SCIENTIFIC ABSTRACT NAYMARK, M. A. - NAYMUSHINA, L. YE.

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• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

RATHM, N.A.
--.r, antlog of the Schmr lamm and Itv &PPlic&tIO3 to the
Plancheral form Is. for complex clanaical CrOuPB- IzT-AI SSSR-
Ser.mat.20 no.1:3-16 ia,-F #56. (KLRA 9:4)
l.Prodstavlene akadaimikon S.L.Babelevyw.
(Groups, Theory of)

rqfi IV m fA f~ V\~' fV1 - 6,
SUBJZCT U3SR/KLTH M TICS/Algebra CARD 1/1 PG - 653
AUTHOR HAIMARK M.A.
TITLE On irreducible iinear representations of the complete
Lorentz group.
PERIODICAL Doklady Akad.Nauk 112,_ 583-586 (1957)
reviewed 611957
After Gellfand and Jaglom have given formulas in infinitesimal form for
the representations of the complete Lorentz group, now the author gives
formulas In integral form. It is proved that the obtained reprosentatioas
are irreducible and pairwise non-equivalent and it is ahown that every
irreducible representation of the complete Lorentz group is equivalent
to one of the obtained representations.
INSTITUTION: Physical-Technioal Institute, Moscow.

16(l) Pun r WOK EXPbDrUTION WW/1857
Naymark., Kark Aronovich
Lineynyye predstawlenlys gruppy Lorentsa (Linear Representations of the Lorentz
Group) Moscov.. Fizmatgizj, 1958. 376 P. 7#000 copies printed.
Ed.: D.P. Zheldbenko; Tech. Ed.: S.N. Milamov.
PURPME: This book is intended for theoretical physicists. The author's basic
results and methods., vhich, although previously published elsevherejare now pre-
oented systematically in this book, may be of interest to specialists in certain
fields of mathematies. The book iny also be used as a textbook on the general
theory of group representations for those vho have had university courses In
analysis and aralytic geometry.
COVERME: The author gives a systematic presentation of linear representations
of proper and full groups. Completely irreducible representations of the proper
Lorentz group in an Infinitesimal form as vell as spin reptnaentation are de-
scribed. In addition,, the theory of ftdwte dimensional representations of the
proper Lorentz group in the form of integrals, the theory of characters,, %ad the
Plaucherel for-I for the proper Lorentz group are presented. An exwt state-
ment of and a solution to the problem of the description to the accuracy of
Card 1/)

Linear Representationg(Cont.)
SOV/1857
equivalence of all completely Irreducible Liorentz groups are given. The book
contains four chaptem The first two are of an introductory chuacter,, where
fun4amentals of a three-dimensional rotation group and of full and proper Lie
groups are given. The p-sixeral theory of the representation of groups is pre-
aented in the form -%ich Is most suitable for the diamAsion of the folloving
chapters. Chapter III. Is the most important and deals vith the study of re-
presentations of the proper and fW2 Lorentz group., wtdch for the first tine
is given In detail. The last chapter Is concerned with a theory of invarloyt
equations whichjalthough not completed,, has Many important applications. The
author thanks I,M. Gellfand,, K.I. Girayev., D.P. Zhelobenko,, and S.V. Form1n for
help in preparing the manuscript. There are 59 references: 43 Soviet,, 13 English
and 3 French.
TABLE OF CONTENTS:
Preface
6
Ch. I. The Three-dimensional RotAtlon Group and the Lorentz Group
1. The ThrO-e-dimensional Mtation group 9
1. General definition of a groups Z. Definition of a three-dimensional
rotation group, 3. Description of rotations vith the aid of orthcgonal
Card 2/9

Linear Representations(Cont.)
W7/1857
matrices* 4. Euler's axwles, 5. Description of rotations with the aid
of unitary matrices* 6. Invariant integral on the rotation grouPe 7. In-
variant integral on a unitary matrix,
2. The Lorentz group 23
1. General Lorentz group, 2. Full and proper Lorentz groups
Ch. II. Representations of the Three-dimensional Rotation Group
3. Basic concepts of the theory of finite-dimensional representations 29
1. Linear spaces. 2. Linear operatorse 3. De-linition of a finite
dimensional representation of a groups 4. Continuous finite dimensional
representation of the three-dimensional rotation group. 5. Unitary re-
presentations.
4. Irreducible representations of the three-dimensional rotation group in
infWtesir-1 form 34
1. Differentiabllity of the representations of the group 174.2. Basic
infinitesimal matrices of the group $t0, 3. Basic infinitesimal
operators.of the representation of the group Relationships be-
tween basic infinitesimal operators of t1w representation of the groupd/O
5. Conditions urder which representations are unitary. 6. General form
of basic infinitesimal o?erators of the irreducible representation of the
group
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Linear Representations(Cont.)
307/1857
5. Realization of finite dimensional irreducible representations of the three-
dimensional rotation group k9
1. Connection of representations of the grolpdy'a vith representations
of the unitary group 7&92. Spin representation of the groupl.,&. 3. Re-
alization of representation ru, in the space of polynomials. 4. Basic
infinitesimal oper%tors of the representation rk.~. Orthogonality rela-
tion*
6. Decomposition of a given representation of the three-dimensional rota-
tion group into irreducible representations 59
1. The case of finite dimensional, unitary represetktatione 2. Complete-
neas theory, 3. General definition of the repreaentatione 4. Continuous
representations. 5. Integrals of vector and operator functions. 6. De-
composition of the representation of the grouplA, into irreducible re-
presentationse 7. The case of a unitary representation,
Ch. III. Irreducible Linear Representations of a Proper and Fall Lorentz Group
7. Infinitesimal operators of the linear representation of the proper Lorentz
82
group
1. Infinitesim-1 Lorentz matrices. 2. Relationships between infinitesi-
mal Lorentz matrices- 3. Infinitesimal operators of the representation off
the proper Lorentz group. k. Relationship between basic infinitesimal
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Linear RepresentationS(Cont.)
507/1857
operators.of the representation&
Dete tion of infinitesimal operators of the representation of the
Irn
P
gr01 V_*
1. Stat%ment of problem. 2. Determination of operators H+, H-, H3.
3. Determination of operators F+, F..' F3i 4. Conditions under which re-
presentations are unitary.
9. Finite dimensional represedtations of the proper Lorentz group 1c-
1. Spin description of the proper Lorentz group. 2. Relationship be-
tween the revresenj;ations of groups d/* and d:P~ 3. spin represents,
tions of the grou]~ OteA. Infinitesimal operators of the spin represents-
tion- 5. Ixredmcibility of the spin representation. 6. Infiniteall-1-
operators of the spin representation In canonical basis.
10. Fundamental series of representations of the group M, 121
1. Certain subgroups of the groupOC,, 2. Canonical decompositions of
elements of the group 0%q*3. Wacent classes with respect to K. 4. Pa-
reme-trization of the Oace Z , 5. Invariant integral on the group 7- *
6. Determination of l'undamental series of representationslof the group#4
7. Irreducibility of representations of the fundamental series,
U. Description of representations of the fandfizental series and spin repre-
sentations with the aid of the unitary group 134
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Linear Representations(Cont.) 90V/1857
1. Description of the space with the aid of the unitary subgroup.
2. The space alization of representations of the f=d&-
mental series in space Representations %Sk contained in L?~ So
5. Elementary spherical functionse 6. Infinitesimal operators of repre-
sentations ofrIjfin a canonical basis- 7. The case of s2in representations.
12. Complemntary series of representations of the group &-E- 147
1. Statement of problem concerning complementary series (of unitary re-
tatio
2,,Conditonl3 fO go. 3. Spaces
it ~ription of omplementary series in
D ption f C of representations
vith th aii S1, contained in
of a =itary 8:tgroU ons
7. Elementary spherical functions of representation* of fundamental seriese
8. Infinitesiml operators of -!~r representations in a canonical baaiso,
13. The trace of representations of fundamental and complementary series 160.
1. Invariant integral on the group &t-,,2. Invariant integrals on the
group K-, 3- Certain relations in the form of integrals. 4. Group ring
of the gx'OUPJ'Cv5. Relation betveen representations of the group Otand
its group ring. 6. The case of unitary representation of the group
7. The trace of representations of the fundamental series, 8. The trace of
representation of the complementary series*
Card 6/ 9
0

Linear Representationc(Cont.)
6"/1857
14. Analog of Plaucherel formda 179
1. Statemnt of prOblex. 2. Certain subgroups of the group K. 5. Can-
Macal decomposition of elements of the 9rOUP K, 4. Certain relations in
the form of Integrals, 5. Certain auxiUary functions and their relations.
6. Decbwtion of the aujil g of the Plancherel formula-P 7. %ItudllY re-
verse formiUs, 8. Decomposition of a regular representation of the 9r0WdT,'.
into irreducible representations.
15. Description of all completely irreducible representations of the proper
Lorentz group E~"c-,r 199
1. Conjugate representationo 2. Operators , , 3 Equivalence of re-
presentations,, k. Ca ilately irreducible ;Ve;;;iations- 5. Operators
k . *1
--.6. The r-ingXKj- 7. Relations betweep rey sentations of rings
P
y and JC~-. 8. Co=nta4iyJty of rings Wr ' 9. The equivalence
criterion, 10. Functional, ~, 4 X)En the case of &I Irreducible representao-
t Of a fitndenental series. U. Functlonse,,(,v) , 12. The ring
13, General form of the functipufl N (4 ). 14. General torn of
tWIinear multiplicative functional A~ in the 7' .4- ring. 15. Com-
plate series of completely irreducible repreaentatioJolf the group dr,,
M. Basic thearew.
16. Description of 02 completely irreducible representations of the full
Card 7/9 Lorentz group 253

Linear Repregentations(Cont.)
SOV/1857
1. Statement of problem. 2. Basic preperties of the operator ~- 3. GIOUP
ring of the group Opt. 4. induced representatkors. 5. Description of COK-
pletely irreducible representations of theilt-4 rings 6. Realization of
completely irreducible representations of the Wgroup tly-O 71 Basic theorem
W
Ch. IV. Invariant Equations
17. Equations invariant with respect to rotations of three-dimensional space ZT9
1. General definition of a magnitude. 2. The concWt, of an eqmstion
which is invariant with respect to transformations of the group 470 .3. In-
v%riance oonditimm in infinitesimal form - 5. General form of operators
Oc A-" Oe-1 -
18. Equations invariant with respect to pro r Lorentz transformations 295
1. General Linear representations of the proper Lorentz group in an in-
finites4-1 form* 2. Certaia particular cases of representations of the
groupV.f3. Concept of the equation which is invariant with respect to
proper Lorentz traceformations 4, General form of the equation which is
invw1ant with respect to transformations of the group q4-
19. Equations invariant with respect to transformations of the fun Loorentz
group 318
1. General Linear re sentations of the fun Lorentz group in an in-
finitesimal form 2. Description of equations which are invariant with
C ard 8,t9

Linear Representations(Cout.) BOV/1857
reqnat the fmU Lorentz gro
20. Equations obtained frou the invariant Lagrange fanction. 325
1. Invariant billnear forn 2. Lagrange function 3. Determination
of the values of a rest was and of a spin 4. Conditions under wbich
charge and energy densities are definite 5. The case of the finite
dimensional equation 6. 9xamples of invariant eVations
SupplMuents 36o
References 374
AVAUABIZ- Library of Congress
LK/Xfu
7-17-59
Card 9/9

,AUTHOR%" 11synark, M. A. 20-.119-5-6/59
M mm~ition Into Irreducible Representations of the
TITM On the M
Tenaoria-L Product of the RApresentationA of the Principal Series
of the Proper Lorenz Group (0 razlozhezLLI tenzornogo proizvedeatya
prodstavienly oenovnoy serii sobstvennoy gruppy-Lorentea n&
aspriyodimyye predatavlaniya)
SSSR
PERIODICAM Moklady Akademii NZW,- 1956, Vol 119, Nr 5, pp 872-675 (USSR)
ABSTRAM The author investigates the decomposition of the tensor product
of infinite-dimensional representations of the principal series
of the Lorenz group, where, as it is usual, inotead of the
representations of the Lorenz group Itself,the author takes the
representations of the group of matrices of second order being
locally Isonorphic to it, the determinant of which to 1. By the
integral f(s, X ) - ff (21 tsda(zl 06201, X)dz1dt2
an isometric mapping St(s 1'Z2) - f(s'?() of the Space Of Complex
funotions of two variables is defined on a cartaln Hilbert space
of censurable functions f(s, X) - f(x,m,1V), where a and alars
the parameters of the representations of the principal series of
Card 1/2 the Lorenz group. By this sapping 3 the desired decomposition of

10a the Decomposition Into Irreducible Representations of the 20-119-5-8/59
Tensorial Product of the Representations of the Principal Series
.of the Proper Lorenz Group
the tensor product of two representations is reached.
F There are 3 Soviet references.
PRESENTEDs December 4, 1957, by A.N.Kolmogorov, Academician
SMITTEM December 2, 1957
Card 2/2

AUTHORs S07/20-121-4-5 '54
TITL9z On the Resolqtion of Irrefteible Representations of the ftadaMt.&I
Series of a Complex Unimodular Group of n-th Order with
Respect to Re reeentations of a Complex Unimodular Group of
Second Order ~O razlozhenii nepi-ivodimykh predstavleniy oanov-
noy serii komplekanoy unimodulyarnoy gruppy n-go poryadka no
predetavleniyam komplekanoy unimodulyarnoy gruppy vcorogo po-
ryadka)
PERIODICALs Doklady Akademii nauk SSSRg1956,Vol 121tNr 4tPP 590-593 (USSR)
ABSTRACTs Let An be the complex unimodular group of n-th order. The author
uses his own results [Hef 1) and the results published together
with Gellfand [Ref 2,51 on the representations of the main
aeries of complex uninodular groups, in order to obtain in the
case n - 3 a representation of ths A in form of a con-
tinuous sum of irreducible representadons of the A 2&
There are 3 Soviet references*
PRBSEHTEDs April 2, 1958,.by S.L. Sobolev, Academician
M-EHIMD: Amh 31s 1958
Card I 'I

HATKARK. N.A.
Decomposition of tansor products of Irreducible represnn-
tatlons of propir Lorentz's group into Irreducible repran-
tatious. Tjdy Mosk.mat.ob-va 8:121-154 '59- (MIRA 13:2)
Groups, Theory of)

4)
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16(l)
AUTHORi Naymark, SOV/20-125-6-5/6-1
TITLE: -De-com-p-osition Into Irredu~ible Representations of the
Tensor Product of a Representation of the Principal Series
and Representation of the Complementary Series of the Lorentz
Group kO razlozhenii ne neprivodimyye predstavleniya tenzarnogo
proizvedeniya predstavleniya osnovnoy serii i prodetavleniya
dopolnitellnoy serii sobstvennoy gruppy Lorentsa)
PERIODICALs Doklady Akademii nauk SSSR,1959,Vol 125,1;r 6
pp 1196 - 11;9 (USSR)
ABSTRACTs With the same methods and denotations as in Z-Ref 1 7 the author
decomposes the tensor product of the representationi of the
principal series and of the complementary series of the T.-Vintz
group into irreducible reprenentations. Instead --' vne Lorentx
group the author uses the group isomorphic tv it of the matrices
of second order with determinant 1 . T'--;.,,eroue error5 from
former papers of the author I-Rof 1,2_7 are corrected.
card 1/2

10
On the Decomposition Into Irreducible Representations 0 V/20-125-6-5/61
of the Tensor Product of a Representation of the Principal Series and
kepresentation of the Complementary Series of the Lorentz Group
There are 4 Soviet references.
ASSOCIATIONs Ifookovskiy fiziko-tokhnicheakiy institut (Moscow Physico-
Technical Institute)
PRESENTEN January 6, 1959, by A.U. Kolmogorov, Academician
SUBMITTEDs January 5, 1959
Card '2/2

NATYARK,W.A.
Decomposition of tensor products of Irreducible representations
of a proper Lorentz group Into Irreducible representations.
Trudy Kosk.mat.ob-va 91237-282 060. (MIRA 13:9)
(Groups, Theory of)

T

AUTHOR: 911 ~r k ~V.. A S07120-13O-2-5169
TITLE: ' Iff-es-olution Into Irreducible Representations of a Tensor Pro-
duct of two Representations of Lorentz Eigen Group Supplement-
ary Series
PERIODICALs Doklady Akademii nauk -oSSR,1960,Vol 130,Nr 20
pp 261 - 264 (USSR)
ABSTRACTs The paper Is a continuation and oompletion of the investi-
gationa Z-Ref 4 - 6 7 of the author an the decomposition
of the tensor produ;t of two irreducible unitary represent-
ations of the Lorenz eigen group into irreducible represent-
ationa. In the present paper the author considers the lant
.
',
possible cases i.e. the tensor product .
of two
;
representations and both belongIng to the
2
oupplemeAtary series. Tho author distinguishes the cases
,,,1+ *12 2 and )I + .2 "2 . The result is summarized In
a theorem. The notations are those of Z_Ref 4,5_7 - I.u. L~'
Card 1/2

t ~ S;,.
Resolution Into Irreducible Representations SOV/20-130-2-5/69
of a Tensor Product of two Repreaentations of Lorentz Elgen Group
Supplementary Series
Gellfand is mentioned by tho author.
There are 6 Soviet references.
ASSOCIATIOlis Moskovskiy fiziko-tokhnicheakiy Lnstitut (Moscow Physico-
Technical Inatitut2)
PRESENTED: September 17, 1959, by A.N. Kolmogorov, Academician
3UBMITTED# Septemb6r 16, 1959
Card 2/2

Tensor product 6f the representations of loreazle characteristic
group supplementary series. Dokl*" SSSR 132 ao*5;1027-1030
Je 160. (HIU 13:6)
(Calculiis of teasors)

88207
S10201601134100210321041XX
/6,1000 C 11I/ C 333
AUTHORs 9 rko - 40'.1A -
TITLEt Factor-Representatione of a Locally Compact Group
PERIODICALs Doklady kkademii nauk SSSR, 196o, vol. 134, No. 2,
pp. 275-277
TEXTs Let G be a locally compact group which satiafies the second
axiom of countabilityl a "representation U of G" is defined to
be a continuous unitary representation g -4 U of the group G in
the separable Hilbert space ~ . U is called fIctor-representation,
if the weakly closed ring M generated by all U9 , g C- G is a factor
in the sense of von Neumann. If Aq -ASb (A) d (,(A) is the decompo-
sition of ~ with respect t- the center Z of It, then U is decomposed
into representations U(A) in tj(A) which are factor-representations
for almost all ~ 6 A . This decompoeition is called canonical
decomposition of the representation in factor-reprosentationa.
Theorem 11 Let ~ - ; ~ (A) do, (A) and U - ( U(A)~ be the
canonical decompositibn of the representation U. Then there exists
a set /\* C A of (0--meacure zero so that the representations
U(A) and U(A') are disjoint (see (Ref.3)) for all ~'s A-AO_A*A'.
Card 1/4

a a 2) 7
S/020/60/134/002/032/041XX
C 111/ C 333
Factor-Representations of a Locally Compact Group
Theorem 2 1 Assume that b - E ~ (A) d (,, (,k) and U - [ U
the canonical decomposition oq the representation U of a group G
of the type I. Then there exists a oet A,, C /\ of (- -measure
zero and measurable families k(A), k 1,2 ...... such that 1.)
for ~,A'G A-A. 4 the representations
U(A), and U(A') are multiples of nonequivalentg irreducible represen-
tations; 2.) 9~ (A) - 7, t k(A) for A E ^- Ao
3-) 1 k(A) is invariant under U(A) for A r. A, ; 4.) if Ae A- Ac,
and then the restriction of U(A) on e (A\ is
% k(A) ~ (0)' d k -
irreducible.
Theorem 3t The representation U is the space ~ is assumed to be
the continuous sum of the representations U(A) in the spaces f0 (A)
0 that d (-(A), U U(A) Assume that there exists
set C of (- -measure zero such that all U(A) for
~c_ A - N are pairwise quasi-equivalent (see (Ref-3)) factor-
representations. Then U is also a factor-representation. If, moreover,
all U(X) for X E A- A' are factor-representatiowof the
type I, then U is also of type I and, therefore, a finito or
Card 2/4

88207
S/020/60/134/002/032/041XX
C 111/ C 333
Factor-Repreeentations of a Locally Compact Group
denumerable discrete sum of mutually equivalent irreducible re-
presentations.
Theorem 4s Every continuous positive-definite function T(g) on
the group G of the type I is representable as
CO.- ~ [ d(t,_(A), where Tk(g,~
A
are elementary continuous positive-definite functions of g and mea-
surable functions of A , where
1*) Tk(g"\ ) and Yf(g,A ) define equivalent irreducible represen-
tations,
20) qpl,(g,A ) and qlf(g#A) for AI define nonequivalent
irreducible representations.
There are 7 referencess 1 Soviet, 2 French, 1 Hungarian and 3
American.
Card 3/4

88207
S/020/60/1.34/002/032/041XX
C ill/ C 333
Factor-Representations of a Locally Compact Group
[Abstracter's notes (Ref-3) is a paper of G. 11. Mackey in Ann.
Math., 1955, Vol. 58, No. 2. 193] -
ASSOCIATIONs Moskovskiy fiziko-tekhnicheskiy institut (Moscow
Physicotechnical Institute)
PRESENTEDs may 6, 1960, by A. N. Kolmogorov, Academician
SUBUITTEDo April 7, 1960
Card 4/4

HAMA K 14-4-
Expansion of an unitary representation of locally cczpact
group into factor-representations. Sib. mat. zhur. 2 no.1189-
99 ja-F 161. (HIM 14 9 5)
(Groups,, Theory of)

IIAV4ARK, M.A.
&xpansion of the tensor product of irreducible representations
of the Lorentz group into IrreducIble raprematatlew. Part
3, Case of the tonsor product of representations of the ccm-
plementary series, Trudy Kaaft%at. ob-va 10:181-216 161.
(MIRA 24:9)
Wilbort space) (Calculus of tensors)

LYUSTERNIKq L.A.; MISHOV, Me.; 'JAYMAIM, H.4.; ULYAIICVI, P.L.
Abram lezekiilovich Plesner; on his 60th birthday. Usp.
mat. nauk 16 no.1:213-218 Ja-F 161, (MRA 14t6)
(Ple=er, Abram Iezekillovich,1900-)

IfAYIIFA.RKt M.-A.
ls=orf..:;ic repracontat-.'.ca of rlag3 and &roupo. DoU. V 3,;,!! 137
no,2:278-2111 :.[r '61. (VLA 1/,-.2)
1. Frodntavlono aknda-~4'com
(Pi.x,a (Vathematics))

IaY~j H. A.
"On factor representations of aLlocally compact group"
report submitted at the Intl Conf of Kathematice, Stockholmj, %teden,
15-22 Aug 62

NAYWHK M.A. (Moscow)
on co=uting unitary operators in spaces with indefinite metric.
Acts. math Szeged 24 no.3/4il77-199 163.
1. Submitted February 28, 1963.
Tt. -Z II I,

NATKARIP M.A*
Structure of factor representationa of a loca2ly comwt
Dokl.IX SSSR US no.4*775-778 F 163. (,,RA glrO,4Up)~
1. MatematIcheskiy institut im. V.A.Staklova. kN SSSR.
Predstavlano akademikom L.S.Pontryaginyu.
(Groups, Theory of)

SAYMARK, M.A.
Unitary representations of a Lorentz group in a 71~k space. Dokl.
AN SSM 152 no.5tlO64-1067 0 163. (MIRA l6sl2)
1. Hatematichaskiy Institut im. V.A.Sviklova AN SSSR.
Predstavleno akadeaikom L.S.Pontryaginym.

WAYMPKe., ~!. A.
Unitar7 representations of solvable groups in spaces with
indefinite metrics. Izv. AN SSSR. Ser. mat. 27 no.5sllft-
U85 S-0 163. (MIRA 16:11)

NATHARK, M.A.
Unitary permutation operators in a YX space. Dokl. AN S~ZR 149
no.6:1261.;-1263 Ap '63. (MIRA 16:7)
1. Hatematicheskiy intititut Im. V.A.Stekloya AN 33SR. Predstavleno
akademikom L.S.PontryagitVm.
(Operators (Mathematics)) (Hilbert space)

NIAX*~Klq M.A. Wbskva)
tary representationa of a Lorentz group in spaces with indefini"
metric. Mat. abor. 65 no.2:198-211 0 164. OkURA 17ill-)

NAWARK,LIJAS. -, .
Commutative algobras of operatorn In 11, spice. DoK. AN
SSSR 156 no. 4:734-737 Je 164. (MIRA 17:6)
1. Matomatichookiy institut im. V.A. Steklova AN SSO"ll.
Prodstavleno akadomikom P.S.Novikovym.
. , I

NAYMARK, M.A, (114 d.,;; ~ V .1 )
CoMtaLtive algebra,% cf opjratore In *;,3 TT.1 3pact. ROT mate,
Rc= 9 no.61499-528 lil.

KUPPYATI"Mr, I.D., Uukt('r M.~ - f z.-materi,
rauk
Conferencu cii functional aru2y2J-!j, t~fj theciy ..f
and Operatcrs in the Comm,, PemocraLc Republic. Vtst.. All SrSH
31,, no.9:101 S IE4. (MIRA 117~ --, 0)

KUDRIArMLV, L.D., prof.; NAIRiM, M.A., prof.
Golloquiun on linear s:paces and linear operators. Test. AN
&IM34no.12t64 D 26+1 (KIRA 18:1)

HAVAla:0 POP'l
Str.L!,tirts of unitary rap"s*ntations of It-f-ally blea=,act
in 4111 44C9, lev- AN WSR- Sar, M&t- Z9 r,'~3-*6S9-r%jO It5e
(MIRA ISO)

NAYI'ViRK, IM.A.
Conditions for unltarj~ equivalence -of cor=atative
algebrao in ilk sPace- 1.okl. AN 57-S-F-1, 1~0 no_.6:11257-12~f) F '6,5.
( M, I ! 11, IF:2)
1. IlAternatichookiy Inotitut im. V.A. Steklova Al! SsIM. Sub-
mitted September 21, L961/6.

NAYHARK, M.A.
Coamtative algebras cf operators in a 'Ik sp%ce,DokI. AN SSSSR
161 nu.4t767-770 Ap 165. (~ffRA 180)
1. Katematicheskiy institut im. V.A.Staklova AN SiSR. Submitted
September 7, 1964.

11hyllyINK, I.I.A.
I
Unitary (X 1y ir, .-: %
fjokl. AN SISSR R.0 rG.;' ,,~A (,r
I ~ : , '~ , ~' '. 11

ALCC NPj AP7011843
AUTHORS
ORM none
SOURCC COGEt UV0038/66/030/00/1229/1256
TITLEs Degenerate operator algebras In pontryagin space pt sub K
SOURCEs AN SSSR. lavestlys. Serlya matamselcheskaye, vo 30, no. 6, 1966,
1229-1256
TOPIC TAGSs algebra, mathemstic space
SUB CODES 12
ABSTRACT: Algebra R is called dageaerata if there exist such a homomorphLon
A -- ),(A) of algebra a In the field of complex numbers and such a natural
m=bar p, that (A - ~(A)I)r = 0 for all A C. & ThG article Includes a
description of comutativo, symetrio. degenerate algebras - to within equiva-
lence - of bounded linear operators In the apw* Ve * Orig. art. has 1 5 formulas.
CeaSs 40.42:37
cad

Let us put an and to Interruptions In processing In the clothing
industry. Leg.(Erom. 15 no.11:15-16 N 155. (MA 9..2)
lothIng industry)

I , //, ~ Pt Pi k ! , -,
"I pr - I
I N~4m -4--,
,nMYA-~~
Coordination of mult1ple-stylo dressmaking procesass In the output
stagea, log. prom. 18 no.1-045-46 Ja 058. (MIRA lit2)
(Drenowakirt,g)

GUMIMTSFATA, S.A.; VIUMMINA. A.M.; WKARK, K.I.
OrOnIzIng the start and accounting In multiple-pattern production
processes. Log. prom. IS W,3:8-9 Kr 158. (win 11:1q
(Dressmaking)

H.I. (~bskvm)
Chart for the distribution of operations e=rg reflacezento for
aboant uorkers. Shveineprome noo5:1.1-15 JI-Ag , e.3-01 161.
(I-MU 14: 10)
(ClothIng industry-Management)

4, ~!--
1. IIAYKM, N. A.
2. USSR (600)
"Vibration of a Thin Remillent Layer Resting on a Resilient Samispace Dun to the
Action of a concentrated Harconic Force Applied to the layer's Free Surface."
jr3dx se-vqijOIOzIch2.qkm Instituta, NO. 127. 1944 (1-15)
9. 14ateorologlya I Gidrologlya, go. 3, 1949. IM Report U-2551. 30 Oct 52

KUYLINI G*Ke; KAIKM# Nei.
Using the &Iectrical analogies nothod for atudving the de-
formations bf textile fibers, Report %ol#! Izy.vywtucheb.
save; tekh,tekst. prow, no.5:12-19, t61. (KM 14:11)
1. Hoskovskiy tekstil'M institute -, I
41)~formatiorin (K~ch&wtcz))-4aactrcwchwdoaI
uAlogies)
(;oxtile fibers, Synthetic)

NATKARKS If.l.
Some pecuUaritive of the defamation of cotton yam*
R4port presentAd at the 23th Uonferance on bj&--aolsm2&r compotmde
mogcqwg 8-n Oct 62

HAMARK, H. 1.
Use of slactrte amlogles for studying the deformtIon of
textile fibers. Im vys. ucheb, sav.; takh tekst. pr=.
n0-099-104 %2. NIRA 15 s 10)
1. Knekovskiy takstillnyy institut.
(Tarn-Testing) (Electromaebanical anotlogles)

URI
----- -------
(m)AP
AP, Cl-Ml A Mt A115D13982
6-77.464.1 f"
r r%i-~e!-t,-,, t, -rtj tz~ f- "r,

Ri N IN ft - All 5013 98 2
..........

TEREKHOV, V.S., arkhitektor: 11APMRK, arlhitektor
.
.9tandardizJng storehouses of ore preparation enterprises of
ferrous metallurgy. From. stroi. 40 fi.c. 411 no.61l2-16 Je 163.
(MIRA 16-10)

typ-) f, ra I - ie .ri z- h, 'or i n
42

SKLYAROV, Yuriy Andreyevich; NAYMARX, S.L., red.
.
Tiumen', Tiumonskoe
(Tyumen' builds] Tiumn' stroitsia.
knlzhnoe izd-vo, 1963. 34 P. (MIRA 17:4)

NATKARK. T.Te.,kand.fiz.-mat.nnuk; GURRVICH. Yn.B..ksnd.teI:hn.nFtuk
Plastic properties of W5N2O modified steel cast'-ngs. Prot!.
netn1loved. I fiz. not. no.4:621-618 155. (MMA 11:4)
(Steel castings) (Plasticity)

~- I-el ~! - , , . r
r - I, . , - . - - .I. V , 1 ~ ,
GUR371GH, Tn.B.,knnd.tekhn.nauk; HATRARK, V.Ye.,Icand.fIz.-ns%t.nauk
Defornability of Ih25N2O steel castings. Probl. notalloved. I fix.
met. no.4:639-647 155. (MIRA 11:4)
(Steel castings) (Rolling (Metalwork)

UYNARK, Te.A -TRITIYAK. L.K.
Treatment with synthozycetin of dysentery and Infdat toricosts. Vcpr.
pediat. 20 no.6:18-20 Nov-Dee 1952. (CIXL 23:4)
1. Assistant, Candidate Medical Sciences for &qwark; Assistant for
Tratlyak.

PONCIA=VAO V.Nl IIAIIW!Ko Yo.A., kand-mad.mulc
Treatment by stages for dysentery patients under conditions of a
children's hospital. Vop. okh. mat. i det. 5 no. 2174-78 Kr-Ap
160. (MIRA 13:10)
1. Iz Detskoy infektsionnoy bollnitay No. U Ok-tyabrlskogo rayons.
Moskv7 (glavWy vrach V.F. Pershina).
(DISENTERY)

UPLAN, G.Sh.; BELUKHIN, V.G.; MAYMARK, Yu.Yu.
Determination of the optimum geometry of a cutting tool
securing chip breaking. Trudy Stud. nauch. ob-va LIEI no.31
39-48 '59. (MIRA 16:10)

NAYMENYO, M.
"The Rocket Arttllerl of the Russian An,-,y,," In the collection: The Histor-1 of
Russian Military-Technical Ideas. M. War Publ. House.. 1952, ppe 64-87

NAYMIS, I.
Ubolwranlya shivotnykh ot nopravillnogo kormleniya i plokbikh kormov
(Diseases ot Animals Caused by rmproper Feeding and Poor Feeds),, VilInyus.
Gospolitnauishisdat. 1950. 44 pages with illustrations. rn the Lithuanian language.
U-5235

HAIrI49SHU"N, K. I.
Crtensivempair of railroad passenger cars without uncoupling. Moskva. ao.1 , transp.
zhel-dor. izd-vo, 1953. 26 p. (54-32098)
TF455.63

KHADZHIDEKOV, G.; UAYMOV, G.
--.- ...... .
Haffuccils syndrome. Suvr. mad.,14 no-4:69-76 163.
1
(DYSCHONDROPLASTA) (HMANGICKA, CAVEMOUS)

NAYWVt G. F.
- ff-~
OTboi Effect of Vegetative Propagation on the Vitality and Viability of Plants (For
,nstance, Kok-saghis).* Cand Agr Sci, M-arlkov Agricultural In3t, Dwlko:v, 1954.
(RZhBiol, No 1, Jan 55)
Survey of Scientific and Technical Dissertations Defended at USSR Higher Mucational
Institutions (13)
SOt Sum. No. 598P 29 Jul 55

L",V
i f "I
UKHOW. B.S.. prof.. doktor teVhn.nauk [decested]: TOROB'T". V.A., prof.,
dektor tekhn.nauk. caslurhannyy dayatell nauki I takhnlkl; UGOROV.
Tu.A., prof., doktor Iskumstvovedcheekikh nsuk; SMIAMIOV, A.Ta..
prof., doktor takhn.nauk; SIROTKIH. V.P.. prof.. doktor takhn.nauk-.
TMOPOV. A.S., dotsent. kand.tekhn.nauk; KRILOV. B.A.. kand.tskAn.
nauk; SMIM, A.K., k9n4.tskhn.naukj OSKOUYWSKIT. H.S., dotilent,
lmnd.arkhltertury, Inzh.-arkhitektor; POGODIM-ALMMMIEW, G.I., prof.,
dcktor takhn.nauk, obahchly red.; HATKOV, N.A., dotsent, kand.takhn.
nauk, n(nichnyy red.; KOKOSMO, A.(F.~-redO-'i#-TWIKOV. K.14.. takhn.red.
(Industrial and residential construction; textbook for higher party
schools] ProaWshlennoe i grashdanskoe strol.talletvo; uchobnoe poso-
bie dlia vysshikh partiinykh shkol. Koskva, 1959. 434 p.
(HIRA 13:2)
1. Nommmistichaskaya partiya Sovetakogo soyuza. Tyashaya partlynaya
shkols. 2. Chlen-korrespondent Akndeali stroitel'stva i arkhitak-
tury (for Stramentov). 3. Rukcvoditall kafedry promyshlennogo proie-
vodstva I stroitalletva Vysshey partiynoy shkoly pri TEentrallnom
komitate Kommunistichaskoy partii Sovetskogo soyuza (for Po,-.odin-
Aleksayev.)
(Construction industry) (City planning)

UWchemixtry - Aeotle Acid ftstm AM
r1hysies - XleetrocondimetAvity of
Acetic Acid
w1loetroconductivity and Viscosity a4! the Sys-
tea Acetic Acid-Monochloroacetic Acid, rV,-
A. B. Waysiovs, Lab of P" Chem, Tomar PolytAwh
X"t imeni S. M. nrov, 1i pp
"Mwr Obahch M1W Vol X3X, No
%hv*stigated electroconductivity at 40, 60, 750 C,
rtv *ling a x1mlymim on temperature curv for eo-
efticlent of electroconductivity vhen molecular
fttios of components vere 1:1. Studied vineasity
at these temperatures also, and derived an 8-alm"d
4M 149ni
US W/Chexistry - Acetic Acid System Aug 49
(Contd)
e%wft,, indicating formation of a compound vhwo
viscosity Is intermediate between those of its
Oftoobeents. Subadtted 3 Apr 48.

ABUIAJM, X.A.1 AMILSWOK. Tu.A.,nostovoy naster; ITATHUSHIM. A.A..starshty
dorachnyy master (Sevastopol'). KRIUSHIN, I.A.,dorozhnjy-rAst9r
(stantelyn Adadym Krasnoyarskoy dorogi)
Lotters to the editor. Pne I pitt.khoz. no.12:35-36 D '58.
(MIRA 12:1)
1. Machal'aft rellaosvarochnogo poyeada, stantelya Orsha Halo-
rusakoy dorogi (for AbOadze).
(Railroads--Track)

RAYMUSHU11, A.A.0 starably dorozhr*7 mster (g.Sevastopoll)
Track iaspector Skibao Put' I put* khoz. 5 no.3:14 Mr 161.
(ICRA 14:3)
(Railroads-2mployeas)

FAYMUSHIN, A.3.
Remr,deling a gas uril~. Nofteper. 4
no~7:43-46 163 N " P.A 17 : 11 )
1. ~cmnkly Yiet'v;jpcra,-:itAity7,t-
yuglicidy zavod.

SC111/99
14(10tll)t 18(5)
AUTHORSs Saymushin, I., [lead, Gindin, A., Chief Enginer-r, Shergin, it., Sp,~-
rotary of t Party Committee, Georgiyevskiy, S., Seer"taF-y
TITLEt Open Letter From the Workers on the Bratak Construction Pr~jjj!ri
j
PERIODICAL: Gidrotekhnicheakoye stroitallstvo, 1959, Nr 8, pp 3-4 (USSR)
ABSTRACTs An mentioned in the opening article, this is itti open leti,ei ic-A'
to all construction sites, industrial undertakings, tcelinical in-
titutes, and to the workers on the Krasnoyarsk G13S prrjF!ct in
articular. Based on Clio resolutions of the June Plenum of the
;
Central Committee of the Soviet Coamunist Party, and born of n
desire to hasten the fulfillment of the plan, the letter call!~
for help to be extended by more experienced teams to those in !i
less fortunate ponition. In particular, it calls for- aid fz-(,m tnt
workers of the town of Angarsk, the Glavmoe8t--Oy and the Glav-
mospromstroymaterialov of the Mosgorimpolkou (Moscow City Execu-
tivo Committee) in this field of housing construction on the
Bratsk site, admitting its inexperience in this sphere; from the
Card 1/2 Krivoy Rog ore-mining toom in the construction of the Korshunov

SOV/98-59-8-2/33
open Letter From the Workers on the Bratsk Construction Project
iron-ore combine (output 12 million ton& a year); from timber com-
bines, in order to help with the construction of the largest wood-
processing enterprise in the USSR (output 4 million cubic meters
a year); and from the Academy of Construction and Architecture of
the Ukrainian SSR in the field of the removal of earth and rock
by means of explosives. In return, the Bratsk workers on the Pa-
dun Falls offer their help and experience to all who need it, es-
pecially to the workers on thr,- Kraguovaralc site on tim Yenisey,
who lag behind the former somewhfit iii the fulfillment of their
part of the plan to provide a network or pow~-r atiu~ion&i in Siberia.
ASSOCIATIONs Bratskgesstroy (Bratsk Construction Projett) (Nayjaiiihiii): Bratskiy
gorkom KPSS (Bra:tsk Town CoaWttee, cpsu (Georgiytviskiy)
Card 2/2

TOLXACHV. A.V., dote.; HAYVESHIN. I.G., inzh.: Y2M. G.A.
Operational experience of the U2 diesel locomotive in passenger
traffic. Zhel. dor. transp. 41 no.5:64 Ky '59. (MIRA 12:7)
I.Zaveduywhchly dinatmometrichaskim vaganom Tashkentskage instituta,
Inshenerov thelaznodorothnogo transporta (for Kraft).
(Diesel locomotive@) (Ballroade-Paseenger traffic)

Firat units of the Bratsk Hydroelectric Fouer Station sliout
to 90 Into operation. Na atrol. Roo. no.10:4,-7 0 161. OM, I4zUj
it FhoWltoW Bratskoy g1droalektrostastaii,
(Bratak Hydroelectric Power Station)

4STADIKO. A.F.; KEJCIMMIfKO. V.A.; PAVLEM. A.S.; GRISHMOV. 1.A.;
MWV, V.S.; WAS MV. Z.A.; TEYMMY. H.T.; SHIRMT, H.S.;
CHIZE10VO D.O.; NOTIM7, I.T.; 10507, R.P.; ASEDCMSrff. A.N.;
NIMUSOV. A.M.; LATREMM. K.D.; TARASCV. N.Ya.; GABDANK. K.A.;
LVIN. X.A.; anMURG. S.Z.; ALWAMMOV, A.P.; MMINo I.T.;
OZMV. I.M.; SOSMIN. L.A.; BZMAMN. A.A,; . 11. 1. 1. !
IMSHIN. H,V*; ACEIXASOV, D.I.; RUSSO. G.A.; YSM. A.I.:
PLATONOT, U.A.; MUCRIN, D.G.; PRokyswv. Va.; MUSTOV. Vl;
SAMNIMV, F.V.; KASATKIN, K*V*; ALMMANDROV, K-Ta,; WTILEVS11Y,
D*G*
Fedor Georglevich Loginov; obituax7. glak.sta. 29 no.8:1-2
Ag 05 $. (HERA 11: 11)
(L*ginov. Fedor Oeorgievich. 1900-1958)

Nflym t) Z, /I / /V 10 k. I
MAYKUSHZB, K.I.; SHCEMANOV. V.P.. redalctor.
---------
[Xxtensive repair of railroad passenger care witb,=t naccupling]
Ukrupusanly besottsepoohnyy remont pasgachirsklkh vagonov. KosL-va.
Goo. transp. shel-dor. Ltd-vo, 1953. 26 p. (HLRA 7'4)
(Railroads-Fassenger cars-Katatenance and repa1r)

UNUSMS. K.I., (g. Sverdlovsk)
R"eIrIng passenger cars without uncoupling. Zhol.dor.transp.
37 no.1:76-77 Ja 136. (KLRA 9:3)
1. VachIlmik v&Co=o4puch&4tk&-
(Railroads-Cars-Raintanaace &md repair)

L 6962-6 .6 1WT(1;/F'C3(k)'/T Wit
'ACC HR: AP5020366 SOURCE CODE: UR/0141/65/00810031054010546
AUrHM ' Haymushin, M'. P.
ORG: Moscow PowerEngineering Institute.(Hosko~skiy energeticheskiv institut)
TITLE: The excitation of a cylinder with variable surface impedance
SOURCE, IVVZI Radiofizika, v. 6, no. 3, 1965, 540-546
TOPIC TAGS- electric impedance,.numeric; integration, cylindric flow, antenna con-
figuration, waveguide antenno-
ABSTRACT: A two-dimensional problem associated with the excitation of a circular
cylinder with~a surface impedance varying along the circumference of the cylinder
is considered. The integral equation for the surface density of the electric or
magnetic current is solved by the numerical method of Krylov-Bogolyubov CL. V.
Kantorovieh, V. L Krylov, Priblizhennyye metody vysshego analiza, GIFUrt, K-L.,
19621, A digital computer used this method to producethe results given in the
figures., In Fig. 1~, the antenna is placed on an ideally conducting cylinder and
excited by a longitudinal slit. The m%rrent phases for the various cases are al-
UDC: 621.396.671
Carci 1/3:

--Omit

L .6q6 AA
ACC.NRt AP50203d
mo3t Identical... ~Ths.*iwpedance distribution In- the same for all antennas. The
region with the 6apacitive reactance situated behind the alit verves the role of a
reflector and absorbs the source radiation in the reverse direction., A region with,
Inductive reactances Is situated on tha opposite side of the slip. The linear va- I
riavion' In the phase shows that.the -current is*of the traveling wave-type. This
can also be observed from the email oscillations and the value of the current along
the Due to the discontinuity in.the surface wive, radiation takes place
along the 'entire length.!Df--;the'anteAna and the.amplitude of,the traveling wave is
decreased., A directional diagram shous that the banding of the antenna produces
an incr*ease1n,the radiation pattern minima and an'sxten.sion of the principal lobe.i,
The current dLetribution:on the-anterma radiatio'npattern coverill -the entire cir-
cumftrence of the cylinder is shown. In.,.this case whiU a large part of the cylin-
dcr impedance has a constant value near the slitj the value varies and eats up a
..traveling vave along the circuMference of the cylindeV, T1w traveling wave atten-
,uates very little after passing over the cylinder.due.to the high value of impe-
dance and thirelatively small curvatumi Zn this case the radiation pattern also
,.follovs approximately the law of the attenuating traveling wave bud does so with
"greater nonunLforiiity pro duced by the natural radiation of the alit. "The author
~exprenses hia'deep gimtitude io'G. T# Markoy -for supervioirg the vft*."- Or1g. art.'
has: -11-9quationog 4 figures,
SUB CODEI EMI GIUBM DATES ~' Okp64/-,4 0AIG REFS 003/ MH REFs 002.
.-Cord .3/3.

BRODSKIT. A.M.; IAVROVSKIT, X.P.; HATHUSHIN, N.Y.; TITXOV, T.B.;
FIL&TOWA, Ye.D.
Chronavogintphic analysis of mixtures of alk7lense and diolefins,
XhIm. L takh.topl. I masel 4 no.3:30-32 Kr 159.
(MMA 12:4)
1. Instittit neftl AN SSSR.
(Chromatographic analysis) (Oleflue)

KkLUIENKOP R.A.; IIAYMSHIN, N.N.
Gas-liquid chromatographic analysis of complex mixtures of oxygen-
compounds. fieftekhimiia 1 no.1:117-120 Jm-F 161. (MM 15s2)
1. Institut neftekhimicheskogo sinteza All SSSR.
(Chromatographic analysis) (oxygen compounds)

ANPIWaOT, I., elektrostarahchik; MKISHIN, P.; CHISTOT, S., InSh.;
XURUNUMM, A.; S&TITAdHMM3, is.
Worker correspondents of the periodleal, of the All-Union,
Central CouwIl of TrMs Unions 00khrene trtLda I sotaftl1wo
strakhovanial make a surprise inspection., Okhr-truda I sots.
strakh. 3 no.6:46-50 Je 160. (MM 13:7)
1, Rerdovsym brigula shurnals, w0khrana trrA& I totsiallwye
strakhovwdyao (for all). 2. Uflmekly neft6parerabatyvanshohly
sayod (for Aupllogov). 3. Otvetstyannyy sakretarl gazety
49aftepererabotchILI(for Maymmshin). 4. rekhnicheskly in"Ictor
oblastnogo soveta profsaynzov Ushkirskogo awnarkhoza %for
Kurbangs.leyew). 5. SpetsiallrWy korraspondent thurnala
60khrana truda I sotstallnoye strakhovantreg (for Tretlyachanko).
(Bashkiria-Industrial hygiene)

NA YMS11 IN f1, A.
Oporations at the ?;fjvc-,1f!mKa Petroleum Reftnery. fiefteper. i
nof toichim. no. 4:3-6 164. (MIRA 17; 5)
1. 11ovo-Ufimskiy neftepererahatyvayushchiy vviod.

6902S

AUTHORS: Toropovap V. r., raymushin&P Ko To S/07SJ60/005/04/017/040
B004/BO07
TITL3% Palarographlo Investigation of the
Complex Compound of Cadmium With Thioaemicarbaside and
Somicarbaside
PERIODICAL: Zhurnal atorganiaheakoy khlmilp 1960, Vol 5, Nr 4. PP 874 - 878
(USSR)
ABSTRAM. In this paper the investigations of the thlosealoarbaside con-
plaxes of mercury and silver carried out In reference I were ox-
tended to cadmium. The investigation was carried out by means of
the polarograph of the Gintevetmet (Gosuderetvann" Institut po
tevetnym metallan - State Institute of Nonferrous Ketals) on a
dropping mercury electrode. For measuring the pH an LP-5 tube-
potentiometer was used. Table I gives the measured half-wave
0
potentials of Cd2+ In the presence of thionamicarbazide at 25
figure I shown the linear dependenor. of the half-wave potential
on the logarithm of thiosemicarbaside concentration. The angular
coefficient of the straight line is 0.064. The solution therefore
contains complex ions with the coordinate number 2:
]2+ -,NE[NH
. (TS - SCO 2). The instability constant was cal-.
[Cd(TS )
Card 1A 2
\NH2

69022
Polarographic Investigation of the Complex Compounds 8/078
,/60/005/04/OIT/040
of Cadmium With Thiosemicarbaside and Semloarbaside B004/BO07
oulated, as being 5.5� 0.15. In figure 2 the dependence of the
stability of the oadmium-thiogesicarbaside-conplex on pH is
shown* The complex In stable between pH 5 - T- With pS