blern is unsolvable-iinqk7r the iiihitift
IjGiP-iPG4 -for any word P"~[Post op; tit --(1943)3-Thcn
a_ system for theorem 2 is obtained. by adding! the new
letters d, f, ej to- the alphabet and taking as relations.
ej-feii iG.a-atGi, eGd4-Gi'd (azA, i= 1,
M. H. A. Neumian (Manchester).
Vol No.
Source:., HatheriaticalrReviews,

--M%Tkoy, A. On certain insoluble problems muccornial;
DoIrlaely Almd. Nauk SSSIR (N.S.*, 57,539-
542 (1947). (Russian)
Let a- square matrix AvitIl integeri an &-,mePts and del generate a fice sciiii-group S(A, B) Nielsi)-ji, D-uisk-e
inant I be cn-lied "adniissible." 11 ffXt, Vid. Selsk. Math.-Fys. Nitdd- 5, no. 12 (1924)]. Bt:nce the
X r
a finite set of
admis,sible P-matrices, the sen r -cci ZI, fl, vach
questioli whether, given P pairs of niatn
Matrices emprcssfW,as products of X'f. is denotLd L, y' we-qtial Io A or B, there exists a jelation i.;
SMIX ...... X'). ncoMqi I. " f r, -~-4 &re is no algorithin uUtlecidable; or. what i5 the samL, t]1,- quC'Stio7l whe!hCr.
i Oll the sense of Church-KleenL-Turini'-) for deciding whethcr. sonic fl(Zi,+Zf,) is in S(A +A. B+B), where + denotes
given two finite sets, X1, X,, X, and. Y~, F', Y. the direct surn (44natrix). This pruvLs the case
4, and
oUadmissiblez-niatrices, the sets S(X%, Xi, - - 1, X,) and the "It-11SIM-to ~t>4 [a irivia
JS0'iiY"--!,-Y0-bave-a common menibet.-?'&ft-over fliwit-ni 2. It ft-~' is 110 611gbilihffl t& deciding
(corollary) 60 the Y's, and A X's but one, can be chuseil VdIVOILI, gli"M fillilliSSible 4-htdfflt~S k, ~Yj AOL]
and fixed,('6a that the quvdtion rentains undecidable when ~n~
tile set S('Yl' X1.
~the remlining X varies; the number q can here be 2, and p gi-OUP L(Ill Y2, - ' ', Vj geilvrai~ by 111L Y~' I'd-ve il
can aldo be chosen independert of n. curn#ion member. All Oe Y's, and A the X'3 but une, than
prool, By a the,)rera of E. L. Post [Bull,, Amer. Malh. L--c fixed [vorollary. i]-, or ill ihe X'3 cin be fixed tt-OTUlkiry
Sue. 62, 264~-208 (19,16 Fev. 7, 40i3 ilierv i,i n?j -2] and tf%f stion is-,, ill underidable whoo th!" lz-fnakliru
0, thE (jut
i~s' Gil G-1 of
algorithm for &ciding -.0ict.her, ~Jvc-" P Va. IV or tht. Y'S, vary, fitt-re q ENIII be 5, and '5
j
m identity 4.
I-Word'a in-tvj* letters, a aid k iheri., z, of rhi-i proved sirnilariv, by tal"ing I'l. 12, Ii. Ill
"Ild Dm'A jroof thal foll*e 4-juat;-iLu~:
C, -Git'GI, whvr~ E,' :t3 1 in
G'As - Tbe-
I
all the.Gs a all but o"le o! III- '.w . 61U.- limt CU
G, bL no-V !oil (r, 3) a6d 0
the questim 1-4 561! u-nde-6-jable wh~%n tl~c :&m..i.jing G' of a~f matcices'?+ Z (Z adill ki'lib lel.
Vari 9. The two matr!cr Ntlanchester),
'So 19:4 8
5 A.

F-f PC,j
Warkov, A. The lrapossibWty of cerWn sjgad In the.,
U. ladyAkad. Nauk
A
SSSR (N.S.) 58, 353-356 (1947), (Russian)
The first pz&t of ihe paper is concerned with sharpening
the author's theorems I and 2 [same Doi,
583-586 (1947); the&-- Rev. 8, 5583 on lihe unsolvability of
the word problem in associative systems [demi-groups, Thue
systf.118], and on the ursolvabilit ty of the division problem
-C*a3-XQ"R-a- solution !or-given Q and-R?~-'),respecfively-
(Notations. X 1- Y means that word X may be replaced by
word Y, X I Y ineans X F Y and Y FX, X+-* Y means that
PXQ-LPYQ for any. P and Q.) (A) A system may have a.!
solvable word problem and 6olvable-left-division problem,
J
but unsolvable right-division problem, XHI"R; and here
410uraf t, - Mathematical RevievB, .
Vol

0
=r
q
0 '
ven
171 can be a fted word (13) Aa ass6ciative systems,' gi
haykg no'decision ;~,;rittwn for X--* (the mp ,word)..
Proofs rest an F- L. Post's unsolvable word problem under.
a tet of one-way substitutions GP t'PG1 (i - 1 2
'Gi and G4' fixed, P arbitrary [Arner.' J. Math. 65, lk,)7-215.
(1943); these Rev. 4, 2&3.
Cen by
In the second ppxv fof the paper a, new step is 14!
the construction of a 64m of a&soclative systems w1th un-
sohmble wordproblem, having only a moderate nun~ber of
defirung relations which can casilv be viitten out *ithdut.
ahbreviation. In exarnp)es hitherto co-'structed the relatio,12s
contain in effect a specification of thw class of ursive
Fro~-n the
functions and are correspondingly complicated.
qxv.- indications givien in
the present paw, it appears
that thecomplicatiGns are transfeirred~ from tile relatibris to
the class ofwords within the system to.- WbiChL the eiui-t
lence problem is posed, The rnain theorem is as WHows.
The alphabet consists of (a, b, c, d, e). Let V be an arb. j U-Ary
word in the letters a and b. and U any word in 4, b, r, d
beginning and ending with d. in -which every two c4is are
wparated by at least one d, Then there iz noalgoridaln
for
deciding whether Ue V goes into Vea by me= of the iingle
rule (a) P4QcPdSeQT.LPdQcWe.TP, where P, S, :t am
arbitrary words in'd, b, c, d, z; Q and R arbitrary words in
a. 6. The following two results are to be. U%td in the p1roof.
(1) In tht problem of Post referred to above the oneLway
rmbrtitutious GiP l-JGi' may be replared by Gy= ricW
P-LPK!. [Cf. leram., 11 of ~ 11cat, J. S);=
ones lic
Logic. (1947); these Rev. 8, 558.] (2) If Lij L"
- 1, - - -, 9), V. W are words in
i a, b. a necesnry and Outf,
(
cient condition -that Y go into W by m" of L.P-LPZ4' I'S
that dLcL,' - - - dLcL,'de Vgoesinto dL,,rL,' - - dL,,cL,4W
by We2M Of (a). AM ar,3002ti-M system Ca on 13 lett~~-s is
given. with 33 defining ntlations. X+-*Y, where no X or I'
contains more than threc letters, which can be shou-ii by
t1w. mal'i theorem (p*L-sun--ably using the examplm-, t~on-
3tructed in the first part of the paper) to have an undcs-,id-
ableword problern; in t stightly more.,wmp1iaxtt:d sN~Jcm
CO the problrmX4-1f. ;s undc6dable, ivnere'lfo is ki fLlv-d
3-letter word, NoAetaiLs sif the proof am given.
11, A. Aleamidn (,Nfaricheut~r).

fi
Ive functions.
Markov A a the repre?,entation of recurs
1., 4: ~~~k A. Nj S-SSR 58, 101-1892 (1947).
A
(Russian,
--6 ry-jenera
S. C. Klewc has pro (A~tKaf w. recum. ive
function of ti variables tan be represented in the forin
(1) P(Py - Q(XII -x"' Y) 0, 1
iv and -X' I t!a s t
v6,h&e P and Q are printitive recurs c, jjy is the
rat numbc r such that X holds, or 0 if tlicr~ is no'ne
natu y
[Alath,.Ann. ~ 12., 727-742 (1936)], and (B). tl~at a fin. C
p 'tive recursiv ' fun (ion P can, be found,
universil" p imi C c
-curb A by
such that all encral rc ive functions,are obtainL
-wirsive Q in (1) CTrans, Amer.
suitable cliofc of primitive t
Math. Soc, 5 , 41-73 (1943); these Rev. 4, 126]. In the
3
present note tl e theorem is annourlMd [wit'hout prODfI that
a necessary an I sufficient condition for a, primitive recursive
function P-Ov) be universal, in the above wnse' is that it
take 9 every nz tural hUrnberraS value an infinity of times.
-M.-II. A Neumn n (M-neb ester).
Z_ -il

I I",` - -- ~;~ -;- - F4 %-- I ~!~ -~ I, ~ ~ % -I ~ r~ ~ ---4" Al 4r', "I r~f
.-., ~l . . . - . 1. - ~ I ~ - . .:
~r!AZA4- - '. -W -1
.4 - 4 //
- - : ~ , ~k ~

-A.
Msdcoy A. On the to
'
-
Ser. Mat.
13, 41P
Mr-Mestlya Akad. -Nauk SSSR.
-
..
(Russian)
424 049).
This paper*givc* a detailed proof that a necessary and
sufficient co6dition that a primitive recursive function P(x)
be such -that eveq recunive function of n variables can be

represented, for suitable primiti __ recursive in the form
i
-F[uy-Q(x~.- - -.,x%,y)-0] ia that P(x) take every natuM
-
V_
number as value finitely many times. This result was
k1
d
Ak
d
k SSSR
ed
li
N
Na) S8
.
au
o
a
a
announc
ear
y
(
,
er Ile sufficiency part
1891-1892 (1947); them Rev. 9. 403].
is construc~.,e in terms of certain results of Kleene's Icittd
in the above-mentioned reviewl the necesBity proof is non.:
constructive, but has a weakened constructive counterpart..
11. B_ Curry (State Colle,'ge, Pa.).
sourcV, xvithemetical N

WURKOV, A. A.
USSR/Mathematics - Approximations Jul/Aug 51
"Ideas of P. L. Chebyshev and A. A. Markov in the
Theory of Limit Magnitudes of Integrals and Their
Further Development," M. G. Kreyn, F. G. Rekhtman
"Uspekh Matemat Nauk" Vol VI, No 4 (44), pr, 3 -120
Discusses fundamental theorem concerning positive se-
quences, max mass, main properties of Chebyshevl-
system of Ainctions, canonical representations of a
positive sequence, existence of the main representa-
tions, motion of tie masses of canonical representa-
tions) mech quadratures and soln of an extremal. prob-
lem, Chebyshev-14arkov inequalities, case of infinite
integral, the phi-psi problem of Markov, and a min
problem.
191T75
01 71?5

V -/I ff
-t of the claim that this give :j a satibfactory
In suppol
M&A" ov' A-.& The theo of fil L-on'thM, Tmdy Mat. meaning of "algorithm" it is aswrled that (1) every algo-
ry
rithm 21 in the rather vague oen-m- of ordinary matlwmatics,
~_WUV4 V. 38, pp. 176-T89. _14dat. Almd. Nauk
R.-Moscow, ian) 20 uivalent to- some normal algorithm T, Le.
-1951.- - (Russi rubIes. 7 is EQ applied w
The author considers that the Church-Kicene--i - any given word X, T terminates if and only if 21 does. and
uring then T(X)=?I(X), (2) various specified combinations of
theory of computability touches the idea of "algorithm" so normal algorithms (iteration, juxtaposition of results, etc.)
'indirectly as to make an independen t development desirable.
re equivalent to nonnal algorithms, (3)a "universal nortnal
'After somewhat lengthy prehminaries (e.g. definition of an a
"occwrence" of one word in another) an "algorithm W in -algorithm" It eyists tiuch that, if the institictions s-ye-c-4vipg.
normal fornl" isdefinedas follows It is (or is dettrmined by) W are combined in' an obvious way (with spacing symbols)
7- i a list of instructions in one- of- the form, s into it single word-W, II(WP) -21(P) (if either exists. _21'.P
-P denoting mere juxtaposition). No indications of the proofs
--,Q. or P Q,
! are given. The word 21*, translated inton 2-letter alphabet,.
whiere P and are'words in'some alphabet ~, either-or both
is the "signature" of the algorithm TI. A nornfal algorithm
of P or Q may be the empty word (ix absent). Thus ab-,ba
LId-and . - - - is "self-apolicable" if its application to its own signature
ovdzr of-the ; - - - I -
ai, 1. - e i -
tenannuiates.-TI Ich t Tin natef
:~_m5trdct o-M.-Wthe Hat- must :be -specified; -To - -apply the -
for idit those words that are signatures of non-self-a plicable
id ithin--to:a. given-w -X-. tak-e-the firalInstru&ion- iw? p
gon
o Ila -whose Idt;hand sidcoccurs-irf X (the -empty-word
_`6&tirs A;ifore--and After every letter), and replace the. first-,
6c~urren6e of P by~ Qi If thm is a dot after the arrow this
d sarn
en- s.the- process; it. not, apply,!K in the e way to the
y
.~.resulting word; and so on. If the process terminates the final
_resiilt is!K(X).
BoAirca Z' I_
JUthe via tidal- Reviews, VO NO- -
7 7_7Z
7

normal algorithms (priDved by the sual -~'ntor-tye argu-
ment). It follows by familiar aTgilments that thc:-.angc of
U (above) is not discernible, i.e. there is no normal algori tbm
that tcrminat2s for ~every X and is such that ?[(X) is the
empty word if and.only if 11 terminates when applied to X.
Jn 9f)ite of his initial reterences, the author nialte3 no
mention of the to every reader:
_question that will oceti~r
-el what.is relation between "normal algorithms" and com-
putability A la Churcli-Meme-Turing? It is obvious that
normal algorithms can be programmed on a computing

machine, indeed they. tscinble instruction-t.
ables for existing

machin
en
m
ood deal ore clOSCly than do.the tables for
a L
I
_
'
Turing a original "papeer machine [Proc. Ix d Math.
n on

-Soc. -42,2,30-265L(1036)]. The stronj
_: (2) rese
tween the general course of this theory and Turing's [OP,
Cit.] makes it likely- that. there-is full equivalence. Af that
is so. thi
iii~Wncliester)
-source!. Ma _13 -No. 9`
views

Ms
0 the im,?ossibillty of certain'algor4bms in the,
41"Itt,uI-6f associative Vstems., DoMad :Akad Naak
SSSR (N.S.) 77, 19L-20 (1951). (Russian
In this.icvieu- (but not in the paper) C(7, A r CC] de-
notcs'tht ~aisociative system detcrmin~d in- tht alphabet ~A
~i' by the set of relations C, The probl,!m of the. emutence of
zirilvorithmq for 'din-v the fallo% ti ia, con.',
dect vil clues ons
~1 sidered:: e0tn an alphabetel and Mtge:sets. Ci and C:. of
0 relations,(1) are [Cjj and CC2] isomorphic? (2; does IQ
Fl- contain only one memb-,r? (~) is it a group? (4) ~ontaiqd
0
0:- in, ;rouli Civith 'cancellaiion]?
a p? (5) is it a, semi-g
(4Zdpeta-problera of identity") is ECj] a systern in
(6)
M which Ole, iden ti tv-problem word-problem] is solvable?
no such. algorithms.
;I A negaUve ans)xer is given in all six.cases.
P-Nist for an alphabet. with 4 or more letters.
An outline of,the proof is given. A system, [Cs, As] of an
earlier paper [sarne DoWaey (N,S.) SS, 353-3S6 (1947);
these ReV. 9 321] is first transformed by Po st's method
E E. L. V6st. Bull. Amer. Math., Soc.: 50.'284-3116 0944):
[D, A a]:where A o is tht
the-se.Rev. 6,.29] into a system
2-lelter alphabet Ia. 61. Given,any two words G, H of.AO,
-K4 let Davt~6 the set of relations in B = (a, b, i. d) formed by
.0
Padjainihg~tht relitionscGd+,Oindtclld*-~cHz.!(Z=a,b,c,d)
to D. In the svst~,rn [Dajr, B] the answer to questions (2)
"'Yes" if~ and onl%'if
to' (6) it., C n
-H i CD, A,3. Since
[Cs. Asl and therefore also ED, Aol, has. an unsolvabl,e:
problem r.%-farkov, as above] this praves the unsolv-
L
ability of! (2) to (6) 'and-hat of (1) follows.
M. 11.'A. Newman (MarichasteO..

Markofv~'-A. TheimpossibUit tile recog-,
y of algorithms for I
=9Bff6_ff4Wqxrtain properties of asaociati~ve systems.
'0 !A lady A"d! Nauk SSSR (N.S.) '77, 953-956JISPSI).~
(Russian
CD Led, roof-
A gener~al theorem is announ with %an outline' p
from which 'the, results of a previous Lper [samt vot
19-20 (195 1 .1% 11 in this're.
1);. these Rev. 12, 661. c,al ed
C," Vic 6Lcial cases. Let
a, assod.
t
::r, 'With a finite set of generatinVrelationa".~ A
att
-said to be included 'in another, T., if, S
Cf- ~P of 'syste
isomorph i6, to~ a subsystem of T, A,property'. K. ma
s
if it. is preserved under'isomorpb isms'. As in the,
(:I((.fl revieW, we dC116te 6V CR, A] the K-syste~i definW by
t lie,rdat tons R in the alphabet A. Th*e "reminition Orob~
I' 14L:i;i" f4ir a property P and an alphabet A is the problem' of
findin an algorithm for dcciidinZ, for any finite set of rela~-
tions I? in A, whether or not [R. A] hats 6e property'P.
'Fh( I
!0rem I Let P be an invariant property of K-sys
tenm
if fliere exist botliji K-system having the property, and!a
K-~iy_stexij not included in atij, K-system having tfie,p~op.
ertv. t lien there exists an alphabet for which the recogni6;ri i
i froblern for P is unsolvable. If a K-systern with the pro pty
P is del'itiable with n letters, the recognition problem for P
.4; is upsolvable f6ralpliabets of -tr+4 letters.
0 i The 11 1(i-diod of proof is a generalisation of t1lat used i N11,
the r0atil?ins D and alphabet B- 1,a, b, c, d) of that p'aper
b
n
6 g re f hiced by R2v R4 and, Bu B4 respectively, where
R.11P., i~nrl'.64 are asIfollows. (Ra. la, b I ] is a K-system that
includes (in, the above sense) the "direct product" of a
01
K-systern, S, having an unsolvable word-problem, and a
I K-systeril -S~ not included in any having propertyp. (Heie ihe
""direct produ t" f [R, Ajand CR', A'] is [R%j R', AU A']$
c 0
provided that An A'= 0.) The system CR,, B4] is a'K-sys~-
twn having property P, such that BnB4=0. An imm ate
corollary of the theorem is that if P is a hereffitary ptboert~y,.'~-
i.e., holds fox- all subsystemsof X-systems, that have the
property, and if.there exist K-systems that have, and K-jys.
terris that have not the property, then the recogmition prob-'
-iore Icttrrr,. A
abets of 4 or r,
lem is unsolvable for alph
di.-duction from die inlin thccrtc4-n not inciu ided in N-11 is that'
there is no algorithm for dc6ding if givert K-system is,
finite. Af. 11. A, Ne-wonan (Mancheskitr).

AUKkov, A. On, an unsolvable problem coaterning ma-

--Dokl, 109
MS, ady Akad. NauLS&Sll (N.S.) 78.1089-
V

: ~
T9_1 . (Russian)
57
A The- following- theorem is proved. If naG6, avt of IN-
matrices Uj with-Tational integral elements-,
anb found,suchth
c, C at the prDb',-,jn of deciding whetherany--
given integral matrix V of the same size'is expressible as a
finite product JjUj is unsolvable (in the usual
that
no algorsthun or machine routine exists). The proof, which
is given in full, depends on an earlier unsolvability theorem.
of the author on inatrices 'Lsame Doklady 57, 539-542
(194 7); these Rexr. 9- 221]. The transformation of the one
problem into the other depends on ingenious but elementary
algebra. The author believes that the number 102 can prob.
be lowered. At. 11, A. Net-inan (Manchester).
Soumet Matheratical Mviewe,. Vol 13 NC2

_z

MMOVY A. A.
Impossibility of Certain k1gerisrz in the
Dok. All, Vcl. 7r,, Nr. I', 1 )51
Discusses 1-is %,,Yic'-~ ar-7w 1% sllidoy ass(,ciat"vi, -n
by finite systems of relati(,ns in give-i Edgebra A: isamor-phy, 1~nlty,
recognition of i_,roups, Incl-usiveness in L-,roup, recognitlon of' suhgr-ui~, a!-'. mc-a-
problem of identity. Finds for each lettr-r A containing more than -' 1,--+ter,- -a-1.
of the above probleuo in unsolvable: The sought-for algorithir, in this
is impossible. Submittted 4 Jan 'I bv Acad 1. M. Vinogradov

DELONE, R.N.; KMCSH, A. -,.; KOUMOROV, A. "!.; YAITOV, A. I-; SMITMP A. '.;
Algebra
Development of algebra. Usp. mat. nauk 7 No. , 1';52.
2
9. Monthi List of Russian Accessions, Library of Congress, November -, C) -Y~ . '-'n c I .

USSR/Mathematics - Symbolic Logic Jul/Aug 52
Unsolvability
'Unsolvable Algorithmic Problems," A.A. Markov,
Leningrad
-iatemat Sbor" Vol XXXI (73), No 1, PP 34-42
A lecture given at conference on algebra and
number theory in Moscow in Sep 51, representing
a summary of results obtained by the author in
recent years in the theory of algorithms. By
"algorithm" one understands an exact instruction
(order or direction) which defines a computational
220M
process proceeding from original data that can be
varied to the desired result. Cites E.L. Post,
"Recursive Unsolvability of a Problem of Thue,"
Jour of Symbolic Logic, 12, 1947, 1-11-
Submitted 22 Feb 52.
4NM

2WT75
USSR Afathematics - Algorithm Theory 21 May 51,
"Strengthening the Theorem of Reduction (Adduc-
tion) in the Theory of Algorithms," N. M. Nagornyy
DAN SSSR, Vol 90, No 3, pp 341-342
''h. A. Markov
Strengthens the theorem given by
(Trudy Matemat In-ta imeni Steklova, 38 (1951))aB
a consequence of the theorem on algorithm reduction.
This theorem states that each normal algorithm over
algorithm A is equivalent relative to A to a certain
normal algorithm in the alphabet A cup (a,b), where
a and b are letters not belonging in A. The
260T75
theorem permits one to reduce any normal algorithm
over alphabet A to an equivalent, relative to A,
normal algorithm in a 2-letter expansion of al-
phabet A. Acknowledges-attention of Prof A. A.
Markov. Presented by Acad V. I. Smirnov 18 Mar 53.

A. A.
WbA/KRtnrMT,IC6 - IDequa.L.Laes
"Generalization of _Tnequalities of S. N. Bernshte~
ana A. A. Markov, i': N. K. Bari
DAN SSSR, Vol 90, No 5, pp 701-702 t~O
Subject inequalities and those of A. Zygmund are
videly used in studying the best approximations
of a function by means of trigonometric polyno-
mials and also in investigating convergence and
summability of Fourier series and their con-
joints; however, in order to utilize these in-
equalities one must know what properties are
possessed by the considered function on an inter-
val of length 2v, which means that, if the
260T76
funrtion's behavior is investigated on an inter-
val fa,b7of length less than 2r, the corre-
sponding'fteorems lose some force. Generalize
3 theorems apropos of this case. Presented by
Acad A. W. Kolmogorov.

XMOV, A.A.J__ PEMVSKIT. I.0.. Wademik, rodaktor; NIKOLISKIT, S.M.. pro-
IrWj6j; SAZONOV. L.S., redaktor; ARONS, R.A., tokhnlchesk:iy re-
daktor.
Theory of algorithms. Trady mat.inst. 42:3-374 '54. OuAk 8:5)
(Algorism)

'-LkRKOV, A. A.
"Work of -'oviet i:~ ule Dollial", I,
"On thO -,rA-nc4 le cf' -,onstructive Selection,"
paper either presented or distributed at tl-.c- Intl. Coliz)(4,jium on L:.c-- jiffere;it
Notions of Constructivity in -athematics, 26-31 Aug 5?, funsterdam,
B-3,095,946, 2-~~ Jan "'953

OW AUTHOR: Markov, A.A. Corresponding Yember of the AN U33R 30-,E- 3/ 3 7
TITLE: Mathematical Logic and Determination Mathematics (katemati-
cheskaya. logika i vychislitellriaya matematika)
TWIODICAL: Vestnik Akademii Nauk SSSR, 1957, Vol.27, Nr 8, pp.21-25 (USSR)
ABSTRACT: The author at first gives explanatory specifications on the
reoiprooal cormection between the two fields of science
mentioned above. One of the b&sic methods of mathematical
logic is the construction of proof. Formulating of the axioms
and theorems is, by mmking use of a special system of sym-
bolics, represented by the usual formulae. After concrete
specifications on the "method of determination" the author
gives an example for one of these possibilities (in form of
an equation proof, see page 22). In conclusion the author
deals with algorithms and underlines their great importance
in mathematical logic. An important task is imposed upon
mathema.tical logics with respect to the programmatical
working through of the further development of electron compu-
tation machines. It may be expected that the attitude towards
Card 1/2

Mathematical Logic and Determination kathematics
3C -8-3137
these probleum will have a stimulating effect on one of the
most important fields of mathematical logio, the algorithm
theory.
AVAILABLE: Library of Congress
Card 2,12

AUTHOR: IUIU37, A.;-. Corresponding Meemb~er Acad. Sc. !JSSR 42
TL1E t Or, tho Inv I exi ty (-f F-.:i-- t n-
noy slozY.rcati sister,
PERIODICAL: Doklady Akad N%uh, SSSR, 1 (,~7 7o 1 - 1 1 19
ABSTRACT:
c E.N. 'ill~ortls invi,sli,~-a*ionn
Gene7-alizinr
the inversion of a Pc,,-)lean n '".e ~~-~n-
-'s-M
siders the inversion comr2exity Inv (f1 f - r" __
f 1 ...,f of m Boolean 1'~:nctions (.1' n rir,- :-,Pr.ts.
,m,n
(f _7,9*
.en
Let the maximum Inv 'If of the s
f19...1f be I(n, m) !,en i t i s t and
M
2. I(n,m) = -:)(,n) for 7, > 1 . Here _)(r) is the s~:.a' I --st na-
tural number ~ for which it holds r