SCIENTIFIC ABSTRACT MAKHOVIKOV, V.I. - MAKHSUMOV, A.G.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001031610003-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

28808
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Some problems of the theory . . . C111YC222
2F 2F 2F 0 (13)
- -~,-2
x2 ~.2
the author obtains the expression
n-1
F = f(z)T2n+l + f'(z)'y2. + Z [f (2n-2k )(') (T2k+1 + Ck+l) +
k-0
+ f(2n-2k+l) (z)(T2k + ~2k)] (14)
where f(z) is a polynomial of (2n + 1)8t degree, 'Ps , '98(t) -- analytic
function,
n-k
z ( )m +2m a (15)
m=1 4 M!
m
Here denotes an m-fold integration with respect to 9, and the prime
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Some problems of the theory C111/C222
denotes the conju.-ate complex magnitude. For the functions Foo Flo F2
satisfying (;1) it follows
FO == Re 1(Az)~Zn+l +P (Z) ~In + [Pn-2kI(Zm2k+1 + 'Ir 2k+1)+
kmo
(Z) (~Ijk + '1'2011 1
n-'
Fs Re jf(z) ),2.+. + f I (Z) A2. +Y ( f(2,,-2k) (Z) (X2k+ I +A2,6+1)+
A-9
+ f(2n-2k,, 1) (Z) ()".0 + (16)
n-1
F2= Re Az) Tall+, + P (Z) T2. + j f (2n -1k, (Z) (,?2,t+ I ++
k-0
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28808
Some problems of the theory . . .
-.Yi th
+ f(2n-2*+)) (Z) (72k + 02A)1)
3/14 61/000/005/004/007
Cl*iIYC222
n-k
IYO Y ajmS ~1+2m A A, bj ).,+2m dt,
M-I M
am~
4 rat
M-1 M
M
bm b' . "2
4 )M;I 4 ml
(17)
where are analytic functions of and s 0,1,.. 2n+!. The
a 8
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Some problems of the theory . . . C111YC222
shifts (10) after the substitution of (16) read
W= Re If' (z)(C1'.,n,, + CST"",) + P (Z) (Cd-2- + cvp"d +
n-1
+ I I f(2,.--211+11 (Z) (CI).2k+ I + T2,t+ 1) j_ f (2,,-2k+2) (Z) (C X,,, + T,,)jj,
k-0
U-iV=f(Z)(k2.+l +T2.11 +
n-1
+ Y.( f(2.-2k) (Z)(k"
k+1 + ?2k+1 ~2k+l + Q.'k+l) +
k-0
+ f(2,,-2k+l)
(Z) (~21 + +11 + Q2.~ 1,
(18)
with
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Some problems of the theory . . . C111%222
T c IF + a + 0 2 -L [Re (4 +1~.) + i Re iY,,] (19)
2 s s 2 0,' Q13
where etc.
The boundary conditions on the generated surface of the cylinder can be
satisfied if the shifts on the generated surfaoe are given in the form
n
(2n-2k+l)/z) + f(21n~2k+2)
w Ef t2k,1 (Z) t2k]
k=O n (2n-2k) + (2n-2k+l) (20)
U iv = 7 [f (z)q2k+l (z) q2k]
k=O
where t q8 (s - 0,1,..., 2n+1) are functions of the arr of L.
Detailed formulas for the case n - 2 (i.e. f VI (z) - 0) are given. The
case where u and v are missing and w does riot depend on z is considered
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Some problems of the theory . . . Cli"/C222
in detail, where a three-fold connected region bounded by ) circles
and an elliptic region, respectively, is chosen as D. In all cases the
boundary conditions are satisfiec! approximately only on the generated
surface.
There are 2 figures, 1 table and 6 Soviet-blr.,c references.
ASSOCIATION: Kharlkovskiy avtomobil-no-dorozhuyy institul 1,Kbarlkov
Automobile and Highway Institute)
SUBMITTED: March 3, 1959
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MAKHOVIKOV_j_V.I- [Makhovykov, V.I.] (Khar'kov)
Solution of the wave equation. Prykl.mekh. 7 no.5:566-568
161. (YdRA 14: 10)
1. Khar'kovskl.y avtomobil'no-dorozhnyy institut.
(wave mechanics)

S/140/62/000/003/005/007
C111/C333
AUTHOR: Yakhovikov, V. I.
TITLE: The plane problem in the theory 9f anisotropic elastic
mediums for the exterior of an uAbounded number of equal
elliptical holes
PERIODICAL: ~ysshiye uchabnyye zavedeniya. Izvestiya. Matematika,
no. 3, 1962, 84-90
M.T. Considered is an anisotropic plane with infinitely many
equal elliptical holes which axe arranged equi-distant from each other.
In order to solve the elasticity problem where all holes are under
equal stress, the circles K11 with the radii 1 and the equations
io
+ )h, h > 2, C" = e
are mapped on the exterior of the ellipses. The mapping is approximate
and done with the help of the function
Card 1/-5 + moY(5 -1) (18)

!5/140/62/000/003/005/007
The plane problem . . . C111/C333
where ~ 0 is a cons iant, m I and Y is defined by*
00
Y kh)
(2)
k- oo
It is shown that, if 00