SCIENTIFIC ABSTRACT A.M. FRADKIN - G.M. FRADKIN

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000413520019-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 13, 2000
• Sequence Number: 19
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

SOV/110-58-12-20/22
An All-Union Conference on Electro-Painting and Radiant-Heat
Drying of B),rts in Engineering
erection and testing of an experimental installation
for electro-lacque ring of galoshes. Engineer
M.G.Belokon' reported experimental work on electrostatic
painting of wood. Doctor of Physical and Mathematical
;3ciencesYe.M.Balabanov explained the physical basis of
electrostatic painting. Doctor of Technical Sciences
D
"D.Ijebedev described the physical basis and methods of
hel-t exchange in radiant-heat drying. Engineer
Ye.N.Vladychina showed how the best conditions of
electrostatic painting may be determined: she gave the
results of a study of methods of painting products with
sharp edges that -LLorm. positive corona. Engineer
PA.A.Slutskaya described electrostatic painting and
Engineer A.P.Alekseyev compared the different methods.
Engineer A.M.Fradkin reported on the technique as
applied to painting electric motors and Engineer
L.I.Rozno recounted its use in an automobile works.
Similar reports on production experience were given
by Engineer V.P.Utkin (tractor engine manufacture),
Card 2/3 by Engineer M.B.Kravehenko (bicycle manufacture) and

SOV/110-58-12-20/22
An All-Union Conference on Electro-PaintinS and Radiant-Heat
Drying of Parts in Engineering
Candidate of Chemical Sciendes L.Yu.Martts (small
instrument arts). Engineers M.I.- Ts.:LrUn and
V.Z.Gurevich reported their experience with radiant-
heat drying of paint. Engineer A.G.Ryakin described
the successful operation of a complex conveyor line for
electrostatic painting of agricultural machine parts
with subsequent radiant-heat drying. Engineers
M.N.Livshits and G.S.Nezhinskaya gave further accounts
of the electrostatic technique. At the conference a
number of recommendations were made about technical and
organisational measures that could be used to extend
electrostatic painting and radiant-heat drying.
Card 3/3

-FRADKIN, A.M.
Mechanization and automation of painting and impregnation and
drying sections in electric machinery manufacture. Lakokras.mat.
i ikh prim. no.2:02--65 162. 04MA 15:5)
(Electric machirwry industry)(Faint machinery) (Automatic control)

FRADKINP A. YE., Engineer
"Effect of Temperature Conditions of Baking High-Voltage Porcelain on Its Mechanical
and Dielectric Properties." Thesis for degree of Cand. Technical Sci. Sub 22 May 50,
Moscov Grder of lanin Chemicotechnological Inst imeni D. 1. Medeleyev
Sum-ry 71, 4 Sep 52, Dissertations Presented for Degrees in Science and Fulneering in
1150. From Vechernyan Moskva, Jan-Dee 1950.

A
GINZEURG. David Borisovich. doktor takhnichookikh nauk; DELIKISHKIN. Sergey
Kkolayevich. kandidat takhnichaskikh nauk,- KHODCROV. Tevgeniy
losifovich. kandidat tekhmichaskikh nauk; CHI?MKIY. Anatoliy
Yedotovich. kandidat tethnicheakikh nauk; ZIKIN, V.N.. doteentj
retmenzent; IUZYAK. V.Aq, doteent, retsenzent; NOKHRATUN. I.A..
kandidat takhnicheskikh nauk, rateenzent; IVANOV, A.K., ti6taent.
reteenzent Cdeoeanad]; BUDNEKOV, P.P., redaktor; QARX!I*p*o
kandidat takhnichaskikh nauk, nauchnyy redaktor; GOLIDINBM. L.0..
inzhener. nauchqy redaktor; GIXZAROVA, I.L., redaktor; GIADKIKH, NA,
tekhnichookly redektor
[Frqlr-cas and driers in the silicate industry) Pechi i mushils
siliketnol promyehlennosti. Izd. 2-ose parer. Pod red. P.P.budnikova.
Nookva, Goa. izd-vo lit-ry po stroit. materialam. 1956. 455 P-
(MIRA 10:3)
1. Daystvitelinyy chlen Akademii nauk USSR (for Budnikov)
(KLlns) Olmy industries)
(Drying apparatus)

MDKIN, A.Ye.1- kandidat takhaicPaskikh nauk.
Study of the tunnel kiln of the "Proletariig plant. Vest.slaktro-
prom. 28 no.2:50-56 7 '57- (MIRA 100)
1. Gosudaretvannyy looledovatel'skiy elektrokeramicheakiy institute
(Kilns) (Insulating materials)

11 o A I
AUTHORS: Fradkin, A.]Le. (C&nd.Tech.Sci.), Kuzuetsova, U.S. (Cand.Tech.Sci.)
& Genin, L.G. (Engineer)
TITLE: Residual stresses in porcelain insulators. (Ostatochnyye napryazheniya
Y farforovykh izolyatorakh)
PERIODICAL: Vestnik Blek-tropromyahleimosti, 1958, 140.21 pp. 37-42. (USSR)
ABSTRACT: Internal stresses in materials are classified into three groups, but
the article is concerned only with the first of these, namely,
temperature Weaties during cooling. It is possible to calculate
temperature stresites in metallic bodies of simple shape, but little
work of this kind has been done on porcelain. The difference between
temporary and residual stresses is explained. The method of
determining residual stresses is explained. The method of determining
residual stresses in porcelain specimens was adapted from metallurgical
methods that have been described in the authors' earlier work. One of
these methods in the ring method, which is used to determine the
stressed condition of hollow cylinders and rings. External (or
internal) layers are successively removed and measurements are made of
the changes in the internal (or external) diameter. The internal
stresses can be calculated from these changes. The rod method was
developed by Prof. N.N. Davidenkov. Here one surface of a rectangular
oylinder is ground off in layers. The resulting deformation of the
opposite side of the block is measured and the stresses are calculated.
.Card 1/3 Stress diagrams for the speciments are then constructed.

Residual stresses in porcelain insulators. 110-2-11/22
When the porcelain speciments'are cooled in the hardening-
te*erature range at a speed of the order of 4 0 per our,
compressive stresses of some 80 kg/cm2 are set up near the surface and
tensile stresses of the order of 40 kg/cm2 occur near the contra.
With slow cooling, at 5 - 100C per hour over the same temperature
range, there are practically no residual stresses. When cooling at
the rate of 250C per hour, which is common industrial practice, the
tensile stress near the surface of the speciments is about 20 kg/cm2.
Residual stresses of thermal origin are always compressive ne&r the
surface, and the stress diagrams obtained indicate the existence of
structural stresses. To establish the temperature interval in which
stresses are set up, a number of porcelain rings were made and annealed.
They were then subjected to various heat-treatments with different
rates of cooling. The results of deformation measurements and the
corresponding results of stress calculations are given in Figs. 1 & 2.
Internal stress can be completely relieved by treatment at 11000C, and
stresses can be set up again by re-heating and relatively rapid
cooling. It was then established that changes in the magnitude and
sign of the residual stresses depend on the rate of cooling in the
temperature range 800 - 5000C. The development of tensile stress in
certain cases was attributed to structural changes and in particular
Card 2/3 to modification of quartz. Insulator porcelain contains up to 17~

Residual stresses in porcelain insulators. 110-2-11/22
of free quartz, which is converted from the a to the.? form on
passing through the temperature of 5730C. Special experiments were
undertaken to confirm this hypothesis. The results, given in Fig.3
and Table 2, show that the effect is most marked when the quartz
content in high, and is absent when the quartz content is very low.
Hence, insulators with no residual stress can be made by appropriate
heat-treatment, if the quartz content in kept very low. Another
method of reaching low residual stresses is to adapt the beat-
treatment to the quartz content. The method by which temperature
stresses are set up when porcelain products are cooled, is discussed
in some detail. It in considered that residual stresses are unlikely
to cause cracks during cooling because they reach their maxiva- value
only when the temperature is uniform throughout the product, i.e.
at room temperature. However, they may cause spontaneous cracking
during storage, or in service. There are 2 tables, 4 figures,
2 literature references (Russian)
ASSOCIATIONt GIEKI.
AVAILABLE: Library of Congress.
Card 3/3

FRADKIN, A.Ye., knnd.tPkhn,.nauk; RJUNIIIIIA-1, I.S., Inzil,
Stabilization and remote control of ti-,e consumption of liquid fuel
in industrial furnaces. Trudy 6IEKI no.4:9)-98 160. (MIRA 15:1)
(Ceramic industrJes--Equipment and supplics) (Remote control)

FRADKIN, A.Ye.; KHLOPIN, G.M.
Natural gas kilns in tho insulation industry. Gaz.prom. 6 no.8:
15-18 161. (14IRA 14:10)
(Gas, Natural) (Kilns)

:I - T A 7
i ; I , " . - .
"Superhigli Frequency Antennas," (book) 647 PP. published by tilie Publishin6
House "Soyetakoye Radio". Moskva, 1957-

ZIMANOV, V.S-, insh.; .insh.
Further improvement of navigation and power facilities in the
Moscow Canal. Rech.transp. 18 no.10:41-43 0 '59.
(Moscow Canal) (MM 13:2)
(Automatic control)

FRADKIN., B. M., Engineer
Cand. Tec'.-mical Sci.
"-'-"erronagnetic Ball in a Magnetic Field and Some Problems of the Theory
of Magnetic Dielectrics." Sub 8 Jun 51, Moscow Order of Lenin Power
Engineering Inst imeni V. M. Molotov
Dissertations presented for science and engineering degrees in
Moscow during 1951.
SO: Sum. No. 480, 9 May 55

USSR/Ragineering - Paver Stations Apr 51
"Measures Against Ground Ice and Floating Ice in
Water Channels of Hyd:roelectric Paver Stations,"
B. M. Fradkin, L. S. Kuskov, Engineers
"Gidrotekh Stroi" No h., pp 14-16
Describes numerous cases of frosting and clogging
with ice of grates in feeding cb-nels of many
hydroelec stations during winter of 1950. Con-
cludes that clogging of grates may occur in ma-
jority of stations located in the middle part of
European USSR and suggests 2 preventive measures:
197T52
USSR/Engineering - Power Stations (Contd) Apr 51
8p davicea fo:r bentIngir the _-r-!kt-eLz k>r.removing
ice from grates with steam or water under pres-
sure and devices for complete or partial lifting
of grates.
197T52

VRAPIKIN, 13. M.
MR/Faysice N*wtodiolectrics Jul/Aug 52
"Some Problems ct the Theory of Magnetodielectrics,"
B. M. Fradkin,-14oscow Power Engr_Inst imeni Molotov
111z Ak Nauk, Ser Piz" vol 16, No 4, pp 481-497
Investigates unt;atisfactory interpretation of Varli-
statistical theory of magnetodielectrics. Stuaies
their permeability in variable fields and dielectric
losses at low frequencies. Indebted to K. M. Poli-
vanov.
PA 241T92
241T92

FaADKIN, B.M., kandidat tokhnichenkikh nauk
- 7
Ferromagnetic ball in a weak alternating magnetic field. Trudy, MEI
no.14:95-121 153. (MIRA 8:7)
(Electromagnetism) (Magnetic fields)

,; 1' 0
B, !,,,. POLIVIMV, K. M., KATYGV, N. G.) '11,TGMz~;V, V. V. (Moscow)
"To the Theory of Artificial Magnetodiclectric from J~Latuljjc pawdor,"
paper presented at the International Conferen" on Physics of maenetic Phenomena,
Sverdlovsk, USSR, 23-31 May 1956

AJ
.LLPSHIN, ~.S., inzhener.; NITUSHIL. A.V., doktor takhnicheskikh nauk,
professor; PR&DKIN, B.M., )mndidat tekhnicheakikh nank.
Selective heating in a hieh-frequency electric field. Trudy NEI
no.18:46-56 156. (MLRA 10:1)
1. XmfedOa teorOticheekikh oanov eiektrotakhniki.
(Induction heating)

USSA/Electrici;ty -- Dielectrics G-2
Abs Jour : Refer-at Zhur -Fizika, No 5, 1957, 12115
Author : Lapshin, M.S., Fradkin, B.M.
Inst --------
Title Measwement of Characteristica of Glass and of Adhesive
Film in High A,equency Fields.
Orig Pub Tr. Wisk. energ. in-ta, 1956, vyp. 18, 172-182
Abstract Measurements were made of the dielectric constant E
and the loss angle (tan of various substances with
the aid of the Q-meter KV-I with the temperature ranging
from room temperature to 80 --- 1500 and in the frequency
range from 1.5 to 24 Me. Specimens of plate glass, of
contirraously-rolled glass, of co=ercial rubber, and also
of adhesive film of 18% plastification at a moisture con-
tent of 1% were all measured. The investigated substance
was introduced between the plates of a capacitor, placed
in a thermostatic oven. The capacitor was connected -with
Card 1/2
LISSR/Elec.,trici.ty ... Dielectrics
Abs Jour Ref Zhur - Fizika, No 5, 1957, 12115
the Q-meter by means of a coaxIal line. TakJng two
measurements (with and without the specimen), the values
of C. and Q, were determined from derived formulas. The
errors due to disregarding the effect of the coaxial
line exe calculated.
Card 2/2

Zurn.techn.fis, 2-6-, fasc-5, 1048-1059 (1956) CARD 2 / 2 PA - 1327
upon the sphere, H 1 - the field strength due to polarization of the not re-
magnetized domain H 2 - the field strength due to the polarization of the re-
magnitized domain: H T - the field strength due to eddy currents, Hs - coercitive
force.Next, the field strength due to the polarization of matter and the field
due to the eddy currents are computed. Now the equation of motion of the wave
front of re-magnetization is written down and transformed. The process may be-
gin with a negative value of & H and may continue at the expense of the
magnetizing effect of the not re-magnetized domain (which, at the beginning of
the process comprises the entire sphere). Therefore a supporting exterior
field is necessary for the maintenance of a totally magnetized state in a ferro-
magnetic sphere. The dynamic characteristics of re-magnetization are univocal
in the case of arbitrary values of the parameters H s, J ( = magnetization of
the matter), JP ( - electric conductivity of the matter) and some other para-
meters. The entire magnetic moment of the sphere consists of the magnetic
moment M 1which is due to eddy currents and the magnetic moment M 2which is
due to the polarization of the material of the sphere. Both moments are com-
puted and discussed.
f
IUSTITUTION: Moscow ME1 (probably - Moscow Electrotechnical Institute)

ZHDANOV. V.S.., inzh.;-FRADKIN, B.M., inzh.; YUDOV. M.P., inzh.
Simplif7ing the starting circuit for synchronous motors of large
pumping units. Blek. eta..30 no-3;53-56 Hr '59.
(KIRA 12:5)
(Alectric motors, Synchronous) (Pumping machinery)

NEYMMI, Leonid Robertovich; DEVIRCHYAR, Kamo Seropovich; POLIVAIIOV, K.M. I
prof.~ retsenzent; FRADKIN B 14 p dote., retsenzent; KUPAIZAN,
S.D., dote., retse zent; SKAYA, G.Ye.,, red.; MURASHOVA,
V.A., tekhn. red.
[Laboratory manual on electromagnetic fields] Rukovodstvo k la-
boratorii elektroragnitnogo polia. Moskva, Gos. izd--vo."%Iysshaia
shkola." 1961. 219 p. (MIRA 15;4)
(Electric engineering-Handbooks, mauals, etc.)
(Elec'tric fields) (Magnetic' fields)

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Fwn%f, D.P.
Zadachi laningradakogo Opytnogo Slantseperegonnogo Zavoda, Cory-uchiya SlantBy,
1933, Ito. 1, 8.
SO: Goryuchiye SlantaY #1934-35, TN .871
G .74

tunnel Inaya Fech I 71.11ya Fhvelevaniya "I antap, F-oh i,-,Ya Y -Y c a I,n ts iya
Na Lsnz, -icryuchiye Slantry, 19-33, lio 6,28
SO:
Gonjuchi-ye Slantsy 4" -1934-335, 11-T .8371
G .74

CHERNOZUBOV, S.A., inzh.; FWKIN, B.P., Inzh.; PEIMIN, V.M., ITzh.
Converting a sand-lime brick plant to the production of
large panels. Stroi. mat. 10 no.604-27 Je 164.
(MIRA 17;10)

D A-.
- .
:j'. C. " ~-Ii,
lletc-]Y Rez)d Stekla. "Lek-1.0 I i "" , ~ ~- -, - , , , , -
ICI
so- LZrOP13' NO- 31, 19",

C
IMBMVSKIKE, Seraf im Maksimovich;' FRAMIN, David Arkadyevich; ISLANKINL,
T.F.. redaktor.- DKITRIUVA,~ K41 - MWkIy redaktor.
Nodern techniques In the manufacUrs, of glass] Savremennais, takhniks.
stskollnoge prolsvodetva. Moskva, Isd-vo OZumie,l 1955. 31 P. (Vae-
solusnoe obahchostvo po ramprostranentiu. politicheskikh I nauchnykh
snanlig Sere 4, noolO)m (MIRA 8:5)
(Glass mamfactmro)

USSR/ Kiiseellaneous - Conferences
Cam 1/1 Pub. 104 - 11/11
Authors i Fradkin, D. At
Title I Meeting on Mglxtension of the exploitation and reduction of repair
periods for glass furnales
Periodical IStek. i ker, 26 30 - ~2, Feb 1955
Abstrs,Ot, tMinutes are presented of the special meeting held in January 1955 at the
Gomelsk Glass Plant At which the problems of extending the service life
and reducing the repiir periods of glass furnaces were discussed.
Institutiont
Submittedt

82
AUTHOR: Fradkin, E. A. Cand. Tech. Sci.
TITLE: Study of a Tunnel Kiln at the "Proletariy" Plant
(Issledovaniye tunnel'noy pechi zavoda 'Proletariy')
PERIODICAL: Vestnik Elektropromyshlennost, 1957, No.2.
pp.50-56 (USSR)
ABSTRACT: in the manufacture of ceramics there is a strong
tendency to use tunnel kilns which permit the use
of conveyors. Three such kilns are installed in
different insulator factories in the USSR. The
Ceramic Institute in co-operation with the
"Proletariy" Plant mastered the firing insulators,
typesV11 -329 and 1A11-257, in a tunnel kiln but the
results were not satisfactory because fuel con-
Card 1/5 spmption was high and the output low.

82
TITLE: Study of a Tunnel Kiln at the "Proletariy" Plant
(IssledovaTtiye tunnel'noy pechi zavoda 'Proletariy')
This article describes a study of a tun'nel kiln
at the "Proletariy" Factory made with the object
of establishing optimum conditions of operation
when firing insulators (mostly type WT -35.)
The oil fired kiln is 121 metres long 2.3 metres
wide, 2.175 metres high and will hold 60 loaded cars.
The cycle lasts 68 hours so that the throughput is
21 cars per day. The number arrangement, the type of
furnaces, and the air cicrulating system are
described.
A long term investigation of the kiln's
operation was made under production conditions.
Temperature distribution was investigated by
Card 2/5 placing thermocouples in the cars.

82
TITLE: Study of a Tunnel Kiln at the "Proletariy" Plant
(Issledovaniye tunnel'noy pechi zavoda 'Proletariy')
The products of combustion were analysed. The
flue gases were analyzed an4 found to contain ex-
cess oxygen. The temperature distribution within
the kiln is presented in several graphs.
It was found that in order to obtain high quality
products correct gas conditions are even more
important than temperature conditions. The CO
content should be about 4 - 5% in the reducing
zone, and there should be no incomplete combustion
card 3/5 products in the oxidising zone. Considerable

82
TITLE: Study of a Tunnel Kiln at the "Proletariy" Plant
(Issledovaniye tunnel'noy pechi zavoda 'Proletariy')
temperature variations in the first part of the
kiln were caused by air drawn from the inspection
to the working channel. Much can be done to im-
prove the temperature distribution by providing a
free channel near the bottom and hindering the flow
of hot gas around the sides of the cars. As a
result of this study the gas and temperature con-
Card 4/5 ditions in the furnace were stabilized, and the

82
TITLE: Study of a Tunnel Kiln at the "Proletariy" Plant
(Issledovaniye tunnel'noy pechi zavoda 'Proletariy')
furnace has worked for a long time now with only
1.5% of firing rejects. A considerable part of
this success is due to stabilization of the fuel
supply by the installing J>pM type regulators.
The article contains 8 diagrams; there are no
literature references.
ASSOCIATION: State Institute of Electroceramics WZ K W
(Gosudarstvennyy elektrokeramicheskiy institut)
PRESENTED-BY:
SUBMITTED:
AVAILABLE: Library of Congress
Card 5/5

p S-M til
MaUll., E. Mbter W Sui - (uvm) "Certain protums in tije Tw3ory oi:
P" uiciev Tiivi Creator SpULS". Leningrad., v pp. (Uu u.L Ecbzc RSFSRp
Leningrad S.uta N-uspeo I"ut. A. I. G t.-sen. Dept of T"wret.PLqsics),
Ml 14- :N, .05,11 P.V4)

AUTHOR FRADKIN E.E.
UTLE With Spin 312
(Ghantitsa so spinom 3/2 v
FERIODICAL Zhurnal Eksporim. i Tooret.
(U.S.S.R.)
Received 5/1957
AMTRWT
Card 1/2
PA - 2686
in the Electromagnetic FieId
*loktromagititnom pole - Russian)
Fiziki,1957, Vol 32, hIr 2, pp 363-365,
Reviewed 6/1957
The author investigates in his paper the relativistically invariant e-
quation for a particle with spin 3/2 in an eletromagnatic field
(akffk + i ?e ) Y a o. ffk - a/axk - 'eAk (k w o,1,2,3)
The matrices ok are given in their parametrical form by M.Petras, Chokhool.
fin. zhurn. 5, 16o (1955). The author of the pater under review derives
from the abo** equation additional conditions in relativistically cove-
riant form. After xiiv*ral simplifications, we obtaii the following *qua-
tion of the Schroviinger typos i BWa x - HY . H is the Hamilton func-
tion of the particle with spin 3/2 in ligear approximation with respect
to the small parameter &Fnm. (Fxmstands for the tonsor of the electro-
magnetic field.). The extraordinary smallness of aFrm permits us to ne-
glect the share of the higher approximations of aFIIM in the Hamiltonian,
and this nglect is permitted oven at very strong fields. The Hamilton H
is given explicitly. The particle with spin 3/2 has a kinematic dipole
moment and a kinematic quadrupole moment. In addition, the Hamiltostian H
contains also a specific term of the dipole type. This term depends on
the momentum. Because the mean value is ascertained over the charge don-

The Particle With Spin 312 in the Electromagnetic Field FA - 2686
sity, the normalization condition readsfY 4S' ~J(10- 1. The mean value
of the energy of a particle with spin 372 in the electromagnetic field
is expressed by the following formulaso 0, *
E-fi,l i woxoff (4) -)Y Y HY (,rr)
Finally the paper gives explicitly also an expression for the energy in
linear approximation with respect to the small parameter aF=. Thus', in
addition to the term of the Hamiltonian Ho of the Dirac type, also the
momentum-depeadent additional terms of the Dirac type as well as the *-
lectrical and magnetical quadrupole moments yield a share in the energy.
For reasons of comparisons The particle with spin 0 and 1/2 have no ki-
nematic moments. The partialis with spin 1 has a kinematic dipole moment
which yields no direct share in the energy.
(No figures or reproductions).
ASSOCIATION Leningrad State Pedagogic Institute.
PRESENTED Br
SUBMIT TED 0.7-1956
AVAILABLE Library of Congress
Card 2/2

AUTHOR FlkDKIN E 5()-"7/56
TITLE ia ~'hc of
Spin Particles.
(0 metode I'larita-Sbringers v teovii a
-hussian)
PERIODICAL Zhurnal Eksperim. i Teoret -Fizi%i, 1957, Vol 32,Nr 6,p,,) 1479-11"82
(U.S.S.Ii. )
ABSTUCT The author here invootigatc.- a ~;eneralization of thic ;.,ic-
thod to particlcr, -.-jith a hi-h~~r :;nln (s>31/2). The present pa-per
shovia the followirie,; The density- of the La~;raxijaxi as viell as th;:-
the field equatiOlLs resulting herefrom and the additional condi-
tions givan by P.A.Lroldauer and z;.Rev.1o1,279(1956)
are applicable orli to particles vit'a spin and cannot be extendcd
to particles -~iith a hi,-,her spin.T'Iie re-.ults of this paper,which
concern thz! ma6n!tic moLrnt and the quadru.pole moment of the par-
ticl,.-z ri.,,.y thcre-fort, be- looked a7jon 3s c-,-,,-IWabli,ihed only for partic-
les with spin 3/2.Lt firut Lhe evasity uielitioned of the La6raii&ian
in again v.-rittez, do-in explicitly.In caue of free particlev. this
function =uot lead to the DIiAC equations (];~--)AA~+ --I)'FVj U2 ... On- 0
with the additional donditions )~,Y402 .... On - 0 1 1 A~ 7, 4 V 2 - . . vr, - 0 1
The follo,.An- has; to be takcii into account for the derivation of
U
equations %ith a Iii.;hc-r spin than 3/2: Thi7 s;a.;ie',rLr conditions of
the tensor indicefj 701 t'2 .... V11 lead to the fact that the variations
Card 1/2 6T~IV2 ... gn are not indeptndent.It 13 esp,_-Cially C;34tntial that in

On ~.in in the Theory of H----lf-
I
inteZx~LI-31,in 5&6-2T/56
the ca5e of the variation OC L th,~ G~- of T~ On. - -1:11 'ith r,
upact to the indcx -C ir, tal-f--n into account."lic-
11 -,-Uaticlio revultin~,
from tht --:fact variation foa.- a iarticIv, with -,jpir. a - n +(1/2) are
ex- -.,. - to
- writ'L~~%r down. St:ixtin- 6ith ~i ta As
,~,~U*,tion.- than u.,O~.novtn au,~,-Aitic2 and th~! c-,,ual.ionz incor.-ipa-
tib1--.I,ie:-.-t,thc aut-hor Inve~--tiLat,'!z the o1: the aCplicaluiliti
of t!-.,- met.`iod bi R-kVITA-LSC*MINV,---2 to th,!~ 1,a~-ticlca vii,.111 zpin 1j,".
The nf~thc~ Iq Ptridshtg no I~ositive rd-
sultj for a particle with spin 5/2. A Vo~~--;iblc for t*-i-. fzA-
lure lo. :.;ointed out.
(No illu,,tr-lt~-011;0-
SU3%-IT'~`ED 10-10.1-956
A V-k 1 I-AU3 L EUlbrsr,~ of
card 0-12

20-2-12160
'AUTHORSt Fradkin, E. Yo. Izmaylov, S, V,
TITLE: On the Permissible Transformations of the Equations for
Particles With Higher Spine (0 dopustimykh prebrazovaniyakh
uravneniy dlya chastits a vysshimi spinami)
PZRIODICALt Doklady Akademii Nauk SSSR, 1957, Vol. 114, Nr 2, pp.277-280
(USSR)
ABSTRACTs The particles with any spins are described by equations of the
type (L'(8/d-xi) + 1-4 W(x00 X19 X20 X3) - 0. In this connec-
tion Y(xo j XIt X2. x3) alr(ot, xv yo Z) signifies the wave
function which is transformed according to a finitely-dimen-
sional representation of the complete Lorentz groupi
Li(i - Opl,2,3) - quadratic matrices, X- a real constant
different from zero. The invariance of the above-mentioned
equation with regard io the just mentioned transformdion is
guaranteed by the following additional conditions for the
Card 1/3 matrices Lit

20-2-12160
On the Permissible Transformations of the Equations for Particles With
Higher Spins
ILi I~k] ''a L' jjk _ IjkLi . gijLk _ gik Lj; (ijjjk - 011020)l
[LiTI - 0. In'thia connection the I jk signify infinitesimal
transformations of the corresponding representation of the
specific Lorentz group end Tois the transformation correspond-
ing to the ref leotion x -.* x , A_ e, (or- 1 2,3). At f irst
the authors investigate the possible linear transformation
of the wave function 4r(x x X230 X )' iseo transformations
of the type V(X I XI I x0: X11 ;qx t X1 t X X ) which
0 2 3 0 21 3
do not change the essential properties of the initially given
equationso The form of the S-matrix for.the permissible trans-
formations is determined here. To the permissible transforma-
tions above all belong the transformations V which do not
change the form of Ijk and T, i.e. V-I,JkV.Ijko V-1 TV-T,
(Jjk - 01112,3)o The matrix A plays an important part. The
essential properties of Ijk, T, L" and A do not change in
the caae of any unitary transform tionso The permissible
transformations have the general form S U1VU 2t' wher 'Ulf
and signify any unitary representation
Card 2/3 U2 ns and he fo m

20-2-12160
On the Permissible Transformations of the Equations for Particles With
Higher Spine
V is also given. For the particles with higher half-integer
spins a . n + (1/2)(n - 1,2,....j) only the density of charge
of the free particle at rest is an invariant of the per-
missible transformations. Finally these transformations are
more closely investigated for a particle with spin 3/2. The
essential feature of these transformations lies in change
of the metrics in the "additional" space with the spin 112.
There are 5 references, I of which is SOV14rt.
ASSOCIATION: Leningrad State Pedagogical Institute imeni A. I. Gertsen
(Leningradskiy gosudarstvennyy pedagogicheakiy institut im.
A. I. Gertsena)
PRESENTEDt December 299 1956, by V. A. Fok, Academician
SUBMITTED: December 21, 1956
AVAILABLE: Library of Congress
Card 3/3

AUTHOR: Fradkin, ".Z. re. 20-5-16/54
TITLE: The Algebra of the Matrices in the Theory of Particles
with Spin 3/2 (Algebra matrits teorii, chastits so
spinom 3/2).
PERIODICAL: Doklady Akademii Nauk SSSR, 1957, Vol. 115, Nr 5,
pp. 907-910 (USSR)
ABSTRACT: The present report determines the most important relations
of the algebra of the matrices ak which occur in the wave
equation ak 8 + ije ) T(x
x
1x
9x
i -T
)
2
i
i
3
-k
for the particle with the natural spin 3/2 and positively
defined total charge. Here
) a T (t,x,y,z) denotes the
T (x
Px tx
lx
2
0
,
16-component wave function of the particle with spin 3/2.
The ak are ;6-dimensional square matrices the concrete form
of which has already been given in various previous works.
CARD 1/4 Z denotes the mass of the particle. The minimum equation

20-5-16/54
The Algebra of the Matrices in the Theory of Particles with
Spin 3/2
for the matrix of the particle with the natural determined
spin a has -the form
(L n) (L 2_1) - 0. For the particles with spin
1/2, 1,3/2 or 2 n 6 2s - 1 is true. However, the
commutator for the particles with spin 0 and 1 resulting
from these equations are given. For the particle with
spin 3/2 the exchange relation
7- a iak(a 1aM - 9lm 0 is obtained. Neither of the
p
three types of exchange relations with partial sym-
metrization with respect to two or three indications, nor
their linear combination are satisfied by the matrices
k
a .Therefore the general exchange relation is true not
only for the mairices ak of the theory of the particles with
spin 3/2 but also for Dirac's matrices (dirakovskiye
CARD 2/4 matritsy~tDuffin-Kemmer matrices (deffin-kemmerovski~e

The Algebra of the Matrices in the Theory of Particles with ~~5-16/54
Spin 3/2
matritsy) P k, for the matrices of the theory of the
particle with the mass Z.and both spin states 3/2 and
1/2 as well as for many other matrices. For this reason
additional conditions have to be determined for the
algebra-of the matrices of the particles with spin 3/2.
These relations are here written down explicitly. For the
complete construction of the algebra of the matrices of
the particle with spin 3/2 it must therefore be pssible
to represent the infinitesimal transformations I
of the wave function xy in an infinitely small Lorentz
transformation by diagonal combinations of the matrices
ak. The transformation T corresponding to the reflection
X0 _'I' X 0xv I xv has the f orm.
T (3/4) icx'aiao + a0aiai -(8/3)ao - 4 (ao)31 T-1
CARD 3/4 There are 11 references, 5 of which are Slavic.

The Algebra of the Matrices in the Theory of Particles with 20-546/54
Spin 3/2
ASSOCIATION: Leningrad State Pedat;OKical Institute imeni A. I. Gertsen
(Leningradskiy gosudarstvennyy pedagogicheskiy institut im.
A. I. Gertsena). -
PRESENTED: By V. A. Fok, Academician, April 5, 1957
SUBMITTED: March 27, 1957
AVAILABLE: Library of Congress
CARD 4/4

'11:0 ~
LAMILI-My G.All.; S'~LALI:, V.3s; C11'r, .P.
Resolution of a monochromtor uith photoeloctric rocording. Opt.
I --pol-.ia-. 7 no. S.-780-7 U-,. D 159. ("al'. 14:2)
(monocilromators)

-~.Ye.; ClUXUls A-P,
paratus function of a Fabry-Parot spictromator with a
Ap
rac-".,~Uular orifica 1).Lato. Opt. i spe'ctr. 7 no. 6:765-786,
D 159. 14:2)
(Spoctrometar)

F Y"
:'Othcd for tm~,.,;n-orraing ,pctral linu, Shapes and its :,L -,-dicatlon
-to tito matisuroubnt of thLy touperature vrA othar parar--.,~rs of 4i
light oourco. Opt. i z-,olk-tr. 7 no. 6:S2C-823 D 159.
(',-al~ 14:2)
(Spectromater)

21' (1)
AUTHORS: Kaliteyevskiy, N. I., Chaykaq M. P.? SOV/56-37-3-57/62
Pacheva, I. Kh.,,Rradkin, E. Ye.
TITLE; nuclear Moments of the Odd Gadolinium Isotopes
PERIODICAL: Zhurnal akeperimentallnoy i teoreticheskoy fiziki, 1959, Vol 37,
Nr 3(g), pp 882 - 884 (USSR)
ABSTRACT: The present "Letter to the Editor" contains an abundance of de-
tails partly.taken from the authors' own investigations and
partly from other publications. In an earlier paper (Ref 1) the
hyperfine structure of the 3 lines of CA 1: 5015, 5103, and
5251 1 was investigated by means of a photoelectric spectrome-
ter. The investigations were carried out on the very pure iso-
topes Gd'55(97-3%) and Gd157(91.4%). Both isotopes have the
spin I - 3/2. The magnetic moments: p 155 ' - 0-3L+0.04, 24 2
"157 ~ -0-4C�0-04. The quadrupole moments: Q 155 - 1* 6~1o- cm
Q157 = 2!10-24cm2l these values are nearly double as high as
those found by Speck. The internal quadrupole moments
Q155 . e~10_24CM2 and Q157 _ lc?10-24CM2 agree as to the order
Card 1/2 0 0

Nuclear Moments of.the Odd Gadolinium Isotopes SOV/56-37-3-57/62
ASSOCIATION:
SUBMITTED:
Card 2/2
of magnitude with those obtained according to the method of
the Coulomb excitation of the gadolinium nuclei. The deforma-
tion parameters were found to amount to 6 155 ' 0.31 and
6157 ~ 0-37- With respect to the gyromagnetic ratios g K and gR
(of the internal and collective motions) data, which were ob-
tained front Nilsson's tableaq are compared with those obtained
by other (Western) authors. Calculations resulted in
9K 155 - - 0.8 nuclear magnetons and g K 157 ~ -0- 9 nuclear mag-
netons, gR 155 - gR 157 = 0-7. The data concerning the g and 6
are finally compared with those obtained by Gauvin. The authors
thank V. S. Zolotarev for placing the isotopes at their dis-
posal, and L. K. Peker for his advice and discussions. There
are 9 references, 2 of which are Soviet.
Fizicheskiy institut Leningradskogo gosudaretvennogo universi-
teta (Institute of Physics of Leningrad State University)
June 19, 1959
0!

683C&
-AUMORS Kaliteyuvskiy, L.I. , Chaykn, M.P. , Pacheva, I.Kh . and.- Fradkin, S.Ye.
JtA
TI TLB Spectroscopic Determination of 'Nuclear Morients of Odd GLAdolinium
Isotopes 1~
PERIODIC"'. Optika I spektrooicopiya, 1960, Vol 6, 11r 1, pp 13-22 (USSR)
ABS MCT: The authors Investigated photoelectrically the h-oarfine structure
(h,f.s.) of the 5015.04 1 (_,"G9--a"FO) , 5103. 45 V (Zf G8--at'Fo) ,
0 8 7
5251.18 lines-of separated gadolinium isotopes and
natural gadolinium. The purpose of the investigation was to
determine the quadrupole moments 01,Gd155 andGd157 and to confirm
optically the spin of these nuclei. me auth.;rs ased a photoelectric
spactrometer -with a Pabry--Perot interferomoter (Rafs 7, 8) and a
photoinultiplier FEU-17 with a good signal-to-noise ratio at low
light intensities. The spectrum of Cadolinium (used in the form of
Gd203) vms excitod in an argon-fillol dischargo tube with a hollow
cathode. In order to minimize the Doppler broadening, the hollow
cathode was cooled with liquid air anJ the lischarSe currftnt wag
kept below 30 nA (the line-vidth roie linearly -with current, Fig 1).
Ca rd 1/3 Under such conditions the line width corresponded to that in a gas
at 2500K. Even then it was riot nossible to resolve all the h.f.s.

68308
OV/ 51-8-1-3/40
Spectroscopic Datertninrttlon of NuclavAr Moments, of Odd Gadolinium Isotooer~
components. Gadolinium samples had c=positic-na shown in Tq-bla 1:
~f
lir 1 had 97.3;4 Gdl-"5, Nr 2 had 91.4~; 0-157, Nr 3 (natural Gdj' had
0.2~,, GdJ52, G4154, 15A1% Gd155, 20,59%Gd156, 16.42% GdI57,
23.451. Gdl58, 20.87% GdlfO, Sane of the rasult;E obtiined- are riven
in Figs 2 and 3 and in Table Z, Fig 2 shmva the relative po~4itions
of the h.f.s. emponents of C-dl57 and of Gd!60, GIJ158 anti GdUC' Jp tila
case of the 5015 4 31ino, Fif; 3 sho-01, the anfftly5ll of the C,(-'157
6015 4 (a) and 5101 lines into their camoonent- Table 2
lists the valuea of the hyperfine sa~er?tio:- '17(in and
of ca-ictlated and clundiapcIs mcm6nts R (in 10 -n~).. i'ig 4 Shows the
transitions of the three lines invetiti&AteO i-, ~chem--tic foria. The
authors found that Fadolinium lines car. be analysed into their components
only if four ectuponents are ass=ad for both GdI57 and C055. Thir.
means that the spin of both theBe nuclid*3 is I = 3/2, in agreement
with Low (Ref 5), Manenkov and Proknorov (Ref 6). Depending on the
assumptione mada,the authefs obtained the following value-3 for the
quadrupole moment;$ either
9157 = 1.6 ani ~155 = 1.2 x 10-24~.,m2, le(
or
Card 2/3

f 683U8
60V/51-8-1-3/40
Spectroricopic Dotermination of Nuclear 'Moments of Odd Gadoliniuri Isotopes
0-157 ~I and Q-155 = 1-6 x 10-24cLa2-
The magnetic moments were also f ound -
11157 = -0.40 t 0.04 n.m. ard. 1i155 = -0.321 L 0.04 n.m.
Consequently the moment ratioG naro:
ql5c-/ql57 = 0-8 � 0-1, "155/11157 = 0.79 � 0,02,
The deformation parameters 8 of the t-no nucliles ware found to be
8157 = 0 - 37 and k55 = 0.31, and their ratio Aqas 6155/8157 = 0-6-
The gyromagnatic ratios for the internal (gk) ani the collectivo (gR)
motion %vare also detarminod. They -.,are GU57 ~ -0-9, Glc155 = -0-8,
SR157 ": 6R155 ~ 0.7; gkl55/&kl57 = 0-9 � 0-1- Acknov.,ledoents are
made to V.S. Zolotarev for supplying separated gadoliniuja isotopes and
to L.K. Peker for ht'sadvica. There are 4 figures, 2 tables and
21 references, 6 of which ura Soviet, 10 Enrlish, 4 German, 1 Suiss
Ca rd 3/3 and 1 Danish.
SUBMITTED: June 19, 1959

S/O 56 /60/0 3 /046
24,4119, DOO-'1/'B0", 0
AUTHORS: Kaliteyevskiy, N. I., Fradkin, E. Ye., Chayka, M. P.
TITLE: Quadrupole Moments of Odd Barium Isotope ail
PERIODICAL. Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1960.
Vol. 39, No- 400), PP. 954-956
TEXT: In order to determine the quadrupole moments of odd barium
isotopes, a study of the deviation of the hyperfine structure from the
interval rule was made. The atructure of 3P1 term of both the lines of
Ba I: A = 4599.7 A and X =t 4573.9 A was;determined by means of the
hyperfine structure of highly enriched separated isotopes Ba'35 (a9-3%v)
and Ba137 (78.8%). Both the isotopes have spin 3/2. Therefore, the
structure of the 3P, term is characterized by two independent intervals
of the hyperfine structure whose magnitudes are related to the constants
A and B of the interval function W P . Wi + (1/2)AC + BFC(C+1)
- (413)I(I+I)J(J+1)1 ; C = P(.F+l) - I(I+1) - J(J+1); F = 5/2, 3/2, 1/2.
Card 1/2

quadrupole Moments of Odd Barium
Isotopes
84390
S/056/60/03n,'100
B000070
The experimentally observed values of the intervals and the constants A
and B are given in a Table. The quadrupole moments were calculated from
the constants:
-12)-10-24 cm 2, Q(Ba 137) . (0.210. 1).10-24 cm2. Since
Q(Ba135) = (0.25tO
for both the isotopes Q*70, Ba 135 as well as Ba 137 must have a hole in the
2d 3/2 neutron level. The authors thank V. S. Zolotarev for making
available the isotopes, L. K. Peker for discussions, and B. A. Strugach
for calculations. There are I table and 9 references: 4 Soviet, 2 US,
3 German, and I Swedish.
ASSOCIATION: Leningradskiy gosudarstvennyy universitet (Leningrad State
University)
SUBMITTED: May 12, 1960
Card 2/2

S/054/61/000/001/003/008
7, 113 5j B117/B203
AUTHORS: Kaliteyevskiy, N. I., Chayka, M. P., Fradkin, E. Ye.
TITLE: Application of methods of optical spectroscopy to study
the properties of atomic nuclei
PERIODICAL- Vestnik Leningradskogo universiteta. Seriya fiziki i
khimii, no. 1, 1961, 25-33
TEXT: The authors studied the possibility of applying the methods of
optical spectroscopy to study the properties of atomic nuclei. When
checking these methods, they used, above all, the data found by them-
selves in 1959-60. The relative intensities of hyperfine structural
components were measured with a photoelectric spectrometer with a
Fabri-P6rot interferometer (Ref. 2: N. I. Kaliteyevskiy, G. M. Malyshev,
M. P. Chayka. Optika i spektroskopiya, VI, 820, 1959). The light
intensity of this instrument was higher by at least one order of magnitude
than that of a monochromator with diffraction grating of equivalent
resolving power. The investigation of only 1 mg of LU203, which was
Card 1/5

Application of methods of...
S/054/61/000/001/003/008
B117/B203
enriched with Lu 176 up to about 30 %, yielded quite clearly a spin value
of I = 7. This investigation proved the importance of the optical method
for determining the nuclear spin, as well as its suitability as compared
with other methods. The same conclusions were drawn when considering
results obtained in the measurement of sublevel ranges of hyperfine
structure. With sufficient resolving power of the spectrometer, the
reading of components with I >J gives a unique spin value. If the resolu-
tion of components is limited by the Doppler broadening it is generally
possible to disintegrate, with sufficient uniqueness, the contour of the
line into a certain number of components at a high signal-to-noise ratio.
When determining mechanical nuclear moments, the interference method can,
of course, not yet be regarded as perfect. The problem as to the accuracy
of the method of determining magnetic and quadrupole moments requires a
closer investigation, since direct measurement of these moments is
impossible. In experimental determinations of hyperfine structural
constants, systematic and random orrors are unavoidable. Here, the
authors deal with the Tole of ranlom errors. An analysis of experimental
data shows that in the investigation of a well resolved structure the
measurement of hyperfine structural ranges is well possible at present
Card 2/5

S/054/61/000/001/003/008
Application of methods of... B117/B203
with an accuracy of -0.5-10- 3em-1 The errors of measurement increase
with a worse resolution if it is necessary to disintegrhte the contour.
Table 3 gives the results of measurement of the hyperfine structure of
barium isotopes as an example of such an estimate. All data are given in
millikaiser (I mks - 10-3cm- 1). The errors of measurement are shown to be
no less than 0-5 %. Approximation methods must be used to calculate
absolute values of magnetic moments. For this reason, resonance methods
permitting a direct measurement of Blare preferable to the optical method.
In those cases where direct methods are not applicable, values of magnetic
moments may be calculated both by optical and radiospectroscopic measure-
ment with the same accuracy. When determining quadrupole moments,
quantum-mechanical approximation methods are indispensable for all methods
basing on the interaction of nucleus and electron shell. When estimating
the accuracy of such calculations, the authors made the following state-
ment: In single-electron systems, the entire theoretical calculation
error is 5-10 % for magnetic moments, and 15-25 % for quadrupole moments.
In each individual case, the admixture of many-electron states can be
considered, and Zl/r3> can be determined from the totality of data. This
Card 3/5

Application of methods of...
S/054/61/000/001/003/008
B117/B203
increases the accuracy of determination. For many-electron systems, it
is difficult at present to make a numerical estimate of calculation errors
which may be different for each individual case. In each case where it
is difficult to estimate the errors occurring in the calculation of
nuclear moments from the hyperfine structure of the term investigated, it
would be convenient to study other terms of the respective isotope.
Similar values of moments for several terms of varying configuration give
a certain security that errors do not become too high. It can be expected
to increase the calculation accuracy by completer joint theoretical and
experimental investigations of hyperfine and fine structures of atomic
spectra, as well as of gyromagnetic atomic relations. The authors thank
B. A. Strugach for making a number of computations. A. A. Manenkov,
A. M. Prokhorov, and G. Kopferman are mentioned. There are 6 figures,
4 tables, and 16 references; 8 Soviet-bloc and 10 non-Soviet-bloc.
Card 4/5
7. _7,7'

3/054/61/000/001/003/008
Application of methods.of... B1-17/B203
Legend to Table 3: Results of measurement of the hyperfine structure of
odd barium isotopes. (a) Ranges and constants of hyperfine stru.cturej
(b) isotopes.
1130TOW
HIlTepnoma 11 KomauTtA
CTC Balm BaIN
512-3/2 83,6 t 0.6 93,1:LO.4
5/2 112 137,4�0.7. 151,5�0,7
34.0�0,2 37,7�0.2
-1,2�0.6 -0,9�0.5
Card 5/5
AN

S/048/61/025/001/020/031
(A 6 7 00 B029/BO60
AUTHORS: Kaliteyevskiy, N. I., Chayka, M. P., Pacheva, I. IM-1
Fradkin, E. Ye.
TITLE: Nuclear momenta of odd isotopes of gadolinium
PERIODICAL: Izvestiya Akademii nauk SSSR. Seriya fizicheakaya, v. 25,
no. 1, 1961, 111-114
TEXT: This is a report of studies which have been described in a previous
preliminary communication. Several data have now been better defined by
additional measurementa and by improving the calculation method. The
authors used a photoelectric spectrometer and a Fabry - Perot spectrometer
to study the hyperfine structure of the three lines of GdI:
x - 5015 A (z 11G9 - a11FS); k - 5103 A (z 11G8 '* a11 F7) and
X = 4743 A (y 11F3 - a11F4). The measurements were made on separated
isotopes of gadolinium with a high-purity degree (Gd 155 .. 9715%1
Card 1/6
1v

- C ~,"
Nuclear moments of odd isotopes of ...
S/048/61/025/001/020/031
B029/Bo6o
Gd157 - 91.4%). The components of the fine structure of gadolinium lines
are so close to one another (15 to 20 mK) that the fine structure under
the given experimental conditions could not be resolved. It can be
resolved only if one presupposes four sublevels of the hyperfine
structure of the investigated energy levels of Gd157 and Gd155. This
unequivocally yields for both isotopes the spin 3/2. The position of the
components of the hyperfine structure was determined on the basis of the
splitting of the line structure taking account of all superimposing
isotopes belonging to other elements. The calculations were carried out
for the four intensive diagonal components of the line investigated. The
three independent intervals o(1-2), W-3), W-4) were ex-perimentally
determined for every line of the two isotopes. The ratio of the magnetic
moments of Gd155 and Gd157 was established by the direct combination of
the experimental data:
11 a (1-2) cr (1-3) + a (1-4)
"155 = 155 1-2) 1155 (1-3) + a155- (1-4) ' The ratio of the quadrupole
"l 57 "' (P, (n) - P4 (y%
(Y) 1 Y2
P
6 - lny, Y_+ +
2 P, (Y) 3
Y R n+1
Ro V 79:FS W < n + 3'* 2
P (n) and P N are voluminous functions of n; oc- e /Itc. In the range
1 3 1 ..- .
Z s;80, f (Z) -~, 1 with an error