SCIENTIFIC ABSTRACT ZHUKOV, A.I. - ZHUKOV, A.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R002064920007-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 19, 2001
• Sequence Number: 7
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

ZRUKOV, A.I.; NAZAROV, A.S.
Sorption of ''titanium (TV) on the KU-1 cation exchangere MMr*
neorg, khim. 9 nos6tI465-1471 Je 163 (MIRA 17:8)
1. UrallskI7 politekhnichaskly institut imoni Kirova.

LEN8KTYj Vasiliy, Aleknelrevich; PAVLOV, Vasiliy Ivanovich (deceased];
ABRAMOV, N.N., retsenzent; ZIIUKOV, A.1.0 rettienzent;
YAKOVLEV, S.V.,, retsenzent-j-'MIACrEV',-T'.V.p retsenzent;
REZVIN~ Ye.Ye.:, retsenzent; TIKUNOV, B.S., kand. tekhn. nauk,
red.; MARTYNOV., A.P., red.
(Water supply and sewerage) Vodoanabzhenie i kanalizataiia.
Izd.3., perer. i dop. Moskva, Vysehaia shkola, 1964. 386 p.
(MIRA 17:10)

ZJIUKOV) A.I.; MIARKOVA, V.M.; PAVLINOV, R.V.
Sorption of pyridine by carboxylic resins. Zhur. prikl. khim.
37 no. 4:860-864 Ap 164. (MIRA 17:5)
1. Urallskiy politekhnicheakiy Institut Imeni Klrova.

Z.HUKOVP A61, Werdloir-sk)
41
MetaLlAted,-M"type glave slectrodo for moaauring pH, Zhur.fis.kbim.
37 J& '163o (MIRA 170)
1," fJrtLlsskiy politekhaicheakiy inatitut Imeni Kirova.

ZHUKOV, A.I.1 KAZANTSEV, Yeol.1 YAKOVIEV, A.V.
Separation ofthorium and uranium M) on tho rouin KU-2. Zhur.
prik-lo kh1m. 36 no.4x743-750 Ap 163. (MlU 16:7)
1. Urallokiy politekhniaheskly institut imeni Xlrova,,
(Thorlum) (Uranium) (Ion exchange reuim)

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F,031/E435
AUTHOR: Zhiikov,_ A.I. IG .1-4 10 0
TITLE: On.the Problem of the Convergence of Difference
Methods for the Solution of the Cauchy Problem
PERIODICAL: Akademiya nauk SSSR. Vychialitellnyy tsentr.
Vychisliteltnaya matematika; abornik, No.6, ig6o,
PP,,34-62
TEXTs As an introduction to the main thesis of his paper the
author considers the o e-dimensional heat conduction equation.
If an attempt is made to solve this equation over a rectangular
mesh whose step lengths do-not satisfy the stability conditions,
It is observed that the unstable solutions always oscillate about
the exact solution. Thus the question arises of the existence of
a functional space in which the solution of the difference equation
converges to that of the differential equation even when the
stability condition is broken. Such a space will be shown to
exist and in it the following fact is true: if, as the step lengths
of the mesh diminish, the difference equation tends to the
differential equation, then the solution of the difference equation
converges to the solution of the differential equation. In order
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On the Problem of ... E031/E435
to take advantage of this it is necessary to find a way of
transformin,~ the convergence in the functional space into
convergence of a more "usual" kind. In the sequel only equations
with constant coefficients will be considered, although
generalization to equations with coefficients depending on the
time and to systems of equations is not difficult, The difference
formulae discussed are not the most general. Consider the space
Z of all integral analytical functions (p(z) of the complex
variable z , which satisfy the condition
Z (P (z) Ck ealyll (k 1121
where the positive constants a and ck depend on the function T.
For any locally integrable function f(x) which increases not
faster than 5omei power of JxJ, as JxJ-4 00, a continuous linear
functional f tan be defined over the whole space Z . The term
"generalized function" will be used for f . Generalized
functions form a full linear space Z' conjugate to Z. The
Fourier transforms of the functions y in Z form a full linear
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On the Problem of E031/E435
space K, and conjugate to K is the full linear space KI of
generalized functions over K . Three operators (the shift
operator, the cliff erentiation- operator and the operator corresponding
to multiplication by it function) which act on f are defined. As
a final preliminary it Is necessary to say something about
convolution operators,, The following theorem im proved: every
convolution operator A in the space V is transformed by the
Fourier transformation into an operator corresponding to
multiplication by a function in the space KI, this function
being the Fourier transform of the kernel of the operator A (the
kernel in the functional A6, where 6 is the delta function).
It is further proved that if the sequence of operators
An = v,(iD) (where 0 is the differentiation operator) converge
to the operator A as n tends to infinity, then the sequence of
operators I An n
~B +
tends to the operator B OA.. Turning now to the consideration
of the convergence of the solution of the difference equation to
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20755
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E031/E435
the solution of the differential equation, the equatioa
bf/Zt = Af (where A is an arbitrary convolution operator) is
considered, If we write f t ~ T for f (x., t + 1), where
n% = t, - to (the dilrference between the initial and some later
values of t) and approximate to the operator e 'CA by the
operator B, then the following theorem can be proved; if the
equation ft +.V. = BTfjt can be written in the form
ft+r ft AI
and if, as v-) 0, the operator AT converges to the operator A,
n
then the operator B. converges to the operator
(tl- to)A x n
so that the functional f. M BTfo converges to the
differential equation for t =t1' The problem of uning -this
result can be stated in the following general manner. given a
sequence of functionals f-p in the space Z' which converges to
a regular functional f =-f(x), it is required to construct a
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.On the Problem of E031/E435
sequence of functions. *x), starting from the fj which
converges to the fun t, on f(x) in some "ordinary" sense. This
construction will be called "smoothing". Two techniques are
available. In the first we select some family of approximating
functions v(x,,ck) depending on m parameters ck , and assume
that the functiLon f(:x) can be sufficiently well approximated to
by such functions, rhen in the space Z we select m functions
It and for each functional fV choose an approximating function
v x,ok) so that m equations of the type (v,ji) are
satisfied 0,1y)= f(x)y(x)dx
Such a function we denote by qx(x) and this sequenc .e will have
as its limit f(x). The second method is known as the method of
moments. The functional f (belonging to ZI) has a moment of
the m-th order if its Fourier transform g (belonging to KI) is
a functional which is regular in any neighbourhood of the point
x = 0 and which has there continuous derivatives of all orders up
to and including the w-th. The value of the moment is given by
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-20755
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On the Problem.of ... E031/E435
the expression pm i) M g (m) (0) The following theorem is
proved3 let there be given in the space V a convergent sequence
of convolution operators A-9. If the functional fo has an m-th
moment, then each functional fV = A9fo also has an m-th moment
and the sequence of these moments converges to the m-th moment of
the functional f = lim A-Vfo. To illustrate the foregoing theory,
the equation Zf/ft = aZf&x is conBidered, with the finite
difference formula
f(x,t + 0 = f6c,t) + a--!- f(x + h,t) f(x - h,t)
2h I I
which is unstable. T'he values a 1, h and the initial
conditions,. fo =:1 for - 1.6 4 x 1.6
fo = 0 for jxj > 1.6
are chosen. On the basis ofthe initial conditions and the form
of the differential equation, a function v(x,a,b,c) is chosen so
that v = 0 for x < a and x > b, and v = c otherwise.
The moments -1t0, jil and U2 of this function are determined in
terms of a, b, t and. the equations solved to give a, b, c in
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terms of the moments.. From this it follows that the method in
applicable if 1110112 > ~'J. The results are illustrated for
h 0,1 and h = 0.2 As h diminishes, the function v
approximates increasingly better to the solution of the differential
equation. An alternative finite difference formula is briefly
discussed but, since the calculations do not differ in principle
from the example just given, the details are not pursued in the
paper, As a final example, the solution of the equation
laf/at = Z2fAx2 is taken as initial data for the solution of the
equation ,f/,Dt '$2f/C)x2
(lei The finite difference formula is
f(x,t + o,o625) = f(x,t) - I f (x 0. 25, t) - 2f (x, t) + f (x + 0.25,4
and thts Is unstable. We calculate the moments of the solution
for t =-0.5 from the expression
k-
I&M h, k'f (kh)
k=-28
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Now f is ext)anded'in,the form
(2) (6)
f c 0ip + c 2Y 4 c4Y + c6(P + C89
where (P ( 2n ) - 1/2 exp(-X2j2) and superscripts denote
derivatives. When the ck are determined from the moments, a
function is obtained which is a good approximation to the solution,
of the equation 3f/at = b2f/fIX2 for initial conditions
corresponding to two like sources of heat concentrated at the
points x = - I and x =1.1. The examples show that the
application of unstable formulae for the numerical solution of the
Caue,',Y problem is, in principle, quite possible but the process of
smoothing requires considerable additional calculations. Moreover,
the calculation of the moments of a strongly oscillating function
lead to the losis of significant figures. Ilence unstable formulae
ca n scarcely compete with stable ones at the present stage of the
-development. It is true, of coursed, that there are problems for
which stable formulae do not exist and', from what has been said
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On the Problem of ... E031/E4319
a b 40
ve,it is clear that this view may have to be subjected to
reappraisal, bearing in mind nevertheless that the method of
3
finite differencea may not always I)e the beat approach. There
are 6 figures and 4 Soviet references.

B/044/62/000/002/061/092
jqH36
C111/C222
AUTHOR: Zhukov, A. I.
TITLE: The'application of the method of characteristics in
solving one-dimenBional problems of gas dynamics
P11"RIODICAL: -Refarativnyy.zhurnal, Matematika, no. 2, 1962, 36,
zlbstract 2V204. ("Tr. Matem. in-ta AN SSSIO, ig6o,
58, PP. 150, ill-)
TEXTs The author donorlbou in datail tho characturistios ojethod,'.
for the equations of gas dynamics which are oboyed by tho one-dimensio-
nal. instationary flow
;)U
Le- + U a _ZU _P
0
t + J' d u +
Tr r A +u r
+ U r- 0, p P(?,
0 r
Hure t, r are independent variables; u, 0 pt a are the sought func-
tions; 9 0, 1, 2~ correspond to the plane, cylindrical and spherical
cases, respectively. The dependence p(-R a) is arbitrary. The original.j,
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The application of' the nethod of C111/0222
ations are derived in an integral and a differential form. The first
e
qu
in the more :Genoral a8 it allows discontinuous solutions. The equa-
tions of the characteristics are given; the Riumann invariants and the';
LaL-,range coordinates t, R LLre introduced. The principle of the method
is the followin6:,. The differential equationa of the charactoriation
i~u-o aritten a3 differonce,equationo. These allow, for example, the
calculation of the coordinates and the cougbt functionri at Lhe inter-
--iction of the characteristics throuah two known pointo on tho to
plane. The applied diff(~rence formulas have a remainder of order h~f
ahere h ii the step in the coordinate t. The error of the method in
calculatinr,, a t;ivon point of the tf R-plane has the order h2. Various
ethod3 of cotimuting tho error are suggeated, and their simultanaoun
application L41101.1 011C. to 6ravi practic.My dependable conclucion.- on
the exactn,;;3!3 of the calculation. Formulas are doriv0d for the. three
re!Ltionsshipo of p(P , f,).- p-kg', p-a(kg' p=b(g"+ k32"), where
0
k, a, b, w- sire constanti3. The calculating scheme by using the
boundary - conditions is considered. Formulas for. an example P-re: given.
In particular, special flowu -- extension waves and strong discontinu-
ities are exanined. Condition s are given for.the development of V,
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B/044 62/000/002/061/092
'rho apj~licLtlon of the v-;c thod of C I I 1YC222
extenzion -raves, and the propaaation process of tho diocontinuitie:j
of the firrt deriv.!tives of the functions are do-,cribed. RolatiQn-
~-hips of 1~u di~;:continuity points of, tvo possible -kind!~ are- j;1
Von;
vn th;-- cont: Ict-d i scontinui ties and on the shock-waves. Various schomes
are for -the calculation of flovis with contcict- discontinui ties.
Calculation rchui;ius covoring tho presence of nhock-wavou are conc-Adered
in do-tail. Weak shork-waves requirec npecial method of calculation.
.4 iilethod for calculatin6 shock-waves wiich originate somewhere in the
given. The initittl.values of the problea may contain
t, R-domain is 4,
~~rbitrary,dic;continuities,.which may satiefy neither the conditions
at thL. startina point:of the extension wavts, nor conditions at the
stronE; diacontinuity pointa* Such discontiniAties generally split
into three discontinuities$ each of,which can be, either a shock-waveo
a contact-discontinuity or an extension wave which can also be called
a discontinuity.:
acial partof the'paper is :devoted,to the calculation of the
J
spe
splitting of an arbitrary discontinuity. In aome p(3,a)-rolationshipst
p can become,negative in the t) R domain. The physical requirement
that 'the pressure p may not be 'negative leads to the development of
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fik
3/044/62/000/002/061/092
The application of tho method CM/C222
"zieparation" domaino in which p 0. The analytical solution of the
-oter of
oriainal equations for the separation in obtained. The chart.
this domain is examined. It is shown, among others, that the separation
is limited on one side by a 3hock-wave. An integral control method is
sug-ested, according to which the exactness with which the initial
integral ecuation are satisfied are tested by some closed contours of
the t, R domain. Appendix I gives suggestions for the set-up of progrbis
for electronic computers.:Appendix Il gives an example.
Abstracterls note; con, lete, translation.]
P
Card 4/ 4

ZHUKOV Anatoly ivaD)vicbp, KOZWVp V.D.p red.; YEMUKOVAp Te.A.p tekbn,
red*
[introduction into the relativity theory] Vvedenle v teorliu otnosi-
tellnosti.~ Moskvap Gos, izd-,Yo fiziko-matem. 34t-r7, 1961 171
(Mii 24,
(Relativity MWoico))

ZMMOVI Ana~q~IA. Ivanovich; PETROVSKIY$ 1.0., akademiko otv.red.1
WML'SKIIj,'.SX-,prof.# zem.otvetstvennogo red.; RYVKIN;!A.Z.,
redvisd-vayMALAGONOVA, I,A.p tokhn.red.; GUSIKQ'VAs O.M.p
t khn red
(use of the characteristics method in the numerical solution of
one dimensional.gas dynamics problems] Primenenis metoda kharak-
-5 teriktik k ohialennomu resheniiu odnomernyW zadach gazovoi
dinamiki. Moskva$ Izd-vo Akad.nauk SSSR. k960. 149p.(Akademiia
nauk SSSR. Matematicbeskii inatitut. TrudyO Vol. 58) OGRA 14:3)
(Aerodynamics)

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Moskva. Gostoptekbizdat, 1946. 43 p. (V pomoshcbl novym kadram neftJonoi
Prmwahlennosti. k50-4063-3)
TN8-r,. Z5 1946

ZHUKOV, Aleksnadr lvnriovirlh, IF-?9-
The operntion of oil wells; textbook. IM-) Ekv n9 c E; .rnuc'h, -tekhn. lzd-vo nt,~ftlrrm! J

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Technology
Podzemnala AlJtratsiia stochnykh vod (Undergr,-1jn'd filtration of sewage). Moskva,
Stroiizdat, 1951.,-176 p.
2
9. Monthly List of Russian Accessions, Library of Congress, flevemb-
;r.195$. Unclassified.

Z K011 A. T.
Zviukov, A. I.
"The use of pyridino in separating.the, allcali-earth elements usin-- the
method of ion exchca fre"I I 1-ir ',,cation Ural Polytechnic
r
-Iin Hir
Inst i-noni F. 71. Kirov Sverdlovrk 1956. (Dissertition for the nc.-Tce
of Candidate in Ch m., ical Sciences~ .
Kni7hnaya Ictonis''
No. 21, 1956. Moscowo
moil.

radaktor; BOOOLTUBOYA, B.Po# redaktor; DUBROTSKIT, T.Y., redaktor;
-,A I redaktor; KDEPICHNIKOV. A.A., redaktor; KONYUSHOV,
A.M., r6diWor; KULICHUMN, N.I., redaktor; SV4=Y, K.P., redaktor;
TURK, V.I., redaktor; TURCHINOV. V.T., redaktor; ROSSOVA,S.M.,
redaktor; GLYMU, O.A.. tekhnicheekiy radaktor.
(Sinking, equipping and operating wells for the rural water supplv;
proceedings of the conference of May 18-22. 19541 Soorushenie.
oborudovanie i.ekspluatateila skyazhin dlia sellskogo vodo3nabzhenlia;
trudy Sovesbehamlia 18-22 maia, 1954.goda.-Koakva, Gon.nsuc6o-tekhne
izd-vo lit-ry po geol. i okhrane nedr.1935. 220 p. (MIRA 8:11)
1. Sovesbchanipopo voproeam soormsbaniya I oborudovaniya burovykb
ekvazhin dlya aellskogn khozyaystv'd'1954.
(Vells) ' '(Water supply, Rbdial)

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