"SCIENTIFIC ABSTRACT LOGUNOV, A. A. - LOGUNOV, N."

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000930420002-1
• Release Decision: RIF
• Original Classification: S
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• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

Dispersion Relations in Cases of Weak Interaction 20-5.1V54
studying the dependence of these functions of the trans-
miesion of the momentum to the nucleon, the "meson-
neutrino structure" of the nucleon can be determined. The
effeotive measurements of the 11me9on-neutrino structure"
are apparently the same as the "meson structure". The
results obtained here are well suited for the P-decay
and for those processes of decay of hyperons and K-mesons,
in which, together with particles which are in strong
interaction, also &k, e- and Nr- particles participate.
From the point of view of the verification of the causation
principle the study of angular- and energy distribution
of the electrons and myons in the processes of decay of
the hyperons and K-mesons is of special interest. There
are I figure, and 2 Slavic references.
ASSOCIATION: United Institute for Nuclear Research (Obfyedinennyy
institut yadernykh insledovaniy).
SUBMITTED: May 22, 1957
AVAILABLE: Library of Congress
CARD 3/3

AUTHORs Logunov, A* A-# 20-117-5-17/54
TITM Dispersion Relati3ne forflittual Processes (Di:3i;r;rsio-.,ryye root-
nosheniya dlja virtuallnykii protseaBov)
PERIODICAL# Doklady Ali SSSR, 1957, Vol- 117, lir 5, PP. 7~)2-7-94 (USSR)
ABSTRACTs The lajing down of the dispersion relations for the vertex parts
shows good prospects, that is for the "block.-ill occurring in the
matrix elements of the processes. The most simple examples are
the "blocks" of photoproduction and of the Compton effect, they
are given here in a schematic set-up. The "block" of photopro-
duction possesses a virtual quantuo (the second quantum is assu-
med to be real) as well as two virtual quanta, respectively. The
"blocks" presented here differ from the real processes of photo-
production and of the Coiaptor, effect by the circumstance, that
here the relation k2 ~ 0 holds. They are obsiously parts of the
matrix elements of real physical proces3es. Numerous other exam-
ples may be given. It is possible to obtain dispersion relations
for the 11blook" o4pbbt oproduction, which may be used for establish-
ment of approximate equatins juat as in the case of real photo-
production. The range of negative energies in the dispersion re-
lations may be co,,uauted into the range of positive energies, if
Card 1/2 the parity of the "block" of photoproduction with respect to the

Dispersion Relations for Virtual Processes. 20-117-5-lT/54
energy is drawn into account. This parity obviously is an-aloguous
to the parity of the aLaplitude of real photoproduction. The do-
main of integration in the dispersion relations is split into two
parts. The single nucleon states (ri-O) are the only ones that
contribute towards the first domain, whereas all states with n~pi
contribute exclusively to the second domain. By means of an ex-
pression given here it is possible to reprsent the phases of the
"block" of photoproduction through the phases of the process of
meson-nacleon scat~.ering. There are 3 figures and 3 Slavic refer-
enoes
ASSOCIATIONt United Institute for Nuclear Research (Obl'yedinennyy institut ya-
dernykh issledovaniy)
FRLSENTEDt July 18, 1957, by N.11. Bogolyubov, Academi~.iin
SUBMITTEDo jaij 6, 1957
Card 2/2

6(2),21,(7)
UTHORS: --~O~VA.A,.' and Tavkhelidze,A.N. SOV/155-58-3-52//'~7
'ITLE: Generalized Dispersion Relation3 f0ltobshchennyre
sootnoqheniya)
'ERIODICAL: Nauchnyye doklady vysshey shkoly. Piz iko-matomat irhr,.'-k iye natlki,
1958, Nr 3, PP 178-185 (USSR)
.BSTRACT: The present paper continues the earlier investigationn of ti,,e
authors f-Ref 1,2,3,4 7
The authors propose a method for
obtaining dispersion relations for the reactions a+b---P'a1+-'7+d.
At the beginning of the reaction there is a nucleon and a boson,
at the end there is a nucleon and two bosons. In contrary to
f-Ref 112,394 7 the authors do not assume that the energit---.-, of e.-
and d are equal. The ratio of these energies is fixed as Polking-
horn has done. An explicit calculation la made for the double
Compton effect (C+p-2r+p). The paper contai,.j three paragraphs:
�1 Kinematics of the process, �2 investigation of the anti-
Hermitean part of the amplitude of the process, �3 Disper3ion
relations.
There are 6 references, 3 of which'are Soviet, 1 Ampricftri,
1 Italian, and 1 German.
.SSOCIATIOII:Obllyedinennyy institut yadernykh issledovanly
of Nuclear Research)
UBMITTED: April 4, 1958
ard 1/1

7/3
21(7),16(2),16(1)
AUTHORS: _IaffanqL~ ~ilenlkiy,S.M.,and
Tavkhelidze,A.M.
TITLE: On the Theory of Dispersion Relations
(K teorii dispersionnykh sootnosheniy
PERIODICAL: Nauchnyye doklady vysshey shkoly. Fiziko-matematicheskiye
1958, Nr 3, pp 186-195 (USSR)
SOV/155-58-3-33/37
for Corplex Prom-,LeC
dlya glozhnykh protoessov)
nauki,
ABSTRACT: The present paper contains the proof of the dispersion relations
for the process lr+p--.,*21(+p in the case when the non-observable
domain is missing. At first with the aid of the principle of
causation (in the formulation of N.N.Bogolyubov f-Rof ~_7) the
lagging and the 'Leading amplitudes of the process are constructed;
the first one is combined with the direct process, the second one
is combined with the recurrent process. These functions are
defined for real values of energy 1-~-ing above the threshold of
the process. Then the functions (V(9,E) and ~a(., E) (compare
~Wtheupper".qnd ower halfplane E,
L-Ref 6_7) are constructeqvh4 -
respectively, are analytic and i~ich-agree on an interval of the
real axis. These functions define a single function being
analytic in the whole complex E-plane vith the exception of
Card 1/2 '

On the Theory of Diapersion Relations for Complex SOV155-58-3-33/37
Processes
certain cuts along the real axis. At the banks of the cute the
~r(,',) and ~a(q,E) for 9--*0 tend to the lagging and leading
amplitude, respectively. The dispersion relations appear an
conclusions by the application of the Cauchy theorem to these
functions.
There are 6 references, 4 of which are Soviet, 1 Italian, and
1 American.
ASSOCIATIONiOb"yedinennyy institut yadernykh issledovaniy k Joiht Institute
of Nuclear Research)
SU'BMITTED% April 25, 1958
Card 2/2

_247L)_ 1q, 6000
AUTHORs __Logunov, A.A. SOV/155-58-4-33/34
TITM Analytic Properties of the Anti-Hormitian Part of the
Amplitude of Virtual Processes (knalitioheskiye svoystva
antiermitovoy chasti amplitudy virtuallnogo protsessa)
PERIODICAL: Nauc hnyye doklady vysshey shkoly. Fiziko-matematiaheskiye
nauki, 1958, Nr 4, pp 207 - 216 (USSR)
ABSTRACTs The author starts from the representation of the anti-
hermitian part of the amplitude of a virtual photo generation
by the Fourier transform of a certain function F,.,, 10 (X)
(see Vladimircy Z Ref 3-7) , he introduCeB the nucleus
operators and raduces the investigation of the considered
part of the amplitude to a theorem on distributions at first
formulated by Bogolyubov and recently prove& in more general
case by Vladimirov, Z-Ref 3-7.
Card 1/2

34
Analytic Properties of the Anti-Hermitian Part SOV/155-58-4-33/34
of the Amplitude of Virtual Processes
There are 5 Soviet references.
ASSOCIATION: Ob"yedinennyy institut yadernykh issledovaniy (United Institute
for Nuclear Research)
SUBMITTED: April 10, 1958
Card 2/2

4.
24(4)
AUTHORS: Logunov, A.A., Solov'Yev, L.D. BOV/155-58-4-34/34
TITLEj Dispersion Relati6ns for Virtual Photo Generation (DiB-
I persionnyye sootnosheniya dlya virtuallnogo fotorozhdeniya):
PERIODICALs Nauchnyye doklady vysshey shkoly. Fiziko-matematicheskiye
nauki, 1958, Nr 4, pp 217 - 225 (USSR)
ABSTRAM The au-thors consider the dispersion of an electron at a
nucleon with generation of a meson (N + e -.9, N + e + Tr)
Approximately it concerns the radiation of a photon by
an electron, whereby the interaction of the photon with the
nucleon leads to the generation of the meson. The process is
denoted as virtual photo generation. Dispersion relations for
the amplitude of the process are obtained. It is assumed
that-for high energies the..amplitude is constant as a function
of the ener The assumption leads to the occurrence of
(in goneralFuIndetermined constants in the dispersion re-
lations. By the postulate of gradient invariance, however,
these constants can be uniquely expressed by integrals of the
imaginary part-of the amplitude. The relativistic spin
structures f6r the amplitude can be chosen so that the dis-
Card 1/2 persion relations in the relativistically invariant form do

35
Dispersion Relations for Virtual Photo Generation SOV/155-58-4-34/34
not expl-Acitly contain these constants. The single paragraphs
of the paVaT deal vit h,: The matrix element of the el6etron
dispersiad- -= the irmoleon with Ti- - meson generation 2e A.Mpli-
tude of the virtual photo generation 3. Dispersion relations
in'the coordifts e system with
p + 0 4.Mononucleonic
term 5. Dispersion relations in a relativistically invariant
form.
There are I figure, and 11 references, 6 of which are Sovietq
and 5 American.
ASSOCIATIONs Ob"yedinennyy institut yadernykh issledovaniy (United Institute
for Nuclear Research)
SUBMITTEDt April 10, 1958
Card 2/2

. . 1 20
21(1)
AUTHORt Lpgunov,.!..j:.,' :30V/155-58-5-20/37
TITLEs On the Theory of the Dispersion Relations for Virtual
Processes
PERIODICALt Nauchnyye doklady vysshey shkoly. Fiziko-matematicheskiye
nauki,1958,Nr 5,PP 108-119 (US.';R)
ABSTRACTt In Z-Rcfl7 the author considered the dispersion relations for
virtual processes (e.g. Y + p---Ye+ + e- + p) . With the aid
of the method of R.N. Bogolyubov the present note gives a
rigorous theoretical foundation of these relations in the case
of virtual photo generation. � 1 Reaction amplitude of the
virtual photo generation � 2 Analytic properties of this
amplitude in the fictive domain 3 Analytic continuAtion
with respect to the variable V
The author thanks N.N. Bogolyubov, Academician, and V.S.
Vladimirov for valuable discussion.
Card 1/2

On the Theory of the Dispersion Relations for Virtual I)OV/155-58-5-20/37
Processes
There are 2 figures, and 7 Soviet references.
A330CIATIONs Ob"yedinennyy institut yadernykh issledovaniy
(United Institute for Nuclear Research)
"JUBMITT ED jMay 5, 1956
.Card 2/2

21(l)
AUTHORSs Logunov, A.A., Tavkhelidzeo A.H., .90V/155-5B-5-21/37
MrfiTrW1 'r.A.
TITLE% On the question of the Dispersion Relations for Reactions
With Variable Number of Particles
PERIODICALs Nauchnyye doklady vysshey shkoly. Fiziko-materiaticheakiye
nauki,1958,Nr 5,PP 120-123 (USSR)
ABSTRACTs In Z-Ref 1 7 Logunov set up dispersion relations for processes
-
with variaBle number of particles. In Z
7 the analric
Ref 2,3
_
proporties of the amplitude were treated. The authors use the
results from Z-Ref 1,20 7 in order to give in the present
paper for reactions of tRe double Compton effect a further
extension of those dispersion cases for which the dispersion
relations do not contain the nonobservable enf~r;,-j range.
� 1 Kinematics of the process f, 2 Dispersion relations.
The authors thank U.N. Bogolyubo~, Academician for discussion,
There are I figure, and 3 Soviet references.
ASSOCIATIONs Ob"yedinennyy institut yadernykh issledovaniy (United
Institute for Nuclear Research)
SUBMITTEDs March 26t 1958
Card 1/1

"Dispersion Relationi3 for Weak Interactions," Nuclear Physilib 5, No. 2, Jan 1958.
(North Holland Publ. C(~~. Amsterdam)
Joint Inst. of Nuclear Research, Laboratory of Theoretical Physics, Dubna, USSR.
Abst: Dispersion Relations for weak interaction processes are obtained in the
present paper.
It is shown that in processes which involve not only weakly Interacting but
strongly interacting particles as well, the dispersion relations are equivalent
to the statement that the unknown amplitude functions, which are determined by
strong interactions, depend only on momentum transfer between strongly interacting
particles.

DCGLINOV, A. A. and FRENKIN, A. R.
"On the Dispersion Relations for the Compton Effect." Nuclear Phvsics, Vol.
No. 6. , P. 573-578 (No. Hol-land Publ. Co.) 1958.
Abstract: A basis underlying the deduction of the dispersion relations for the
Compton Offect on nucleons in the absence of an unobservable energy
region is presented.
Joint Inst of Nuclear Research, Laboratory of Theoretical Physics, lh-,bna, USSR.

LOGUN f, A. A. and TAVKHELIDZE, A. N.
Joint Institute of Nuclear Research, laboratory of Theoretical Physics, Dubna, USSR.
"Some Problems Encountered in the Theory of the Dispersion Relations."
Nuclear Physics, v. 8,JPP. 374-393. (1958) (North-Holland Publaishing Co.,
Amsterdam)
Abstract: Dispersion relations are obtained for a reaction involving a variable number
of particles (a fermion and boson prior to the reactbons and a fermion and two
identical bosons after the reaction.) cases are indicated for which an unobersvable
energy region is absent in the dispersion relations. A justification of the dispersion
relations in the absence of an unobervable energy region is presented for the particular
process.~, j-

AUTHOR LoE;unov, A. A. S0V/2o-1;,Q-3-17/67
TITLE. Dispersion Relations for Reactions InvolvinE; a Variable Number
of Particles (Dispersionnyye sootnosheniya dl,,a reaktsiy s
peremennym chislon chastits)
PERIODICAL: Doklady Akaderiii nauk SSSR, 1958, Vol- 12o, Nr 1,
PP- 501 - 503 (USSR)
ABSTRACT: On the basis of tile example of the process (y + P + 2y + P)
this paper examines the problems of the theory of dispersion
relations with a variable number of particles. These consid-
erations may also be applied to other reactions. In this
connection the electromagnetic corrections of hieller order are
not taIzen into account, but attention is focused upon the inv~!s-
tigation of the principal term of the amplitude. By basing on
the causality principle in accorda.:ce with IT.,..Bo,,olyubov
(Ref 3) and the properties of t~,,e translation invariance of
the matrix elements it is possible to write down tne retarded
and the advanced amplitudes of the double Compton effect. Also
for tile anti-Hermite part of the amplitude of tile process a
Card 1/3 formula is written down, For reasons- of ~.,reanter simplicity tile

Dispersion Relations for Reactions Involvint; a SOV/2o-12o-3-17/67
Variable Number of Particles
author investitrates the case of equal energies. The dispersion
relations are of particular interest if tile not observable
energy range is lacking, for in this case the diopersion re-
lations connect only observable quantities. In the disperhon
relations which connect the Hermite- (Ermit) and ti,e anti-
Hermite part of the process, there exists an unobservable domain.
The amount originating from t'..,.e unobservable domain can be
calculated, for which purpose a formula is given. To the non-
observable part a contribution is made by the one-.nucleon state
(in tile interval[El< Ec ). Tile coritinijous spectriim on tiie whole
comprises part of the non-observable eneray rarol,e. In con-
clusion, the author thank& 11.11.Bo~,olyubov, lilember,Academy of
Sciences, USSR, for valuable discussions of this paper, and lie
also exprerioon hia j,,ratitudo to A.11.Tavkhelidze and 11-A.
C"hernikov for their valuable advice, There iic 3 references,
2 of which are Soviet.
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Dispersion Relations for Reactions Involvinr, a Varia:-..Ie SOV/2o-12o-3-17/67
Nu,mber of Particles
ASSOCIATION: Obl'yedinennyy institut yadernylh isoledovaniy (United Institute
of Nuclear Renearch)
PRESENTED: February 17, '1950, by 11.11.Bogolyubov, Movibor, Acado!-.Iy of'
Sciences, USSR
SUBMITTED: February 5, 1958
1. Particles--Speetra 2. Particles--Scattering 3. Spectroscopy
--Theory 4. Matbematics--Applications
Card 3/3

1;, ff%r,~hclilzt-,
T T T L';' T N, A I I I It i rw I !I. t 4 ,.,1 (jT' th-, .%i ~ 1u 1 Tn-
V,~riil,,Ie ':umber of' 1;artivics
amplitudy protserna _ peremonnym cli:~Ilo-
:1 T C T, Aki;dt~:nii r:ukil: 1 I'lo,

A133TWACT A. It. Lo,-,i~nov in the nourr-e of w; earlier !a,.er inve!Jti.,,1jte,1
the relatiow, for rroceuoes iforclvin,- P_ variable
number of narticles. fn the ,,reseiA -in:,t,--.r,.ce t~,e ~7etho:l (10
volore,i b-,r N, N. Bo,,,-O1yubOV (I?cf i!7 m~ed for tho 7L1-T10C+1
Of Provln,,~ these i,-!1atiom_- for ttil(! CRVP In t~lere r I.,, t.-?
no enk;~rgy domoin that cennot be oboprv~_,d. Fir-,t the ''o tir
.repr-=?:7entatiomoi' the retard-A and of t',je idvanced matrix
element o.' tne r1ouble 'cmr1;-)n effect are explicit1v --ritten.
down. The !jutho.-.1 inveoticato tho function T(
Tr,-) t(F, T' dv T~ L), tile en,~)v-y vroctnin Of
,N); i 0'. le I I t r,. tt i
in form of a drawing, Tile E, 1. nf,
IrtritJ Of t1w IC""I, c~m be eliminttf,,il
Card 1/2 ceipctine.,* u ruitalcic, !)ul.-momial giver. here. The further

The Analytical -Praccrties of thr. ilm!)).:tude of a froccs t3 T nv o 1 v i n c u Var, E--- I* I e
Number of
contento of this purel:,, mathernatical -4,! a detuilr.A ri,-. -
scription of thl-, vnr-I ous stables o-f the r-omr-utation, Th4? ex
Preocior. fou.-i ex,-Iic!tl.-,, irittrri lorri, ill critic] 1):,i o,-,
authorzi thank N. !~ojollyuljov, U';3R, for hii3
vuluable discus,,ion of thio raner. 'P',iere are fillUres and
2 referencer, 2 o1' which are Soviet.
OC I AT 1 ON Ob"yedine!.r.,,y in:1titut (Unit I,! ,-. t i -
tutta of
y 711.
t . S '01 T N D February 17, 1958, b Bogolyubov, of
Sciences, US-1)
SV'3.'.',TTT~D: 17,21; -,*!1'- r 11
1. Mathematics
Card 2,12

of

3.6.8100 3
05699
AUTHORSt Vladimirov, V.S., Logunov, A.A. SOV38-23-5-3/8
TITLEs On Analytic Properties of Generalized Functions of quantum
Field Theory
FERIODICALs Isvestiya Akademii nauk SSSR, Seriya matematicheeka a, 1959,
Vol 23, Nr 5, pp 661 - 676 (USS R~
ABSTRACTt The wathora prove the following generalization of a well-known
-theorem, of Soqolyubov s
Fundamental theorem t Lot four transl.&tion-invariant functions
of 4 four-dimensional vectors
Fij (XI, x20 x3' X4 ) i,j - r, a
be-given with the following properties t
a.)- Tij are invariant with respect to the transformations of
th; complete Lorenz group
b. FIj satisfy the causality conditions
Card 116

o5699
On Analytic Properties of Generalized Functions of SOV/38-23-5-3/8
Quantum Field-Theory
F rr - 0 if XI -,x 4
Far m 0 if xl~~ x 3 or x 2-'-',x4
Pas, - 0 if xi 1>1 x 3 or x 2 i ~" x4
c.) the following spectral conditions are satisfied
I%/ Ili 2 2 2 2 2
F rj ' F&J if PI + t + I V(2t+ M +1e- V
(M 07 4t
~~2t M -p,) 2 if
The-,numbers M, ej, are chosen so that 4j> 0 for
0, t >' to
3.) For real (Plvp2lp39p4 from (1.1) p I + P2 + P3 + p4 0
for which the magnitudes 2 2 2
Card 5/6 zi pi Z2 p 2 z3 P3

05699
On Analytic Properties of Generalized Functions of SOV/38-23-5-3/8
quantum Field Theory
Z a p 2 , z ft (p + 2 belong to Dt, there holds the
4 4 5 1 P2)
representation Pij(Plg.--,p4)
. ~ [ 2 2 2 2 2 1 2]
Pip P29 P3 9 P4 (pi + P2) 9 i /(Pl + P3)
iqj - r,a , for t - -1 V (Pl+ P3)~' 2 > t and p + P30 >
2 0 10 0
Sobolev is mentioned in the paper. The authors use results
of Jost,, Lehman I-Ref 20-7 and Dyson Z-Hef 12-7 -
There are 21 references, 11 of which are Soviet, 4 American,
3 Italian, 1 French, 1 German, and 1 Swedish.
PRESENTEDs by N.N. Bogolyubov, Academician
SUBMITTEDs October 30, 1958
Card 6/6

2,'+(5) SOV/56-37-3-33/62
AUTHORS: Bogolyubov, N. 11., Logunov, A. A., Shirkov, D. V.
`L'ITLE; The Method of Dispersion Relations and the Perturbation Theory
PEHIODICAL: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, 1959,
vol 37, Nr 30), pp 805-815 (USSR)
ABSTRAOT: The present paper is in close relationship to a paper by
Redmond (Ref 1 ) , in which expressions are derived for the
Green function, which correspond to the perturbation theory
and, at the same time, contain no known logarithmic singulari-
ties. In the introduction Redmond's method is described, and on
the basis of the example of the Green boson- and meson functions
the setting up of these expressions and the elimination of non-
physical poles is discussed. The method employed by the au-
thors is discussed on the basis of the elimination of
"logarithmic" poles from the Green photon function. In contrast
to Redmond's method, which is based upon the interrelation of
the spectral representations for the Green function and for the
polarization operator, the authors proceed from the principle
of summating the information deduced from the perturbation
theory under the sign of the K&114n-Lehmann spectral integral.

SCIV/56- 37-3- 33/62
bQ Method of Dispersion Relations and the Perturbation Theory
If the contributions from tlie "main logarithmic diagrams" are
summated in this manner, expressions are obtained for the
photon propagation function in quantum 54~IZ`sa~~d for
the meson propagation-Lan n the theory of charge symmetry;
theau Hzprsodf6ns have all essential properties of Hedmondlu
result: He,-,-ular analytical behavior in tho complex plane of the
2, - -1 - -c -th-
momentum variable p and a, InE_ .1 riis'pect to the
vaviable e 2 (square of thL charge) at the point e2 . 0. Whereas,
however, Redmond's result yields only the lowest order in the
perturbation theory, the expressions of tne present paper cor-
respond to expansion terms in perturbation theory in the range
of large p 2 of arbitrary order. Consideration of the lowe:3t
logarithmic terias shows that the range of applicability of the
new formulas is the same as in the older formulas which have
logarithmic singularities. For the occurrence of a logarithmic
pole the following causeo are determined: Either the initial
Lagrangian is not physical, i.e. its function system does not
satisfy the demands of the spectrum, or the approximation meth-

SOV/56-37-3-33/62
Method of Dispersion Relations and the Perturbation Theory
od is not advantageously chosen. The reduction of the expr,:--.-
sions found to a renormalization-invariant form is demonstrLt-
ed in part 4 of this paper on the basis of the example of
Green's photon function, and in part 5 a possibility of ap-
plying the summation method within the framework of non-
renormalizable theories is discussed (on the basis of the
example of the nonlinear fermion theory). The results obtained
by this paper are summarized, and the authors thank
Professor D. 1. Blokhintsev, B. V. Medve&ev, and M. X.
Polivanov for discussions. There are 13 references, 5 of which
are Soviet.
I
Obl'yedinennyy institut yadernykh issledovaniy (Joint Institute
of Nuclear Research)
3U_`MITTED: April 17, 1959
Card 3/3

W16
3/020/60/135/004/009/037
.9 Z/, 4'5-o 4 0 /J q Sj- 1,573 P) B019/BO77
AUTHOR: lj_~ ~A. ~A., Tavkhelidze, A. N., Torodov, I. T., and
Chernikov, N. A.
TITLE- Majorization of Feynman Graphs
PERIODICALs Doklady Akademii nauk SSSR, 196o, vol. 135, No. 4,
pp. 801 - 804
TEXT: The autbors prosont the results of a further development of the
idea of the majorization of Feyninan f,-raphs as eur~rosted by Nambu and
SymRnzik (Refs. 1, 2). Every Feynman graph D represents a quadratic form
4D of the external momenta p at On the condition that the law of conser-
vation holds for the four-momenta k -in the inner lines of the graph k,-
are linear functions of 1) a an,,'. of tho inflepondent inner momanta tit if
the follo~xing relation is valid for K D(-?,P,t),
Card 1/4

89016
Majorization of Feynman Graphs 3/020/60/135/004/009/037
B019/BO77
K O(Y(k 2 - m 2 a t t 2~ b t + C
D(-~'P't) -A.7- V V, ij i j i i
where I is the number of inner lines of the graph, then the cua,'ratic form
can be determined fromt
aijb
c
QD (:4, P) (2)
j~ij
On the basis of known results, the following lemma and two more theorems
are proved3 lemmat the quadratic form Q is equal to the least value of
D
the quadratic form K D if the vectors kv, fulfill the law of conservation
of momentum in every unit of the graph, and if they assumv a value from
Card 2/4

Majorization of Feynman Graphs
89016
S/020/60/'135/004/009/037
B019/BO77
the quantity P of all vectors of the type p -.'EA p (A are real numbers).
a a a a
Theorem 1 reads as followss Any graph can be majorized by any of its sub-
graphs. Theorem 2 reads as followss If a graph D contains a polygon of
(n+1) sides which has the mass M on n sides and the masfi'ml~M on one side,
a new graph DI will be obtained if the change of mass is of the forms
M--* m and m --,PM wi th
G(DI) 9; G(D).
As an example the authors investigated the amount R Of Ell graphs with
a strong coupling in the pion-nucleon part. In every intersection of this
graph only three lines do combines 2 or 0 baryon lines, and 1 or 3 meson
lines. It is shown that any graph of the sub-part R** cE.n be majorized
by one of the two diagrams shown in Fig. 2. R** is that sub-part of R
where a nucleon polygon and pion lines appear in its graphs, and where
the external points a and b are characteristic points . N. Bogolyubov
is thanked for a valuable discussion. There are 2 figures and 5 refer-
ences: 1 Soviet, 3 US, and I Italian.
Card 3/4

89026
Majorization of Feynman Graphs 3/020/60/135/004/009/037
B019/BO77
ASSOCIATION: Ob"yedinennyy institut yadernykh issledovaniy (Joint
Institute of Nuclear Research)
PRESENTEDs
SUBMITTEDt
June 21, 1960, by N. N. Bogolyubov, Academician
June 7, 1960

a
Fig. 2
a c 1b
Card 4/4

LOGUNOV,t A&A,j-,
I ..
Surface
fiz mat
TODCROVO I.T.; GHERNINOVk NA,
of singular points in the Feymn diagram. Godishnik
55 no*2:117-137 160/161 (yubl. 1621.

ARBUZOV,, B.A.; LOGMOV2 A,,A.;-TAVKJIELIDZEO A.N.; FAUSTOV, R.N.;
FiH.r-dr-.A-.T-- -i~WBIIIA, I.S.[transletorl; SARVITSEVA, V.R.,,
te r9d. * "
Regge polea and perturbation theory. Dubna, Ob"edinennyi
in-t iaderrjykh issledovanii, 1962. 4 p.
(Ho subject heading)

ARBUZCTV, B,A.; LOGUNW, A.A. ; TAVIUIELIDZEP A.N.; FAUSTOV, R.N.
The asymptotic behaviour of the scattering amplitudes and
the renormalization group method. Dubna, OblledinenrWi in-t
indernykh issledovanii, 1962. 7 p.
(No subJect heading)

I-CMII; TODOAOV, I.T.; CHEM11KOV, N.A.;
SARANTSEVA, V#R.j taklm. red.
(Dispersion relations and cnalytic properties of partial
amplitudes in the perturbation theory]Dispersionnyo sootno-
sheniia i analiticheskia svoistva partsiallnykh amplitud v
teorii vozrushchenii. Dubna, Obnadinenrqi in-t iadernykh
iml. , 1962. 31 p. (MMA 15110)
(Mesons-Soattering) (Nucleons-Scattering)
(Perturbation)

LOGUNOV, A. A., TODOROV, I. T. and CHEMINDV, N. A.
"Analytical Properties of the Feyman Graphs"
report presented at the Intl. Conference on High Energy Physics, Geneva,
4 -11 july- 1962
Joint Institute for Nuclear Research
Laboratory of Theoretical Physics, Dubna, 1962

LOGUNOV, A. A MESHCHERYAJOV, V. A., and TAVKHELIDZE, A. N.
pr- *~:invariance in strong Interaction thear
"On the a roximate, 'Y
report presented at the Intl. Conference on Figh Energy Physics, Geneva,
4-11 July 1062
Joint Inst. for Nuclear Research
Lab. of Theoretical Physics, Dubna, 1962

WGUI.70V, A.A.; TODOLOV, I.T.; CIMMUKOV, N.A.; SARANTSEEVA, V.R.,
EUIORi.- rod.
(Surface of singular points of a Feyman diagram) Poverkbrost'
osobykh tochek diagramny Feinmana. Dubna, ObIledinennyi in-t
ladernykb issl. 1962. 29 p. (MIRA 15:3)
Nuantum electrodynamics)

S/056/62/042/005/023/050
B102/B104
A UT It 0 R S Lo,,.unov, A. A., Todorov, I. T., Chernikov, N. A.
TITLE: Generalization of Symanzik's theorem on majorizatio'n of
Feynman graphs
PERIODICAL: Zhurnal eksperimertallnoy i tooreticheakoy fiziki, V. 42,
no- 5, 1962, 1285-1293
EXT : In an earlier paper (DAN SSSR 135, 801, 196o) the authors showed
that a maiorization method developed by them made it possible to reduce
6he consideration of all strongly connected Feynman graphs of one process
to that of a finite number of graphs. Such a graph may be considered to
be stronoly connected, if, upon one of the internal lines being broken,
it doez not become dissociated, the square of the outer momenta being
of all diaerams
re~;arded as independently variable. The so' of classes Ro
is zou:-ht in a maximum enclosed Euclidean area of outer Momienta wherein
the Feynman integral does not display any singularities. ?or NN
3cattering R for the noson-me4on scattering Ro - 3, and for the mecon-
nucleon sclaAering Ro - 14. The method of determining class Ro is discussed
Card lle

5/05 62/042/005/023/050
Generalization of Symanzik's 3102Y3104 .
at lon-th. For the purpoou o.: comparing tho diagrams of claaa it Q 4
detailed examination is made of the quadratic form of -eneral Feynman
6raphs and an explicit expre3;3ion for.thiG form is arrived at terims of the
identify z :* i x .This natrix with n rows and I columns then forms the
x.2ac r-haracteristic of any graph havine n nodes and 1 internal lines. An
Is also derivud fo-,- the conjuCated (inverse) quadratic form.
Furt;ler, the minimum expressi)ns are obtained for the Fe,, rnman parameters
(a) relatint; to the conjugated quadratic form and finally the results are
transferred to the Synanzik theorem of graph majorization, which is
C~
thereby proved. The 3enoralization of this theorem is discussed. The
results following from the narticulaar and the generalized Symanz4.k
are discussed for the S.-pecial case of a INIT scattering. It can be shown
the set R 0 of the graphs for the ,;IT scattering are majorized by the
~,-ao former (I, IT, FiS. 1'). kli strongly connected graphs of the meson-
nucleon scattering can be majorized by the sum of the four graphs in Fig.2.
There are two figures.
ASSOCIATION; Ob"yedinennyy institut yadernykh issledovaniy (joint Insti-
tute of Nuclear Research)
SUB'.11TTED: Decembor 9, 1961
Card 214

8/02o/62/142/002/012/029
B104/B138
.AUTHORS: Logunov, A. A.# Moshcheryakov, V. A., and Tavkholidz*, A. ff.
TITLE: Approximate 15 invariance of the theory of strong interactim
PERIODICAL: kkademiya nauk SSIR. Dokladyj v. 142t no. 2, 1962p 317-318
TEXT: The hypothesis is verified, that the matrix elements of all
physical prooessevarv invariant with respect to 75 transformation of
spinor particles at high energies and great momentum transfers. For
scattering processes of the type 0 + 1/2 --+-0 + 1/2, the requirement of
15 invariance has the consequence that a Fermi ion polarized longitudinally
before the scattering process is also longitudinally polarized after it.
The same in true for a nonpolarized Fermi ion. In particulart a similar
result is obtained for nucleon-niaelson scattering. From an examination
of the terms of lowest order in -the perturbation theory it is shown that
the mass terms are of no significance at high energies and considerable
momentum transfers. Thus & 15 invariant interaction leads to 15 invariant
matrix elements. N. No Begolyubov, So M. Bilealkiy, So So Gershtsyn,
Card 1/2

S/02oj62/142/002/012/029
Approz'm&t& 15 invariance ... B104/B138
m. *,L meshcheryakovq A. M. Baldinp R. M. Ryndin, and Ya. S. Smorodinakiy
are thanked for advice and discussions. There are 4 references: I Soviet
and 3,non-Soviet. The four references -to English-language publications
read as follows: M. Gell-Mann, Preprintp 19611 Y. Fujui, Progr. Theore
?by*-# ~U, 232 (1959)1 1# 1. Sakurai, Ann. of Phy "; 1 11, 1 (1960)1 Y.
Nambyg J. Ionn - Laminio, Phys. Rev. 122, no. 1, 3 5 T-1961).
ASSOCIATION: Ob"yedinennyy institut yadernykh iseled*vaniy (Joint Insti-
tute of Nuclear Research)
PRESENTED: August 14# 1961, by N. N. Bogolyubov, Academician
SUBMITTID: July 20, 1961
Card 2/2

U~qqNqY- A.A. (Dubna); LYU I-';HEN' (Liu 1-ch'Sn] (Dubna); TODCROV, I.T.
Oubna); CHERNIKOV, ?1,A. (Dubna)
DisperBiOn relations -ind analytic properties of partial
amplitudes in perturbution theory. Ukr. mat. zhur. 15 no.3:
250-276 163. (MMA 16:12)

LOGUNOV, AiA.; UU I -CEN; [Liu I-ch'Sn]; TODCROVY I.T,; CLM.IKOV, 1~'.A.
Dispersion relations and the analy-tic properties of w
amplitudes in the pertubation theory. A-lele mat 17 no.4:F2-
112 O-D 163.

5/056/63/044/004/039/044
B102/B186
AIUTHORSt Arbuzov-, B. A., Logunov Tavkhelidze, A. No,
Faustov, RO No$ ppov, A. To
~,,ITLZi. A Ejuasioptical model and the-asymptotic behavior of the
scattering amplitude
PqRIODICALs Zhurnal eksperimentalinoy _f teoreticheakoy fiziki, v. 44,
no. 4, 1963, 1409 - 1411
TEXT: As E-hown in Ref. I (Preprint Mal, B-1145, 1962), a two-particle
system may be described in quantum field theory by a Schr8dinger-type equa-
tion with generalized complex potential, which in the came of'scalar
psrtioles reads 03
V:1: E) - VF1 ~ Uv)) dv.
IV q' (2).
This quasioptical treatment yields the zoattering matrix and also the
structure of bound and resonance statos. Tho wave function is only a func-~
tion of transferred three-momenta (q,q'), and the energy
Card 1/4

5/056/63/044/004/039/044
A quasioptical model and the... 3102/B186
(El - q' )fqlI+ MI (q, q'; E) 'P� (q) dlq'. (1))
V+(-) is thq potential for even (odd) states with respect to cos 9; U(E;"))
.2 2
is the spectral function which is complex irA the region Ell 2~-mi. The am-
plitude M(E,t) of the process is asr-umed tc Latisfy the 4ispersion relation
and its projection onto even and odd state_- is given by
Mt(E't) . Co C+(E,V) dJ. The imaginary part of V charaoterizes inelastic
2 9+(q-ql)2
scattering. Regge has shown that when the potential is a superposition of
Yukawa potentials, the scattering amplitude with t-ila) may be given by
M (E. t) = g (E) lall':'.t(q q')2, (4),
where ~ and qlare initia I and final mo-_enta. It is now ethown that a
Card 2 4

S/056/63/044/004/039/044
A quasioptioal model and the... B102/Bi86
POtokItial Of type (2) leads to Regge asymptotic behavior (4). The solution
of the amplitude eqwition
r* (q, q') = VI ((9 q')', E) +V� ((q - p)', F;) T� (p, qd3 P.
Rr; I. 1r), ... nil PI) (5)
~14 aought as a function like
T� (q, q')
The equation of the spectral function -v for the asymptotic region (a-IW
has a oolution of the form
v� (q", q', v, E) (0, 0, VQ(C (9)V
where -r. will satisfy
Card 3/4

'A quasioptical model and the...
S/056/63/044/004/039/044
B102/B186
(U'- S, E) R~- (u, u', s, E) (U" S, E) dit'.
(El - M, -- U') If ~7~
dx-x" 0 (U' - ux - vxj(j - x)) (10).
U�(E,v)dv' 0 -
X)V. 1-11 ~ Ux - vx/(t - X)j
From the latter relation the eigenfunctiun T. and the eigenvalue a, which is
a function of B, can be determined. For E2 < M2 U(E,v) is real and therefore
also a. Eq. (6) together with yieldc
T (q", q2, s, (q'2, q1, E-) ji 4-
sin na (E)
for large s. A aimilar result ij obtained froa (1) in partial-wave re-
prescntation.
ASSnCIATIOX; 'Ob"yedinennyy institut yadc..rnykh issledovani:v (Joint Institute
of Nuclear Research)
IlUBIMITTEDt January 3, 1963
Card 4/4

L 12408-63 EWT(I)/FCC(v)/BDS AFFTC/ASD/ESD-3 IJP(C)
ACCESSION NR: AP3001394 S/0020/63./150/004/0764/0766-~q
AUTHOR: Arbuzov, B, .; Logunov, A. A.; Tavkhelidze, A. .; Faustov, R, N.
TITLE: Rogge polJ'and the Bethe-Salpeter equation
SOURCE: AN SSSR. Doklady, v. 150, no. 4, 1963, 764-766
TOPIC TAGS: Rogge poles,, Bathe-Salpeter equation
ABSTRACT: The properties of Rogge poles were investigated by these authors on
the basis of the perturbation theory. It was also shown by them that this
analysis is connected with certain difficulties. The purpose of the present work
is the study of the structure of Regge singularities an the bais of an equation
of the Bethe-Salpeter type. Orig. art. hasi 19 equations.
ASSOCIATION: Ob*yedinenny*y institut yadernykh issledovaniy (Joint Institute
for Nuclear Research
SUBMITTED: 15Nov62 DATE ACQ: olja163 ENCL: 00
SUB CODE: 00 NO REF SOVs 000 OTHER: 006
Card 1/1
--------------------------------------- ----------I........ ...... .........

ACCESSION NR: AP4025941 S/0056/64/046/003/1079/1089
AUTHOR: L~nunoy,_.4!, .1 Nguyen, Van ]Khlyeul Todorov, 1. T.;
Khrustalev, 0. A.
TITLE: Asymptotic relations between cross sections in local field
theory
SOURCE: Zhurnal eksperimentallnoy i teoreticheskoy fiziki, v. 46,
no. 3, 1964, 1079-1089
TOPIC TAGS: local field theory, cross section, asymptotic cross
section relations, Phragmen Lindelof theorem, Pomeranchuk theorem,
antiparticle, neutral pion scattering, kaon scattering, pion proton
scattering, kaon proton scattering
ABSTRACT: It is shown that, by starting from the Phragmen-Lindelof
theorem and using the general principles of relativistic local quan-
tum field theory, several asymptotic relations can be established
Card 11A

ACCESSION NRt AP4025941
not only between the total cross sections of various processes but
also their differential cross sections. Starting with the related
processes of scattering of scalar particles
a1 + b1 a2 + b2 M
a + b a + b
2 1 1 2
(the bar denotes the antiparticle), the asymptotic properties of the
scattering amplitude are derived under certain assumptions and, in
particular, the Pomerancbuk theorem is obtained for this case. The
method is then extended to include the case when the particles b have
spin 1/2 while the particles a have spin zero and to process which
are described in the e2 approximation in terms of electromagnetic
form factors. All the deductions are based on the assumption that
the cross sections do not oscillate at high energies. it is con-
Card 2/4

ACCESSION NR: AP4025941
cluded that the differential cross sections of processes (I) and (II)
are asymptotically equal, that the total cross sections of interac-
tion of particles and antiparticles are equal if the forward elastic
qcattering amplitude does not grow too rapidly, that the forward dif-
ferential scattering cross section is proportional to the square of
the total cross section in the case of scattering of neutral pions
or kaons by protons, and that the limiting values of the form factor
are equal when the momentum transfer (t) becomes infinite. "In con-
clusion the authors are deeply grateful to N. N. Bogolyubov for in-
terest in the work and for stimulating discussion, and also to S. M.
Bilen'kiy, D. I. Blokhintsev, V.-S. Vladimirov, M. A. Markov#,N. N.
Meyman, Kh. Ya. Xhristov, and P. Suranyi for useful remarks." Orig.
art. has: 43 formulas.
ASSOCIATION: Ob"yedinenny*y institut yaderny*kh issledovaniy (joint
Institute of Nuclear Research)
Card 3/W11-i-

A
CCESSION NRv, AP4031148 6/0056/64/046/004/1266/1280
AUTHORSt Arbuzov, B. A.; Logunov, A. A.; Filippov; A. T.; Khrusta-
lev, 0. A.
TITLE: The Fredholm method in the relativistic scattering problem
SOURCE: Zh. eksper. i teor, fiz., v. 46, no. 4, 1964, 1266-1280
TOPIC TAGS: particle scattering, relativistic particle, particle
spin, Fredholm method, Regge pole, asymptotic property
ABSTRACT: The investigation of the analytic properties and asymp-
totic form of the amplitudes for elastic scattering of twa 3pinless
particles with equal masses, obtained from solutions fouid by the
Fredholm method, are described. Thle motivation is to d(ve'.op a
method for studying the analytic properties of the scatzering ampli-
tude and its asymptotic behavior as a function of the cosl.ne of the
scattering angle in the c.m.s. directly, without assuming the exis-
Card 1/3

ACCESSION NR: AP4031148
I.ence of a Mandelstwn representation. The problem is treated over
a restricted energy range but with arbitrary momentum transfer. The
scattering amplitude and the bound states of the particles are de-
scribed by a Schrodinger-type equation with a generalized complex
potential. The analytic properties of the scattering amplitude are
studied as a function of the complex energy (or momentum) and angular
momentum. The asymptotic form of the partial amplitude is found and
it is shown that a transition to the total amplitude is possible by
using the Watson-Sommerfeld transformation. The analyticity of the
total amplitude as a function of momentum transfer is demonstrated,
and conditions for the Regge asymptotic behavior at infinite momentum
or angular momentum are formulated. Some of the results which can
be gained from the investigation are discussed in the conclusion.
"The authors are sincerely grateful to Academician N. N. Bagolyubov
for atimulating discussions and also to 0. 1. Zav'yalov and M. K.
Polivanov for valuable information." Orig. "art. has% 3 figures and
20 formulas.
Card 2/3

MMMMN"~---
ACCESSION NR: AP4031148
'%SSOCIATION: Ob"yedinenny*y institut yaderny*lch isoledovaniy (Joiw:
Institute of Nuclear Research)
SUBMITTEDs 2OJul63 DATE ACQ: 07M~xy64 ENCL: 00
SUB CODE: NP NR REV SOV: 008 OTHER: Oll
card 3/3

WGUNOV A.A.; MESTVIRISHVILI, M.A.; SILIN, I.N.
1-
(Asymptotic behavior of the scattering amplitude at
2arge transfers of momentum] Asimptoticheskoe povedenie
amplitudy raseeianiia pri bol'shikh peredavaemykh im,
pul'sakh. Dubna, Ob"edinennyl. in-t iadernykh Issledova-
nil, 1965. 27 p. (MIRA 29:1)

NR; AP6005465 SOURCE CODE:
AUTHOR: Logunov, A. A.;.Nguyen Van Kh" Todorov, I. T.
ORG: Institute of High-EneM ftsics (Institut fiziki vysokikh energiy); Joint
Institute of Nuclear ReseEch (Cb"yeM7n_enrWy institut yadernykh issledovanfy)
tj
TITLE: Asymptotic relations between the scattering a=11tufts-in local field t
SOURCE: Uspekhi fizicheski)rh nauk, v. 88, no. 1, 1966, 51-91 W/
TOPIC TAGS: quantum field theory, asymptotic property, scattering amplitude) strong
nuclear interaction, scattering cross section, particle productionp differential cross
Bection, meson, baryons fermion, photoproductionj Compton effect
ABSTRACT: This Is a review article devoted to the derivation of rigorous asymptotic
relations between the scattering amplitudes in high-energy interactions and the re-
sultant relations between such characteristics as cross sections,polarizations., and
others, from the point of view of their agreement with the most recent experimental
data. Special attention is paid to the hypotheses on whose basis the asymptotic re-
lations are derived. The authors review systematically the asymptotic relatio=3 de-
rived by many earlier investigators, an well as related papers dealing with the de-
rivation of as M totic relations in the presence of higher symmetries of strong inter-
actions and in processes involving particle production. The section headings are:
1. Estimated upper bounds of the growth of thepross,section at high energies. 1.1.
Limitation imposed by the microcausality princi~ii'o_n-amplitude growth. 1.2. Condi-
tions of polynomial bamdednese of the causal amplitude of elastic acAttering. 1-3-

ACC NR, AF6oO5465
Estimates of the growth of the cross sections. 2. Asymptotic properties of the scat-
tering amplitude of scalar particles. 2.1. The Phragmen-Lindelof theorem and asymp-
totic equality of differential cross sections. 2.2. Case of elastic scattering.
Equality of tot&I cross sections. 3. Asymptotic properties of meaon-baryon scatter-
ing. 3.1. Symmetry properties of the amplitude. 3.2. ArjWtotic equality of differ-
ential cross sections- 3-3. Asymptotic relations between polexizations of fermians
in the final state. 3.4. The complete experiment in the case of elastic meson-nucleor
scattering. 4. Asymptotic properties of baryon-baryon scattering amplitudes. 4.1..
Symmetry properties of the amplitudes. 4.2. Asymptotic equality of the differential
cross sections. 4.3. Asymptotic properties of the polarization effects- 5. Asymptot-
ic properties of photoproduction and Compton-effect amplitudes- 5-1- Photoproduction
of mesons on baryons- 5.2. Compton effect. 6. Asymptotic relations between forward
elastic scattering amplitudes. 7. Higher a~mwtries of btrong interactions and aoymp
totic reLstions between the amplitudes of meson-baryon scattering and photproduction.
7.1. Mason-baryon scattering and phot4roduction in schemes with higher symmetries,
7.2. Higher symmetries and relations between amplitudes. 7-3. Asymptotic relations
for cross sections and polarizations. 8. Asymptotic relations between amplitudes of
processes with variable particle number. 8.1. Kinematics. 8.2. Properties of asymp-
totic amplitude. 8.3. Asymptotic equality of-differential cross sections, 9. Asymp-
totic behavior of form factors. 10. Conclusion. Orig. art. ban: 246 formulas and
I table.
SUB CODE: 201.4 ORIG RM 023/ OTH MW: 032
r-A 212V~I- S'kgq~
T

LOGUNOV. A.I.
Integral inequalities for Volterra type equati,.)ns with
retarded argument. Dokl. AN SSSR 150 no.2:256-258 It 163.
(KM 16.5)
1. Predstavleno, akademikom L.B.Pontryaginym,
(Integral equations) (Inequalities (Mathematics))

LOGUNOV. A.I.; TSALYUK, Z.B. (1zhevsk)
-- --'F, - I - - I ~. . - ,
Uniqueness of solutions to Volterra type integral equations with
delayed argument. Mat. sbor. 67 no.2:303-309 Je 165.
(MIRA 18:8)

"N JT7,: kP5W7551
'0 9v A, 1. 1 TOa`-- k
73niqueniss of soiutions of Vol -nt,
Dokla
TjC;S Jifferentia' equation, differeyic.-~ oquation
rhe authora generalize and davalop a result of A. D. I~ys,-Lkis (U,181, 44#
kin- c,, QQ, 194Q). They show that no T-jitUer what th(, ~7,o-xth of
'A 'ghare i, fl't,y), vl,~-)j thi, -orraq~on' ill,., ac- ~L:;
-Fi t
L SUB XDE: HL
7 6 3
NO RK? SGVt 002 0 Ld7-q C000
r5,

110GUNW-41P A.I. Uzhevsk)
Some aspects of ths, behavior of the aoli:tion to an, int,
f~,7,ral
eauation. Volzh. mat. sbor. no.1:237-239 163.
OCRA 19: 1)

gornyy lnzh.; VELICHKIN, A.N., gomyy inzh.
Using charges with air spaces and igdanite in Kazakhstan
enterprises. Vzryv. delo no.54/111342-349 164,,
(MIRA 17s9)
1. Trest Kazakhvzryvprom.

LiIARI-7, A. J., ~AIYTVIL, L. ~., and A. 1.
'IThe Applllc,tt.ion of 4~%klio,-ctlvc Isoto,,-os for tho Control ji' ilammate~rj
of llovin~i I-let 3teamll
paper presented at the All Union ~;e;,-iinar on the "p,,1 i ca Lion of
HadioacIdIve Isoto,)es in -easurement3 ind Instmunent buildine,
Frunze (Kirgiz SSR), June 1961)
So: Atomnaya Energiya, Vol 11, No 5, Nov 61, pp 468-470

1. LN;U:iOV' F.
2. USsR (600)
L,. Stemi Boilers - Air Fr&eatinp,
7. installing regenerative Pir preheaters. :~lck. sta., 123, 0- 11, 1952
9. Monthly List of Russian Accessions, Library of Congress, Febr",,,-I,,r 1953. Unclassified.

311'28- ASSMILY OF 6-r-,A~C-jj-AjjK-3 Lolvinov, 'V. C.
Fuel Abstracts (Elckt. Sta. oscow), jan. DI tricu It I en
Vol. 14 No. 4 met with In the assembly of cyclones for dist removal are dl,,cus5ed nnd a
description and (Wirrims are alven of a device for hoisting and =,cmbling
October 1953 blockS for a 11-unit hank. A table Indicates the expcnditure of time anvi
Atmospheric PollutioMabour In assenblint, 334 components of a 4 11nit bank of cyclones. nX.A.

LOGUNOV, Y.G.. Inshener.
Installing boilers vith tower cranes. Zlek.sta. 24 no.8:48-51 Ag 153.
(HLHA 6:8)
(Cranes, derricks, etc.) (Steam boilers)

u ~ ~ R
. -, i ,
.1. :: , 7: - , - - - , . . . - -.
.. w

AUTHOR: Logunovq F.G., Engineer. io4-4-li/40
TITLE: The erection of-direct flow high pressure boilers in large
blocks. (Montazh ryamotochaykh kotlov vysokogo davleniya
krupnymi blokami.~
P.&dODICAL: "Elektricheskie Stantsii" (Power Stations), 1957,
V317.720K, No.4, pp. 36 - 40 (U.S.S.R.)
ABSTRACT: The erection of direct flow boilers differs in many
respects from that of drum type boilers because of differences
in construction. Since direct flow boilers are not very
widely used procedures for prefabrication of large assemblies
for erection of these boilers have not been fully worked out,
and the boilers are still largely designed for piecemeal erec-
tion. This article describes the experience of erection of
several dijrect flow boilers type 6?-2-cn of 280 t/4100 atm.and
510 C with considerable prefabrication. The sub-d~Lvision is
illustrated by drawings and details of weights and so on are
given in tables. The erection procedure is described in
detail. Considerable advantages are claimed for prefabrication
but it is clear that sub-division of the boiler into sub-
assemblies can still be improved. This refers in particular
1/2to the inclusion of fuTmace lining in the finished assemblies.
It is concluded that the erection of direct flow boilers

The ezection of direct flow high pressure boilers in large
blocks. (Cont. ) lo4-4-il/4o
can be organised on the high speed large sub-assembly method.
The erection of pipes of the radiation secUon into large ass-
emblies closed in a quadrilateral circuit is both possible and
desirable. The quality of erection of pipes of the radiation
system should be ensured by careful work using special devices
to ensure safe and convenient working conditions for assem-
blers and welders. The boiler-makers should take account of
2/2 the experience that has been gained in the organisation of
assembly of direct flow boilers.
There are 5 figures and 3 tables.
AVAILLBLE:

LOGUNOV Feofan. Goorgiytv ck; SHMUKLER, B.I., red.; VORONIN,
P K*Ps
tekhn.red.
[Walling-up of boiler unitol Obmurovka kotellrykh agregatov.
Moskyaq Gos.energ.izd-voq 1961. 391 p.
(MIRA 14:6)
(Boilers) (Bricklaying)

RZHNKIN, K.S.; LOGUMV. L.A.; KAFTSOV, L.11.
Analysis of near harmonic transistor oscillators for above
critical frequencies@ Radiotekh. i slektron. I no-5:647-653
W 156. (MLBA 9:12)
1. Fizicheskiy fakul'tet Moskovskogo gosudarstvannogo
univarsiteta.
(Oscillators, Transistor)

5W 3/032/60/026/02/025/'057
AUTHORS: Samokh,-n, V, A , Logunov, L A~ B010/BO09
TITLE: Measurement the Electrical Resistivity of Silicon by the
Four-probe Method
PERIODICAL- Zavodakaya laboratoriya, 1960, Vol 26, fir 2, p 185 (USSR)
A,BSTRACT: The curreni two,-probe compen.-tion method for measuring the
electrical resi3tivity of silicun is cumber8ome. It is diffl
cult to u-qp 'he foitr-probe method because of the great in-
stability of the probe contarts This instability may, how-
ever, be eliminated by using tungsten probes and a current
generator, or by molding the contacts electrically Ln
attachment (Fig) which permits the electric molding of con-
tacts using the normal potentiometric circuit is described,.
The attachment consists of an oscilloscope of type EO-7, a
rectifier, and a commutation system- For p-type siliccn, dur-
alumin wire probes are used, for n-type silicon, phosphor
bronze probeo, For moasurementa without current molding
tungsten probps of 0-65 mm thickn,~-ss are uged, For stabilizing
the measuring current an electronic current generator is used-
Card 112 Aleasurement results obtained with the attachment described are

0
Measurement the Electrical Resistivity of Silicon S1032160102610210251057
by the Four-probe Method BDIO/BQQq (.I
given (Table), There are 1 figure, I table, and 2 references,
Card 2/2
- I.-
.i

LOGUNOV, L.A.
Inverted diode as a small signal detector. Radiotekh.i elektron.
8 no.0722-723 Ap 163. (KRA 1634)
(Radio detectors) (Diodes) (Radio)

L 129111-631 EWT (1) /BDS AFFTcASD/RADO
S/109/63/008/00-1+/028/030
JXTHOR: Loguno L, A*
TZIME.- Inverted diode as a weak gIRM dgteotor 2?
PERIODICAL: Radiotekhnika i elektronika, v. 8, no. 4, 1963, 722-723
TEXT: The degree of non-Unearity of the volt-ampere characteristic of this
device is one of its outstanding properties as a detector. The author develops a
mathematical formulation to daterraine the value of rectified current and points out
that by a proper selection of the material from which the diode is made it is po:;-
sible to oifs'et the effect of the temperature factor upon its efficiency. He citoo
the following equation as representing the volt-ampere characteristic of an,invart-
ed diode: const ve-ev
and after additional mathematical manipulation, proves that the value of 6 is in-
dependent of temperature, but does depend upon the material used. For gem-4nium
diodes,, he finds, A worles out to a value of about 35, while for diodes made of in-
dium -and antimonyj the corresponding value of )6 is approx1matelY 125. Thus., he
concludes, by selecting proper materia parameters, it is possible to obtain
2~6:~~>a . e/kT. The inverted diode then becomes, according to him, a very much
Inverted diode as .......
Caxd I/it( more effective rectifier of a weak zifmal, than an ordinary semi-conductor diride.

L 12953-63 EW,(k)/EWP(q)/EWr(m)/EWT(1)/PDS/T-2/EEC(b)-2/ES(t)-2 AFM/
A,M/I~t-3 Pz-4/Pm-4 IJP(C)'/jD S/109/63/X8/004/029/030
AUMORS: Logunov, Lo A., and Fitanoy', V. 3,
07
Tirin.: Vo~l ~e characteristics of tunnel diodel made of
s _Gallium arsenide
?UBLICATION: Radiotekhnika i elaktronika,, v. 8,, no. 4j 1963, 723-725
MT. The authors report on their research into the inverted and direct
branches of the volt-ampere characteristic of pn-junctions obtained with gallium
ar;;enide of the p-type, alloyed with zinc fin a concentration of (4-10)'1619cm7y.
The drop in voltage r. in the series reaistance of the diode vras taken into ac-
count in plotting the characteristics of the Dn-junction, The measurements were
taken while passing., through the diode, currents of from ^-100 to 300 ma, for a
duration of ,-- I /.j -see. The voltage drop was measured in the diode, 7,ttile the
im.pulse current was determined on the basis of the amowit of voltage drop when us-
in,!y a resistance of 10 ohms connected in series with the diode. On the basis of
t'vto measurements of the voltage at various high. current values, the value of r.
could thus be determineds 'No graphs accompany the article. One sho-as the rela-
tionshiD between the logarithm of conductivity of the pr.-Junction and the respective
pn-junction voltage. This relationship is very close to rectilineara The other
graph shows the relationship between the logaritim of the direct current and the
Card 1/2

T, 12953-63 sAog/63/008/004/029/030
Volt,ampere characteristics
shift in the pn-junction, In the negative sector of the characteristic, this re-
Ditionship is closely approximated by an exponential curve.
STIFISITTED: December 18., 1962
Card 2/2

IDGUNOVP'L.A.; TARKHOVA, LF,
Dependence of the parameters of converted diodes on the admixture
concentration in initial germanium. Radiotekh. i elektron. 9
n0.1:181-182 A 164. (WRA 17-3)

-;~p9qNIOV,, L.A.; PLAMMIK, L.A.
Change of the tunnel cu"ent density in 'he proce:3s of making the
p-n Junction. Radiotekh. i elektron. 9 no.1:182-183 Ja 164.
(IURA 17:3)

ACCESSION NR: AP404Z5ZZ S/0107/64/009/007/IZ58/IZ69
AUTHOR: Logunov, L. A.; Rudneva. N. K.; Chernyak, Ye. B.
-riTLE- Inverted diodes
SOURCE: Radiotekhnika i clektronika, v. 9, no. 7, 1964, IZ58-1269
TOPIC TAGS: aernicondtictor, semiconductor diode, inverted diode, inverted
diode parameters
ABSTRACT: The parameters of inverted diodes intended for small-signal
i detection and pulse-circuit work are considered. Formulas for forward and
reverse switching times arc developed with the diode inductance neglected; the
switching time of a Go inverted diode proper is estimated to be 0. 12 nsec, and
that of the same diode operating in a computer, 0. ZZ-0. 25 nacc. The functioning
of an inverted diode as a detector is analyzed. Formulas for the current-voltage
characteristic, the peak current, and the voltage at peak current, wWch connect
.Card

ACCESSION NR: AP404Z522
there parameters with the properties of the semiconductor material, are derived
on the basis of E. 0. Kane's findings (J. Appl. Phys. , 1961, 32, 1, 83).
Labo rato ry mode ls o f Ge, Si, and GaA a d i o d c ow e r etested; their
parameters and I/V characteristics are reported. The effect of the ambient
temperature on backward-diode parameters, experimentally determined, is
ireported: the peak current decreases at rates as high as 0. 310/6 and 0. 1316 per 1C
as the temperature of Go and GaAs diodes, respectively, increases. Orig. art.
has: 6 figures, Z8 formulas, and I table.
ASSOCIATION: none
SUBMITTED: Z5Apr63 ATD PBr,,ss: 3077 ENCL: 00
:SUB CODE: EC NO REF SOV: 003 OTHER: 008
Card 0,
. 2/2

-unc A.
liy ul I e t e r, izrbrl~,' n i
tunrel diode, t. rlic !,ire p i)unctian, gemani=
tunnel diode
un
h1-71 nie rnc,na striirture of th,~ pr-~pOspd ze-mn-ol mn-basc- Umnel diode is mo ted
inult'llayer --h- -;-pri,itp-ncc Fuld
-1,ance ind to trmrov,~! th- -r thr- 7r-~-,q stri-jr-ture, the dlo--ie
nn llrjnu~ar r,-ermruniu=- pitt- vit-~: rtl~ tl7l' -1 :7 ~7 c -~,e , qn.1 a
C ~See Fig. 1
Yh ai I Oy rm -I ~g
qnd is located inside Ithe rin~z. r i 7 P-r-t n pz F, z e

4059

C.,d
0 1
Tun,
ohm-ic

U'l I k v j I "'L.L.
SOURCE C --OR/0,4i~/66/000/011./OCi,'I/CW----
%i=,i'7003482 ODE:
A.; Shkalikova, L Dou-nina,_L. V.
Ku,.,not,aov G. M.; Logunov,
ORG: none
TITIL: Cold-base alloy. Class 40, no. 1839/4
SOURCE: Izobreteniya, promyshlennyyeobraztoy, tovarnyye znaki, no. 14, 19L6, 81
TOPIC TAGS% gold base alloy, tunnel diode
ABSTRACT: A gold-base alloy is proposed for use in the manufacture of tunnel diode
onMIC contacts. For better physical and engineering properties the components are
Au - 52-56; Ag
taken in the following ratios N): - 43-47; Ga - 0.9-1.1;
Cu - 0.001 (max); Ni - 0.001 (max); As - 0,001 (max); Sb - 0#001 (:aax).
1JPRS: 37,,4801
SUB CODE; lit 09 SUBM DATE: -none
UDC: 669.2151221871
Card I 't A

ACC NR, AP70o2679 SOURCE CODE: uR/olog/6T/012/001/0158/0161
AUTHOR: Logunov, L. A.; Polyakov, I. V.; Serebryakov, V. N.
ORG: none
TITLE: Distributed tunnel diodes
SOURCE: Radiotekhnika i elektronika, Y. 12, no. 1, 1967, 158-161
TOPIC TAGS: tunnel diode, ecaki diode, distributed amplifier
ABSTRACT:
The properties of an active transmission line in which the act-I've element
is an epitaxially grown distributed tunnel diode (see Fig. 1) are

ACC NR, AP7002679
"degenerated
ias analyzed. The device is made as
p-type,semi I follows: from the In + 3% Ga
h 9nduc or +7% Ge solution a p-type german-
ium layer was grown on an n-type
t
t 400-450-U Ge plate doped with
u
pu
j As whose resistivity was

-8) x 10-4 obm/cm. The re-
6
(
sistivitZ of the p-type layer was
, 1.4 x 10- ohm/cm. The finished
!.Input
' samples were 15-20 cm long and
degenerate n-typ
e 150-250 V wide. The metallic
semiconductor layers for input and output con-
tacts and biasing were made by
Fig. 1. Distributed semiconductor Idepositing a 1-p layer of Ni.
active transmission line.. Tests, using five samples driven
by 35-nsec triangular current
pulses and 200-400-usec bias pulses, have shown that a nonattennated
signal ma~ be propagated along this line. The propagation velocity varied
(0.4 x 10 -1.15 x 108 cm/sec) from sample to sample increasing as the
Card 2/3

ACC NR. AF(oo2679
ratio of bias to peak TD current was increased up to a value of 1. After
this the sample behaved as a lumped element where all tunnel diodes in the
equivalent circuit switched simultaneously. In other samples which had
linearly varying width, in addition to the above properties, current
amplification occurred as it flowed in the direction of increasing sample
width. The value of current gain was approximately equal to the ratio
of sample width at the output to.that at the input. Orig. art. has:
7 formulas, 3 figurest and 1 table.
SUB CODE: 091 SUBM DATE: 25jun66/ ORIG REF: 004/ OTH REF: 002/
ATD PRESS: 53.12
Card 3/3

LOGUNOV, L.I., LIVOIJ, V.b.
Production Combine "Zar~ii'?
Ag 164.
1. Glavnyy inzii. leloskov.3kofo otyu-,mogo ob"ycFiin.,,riya "Zaryn'
Logunov). 2. ZwnoaLitel I g,-neval Inog:) ~,.iro~',~tora j,cj
vol)ro:3&m Moskovo;wgo ciii.irmot~o

I, It 5 1,. 12-66 EWT (m)/,`;Wt I j j 1,(C) j Llj (]
ACC NR- AP6027245 SOURCE CODEI: Ull/0109/66/011/OOH/1525/16'.Iti
AUTHOR: Kovalev, A. N.; Logunovs L. A.
ORG: none
TITLE: Gallium antimonide tunnel diodes
SOURCE: Radiotekhnika I elektronika, v. 11, no. 8, 1966, 1525-1528
TOPIC TAGS: gallium antimonide semiconductor, tunnel diode, semiconductor diode,
semiconductive material . c24i_L_1vn7 CoMPOUAjo, Aturlrnc)"10E,
ABSTRACT: Tunnel diodes are now being manufactured mostly from Ge, GaAs, and GaSb.
The properties of GaSb diodes have had the least attention among investigators. The purpose
of the present article Is a detailed evaluation of the properties of such~diodes as compared with
the characteristics of tunnel diodes based on Ge or GaAs. The diodes were prepared by the 4
fusion method on both n- and p-type GaSb. The P-type materials were alloyed with
zinc and had a carrier charge concentration of (1-2)- 1019 cm-3; the n-region was formed by
doping with Sn + 5% Te. The n-type material was alloyed withIt and had a charfc cont
"ti,
centtation of 2.1018cm-3; the p-n junction - was ol)tained by fusion In Sn + 10% Zn. Etching%
of finished p-n junctions produced a mesa-structure; the capacitance of the junctions In
Card 1/2
UDC: 621.382.23.011.222

L -ir~~_66
this case was 1-5pf. The authors conclude that the GaSb tunnel diodes now manufactured as
yet do not have a substantial advantage as low-noise ampli-
fiers, due to the high values of forward resistance. Furthermore, GaSb low-noise tunnel
diodes have a strong temperature-dependence of the peak current. The most promising areas'
for the application of GaSb tunnel diodes are, apparently, detectors and mixers. In this case,,
however, the advantages of the shape of the volt-ampere characteristics of these diodes may
best be used only by reducing f orward resistance to values found in. Ge diodes. This
problem can be solved by perfecting the manufacturing technology of GaSb tunnel diodes. (261
SUB CODE: 11, 20/ SUBM DATE: 15Nov65/ ORIG RE F: 002/ OTH RE F: 005/ ATD PRI
5081
2/2 e-UtkjjL--'

I Iwb-ROVq m?Hq
I - I
Broader use of existing pot"tialities in rated capacities. TSvet.
met- 33 no,12185 9 140- (MIRA 13: U)
(Prushing machinery)

LOGUNOV, N.H.; RAHKOV, F.G.; AYDEM, N.Tas, metodist pavillona; SYCHIK,
redaktor; BALIO. A.L. tekhnichaskly redaktor
[mDog breedingl pavilion; a guidebook) Pavillon NSobakovodetvow;
putevoditell. Moskva, Goo. izd-vo selkhos. lit-ry, 1956. 26 p.
(HIJRA 9:8)
1. Moscow. Voesoyuznaya sellskokhozyaystvennaya vystavka, 1954-
2. Direktor pavillona (for Ramko-$)
(Dogs) (Mosca*--Agricultural exhibitions)

SAFOKHIN, Mikhail Samsonovich; KATANCV) Boris Aleksandrovich; LOGUNOV,
Nikolay Fedorovich-, W~KMIOV, Yevgeniy Ivanovich; SOKd7jbV,-A7,IO-'--
otv. red.; ABARBARCHUKj F.Lt red. izd-va; MINSKER, L.L., tekhn.
red.
[Crosscutting and boring machines and drill bits]Buro-sboachnye
mashirW i burovoi instrument. (By] M.S.Safokhin i dr, Moskva,
Goagortekhizdat, 1962. 208 po (MMA 15%9)
(Boring machinery)

RAMKOV, F.: PIAITNIKOV. D.; LOGUIDY,
tekhn.red.
M -
N.: BTRDINA, A,, red,; FRDOTOTA, fi.,
(Hunting, fur farming, and dog breeding] Okhota. zverovodstvo I
nobnkovodstvo. Moakva, Goo. izd-vo sellkhoz. lit-ry. 1958- 91 P-
(Fur farming) (Doge) (Hunting)