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

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SCIENTIFIC ABSTRACT
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T~KiinNOV, A,W. C 0 - 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. 30 z9 Ke 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