SCIENTIFIC ABSTRACT ZAGAYNOV, L. - ZAGIK, L.V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001963410015-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: March 15, 2001
• Sequence Number: 15
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

MEIEKHOUP A., karid. filcsof. nauk~ KUKSFANCV, V.,
filasof. nauk
thai~ty of trf.% world and of iran. Prof.-tekh. obr. ~2 no.1 :14-;;l
ja A '13,4)
Laimt3atittill nachallnlka Swrdlovskogo oblastnop
uprayle,nJy,% profe-),5ton-illno-tektiricheskego obvinvanlyi (for
Zagaynov~
J.

36987
3/044/62/000/03/030/092
0111/0222
AUTHORj zagaynov, I,- s.
TITLE: On-the Riemann'functionti for the equation
ZXY = a(X,Y)z x-+ b(x,y)z.,+ c(x,y)z + f(x,y)
PERIODICALs Roferativrtyy zhurnalt Matematika I no- 3, 1962, 6o,
abstract 3B256. ("Sbo'nauohn. tr. Krivorozhok, eornorudn,
un-t,"1961,__vyp. 10, 407-412)
TEM The author simplifies a result of K. Ya. Latyshova (Nauch.
zap. makh.-matem. f-ta Kiyevskogo gos. un-ta, 1941, 1) regarding the
construction of a Riemann function for the-given equation. IP13o Riemann
function is constructed as a series
OD
r (x, y;
n.0
which oonv~erges uniformly and continuously in the reg4.on whore h(xty)
aa ':
ab + c 5- is bounded. The functions f are defijied by
3C n
Card 1/3

5/044/62/000/'003/0140/092
On the Riemann functions for the ... 0111/0222
re h 0t, 44 x
X roe
b
If h k with k(x9y) ab + 0 _L_ , then the Riemann function lian tha
simpler form y
c0,
G(xjyj gj ef(x,y)-If (Xq Y; 9
n
n-0
with
'Y x
n(xty; P 4 'd Hn-1
(n 1p2p ..
Card 2/3

5/04 62/000/PO3/03C-/092
On the Riemann functions for t.he C111Y0222
and Ho 1, while T is a certain function which satisfies
at b
ax
For the case a b const we'have finally
G(X,Yj ef 00 Eh(y_~q )(X-')]'
7- )2
n-0 (ni
In this casethe--question-re the ---is
garding --sign of--the-Riemann--funation
completely, exas4ned.
CAbstraote'r's fiotet Gom late translation.]
Card 3/3

ZAGAYNOV, L*So
I
,?ie=nr.r,. firict!zr, for thc cl"tlcr
zxy N 14,712,, +b(x,y)r7 +- C(x,y)t 4 f (xty).
500i's naucho jKOK rcl.70:1,07-412 161 (HIPA 17tg)

AUTHOR s SOV/L40-58-3-12/34
TITLE* Unlimited Applicability of Chaplygin's Theorem on Differ,)ntial
Inequalities for the 301utiOn OfthO-Fir,lt Boundary Valuo
Problem for Linear Equations of Elliptic Type flicogranichenna-
ya primenimost' teoremy Chaplygina, o dif-.rerentiiial1nykh
neravenatvakh k resheniyu pervoy krayevoy zade-chi dlya liney-
ny'kh uravneniy ellipticheskogo tips).
PERIODICALs Izvestiya vysshikh uchebnykh zavedeniy. Mateawtika, 1958,
Ni- 3, PP 96-98 (USM)
ABSTRAM Lot G be a simply connected bonnded domain witli boundary
Lot
n n
E(u) a u + a 2-u
ik(x) VxiVxk E 2xi
i#k-I iW1
where the coefficients are ansumed to be twice continuously
differentiable6 Furthermore let
aik(x) Si YO . Purthermore lot L(u) - E(u)-au
Card 1/ 2 i,k-1

Unlimited Applicability of Chaplygin's Theorem an sov,'14o-58-3-12/34
Differential Inequalities for the Solution of the First Boundary Value
Problem for Linear Equations of Elliptic Type
and D(u) - E(u) - f(x,u), whereby f is at;sumed to posses!i in
'C the continuous nonnegative derivative A
4)U
Theorems If the twice continuounly,,diffei-entit,.I)le functions
u and v satisfy the conditions
1. L(u)> L(v) in G and 2. ul r - vjj- j then 1, t is u < v-
everywhere in G .
Theorems If the twice continuously differentiatle functions
u and v eatiefy the conditions
1. D(u)>D(v) in G 2- uIr v1r I then it is u