SCIENTIFIC ABSTRACT KRUZHKOV, N. - KRUZICEVIC, M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000826820004-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 14, 2000
• Sequence Number: 4
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

SLUM, $-
Audio frequencY generator. Radio go.11,5o-31 1 156. (10
(Oscillators, Ilectron-tubs)

KRUMOV, lie
Universal multimeter. 7 pox. radioliub. noo4:%-62 '57. (MIRA llt2)
(Radio wasurements)

Y\ R U /_ H Y~
USW/ Electronics Measurement
card A Pub. 89 - 29/30
Authors I Kruzhkov, N.
Title I Simple oecillator
Pcricldic4l _!__kdio 1, 59 - 600 Jan 56
__AUstraet_-_=j_-- GAeohnical= pool,
ions - -as
___Th fleat,, oni- -anCjn-SVt1-jCt -fox
fori-an oacill
OgraP -Containing an-amp
6ZH4 tube, an amplifier of horizontal deviation and roCtifier-on- a- 6USS
tube, a generator of saw-tooth voltage on a 6N8S tube and a LOw247
electronic beam tube. It is intended that the oscillograph be built by
rad-to amateurs of average qualifications. Illustrations; circuit diagram.
Institution 00.0#
&ibmif.ted *.*40

05390
8(2)t 9(4) SOV/107-59-8-10/49
AUTHOR: Kruzhkov, N.
TITLE: A Transistorized Avometer
PERIODICAL: Radio, 1959, Nr .8, pp, 12 - 13, P 15 (USSR)
ABSTRACT: The author describes an avometer for measuring dirdct
arid alternating voltages up to 1000 volts with an
input Impedance of 100 kiloohm per volt, direct find
alternating currents up to 1 amp and resistances up
to 10 wegohms. The author recommends using bridge
circuits, similar to those shown in Figure 1 a-c.
He based his avometer on the bridge circuit shown in
-,ure 1e. Here, the current to be measured is fed
Fif
,
simultaneously to the bases of two transistors. One
of the transistor resistances increases while the other
is reduced. The complete circuit diagram of the avo-
meter is shown in Figure 2. The sensitivity of the
Card 112 bridge circuit used is about 5-8 microamps when using

KRUZHKOV, Mik.
Their names are not forgotten. Komm. Vooruzh. Sil 46
no.6186-88 Mr 165. (MIRA 18i11)
Sid!-

KRUZHY.GV S.
i:
Hero of socialist labor. Za Wzo#odvlzh.
6 no.8si-3 Ag 163,
(HIM 161g)

KRUZIMNI SAO
Kethoda for deriving generalized nolutionn to the Cauchy
problem for a quani-linoar equation of the first order.
Usp. mt. nauk 20 no.6-.112-118 N-D 165. (MIRA M12)
1. Submitted Feb. 23, 1965.

A-Z
07
020/006/0112/0118
SOURCE CODE.
1,6
AUTHOR: Kruzhkmu--s. N..
ORO i none
TITIZj Methods for tho construction of generalized solutions to CaUchy'spro blen for
a first-ordor quasilinoar equation
SOURCE: Uspekhi wLtomatichaskikh nauk, ve 20, no. 6. 1965, 112-118
TOPIC TAGSt CaucIV problem$ function, viscosity, approximation
ABSTILACT: It is knom that approximate solutions to,Cauchy's problem the
large for the equation A + 4 (M)
of as -0, q"(.)>o
can be constructcd by the moth6d-of-finito differoncou and the method of
11VC-adshing viscooityo 11 The question of the converganco of the apro-ro;dmate
'solutions was considered in articles by 0. A. Oloyaik, uhUo an ax.*,,iclo
:bY K- S. Bakhvalov establiched an evaluation for the arror of a solution
constructed by the method of finite differences. The prwent article suZ-
968ts A cOmParativelY simple p2wf of convergence which makes it possible
at the saw timOtO Obtain An eValuation of the error In an approximate sol ution, To
evaluate the nom of the differ'ence'of two approxinito solutiow, tho Puthor usc3 the
technique of smoothing by moarm of mean functions and tho mothod of optimal (in a
nse) choice ot a smoothing paranotors 0iige art. ha3; 17 fon;-.ulas- 12P.1v
GIM OnnVo 171AITRm nAT'F1?1?;~hA';/ORIG REF:065

-NRi- AP6032935- ---.--SDURCE-CODgi-UlVO208/66/006/00k/OBU/OM
AUTHOR: KruzhkoVo 0 N (Ko8ww)
ORG: none
TITLE: Applying the finite-difference method to a nonlinear first-order equation with many
variables
SOURCE: Zhurnal vychialitellnoy matematikil matematichookoy fa'ziki. v. 6, no. 6, 10669
884-894
TOPId TAGS: nonlinear differential equation, function analysis, mathemaUc analysis,
finite difference, difference method
A13STRACT: This wo;k is closely related to the author's previous investigations
(S. N. Kruzhkov. DAN BSBR, 19640 155, no. 4, 743-746; 1966, 1679 no. 2, 286-289; Mem.
ab. , 1966, 70 (112), no.. 3, 394-415), with the difference that It deals with the substantiation of
the finite-difference method of solution of the nonlinear equation
U1 X. U, Ur) I= 0,
8a Ou-),
X X= (Xi -Ut Z=
I ux h-
a M

ACC NR, AP6032935
with the initial conditions
U, I t.0 UO (X) (2)
by means of a generalized version of Lax's niethod and estimates the error of the approximate
solution. For simplicity of expooltion,'attontion is confined to the equation
Z(u)=uj+j(u.)-O; (3),
where the function f(u), U is (Uj~_!_~ is twice continuously differentiable In the EuclWem
space E n(u) and convext if ff (U) 9/ (U) dul, h) (U) - MAU) Outauji, then
. . . ..........
/Ii (u) IIIj0 (4)
for any. real u and - With respect to the Wual Ametift vew it is
0.
Usumed that' J*vq,),~- uo(y) 14 Kils - YJ m Ks[ (zi - YWI + 4-- TZ-a -'A &W W
Ax) 2no(z) + as(z - Az) 0, (2)
1 b (8, z, a, p) I < Ka (t, z, u, p) (pl + 1). (3)
The function u(t,x) is continuous In Q and satisfies equation (1). A priori estimates

Iij I,L7
AP60~28~5
A
ACC NRI
are made for the modulus of the derivative ux and its Hoelder constants, which depend
only on M, ao, a,, m, and X, Leto without any assumptions as to the continuousness of
the coefficients of (1). The results are applied to the study of boundary value prob-
lems and the Cauchy problem for (1) and for a nonlinear parabolic equation cf form
U1 - a (9, X1 Ut UX# UXx) -
The proofs of the estimates are based on the fact that with the introduction of an
additional space variable, the pr*blem of finding the inner estimate is reduced to a
study of the solution of a new quasilinear parabolic equation near the boundary of a
three-dimensional region where the solution vanishes. Orig. art. has: 19 formulas.
SUB ODDE: 12/ SUBM DATE: l6Dec65/ ORIG FXF: 007/ OTH Fzr: 002

16's6-00
80041
8/02o/6o/i32/01/08/064
AUTHORt Ka~hkov, S.N.
TITLEs Cauch-Z-, Trobi-emlrn the Large for Some Nonlinear First Order
Differential Equations \\D
PERIODICALi Doklady Akadsmii nauk SSSR11960,'Vol. 132, No. 1, pp. 36-39
TEXTt In t >,O the author considers the problem
(1) U.t+ 'f (ux) - 0 Lf"(Y):>a>O y(0) - y'(0) - 0
(2) U(O,X) - U (X)
where u 0W is arbitrarily bounded. The author defines the generalized
solution of (1), (2) and proven its existenoe and uniqueness an well as the
continuous dependence on the initial conditions. The properties of the
generalized solutions are investigatedi in t>,O they are continuous for all
initial conditions. The results are used in order to investigate the Cauchy
problem for
(3) Vt + (Y(V))x W 0 tf"(Y)>'a>O I'M . 0
with initial conditions given by a functional. There are 3 definitions,
Card 1/2

80041
Cauchy Problem in the large for Some 3/020/60/i32/01/08/064
Nonlinear First Order Differential Equations
3 lemmata and 9 theorems.
The author thanks Professor O.A. Oleynik for the theme.
There are 5 referencest 4 Soviet and 1 American.
ASSOCIATIONt Mookovskiy.goeudaretvennyy univeraitet imeni V.V. Lomonosova
(Moscow State University imeni M.V. Lomonoso-0
PRESENTEDs December 28, 1959f by I%Q& Petrovsk-iyo Academician
SUBMITTEDt Decemb*r 24, 1959
Card 2/2

2)~30
8/0 4 2/61/016/00 5/00 2/00 5
~~Q a C1 1 1/C444
AUTHORSt 01eynik, 0, A,, Kruzhkov, S. H,
TITLEs quasilinear pa olic equations of second order with
several indepondant variables
PERIODICALt Uspekhi matematicheskikh nauk, v.. 16, no. 5, 1961,
115 - 155
TEXT: One considers the existence of solutions for Cauchy
problems and for boundary value problems for quasilinear parabolic
equations of second order with several ind*pendant variables. Consi-
dered are solutions "in the large", 1, 9. solutions for an arbitrary
previously given t-interval, In the introduction it is stated first
of all that for an arbitrary parabolic equation
U - a (t9 xf u1 u )U X, U, u
t ij X xix X
with sufficiently smooth a ij and f, there always exists a "local" so-
lution of the considered problems, i.*. for a sufficiently small t-in-
t*rval For the existence of solutions "in the large" it proves to be
necessary that the growth of the a Ij and of f satisfies oartain r*-
strictions
Card 1/16

2 ),"; 3 ()
S/042/61/016/005/002/005
quasilinear parabolic equations.- C1111C444
�2 contains apriori estimations of the solutions of linear parabolic
equations There are mentioned results of the following referencest
(Ref 511 I.Nash, Continuity of solutions of,~arabolic and elliptic
equations, Amer Journ, Math. 60, no, 4095 , 931 - 9541Ref 81 A,
Friedman, On quasi-linear para~_bolic equations of the second order 11,
Journ Math, and Mach 2, no, 40960), 539 - 556;Ref 26t A. Friedman,
Boundary estimates for second order parabolic equations and their app-
lications, Journ. Math. and ldech~ 1, no. 50958), 771 - 791IRef 341 A,
Friedman, Interior estimates for parabolic systems of partial diffe-
rential equations, Journ. Math, and Mach, .1, no. 3.0956), 393 - 417)
as well as the following genoralisation of the theorem of J. Nasht Lot
-ilbe a domain of Rn, fl,~bo the largest subdomain of f). its distance
r If . (.04X (0 ~
from the boundary of 11 being 6,>O, Let Q T)J~ q - jDx(0,T)j-,
lot T be the lower base and S the face of qi in Q one considers bound-
ded solutions of th# parabolic equation
n
(11 u u
xj ) + b, ( t, '~u - + f ( t, x) (2-3)
i-(ajj(t,x) 7)-
Card 2/16

29")0
SIOA916110161005100.,l,, j5
Q~ui!:i i inear par-abolic equationn. . . c I I ;7C444
t~,,! (;OCj'fj(;jCjjtg being SUffietently smooth, a (t, X) a i(t, Xj
a ( t, X) C: lv,2 20 0 k .'..4)
i j 2
b r,'~ B i n. f N. (2-5)
being catiefied. Th,,, i I
Tlw,orem 21 Lot u(t z) LL a nolution of (2-3) ip q; I u(t, 4 M-
TI,,!n for (t O