SCIENTIFIC ABSTRACT TAMRAZOV, P.M. - TAMRAZYAN, G.P.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001754820004-0
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 13, 2001
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

S/.021/61/'000/005/003/012
Conformed mapping of a D215/D304
A 3$P A.) some transformation f9 such that f~(f) --:::: (D(I) where I is
an identical transformation. The author concentrates on the proof
of Theorem 2,, which he claims 1B impler than that of H. Gr8tzseh
(Ref'. 1% Leipz. Ber. 81, j19 1929). Let 1K. * Y(Gnj Ali! A29 A39 A4)
where are sets from bemma 2, then
Gn Mn '6~- Kn+1 "m Yn 1< N'
n ---> oio (7
lei further, F,(Z) be The corresponding exiremal Transformations
and K n ihe eorresponding exTremal regions. Sequence F,(Z) is uni-
formly con7ergence In B and therefore compacto let its limits be a
regular- function J(z) then J(z) tM(B9 A19 A29 a 0 0 A 4). Let K 000
is a corresponding region from C(Bg Alp A29 oco A 4); 'then (F,,,)
1. i.e. P . and K 00 are extremal. Moreover for any zeB9 ReP 00 (Z)=
lim HeF n (Z) < lim 'Kn Or N < lim Mnj together with (7) it
n---+ 00 n __!). 00
Card 4/6

S/-0,'?1/61/000/'005/003/012
Conformed mapping of a D215/D304
it gives lim. kin = K. Assume now that problems P(-B, Ai,-A'29 AP
32 + 00
A4) has some other extremal solution F(z)g 1; then ~(P 00) =!;(F)
=.X..Since K OD and K are different, it is necessary that some ve~-
tical interval d C K should pass by transformation FF_l(w
00 00 OD OD
into a curve dCk, which is different from the vertical alit. let
T. be the image of doo in the transformation F-1 (woo let B* be
OD
the region obtained from b by adding the slit along T it is trans-
"L -
formed by r (z) into a region k* 9 obtained from I by adding a
00 00 00
alit along d OD using transformation (IF)z, b* passes into a region
k* obtained from k by adding a slit along d. M* = M(B*y Alp A29 A 30
A4) then evidently M*< M (11)o There are 4 non-Boviet-bloc refe-
rences. The references to the English-language publications read as
follows: J.A. Jenkinsq Trans. Amer. Math. Soc.t 679 3279 1949; J.A.
Card 5/6

S/02Y61/000/005/003/012/
Conformed mapping of a ... D215 D3 04
Jenkinsp Ann~&' Math. 65, 1849 1957.
ASSOCIATIONa Kyyivalkyy politekhnichnyy instytut (Kiyev Politech-
nic Institute)
PRESENTEDs B.V. Gnyedenko, Member of AS UkrSSR
SUBMITTEDs November 129 1960
Card 6/6

AUTHOR: Tamrazov, P.M.
28710
3/021/61/000/008/005/011
D210/D303
TITLE: Continuity of conformal representation of a domain
on a rectangle with rectlinear sections
PERIODICAL: Akademiya,nauk Ukrayinslkoyi RSR. Dopovidi, no. 8,
1961t 1004-1006
TEXT: When speaking of the problem P(B,A,pA2pA 39A4), the extre-
mum representation F(B,AlIA2,A 39A4) and the functional M(B,Ajt
A2 A39A4 ) it is always understood that the problem P(B,A,,,A 29
A OA ) is not meaningless for the given B, Aj,A A A ; Theorem 1
3 4 2 39 4
etates: A vertical straight line which cuts the extremum domain
divides it into two domains congruent to the extremum domains
(for corresponding problems). The proof is complicated and is
not given in the article. B is then assumed a domain of any
connection with marked non-degenerate boundary continuum P.
Card 1/6 if

28710
S/02lZ61/000/008/005/011
Continuity of conformal ... D210/D303
different boundary elements A, vA 2... are situated on P in the
above mentioned order it will be written Ai(Ai+l (i=1,2 ... ). Two
lemmas are then established, based on the properties of conformal
representation and on Theorem 1. From the lemmas follows Theo-
rem 2. If Alp A2 9 A4 do not vary and A 3 moves along P in any di-
rection, the functional M(B,A1,A 2 vA 3~'4 ) changes continuously and
strictly monotonically. If A 3 moves in the positive direction M
decreases and if A 3 moves in the negative direction K increases.
A third lemma is then needed: Let f(x) be a real function given
in a closed n-dimensional hyper arallelepipedon T: x = (X go**
x"), ai~xj~