SCIENTIFIC ABSTRACT GERONIMUS JA.L. - GORODETSKIY, P.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000514910016-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 17, 2002
• Sequence Number: 16
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

SUBJECT USSR/MATHEMATICS/Theory of functions CARD 1/3 PG -453
AUTHOR GERONIMUS Ja.L.
TKME On some properties of analytic functions being continuous in
the closed circle or sector of a circle.
PERIODICAL Mat.Sbornik, n. Ser. IL 319-330 (1956)
reviewed 12/1956
The paper contains some generalizations of known reoults of Hardy, Littlewood,
Gagua and others. Let flz) -lf(r e io be continuous for r:!~1. Let its modul
of continuity for r - 1 be to( sup lf(e i91)- T(ei'2)1 ' IG1-021
b
Let A be the function class for which W(x,'P ) dx< OD . If it (IR)E L(O 12 IT)
I x
a
is a real 21TI-periodic function and v(G) is conjugated to it, then f(z) denotes
the analytic function 2V
f(z) - f(r ei J ei~+z u(Q)dQ + iC,
2 'IT eig-z
0
The following theorems are provedi

Mat.Sbornik, n. Ser. 38, 319-330 (1956) CLRD 2/3 PG - 453
1. Let w - f(z) map the unit circle onto a region B which is bounded by a
closed smooth Jordan curve C. Let O(s) EA , where 9 is the angle between the
real axis and the tangent on C in the point with the are coordinate s. Then
the modul of continuity t,) of the functions f'(2) and f"(z) on Izi - 1
satisfies the inequation 1T
x
to C 1 ~12.~ dx + C f W (x, 0.1 dx + C W 9)
0 x 2 x2 3
0
2. Let f(z) be regular in,jzj a) *'n
._R(eill) ell, p,,, z). znN(~j /Z), a+ rh 4. 0
IP4(e
n
is sufficient for the uniform convergence of Aim (f;eA )-an(Ae iG
CARD 3114 16K

PA - 3122
On the Uniform Convergence of the FOURIER-CHH'YSHE7 and the
MACLAURIN Development of the Analytical Functionsof the Class
2'
(I + i rbi I
0 in the section rL
Thus, the existence of the asymptotic formula with the error
E 0- 0(1/lgn) satisfied the condition!) of uniform convergence.
A table contains the 5 conditions found here, each of which
suffices for the existence of the here mentioned asymptotic
formula.
(1 Table),
ASSOCIATION: not given.
PRESENTED BY: V.I. SMIRNO 4- Member of the Academy, 6.10- '1956.
SUBMITTED: 4,10. 1956.
AVAILABLE: Library of Congress.
CARD 4/4

A sort ya.'L'' 10- 1 - 5, 42
21TLE: On Soime Entimations in the Theory of ';`;plitz F,)r7is and Ortho-
-onal Polynomials (0 nel-otorykh otsenkakh v terri.i. form Te-plitsa
i ortoQ-onallnykh mnor-ochlenov)
.1
PERIODICALs Doklady Akad.Nauk SSSR, 1957,Vol-117,1;1'-1,r-r,,25-27 (USSR)
ABSTRACT: The author considers the forms
n
Tn ci-kxfxk ' 0-n - On Z) n" I,i_,In , n-0,1,2,..
:L 0
i,k-o
positive definite for If it is denoted
~n~oo >
0
hn - An+1 , then there exists lim h n - h )~ 0
TT n-~ oo
The author gives several estima-ions for the magnitude
/kh - h h and shows that various estimations can be ex-
pressed bylk., e.g. the estimation of increase of orthogonal
polynomials.Ll 5 Soviet and 2 foreign references are quoted.
ASSOCIATI011i Khdr'kov Institute or h~iatioff (Kharl kovsl~iy aviats-tonnyy ins titut)
PRESENTEDi By V.I.Smirnov, Academician, May 23, 1957
SUBMITTED: May 21, 1957
AVAILABLE: Library of Congreas
Card 1/1

,~': ...... - - - , ; -, . -
Ya. L. Geroniumu.3, "The Application of the Tuchoblachow I-W-thod-j in Some
Problems of Dynamic I'Ie-chanism Synthesis."
PAPW PNGantad at 0& 2ad All-Union C(W. an ftAmMt&j fftbl#tw 14 tb#
Thawy of Vachinns " Mechanisma, Macau, LEM, 24-28 Muich

16(1); 25(2) PHASE I BOOK EXPLOITATION OV/I'f 4 1
G.eronimu8, Yakov Lazarevich
Dinamicheskiy sintez mekhanizmov po metodu Chebysheva (Dynamic
Synthesis of Mechanisms According to Chebyshev Method) Khar-kov,
Izd-vo Khar1kovskogo univ., 1958. 133 P. 3,000 copies printed.
Resp. Ed.: Yu.V. Epshteyn; Ed.: D.A.Vaynberg; Tech. Ed.:
Ya.T. Chernyshenko,
PURPOSE: This book is intended for senior students at vtuzes and
for engineers and mathematicians.
COVERAGE: The book deals with the problem of the dynamic synthesis
of mechanisms according to Chebyshev's method and the develop-
ment and application of this method by Soviet mathematicians.
Methods studied and results received in the book may have direct
application to practical problems. The book is an extension of
the author's report on the theory of machines and mechanisms
presented at the meeting of the Institut mashinovedeniya (Institute
Card 1/6

Dynamic Synthesis of Mechanisms (Cont.) -SOV/1741
df Mechanical Engineering) of the Academy of Sciences, USSR,
held on the occasion of the 130th anniversary of Chebyshev's
birth. Contemporary Soviet scientists mentioned in connection
with the problem presented in the book include Academician
V.A. Steklov, Academician I.I. Artobolevskiy, N.I. Levitskly,
Z.Sh. Blokh, V.I. Ivanov, P.N. Gartsht-ein, Yu. V. Epshtein,
L.I. Shteyuvollf, and L.B. Geyler. There are 53 references,
of which 52 are Soviet and I French.
TABLE OF CONTENTS:
Preface 3
Ch. I. Chebyshev's Problem Concerning Approximate Isochronal,
Regulator
1. Statement of problem and derivation of basic equation 9
2. Chebyshev's first method for the solution of the
problem 12
3. Chebyshev's correction method 17
4. Concepts of pblyTiomials with the least deviation
from zero 18
Card 2/6

Dynamic Synthesis of Mechanisms (Cont.) _110V/1741
5. Solution of the problem for a monotone change of
angular velocity 22
6. Determination of a polynomial which gives the solution
of a problem under a specified additional condition 24
Ch. IL Selection of Counterweights for the Best Balancing
of Mechanisms
7.. Geometrical method of determination of the counterweights
Which give the best bAlancing 29
8. The problem of the best,balancing of a one-cylinder
engine 34
9. Principal vector and principal moment of Inertia forces
of counterweights which give the best mean balancing 39
10. Selection of parameters of two counterweights of a
giveq type 1 43
11. Selection,of counterweights for minimizing of mean
reactions in crankshaft bearings 44
Card 3/6

Dynamic Synthesis of Mechanisms (Cont.) SOV/1741
I
Ch. III. Necesaary Information on Functions With Least
Deviation From Zero
12. Necessary condition given by Chebyshev 52
13. Sufficient condition given by author 54
14. Case when all parameters enter (the function] linearly 55
15. The best approximation on a unit circle by means of
a constant 57
Ch. *IV. Selection of a Vertically Balancing Counterweight for
a Locomotive
16. Solution of S.M. Kutsenko 64
17. General method of solution of synthesis problem using
expansion of function In powers of a small parameter 68
18. Approximation of a periodic function with the aid.of a
harmonic of the first order 74
19. Method of successive approximation for the solution-of
the preceeding problem
20. The bost mean approximation as a first approximation
for determination of the best approximatioh 80
21. Adjustment by the methods of S.M. Kutsenko and
P.N. Garshteyn 83
Card 4/6

Dynamic Synthesis of Mechanisms (Cont.) S011/1741
Ch. V. Synthesis of Crane Mechanism
22. Solution of a problem on the synthesis of crane
mechanism by the method of Z.Sh. Blokh and
N.N. Ivashchenko
23. Method of solution using expansion In series
Ch. VI. Dynamical Synthesis of Mechanisms, Which Perform
Lifting Operations
24. Solution of problem on the synthesis of caw mechanisms
of An engine
25. Reduction of synthesis problem to Chebyshev-Markov
problem
26. Concept of the solution of Markov's moments problem
27._Solution of synthesis problem when the velocity dia-
gram Is symmetrical
Ch. VII. Determination of the
Rotary Counterweight
28. Auxiliary Hblder-Riesz
Most Advantageous Shape of a
Inequality
87
92
99
106
109-
112
n8
Card 5/6

Dynamic Synthesis of Mechanisms (Cont.) SOV/1741
29. The most advantageous shape of a rotary counterweight 122
Table 1
Tables 11-111
Table IV
References
AVAILABLE: Library of Congress
LK/Jmr
r
0-22-59
129.
130
131
132
Card 6/6

16(l) PHME I BOOK E(PLOITATION 50V/1642
Geronimus, Yakov Lazarevich
Maogochleny, ortogonalInyye na okruzhnosti i na otrezke; otsenki, asimptoti-
chesk.iye for=ly, ortogonalIxWye ryady (Polynomials Which Are Orthogonal on
a Circle and on a Segment; Estimates, Asymptotic Formulas, Ortiogonal Series)
Moscow, Fizmatgiz, 1958. 240 p. (Series: SovremennWye problemy matematiki)
5,000 copies printed.
Ed.: V. S. Videnskiy; Tech. Ed.: V. N. Kryuchkova.
PURPOSE: This book may be useful to scientific workers and Aspirants working in
mathematics or mathematical physics.
CGVERAGE: The book presents the author's attempt to de7elop and to apply the
methods and ideas of Soviet mathematicians V. A. Steklov, S. N. Bernshtein,
V. I. Smirnov, A. N. Kolmogorov, N. I. Akhiyezer, M. 0. Kreyn and of such
Card 1/5

Polynomials Which Are orthogonal (cont.) MV/1642
non-Soviet -tbematicians as G. Szego", P. Erdo"s. P. Tuxan and G. Freud to
the solution of important problems of the theory of orthogonal polynomials.
The author deals with those properties of orthogonal polynomials, on which
the convergence of infinite prQcesseo connected with orthogonal. polynord&'Ls
depends - the Fourier-Chebyahev process, the interpolation process with nodes
in zeros of orthogonal polynomials, etc. The monograph gives a systematic
presentation of the works of 84xriet and non-Soviet mathematicians, including
the author, in this field of mathematics. The book Is one of a series
published by the editorial staff of Uspekhi matematicheskild, nauk. The
author thanks N. 1. Akhiyezer for reading the manuserLpt and for valuable
remarks. There are 67 references, of which 36 are Soviet, 14 Eng).-fah,
"0 German, 6 French and 1 Czech,
TABLE OF CONTENTS:
introduction 7
Ch. 1. Certain Properties of Polynomials Which Are Orthogonal on a Unit
Circle 10
Card 2/5

Polynomials Which Are Orthogonal (Cont.) SOV/1642
Ch. II. Properties of the'-1~1-(' ) Function 24
Ch. III. Estimates on the Whole Unit Circle
34
Ch. IV. Local Estimates 52
Ch. V. Asymptotic Fbrmaas and Limit Relations 80
Ch. V1. Orthogonal Series
]J.0
Ch. VII. Convergence of Fourier-chebyshev Expansions 124
Ch. VIII. Study of Orthogonal System by Its Parameters 159
C:a- IX. Polynomials Orthogonal in a Flnite Interval of a Real Axis 172
Explanations Of WOls Used iii Tables
Table I. Estimate
199
Card 3/5

PolynorAals Wch Are orthogonal (Cont.) SOV/1642
Table Il. Estimates of (Yrthonormal Polynordals on a Whole Unit Cize-le 200
Table III. Local- Estimates of Orthonoinjal Polynomials in an Are 202
Table IV. Limit Relation on the Whole Unit Circle 203
Table V. Local Limit Relations in an Arc (of a Unit Circle] 203
Table VI. Convergence of Fourier-Chelryshev Expansion on a Unit Circle 2U6
Table VII. Convergence of Fourier-Chebyshey Expansion of an Are (of a
Unit Circle] 207
Table VIII. Conditions for Uniform Permanent Convergence of Fourier-
Chebyshev and Maclaurin Expansions in an Arc [of a Unit
Circle 210
Table IK. Convergence of Fourier-Chebyshev Expansion in an Interval a3
Cwrd 4/5

Polynomials Which Are orthogonal (Cont.) SOV/1642
Rema ks
References
AVAILABLE: Library of Congress
LK/f1c
6-6-59
217
237
Card 5/5

AUTHOR: Ge~:oninuaT-"_", (Kha?kov) 1"07/140- 56-1-3/2 f
TITLEs On Some Properties of the Punctions of the Cla-,7s L p (0 nekoto,.
rykh svoystvakh funktsiy klassa L p )
PERIODICALs Izvestiya vy3shi.kh uchebnykh zavedeniy Ministerstva vysshego
obrazovaniya SSSRj Matematika,1958,Nr 1 pp 24-32 (USSR)
ABSTRACT: Let f(9) be a real 21Y -periodic function of'the class L P P) I
and W p(&,f) - sup jjf(Q + I,)- f(O)II p I lim rd p(S,f) = 0.
lhl,