SCIENTIFIC ABSTRACT TIKHONOV, A.N. - TIKHONOV, A.N.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001755610020-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 16, 2001
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

T~KiinNOV, A,W.
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UU OF PROTOTANKNO " 010OWN GLASS UAPS VI" OURV
IWACU9 1. 4. Tempellaaa MA At.XA-21uftw.~ LoCkays Promet XIC4126-39
(1951)4-Ths methods for coyyIng an image directly wA W some of a nex-
Me film, for conical, spherical, and c.Aladrical shape* are doscritede
A dvwico vith mirror strips insures uniform exposure of shape to the
lights Illustroted.
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IL lim.110 jvj A.11 .
'. 41 -ri the
"Systens of Differential Equations which Contain a Saall P~,ra.-ieter Z.
Derivativr-sll, UWI 7, Ur. 1 (47), ]JtG-ll.,,2. (1~,52).

TIKHONOVP A. N.
PA 237-186
USSR/Mathematics - Small Parameter Nov/Dec 52
"Systems of Differential Equations Containing Small
Parameters in the Derivatives," A.N. Tikhonov, Mos-
cow
"Matemat Sbor" Vol 31 (73), No 3, PP 575-586
Considers the system xI = f(x,z,t), azI= F(x,z,t%
where x,f,z,F are vectors of an n-dimensional
space. Studies the solutions of this system for
the case where a tends to 0. Cites similar works
(1950-51) of I. S. Gradshteyn and A. B. Vasillyeva.
237T86

TIKIIONOV, A. N'.
Pattern-Making.
Accurate lay-out patterns are a Russian invention. Vest. mash., 32, ','o. ?, lr2c2.
9. Monthl List of Russian Accessions, Library of Congress, October - 19A
- - - , Uncl.

U s s R
550,371
2m as t6a "Ad" d me
WFA.*,DN~VLV=A Ookf.Akad.
4~ (1952) Awlim.
At avecto Is made to rei2to do obsavcd varistiom
Ln ft aerth's clectsic and macwtic field by the use o(
Nkxwas equatim and catain simpifyiag assump.
tionc The anunVdm Is ma4c that the csrtb behaves
LU a canducw of dcvth L and cmAuctivity k. The
ftory Is spOW to expainmW data fcf Owco
stations mr.4 good mpmwnt Is obtal(M for two.
L Is found to ba about loop km and k about
0.01 athp/m 1. W, I*XKAI

TiKHONOV, A-N.
PHASE X TREASURE ISLAND BIBLIOGRAPHICAL REPORT AID 685 - X
BOOK Call No.: QC20.T54
Authors! T~ ~A~.N. and SAMARSKIY, A. A.
Full Title: THE EQUATIONS OF MATHEMATICAL PHYSICS. 2-nd ed., rev.
and suppl.
Transliteratedlitle: Uravneniya matematicheskoy fiziki. Izd. 2-e,
isprav. i dopol.
PUBLISHING DATA
Originating Agency: None
Publishing House: State Publishing House of Technical and Theoretical
Literature
Date: 1953 No. pp.: 6T9 No. of copies: 25,000
Editorial Staff
Contributors: A. B. Vasil'-yeva, V. B. Glasko 'V. A. Win,
A. V. Luklyanov, 0. 1. Panych, B. L. Rozhdestvenekly,
A. G. Sveshnikov, D. N. Chetayev and Yu. L. Rabinovich.
PURPOSE AND EVALUATION: Approved by the Main Administration of Higher
Education of the Ministry of Culture of the USSR as a textbook for
physico-mathematical faculties of state universities. In compari-
son with Couzant and Hilbert's Methods of Mathematical Physics,
this book is suitable only for prelimInary study or this subjeot.
1/3

.Uravneniya matematicheskoy fiziki.
Izd. 2-e, isprav. I dopol.
AID 685 - X
TEXT DATA
Coverage: In this book only those problems of mathematical physics
are considered which can be solved by using partial differential
equations. Only part of material pertaining to the methods of
mathematical physics is presented. The theory of integral equations
and metiaods of calculus of variation are not Included, and approxi-
mate methods set out only to a limited extent.
Table of Contents Page
Foreword 9
Ch. I Classification of Differential Equations with
Partial Derivatives
Ch. 11 Equations of the Hyperbolic Type
Ch. III Equations of the Parabolic Type
Ch, IV Equations of the Elliptic Type
Ch. V Propagation of Waves in Space
Ch. VI Propagation of Heat in Spacd
Ch. VII Equations of the Elliptical Type
f Chapter IV)
Supplemenot; Special Functions
Part I Cylindrical Functions 2/3
11
23
178
279
410
456
(continuation
50
569
575

Uravneniya, matematicheskoy fiziki. AID 685 - X
Izd. 2-e, isprav. i dopol.
Page
Part II Spherical Functions 619
1. Legendre's polynomials 61g
2. Harmonic polynomials 633
3. Some examples of application of spherical
functions 645
Part III Chebyshev-Ermit and Chebyehev-Laguerre Polynomials 652
1. Chebyshev-Eiwit polynowww 652
2. Chebyshev-Laguerre polynomials 6~5
3. Simple problems of Schr8dinger's equations 6 3
Tables of Integral Errors and some Cylindrical Functions 671
No. of References: Some footnotes scattered throughout the te xt
Facilities: None
3/3

TIKHONOV, A.N,; SARARSKIY, A.A.
Magnetization of a magneto-dielectric cylinder with the calculation of
magnetic viscosity. Yest.Hook.un. 8 no.2:43-51 Y 153. (MLRA 6:5)
1. Kafedra, matematiki. (Electromagnetism)

TIKHONOV,A.N.; SHTEYN,B.S.
Physical causes of errors received in conducting vertical
electrical prospecting by the compensation method. PrIkI.
geofiz. no.10:74-83 '53. (NLR& 8:7)
1. Chlou-korrespondent AN SSSR (for Tikhonov). 2. Nauchnyy
Botrudnik Geofizicheskogo instituta AN SSSR (for Inenshteyn).
(Prospecting--Geophysical methods)

J LF
Applicittion ofr. M. Lympunov's theory of
atabill to the theory of differential equations with small
coefficients In the derivatives. Alat.SbornikN.S.32(74),
263-286 (1953). (Russian)
Let all quantities excipt ( and i) be finite-dimensional
vectors. The author gives sufficient and highly complicated
conditions in order that a solution of
dx _Ax. Y, 1. 0, dy_ A (X, Y, 0,
~i 71
initiated at ;(0, v), y(O. ?) and converging to x(O), y(o) as,'
1--#0, te
the solution of the
obtained for

athematical Reviews zo
system
17 - 0,

Vol. 14 No- 11 initiated at x(0), y( 0). Similar treatment for a system

Dec. 1953 dx dy
f (.'C, Y, 1. tI 1), 1- , 9 U. 1)
Analysis dt
dl
dz
a>0.
dl
with asymptotic stability
Close conwcLion is esiablished
A la Lyalitinov.
ClItfumnces:1 Grad;teln, Doklady Akad Nauk SSSRI
(N.S.) 64, 441-443; 65, 769-792; 66, 789-,,- (1949); 82,
5-9 (1952); lzveztiya Al:ad. Nauk. Str. Mat. 13, 253-280
(1919); these Rev. 10, 536, 708, 709; 13, 557; 10, 709;
Jihonc)v A N., Mat, Sbotnik N.S. 27(60), WAS6 (1950);
'
v~ i2, 181; ~(x ako the prtceding review.]
dicst: ke
S. Lef~chdz (Princeton, N. J.).

ZRhONOV; A. N.; ENEEISSETEE.', B. S.
Geouhysics
Effect of the processes of setting electric currents in the earth for field
measurements in electrical soundings, Dokl. A:" 333H 88, No. 5, 195"'.
Clarification of the causes of wide divergencies, amphnting to several
tens of percent, in different field measurements conducted in the same locality, which
cannot be due to results of chance errors. Indebted to A.I.Dyifldiov and A.M.Zagarmistr.
Submitted 4 Dec 52. 258T78
9. Monthly List of Russian Accessions, Library of Congreps, _ - INay -1953. Unclassified.

7A V A. ~ 'U"A 11OV,
T 71~ i
"Relationship Between Earth Gurrents and Earth quakes." Tr. Geofiz. in-ta All' SSS"I,
No 25, 1954, 191-131
A relationship between the propaEation of seismic waves and the appearance of
an electromagnetic perturbation, the so-called soismoelectric effect is held possible.
The effect originates in slow undulations of the lverrovtrial core which Mly propagato
as an elastic wave. The noticed coincidences of s&lsinic waves ancl electric perturba-
tions indicate the necessity of recording, the slow motions of the terre:Ar*181 core.
(Rzuizp No 10, 1955 )

mm
&M~A
QWW 4--l' .- -__- = ~ -- 1. -
-r- I - I I
'. . -- -- -- -
?I Wl-,Wr
,
mummi'momisams I

A~~
I

T,T-'.r'Ir,,NWN, Leonid Samuilovich, 1879-1951 (deceased); -ASOV, A.I.,
akade-iik; TIKHOTIOV. A.K.; ITLITUSHIN, A.A. ; SOKOEOVSKIT, V.V.; GALLID,
L.A.; SHaffim'MVI"T.N., doktor tokhnichask-ikh nauk; TMIK, Y.A.,
doktor tekhnicheskikh nauk; GRIGORITIV, A.B., kandidat tekhnicheskikh'
nauk; SIDDY, L.I.. akademik, redaktor;ZVOLINSKIT, N.V., professor.
redaktor: ATASIMINA, T.V., tekhnichookiy redaktor.
[Collected vorks] Sobranie trudoy. Moskva, Izd-vo Al-adwit nmi SSSR.
Vol.4( Hydroaarodynamics. Geophysical Gidroaarodinamika, Geofixika,
1955. 398 P. (MLRA 8:11)
1. Chlen-korrespondent AN SSSR (for Tikhonny, Illyushin. Sokolovskiy.
Galin)
(Geophysics) (Flnid dynamics)

LM,~NZON, Leonid Samullovich, ukademik; NXKRASOV, A.I., akademik;
TIKHOIX)V, A.N.; ILIYUSRIN,A.A.; SOKOLOVSKIY, V.V.; SHCHILKACHN7,
V.N.,doktor zethnicheakikh nauk: TRIBIN, F.A.. doktor tekhni-
cheskikh nauk, redaktor; GALIN,L.A.; GRIGORtM, A.S.p doktor
takhnichesklkh nauk; CHARNYY, I.A., doktor takhnicheskikh nauk,
redaktor; ALEKSIMA, T.V., tekhnichenkly redaktor.
[Collected works] Sobranie trudov. Moskva. Izd-vo Akademli nauk
SSSR. Vol.3.[Petrolnum engineering] Neftepromyslovaia mekhanlim
1955. 678 p. (NLRA 8:10)
1. Chlon-kors-espondent AN SSSR (for Tikhonov, Illyushin. Soko-
lovskiY aid G&Iifi)
(Petroleum engineering)

USSR/ Physics - Magnetization FD-3156
Card 1/1 Pub. 153 - 12/26
Author : Tikhonov, A. N; Samarskiy, A. A.
Title : Magnetization of a cylinder with winding taking account of magnetic
viscosity
Periodical : Zhur. tekh. fiz., 25, No 13 (November), 1955, 2319-2328
Abstract : The authors consider the following problem: a conducting cylinder of
infinite length parallel to the z-axis is situated in a constant
magnetic field such that at moment tsO within the cylinder there is
established a constant magnetic field of strength Ho directed along
the z-axis; at moment twO the external field is abruptly changed from
H*Ho to HuHl, which can be greater or less than Ho, with the possibility
HjuO. They note that the solution on the basis of the Maxwell equations
was first obtained by B. A. Vvedenskiy (zhRFKbO, 55, 1, 1923; see also
A. N. Tikhonov, Sbornik statey pod red. V. K. Arkad'yeva, Publishing
House of Dept. Tech. Sci. of Acad. Sci. USSR, p. 80, 1938). The aim
of the authors in the present article is to solve the problem of magnetic
reversal of a conducting cylinder in the presence of not only elastic but
also viscous magnetization, a similar problem for the case of plane layer
having been considered by A. N. Tikhonov, ZhTF, 7, 38, 1937. The authors
acknowledge that the works of R. V. Telesnin (ZhETF, 18, No 11, 970,
1948; DPN SSSR, 25, No 5, 1950) suggested the present problem.
Submitted October 29, 1952

T 1, r
TIKHONOV, A.U. prof.; SOKOLOV, A.A., prof., otv.red.
[Frogram in higher mathematics; for the ?]Voice Yacultyl Programme
po vyeshei matemetike (d1la fitichaskogo fakulltets). 1956- 7 P.
(MIRA 11:3)
1. Moscow. Universitat. 2. Chlen-korrespondent AN SSSR (for
Tikhonov)
(Mathematics--Study and teaching)

tTr, 7r-f ~_-, 7r- H A.
SUBJECT USSR/MATMUTICS/Differential equations CARD 1/1 PC - 608
AUTHOR BUDAK,B.M., SAVARSKIJ A.A., TICHUNUT A.N.
TITLE Collection of problems for mathematical physics.
PERIODICAL Moscow: State publication for technical-theoretical literature
684 P- (1956)
reviewed 2/19.57
This collection originates in a textbook of Samarskij and Tichonov (The
equations of mathematical physics, Moscow 1953) and a smaller collection of
problems of Budak (collection of problems for mathematical physics, Mau-101I
(1952)). But thin material is still extended, especially it in represented in
a detailed manner. 130 pages contain problems and questions and ~$O pages
contain solutions and instructions for solutions. Only boundary value problems
for partial differential equation3 of second order are treated. The knowledge
of the general theory is assumed. In three chapters the three types of
equations are treated, the chapters are subdivided according to methods to
be applied. There follow again three chapters with the same busdivision which
treat essentially more difficult questions. An important part of the problem
consists in deriving the differential equation and its boundary conditions
from the given physical problem. The method of solution is given so detailed
that a self-study for students is possible. The book represents a sourcearc'.
wealth for the applied maikematician and for the theoretical physicist.

TIKHONOV SHAKH UVAROV, D,N.
%" - ft -IN _d2mi.."..
Method of computing electromagnetic fields excited by an altornating
current in schistose media. Izv.AN SSSR Ser.g~*fiz.no.3:245-251 Kr
'56. (HIaA 9:7)
l.Akademi.va nauk SSSR, Goofizichookiy institut.
(Electromagnetism)

TIKHONOV, A.R.- SHMSUVAROV, D.N.
Possibility of utilizing the Impedance of a natural terrestial
electromagnetic field for studying its upper layers. 1zv.A1 &SM.
Ser.gsofiz. no.4:410-418 Ap 156. (NLRA 9:8)
1. Akademlys, nauk SM. Geofizichaskly Institut.
(Terrestrial electricity)

I Y~ I -A C. N OV, f~j
SUBJECT USSR/MATHEMATICS/Differential equations CARD 1/1 PG - 426
AUTHOR TICHONOV A.N.
TITLE On difference schemes for equations with discontinuity
coefficients.
PERIODICAL Doklady Akad. Nauk 108, 393-396 (1956)
reviewed 12/1956
For the solution of the boundary value problem
(k (x) -M ) - - f (x) (OO with h--~-O . Here
I a b f k-1 (x)dx
k k k! k+1 (X-.Xo) k+1
k-1 f (s) (.,:) 1
k+1 k-s k-S
8 ! (b-x (a-x
8=0 0) 0)
where f k(x) is the remainder term of the Taylor development
Card 2/3 1~

67506 12
On the Development Iffith Respect to a Parameter of SOV/155-59-1-9/30
Integrals the Kernel of ".1hich is of the Type of the -~-Function
of f(x) at the point x = x and a _F= k )d ~ (the
k = 7 ,
-00
into-,rals are understood in the sense of the principal value
at the point x = x Or ~~ - + 00
0 ? -
The proposed method can be extended to the case of several
variables.
ASSOCIATION: Moskovskiy ,-osudarstvennyy universitet imeni 11-V.Lomonosova
(moscow-State University imeni M.V. Lononosov)
~XBUTTED: January 7, 1959
Card 3/3

-07/15 5?- 1 - 10/30
AUTHORS; Tikhonov, A.![,, and Samarskiy, A.A.
PERIODICAL: Nau 5n-y'ye T~,Yady vysshey shkoly. Fiziko-matematicheskiye nauki,
1959, ]-.r I , pp 62 - 70 (Ussa)
TITLE: On the Asymptotic Development of Intoarals 'Jith a '.;loyjly
Decreasing Kernel
ABSTRACT: The authors investigate the asymptotics of the integral
b X-
x
(1) J h,xo ; f -2 -f (x) dx
h
a
for h >0 if the function to(`7,) has the form
n q
k n(,!:)=0 for
W) ~J(q k + +
00
It is shown that under the assumption that I f (x) 1- on
(a,b) and f(x) in x,(a O
Ct 1 9z -
(for air) and z< 0 is then discussed, some special cases are in-
vestigatedl and explicit formulas are written down for H
and E~. There are 2 Soviet references.
ASSOCIATION: Moskovakiy goeudaretvannyy univereitet im. M. V. Lomonosova
(Moscow State University imeni M. V. Loinonosov)
SUBMITTED: April 3, 1959
Card,2/2 .

3 5 8
S/044/62/000/002/056/092
C111/C444
AUTHORS: Tikhonov, A. IT., Samarskiy, A. A.
TITLEs On the best schemes of differences
PERIODICAL: Referativnyy zhurnal, Matematika, no. 2, 1962, 31
abstract 2V171- ("Tr- Vocc.
sialln. uraviieniyam, 1958"-
167-178)
TEXT: One constructo the equatioii
cortain ~;enue is the best one in order to
equation
soveshchaniya po diffurent-
Yerevan. AN Arm SSR, 1960,
of difforenceo which in a
approximute the differential
q(x) u + f(x) = 0 (1)
TX dx
with piecewise continuous coefficients. If on the intorvals of
continuiij the functions q and f are twice, and k is three times
continuousl~~ diffQrentiable, and if the coefficients of the equation
of differences are furictionals of k, q, f, satisfying certain natural
restrictions, then the constructed equation of differences has the
second order of exactness, i. e. its solution is different by 0(h2),
where h is the lattice step, from the solution of the boundary value
Card 1/2

S/044/62/CCO/002/056/092
On the best schomcs of differences C111/C444
problem (1). It is ShOWIL that the equation of differences vjhich
satisfies till the proposed domands and possesses the second order
of exactness, is uniquely determined. Proofs are not given. A great
deal of the results had been formerly published by the authors.
(RZh Mat, 196o, 4570, 14419).
LAbstracter's note: Complete translation.]
Card 2/2

69h99
&,~qoo 9/020/60/131/04/13/073
AUTHORS: Tikhonov,A.N., Corresponding Llember AS USSR, and Samarskiy,A.A.
TITLEs Standard Homogeneous Difference Circuitst,
PERIODICAL: Doklady Akademii nauk SSSR, 196o, Vol.131, No-4,PP-761-764.
TEXT: The present paper is a continuation and a partial generalization
of the earlier investigations of the authors (Ref.1-4). The authors consider
homogeneous three-point-difference schemes for the solution of the boundary
value problem
N L(k,q,f), = !L [k(x) ~Lu I -q(x)u + f (x) = 0, O