SCIENTIFIC ABSTRACT ARZHANYKH, I. S. - ARZHANYKH, I.S.

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• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

SOV/1 24- 57 - 3- 3432
Translation from: Referativnyy zhurnal. Mekhanika, 1957, Nr
3, p 115 (USSR)
AUTHOR: Arzha.nykh, 1. S.
TITLE: The Structure of the Displacement Vector in Boundary
Problems of
the Dynamics of an Elastic Body (Struktura vektora
smeshcheniya
granichnykh zadach dinamiki uprugogo tela)
PERIODICAL: Tr. Sredneaz. un-ta,- 1956, Nr 66, pp 3-20
ABSTRACT: A study is made of the expressions representing the
displacement
vector of a point of an elastic body which satisfies the
dynamic vector
equation of Lam6 for arbitrary initial conditions and two
kinds of
boundary conditions: (a) Whei.-i the displacements hre given
for the
surface of the body (first pro-blerri),and (b) when the total
normal
derivative is given for the surface of the body (second
problem).
Functional equations determining. the displacement vector are
drawn
up in conformity with these boundary problems.
Representations of
the displacement vector by wave'functions are studied. In
conclusion,
integro-differential equations are presented for both the
first and the
second boundary problem. It is pointed out that by means of a
Laplace
Card 1/Z tran~.formation the integro-differential equations
of the first problem

SOV/1 24-57-3-3432
The Structure of the Displacement Vector in Boundary
Problems (cont.)
are reduced to integral equations. The whole paper is a
development of the
author's investigations published in publi.cattions issued
by the Academy of Sciences,
Uzbek SSR, from 1951 to 1954. The paper does not.contain any
actual examples
illustrating the application of the methoeis proposed by the
author. Most Of the
intermediate calculations are left out.
N. A. Killchevskiy
Card 2/2

USSR/7heoretical. Physics - Classical Electrod3naamics.
B-3
Abs Jour : Ref Zhur - Fizika, No 4, 1957, 8397
Author : Arzhanykh, I.S.
Inst
Title Field Method in the Theary of Hyperbolic Systems of
Differential Equations of HithemiAtical Mysics.
Orig Pub t Tr- 3-90 Vses. matem. s"itzda, T.I.M., AN
SSSR, 1956, 42
Abstract : Reaume of a lecture. The methodu developed by
the author
for solving the problem of deteritining the vector from
Ito curl and divergence, vhich muke it possible to express
~%e field in term3 of thei boundary values, are used to
determine the solutions of the Maxwell, Proch, and other
eqLations. The aiv&or studies the properties of the re-
oultant retarded potentials and %Tites down the integra-
differential equations fcr the boundary problems. A
ph)sic&l intezpretation is gIven for singly and doubly
retarded potentials.
Card 1/1

(IRZJMNyt~H, I S
SUBJECT USSR / PHYSICS CARD 1 / 2 PA - 1631
AUTHOR ARMUlYCH,I.S.
TITLE On the Chalnllke System o' r the Meson Field.
PERIODICAL Dokl.Akad.Nauk, 110, fe,sc-3, 351-354 (1956)
Issued: 12 / 1956
The existence of mesons with different inasses, velocities, and
charges suggestis
the study of a system of equations for the m~?son field. Here two
possible
varieties of this problem are investigated: 1.) The field has a
mass spectrum In
the case of one and the same velocity of the mesons,, 2~) Thq
field has a
velocity spectrum in the case of a give,,1.1 masti of the
particles. The mass spec-
trum is here characterized by a constant matrix and the field
equations are
written down according to the PROCA system:
2 ~ 2
div;V __ik _ I,, i + P, , curls_ _k A I - (1/0) a i/et.
1 0 ik k 0 40-J k k+J
-cUrlij, --0/031,/at, kol.m 0c/h, i1.)2...., N.
3. Iq
in the same way P - P g Oik III Is assumed to chara-aterize the
spectrum of ve-
looities, and the field is then described by an analogous system
of equations.
The scalar characteristic of the field is in the first, case given
by a system
of KLEIN", equations: L\-V, - (1/02) a2~,/at2 2 X__ F
and in the second case by aa analogous system: - k 0 k- -I ~4ik_yk
' I
y 2 ) I>
a - k
ri, 2 t2 2 F,
k-1 Vfkla 0

Dokl.Akad.Nauk, '110, fasc-3,351-354 (1956) CARD 2 / 2 PA - 1631
Here the meson f:teld is represented explicitly by the boundary
elements on the
W
basis of the results obtained by I.$.1,RZA11YC11,
Dokl.Akad.Nauk.No 4 (1956).
At first the system that corresponds to the mass spectrum is
investigated and
reduced to the onnonio form,, Here two cases must be
distinguished: Either all
roots of the chal7acteristie polynomial are simple, or there
exist also mul-
tiple roots. In the first case the sy.,3tem is divided into 11
single PROCA
systems, In the degenerated case the ordgine.1 system is
divided into p linked
systems. Both syntems are explicitly written down, AH p systems
of the same
type are obtained, it is sufficient to Inventigate one of them.
On this
occasion a reprenentation of the field is obtained by retarded
potentials.
The structure of the meson field of the linked system is
explicitly written
down.
Next, the field vrith the velocity spectrum is investigated.
Also here the matrix
is reduced to tho canonio form. If the orrespondirg polynomial
has simple
roots, the original system of equations is divided into N
systems. In the case
of multiple rootii p linked systems are obtained as above. One
of them is
examined. The structure of the meson field with velocity
spectrum is explicitly
written down. In the end, a formula for the scalar field is
obtained with
utilization of the boundary elements.
INSTITUTION: Institute for Mathematl-3 and Mechanic
"V.I.ROMANOVSKIJ" of the
Academy of S~Ienco of the Uzbek SSR

SUBJECT USSIL / PHYSICS CARD 1 PA 1792
AUTHOR ARZANYCH, I. S.
TITLE The Representation of tho Neson Field by Retarded Potentials.
PERIODICAL Dokl.Akad.Naukp 110, faso.61 953-956 (1956)
Issued: 1 / 1957
--,A _91
The aim of this report is the integral representation of the vectors
E and H
of the electromagnetic, field as well as of the potentials T and A
with the hell?
of special retarding potentials which oorres-ond to KLEIN's operator
P
2_ k2 _ (1/02)a2/at2. Here the method for integral representation,
which wal)
employed in connection with other operators in the elasticity theory,
hydrody-
namice, and electrodynamics, was applied. With k a 0 the formulae of
MANELLIS
electrodynamics result from the formulae mentioned below, and the
second group
of the formulae for I and H then goes over into KIRCHHOFFtS formulae.
In con-
nection with the problems under investigation the integrodifferential
equationt)
of the boundary value problems belonging to ILEINIS equation are
constructed.
The retardation operator corresponding to the meson field is:
00 J, k
(q v(g,t-r/c) r2
v I t) a r(p,q) - k 10 V (q,t 0 dl
t
The following lemma applies: The field vector lv(q,t), which
satisfies the
equations ourl v and div 1'- 9 within -the domain Q + S, satisfies
also

Dokl.Akad.Nauk,110,faso.6,953-956 (19!~6) CARD 2 / 3 PA -
1792
2 2) 2 2 0
the equation 494v(p,t)w(k +(1/0 )a /at )f dQ + V our! P
v
with (P,t) P'(Sjt)~ dS -f fG(q,,t)j dQ
n v
and F(pvt) - ~ *"' x f-:"(sjt)j dS (,:I,t) dQ..
The following theorem then applies: The electromagnetic
meson field is
determined by its limiting elements In the following form:
-,!Pf -+ 4
47LE.,P, t). V dS - curl f n x ['E j dS + f In fdiv E 3 dS +
4 -->
H H -n- j 'H ~dS -
+ (1/0)(3/at) n x f'j dS, 49 (PI-o- V
4
curl n x H dS -n* x curl H dS,
f f 4)
and the potentials are determined by the following formulae:
2 24 1
k div E, k A . (i/c)A / at - curl H. On this occasion the
vectors
E and H are expressed by the limiting elements for the
potentials:

Dokl.Akad.Nauk, 110,fase.6,953-956 (19--L) CARD 3 / 3PA 1792
4XE - k n f-dS + (1/0)(a/at) ~ 'n x [cUri AdS -
2 f9
4
n A/at)dS + curl dS
( V + 0/08 at
4 4 x 2 + 1 2 -->
4xH n Vy + (k - ~~) A dS +
0 at 2
+V 4 4
Sourl A I dS -curl x (qcarl AdS
There fo owe the proof of this theorem and a conclusion drawn
therefrom. A
further theorem says that the funotion Ir which satiefiee the
equation
(,V 2 -k 2_(1/02) 02/at2) V a 0 is represented by its limiting
elements in the,
form: 4x?(P,t)- �T/anj dS - f [11] dS. The latter formula
introduces the
potential of a aimpfae layer and of a double layer, which at k -
0 go over into
NEWTON'S retarded potential.
INSTITUTION: Institute for Mathematics and Mechanics
11V.I.ROX0OVSKIJ11 of
the Aoaaemy of Science of the Uzbekian SSR.

ARZHANYXH, 1.3.
1
Field of a moving charge. Dokle AN Uz. SSH no-7:5-10 157.
(MIRA 11:5)
l.Inatitut matematiki i meldianiki AN UzSSR im. V.I.
Romanovskogo.
Predstavlano akademikom AN 1JzSSR 8 U. Umarovym.
(Electric, fieldu3 (Relativity (]Physics))

ARZFIANYKH I"8 h".- -
Intririsic fields around moving chargoso Dokl, AN Uz. SBR
11:5-9
157. (MIRA 11:5)
1.Institut matematiki i mekhaniki im. V.I. Romanovskogo AN Uz6-
Predsiavlano akad. AN UzSSR SX. Umamrovym. I
(Blectric chsrCe and distribution)
(Electromagnetic theory)
0

ARZHANYKH, I.S.
Vortex-motion equations of paly-tropic gaseb. Trudy Inst.
mate, i
makh. AN Uz. SSR no,,219.29-~14 157. (MIRA 11:6)
(Differential equations. Partial (Vortex motionD

ARZHANYXH. I.S.
OOW9,f_of the theorem on the universal meaning of contact
,, ~razieformatione, Trudr Inst, mate i makho AN Uze SSR noe2105-39
157. (MIRA llt6)
(Transformations (Mathematics)) (Differential equations partial)

ARZITAITYKH Wj.-, DOLDINSKIT, G.I.; 3ELITIN. A.I.
F
A sig:21ficant error in desigme of some pneu-tic cotton harvesters.
Izv. AN Uz.SSR. Ser.tekh.ne,dc rio.2-.59-62 158. (MIRA 3-1: 9)
1.4stitut matemti)d i makhaniki Ime VJ# Romnovskogo AN UzSSR.
(Cotton picking machinery)

,I- -- 0, Rm P.M. -P.. I,as, ...
Mathomtleal extension of meebanics. Dokl. AN Uzb, SSR
U00:5-3-1
1580 (mm 11W
1. lustitut mtematiki i nekhaniki im. V.I. Romnovskogo
AN USSM
Predsitavleno WmdemikDm !H U&SSR T.W. lary-ftyasovym.
(YAthematical physios) (Mach4nies)

ARMAJFMO I.S.
Notion equations of the ooleotromagnetio dipole. DDkI. AN
Us.=
Tko*5:-5-8 158. (xm nt8)
1. Institut matenstild i neldianiki im, V.I. Romanovskogo
AN UsSSIR.
Predstavleno Wcademikon AN VwSSR S,U. Umarovym.
(Zipole moments)

ARZHiLNMI, I.S.
Characteristica of quantum equations. Dokl.AN Uz.;=
n0-915-9
'58,. (KIRA 11:12)
le Ihatitut matematiki i makhEkAlki Im. V.I*Romanovskogo,
Predstavleno
akademikom AN UzSSR TeNelary-liiyarovym.
Nuautuzi theorp

16(1),24(5)
AUTHORs Arzhanykh,I.S. SOV/166-59--3-8/11
TITLE: Quantum Mechanics as an Analytic Continuation of
Classical
Mechanics
PERIODICALt Izvestiya Akademii nauk Uzbekakoy SSR, Seriya
fiziko-
matematicheskikh nauk, 1959, Nr 39 pp 52-64 (USSR)
ABSTRACT: The equation F(w) = 0, where
a IV 'D W ~W
(4) F(w)E -5-t + H(tjX , . . .' -P~- )
11""xn' -~~-X- X
1 n
and H is the canonical potential of Hamilton, is satisfied
strongly in analytic dynamics and hydrodynamics, while it
holds
only approximately in quantum mechanics. The author asks the
question: Is it possible to construct an operator K( ")
which
for functions of the claos C 1 from the equation K(a) - 0
would
lead to the strong equation F(w) - 0 and from the equation
91(0) - 0, where
(7) 1( t2 dt Tr2dwf .. fK( 4>)dq
j f Lx-
Card 1/3 ti 'A'1

quantum Mechanics as an Analytic Continuation of
SOV/166-59-3-8/11
Classical Mechanics
for ~C C2 would lead, to the Schr6dinger equation
h 'a
+ H 0,
(8) 3: -~-t
where H* is an oper'alor of quantum mechanics?
The question is answarea in the affirmative. K has to be
chosen
in.the form
UL ~Sj + 2
(9) KM) a - 7N-t 7W w II(t'x '...'x ... OPn)
W 1 ns P1 9
and the impulse field in the form..
L=
(10) P DA,
VI-9 - ~q w
The Hamilton-Jaoobi equation FK = 0 arises from R(S)j) - 0
by an addition of the Condition LL(t,x 11 ... PxnW) = 0,
while
(8) follows from SI = 0 with the following substitution
(12) 0-'4Kt,x1P...'x )Oxp( w
Card 2/3 n ih

Quantum Mechanics as an Analytic Continuation
SOV/166-59-3..8/11
Classical Mechanics
Then the author considers in relativistic approximation
systems of particles which reciprocate, further the
relativistic
equation of an electron, and the equation of
Gordon-Schrbdinger.
He shows the universality of the proposed algorithm and
there-
with it is proved that the quantum mechanics can be
understood
as art analytic continuation of the classical mechanic6.
There are 7 references, 6 of which are Soviet, and 1
American.
ASSOCIATIONsInstitut mekhaniki AN Uz SSR (Institute of
Mechanics,AS Uz SSR)
SUBITITTEDt December 16, 1958
Card 3/3

30(l),16(2) 06558
AUTHORSi -..Arzhanykh,I.S.!-Rozenblyuni,.L.M.,
SOV/166-59-4-9/10
dsman,M.I.,and Kellbert,S.L.
TITLEt On the Threefold Treatment of the Cotton Shrub by the
Cotton
Harvester With Vertical Spindles
,,.:PERIODICAL: Izvestiya Akademii nauk Uzbokskoy SSR, Seriya
fiziko-
matematicheskikh nauk,1959, Nr 4, pp 64-69 (USSR)
ABSTRACTt The authors describe the results of experiments
carried out on
November 17-28,1958 on the fields of the Scientific Research
Institute for Mechanization and Electrification of the AS Kh H
Uz SSR by the laboratory of mechanical cotton harvesters of the
Institute of Mathematics and Mechanics at the AS Uz SSR, in
order
to examine the working,of -the new cotton harvesters
SXhM-48M-ANT-1
and 2 which have.ar- additional pair of spindle barrels and
perform
a threefold treatment of thet shrub. The maximal harvest
(88.9%)
reached SKhM-48M-ANT-1. Beceuse of the satisfactory results
corresponding agricultural machines shall be constructed. The
question of the multiple treatment of the shrub was firstly
treated by L.M,11ozenblyum :Lr]. 1949 (patent Nr 86 314, 1949).
There are 3 tables and 3 f:Lgures.
ASSOCIATIONsInstitut mekhaniki AN Uz SSR. (Institute of
Mechanics AS Uz SSR)
SUBMITTED: April 2, 1959
Card 1/1

ARZTWTMI. 1. S.
Boundary conditions of quantum mochaulca. Dole-I.All
U2.SSR
no.8:7-10, 159. (1411LA 3.1:21)
1. lnnti~ut All UzSSR. Predstavlono akademikom All
UzGSR S.V.
Starodubtsevym.
((~aantum theory)

ARZHANYK-H.-I.S.;GUKIROV, Sh.A.
Gonditione governing the applicability of a potential
method for
integrating equations for that motion of nonhomologous
systems in
a case where the Hamilton function clearly depends on
time. Dokl.
AN TJ&.SSR no.10:3-6 '59 (Him 13:3)
1. Institut mekhaniki AN UzSSR i Institut inzheDerov
irrigateii i
mekbanizatail sel'skogo khotyaystva. Predstavleno
akadismikom AN
UzSSR T.K. 7-ary-Kiyattovym.
(Differential equations)

?4 (5)
AUTHOR: --JXzh~,nyk~, I- S. SOV/20-125-6-10/61
TITLE: On the Differential Equations in the Motion of a
Meson Charge
(0 differentsiallnykh urayneniyakh dyizheniya mezonnogo
zaryada)
PERIODICAL: Doklady Akademii nnuk SSSR, 1959, Vol 125, Nr 6,
pp 1215-1218 (USSR)
ABSTRACT: A meson with the rast mass ix and the charge 6 is
assumed to
move with the valo,,,ity v r
and to produce the charge
densit.v 9(t,'P), the curx~.nt J(t,r), and the
electromagnetic
-* --4
field E, H. The elsotromagnetic field is determined by
meanei
of the scalar potential and the vectorial potentiall froal
the Proca-equations J! grad diy K'~ +
Ot
-40 1 2-4 1
H - curl 1, curl 11 - - k A + - j where k - 27VLc/h
0 at c
holds. The motion satisfies the law T T
dt Y91F) - TI-F
Card 1/5

On the Differential Equations in the 140tion of a
Meson Charge SOV/20-125-6-10/61
2(1 12 1.
T - -7 and the force I is determined by the
-/Ac 2
a
Lorentz formula. 'rho present paper is intended to determine
the quantities q, is I A, Ej H from the system consisting
of the above-mentioned equationa. The author here employs tile
methods he developed in one of his earlier papers (Ref 1).
If t e potentials satisfy the Lorentz condition
91 1 -4
+ diY A - 0 1. tile continuity equation 21 + div 0
9t
1.9 satisfied. The proof of this assertion is briofly
outlined..
Next, expressions aret derived :or and Z.
2
grad
v2/c2 W)
VT) c
Also a partial ailferential equation for determining the
arbitrary function. w is written down. In the second part of
this article the author gives an example for the application
Card 2/5 of the equations deduced in the first part. The
"solving

On the Dif1perential Equations in the Motion of a
SOV/20-125-6-10/61
Mason Charge
equations" are written down in spherical coordinates, and the
functions w and '4 iire assumed to depend only on the distance
up to a fixed pointt vr ' v(r), v9 - 0, v, - 0 (radial motiod
of the meson). Besiaes, the motion is assumed to develop with
sufficient slowness (v2 /c2) - 0. Under these conditions
is found for the potentials .14 v2 + const,
A v dwA 2 &
9 A0 = 01 Ay 0; for the electromagnetic
r d
field E E E 0, H = H H 0, for thiB
r F r5 .0 . r .6 - Y -
Lorentz force F = EE - 2,Ua2 P e- FT 0, and for the
r :r r5
2 2
charge density 3 = div I + k2j
r 4~r2 2
Card 3/5

On the Differential Equations in the Motion of a
SOV/20-125-6-10/61
Meson Charge
At the distance r A-1 -!!-from the fixed point, which may be
0 77 1AC
considered to be the center of the atomic nucleus, density
becomes equal to zero, and with a further increase of the
effective radius of the meson, even an unreal function. The
sphere with the radius r0 may be described as an
exchange-zone.
This zone is located entirely in the interior of the nucleus.
.According to the here discussed scheme of the slow motion
of a
meson, the force acting upon this meson is inversely
prolprtioral
to the 5. power of the distance as calculated from the
nucle&r
center. In the relativistic case the Yukava-force is one of
the
particular solutions. There are 2 Soviet references.
ASSOCIATION: Institut matematiki i indffimAd imerA V. 1.
Romanovskogo Akademii
nauk UzSSR (Institute for Mathematics and Mechanics imeni
V. I. Romanovskiy of the Academy of Sciences of the
UzbekSSR)
Card 4/5

On the Differential Equations in the Motion of a
SOV/20-125-6-le,/61
. Meson Charge
PIMENTEDi January 8, 1959, by N. N. Bogolyubov, Academician
SUBMITTED.- October 12, 1957
Card 5/5

24 (5)
'AUTHOR: krzhanylth, I. S. SOV/20-126-1-11/62
TITLEt An Algorithm of Quantum Mechanics (Ob odnom algorifme
kvantovoy makhaniki)
PERIODICAL: Doklady Akademii nauk SSSRI 1959, Vol 126, Nr 1,
PP 45-40 (USSR)
ABSTRACTs � 1i Tho necessity of the algorithm: The problems of
classical
mechanics and quautum machanics are solved by different
methods.
This difference is principally caused by the fact that in the
former case the partial. differential equation (of first
dw LK aw.
order) by Hamilton-Jakabi Ff + H(tp q1t ... v qnp clql P ...
5q 11
must be integrated, in the latter case the Sohr6dinger
equation (of second order) Q- ~ + 0. The method by
i Ot
Dirac (Refs 3, 4, 5) is only applicable to one single particle,
and leads to a system of equations of the Schr6dinger type.
Other procedures give even more complicated equations in the
relativistic case. Therofore, the problem has existed for a
Card 1/4 long time which structure the operator A has in the

Algorithm of Quantum Mechanics SOV/20-126-1-11/62
relativistic case. Such a universal algorithm, however, is
of essential importance to the further development of
quantum mechanics. This universal algorithm is to facilitate,
in all oases, the construction of the operator ?e nf the
equation (h J- + 0 from the function H of Hamilton-
i at
Jakobilo theory. It is more convenient to set the problem
withLn
a larger scopep namely concerning the construction of a
universal algorithm which delivers both the equations of
classical mechanics and those of quantum mechanics. This
producen a synthesis of classical and quantum mechanics making
it clear where there is the difference and the connection
between the Hamilton-Ja-kobi and the Schr6dinger equations.
Such an algorithm is pointed out in the prenent paper.
� 2: The author constructs the operator K over the functions
�a(tlwvql, *qn) of a certain family ('Rr:Cl for classical
mechanics :n*d QC-C2fox, quantum mechanics).-This operator X
has the following propertiest In the realization of theowkind
of conditions connected, witb the operator K, the equations of
Card 2/4 classical mechanics muzit resultj but in the
realization of

-An kUcrithm of Quantum Mechanics SOV/20-126-1-11/62
the other conditions, the Sohrbdinger equation is the result,
For the matter of sho:i.,tnees the author puts T equal to
to;~ /P qP j and chooses the operator
aRICI t' W - ~Q /a W, Qr to 0 q1
X in the f orm: KOZ ) ;E - rw + w H(t tql g W W,
By means of this operator, he then conetructs the functional
It2dt I w'dw K(Q)dQ . (Q) denotes the reference
I W1
configuration space dO - g(qlp ... jqn)dq 1 ... dqn. The
algorithm
suggested here consists of the following: The conditions
X(S?) - 01 Q (t,w,q,,...,qn 0 apply to classical mechanics,
and the conditions 61 - 0, 2 4r(t,q,, ... 1q n)exp(-iw/h) to
qmtLn
madmdIcs. The HamIlton-JakoU cqxdkn is equivalent to the
conditiona
K(2) - 0, S? (t,w,q, p ... qq n) ot 0, and the equation
h 0 0 corresponds to the condition that the
! Tt + Y) 4,
Q
functional I, in the prosence of a periodicity, is periodical
Card 3/4 with the period 2wh with respect to the effect w. The
formulas

AA Alj~orithm of Quantum Mechanics
ASSOCIATION:
PRESENTEDt
SUBMITTED:
SOV/20-126-1-11/62
for the classical and J'or the quantum-mochanical case are
then explicitly derived; an expression for it in the quantum-
mechanical case is also indicated. Finally, the universal
character of the algorithm introduced is pointed out in the
following 3 examples: 11"chr6dinger nquation, relativistic
equation, system of interacting particles. There are
7 Soviet references.
Sr 4 iatskiy gosudarstvonnyy universitet im. V. 1. Lenina
~Ce%fflrdq Asian state University imeni V. 1. Lenin)
January 15) 1959, by N. N. Bogolyubov, Academician
December 27, 1958
Card 4/4

GERUNYIM, D.G. - ARSHASM I S otv."&.; YAKOVNIMO, YO.P.,
rid.izd-~va,- 'GORIKOYAYi, Zi., tak:hn.red.
[1-l'olynomials of optimum approxims,tion whose coefficients are
bimnd ikq by linear relationOdpoll Polinomy nalluchahego pribli-
zheniia, koeffitsienty kotorykh tiviazany lineinymi zavisimostiami,
Tashkent, Izd-vo Akad.naruk Uxbekvkoi SSR. 1960. 235 P.
(MIRA 14:4)
I., Chlon-korrespondent AN UzSM (for Ar2hanykh).
(Polynomials)

FIHME I BOOK EmorrATioN SOV/4796
Akademiya nauk: Uzbeksoy SSR, Tashkent. lastitut matematiki i
mckhaniki
Issledovaniya po'matematicheekamu analizu i mektanike v
Uzbekistane (Research in
Mathematical Analysis and Mechanics ia Uzbellstan) Tashkent,
Izd-vo AN
Uzbeksko~ SSE, 1960- 259 P- Errata alip inserted. 1,000 copies
printed.
Sponsoring Agency: Akadestiya nauk Uzbeksltcy SSE. Institut
matematiki i mechaniki
imeni. V.I. Romanovskogo.
Resp,v.Ed.: .1.8. Arzhanykh, Corresponding Meidber, Academy of
Sciences UzSSR; Ed.:
I.G. Gaysinskaya; Tech. Ed.: Z.P. Gorlkovaya.
PURPOSE: Thi-s collectim of articles la intended for
mathematiclaw, mechanics, A
aspirantai, and students taking advanced courses in divisions of
physics and
mathematics at universities and pedagcg:Lcal schools of higher
education.
COVERAGE: Thet collectio~tcontains 17 artic-les dealing vith the
results of investi-
gations on the theory of integrating dieferential equations im
mathematical
phyaics and mechsaicsi, the theory of numbers, e~nd the problem
of tho beat approx..
imation of l'unctions. Individual articles discuss elasticity.,
flow close to a
GsFA 47(4-

Research In Mathematical Analysis (Cont.) SOV/4796
rotating disk, transverse vibrations of beams,, motion of an
automobile after
imixict, the.mial stress, etc. No persom%lities are
mentioned. References
accompany 14 articles.
TABLE OF CONMITS:
1. Ar2.hanykh, I.Se On the Deformation of Space-Time Under
the Action of
an lre:e~,r&~~-n-etic Field 3
2. Bondareako, B.A. On Oradient and Vortical Solutions of
Dynamic Equations
of the Theory of Elasticity 17
3. Grebenyuk, D.G. On Cortain Weighted Polyncmials of the
Degree;pn, the
Least Deviating From Zero Within the (-- , +- ', Interval,
Whose,Coef-
ficients are Connected by Several Lineex Relationships 30
4. Grebenyuk),D.G. On Polyncmials of Several Variables,
Whose Coefficients
are 06nnect-ecTly Severs-1 Linear Relationships, the Least
Deviating From
a Given Funttion. in a Certain Domain (D) 70
5- Grbbenyuk; D.G. On the Minimum of Certain Integrals With
Infinite
144dto of Integration 84

7, 3,?o S/044/61/000/011/002/049
C111 0444
AUTHOR: C_-A:L-zhanyj5h~~_
TITLE% On the deformation ol' the time-space under the
influence
of the el9otro-magnetic field
PERIODICAL:; Reforativnyy zhurnal, Idatematika, no. 11, 1961,
57,
abstract lIA398("Isel.ed. po matem. analizu i makhanike
v Uzhokistane". Tashlent, AW UzSSR, 1960, 5 - 16)
TEXT: The present article contains tranformation formulas for
the quantities of the elootromagnittic field under
transformations of
the coordinates, bekag more genertl than the Lorentz ones.
The author
assumes thEtt the existence of the electromagnetic field
leads to chan_
ges of the properties of the spaco, being analogous to the
proces She:
in the elastic medium, and he defines the "deformation tensor
of t
space", the "tension tensor of th4i sPace", as well as the
correspond-
ing "Lam& equations".
Abstracter-Is note3 Complete translation]
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26531
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A1o4/A133
AUTHORS: Arzhanykh, 1. S., CorrespondIng Member of the Academy
of Sciences of
th(TIVOM-Rand Nasrotdinov, S. S.
TITLE: Surface stresses of isotropic: elastic solids.
PERIODICAL: Akademiya nnk UzSSR, Izvestiya. Seriya
tekhnicheskikh nauk, no. 6
1960, 27 - 35.
TEXT: The authors referdng to the computation method for the
determination
of surface stresses on elastic solids (lief. 1: 1. S.
Arzhanykh, Izvestiya Akade-
mii nauk UzSSR, 1952, no. 2) give a detailed dosoription of the
mathematical pro-
cess of this problem explaining it by examples. Stresses are
determined accord-
ing to the Hooke's law:
P. -Adiv 0 + 2,ae.
pon -,ae W, (n m - 1 s 2 p 30"
u v w
where div U = U + a- + a + e + volumetric expansion; pmn -
stress
ex ay r-Z 11 22 33
Card 1/8

Surface.stressas of isotropic elastic solids
26531
S/167/60/000/006/001/003
Aio4/.Ai33
tensor component; eWn - strain tensor component and A - Lame
constant. At the
investigation of th surface I - I ( ot, P) with coordinates
relevant to the our-
va-ture lines, Mu,se basic metric forms [Ref. 2: S. P. Finikov,
Teoriya poverldmos-
tc.y, M.-L.. GORTI, 1953] are derived
- 2 -2 2 -2 - 2
I dr - r,,. dcK + rp do
-o2
r
C( 2 (N 2
II R d(S + dV (4)
1
2 -02
r r
48
III I dn = dcK + d~
42 2 42- 2
where rc., A rp, -,B - Lame coefficient,
4 C-0
r5 r., r curvature radii.
%2 AB3
rp
1
and 3
T1 A B
The joint introduction of orthogonal
Card 2/8

26531
S/167/60/000/006/001/003'%.
Surface stresses of isotropic elastic solids Aio4/Al33
vector units n . -AB [fa, i1] which are the basic mobile
surface trieder
and along which the external force F is
4
r
F F Ck + F n (6)
1 A + P2 B 3
results in the permutation.,
r r
Ot + v -13+
U A B wn.
(7)
The surface stress tensor components on the tangent plane are
determined by the
surface force F
P13 = p31 = F1
P23 - P32 = P2 (8)
p F
33 = 3
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26531
s/167/6o/ooo/oo6/ooI/003
Surface stresses of isotropic elastio solids Aio4/AI33
Limiting expressions for strain components are based on
equidistant surfaces
Z) C~' S ) + zn (9)
where mean surfaae of elaztic solids and z - dimensions of the
seg-
ment along the normal at the point (OL, 0 ) and jointly with cX,
P forming the or-
thogonal curvilinear system of coordinates. The obtained metric
form is
-1 2 - 2 2-2 2
dr* . dr + 2z, (dr, dn) 4- z dn + dz (10)
which, basett on Formula (4), results in
~- 2 2 2 2 2 2 2
dr* A* da + B* d~ + C* dz (11)
where . A* - A (I ) , B* - B (1 - iz;)and C* = 1 (12)
R1
Ck--culation results of strain tensor components and (z-- 0)
provide the expres-
sion3
card 4/8

26531
s/167/6o/boo/oo6/oo1/oo3
Surface stresses of isotropic elastic solids A1o4A133
.1 ~u + v BA W
11 A 'a o, AB
m +
12 B'DP A A ~d
e .1 -& + u W w
22 B Fp AB FM i~ (13)
e du- + Ia w+ U
13 6n A FCk R 1
w +v
23 'SXn
e +B bp R2
'aw
33 ?Fn
~ihere e11,e 22 and e33 -relative expansions (constrictions) and e
121 e13 and e23
ft displacements equal to the angle variations between the
coordinates: from which
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26531
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Surface stresses of isotropic elastic solids Aio4/AI33
the volumetrio expansion coefficients
1- ~ Bu + I -d(Av). 1 1
div 'U - + T-) w + (14)
AB WM AB 7p- (F; 2
are derived. The determination of stresses on normal planes is
based on formula
(1) and expressed by p33 = ~)div 'U + 2,ue 33
resulting with the aid of Formulae (8), (13) and (14) in
'dw F 3 91. [L ANI + 1 ~) (Av ) ~' ~ 1 )1] (15)
Fn 7L + 2,a + 2/k AB r6a E 7F R, PL2
div 'U - F3 + 2A L XW + L 'Cl (AV) - (.L + 1
k, 1
?L + + 2/4 AB 'ft AB 7BT- R
By introduction of formula (15) into formula (1)
ca:,d 6/ 8

26531
8/167/60/000/006/001/003
Surface stressed of isotropic elastic solids Aio4/Al33
p U 'A F + 2 Wu r1 Lu '. !r- s A - V, + 6 1 Ly + m- ?-B - w
11 9~ + 2ILL 3 u(A+ 2,a) [A- M 4B R_ (B 'DIN AB IM R
1 2
A V
p v (16)
12 = i ITO W + LA (0 (B
?L 2'hp. ~,Y , u + 16 (1 'Lu + v A
P22 = _T+_21i P3 + F(A + 'gtk) E T~ ' -0 -a R A Vd~ AB RE-)]
P 2 1 -
on which the Hook's law for surfaces of elastic isotropic solids is
based. a-
amples Include a oone*and a oylinder of arbitrary configuration.
Analogous data
are derived for an elipsold by radius - vector of any point on the
surface,
linear surface element and the Lame coefficient based on formula
(5). In the caso
of a catenoid and a pseudosphere the linear element is replaced by
the rirst qua-
dratie form, whereas all other points of the computation process
remain thesame.
In his conclusion the author states that the use of formula (16)
enables: I The
computation of surface stresses of ela,stio solids by measuring the
coRponen a of
the surface displacement vector by available instruments. 2. To
establish the
limit shell theory. There are 2 figures and 3 Soviet-bloc references.
Card 7/8

26531
s/167/60/000/006/001/03 X .1
Surface stressed of isotiropio elastic solids A1o4./A133
ASSOCIATION: Institut, mekhaniki Akademii nauk UzSSR (Institute
of Mecanics of
the Acadewl of Sciences of the UzSSR)
SUBMWED: April 7, 1960
Card 8/8

S/044/61/000/007/022/055
CIII/C222
AUTHORs Arzhanykh, I.S.
TITM On new stability inequalities
PERIODICAM Referativnyy zhurnal.Matematika, no. 7P 1961t 41o
abstract 7 B 176. (I'Vaes. Mozhvuz. konferentsiya po teorii
i metodam rasoheta nelineyn elektr. teepey. no. 7" Tashkent,
1960, 46-54)
TEXTt The author constructs an algorithm which leads to necessary
and
sufficient conditions (in the form of inequalities) that all
roots of
the secular equation dot (Ax + B) - 0 in the unit circle or after
a
fractional linear transformation lie in the left halfplane. A
comparison
with the criterion of Routh-Hurwitz is missing.
[Abstraoterts note i Complete translation.1
28
Card 11/1

ARZHIUMH, I. S.
"On the chain systems of the theory of nonlinear oscillations."
Paper presented at the Intl. S~nnposium on Nonlinenr
vibrations, Kiev, USSR,
9-19 Sep 61
Institute of Mathematics of the Academy of Scienqes of the
Uzbeklan SSR,
Tashkent

KA,BULOV, Vasil Kabulovich, kand. tokhn. nauk; MZHAffjH,-1.9.,'prof.,
otv. red.; KISEIZVAp V.N., red.; GORIKOVAYAj ZoPes tekbno red,
(Integral equations of the equilibrium type and their applica-
tion to the dynamic design of rods and boams) Integrallmye
uravneniia tipa balansa i ikh primenenie k dinamicheskomu raBchetu
sterzbnei i balok. Tashkentp Izd-vo kkad. nauk Uzbekskoi SSR,
1961. 185 P. (MM 15:4)
1. Zameatitell diroktora Instituts, matematiki im. V.I.Romanovskogo
Akademii nauk Uzbekskoy SSR po Vychislitellnomu tsentru (for
Kabulov). 2. Chlon-korrespondent Akademii nauk Uzbeksko SSR (for
Arzhanykh).(Integral equations) (Strength of materials
I

S11661611DO010021005IOD'i

B1 12/E1202

IOR: Arnhany'kh I. Corres,,)ondin, ber of 'he Ac-idemy of
: Mein
ZT7

Scienceo, j-.SSR

"ITIZ: Certain fiets of differential equations
making possible the

application of the method. of potential
integration.

FERTODICAL: Izvestiyft Akademii naukUzSSR. Seriya f
iziko-'natemat icheskiikh

nauk, no,, 2, 19051, 52-58

TLXT: 'The
author studies sets of ordinary differential equations to -which

the
integration method of Hamilton and Jacobi odn be applied. Thus, he

completes a number.of studiep on 6ets of diffei7ential equations
wihich can

be solved by potential-methods. First, 'he author
explains .-,hy the

Inmilton-Jacobi ihtear-~htion method -s a
potential method: in the

L 'Abotitution: P,( ) . appears as
F.amilton-Jacobl El F a F/ ak aw/ax, v

po tential of the vector P
A(P). The possibility of -uch a substitution is

tantamount to the
existence of the followina set of equations:

Card 1/3

....... . . . . . . . . .----- -----
13/1 66j6l/OOO/OO2/0051'-OC)6*
I
Certain sets of differential equations ... B112/B2O2
X21 . 811/ayX, yX Ar/a):X,' H,- -F4V(F), V(F) kXOF/a,~X. The
followinr,
relation - (F) a[HI/Ox where [H] denotes the Hamiltonian in which
the
-A X
variables x* are expreneed by the variables -x-, exists betvie'en
the
X d 8F X3F
D L grangp and 'he Hamiltonian H.
Eiler Lag expressfton: EX(F) '- dt 8:~ ex
The author considers the following cases: 1) set E X(F) 0. it is
tantamount to a[HI/3x 0, I.e., h const %hich can be used to
determine t,,,e potential ri. 2.) Set + k P,%(F) = 0, k = const ;
it leads to
the equation: + k,.,9 h = const. for the determination of W. 3) set:
d
7F P, (F) ~ k; -XFL ) +P, V (F) =:! 0,
,.7bere kX- conut. The equ, t i t),, f o:- `ic (RI-e.-nination of
the potertial VI
tilen reads: 'T + I--
+ h. 4) Set:
Card 2/3

S/166"1'3-0/DO2/005/0D'
Certain sets of equations ... 1
d Ex (F) + UPX (P) + V(F) - 0,
Ft -FU--
+ MP, (P)
n. const., U=U(xl,...,-,-n from wh4ch it re3ults that ',H 2
+ Ur
5) Set: d .I I -~- (E, (F) + UP~ (F) + ' 'U V (F) + V(,-) . 0,
7F d 6 U de
wt
lor which the equation. LH] + Un = hU +'Z1 x 9 + i can be written.
There
are 3 Sovlet-bloc reterences.
ASSOCIATION: Inctitut matemntiki im. V. 1. Romanovskogo A" UzSSR
(Institute of Mathematics imeni V. I. Romanovskiy of the
Academy of Sciences UzSSR)
SUBMITTED: JulV 18,,1960
Card 3/3

ARZIIANYK
Equation-of quatitum mechanics iwthwoa.3e of geometric
coupling.
Izv. AN-Ui.SSR:%~,'Ser-~ fit*-nat, nauk 3ill.21 161.
(MIRA 14:8)
1. Institut matematiki imeni"i.1,Roxanovskogo, AN UzSSR.
Chlen-
korrespondent AN UzSSR.
(Quantum theory) (Differential equations

i ARZIIMJYIWN I.S. .
High-order kinotic equations of' a rank larger than
gero, Sbor.
nauch.-issl. rab. ITI no.15.,1"1-29 162, (MM 16:9)

8/044/62/000/010/013/042
B1130/B186
AUTHOR: Arzhanykh, 1. S.
TITLE: Algorithm of the analytical extension of mechanics
.PERIODICAL: Referativnyy zhurnal. Matematikal no. 10, 1962, 55-56,
abstract 1OB255 (Tr. In-%a matom. LN UzSSR, no. 23, 1961, 1-33)
TEXT: -The article is devoted to the problem*6f "whether mechanics
has
reached its highest state in the qualitative transition from the
classical
(including the relativistic) to the quantum content ?" The author
answerb
this questiDn in the negative, pointing to the-algorithm involved in
deriving quantum mechanical equations and as well as integer ranks
of
hyperquantum mechanical equations. For this purpose the X operator
is
constructed over the functions
12Y. XI.- xa.T)
-Pec 1 for classical, and PceC 2 for quantura mechanics)
x1 x
K(9)= - TW + WIM (t xn,
6ard 3/3

S/044/62/000/010/013/042*
Algorithm of the analytical ... B18O/B186
Here
012
7, j-j. W X
H is the Hamilton function. Then the functional
dt So
: d, If (0) dD,
is constructed, where (D) is a fixed region of configurAtion
space and
dD - qdx1...dxn . The algorithm rests upon the fact that, for
classical
mechanics
Q(tIXI#----In'W)7 0. (1)
and for quantum
/W\
x.)eXpOo., (2).
Taking a Haniltonian in the form
Card 2/3

S/044/62/000/010/013/042
Algorithm of the analytical B180/B166
11 - V (1, + E A, (1, xi..... xn) P.
V
+ ~- Tj x"I P'P
2
the author shows that (1) leads to.the Hamilton-Jacobi equation
and (2)
to the Schrlddinger equation, and also that the characteristics of
the
equation 6J(6) - 0 are solutions to the Hamilton-Jacobi equation.
He uses
this algorithm to consider relativistic equations of a system of
charges,
and derives an equivalent system of quantum oquations. Using F 1
as the
initial operator of the quantum mechanics, and'applying its own
algorithm, he derives a hyperquantum mechanics-of the first rankv
the
equations of which are the extremal conditions of the functions
JAO) -S,'diff dj..;d,,
LV; S(Dj ... V'(0) "dX' dXA'
Xj (9) - -,Fl (w1) Q,3,.
The same procedure leads to hyper-quantum mechanical equations of
different integer ranks. [Abstracter's note: Complete tr&nslation-I
Card 3/3

00
S/044/62/000/009/031/069
A0601000
AUTHORS: Arzlianykh, I. S., Nasretdinov, S. S.
------------------------
TITLE: The limiting theory of shells
PERIODICAL: Referativnyy zhurnal, Matematika, no. 9,. 1962, 61,
abstract 9B291
("Tr, in-ta matem. AN USSR% 19(-;1, no. 2.3, 53 - 64)
With the aid of the equation of eldstic equilibrium the Lamb
strain
coefficients are expressed in terms of the dinplacements, their
derivatives, and
the external load. Variational equations are derived for the
6q~iilibrium and
the boundary conditions of the theory of the limitingahell, 1,e,
of,a shell one
of whose dimensions tends to zero.
A. N. Tyumanok
[Abrtracter's note: Complete translation]
CAi-d 1/1

4145-1.
s/o44/62-/000/009/028/069
A060/A 000
AUTHORi Arzhanykh, I. S.
.TITLE: The solution of the basic problem, of dynamics of the
mathematical
theory of elasticity in the domain of r.epresentations by the
method of fundamental functions
PF-RIODICAL: Referativnyy zhurnal, Matematika, no. 9, 1962, 60,
abstvict 9B285
C'Tr. Tashkentsk. un-ta", 1961, no*. 189, 3 - 16)
TEXT:--- Let the operator L be representable in the form L - A +
By wl,
w20 ... and AP A2. we shall denote the eigenftmetions and .the
eigenvalues of the
problem .(A + AB) w - 0.
Let us assume, moreover, that the operator A has an inverse, and
that the o~era-
tor B may be represented in the form B = MA, and that there
exists an operator C
-such that (Cw,,Awm) - Sn-
Under those assumptions it is possible to represent (at least
formally) the solu-
dard 1/2

s/o44/6PY000/009/028/069
The solution of the ... A060/AOOO
tion of the equation Lv = F by the series
00 (Cw
-1 \_-N 11SAA-1F)
V . A F + Ao I-j anwn; 'an - - ;~n .
n-1 7LC 1.
These notions are applied in the paper to the formal
construction of the solution f
to the equation
ctgrad div v rot rot V -,(s2+k2)v
under the condition that the vector v(X, Y. Z) is specified as
a function of X,
y, z in a bounded region, on the boundary of whic'.q
homogeneous'boundary condi-
tions are satirfied.
V. M. Babich
[Abstracter's notes -Complete translation)
Card 2/2

SM
Slel ()3161/022/004/002/014
(/0 3 2 Ij //32-) B1 I 6/B21 2
AUTHOR: Arzhanykh, I. S. (Tashkent)
TITLE: New inequalities for stabilit;r
PERIODICAL: Avtomatika i telemekhanika, v. 22f no. 4, 1961, 436-442
TEXT: New inequalities for stability are bro-aght which are based
on Schurts
theorem (Ref. 1: M. Kreyn and bl. Neymark. "Metod simmetricheskikh i
ermitovykh form v teorii otdeleniya korney algebraich,3skikli
uravneniy"
(Method of symmetrical and Hermitian forms aFplied to the theory of
separa-
tion of roots in algebraic equations.) Cos. nauchno-tekhnicheskoye
izd-vo
Ukrainy, Khar1kov, 1936). These inequalities are used to
investiaate the
stability of systems expressed by differential eqtiations which
have constant
or periodicalcoefficients. The following variational equations with
constant
or periodical coefficients are written down:
d~s n-
psrP (s n)
r. 5r
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2-170
S/1 03 61/022/Q04/002/014
New inequalities ... B1 XB21
The asyiatotic stability is solved with inequalities. These
inequalities
Cuarentee the position of the roots of the characteristic equation
located
in the left semi-plane in the unit circle, respectively. Usually,
the
criterions for the u)osition of these roots located in the left
semi-plane
are determined by inequalities of Ravs - Hurwitz. But this
criterion is not
favorable since it makes it necessary to write the equation in an
explicit
polynominal form. In this paper it is shown that the correspondina
inequalities may be obtained without.changing the equation into the
poly-
nominal form. The inequalities guaranteeing the roots to be within
the unit
circle are determined, and the small,changes. are shown, which are
necessary
to obtain the inequalities for the pc~sition of the roots within
the left
semi-plane. The characteristic equat,ion
f (Z) Cox" + cix"-, + - -+ C7'_jX + C.
(2)
ajjz+ b1s, ... , a,,,z -F b1n
I.Ax + BI 0. (2)
a,lx + bnl a
I nn-+ bnn
Card 2/5

New inequalities
21795
S/103/61/022/004/002/014
B116/B212
is written. According to Schur's theorem the necessary and
sufficient
conditions (so that all roots of (2) are located within the unit
circle) are
that the inequality
c0 0. (3)
is fulfilled and also the polynominal
n-1
f M (1) M
1W -a a x + 4 a (4)
0 n-1
determined by equation xfl(x) ~ cof(x) - Onf*()..) (5) with
fo(x) _ xnf(,/X) (6)
having the same property. This algorithmic rule is used to find
the stability
inequalities without representing f(x) in an explicit form. The
following*
theorem is formulated: The conditions that are necessary and
sufficient for
the roots of the equation (2) to be located.within the unit
circle are given
if the followint; inequalities are fulfilled:
Ic
lol ::-- Joni (24)
c(k)j::,~(k)' (25)t
Card 3/5 0 n-kj (k - 1 , 2, n

21795
2/103161 /02 2/004/00 2/014.
New inequalities ... 1116/B212
where the numbers c (k) and c (k) are determined by the formulas
0 n-k
k
CM -11M/'(X)--Lj' (JAx + B) p,_, (z) A + Bx] 9k-j(M)) (20)
"-k k1 dxk X-0 (20)
and
C'('k) _ I JM dk-1
(k- 11) JWx-k-1 ([A + DzI p~jx) [Ax + BI 9;_1(x)) (23) (23),
LO
respectively, and the polynominale pi and..qi successively from the
formulas
PO n) n)
(a qO (b (15) and
W + C(1) k xq~-, W
P't W - C lk)pk-x n- (17)o
_(17)
9k W - C(')qk--l W + C' *�k XP; W
rvapectively. If the system of variatio'nal equalione consists of
equations
of hit;her (than first) order it may be reduced to such a system
where each
equation will be of first order by introducinE; new unknowns. And,
now, the
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21795
New inequalities ...
s/lp3/61/022/004/002/014
13116/B212
inequalities shown above may be applied. Such a case may be
investigated
directly by calculating Schur's polynoodhal in a
corresponding manner. There
is 1 Soviet-bloc reference.
SUBMITTED: October 25, 1960
Card 5/5

ARZHANYKH Ivan Semenovich; KABULDV, V. K. , oi;v,
red. I SOKOLOVAO A. A. ,
rOK-; -G-0-ATKO-Vffi-, -Z. P. , tekhn. red.
(Canonical equations of a rank higher than zero
]Kanonichaskie
uravneniia ranga, bollah*go nulia. rashkent, Izd-vo
Akad. neuk
Usbakokoi SSR, 1962. 143 P. (MIRA 16t1)
1. Chlon-korrespondent Akademii nauk Uzbekskoy SSR
(for Kabulov).
(Equations)

PHASE I BOOK EXPLOITATION SOV/6137
Arzhanykh, I. S.
Obra-~;hcheniye volnovykh operatorov (Ipvexision of Wave
Operators)
Tashkent, Izd-vo AN Uzbekskoy SSR, 1962. 163 P. 1000 copies
printed.
Sponsoring Agency: Akademiya nauk Uzbekiskoy SSR. Institut
matematiklim. V. 1. Romanovskogo.
Resp. Ed.: V. K. Kabulov, Corre,sponding Member Academy of
Sciences UzSSR; Ed.: V. N. Kiseleva; Tech. Ed.: Z. P.
Gortkovaya.
PURPOSE: This book is intended for aspirants and scientists
working in the fields of theoretical and mathematical physics.
COVERAGE: The author presents the resulte of investigations
of the general equations of classical field theory, discusses
their various applications to electrodynamics, mesodynamics,
and the mathematical theory of elasticity, and sets up
Card 1/6

inversion of Wave Operators
SOV/6137
integrodifferential equations with tine delayed arguments
of boundary-value problems associated with wave operators.
The problem of wave-operator inversion is studied in its
classical formulation. In addition to purely mathematical
problems, attentionAs also given to thosephysical phen-
omena which can be reduced to a study of the corresponding
operators. No personalities are mentioned. There are
12 references, all Soviet (including 5 translations from
the English and German).
TABLE OF CONTENTS:
Author's Preface
Ch.. I. The Operator A - k2
5
1. Origination of Oreen's formula 8
2. Fundamental formula of the field theory 14
3. Fir3t boundary-value problem of the field theory 17
Card 2/6

ARZHANM9 I.S.
Potentials of quantum mechanics. Izv. AN Us. SSR. fiz.-mat.
nauk 6 no.40-11 162. (MM 150)
1. Inatitut matematiki imeni V.I.Romanovskogo AN UsSSR. "
(Quantum theory)

AN;Qh-avi jm*741-4 - I ----
ftL*j
ARZHANM I. S. and GUMEROV, Sh. A.
====;L -- --: ~
"Contitions for use of a method of the Hamilton-Jacobi type for
integrating
equations of motion of nonholonomic coneervative systems"
Report presented at the Conference on Applieel Stability-of-Motion
Theory and
Analytical Mechanics, Kazan Aviation Institute, 6-8 December 1962

ARZHANYKH$ 1*3.; KARD40V, A.U.
Conditions for the existence of entire integrals..
algebraic
wo'.th respect to velocity, in conservative scleronomous
sys-
temae Sbore bauch.-ioal. rab* TTI nool5tl63-171 162.
(WRA 16:9)

ARZHANYKHj I.S.; KARIMOV, A.U. (Tashkent)
"Linear and non-linear Integrals of equatlons of analytical
mechanics
resulting from the Invariance of the kinetic potential In
relation to
Lie groups"
report presented at the 2nd All-Union Congress on
Theoretical and
Applied Mechanicss Moscow, 29 January - 5 February 1964

ARZHANYXHI I. S.
ItCanonic equations of a rank greater than zero"
Report presented at the Conference on Applied Stability-of-Motion
Theory and
Analytical Mechanics, Kazan Aviation Institute, 6-8 December 1962

ARZHANM, I,S.
Now interprotatl-on of the spectral prDperties of the
hydrogen
atom. Izv. AN Us. SSR. Ser. Cis.-mat, nauk 6 no.5:86
162. (MIn 15;11)
1. Institut matematiki ime*'V.I. Rcnoanovskogo AN UzM.
(Hyq~rogen--Spectra)

3,11100 (2.70
/166/62/ooo/oo1/ooi/oo9
3125/B104
AUTHORt Arzhanykh,_j,_.~., Corresponding Member of the AS
Uzbokskaya
SOR
TITLE": Stntionary b9undarios of rravitation clusters
PERIODICALs Akademiya nauk Uzbek3koy SSR. Izveatiya. 8orlya
fiziko-
matematichoskikh nauk, no. 1, 1962, 5 - 10
TEXT: Three examples tire used to show the application of the
theory of
olanet figqires considered as gravitational cliisters. The
application of
thia theory i* mtich more extended than that of the clausical
theory of
liquid figures ( 0. Yu. Shmidt, Trudy goofizicheakoeo In3tituta
AN-S'W,
1950, no. 11). The influence of a cluster-on one of its
pArticloa of mass
m is equivalent to the attraction of a distributed mass of
density,,- and
the gravitational potential
U (x, Y, Z) )/R)d d, , d' (11
T
where f denotes the pravitation constant and T the bounding
volu,ne of the
cluster surface Z which is sought. Z is defined as the boundary
of all
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X
S/166/62/000/001/001/009
Stationary boundaries ... B125/B104
possible positions of the cluster particles In form of a
potential barrier:
'dr %I-
V2'~ 0 out3ido v2 _ 0 on.., v2 ;~' 0 inside/ i..From the cnorey
integral
of the relative motion the following expression is obtained:
)/R)d d,~, d ~+ Q(x2 + Y2 G where 6,; 2/2f to determine
T
at a given A. _C'j2/2f is changed into a more suitable form
4 2 2
(,,.(n R/R)dr ((Izrad , R)/R)dT + 2.'-2(x + y const (5). if
/ T r
1,A is constant the conditions f2