SCIENTIFIC ABSTRACT ALEKSANDROV, A.A. - ALEKSANDROV, A.D.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000100820005-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 5, 2000
• Sequence Number: 5
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

AT-MMA R V, A.A.
,Wjw~
Ityeing and finishing chrome glove leather. Leg.prom. 14 no.11:14-15
N. 154. (91-Rk 7:12)
(Dyes and dyeing--Leather)

ALUSANMOV, A.A.
_A- - t .
,.6,0-w- --v- ---
~-7~m P-,
Smooth improved-grain finish for leather. leg.prom.15 no.2:53-54'
F '55. (HLRA 8 a 4)
1. Glavny7 dispatcher Moskovskogo khromovogo zavoda.
(Icather)

ALICKSANMOV, A.A.
-: ...
Lat us do away with losses In raw materials. Leg.prom. 15 no-9:
44-45 S '55. (KL'RA 9:1)
(Leather)

AUEUNMV, A.A.
-Drum dyting and staining of leather. Log.prom. 16 no.5:36-37
Xy 156. (Dyes and dyeing- .Leather) (MLU q: 8)

ALUSAKD minh; VOLKOV, V.A., rateensent; FRIDNAN, B.O.,
reteenzent; P1914YANNIKOV. M.B., reduktor; MOVEDBU, L.A., tekhol-
cheskiy redaktor
[Manual for specialists in chrome leather tanning] Sprevcchnik
masters protsvodetys khromovykh kozh. Moskva, Goe.nauchno-takhn.
izd-vo M-va legkoi promyshl., 1957. 386 p. OILKA 10:10)
(Tanning-Handbooks, manuals, ate.)

\,. AL&SANDIROV, A.A.
,
k
Using the method of diazotization in dyeing chrome-tanned eruede
in various colors. Ieg. prom. 18 no.2:42-14 F 158. (MIRA 11:2)
(Dyne and d"ing--leather)

11r.1? SANWV, A.A.
Drying leathers by the method of gluaing on glass. Kozh.-obuv.
prom. no.5:28-29 My '59. (MIRA 12:6)
(leather-Drying)

ALF.KSANDROV, A.A.; FRIDMAN, B.I.[deceased]; PAVLOV, L.P., retsenzent;
--'-RILSMWMV, Ye.M.,, naucbMy red.; GRACHEVA, A.V., red.; SHVETSOV,
S.V., tekhn. red.
[Handbook of master worker in the saddle and industrial leather
industries] Spravochnik mastera proizvodstva shorno-sedellnykh i
tekbnicheskikh kozh. Moskva, Izd-vo nauchno-tekhn.lit-ry
RSFSR2 1961. 411 p. (Leather) (MMA 15:1)

ALUSMIDROV;' A. --D ~ - - . - ~ . . I .
- * f -I . . . , . . .
Kadochnaia kal I ttura lj-:-:oria 5--mon culture in ioad~-.n tub,~.;T.
I
Ta-y'---a-zdat, 1952. 51 P.
SO: Zioll U,. 1-Y List of Russian Accessions, Vol. 6 110- 7 October 1953

ALEKSANMOV, A. D.
Lemon
Cultivation of lemons indoors., Sad. i og., no. 2, 1952.
9. Monthl List of Russian Accessions, Library of Congress, _ may .1952, Uncl.
- - - - 1~;*61-11-2
- ~~ ~- - ^71"- -: L--Y, -~ 4 ".~. - -- , -
~ ~ , ~t -, -. 7t. . Z~- - -i. - - 4 - - .:

ALEKSANMtOT, A.D., professor.
Citrus fruit in the north. Nauka i shisn' 20 no.8:14-16 Ag '5).
OGMA 6:8)
(Citrus fruits)

AIXKSANDROV, A.D., doktor sellakokhozyaystvennykh nauk, prof.
Viticulture and wAne making in France. Izv- TMfbA no.6:221-231 160.
(MM 13:12).
(France--Viticulture) (France--Wine and wine W-king)

'---AUKSA.NDROVj_'4~
Yor you, medioal workers. Okhr. truda i sots. strakh. 3
no. io..67-69 o 16o. (MIRA 13'.11)
1. Zaveduyushchiy otdalom okhrany trada TSantralinogo
'komiteta profspyuzov meditsinakikh rabotnikov.
(Hospital--Staff) (Hadical lav and legislation)

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I W202; -NOV- L IM; Ix EOIW--It 6 PMvd that the quantuni
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ALaMSM-IMOV, A. D.
,,Con-.erning Theorems of Unicity for Closed 3urfaces," Dold. AN 22, No. 3, 1939.
Steklov. Inst. of Math., Acad. Sci.

ALASANDROV, A.
"Existence of a '-,iven Folyhedron and of a 'onvex Surfa.--e with a Given Metric.,11
DoU. AN 30, No. 2, 1941.
Inst. On Math. Acad. of Sci.

AIJ ANDROV, A.
Roentgenological diagnosis of high location of gastric tumors with
a double contrast method of Copelman and Tagger. Suvrem.med..Bofia
n0-11:33-41 159.
1. Ix Katedrata po rentgenologiia i. ragiologiia - ISUL. Zav. kit.:
prof. G. Tenchov.
I (STOMACH neopl.)

ALEKSAINDROV, A. D.
It.rhe Inner Geometry of an Arbitrary Convex Surface," Dokl. An 32, No. 7, 1941.

b.'
AUTTSI:A)DO"., A.
0 g---up,~,-4kh s i,7.rLri:m!x,-- rl-3--o: T)~m, (1- "-12
a
', aces Matem. ab., 8(50), (1940), 306-348
Aract sp
Additivo set-functions in abstractsspaccs~ nuitem. sb., 9(51),
Additive set-fu-nctions in abst'ract sPaces. matem.. sb.,13(55), (15"13).
0 beskonechno maljlkh izgibaniyaldi neregul~,arnyllj-i pove khnostcy. mlt-em. rb., 1(41),
(1936), 307-322. L, I
Osnovaniya -mutrenney --cometrii poverl:hnostoX. L., nauchn. byall. un-ll-q,
16
7(19" ), 3-4
,T: Yatheriatics in the U55R, 1917-1,047
edited lay Kurosh, A.G.,
-ushe,.ich, A.I.,
P.K.
194C,

AL:i-iSANDMV, A. D.
"On Grours with an Invariant Pleasure," Dokl. AN, 34, No.1, 1942.
Steklov Inst. Math.; Acad. Sci..

ALEKSANDROV, A.
I11121tistence and Uniqueness of a Convex Surface ,rlth a Given Intefral Curvature,"
Dokl. AN 35, No. 5, 1942.
Steklov Math. Inst., Acad. Sci.

ALEKSANDROV, A.
I 113moothness of the Convex Surface of Bounded Gaussian Curvature,ti DAL AN
36, No. 7, 1942.
Steklov Math. Inst.. Acad. Sci.

ALa,SANDROV., A. D.
"On the imtension of a Hausdorff Space to an H-Closed ipace," Dokl. AN,
3?, No-4, 1942.
Math. Inst., Acad. Sci.

ALEKSANDROV, A. D.
. "The Inner Metric of a Convex Surface in a Space of Constant Ciirvature,ll
Dokl. AN 45, No. 1, 1944.
Steklov Math. Inst., Acad. Sci.

ALEKSANDROV, A. D.
l'Isoperimetric Inequalities for Curved 3urfaces." Dokl. AN 47o No. 4, 1945.
Steklov- Inst. of Math. Acad. of Sci.

AIA SANDROV, A. D.
t'Curves on Convex Surfaces," Dokl. AN, 47) No. 51 19145.
Steklov Inst. of Math. Acad. of Sci.

.1
AL-MANDROV, A. D,
C"Ve
(Russian).
Alaksandrov, oL-: r~. 'Curvature of.convex surfacoi&
---Doklady Akad. Nauk SSSR (N.S.) 50,23-26 (1945).
Ak&somdrovi A.- D. Convex surfaces as surfaces of0ml-,
Ave cuiv 1361clady Akad. Nauk SSSR (N.S.) SO
ature.
z--jA7-30 (1945).- (Russian)
Tkiksandrov,ALD. Anisoperimetricoroblem. Doklad:'
W;
Akad. Nauk SSSR (N,S.) 50, 31-34 (1945). (RuWao):
these results have since also appeared in the auth"
iik5_6k'?;- Intrinsic geornetrk, of convex surfaces rMOWOWI!_.,
d 1948, them Rm 10, 6191 and -are mention I6d
gra
m
review. ~~,,*iBusemaffn (Los Angeles, Calif
SO: Mathemati9dal Review, Vol. 14, No. 6, PP 523-608, 1953.

nnv~ i v0
V..'s
'A S119m isisometric o a
trks t
..

Wil ex "CV,

ul, -1
3~ irqpn~TA~d space -o - coils ant':
I)II is%onitw~or
itc to an
p .7
qjL W .9f) .

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f H cm

4.
n
_w~gme has a,

iiq P~ of
IIti~ or, ' any trimig 6 jn.~ U (that.-Is
a set so-gille'lits corine~dng tWm). die

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-rda on if, - -c. itr~l K~ ho 9~- wher e

aie"angi -at
ai
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_4a.j Anil .

J.'a-the ni~q tic I - Revi
a, evrb

q

rov

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eir

441 (1041)

to

ALR,SA,N:)R(-)V, A. D.
"Homological Aelationships in Regions of Duality," Dokl. V4 N;-3, 1-94-7.
Corr. Mem., Acad. Sci.

ALEKSANDROV, A. D.- PA 53YO----
UM/Mathematice - Geometry Sop 194T
~Xathmatles . Surfaces
"Mathod of Coubining In the Theory of Surfaces,"
A. D. Aleksandroy, Corr Ylam, Mad Soi MR) Math
Ust .9 immi TA, A. StekloTl Aoad; 361 VW., I vp
*Vok Akad Nauk SSSR, Nova Bar- Vol LVII, No 9
Noments series of theorems and theories dealing
with process of constructing geometric figLiree by
cenenting together other figures. Process is old as
gfxmetry itself, nevertheless still need for theo-
rotical vork. Submitted, 23 Jun 194T.
INK 53TO

ALSKSAIM.IOV, A.D.
Formalism in the mathematical sciences. Vest. IMI 3 no.12:137-M4
D 148. (MIRA 12:9)
l.Chlen-korreepondent AN SSSR.
(Mathematics)

17
Melcsiin A. 1). Foil tiong oi th6l
d .0
".i-vlyA
kaAl Nauk WSR CV.S, 1
RuF_sian)l~::~
C,
et M topological mwiifbld metriti
in urkt 3 ii !I ~,t t tile di6t~mce -bf two Poiiiis,
lenvfh cif ;i 0--first Onn, AsjeWeg;~
C er-pon Orthe"PoInts,
is; a sct~ h* td r4idc',,
triang], ah, ~l hoineomorp: ic ito a circ a'.
to wh,~.Our,Lil, .,insists of Aortestconatction's'fr-a''m";'a to,40,;,,
f r0ill 6 to , ;I i t h ()M c to For an~ ie~disid iri;ili 1e"A
cm Af let A Ri i. note the:~ vnlid,~ai7 tAgne-li-Wht
"I equal the O,st.. I.; of the~o
jire (,it-, ~-n Af isGU'Tg rom a point 4n
f 0
0 meau'ure
V ft, Xipl ;Ind iis aJ '
MZcd the UPPP7,afi I
ki I'l w. 0 It it
mit exts~s, ang e:., is us Lns~--
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go
Ic abl. I it- 'r, is cz&j the exdeiWc.(4W Iof,
CUT'%IJLMZIe 11 h- -'Pry 'oonv.on rwt St'.
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U013 of non,ws-fla"Pin 16~1 C. t
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fa
is tjjj~r n
Tbe 17mill I has I:
finit
ture if 3and ('111, ~f Jr. re ;a:
every o it c
gion
luced in dt by the.iri
a ted by i 'emanni,
uniform)y art, tnqtrj6,,-;
~'Irc boun* (in their jbtaljt~)~ er
r esul t r, a, iv: .-j Finitely b6itinded curvature theri ~iivjlei
exist (OV avi I-f izccdest~_' arm (Shortest
is~-unig Iran, i w0: if the'6ccess of every triang 6 iriN
.(The 4 zus-, 1% 1 - an ~ obvious way a Bet unicti6fi
n on Ad, . . .... -nding t~ the integral curvature; li
tl
w (T) '0 be th61standard Arcrom lOcn~,6f.l.
Piosi
.,(T) int-~ i r and n6g~tive parts- Let P be a
4 , iip_'.
desic pahrV-, 11 and Z: !Zahr_ a SIMP to
fut1cm of P )f( wlesic tnIiatigles. If Dz is the
J iarnctei of wJ., , and crcM~ the surn of the i a
-ianr
oim a -~Iim a(Z) existi;
ang Ime CML
)f appm"Ci7M] 1 tol )t (Z) to V(P can be'
"mated bj~
P
J
NO P")Of ~U 4,;,n
7.1717
J,

the "d Ot!~ of
a .A6j.-446V- 'id V b6U, Ild,
Z (enel it (6r p,ar In Y: WI
aut G.:! '0 (V
and L u. th~ scv
an
'S I AT _vf ~Lf inad I sZ' dtTrdnatdv__.p mil.q..ii m -d iti -~G an I Vj -the suctor Angles -Of-.Q-:RrAs
_Aq
Without any inllivatl%%, (if the procifs.-Let jf be .1 140__vertim measured in the iompleinerit of G. Irlieli the sdln,
dinwmiotlal 111IM4ifuld witL boutialvd-mri ihituria [sce~X,D, - a+O+E(r-pj) approacles a limit as Q approaches-L,
Al of, -1486 (1948); '-which isjuilled the righ t total geodesi.'
-]a([)- (N.S, 60,44U - (t.g
z.. .136ill ill' ri-ht and ti le lift t4m. s
I I I Ow V, 1 17; uoted'ag-Al. 4 curve o J - wi It inill of;i! h test- conne&-.i
re on if, it, fori is-, nonpositive, but r t.,ed not -be zera. Man are L lies
point P jlas~ J? a i Cd I _Oith,itself at tio arc
It rte, I.
angle. Csm-~ -A], which. then equals f1 Shortest, connections on the boundary of a cloted domain G and is 4 s 6 --q
6suing fron).-p have directions [see Al-at,p.~ All cut-yes connection of its end poir ts in G, then has norip'Ositive
t.9.cf towart! G. ljjideraa~additional hypothesig oil tile
j"Otlig -froth -p exists and Integra convem~ holds.
J~ntgle of. t.vrQ curves XT 1, curvaturc of tile s ibregion ilif a- tile
L iu,,Is Ile limit oUthe an I for sul idently small subar. m. ef ill
gle bW-V,'C'ClIJwD:s toltest collnec- e 110tindary of 6. A curve
t -aid LC have right grwivq, c cUrvattli-C of I)OU"ded Va
p to poiInts XCX, anfl~ yz Y -will) is f. riation
oriker to laki,- piviiiii like wrtices of -.I cone int o account, Ole (9-c-b-y-) if fur vwry finiie subdivijion 4)f L into subarc,
-ectur I lie sum of tile ahwItite val jes of tile. eight f gx.st#sbel
ngle hemwfl.x and - Y is defitled-As, the Suprealtall t OW
f the still t&..wigI(:sforic;edbyX-. anumber 21, and Inf H i-. the'variation DfAhe right t~
is right _gxb.v.- thiaw-thia
0 c1l"tS ~MI19 -:front bitw-ecn.-,X a__r
ini user' 1-tely 6-dditi zinj 1i 6s r,
':ant t6r p ve fu icti6fi i if - tit,
unge"llala W:;pxcept at all a t~ Ijio~kt. coiiliiit~ie I~u ini;
t 4 .9 r'st t;l ction of its
points. 1 Ili 09 LI

ALX-K.", -- IDWT~ It ... - -, -
--m
Additive functions of a domin in the theory of convex surfaces.
Uch. sap. IOU no.96:82-100 148. (NM 10-8)
(surfaces)

ALEMNDROV, A. D.
."Tensars Jan/Feb-,49'
Mathematics - Geometry, Differential
Iteview of V. F. Yagan's Bdok$ 'The Bases of the
is,," A. D.
:-Theory of Surfaces In Tensor Analys
a
~-Aleksanarav, 5 PP
.IUspekhi Matemat.Nauk" Vol IV, No 1 (29)
Very favorable review of subject book, very com-
prehensive work on differential geometry of our-
L
36/49TY_~
Also see INI report U-3081, 16 Jan 1953.

t
Put
~~'JP=dawntals'6f Differential Geometry and Their
-Imposition,' A. D. Alelmandrov) 31 PP
J,',$~kPekh'Matemat Nauko Vol 17, NO -3 (31)
;t.~C'kiticizes lack of sufficient striotness in basic
',definitions of concepts cont~ine& in recent
differential P_43omei*y_ tAxte 'by Vi, i. r
Pe K. Rashevskly., S. P.Iinlkov, S. S. B,-wbn_eua,
V. F.. Mign , and others. P. K. RashevskiytB book)
*A Courife in Differential Gecmetr7,0 is evaluateA
the best text, both foreign and Soviet, In this
64/49T64
tOM/Mathemstloo (Cont&) may/jua 49
:i.lpl.ld. Gives complete rigorous definitions ofa
0, sai-face, and. wn1fold, and lists require-
muts for a differential geometry textbook.
64/49T&

I - -.
"Quasi-podesics." Dokl. AN., No. 6, 1%9. Leningrad.
Steklov Inst. of Math., USSRO Acad. of Sci.

ep
7-~--
7 :7, - - , '. , -. , , - - %~ .--, ., _:. - .

-Alek-~,Ladlrov, A. 1). QuO4i:Ceoj#',-'sIm 1D6kJa4Akmj
-CA"
1;0 011 surface W Cle ght aiid leit
jtO bDUridid -6umture 77
s~ ~every ctwte ma whic.i.
warc
his at ~!.arh point i definite'diradonlm&~r~rd ~nd for
1,-Defirw the total geodesic -A.I~ai t6 lea- ~2p
rj(j,,'j) over a)f
'44Mr---itiorm of A into afinitenjimbgrofar
6S.4 A quasi-
curvature is zero.
LWcsic is a curve wflose toWl~jjendem-r-'
IN rtest arc is a qk1aS1ge6demj&. but.mot,conwarsely.
ry
7.::,For con-1: Burface3 t1ais d"tioix cbri hrAilm with th~ Pre-
-ViOuv d,-finition of the author, 56e.-Intrina;r, :7,.~
14=. VL~IL. Moscovi-Leningrad, 194-8
-RL
v. 10 6191 A quasigeodesic has,(with an obviol. fic
nw'm-, '4ria and left integral'kepdedic curvaturm of bour d
and in rectifiabl
varintion e.
'~~,Thc !!.(.,.Wcnce of cADinpletejy.:a'~:diii~'P-Iset'functioni
"d
on a mantkAd R is 4-u to wnverge W63dy tr
ei*y contnuous function which differs4rom zero I,
On U SL17
_a~ rjpact set,
lot ~CT metrirs P1. PA. of bo4ifA-,A curvature be c
Th-, P, is said to tend regularly, to" 'if d, . .....
PC I P Ur) 9 uni I
V jj* on ("Very cornpact subset of Rah&if,the pbsitivt
~-jru ot te. SiJaTi I I Purvatur,4~of P. L." 7. i
negar L~
1,`ivia~-Is t1i se of p, tor a 4
cr a- n
pa. there. erj5t iie
at hul Ine-trics ,o. W.1lich pa~ If und,
m
cutivergenm of,),, to p4;j sequence,6f qu"geodc-41(-
P. Converges
and every qp mod6sic;,- f !pjC,' Oinit of
0, Ag ~,d
:Ii`j-8eq~Pnct- of quasigeodimics th
-'r ;mild' of i iiegral curvature to are 9~bounded,'Cwery qu,.
Gi9wft3ic is) a gcodesjc~
A. B
.0
-17
iu:

4.
JA
hudarstv. lzdat. Tehn,-T~-br' I
hingm '1950- 429'~
d icussesi~
I k robli 9 of i WM
e,degl, ~of i 0m In prescri it '6it I
n
vOx 11 icb then determi
poly1tedro, ne e~
~,.:Up. to -a icertain, OlemMary titinsformation'On6 -n-
~imilitudo)?~ The 6bok i6 encyclop'~dk Wit
wut~ doe' 4 not jivat PrO616171"S k6i, "t I
Steinitz' OIZ47,16&use there uniquen
".:Man W~:
stion.'~Tbti most no%~tl feature; 6is!
e Ne
t
I'llAi~tO.'Unp"Alislio niinoniesiii
j vimitil 6&hded wid unbo, n e I
F." botft~ caselVtni, tn
~nibei4 ~f'44rtices
in 6e')
'~%,SMOO ~d jM'a-YA*In e rays, co,
A
64aciis- may ex, end to.1 LYbubly cover6TP1Rt#--.dOnV*x
.-po j1j;jd re 4d as
ygo gions are cotist er*
ionloi the thioretnii.
ej first; ch0tei the-de(inl Lion and iemeat r prop
11 e
fi th t
mi'!'Ccmvex~031ybeckiih ar~~ treated. The~ljtark~'Ikh
~~fff. Irv,
''.."'0 ~s defitied as, f
'a Nl~ hedron a set 0 ~ convex,-polygonal
Jregions in the pW'eAvith i ",identificitiori ~61; ed'
given, ges an
*&,ti ~.~The element-ary.:'topolo of convex,polyhedM- IS'
ces.,
.71
m
~veloped; it is shown that a bounded polyhedroa,ts 9 e4>
h splie ft~ d--
tc'~ to a and that this is the CZSe if 'an L Only-1
0
e--~; k+f 2. For ;w unbounded'polyhedron. horneontor hi'
-p 1e
to 3~ plane O-k+f-l. This is thentio"ed hero ino er to
iadicat~'itliat prixtically.no, &niands
mideir's'.Unowledge. Chapter 2 describes the' methods a
reS ts,~M ni-nvoa-
~77' jobib- - in
di' I ;Jti( of pli6 ani minus signs. For a given p a
kbeme tot, be the W, eme of a Convex polyhe~dr=14f is, 0
I s ive curva ur.
W try that it have "pop t, t ih tl
esitm of thit~anjl 'with ilie same Ve"
t" e9
~J
ovni.. tat c -it for 4:
ppters'3 anti 4 th,
-Urvature and e-k+j,
ve-V
ac y7ne-b nded,~on ;)Olyll roW n t
T
~~exists~'Thb problem j~ also Sol in nit i~~
ri,~ but far litiiquene~M;, additional hypoth 6111 '0
Y
T;~O ndntlb~r of actui! edges nia..y,,be'-.s'
Mall
A"
deterriii~ar~on of the ~,ctual rlutnbe~.O`
qarried"th gh. ~Citipt~t S~~'treatq~. & .111a1
ary.
lyhedi~a~ w,41; a ~ ound
for ~Cbn
Y"tXj P D b

Yj', 15QT37
ALEKSAIUM,oV, A-3,
USSR/Mathematics,- Differential Mar/'Apr 50
Geometry
"Unique Determination of Convex Surfaces'of Revolu-
tion," A. D. Alexanclrov, Leningradp A. V. Fogorelov,
KharIkov, 22 pp
"Matemat Sbor" Vol XXVI, No 2
Considers triply continuous differentiable convex
surfaces with Gaussian curvature everywhere posi-
tive. Submitted 30 Jan 48.
159T37

AL&~SAIDROV, A. D.
I
"Quasi-eodesics on Aultiform Homeomorr-hic ipheres," Dokl. AN, 70, No. 4) 1950.
Steklov Inst. of Math, Leningrad Div., US3H Acad. Sci.

of iti, gtpplicatfow.:
pp. 5-23. lzdat Akad. Nauk
'Moscow, 1951. (Russ 'ian) 20 rubles.
A segment T(a, b) from a to b in a metric space is a c
from a to b whose length equals the distance ab of a and b.,
Let a?&= e T(a, b), a0y t T(a, b). On a surface with
at .ant curvature K construct a triangle a'xy' such thai,:-
d'Y-ax, ay'=ay, xy'=xy (if K>O, this is possible only"!
when these three numbers are sufficiently Bm_-Jl) and denot ,6-1
W.,yjc(x, y) the radian measure of the angle at a' in ale__4`11
The upper angle a between T(a, b) and T(a, c) is defide&
as'ct,liznx~supv~ tic(x,y). This number is independeji# IA
of K. If the limit exists, we call it the angle between T(a,
add T(a, c). The K-excess of a triangle abc formed by sej~~
mints T(a, b), T(b, c), T(c, a) is the sum of the upper angles~
minus the sum of the angles in a triangle a'ble' on a surhace~
of curvature K with ab=ab', bc=bW, ca-ca'. The
result is - If as: is the angle at a' in the triangle aWc' andi.-'
is the least upper bound of the K-excesses of the triangle axy, .
where a P6x c T(a, b), b;dy e T(a, c), then a - ajcgv. I'-
The applications of this theorem concern spaces in which.
the curvature is less than or equal to K, that is, the K-excesi, .
is non-positive. The function -yjc(x, y) is then non-decreas-
ing: if xo is the center of a and x on T(a, b), yo the center of
a and y on 7"(a, c), then -yjr(x*, yo);9-yX(x, y), I t follows fro m'
this inequality that xoye:_Sxoyo1 (but not conversely). Their
r6riewer has shown how strong the implications ot the ists .C
inequality above are for K=O, i.e., of 2xayo;9xy, [Acta
Math. so, 259-310 (1948); these Rev. 10, 6233. The anglei,-
between. any two segments-T(a, b), and T(a,. c) exists, evew,"
in a strongi~ sense tfianib6've_'Segmints'am ru ~;g
A~jO* Calif.
p
SO: 14athematical Review, Vol. 14, 1192,, 19~~.

USSR/ftysics - Quantum Mechanico 11 May 52
9~
M "Concerning Zinsttln'r Paradox in Quantim Mechan-
C*4 ica," A. D. Aleknondrov, Corr Mem, Acad Sci tv-SR,
Leningrad State U Imoiji Udaricn,
"Dok Ak Nauk WSW' Vol 8)1, No 2, pp 253-256
Author states that in 1935 Einstein, from consid-
eration of a concrete example, came to a conclu-
sion concerning the inccmplattmess of quantum
mechanics. The author calls 'this "Einstein's
paradox." Bohr offered a soln of this problem
it
on the basis of hia "complementarity principle.
231T95
Another soln -mas given by L. 1. Mandellohtam on
the basis of a purely statistical concept of quan-
tum: mechanics. This viewpoint was developed by
D. 1. Blokhintsev as a counterbalance to the con-
clusiorB of Einstein and Bohr. In the present
article the author gives a different solu of the
paradox and clarifies the errors of the others
mentioned. Also gives 2 views on quantum mechan-
ics. Submitted 1-4 Mar 52.
231T95

ANEKSA-MROV) A. D.
Si(--:nificance of the L'ave Function, Corr. Ybr., Acad. Sci.,USSP - A,D.A.Ieksandwav.
DA14 SSSR, Vol-65,no.2, pp.221-113 Jul 152.
1n the problen of the sigi-iificance of the psi-function there u-e three points of
vimr ) ~or brevity, in Vie cL,-e of the electron): (1) psi characterize's the ob-
jective state of the electron; (2) psi- is a I'description of infoi,~nat-ion concern-ing
the state." (see Fo~;k, Einstein, and Bohr of 1936); (3) nsi relates not to the
electron but to the "ensemble" (see D.I.131okhintsev, Fundmentals of Quantum Ix-
chanics., 1949; L.I.I.11andel'slitam, ',,corks, 5, 1,050). Shoirs t1he 1"alsity of (2) and
(3), on basis of Stalin's preccots, and extends ami enlarres (1). Presented 20
~',ay 52.
252T88

ative U
Wz-;
i--f
suaW
7
l
I
tic of RV, Z):~
'CI SO
iv 1-ZI

X F. G for
u U(jr) IC 't 0 1 ~
a
t~ -,
and t, ~ X, , _~
i~ don not at
~d in
(
defin C 1.1 X
iind .11l Rill! -
or ula'
W I__*
rt
n'ura
N
f
d by th
ior 4D
t
,re
er
-V I
in the in
Ilis core sur
11'rent trill", convex
fill
ioijy on
g

50

ALF,KSAVIIROV
On filling space with polyhedra. Vest.Lon.un.9 no.2:33-43 F '54.
(Polyhedra) (Spaces, Generalized) (mm 9:7)

SHISHKIN, B. K., professor; ROMANKOVA, A. G., kindidat biologic!ieskikh nauk,
starshiy nauclinyy sotrudnik; MARKOV, G. S., doktor biologiche-skikh
nauk., dots-~nt; DANILMKITY, A. 3., kandidat biologiches-.:h nauk..
dotsent; SHTEYNBaW, D. M., doktor bioloSiclieskikh nauk; LONIAGIN, A. G.
aspirant; SELL'-BM-LW, I. Y., mladshiy nauchnyy sotrudn:Lk; ZHINKINp
L. N., doktor biologicheskikh naulc, professor; IPATOV, V., S., student
V kursa; KOZZWV, V. Ye. kandidat biologicheskikh nauk, stArshiy
nauchnyy sotrudnik; KAITASHEV, A. I., kandidat biologicheskikh nauk,
starshiy nauchnyy sotrudnik; NITSEEW'01 A. A., starshiy na.yehnyy so-
trudnik; VASILEVSKAYA, V. Ko, doktor biologichoskildi nauk, dotsent;
RYUMINI A. V., kandidat biolagicheskikh nauk; NAUMOV, D. V., Kandidat
biologicheskikh nauk, mladshiy nauchnyy sotrudnik; KHOZATTIY, L. I.
kandidat biologicheskikh nauk, dotsent; GOR03'-4TS,A. M., kandidat
biologicheskikh nauk, starshiy nauchnyy sotrudnik; GODLEVSKly, V. S.
assistent; G---RBILISKIY, N. L., doktor biologicheskikh nauk., professor;
ALEKSANDROV A D . professor; KOLODYAZHNYY, V. I.; TIRBIN, N. V.; ZAVAD-
SKII, A. .
,rTheor*y of species and the formation of specief. Vest.Len.un. 9
no. 10:43"92 0 154. (MLRA 8:7)
1. Chlen-korrespondent Akademii nauk MM (for Shishkin, Aleksandrov)
(Continued on next card)

SHISHKIN. B. K., professor; RO'WIMA, A. G., kandidat biolog.icheskikh nauk,
starshiy naychnyy sotrufnik, and others.
f'Theory of species and the formation of speciesT Vest.. Len. Un. 9
No. 10:43-92, Of54. (M.A 8:7)
2. Leningradskiy gosudarstvennyv universitet (for Shishkin, Romankova,
Markov, Ipatov, Kozlov, Kartashev, Godlevskiy, Gerbillskiy, Aleksandrov)
3. Zoologicheskiy institut Akademii nauk SSSR (for Shteynberg, Naumov)
4. Kafedra entomologii Leningradslcogo gosudarstvennogo universiteta
(for Dani-levskiy). 5. Kafedra darvinizma Leningradskogo gosudarstvennogo
universitete (for Lomagin, Gorobets). 6. Kafe,lra goobotaniki Leningrad-
skogo gosudarstvennogo universiteta (for Nitsenko). 7. Xafedra botaniki
Leningradskogo gosudarstvennogo universiteta (for Vasil-avskaya). 8. Ka-
fedra zoologii pozvonovhnykh Leningradskoye otdeleniye 'Isesoyuznogo in-
stituta undobreniy, agropochvovedeniya i agrotekhniki (for Sell'Bekman)
10. Institut eksperimentallnoy Meditsiny Alkademi-i meditsinskikh nauk
SSSR (for Zhinkin)
(origin of spec~ies)

j"
.

P031
yai ed., vol,:
':70

Aly, ANDROV, A.D.; SM3, Ye.P.
Non-deflectivity of convex surfaces. Yest.LaIL.un.10 20.8:3-13
Ag '55. (MLRA 9:1)
(Surfaces of constant curvature)

redaktor; KQIXO(IOROV,A.N., akademik, redak-tor; IAVRENT!Yly,
a e lk, redaktor. RYVKIN, A.L. redaktor izdatellstva; POLI-
VAIVOYA, Ye.S., tekhnicheskiy redaktor; ZELUKOVA. Te.V.. tekhaichookiy
redaktor
Nathematios, its content, methods. and significance) Hatematika, ee
sodershanis, metody i znacheuie. Moskva. Vol.l. 1956. 294 p. Vol,2.
1956- 395 P- Vol-3- 1956. 336 p. (HlRA 9:12)
1. Akademiya nauk SSSR. Matematicheakiy Institut. 2. Chlen-
korrespondent AN SSSR (for Aleksandrov)
(Mathematics)

AMEUMOV, A.D. i MIKIN, Ye.p.
Supplement to the article "Nondeflectivity of convex surfaces.*
Vest.Len.un. 11 no.1:104-106 '56. %"MLRA 9:5)
(Polyhedra) (Surfaces)

F If for a'
y a rtin~at
onsina es ton)
closed corivex surfacc S the functiLm (k,, k, u; ha!;
the sarne values.st points with Pormals which are siyin-
I AV P, thell S has a plaric of
metric with r6*t to it p a
Symmetly pardel tok.
Vnder more- gen*etal hypotheses oil the following
FA. Let SO h e wiw ana Vtie Sliff[IM'S,
holds ill -
-d'S' "niply &Ilmected
e ur an is m
~
I k0 k,-0 art! 1W,
Ve -
a id Closed, (Self-ilittre,
,
thm allow!d)A
prificip..A elitviltutes t), it t
~(,-int witil
normal i

>0 1wm)jk,xv
all ith ki Ile 0, k

(k ~2 fi)-fur poillis, Of S' alid, SO
and
with'alt 'lamb- nornial It-. tfiul S" is Congruen t to so. Whe'll
'
S 1~
the c6ridi;flofi for. 0 (siypusing it ill-
I Sphere i4en
=1?2 and
f Vet(-sni~s P~/Ai, ~ N~)M, ~A for h,
~-cjjjjst oil S% wid is t6t N a sphLIte,'
to 1-L hipf
t
Ndfiowq Conclude ti
ff btm-eifiawt (Lb� Aiig
R
l
Cafif
)
e
.
.
e
j

..-i'SHEYANOV, A.N.; TOPCMTZV, A.Y.; KURCHATOV, I.V.; SWBFT-ITSYN, D...;
UPITSA, F.B.; IOM, A.Fa; YINOGR&MY, A.P.;ERX I , I.G.; TIENONOV, , -
N.S.; FAUMV, A.A.; FRANK, I.M.; VEKSLER, V.I.; IOMYCHUK, A.Ya.;
POPOVA, N.V.; T-31M VA, Z.A.; VASILEVSKAYA, V.L.; PETROVSKIY, I.G.;
AL~KSANMOV,AA%j. ARTSIMOVICH, L.A.; MESHC1MRYAKDV, M.G.
, - ~ 5:~
Irana Joliat-Curia; obituar7. Vest.AN SSSR 26 no.4:73-72 Ap 156.
(Joliet-Curia, Irene, 1897-1956) (mk 9: 7)

AIM-RANMOV, A,D*
ot -1 P.
Ruled surfaces in metric spaces [with summary in English, p.2071,
Vest.Lon.un. 12 no.1:5-26 157. (MLRA 10:5)
(Surfaces) (Spaces, Generalized)

AMSAIMHOV. A.D.
Unicnienass theorems for surfaces in t',e large. Part P. (with
sums.ry in 24110h). Vest. U;u 12 Z0.7115-44 157. NLRA 10:6)
kSurfaceE) (Differential equ&tions)

e_A
3-3-2/40
AUTHORt Aleksandrovi. A.D,p Profesoorp Reotor of the Leningrad State
A. Zhd an ov
TITLEs Student Education is the Most Important Politioal Problem
(Vospitaniye studenohestva - vashne$shaya politicheskaya
zadacha)
PERIODICAL: Veetnik VysBhey Shkolyq Maroh 1957t 3, p 12-19 (USSR)
ABSTRLCTt The article says that student education is one of the most
important tas1cs in building-up Communism. The aim is to
create an"intelligentsia"whose creative work is to solve
the problems of developing science, technics and culture on
the road to Communism. The 20th KPSS Congretis called for
increased student activity. However, there are occurrences
which prove that a certain part of the students lack oon-
sciousness and high performance standards. These students
often discuss questions and supposed "lacks" in their train-
ing programs without comprehensive knowledge of the subject
or principle involved. Some even create disorder and commit
immoral deeds. Yet, such occurrences are rare. The main
evil in the author's opinion is that the students and
Card 1/3 occasionally even whole organizations lack the ability to

3-3-2/40
Student Education is the Most Important Political Problem
discriminate between demagoguery or what is "in vogue" and
what is fundamentally sound. The author is not convinced
that these are solitary instances and that tho mass is
sound. He says it is necessary to eliminate the general
deficiencies in education which cause the abovementioned
situation, through the increased influence of social orga-
nizations, such as Komsomol, Professional Union and the
Students Dormitory Councils. An indispensable part of
communistic education is general oulture,(broud marxist
training and a lively interest in public affairs, all
science and art). An important element of communistic
education is to develope the communistic attitude towards
work. Students are told time and again that eivery man is
obliged to work to his utmost. The author urges very close
contact between otudent,and instructor avoidirigg howeverg
familiarity. The basis of education is inotruction (the
lectures and seminars). The main object of education it
the transmission not of a certain amount of ktowledge but
of 'training. The school can only convey the funiamentals of
Card 2/3 science, a man becomes a true specialist only thru practice

Student Education is the Most Important Political Problem 3-3-2/40
and study, Student independent work is strongly recom-
mended.
ASSOCIATION: Leningrad State University imeni A.A.Zhdano,r (LeAingradskI4
gosudarstvennyy universitet imeni A.A.Zhdanova)
AVAILABLICt Library of Congress
Card 3/3

ALEKSANDROV., A.D., Rector, Leningrad University.
e>
"On Differential Geometry in the large and on PLatric Watbods in Differential
Geometry,"
paper submitted for Eleventh Intl Congress of M;Ltheimticians, Edinburgh, Scotland,
14-21 Aug `1's.

AUI Rs
.LHO
-LD. 43-1-1/10
ALEKSANDR91,
TITLE- The Diriehlet Problem for the -qi:ation Det
I . 17~dacba ~Ilirilqla d1ya urav-
"" 'K
(7'
"" Z
' Z9 X
)'
n
l
n
V
neniya Det Z. i = D
i . __. z 7. x
j (71 . 'I,
if , -n

FERIODICALt Vestnik Leningradsko[;,~ UnI-.;ersJkZ.?'a, Mc~ t e m a t. iki, Ye-
khaniki i Astronomii. 191,16, Nr
ABSTRACT: The author irivest'igEtei, the equatior
f (-'~,z,,x) Det z. ji ~ h(x)
where grad z (X) ; x is the total-Ity x.,, x ... x
'
n
2
of the independgnt. var.JL~,.bjI*e3, 7J5 ar? the se.;ond derivatives
of the unknovin functioi.. ~ a rl~, f is zubject to certain oor,
ditions of boundedness a-nd contin-aity. in connection with his
former publications (T-le-f.1 - 7-1 the aut'hor ap-Ilies his speci-al
geometric methads Tihi,%_'- are based th--- approxImation of sur-
faces by polyhedra anif-I o.jf zsol.- fitir-.tionE by functions consisting
I
of a fin-11te number Of J)--'T,;.--17,3SSeT-. Ir. orde-- -..o be able to
apj)ly these metned'a the n_--ion ~~f no-rmal mapping P is in-
troducsd which is del-armf_-~~ed ,y a surfa,~e S , ard then a set

Card 1/2 X.
~uncticn LJ f (M.: S) is def-LIE-'a

The Dirichlet Picblem for the Equati-)n 4"/--1- 1/10
Z Y Z, x x
n
z x d Z
(2) ")j(1j;S)
kit)
where 1"r- D , D is the rari~a in the Y.-space,
_?s (M) is the normal. mapping of 11 do t ermined by S and de-
notes an n-dimenaiowii cpace. 1_71hen (1) is equiva-
lent to the equation
I') ,Y;s) =v(lf)
(3) . fk
and the nroblem is to delermln,:~ a surfa_-e S for wh-1.C:h tine
funeticlrl t1;f(M;S) is aqw~i to z`he sei iunction J) (19).
In ihe present first paragiapiiv of the pa_pz~r -.he existen-.e
of a ocnvex surfa-e S j.5 r; Vjjj_*1L~L'_1 nCj~~jSfjeS (3) , fror
this one concluden the zf a gonez-alf'sed solution of
N-
A detailed English summary( is added tc. the papers 12 Soviet
references are quoted.
SUBMITTED: 25 June 1957,
AVAILABLE: Library of Congress
Card 2/2 1. Normal. mapping 2. F~xn~tions 3. Surface!E

GALIPFM, S.A. (~bskva): IOPSHITS, A.H. (Mostva); BALK, M.B. (Smolensk);
ZHAROV, V.A. (Yaroslavl'): BYPKIN. V.I. (Llvov); ARIOLID, V.I.
(Moskva); KUTIN, I.Yu. (-Moskva); DYNKIN, Ye.B. (Moskva); PRDIZ-
VOLOV, ~. (Moskva); ALFXSAIfDROY, A.D. (I-eningrad): VITUSBKIN, A.G.
(Honkva .
i- .
Problems of elemen theiii~flcs. I-kLt. pros. no.3:267-270 158.
(Mathematics--Problems, exercises, etcJ (MIRA 11-.9)

A ~OROV~,A Do~,-
Studying the maximum principle. Part 1. Izv.vys*uc;aebozave; mat*no-5:
126-157 158- (MIRA 32:u)
1. Leningradskiy gosudaretvannyy universitat im. A.A. Zhdanova.
(F6ct16nal axLalTBis)

AUTHOR: A 43-7-2/18
TITLE: Uniqueness Th 'eorems for Surfaces "in the Largell.III (Teoremy
edinstvennosti dlya poverkhnostey 11v tselom".III)
PERIODICAL: Vestnik Leningradskogo Universitetat Seriya Matematiki,Mekhaniki
i Astronomii, 1958, Nr 7 (2), pp 14-26 (usn)
ABSTRACT: In the (n+l)-dimensional Riemannian space let be given a
continuous family js~ Of surfaces S. Por S let (at least locally)
the representation z - z(X1, ... Px n) be possible, where z is two
times differentiable and has bounded second derivatives. Let
the function 0(kj,...,k ni#z,x'), where -the k ~~-k2... >k
n 1 ,, n
are the principal curvatures and n i are the covariant components
of the unit normal in x i be continuously differentiable with
respect to all arguments; let the derivatives of 0 be bounded
everywhere; let 4! >,,O (i.l,...,n) and for a certain neighborhood
1~ 0 -
of each point of S lot Tk- >oonst >O. Let 9 be a smooth
i
n-dimensional surface in the domain G which is covered by the
Card 1/2 family fSj. Let S1 C-fSj be a surface such that for points of-i

Uniqueness Theorems for Surfaces "in the Large".III
43-7-2/18
and S' with the same (-xi) and (x") always zl,~~,3 (or zl:!!~3).
Theorem: If under thelgiven assumptions in a certain neighborhood
of every (xi) holdst 41'> 1 4 ), then I lies on S1.
.., (or
From the theorem which has Itill ttree temmas there result
numerous conclusions which are composed in further eleven
theorems. As special cases there result several results of
Blaschke, Sites and Grotemeyer on spheres and affine spheres.
3 Soviet and 5 foreign references are quoted.
SUBMITTEDt 27 January 1958
AVAILABLE: Library of Congress
Card 2/2 1. Surfaces-Theox7 2. Mathematical analysis

AUTHOR: Aleksandrov, A.D., Volkov, Yu.A. 43-158-13-4/13
TITLE; Theorems of Uniqueness for Surfaces in the Large. IV (Teoremy
yedinstvennosti d1ya poverkhnostey"v tselon' IV)
PERIODICAL: Vestnik Leningradskogo universiteta, Seriya matematiki,
mekhaniki i astronomii, 1958, Nr 130), pp 27-34 (USSR)
ABSTRACT: The paper contains a detailed representation of the results
partially announced in [Ref 11. The theorems and their proofs
correspond to those ones of [Ref 31 - In contradistinction to
[Ref 37 only Euclidean spaces are considered where the principal
curvatures are understood in the sense of the relative differential
geometry. The analogy to the results of [Ref 37 is considerable
so that the author points to [Ref 3] because of the numerous
conclusions. One of the conclusions contains a result of Stiss
[Ref 41 -
There are 4 references, 3 of which are Soviet and 1 German.
SUBMITTED: March 22, 1958
1. Mathematics 2. Surfaces--Theory
Card 1/1

AIKMNMROV, A.D.
I ,
Uniqueness theorems for surfaces in the large. Part 3 [with summary
in English]. Vast. IOU 13 no.7.14-26 '58. (MIRA 320)
(surfaces)

ALIKSANMV, A.D.; VOIKOVp Yu.A.,
pniqueness theorems for surfaces in the large. Part 4 [with
summr.v in Bnglish]. Vast. WU 13 no.13:27-34 158- (MIRA 11:8)
(Surfaces)

16(1)
AUTHORt Aleksandrov, A.D. SOV/43-58-19-1/16
x
TITtEs Uniqueness Theorems for Surfaces "in the Large".V.
(Teoremy yedinstvennosti dlya poverkhnostey 11v tselomll.V)
PERIODICAM Vestnik Leningradskogo universitetalSeriya tatemattki,
mekhaniki i astronomii,1958,Vr 19(4), PP 5-8 (USSR)
LBSTRACTs The,foll-owimg theorem already formerly formulated by the
author tRef 11 is proved s Let S be a two times differ-
entiable closed surface without self-inters-ection in an
(n+l)-dimensional space of constant carvature. Let the prin-
cipal curvatures k 1>'-"/kn of S be bounded. Let ~(kj,...,k d
continuously differentiable 1
0, 1 = 1,..,n. If 0 is constant on
?k i
S, theri-S is a sphere. + needs not to be symmetric.
The-theorem,also holds for self-intersection, if this is
small in a certain sense. The boundedness of the second de-
rivatives can be replaced by Lipschitz conditions for the first
Card 1/ 2

Uniqueness Theorems for SurAfaoes "in the Large".V SOV/43-58-19-1/16
derivatives.
There are 5 referenoes, 4 of whieh are Soviet, and I German.
SUBMITTEDs May 6, 1958
Card 2/2

16(l) SOV/43-59-1-1/17
AUTHORt Aleksandiov, A.D.
TITLEs UDi,queness Theorems for the Surfaces "in the Large" VI
(Teoremy yedinstvennosti dlys. poverkhnostey 11v tselon". VI)
PERIODICALs Vestnik Leningradskogo universiteta, Seriya watematiki, me-
khaniki i astronomiiP1959, Nr 10), pp 5-13 (MR)
ABSTRACTs Tn the preceding contributions of the author Z_Ref 1-5
~7 there
figured a certain function ~ of the principal curvatures
and of other magnitudes in the statemen,ts of uniqueness. In
the present paper it is shown that the uniqueness theorems
can be formulated without (P with the aid of purely geometric
relations in many important cases. In ZR-ef 52 it was proveds
if ~ (k I ...,k ) is constant on a closed surface without
self-intersection in a space of constant curvature, then the
surface is a sphere. Now a geometric statement is givens Let
kip ki be the principal curvatures in the points x, x E S.
Then there are either all A k i k1.0, or there are A k i
Card 1/2 of different sign. If for variable x, x all 6k i--->O, then the

Uniqueness Theorems for the Surfaces "in the Large" I'l SOV/43-59-1-1/17
ratio of max A k and min A k. remains bounded. Then S is
'N I i I
a sphere.
There are 9 Soviet references.
SUBT,F,ITTED: JulY 31, 1958
a
Card 2/2

AUTHOR: Aleksandrov, A.D. SOV/140'158-5-12/14
TITLE: Investigations on the Maximum Principle.1 (Issiedovaniya o
printaipe maksimuma.1)
PERIODICALs Izvestiya vysshikh uchebnykh zavedeniy. Matematika,1958, Nr 5,
pp 126-157 (USSR)
ABSTRACT: In the domain G of the variables x Xn let the linear
operator iku
(1) L(u) - a ik + A i + cu
be giveng where the-matrix of the ccefficients aik is assumed
to possess-nowhere negative eigen values. What can be said
about the point set on which the solution u of L(u)=O (or,
more generally, a function u for which it is L(u)'~,O or
L(u),4. 0) attains ite absolute maximum or minimum? The author
announces several contributions (at least six) which are to
give rather a general answer to the question, which simultane-
ously will contain several statements on-certain boundary value
problems connected with the problem, and which are to extend
essentially the well-known results of Hopf [Ref 9 and Nirenberg
[Ref 2D .
Card 1A The present contribution contains a detailed introduction and

Investigations on the Maximum Principle.1 SOV/140-58-5-12/14
a survey of the obtained results, as woll as the following
main result from which all further results are obtained as
conclusions.
Let aik bi and c be bounded, the admisoible -functions u are
assumed to be two times differentiable in G and continuous in
T=G+r together with their first derivatives. It is asked for
the set of the zeros of a function u-which satisfies the con-
dit-ions u,>09 L(u)< 09 whereby it is known that u vanishes on
at least one point. The answer to this question is-denoted as
the principle of zero extension. It is said that u touches
zero in the point x0' if u(Xo)=ui(xo)=O, i=1929 ... pn.* It is
said that xOE r is an oxflina y point w*ith respect to the
operator L, if from u:~O, L(u)4 0 and from the assumption that
u touches zero in the point x0 it follows that in G in the
neighborhood of xo there are points where u=0. It is said that
L does not degenerate in a domain U i I the clixection. 1p if
after a rotation, bringing the axis x into the direction 1,
the condition all> const> 0 is satisfied in 'U. A surface which
possesses the equation xi = a[ (Xi);T/2, a> 0, p> I in a
Card 2/4

Investigations on the Maximum Principle-1 SOY/140-58-5-12/14
certain rectangular coordinate system, is called a paraboloid.
Fundamental theorem (principle of zero extension):
If the point xoE r in the interior of G can be touched by the
vertex of a paraboloid and if L does not degenerate in the
neighborhood of xo in the direction of the axis of the para-
boloid, then x 0 is an ordinary point. If, however, such a
paraboloid does not exist even for smooth r , then x 0 cannot
be an ordinary point also for strongly elliptic L. If the con-
sideration is restricted to functions u which are two -times
differentiable in 6=G+r , and the first der-ivatives of which
satisfy theH61der condition, then x 0 is always ordinary, as
soon as r possesses a tangential plane in x 0 and L does not
degenerate in the neighborhood of x 0 in the direction of the
nowmal.
The author announces 14 theorems which follow from this main
result, e.ge
Theorem: If the boundary value problem L(U)=O, 0~11 +8u-0
Card 3/4 possesses a nonnegative solution uft, then every other solution

Investigations on the Maximum Principle,1 SOY/140-58-5-12/14
v is proportional to this solution u.
There are 4 references, 2 of which are Soviet, 1 is German,
and 1 French.
ASSOCIATION: Leningradskiy gosudarstvennyy universitet imeni A.A.Zhdanova
(Leningrad State University imeni A.A.Zhdanov)
Card 4/4

24(si upwrrATrox 30V/3313
Akedodya nauk SUR. Inatitut filosofll
?114~.-ofaklye voproxy nowromennoy fI%Ik1 laborniki; (Philosophical
Problems of Modern Physics-, Collection) Moscow, lzd-wo AN SSSR,
1959. 426 p. Errata slip inserted. 7,000 copies printed.
9d.z 1. V. Zuznetsav and A. X. Onellyanovskly; Ed. of PublishIms
Mouses V. r- NGroz1 Tech. 14.: S. 0. FArk*vlch.
PURPOSE: This book Is Intended for phroLcists but vay be read
ggfnfully by other scientists and the educated layman interested
In the philosophical questions of adwmced physics.
COWNRA=s This book contains 12 articles on philosophical problems
In physics. Problems are divided Into three subject dIvIsIonst
1) general problamai 2) problems of quantum theory; 3) Problems
In the theory or relativity. The views of Einstein, Bohr,
Rom, 71"ek, Paull, SchrUdIngor, Heisenberg, Janosay, at al.
are presented, and subjected to criticism from the Soviet side
by Ovellyanovskly, Polikarove Put. at Al. Questions dealing
itbFidealism, agnosticism, and dialectical materialism in the
philosophy of ph"Ieseare dl:cussed. This collection of Arti-
else I the th-rd In Berle under the me" tltl*. Earlier
volume: ... published In 1952 and 195a. References accompany
each article.
TAWJ OF COWfMMs
Vorevord 3
M X Dialectical Natwriallss end the Problem
=INFMA;~W" Physics,
_EjEomsy!- L. Philotophlesl Problems of Modern ftyolcs 55
guzoetsov, 1. V. Basic Ideas In the Work of Paz Planck 81
yoke V. A. ii.~terpretaticn or quantum Nothanie; 154
-~~~Imcussloz 6 With A. Einstein an Rplatomologicsl
itc'mid
-.9, Pau~ Answer to the.Crltlclsm lof X. Bohro V. Paullo 223
~ZarlatskU_IL--r_ The Intertransoutabillty or Elementary
FartIclem 249
4 eke The Theory of Relativity as a Theory of
'A4o:-Nut. 269

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16(1)
AUT90R! SOV/1 40-59-3-1/22
TITLEs Investigations on the Maximum Principle. II
PERIODICALs Izvestiya vysshikh uohebnykh zavedeniy. Matematika,1959,Nr 3,
pp 3-12 (USSR)
ABSTRACT: This paper is a direct continuation of th6 author's paper
f-Ref 13. In the domain G of the n-dimensional space (X,,...,x n)
the author considers two times differentiable functions u and
the operator Lu -Za ikuik',Zi'i'Ou' where it is assumed that
the matrix 11aik 11 nowhere has negative eigenvalues and that all
coefficients are bounded in every closed domain contained in G.
Let u,,--O, L(u),,R2' be the principal radii of curvature of !31 and S".
1~ R 2' 1 1
Theorem 21 Let the difference HI-H" be two times diffe:,,,entiable and for
almost all points adjoined to pairs 'Let the diffprence!3,&Rl ' R1, -R', 9
AR R21-R11 be either equal to zero or of different sign, where almost
2 &R
everywhere A Then S ~ and S11 are equal and lie parallel.
ISR2 A
Theorem 2R. assex+s that theorem 2 holds also if H = H1--H11 satisfies the
ocnditions of theorem Ia. Conclusion: If a general closed convex surface
by a change of r, the support function is dpformed so that the conditions of
theorem 2 or 2 are satisfied, then the deformation is a parallel transfer.
Theorem 3: The conditions of theorem 1 can be replaced by 1) in every oint
it holds either R1 = R2 - 0 or RlR2< 0,; 2) if a point X wiAh RA, R2
Jirary fixed point Xo, then it holds j-2j)r(XXO)_:~,0,
appr3ximates an arb- R1,
where r(XXO) is the distance between X and Xo.
There are 10 references: 9 Soviet and I American.
Card 2/2

86175
S/14 6o/000/005/002/021
/L,-5500 16,14 b 0 0 C1 1 IYC222
AUTHORs Aleksandrov, A.D.
TITLEs Investigations, on the Maximum Principle. V
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy.Matematika, 1960,
No. 5, PP- 16 - 26
TEXT: The present paper is a direct continuation of (Ref. 4). It is
assumed that the functions u(X) and the operators L(u) satisfy all
assumptions of (Ref. 4, � 1). Especially, u(X) has almost everywhere a
'first and second general differentialr and the coefficients of this
differential are called the derivatives. In (Ref- 4) the author formulated
the following condition (A) s
(A): Let the surface S have the equation z = u(X) = u(X19--'xn). Let U be
a subregion of the region of definition G of u(X), and lei; STj be the part
of S lying over U. Let MU be the set of points of SU, in which there exist
supporting planes. It is demanded that for every UC 0 every set contained
in Mu with the measure zero has a spherical image with tho measure zero.
Card 1/5