SCIENTIFIC ABSTRACT MARCHNKO. T.V. - MARCHENKO, V.G.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001032220014-6
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Sequence Number: 14
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

Nonsteady motion of gas ...
33591
S/207/6l/000/004/0v_,/ol2
E032/E914
be solved by approximating these functions by the power tiinction,;
P
Q(t) = cqta, N(t) = Cnt , c = const. (I)
with the cross-section of the tube at a distance X from the
orifice given by
FW = cx
provided
(I + a) (2 + V) - 1) (P + 3) = 0
The latter condition ensures self-modelling of the problom
provided the initial pressure in the tube PO may be neglected,
Tt is then shown that the prohlem may be reditced to the solittion
of a set of ordinary differential entiations which have been
considered by L, I. Sedov (Ref.l: Similarity and dimensimi-11
methods in mechanics, Gostekhizdat, Moscow, 1997), The ~n I ii t i on
exists provided
Card 2/3

33591
Nonsteady motion of gas ... S/207/hI/O()o/Oo4/Oo2/oI2
E032/ES14
P + 3 6 > 2
2 + -j 2 + -J
A detailed discussion is given of the conditions (in th(- -tiork
front and the numerical solution is reported for a conical tube and
-j = 3 for 0 = 7, YI = Y2 = 5/3, 6 = 2. There are 7 figtjr(-,q and
3 Soviet-bloc references.
SUBMTTTED: June 7, 1961
Card 3/3

MAROliNKO# T.V.; DMIULDWAt G.B. [DOWte-iiaVO-P ILB-')
Method for the determination of~ copper in biologi -I material in
forensic chemistry. Farmatsev. zbur. 16 no. 2:58-60 161.
(MM 14 - 4)
1. Kafedr-a sudovoi khimii Kharkivalkogo farmatsev-tichnogo institutu.
(COPPER~ANAYSTS)

CHERNYAK, Yu.A.; KARCHWT, V.A.
Improved circuit of an electroiragne,,Jc flow-meter. Avtom.
prib. no. 1:53-55 Ja-Mr 164. (MiRA 17:;,,'

Effect of minaral fertilizers on the amino acids of potato proteins.
Dokl. Akad. sallkhoz. 24 no.7:37-110 '57. (MIRA 12:10)
1.Institut kartofelltogo khozyaystva. Predstavlens. akademikom
S.S. Perovym.
(Potatoes--Fer-tilizers and manures)
(Amino acids)
, 'I,

K&RCHENNO, V.A.
Xffec~ of water and sewage irrigation on the u%lity and yield
of potatoes. Dokl.Akvd.sel'kboz. 21 [i.e.231 no.12:40-43
158,, (KM& 12: 1)
1. lauAno-issledovatellakiy institut kartofellnogo khozyaystva.
Prelstavleno akademikom I.A.Sharovym.
(Potatoes) (Irrigation farming) (Sewage irrigation)

MARCHENKO. V. A. Cand Agr Sci -- "Effect of various agricultural -engineering
methods upon the yield, vitamin content, starchiness, and aminoacid composition
"Z
Of ttdMot"ato-tuber�;r"otein." Kiev, 1960 (Min tf Agr UkSSR. Ukrainian Acad
6~
Agr M, 4-61, 205)
44
- MM_

I

ACC NRi AP6015956 SOURCE CODE:
AUTHORS: Marchenko, V. A. (Kharlkov); Suzikov, G. V. (Kharlkov)
ORG; none
V1100351ffRo~-
TITLE: The second boundary value problem in domains with a complex boundary
SOURCE: Matematicheskiy sbornik, v. 69, no. 1, 1966, 35-60
TOPIC TAGS: boundary value problem, mixed boundary value problem, Green function,
continuous function, mathematic space, harmonic function, existence theorem
ABSTRACT: Second boundary value problems in domains whose boundaries are closed
surfaces vrith a large number of holes are examined. The behavior of the solutions of
these problems when the number of holes increases without bound and their diameter
approaches zero is studied. A Lyapunov space r with the Lyapunov index equal to
unity in a three-dimensional space R3 is considered:
D = Rs\E = D+ U 0- U S,
S U Sj; I = r\s.
In the domain D, the second boundary value problem for the Helmholtz equation is
Au (P) + klit (P) (P); au (P)0
Card 1/3 an - 1Z_ ) UDC: 51M46.9

ACC NRs AP6015958
0
Bounds of the Green functions Gi(P, Qp i;k) and Ge(P, qp iA) of the internal and
external Neumann boundary value problem
au (P)
Au (P) Mu (P) = 0;
I V (P)
are introduced. The existence and properties of the Green function of the boundary
problem are shown. The principal theorem is proved: When n -** 00, 1) the diameters
d~n) of the pieces S(n) removed from the surface approach zero uniformly
I i
'Jim (max d(')) 0;'.
2) the function
6 (P) = Jim max
r, .) d-C(-A) =ff(n)'.) G(x) Ix
where f is a function in CQO vELnj.sn,,ng out:ilde an interval J Cortaining thf--
origin and 'C is the difference between +wQ non-.decreasing functions 3 and s(, ona of
+ n
satisfies the condition .13 M( R ( / IN,
which, e.g. 90 ~o 0
--.-c0 ), for some X >0. Knowing the properties of G at the orig'n, it is
0
required to estimate the differbnce V for large IM, or, more general.Ly, e8TLmala
the expression TN(*A)d C(X) fur large N, where, roughi.y speaking, T R appioache.9 1
as N this, the author puts in (1, ) f - tfS- I'TB, where f4EC"' vanishes
outside J and equals 1 in a neighborhood 3f the origin. Then T (A)d
f(.n) I N
S(SS-' - SfS_')T,(-A)d-C()~.) + f (x)G(x)dx. A Tauberian theorem is obtained by
estima+ing the right side under suitable assumptions. The estimates are precise
but too complicated to be given here.

SUBJECT USSL/MATHEMATICS/rFunctLunal analysis CARD 112 PG - 187
AUTHOR MAR NKO V.A.
TITLE Establishment of the potential energy in terms of phases of V~re
dispersed waves.
PERIODICAL Doklady Akad. Nauk 104, 695-698 (1955)
reviewed 6/1956
Consider the differential operator Su = -u" + V(X)u, (-x t 0, V real) with
2
the boundary condition u(0) - 0. Let u(;k,x) and a( Xx,x)E L , k - 1,2,...,
2
be solutions of Su u and Su A2 u respectively normalized so that
00 k
u( -A x)u( -A, y)d -A+ 7-u( xkpx)u( Xkty). Then for large x, u( )k,x)
0
behaves like tf ( A,x) - -V2-1'7"r- sin( x + j( 'A)), is the asymptotic phase)
and u(-A kv x) like V Ak") - mke- k1. The converse spectral problem consists
in finding V in terms of the functions If and was solved by e.g. Gellfand and
Levitan (Izvestija Akad. Nauk, Ser.mat . 15, 309 (1951). A variant of their
solution is obtained as follows. Put
2 -71%kx 1 fw(021,(>Q_1
f(x) M 'Emk e (2 )- , ) e'A'd W

Doklady Akad. Nauk 104, 695-698 (1955) CARD 2/2 PG - 187
solve the integral equation f(x+y) + A(X#Y) + f f,y+t)A(x,t)dt - 0, (x N)
proved by H.Weyl (Ref 17 for the selfadjoint case: Now !? is a
generalized function in a topological space Z. At the same time
the expansion formulas Of Weyl [Ref 11 are generalized too The
authors give conditions Lthat a generalized function is the 2pectral
function of the problem (1). The generalized functiona used by
Card 1/12 the authors correspond best to the scheme of Gellfand and Shilov

Expansion in Terms of Eigenfunctions of Non-Selfadjoint Singular 20-120-5-9,67
jr.fferential Operators
[Ref 21. Altogether five theorems are announced which essentially
represent an extension of results well-known in the selfadjoint
case [Ref 4,51 to the non-selfadjoint case,
There are 7 references, 5 of which are Soviet, 1 German and
1 Swedish.
ASSOCIATION-.Kharlkovskiy gonudarstvennyy universitet imeni A.M.GorIkogo
(Khailkov state University imeni A.M.Gorlkiy)
PRESEITTEDs February 3, 1958, by S~N.Bernshteyn, Academician
SUBMITTEDt February 2, 1958
1. Matheuatics 2, operators (Mathematics)
Card 2/2

M P~ H F_ N r,, C) V ~) -
PHASE I BOOK KXPLOITATION sov/5164
Agranovich., Zalman Samoylovich, and Vladimir Aleksandrovich Marcheako,
0bratnayn zadacha teorii rasseyaniya (Inverse Probleiq of the Scatter Theory)
Kharlkov, Izd-vo Kharlkovskogo univ., 1960. 267 P. 4,000 copies printed.
Reap. Ed.: N.S. Landkof., Docent; Ed.: A.N. Tretlyakova; Tech. Ed.: A.S. Trofimenko.
PURPOSE: This book is intended for scientists working in the field of mathematics
and theoretical physics; it may also be useful to advanced students interested in
the spectral theory of differential equations.
COVERAGE: The book deals with one of the new problems in the spectral theory of
differential equations - the so-called inverse problem of the quantum theory
of scatter. This problem, which has its origin in theoretical physics, is,
in the simplest case., reduced to the formation of the differential operator,- based
on the asymptotic behavior of its normed eigenfunctions at infinity. The book
contains a rigorous investigation and solution of the above-mentioned problem.
The mathematical apparatus developed for this may also find application in other
related problems. Conventionally, problems that indicate which spectral data
CaX&-I/&

Inverse Problem of the Scatter Theory SOV/5164
unequivocally determine the differential operator, and present methods for re-
ducing the operator according to these data, have bew called ninverse spectral-
ang.lysisn problems. The following personalities are mentioned: V.A.
Ambartsanyan, V.A. Marchenko, M.G. Weyn, I.M. Gellfand, and B.M. Levitan.
There are 14 references: 10 Soviet -nd 4 Euglish.
TABLE OF CONTENTS:
Preface
Introduction
PART I. BOUNDARY PROBLEM WITHOUT SINGUIARITIES
3
5
Ch. I. Particular Solutions of a System Without Singularities 13
1. Preliminary information and symbols 13
2. Fundamental system of solutions with given behavior near zero 14
Cq6r,a. ~,-

84302
L16 0 0 19, I-IOU S/039/60/052/002/004/004
C111/C222
AUTHOR: Marchepko, V.A. (Kharlkov)
TITLE: Expansion in Toros of Eigenfunotions of Non-Selfadjoint Singular
-Second -OzdOr Uf f erential Operators I ~
PERIODICAL:'--Ngtdzddti-cheiskiy sbornik, 1960, Vol.52, No.2, pp-739-78R
TEXT: Let W?-b* the se-t of all even entire' functions of exponential type
whigh. on-tke-zaal axis are au--&ble in the square. Le-t Z be a linear
topological space consisting of all even entire functions of exponential
type being summable on the real axis, where the addition and multiplication
w-i-th`-8b&pldx numbers are defined in the usual manner, while the convergence
00
is defined as follows: F n (n)e Z converges to F(7--) if lim jF0L)-Fn (X)IdX.O
n4oo I
00
and- the degrees S' of the functions F (AV) are bounded; max 6' < oD . The set
n n n
of functions b Fi(X)Gi(7L), where Fi, G EW 2, b complex numbers,
~(X) - Z i i i_
is a linear subset everywhere dense in Z. On this set the functional R is
Card 1/4

BL302
S/039j6O/O52/002/004/004
CI11/C222
Expansion in Terms of Eigenfunctions of Non-Selfadjoint Singular Second
Order Differential.Operators
00
defined by R L~(A_)] - 9 where V~Z This continuous
-OD
functional is extended on Z and is interpreted as a generalized function
over Z: R [-~(hj - (R, 4$(?L)).
Then a well-known result of H. Weyl (Ref,l) can be formulated: P To every
serlfadjoint boundary value problem
(A) n d y(x) - q(x)y(x)
I[Y] d.2
(B) yI(O) - hy(O) - 0
there corresponds a certain generalized function R defined over Z so that
00
if (x)g(x)dx - (R,Ef(X)E9(711)),
Card 2/14

84302
S/039/60/052/002/004/004
C111/C222
Expansion in Terms of Eigenfunctions of Non-Selfadjoint Singular Second
Order Differential Operators
where f(x) and z(x) are arbitrary finite functions of L 2rO.oo). If the
w-Foarier tran-S
;formation E (-&) of the finite function f(x) belongs to z,
then f(x) - (R,Ff(70W(,%XV-
2
Here 44(h,x). is the solution of 1[y]+X y - 0 with the initial values
(1) W(k, 0) - 1 , w I (-%, 0) - h.
The author shows that the assertion I, can be extended to arbitrary non-
selfadjoint-boundary value problems (A)-(B). With-the aid of the method
of I.M.-Ge-11fanA and B.M. Levitan (Ref.5) the author finds conditions which
must be satisfied by a generalized function over Z in order that it is a
spectral function of a problem (A)-(B). The analytic form of the spectral
function can be determined in exceptional cases.
Card 3/4

8
0'
S/03 6 522/002/004/004
C1 1 1YC222
Expansion in Terms of Elgenfunctions of Non-Selfadjoint Singular Second
Order Differential Operators
A part of the results are already published in (Ref-5).
The authcr mentions S.N. Bernshtevn, G.Ye. Shilov. M.G. Krevn. 1.M. Glazman.
B.V. Lidskiy and M.A. Navmark.
,rnere are 15 references: 10 Soviet, 1 American, 1 German, and 1 Swedish.
SUBMITTED: March 6, 1959
Card 4/4

MARMOM) V. A.
'*Phe generalized spectral function"
report submitted at the Intl Conf of Mathematics, Stockholm. Sweden,
15-22 Aug 6P

37055
S/057/62/032/004/001/017.
B125/BIO8
AUTHORS: Agranovich, Z. S., Marchenko, V. A., and Shestopalov, V. P.
TITLE: Diffraction of electromagnetic waves on plane metal gratings
PERIODICAL: Zhurnal tekhnicheskoy fiziki, v. 32, no. 4, 1962, 381-394
T-7XT: The authors have calculated the diffraction of a plane polarized
electromagnetic wave incident perpendicularly upon a periodic grating
parallel to the x-axis in the XOY plane (Ey, Ezy Hy, Hz . 0). 1 is the
grating constant, d is the gap width. The metal is a perfect conductor.
The two special cases of E polarization (~OJJOX) and H polarization (9,11%
can be calculated similarly. The sought electrical field is
2.1 (3)
E" e- 4k. -4- a,e FIFY e-1
above the grating (superposition of the incident and reflected fields) and
E.=-E be 2 22 (Z < 0), (39
Card 1/ 5

Diffraction of electromagnetic ... B125/B108
below it. The equations
r-d (7)
ke'" = 0, -, < I'F I <
d
j?j< ". (P),
7-
with the assumption En -~,O for InI-->oo, with b0 - I + ao;. b. an (n 0)
and bne(2nin/l)y 0 (on the metal), give with the s .ubstitution
n.-Oo
j d) A & E LI),
V. (r
(17),
V.- V. (e") R Wv) e--?dP,
2,,j
Rim R WY) e--""d'f; RI-I
2%
Card 2/ 5 1
S/057/62/032/004/001/017

S/Or~ 62/032/004/001/017
Diffraction of electromagnetic ... B125Y1,106
the infinite set of equations
X. ixbOVO. ixV.O -i- Ln-1 a V"--i- 2cR. (m 0),
1/0 ix V.0 -
O=ixbo 0 -f-I x. e. Vn 2cRO,
(19)
0 -1- 2cR,,,,
-bo =: i-Ab-V['.]-i"V1 1, X.
x. = b,,n.
for determining b 0, xM, and bmt where xn bnn. (19) can be solved
numerically e.g. by successive approximation if E-is sufficiently small.
The authors consider the case in which 0 /,x< 3 (so that F- +1 1 F- +2' F_ +are
-3
of the order of unity~ In this ca3e, the longwave approximation does not
hold any longer, the shortwave one does not yet. (19) gives with E. . 0
at every lnl>N a finite set of equations:
Card 3/5

3/05 6210321000410011017
Diffraction of electromagnetic ... B125YI3108
bo b. i -i-D(n) (21) with
i-LA -v- D n ixa -*- D
4jej -4- 1 Aijej8j -4- Aijoi6j4k -4'-
(23)-
4 e_i 4