SCIENTIFIC ABSTRACT RASHEVSKI, S. - RASHIDOV, T.

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• Collection: Scientific Abstracts
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• Document Page Count: 100
• Document Creation Date: January 3, 2017
• Document Release Date: August 1, 2000
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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RASHOVSKIY, P. K.
Un Schema unifiant la The"oric des Gmunes Abstraits avoc la I~lcorie 4-es Gro-.-,nc-z
Infinitesimaux de Lie. C. R. Acad. Sci., 202 (1936), 10.2-1013.
Les proble"mes les Plus Simples do L Al E;ebra Quasi-Comutative" en Con!teyion
avec la Th(loria des Valcurs Cbxacecristlques des Op;rateurs Diff"~rcnticls.
Yaten. SB.,- 9 (51), (191a), 511-544.~
Les rrob3e%z~es les Plus Si.--ples do f1i 1JUg'ebra Quasi-Com-utative" en Con-exion avac
la The'orie des Va2eurs Caract6risticiues des Op6rateurs Diffre"rentiels. Troiric%me
et ',~Lmttieme Fartie Matem. SB., 16-02), (1942), 955- 142.
z + B
kt~erf E2, M 2,
Un Cr xurn Caracteristiaue des Repre/sentations Conforms
C. R. Acad. Sci, 197.(1�33), 291-~94.
n 2
Representatippas Conformes Z E W 2 au.PoInt do Vue do Gc'orakrie Confonne.
IMatem. SB-, 42 (19135):, 157-168.
Sur les Espaces sous-Projectifs. C R Acad.' Sci.) 191 (19.30), 547-548.
Kharakteristicheskiy Priznak'Seneystva Goodazicheskikh Afinno- Sirfamovo Frc-
stranstva,Dvukh Izmereniy. Matem.- SD-i 39: 1-2 (1932), 72-80/
Caracteres Tensoriels,de 1"Espace sous-Projecti.f. Trudy Sevain. Po Vfr--k,,orn. i
Tenzorn. Analizu, 1 (1933)1 126-142.

RASIEVSFIY, F. K. cen't.
Geodezicheskiye Linii DviLkM. ernoCo Prostranstva Afinnoy Svvazi V Peskoncelmo
Malom S Tochnost~u Chetvertogo Foryadka. Dan, 3 (1934), 1113-316.
-cc -,c nllo
Geoclezicheekiye Linii Dmklr.,.ernogo Afln o- Siriamogo Prostranstva V -ko,-c*
Malom V Suyazi.S lzmereni,,en Ploshchadey. Dan, 3 (1934), 570-5171.
Coneruence Rectiligne Dans IlEspace Euclidien a N Dimonsims. Tridy Se in. P0
Vektorn. I Tenzorn. Analizu, 2-3 (1935), 212-229.
Geormetriya Yonusa Nulev.ykh NapIravloMy. M., Uchen. Mr. Ped. in-ta, 1 (1937)173-93.
Sur llUnicite do la Cr~orltetrie Projective dans le Plant Matem. SB-, 8 (50), (1940),
107-120.
SO: I-lathenatics in the US-4R, 1917-1947
edited b~,. K~rosh, A. G.,
1,11arkushevich, A.
Rashovskiy, P. K.
Moscow - Leningrad, 1948,;

'.:;~
MZU

--2ng
k- d$ between tWV Cwtiguous r
un -Ana
ensoratialysis Crrudy Sem.-Yektor.. Tenzor. -cr metric Serve
of thesiv I metric; the geodesics of the given
--lizu- 1). - (Russian)
-15, 21-147 (194 [MF 15600) -
as null curves for its angular metric.

ai ' is W construct a generalized geometrical system
The in
After these preliminaries the author introduces two inde-
A ' which preslervetas much as possible (only locAly, of course) pendent ZUguira each givtn by a first order differential
the metric dtidlity -typical of the elliptic plane, that -meaus formi the two having equal rights; the two metrics deter-

1 -analogues of
- teat in the. neliv met - there.should exist
rd
i
d
i
Ii
h
i
h mine two dWifferential ol?~rators (infini
tesimal transform.2-
i
es an
nes w
it 3 an stra
t
t
points with d
.an
g t
ons of the Lic theory). One can also give the system by
that these, two things should, have equal 'rights The pur- giving the operatom; they determine the inctrics; the Sys-
pose, then,. islo deal with two metrics which haiirc equal tem possesses six invariants~ In terms u( this analytical
be -called- bimetric - By-way
----lights- such-a-keometry would t s-of -the -inciescs

appara us propettic in
YLTY

tr -ti
---of-in "flue toii-the-author-miisiders~..a-E.uclidc,~A-plane-in-
-
- --cotM~~o-fom.-Diffeivat--viatimhip~F-betwee

"ne-
twu
I
osCn-as the fundam en o --
tal-
blect
-
-
' --
-metrics. are investigated - One May be geo(Icsic Ily
a
conjugate,
.-
-And cq
,(dyzm;zdx) as the funtlatnental rebtion; prop-
77pit~ _
metricall canjugate. and completely conjugate to the other
y
.T cities t~ be cousWered are those left invariant by contact etc.The case which occupies most of theauthor*is attention
transforniatiorrs. One invariant Conception is that of a
- is what he callsa dualsystum; here each metric is conformal.
"cu
rve" itied asa one-Ixtrameter family of line elements
der
to the angular metric of tlw other. The ideas of triangk-.

-i eighligring ones -a ints-and
re contiguous; po
sucluthat two
-
-
-
- area 5 n ryalilwaring( --ne -liz&,-,

and some notion (if trigono ra
let
-
A-
of this.
Ollin
ariant special cases
ordirii" curvcs are ii v
and dualis ir r
t
~.,Anetricis-intrmluced by.spLcifying.a firBt ord&...,differential -After a chaptcT in which the pn"CiAllik vitsisidentimis are
I allowable
fornt which on "Curves!' gives 1 5, 'I'licre exists an. tmaletfin it-rills of, the, Grwssmalill-Gii ull Calculus And ia
I.:.transformation of coordinates which takes null-cums (those -%vilirit isgrot-r.ilizvil fo-r (Ilt-41LIAl
On WIJiC-JJdS=0) iIIt0IK)hA.';,in thPilf-W "Can(inic;ll"Coordi, sysivul tilt. ,Illthfir pa,-A-s fit ;1 1.4 41i'm f-f his t1wfirv
V, natesystLin the metric rcilurc-4 iii ;I Hasler inctrieaniong to '11 Ice. lit ititirt Ili, l-l mit if %* die IiLL%%'
atv% h0p -
-flill' ate with
OtI1VC thing"t ennollical ('(Ali Its nsqwi. a -fit lim; t-k-lilents is Lilit'll 11% aw i-lat 1.

(Iltesll.t..
if- ",`1 r, -lit ilar mi-tric" Which givi's hirlilitesitual
glvzll MC.r gi If Jr '-"1IvvlIit~Ik1v i'-4 a%sillilill I-, I v Ili, 11 rllw'fifill~-

'J
N
PHASE II TREASURE ISLAND BIBLIOGRAPHICAL REPORT LID 2c8 - 11
ECON Call No.: QA381.R28
Authors RASHEVSKIY, P. K
Full,Title: GEOMETRIC THEORY OF EQUATIONS WITH PARTIAL DERIVATIVES
Transliterated Titles Geometricheakaya toorlya uravneniy 9 chastriymi proizvodnymi
Publishing Data.
Originating Agency: None
Publishing Houses State Publishing House of Technical and Theoretical Literature
~(OGIZ)
Date: 1947 No. pp-t 354 No. of copies: 7,000
Editorial Staff
Editor: None Tech. Ed.; None
Editor-in-Chlef: None Appraiser: None
Text Data
Coverage* The book Is primarily a discussion of Pfaff's system in great detail
although not to the extent given in Schouten and Kulk's Pfaff's
froblem, and Its Generalization (1949). ,The first two chapters
(algebraic and differential oblique forms and applied vector analysis)
may be regarded as an introduction to Pfaffts system. This information
may be found in many English texts (e.g. IT. L. Wade's The Algebra of
Vectors and Matrices, J. H. Taylor's Vector Analysis, H-V. Craig's
Vector and Tensor Analysis and 3thers).. The author introduces the
.1/6

Geometricheakaya teoriya uravneniy a.chastnymi proizvodnymi AID 2,508 - II
In addition to the authors mentioned, the:worke of A. R. Forsyth,
Go A. Bliss and Go E. Hay were studied for reference.
:Purposet Not given:
TABLE OF COW ENTS PAGE
Cho I, Algebra of Oblique Forms 5-44
Analytical space, Vectors.~ Vector field, Linearforms,
Polylinear forms. Oblique form. Outer product of
forms. Obliquen-forms. Polyvectors and the principle
of complement.,Basis forms and vectors. Rank space of
a given
form..Simple forms and simple polyvectors.
.
Canonical expansion of an oblique bilinear form.
Criteria for divisibility.
'Ch. II Differential Oblique Forms, 45-68
Differential oblique form and polyvector of a
k-dimenBional infinitesizal area. The integral of
k-linear oblique form on a k-dimensional oriented
space. The integral theorem. Criterion for a given
oblique form to be a derivative.
Ch. III Fundamental Properties of Pfaff's Systezz 69-100
Pfaff's system. Pfaff's system in geometrical re-

resentation A fully integrated Pfaff's system.
p
3/6

Geometricheskaya teoriya uravneniy s chastrjymi proizvodnymi AD 258 -~ 1-1
PAGE
The same in canonicalrecording. Characteristic
elements of Pfaff's system. Theorem of Frobenius.
Chi IV Integrals of Pfaff's System 101-110
Basis differential forms and vector fields-Integrals
of.Pfaff's system. The determination of a complete
system of integrals in the case of an arbitrary
Pfaffts system.~.
Ch. V The Class of Pfaff's System and its Characteristics 111-137
The class,of Pfaff's system and its characteristic
system. Characteristic.system and the claas of one
of Pfaff's equations. Characteristics of-Pfaff's
system. Cauchy method.
Ch. VI The System of Forms, Its Class and Its Characteristic
System 138-155
The general theory. Class and characteristic system
of a linear form. The transformation of a1inear
form to a canonical type.
Ch. VII Canonical Representation of Pfaff's Equation and the
Complete Integral 156-189
Canonical representation of Pfaff's equation and
4/6

G-oometricheakaya teoriya uravneniy a chastnomi proizvodrqmi AID 258 - 11
PAGE
Its integration. Canonical space, Lagrange
complete integral. Jacoblan theorem. Geometrical
interpretation of the preceding results.
Ch. VIII Geometry.of,a Linear Form of the Even Class 190-222
Poisson brackets. Canonical representation.of
Poisson brackets. Special system of coordinates.
Canonical transformation. Motion in space of
a linear form of an even class.
Ch. IX Geometry of a Linear Form of the Odd Class 223-262
Jacobian brackets. Canonical representation of
Jacobian brackets and canonical variables.
Contact transformation. Geometrical:interpre-
tation of contact.transformations. Connection
of canonical.with contact transformations.
System of equations of the lot order with one
unknown function.
Ch. I Finslerian Geometry and the Fundamental Problem of
Variation Calculus 263~-289
Hypersurface in.the centro-affine space. Finsler
space. Geodisics of Finsler space. Congruence of
geodesice.
5/6

Ittow I
4
V, lltaftveki~_ IL The scalar field in a stratified CV-31
rrudFsern. Vektor. Tenzor. Analizu 6, 223-2418
(Russian)
The notion-of stratified spaces has been th ughly de,
veloped by the Moscow seminar during the pas de wi
Mathematical Reviews, many interesting and significant results. The piresent paper!
!
Vol. 15 No. 1 is too highly specialized to be of much significance. Given

Jan- 1954 a space of 2n dimensions with coordinates X1, X1, . . .. X4.7

'
Geome
t r7 U, sit, ...,U% the stratifyi paces are then. x1 ' d
ng s -c an
I,, =A It is assumed that a scalar function U(x, v) is givem
such that jalUlOxIdull PdO which is taken as the metrics
tensor in the space. Since the above condition is not invari-~~
ant under a general coordinate transformation, the problem,
is studied under tra nsformat ions of the x's and Ws sepa-i
'

ately. After calculatin s Christoffel
. L, the various set of
r
symbols one can see that the.,itratifying spaces are totally'
a
geodesic, admit absolute Parallelism and h ve null length.
ast halt of the paper is devoted to proving a replace.
The 1.
nietst theorem in this special space. a theorem that has been
established for ceneral spac s. U. .5. Knebelman.
C

, I
TIM m

-_7~- 71

lRaUvWiT.:-P.' K.- Galois Wiiiry, --fliffi-odf -gediiiial-e-.
-a Lie group of this sort fok which tile system F= 0 satish
objectsi Sent, Vck- tor.- Tefiz&~ An alizu 7, 167-186 certain other conditions is tcrmed "rational." It is show
(19-19). 1 Rusimn
that. for any rational Lie group G there exists a rational 'F,
I'lle '.1tuffibr. considers ~Comctric objects -and (po~siW
it L'
r
homeo
i
f
u
sol translormations ill a snc~X geoinctric object lp, which is invariint tinder (every trans-
f
i
i
G
d

-
i
n ini c
i
o
t
: z
.
p
.- .
;, ,
orm t
on
a
an
n)
tinder no analytic tran.-formation not
h- -
- rrirs with it a
th a rcgion in n-space R
morp ic wt in G. Given two coordinate systems (x,), (/J for X., the
ect. of coordinate systems (terined admissible) such that th-a components (with rcipect to (xJ) of a rational geometric
pa%.-ige from one coordinate system to another is effected object 0 are analyfic functions of (IJ; tile author shows

by annlytic ~~ functions. A geometric object -ip is termed that ifk is invariant tinder G then the components of 0 are
"rational" if,olter rin admissible change in cnordinatc sys-
'
-
-- ratiomil functions of the comimnents of v and their par
nCV.F component are functions ol
s o
Cr
n. tile
rivatives
de with rkT.I)cct to 1i of v-.1rious orders. The S-t of
tile old compbnentsand of the Firtial derivatives of various all geometric objects which ran bc~ expresstA ill this way in
orders of tli~~ new coordinates with respect to the old.
gle rminnal goometric object - h;
ternis of a sing 0 called a
V;ich-Lie gmulvis astitimed if) be-given bY,tk systeril OF "field (if If this v, adinits a frawsitivc

2 of, file 'in
dff filial cc.It-latiolls ill U" '11OWSIS X1. -lot
i ere
Lie grotip file field is valled "transitive." It then is provtd
VM
where F is a polyimmial ill the. partial deri t ivrs
tha t t here k ;% orte- 141-one corres v Iw(wivri transitive I~
"pondem
'~! 1) with
I+ - + i. r-
. .
fields of geollietric Objk-ct4 11141 raliollat Lie gn)IIIYA.
I
cients hilalvor. ill XF, X~, lod 11,' pr(M)rs 111.1ke 11141* of 1.1-mlis W11;J 11 lodw TVviewer's k fit 110clize

11C t x-Cri(.01111
I sit it lyitLsl.Lbl~ 4 E~ K i
I R. OW1 nr
VA
U.C,11- Reviews 12i No.- 3
PIRM _4~

CK
,

4AiiAdkX-- Th2ptativicl f 11,va-Ein6foln and Fcrjni-
1
14wi
I)Irsic frviIi th6jim.4o -Adviow., TruglyS,niNuktur.
-7

I_(Jr. Aw
alizit 7, 362-31:0 (19-19)- (Ru'Aan)
III the IfIc"ify of -a-11
i Ow ictusur 110,111t fif view is

V wit, .1whor chims
oft)1116"Iy~ Slot prewrvid thfough The
I Ic
Onalf tile tovsm- jKlill.1- ;)f-.ViL'.V i", re ijiuflAbroifgf~oid- II
W 6C
noulion- i iii) p-r."pt -Ttif's 4 are followtA

6'. 11. 11olkoff (Vauvotiver, It. C.),
f,

f) VC, P -11- fieIvi dvis i :12
Vol O
ma tfif'"La fAc,
oi~

16(l) PHASE I BOOK EXPLOITATION, sov/1964
Moscow. Universitet. Nauchno-issledovatellski3~ institut matematiki
Trudy-seminars. po vektornamu I tenzorncmu analizu r, ikh prilo&eniyami. k
geometrii., meldhanike I fizike, vy~. 8 (Transactions of the Seminar on
Vector and Tensor Analysis and Their Applicatiom to Geometry, Mechanics.)
and Physics; Nr 8) Moscow, Gostekhizdat, 1950. 429 P-'1,500 copies
printed.
(Title page): V.F. Kagan,, Professor*;;Eh. (Inside book): I.M.
Yaglom; Tech. Edi. N.Ya- Muraphova.
PURPOSE: This book is intended for professional mathematicians especially
geometricians', and fori~nyslcists.
COVERAGE: This book contains some contriIbutionIs, to geometry presented by various.
leading Soviet mathematicians at the Seminar on Vector and Tensor Analysisjhelcl
from January 1J. 1948)to July 1, 1949. Applications to physics'and mechanics are
not discussed in any detail. However, each article Is significant for its possible
applicationeJa phy3ics,, especially the three articles by V. V. Vagner. In his
Card 1/5

Transactions of the Seminar -(cont.) sov/1964
Vagner V.V. Theory of,the Complex Manifold
ShirokoVY P.A. (Deceased). P rojective.Euclidean Symmetric Spaces
RaabgvskiT, P.K., Symmetric Spaces of Affine Connection With
Torsion/
Norden, A.P. On Conjvgate Connections
DubnovY Ya. S. Central Affine,Gemetry of Curves on.a Plane
Dubnov., Ya.S.~ and N.V. Skrydlov. Central Affihe,Theory of Surfaces
Yagner, V.V.'Geometry~of,a-Space With a Hyperareal'Metric as the
. qTh-- ', ^+' . W4 -1 A --P T - 1 4 - 444- 11-1 -- kt.-4 P-I A

'

valuts and which pws
inj
0 each Mitt by paraflel disIlacv-
rncnt~ An admisO)Ic frame depen(13 on the x~ and on certain
s
-call --d seci - ameters. It e*'=Akei represents the
o t . midary par,
ansform
tri ation at a point from one set of measuring vixtor.,
:ei of 'ati~adrilissibtc hailic to another 4', then these trans-
formations (win the gtoup.of isotropy. 'I'll(- infinit Arv.
'I_pr'!K- S.

o affine tqjinecti
t ansfarinations o ly
f thi-,i group are expreswd by r linvarly
d~ r
'Trudy Sem Velctor Tert c.~ Anali '', inderk-rident rrlatri(vI_i'aj.((v It r), these al. "ire crifl-
I roicin. ZO ZU.

2-(19$0). (RusMan) fit'Ints sati.4fviug to Jr-
it' (1111-a 1.7' -eZoal', Now the curvature
in the-fort R-` Ov
is calle, yrn n rij w1j,, vv 1(:r(
u ne cnection with asymmetric Pj,
l
0, V.Ri;il

0; j. A, -p v~j
t V-Si f re uhiquely deterinined constants. Study of tilt, C, U'l-
RE ornis wi, 0,
wbere' r5lou'and curv;lJiture tenscir re5pec- Cons of
S and R are tbe to
-

-Sj'w-%-haw bu-n audit-d y Cairt~n:
LtIve Y _n' a
-ca&

'llip I
in in 'd
nsiatial manifold of.admi~L,'blv framcs
,
lca& to the:inverse dimem that if an (n-M-dirnensional
th-_ 3 p4 0 iii1mis5ible frariv of refere e-a introduced,
a case es nc re
Ar with )t+r finearly indervrident forms wi, 6, k
thOamenu-merical
given.and tbcs4L! forms satisfy the given equation-i of .3truc
ture,
dien thi.,01 can always be miplwl ina onc-to-ono wiy
0
n a manifold of admissible frarrics of refurenct, in n cortall)
w -itio
sy!nmetrical space. The study ends ' ith a deriv. ri of
:the'algebraic relations be-tween the structural con,"tarwi
Vil. G'J' and
D. J. SlruiL
So'u'ree, Ma t6ema C81:96views
va
No

7-
-44
71. ... ...

at

on
,
!
l

:
~ b, _4
a: 211;1 iwensdo~al stratified -.apace.`.
lal lm~M
ei

(> (195
(Rus5iany
M)e Speq ~fid+Lr consid r 2 -d
erapoi is onle n imensibi 11
which there exis j

v
:and : me tA C7x1C)u7tj1~dU; Tin.^, nietric vsk
a C 4 62Mx, if), , 3 1
' Vt'
Audied ulidier..ti-an4ormations. aniong the x's a
nd a-malb
tile if's sCP4r,1ieK,-, I f S. is a.subspacc.

IT '
'
C

Ok 41 the
U
ei
two jacobians b ng di ffeure n t iron.1
xero, it~eu a %Tctor t-. in si~ "~ Components in dhe envelopulz

and :i&jm magratude-,
space
,
'
'
2
Yli-, io i.,i given.
tlo be premrted, th
=
ducedinet
bv i

'
t
f
i ~7

, to
ined in two NN, ya
mcn
may be de. with~! mspec
tiie~ -~acx~
it-coast. or x -const.
o affine maneo-
wbich~ yields t%i~
.
,
Umo
A and,,~
~ axid the re uire
q ment tisat length is' to bg
~
,
erved tindcriparaflel"diiiihicemeni gives

0 The author Olen considers a~prqp~ctxvejy- flaE space S,. M
two connections,an
0 a seinimetric.jenspr G,). -mtisfying
.
i-andshows 'Alp, a lid A,P /0-9- A,~A,
tliat if
'
'
'
t1icn
1-
1Gy& wbere A is hlecmitiriiy a 1114,
A4-.3ff?
l
~

0~
-t simpl rt, . ..a.6 n of 'i 4rmtA -bit!
author then constructs, C a
iz

hich xi'are the nenrin,
sra" in w G nates
point in, P. ~aad,ul the nonhomo~eaeoxis crximLnates of its
dual hyperola~e. If incidence is de6ned by xla~+ I - 0 ;wd:
IV 1~ (XU*+I), 6ni obtain's tile projeCtlively tft~,~ c.annection
in which A.--- "0411x' 7+1). Convemb, eve-ry praiectively

-it connection for whidi I AiJOG may be ri~ahzvd as a sub-
f
L
-pace
-ice of 2n dimen.
S. o" a stra6fiable qm sion-s-
S. KnebdfiIi~n (Pullman, Wash.).

r1,,7rvSpif. 1'. 1, Ott till- "0112tion of 1,0111111.1ty Problems by
foulb.1d, of 11011C11111111111ative 111gebra. Vc.~tllik Moskov-
Mathorafttioal Revievis P)SO,
11;tiv- Nr, Fi--Nht~ N~ojL 1), 3-12
'Vol, 14 1108 7
July -1 August 195-3 i ctoplo%ed (.1 t.l.t.litt cilliclitilin..,
!J. c Whil It Af officie"t for the existelic
e
Analysis
"Itl6i'll I,( tit probivill
(I-Y)c(I-Y*)PY)3 -Gjy2+by+r)f(y -,0
=J(I) =0.
fly)-yfly), .11141 P: fly)-4(1 -YZ)f'Cv),
0 'It-rate a 11011t,orntimmfive v~~wiativc alizetwit of operators I
111C romplex field, mil the differential etitiatioll tlLes
(P'-ay1-bY-r)flY)=f). The'disetts.-imi is carried I
'tough Ity ittactiptibli(in (if theto pecat(ir in the parcrithm-s-,
J. G. Wendel (Ilaton Rottge, Lt.).

4'.
RalavsO, P. K On the P22m Of
f Voklady tUcad
0 Nauk SSSR (-N,S.) so, 169-1% (1951). 1
(Russian),
A homogeneous space K. is defined as an n-dimensional
space with 4 (transitive) Lie
group 0. Let 11. be the sta-
are ~ I I The
tionary sdbgmup of G~ All ~corisi
dgebea of Liebelonging to 0, is gi subal
ven by G,, its gebra
by H.` A K~:in-*Ixich the Cartan metric in G,', is non.
ii. degcncr~te at Iiiast on the'planeIt.' iscalled affine-homd~
gtneous.~ Thcll~there exists in G,.a plane E.'. r-in, N~hich
complement'of 0,'. With: the aid of, this a
-orthogoh~d
is the
canonical n6cction is.dAned.*UIten we caninsert into
Cq
is alled
a iemanntan metric admitting C., the K
K.
F6 Metrical-
Necessary and
officient,condit.ion'that a curve in an
affine-homo&n6ous K. be geodesic (in * the sense of the
carionical'tonnectionYis that it lic, a trajectory of the sub-
provided -that. the,operator X, of. -the sub.
G, of V,,i
coup lies m Zj"Ior every, paint 6rv -for this
Ar of thie traject
9T
it den' 'hai. the' co iiibn
is suffi v i ad :holds at'_one,arbitr~rv
int 31, 4 affiiic-fioniogeneous cither if G.
o
P
I ct- 'r if, H. %vrv Ric-
'be semi-simp e compa o be semi-simple.* E
%nannian V. with ds3>0'admittink.a transitive group o
rn
otions G~ a metrical' K. iadmitting G, The papc~ ends
with some rem 41ks on the fact that'ihe canonical connection
f
oa K. ote 6, bat to its least
need not correspond io.rthc;wb
subgroup contain' perator X of the plane, F_
Ing every 0
When thia canonical connection has curvature =a- we ob~
tain the symmetrical spaces of Cartan. D. J., Strua.
11-44.

-~.,Xsevskil. 11. K. On the groinerry of flonlogenerios prices.
Mathematical Review. v~rrutvi- Svltl~ Vcktot. (4 Aom,,~.ij 9, 19-7-1 (19.12).
Nel. 14 110.
Hw j~ttrjio-w of (lie p,1p,!- is to imlAenivot Kli-4."~L pvivraln
S-3pt. for t emnori% A teal Lie glotlj~ C, beillt 1%'t li, Ille pro .bl(In
r g p f
is to coristr1irt a lit ium ovujtv, tit-; %~ ff'r whiell G, is
spare
lite filittlamuslat gtotip. This ptnblcril iv~is ~wilvt:d I,V Camm
for Fem i-sim file groitp-n aml tlli-- I rr5rlit atithor's, work,
tholigh [lot t-mll)ICtely suck-Cr4ill, i% .1 c0twiferable forwaril
Slep. It is a-smiled that G, is transitive havitig a station3rV
subgroup 11- so that tit = r - it; flicut it is 1xvisible to intro.
duce in K. an affine conliection whit-li is itw.iriant tutdcr G,
-in(] is symmetric (iii Cat vin's sense). k%, ~ %,j-R,,jj
w1wre R is the cut-Vatute lew-or and 3 is tit
torsion. This comiurtion is exprt.
io ccrtain
tile structtire c mstatits of the grf-ptili. For Ilse
vectors and
affille hoillogelleolli 511.1ce's itis asmolled that tllt.-
sttldy of
J.
Cartatt metric of G, gq- C-,,iCJj. is non-degetterate oil If..
"I'lien the stifficient coriditions are giveii fly: if G, of a
homogeneous space K. is -emi-simple and compact, K. is
affine hoinugenemm A similar theorem holtis if 11. is scmi-
simple. The atithor also proves some known theoreins oil
nietric spues and gives sojtic illustrations.
Al. S. Knebelimit0hilluttan, W:ish).

"I"EMERM-N-F-727 -W-7-1
-'"PHASE. I, TREASURE ISLAND BIBLIOGRAPHICAL REPORT AID 255 1
BOOK Call No.: AF589978
-Author: RASHEVSKIY, P. K.
Full-Title: RIEMANNIAN GEOMETRY AND TENSOR ANALYSIS
Transliterated Title: Rimanova geometriya I tenzornyy analiz
Publishing Data
~Originating Agency:, None
.'Publishing House: State Publishing House of Technical and
Theoretical Literature
~,Date: 1953 No. pp.:, 635 5,000
No. of copies:
Editorial Staff
Editor: Lapko, A. F. Tech. Ed.: None
Editor-In-Chief: None Appraiser: None
Text Data:
Coverage: The text includes: tensors In three-dimensional Euclidean
space; Euclidean space of n dimensions; mathematical prin-
ciples of the special theory of relativity; curved coordi-
nates In the affine and Euclidean spaces; manifolds;
Riemannian spaces and spaces of affine correlation; absolute
differentiation; curvature tensors in space; and mathemati-
cal principles of the general theory of relativity. The
book presents an instructional compilation from the very
voluminous non-Russian literature of the past 20-30 years
on vector and tensor analyses, and gives in introductory
1/2-

7

RalevsK P.'K* -'On some fundamental theorem of
the
,
Meory of kajUM Uspehi Matem, Nauk (N.S.
no. 1(53),3-20 (1953). (Russian) 41
The author's purpose is to give proofs for several theorems
111WO of Lie theory,which have not been available in the Russian~
* >.
Moo 1 literature, namely. for the theorem. of Levi, with Malciv's

195 refinement, and for the theorem on complete reducibility
f'

of representations of semi-siniple' groups. These theorems ,
v
are deduced from the following new theorem: An affine
(linear, non-homogeneous) representation of a semi-simple
Lie algebra always has a fix-poinL~..Two proofs for this are
e
given.: (1) For a compact (i. ., definite Cartan form),real
Lie algebra one utilizes the corres nding simply connected
PO
compact Lie group; the induced representation obviously
x representation'of a
fix-point. The case of a
has a
comple
.
,
complex Lie algebra is easily,reduced to the consideration
i l of the compact form. For a real non-compact Lie algebia
mplexifies the Lie algebra and, the.. representation.
one co

assume, by induction, "that
'11) Algebraic proof:iOne can
hoiogeneous-affte,~, representation." is,~irie_~
the induced, m
:

hen proves th~ known fact th thi
ducible. The adthor-t at' i; ,-

Casimir operator of'this h resenti - it'.
omogeneous rep 66n
non.zer(i (positive rational) multiple of the identity.'-Tbe

-4.
TJf

P. IL
On the extensioi. of the opemdorliAll;
calculus to boundary problems. Uspehi Matem. Nauk .4
(N.S.) 6, 0, 4(56), 65-80 (1953). (Rusg;ah)
I t is well known that in the application of the Heavisidi:
calculus to ordinary differential equations, boundary condP,
1
tions may be incorporated adroitly by the use of delta func-
tions a*nd their derivatives. The f uthor develops this id
a
First, he considers the differential equation (D+a)x-# ti,
~
,
where a is a constant, D=dldx, and $ (and hence X) is a:
lized function that is, a combination of a proper--
genera
-
d delta functions and their derivatives. He then'j
f nc n a
u tto n
Mathematical Reviews passes to an equation of higher order (with constant coefti
NiY 1954 cients) and to systems of ordina- y linear equations. When 1'

Analysis D is the operator tPldxl, two-point boundary conditions are
introduced, and consequently the delta functions and their i
derivatives have two singular points.
To some extent the method can be carried over to systems, 4
10 :of linear partial differential equations where D is-replaced
by Laplace's opL-. ator, and Dirac's delta function by the
delta function appropriate to the boundary of the region tn.
'which the differential equations are studied. A. Erdflyi.

:"r, , Z-
ili
161: ~*,~
0~ I :~~

iMERME.-
Res" EVS K 1)"
S S R.
U
'
'
'
6
MAW reges"tations of nonaml-
n
1414TAN P. IL
shople me grodpe wfth nflWout radical. Doklady Akad-,
Naulc SSSR (N-%) 97, 781-793 (1954). (Russian)
A Lie group G has an idgebra Ewhose semisimple cDm-
'ponent forms a space S and.-*h6si nii6otent radical form
,a space X If 4 'and b In R, the product is
are vectors

V., e-a, IM.;:whem &.~ are the structurc constants of
the group. The'author considers a *-stem of cuvariant

tensors V V aggre.
V V.,....i which he calls an

te are ivAject to the conditi6o
P am

A system d,such aggregates 17.... with i-1,
N being the dimensionality of transform fir,
contravariaht Vectors in 5 form the representation - space
i
of the group. A dual theoriun is pr
oved for a space W& -
J1. S. K*eWxwu (Pul1man. WaA.).
7,
7
~J

U S S

K Unear differential-geometric objects. F/W
-ady A Nauk SSSR. (N.S.) 97, 609-611 (1954).

,
(RUM14n)
-
By differen list v is understood the group
of la
tiii group 4
of linear transformations in apiice V. eitonded v times.
a
'
7 This, means
that. the cocindents we xt xt xt
... i
l
.
t
A
l
.
This gm'6
computed it some fixed poini ecomposes into
t
.
.
the semidirecto'liiiductr-ofAti semisimple 6mponent S,~
x detlxd"l mi and its radical W" x" --x~ ... t.. A repre- i
i
t
f
ti
f
l
t
ti
n
f thi
ou
A 1
l~ i
le
rans
orma
sen
ven
o o
n
a
o
o
s gr
s z
p
'
scalar functio
r and Its partial derivatives up to order v.
_
"
Ewitiofivg
the totality of.componen si,i
ts
~
umnod In lei:~raphic order. by 1. w an then the coin-,

A'
J ponen o a.supervectm. contravarlant supervector
f

fting pre to be a scalar. A pertensor'
is obtained by requ su
.,ZA, *~ is obtained in'the usual minner and its transforma,
tions ;&nsfitute all theiipresentations of class v.
M. S. Kivebdmats
r

U 777

RageysIcil. P.JL The theoij o sphiors' Uspehi Mat. is F/W
4
~-~a--gre-klO(1955yno.2(64),3-110. (Russian)
~~a u
This is a largely.expository article, aimed at icade'
with only a modest background in-~and a"rj4.
Let R,+ be complex Euclidean (not unitary) x-dim ' al
ension
space, with an orthonormal basis fel, - - -, ej and inner
produc -t (2;j%j a,e,, J;;.~j asbi (where thea,and
A concrete construction o the
are complex numbers).
-algebra C,+ of dimension 2m is given, as follows.
Clifford
Basis elements of C.+. are the'identity element I and the
skew-symmetric contm,--ariant tensors eh-,, of rank A
(k=~ 1, H;P1. 2, - - -, n) whose co-ordinates
a',-*. in the basis (e1, - - -, e.) are + 1, - 1, or 0, ac-
cording is (ij - - - i.) is obtainable from (PI by an
ta
even permutation, an odd permutation, or n permu
tion, The product where the
F'S are the indices appearing exactly once among the P
and 4nd the number N is determined by the condi-
tions e, e, e,e,=-e,e, if i0j, and ee =1.
lie, ~i~iplicity of C + is'demomtrated for the case
n=2y, V being a pQsitivC in(C~M An explicit isomorphism
is set up in this. cise betwcen C. I,- and the algebra of all
linear transformatidas on complex affine. space Se, of N
dimension 21. Thisi isouinrphistn is constructc~d by use of i

Q1
J
uu
the,Clifford algebra C~+,' which -is identified with
The . representation so obtained is -called . the spinot
representation 'of C.+, and the elements of Se are called
ntial uniqueness of this representation is
spinors. The esse
proved. Fundamental tensors in Se corresponding to
various automorphisms and anti-automorphisms'of C +
are studied in enornious detail. The spinor representations
of the -rotation group are. constructed carefully. In-
variance, or, the precise degree of non-invariance, of each
of the tensors defined, is carefull discussed. Wrious real
y
subalgebras of Ci+' are studied. As each new concept is
introduced. it is examined in detail for the cases n=2 and
n-4.The Clifford algebras C.+ for odd-4 are also studied.

ri al i is to establish c wil
A
ncip aim 10pnec With the spinor
r
A

connections
I h
t
ese
appara us of mathernatica p ysics, a
(even to the point of discussing various auffIrs'notations)
a phasized continually. + Parts, of the' treatment

dejmZd the author's "Riemannian geometry and tensor
0
a (Gostehizdat, Moscow, .1953: MR 16,. 1051).
For those unfamiliar with this work and unable to make
their own computations,- the present papep-may in places
be obscure. However, being carefully *Weh and nearly
'self-contained, this 'paper ~should -be ifseful. to a large
group of mathematicians and physicists. E. H

WORM",
v
-.7i

H n
H.,-. Multidimmsional, Miin ga;~and dif
P.
-
-

F\W
fereutiat
--T -geome
Uspehl Mat. NM (N
34
5
~

W956) 2.
1- ad, 4 (6
6)1.1 4
'
A otie-4 xial 6-function is a.L- Schwartz distii-
memsio

Was is.a.fancdok
butJo4,,whIch in the langi
44e of. ph~
of.a r641 variable that: is zero everywhere ex~cpt at one
'
'Point'Xo and who-i~
idegral e4ws I., The pmsent pape
'
'
-space kh n
generalvc8 this idea- ton
iriwW a
i*dirnensional
'
'

dihe
u I
point Xb or, as thd author
I
rface plays t
v
he, situat;on in which the simplest, a-
says !siadtarly to
argUHIOn. nttated" in - one
functions of one t. are once
point, - our Imany-'dim'ensional - a-functions are !'conce
n-
i
tmted" on a:nj-dimension
al sfirface~U~CX..
'

j Thii author'-considers an
-m-dimensional manifold X
es x i -W
local c6ordinat hlch-he~assumeslto have a
xm)- in the aml coordinates, and -
stalar densi Y, Y
`

_nt yd;jI. A relative, Co-
tlierefore a, VojLjjjjk
tj~Mp
in loc-
$" Itilant hyper-~vedor of,clasgo js givei at coordinates
:,by functions

where these'transform like-
Vo

with'4)~ a sc,
alar density. A rdativ6 contravariant h)Tcr-
-
vect6r A*, All"
Atde, i'llso

,,~ ~,t - ~
. _: I g

LOBACHEVSKIY, Nikolay Ivanovich, akademik; ALEKSANDROV, F.S., akademik,

~Zlj .11,111,-a'm " 1 -1, . -1- 11-1-.T-15~?~ ~,- m - - - :-

AUTHORS: Liber,A. ye, Penzov,yu.ye, aad.,ashevskiy,P.X- 501/42-13-6-429/3"
TITLEs Viktor Vladimirovich Vagner (on the Occasion 0 1fIhis 5Othl
Birthday) (Viktor Vladimirovich Vagner (K pyatidesyat'.-
letiyu so dnya rozhdeniya))
PERIODICAL: Uspekhi matematicheskikh nauk, 1958,V01 13,Nr 6,pp 221-227 (USSR)
ABSTRACTt V.V.Vagner was born at Saratov in 1908. In 1927 he has
finished the vedagogical~technicAl school at Balashav, 1930
the correspondence course at the-2nd Joscow State University.
Since 1932 he was aspirant under~-ftcf. V.F. Kagan at Moscow.
In 1935 - doctor dissertationon.the differential geometry
of non-holonomic manifolds. Since 1937 chair for geometry
at the Saratov University. Domain of scientific works
non-holonomic, Riemannian, and Finsler geometry, geometric
theory of partial differential equations. Vagner has
publi rs (1935-1956). There is a photo of Vagnel-.'
shed 62 papO
Card 1/1''

ku T'f OR: Rashevskiy, P.K Z 91~,'4 2 - 1 7- 73 -
'ftTLE- Liathematical Poundations of Quantum Electrodynamics
(0 matematicheskikh oenovakh kvantovoy elektrodinamiki)
PERIODICAL- Uspekhi Matematicheskikh Vauk, 1958, Vol 13, Nr 3, PP 3-110 (USSR)
ABSTRACT: The present paper has its origin in the lectures delivered by
the author at-the Moscow University in 1955/56 and it is the
mathematically most correct representation of the subject in
the international literature. Of course, the author restricts
himself to the foundations,of the theory without treating the
principal.problem itself - the calculation of the scattering
matrix. The representation of the foundations is indieputable.
It deviates,from the usual way in.so.far as the well-defined
notion of the state of a photon- and electron-pLsition-field
plays the central iart. Then the necessary operat:)rs are certain
precisely defined operators in the space of stat,~-. The general
program of the paper is as follows: In � 1 the necessary
knowledge on coordinate spaces, impulse spac:s and spinor spaces
is summarized. The �� 2-10 treatAhe phston field. At the same
time the necessary mathematical equip:iient is introduced,
especially linear functionals with operator values serving for
the comprehension of the mathematical sense of the operator
fields of the theory. In the �� 11-17 in a similar manner the
Card 1/2

H

134 ecl.4c%-nika A., 'ash
Icss x7c;)
Statlysi A-L., 6idwova. S.,A. Za 7zJ-7,
Akad. Nauk Ssur, 19`~4- 344 S. Sc skniom 0' L. Ili. ! Ljr~-f- 2)
Sssl-. I.-I isLcrii. .11 10. Arkit'vnc~ p
Filral Tsy;.,7-,tr. Goa. Vc -er. ts, Ark va Sssr L
~L. Sc~T,: A.
TC-1 ".-,c za~,I. selli .--G4-14 :~50Zil)

-,, Iw v W.W w w
0 *:; We we 190 low W* 9 0
v
L I j A-A

p"I"t 4-0 fewtafR6 "."s

I# do iii
'
=MAiww,
V. K-JOAktaot J, (1,.,
led. (u48, a ma.
w 0=. 29
chine is th
i
f
m s a*~ re
r
plAtur. TJw
Inct"My to=. Iff OPLO(ift tk EMMM mv Ajvx.
40 M. hj,U 600
04 goo
004 0
6*0
w goo
goo

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JL. Zvi z
t-'- ACC M. J ESIAIA
SOURQE CN 16MOU/001/0139/0141
M60, 8 :T)E: UR/ 2
I C
EWP(v) IJP(c) AT/RWWH DJ
'AUTHOR:~ Kozhukhov, 1. V.i Mu atoys Yu. V. Rasheyakiy, V. P.; Rylltsey, P. I.;
r
-~Sakinltsev. N7.- P. Smirii-ov. Y6. V.
,ORGs.:.Joint Nuclear Ron arch Institute (Ob"yedinennyy Institut yadernykh iseledovanly)
21% 4*T-,
TITILEE:~Atse of a plasma gun for producing high electron-current.22&ks
`SOURCE: ~Pribory I tekhnika eksperin-*utat no. 1, 1966, 139-143
-''.-.TOPIC TAGS: plasmagun, pulse shape
BSTRACT: A new plasma '61'ectron source (see figure) camists of three
electrodes: discharge electrode 1, diaphragm 5, and
extractio,n,'electrc)de 6 mounted on two stainle as -Steel
d sks'a- PlexilglaiN%ushin ja citt4e material) Is fed b
sprip- 9 _to'ward.the gap as the',buishing end is burnea
9
up., ~~ihe` discharge electrode In filoulated by porcelain-
blushi'lig ~ 3. The tungsten diaphragm has a I -mm port.
lnsula~ted cathode 2 is intended for improving the
extraction conditions and focusing., Its insulation is
des gne to s an The ma-gun- electron source
I ci with t d a working voltage, of 30 kv. plas
Carii 4/2
C
3
-L-IM-421. 384. 6 2

~~'W'Aala age 0 0
-*~ W
04 0 C
Is Is .
ti
Is If a a if 22 211, 3d is 14 v a IV ju 11 9 It w J5 is to 't a
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Abstract: No abstract.
Card IA

6- EWTW/ (j)/T M
-.ACC NRs .4. P :SOURCE CODE: UR/0413/66/000/003/0050/0
6oo768o 050
AUTHOR Fakushin,*G,
14 1~ush, V. P.; Sandakov, Ye. A.;-Gazizov, R.F.1
F.; Todyshev,,-yu; Ge; Kireyev V. 0.
none
:Mastic co tainer for storing nd tra
-TITLE: n a nsporring liquids.
No.
178459
SOURCEv, lzobreteniya, promyshlennyye obraztsy,, tovarnyye znaki,,
Poo 39~1.966s 50
TAGS: liquid container, portable container, elastic container
-MSTRACT: An Author Certificate has been issu d describing a port
e
~-~able el stic containerfor'.storing and transporring liquids, which
a
has' a detachable fastener for
-the filling opening. To facilitate
cleansing of the Internal.surface, the detachable fastener is a part
of-the-filling opening whi
oh is equipped with clamping strips and a
lock. To prevent the liquid from shifting in the con-
tainer when it is partly full,, there is a tightening belt attached
to one of the clamp strips at-' the bottom of the container. (see
Fig. 1). ILDI
MK: 613~ W1 - 32
64 1/2

Card ? LG-
Z2

26532
S/167/60/000/006/002/003
4-0 Alo4/Al33
ALMHOR. Rashidov, T.
TITLE:: Stresses in pipelines occurring during seismic action
~PERIODICAL: Akademiya nauk UzSSR. Izvestiya. Seriya tekhnicheskikh nauk,
no. 6, 196o, 36 - 4o
TEXT: Former papers [Ref. 2: R. M. Mukurdumov,Voprosy seysmost,oykosti pod-.
zemnykh truboprovodov (Problems of the Seismic Resistance of Underground Pipelines)
Tashkent- Academy of Sciences of the UzSSR, 1953 and Ref. 3: Sh. G. Napedvaridze
SeysmostDkost' gidrotekhnicheskikh sooryzheniy (Seismic Resistance of Hydraulic
~structures) M., Gosstroyizdat, 19591 dealt with formulae to determine the stresses
In underground pipelines If the seismic waves propagate parallel to the axis of
the pipelines and with the same velocity in the pipe and the soil * Coefficientn
1W
taking into account the effect of the soil settling or the effect of the pipeline
lag from the deformation of the surrounding soil, is assumed as one unit, accord-
Ing to Ref. 3. Assuming that the oscillations of the soil and the pipeline are
equal, the propagation velocity of the waves differ from the propagation velocity
in the pi.pe and in the soil respectively., As this velocity is expressed by the mo-
Card 1/8

26532
S/i67/60/000/006/002/003
Stresses in pipelinesocoz7ing during seismic action Aio4/AI33
-y of mate als,participating In the joint movement, this modulus
dulus of elasticit ri
will also differ from the modulus of~elastlcity of thepipe material~and tlie soil
respeetiVely. Therefore the present investigation of the joint motion of pipes
and the soil will be based on a new,modulus of elasticity called "pipe soil" Mo-
dulus and determined by
P
9 E F
~s s
where E.5, Ps modulus of elasticitythe cross-sectional area of the soil surround
the pipe, respectively, and P -resultant force affecting the cross-sectlonal
area of the soil. [Abstracte'rls note: subscript s.(soll) is the translation from
th-3 Russiaxi r' (g:-unt)] The degree of the pipe deformation is determined by
CS,
E F
P P
where E F modulus of elasticity and dross-sectional area of the pipe respec-
tivf--y Find PP resultant force affecting the cross-sectional area of the pipe.
p
Card 21
8

2b532
S/167/60/000/006/002/003
Stresses in pipelines Oczul-ring during seismic action A104/A133
[Abstracter's nolle:~subsoriRt p (pipe) Is a translation from the Russian T(truba)]
The deformation of the 11pipe soil" Is determined by
P
ar
ar F-F
ar
~where E3,rl Par modulus of elasticity and the cross-sectional ax-ea, of the npipe
soil" respectively [Abstracter's note: subscript ar (area) is a translation
from the Russian op isrsda). Therefore
P P + P P F + F (5)
ar S _P ar a P
In view of the applicability of the hypothesis,of plane sections it is assumed
that
E (6)
p .ar
By determining the meaning ofP I P and P in formulae (1) (3) and Applying
e p ar
these values in formula (4), taking into consideration formulae (5) and (6), the
modulus of elasticity of the area will:be
Card