SCIENTIFIC ABSTRACT BOYARSKIY, A. Y. - BOYARSKIY, M.

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• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

Matbematical. Statistics 385
4. General method of the construction of an Interpolation formula
using
eqmlsWdd values 16
5. Basic ' rtles of the Interpolation formulas usim equisiwed
function values 17
6. Zzamples of practical use of the fundamental rtl a of
interpolation forma" 20
7- ExtraPolation 23
Ch. 3:1. Smoothing Bwkd on the Method of Least Sqw%res and the
Method of
Moving Averqps
1. Connection between arithmetic man and the method of least squares
26
2. Straight line smoothing 27
3- Parabolic smoothing 30
4. Method of moving werages at.given, Intervals 35
5. Method of moving averapsj, when lutarvals are not
pre-estabillshed 36
Ch. III. Mathematical Theory of the Law of Means (of the Lav of
Large
N=bers) and its Importance In Statistics
1. Introductory remarks 42
Card 3/6

MathamtIcal, statistics 385
2. Summary of fundamentals in Vie nathemUcal tbeory of the law or

Ms.=
44
Chance,, VwbabIlity and tw t-b"rees concerning the

calculation
of probabilities
44
Randas variable and Its parameters
44
Buie theorem
conceraln mutbasetilcal expectations
46
ZmVirical and sUchastic usaw
of randam variables
46
On the probability of a.devIatinly-of the
eWIrIcal mean

tte stochastic man
48
Theorem of Chebysbey
50
Limit
theorem of Lyapww
51
3- Basiv principles of the correct organization
of sapplIM

observations
53
4. Hypergeometrk distribution - the tbeory
of noweplacUS sampling
58
Ch. W. Variational Series

1. Variation an a significant characteristic of ~n *ewmna 61
Card 4/6

Mathenatical statistics 385

2. The man as a genersUzIng
characteristic or mny variants or the

index of mas pbenamna.
62
3- Teebaftut or construction or norml distribution
67
4.
Calculation of the degm or closeness between calculated, ad

observed distribution frequencies
74
5. Analysis of the
distribution, vbose asymetry is caused by

changing the averages
77
6. Analysis of the distribution, when asymetry is caused by
the

variety or the aggregate conosition
81
7. Manifestation of
the lm of mans In the process of vAssproduc-

tion of Industrial
goods
91
8. Pbison's distribution - tJw 3Aw or small mobers
1o4
9.
On the distribution or essentially positive values
lo6
Ch. V.
Various Form or Wan Values and Tbelr Quantitative
Relationships

I. On different form of mean vaues LU
2. QMnWAive relationships between the mans of different povers
U4
3. On monotone sequence of power =me I U7
4. Applications or the Interdependence between different power
maw U8
Card 5/6

statistics 383
Ch. TI. Statistical Theory of D7namic Series
1. On specific features of a dynamic series
2. Method of differences used in deter-W the average and the
fluctuation of dynamic series
Ch..V3:1. Theory and Practice of Correlational Calculus
1. On the IWrtance of the c6rrelational calculus: inL practical
statistics
2. On the measure of the relationship degree
3- Other exwW a of the use of a correlatlowl relationship
4. SIzplIf#d procedure of measuring the correlational
relationship
5. General wd partial coefficients of correlation
6. Correlational ellipse
7- Special features of the accepted method of the presentation
of a
gi"n problem
kppndix 1
A"and1z 11
HAIUM: TAbrary of Congress
Card 616 Wool
Jume 30, 1958
124
125
140
143
144
149
150
163
165
170

VINITSXIY, Illya Grigorlyevich; IILsDISHIV. Grigorly
Samenovich: BOYARSKIT.
A-T46,w.professorv nouchn" redaktor; SONSIS, Ta.Me.
re"Iny"Iftftwo
VINOGRADOU. V.A.. takhntcheakly radaktor
[Manuel of mathematical statistics] Pos'oble po
ustaustichestoi stati
stike. Moskva, Oose statiatichaskoe Isd-vo. 1956. 201 p.
(KI-RA 10:3)
(Nnth*w%IcaI statistics)

_�~WSLS# Ye.M., re1ektor; VLNOGWOVA. V.A.,
[Mathematics for sconmists; elownts of the analysis of
infint-
tesimals,0'theory of probabilities and wthoutical
statistical
Matesiatika dlia skonmistov; elementy analiza baskouschno
malykh,
teoril veroiatnostel t matemeticheakoi statiettki.
Moskva, Goo.
izdL-vo. 1957. 366 p. (Mai 1020)
(Sconomics. Nothenatical)

AUTHORs
TITLE#
None Given
2-4-2/7
The All-Union Conference of Statisticians (Vsesoyuznoye
soveshchaniye statistikov)
Vestnik Statistiki, 1957, # 4t pp 12 - 49 (USSR)
By order of the Government, the USSR TsSU (Central Statistical
Administration attached to the Council of Ministers) held an
All-Union Conference of Statisticians in Moscow from 4-8 June
1957, in which more than 650 persons participated. V.N. Sta-
rovskiy, Chief of the USSR TsSU, reported on the first subject
on the agenda#" Practical and scientific problems of statistics
arising from the decisions of the TsK KPSS February Plenum
concerning the further improvement in organizing the administra-
tion of industry and construction trade". The main problem
before the Soviet state statistics is presently, to ensure a
centralized system of recording, primarily in industry and the
construction trade. The article deals further with the present
inflated system of statistics, stating that with the reorgani-
zation of the administrations of industry and the construction
trade, it will now become possible to deliver and process all
statistical records within the organs of state statistics. The
PERIODICALs
ABSTRACTs
Card 1/ 7

The All-Union Conference of Statisticians 2-4-2/7
latter will receive all the required statistical records direct
from the enterprises controlled by the Sovnarkhozes, process them,
and submit the required data to the Sovnarkhozes, local Party and
Soviet organs, Council of Ministers of the USSR Republics and to
the planning commissions. The TsSU will process-the statistical
data according to territory and branches, and submit it to*the
USSR Government and the Gosplan.
Computer stations will be organized at the statistical admin-
istrations of all the oblast's, krays and republics where Sov-
narkhozes were established, and central computer stations will be
set up at the USSR TsSU and at the statistical administrations of
those republics where several Sovnarkhozes exist. Beginning in
June 1957, all the records on industry and construction trade will
be submitted to the local TsSU organs. In addition to those
already in existence,10~ new mechanical computer stations must be
established by June 1957.
The reporter further pointed out that the centralization of
statistics will also be extended to other branches of the national
economy, such as agriculture, trade, health service, educationi
and to industry controlled by local authorities. He also mentioned
Card 2/7 the publication of a number of statistical journals
which began

The All-Union Conference of Statisticians 2-4-2/7
in 1956. A continuation in popularizing statistical data and
in furnishing scientific institutions with statistical material,
is regarded as one of the most important duties of the TsSU.
The reporter mentioned a conference held by the Moscow
Economic-Statistical Institute (Moskovski-y ekonomiko-stati-
sticheskiy institut) on questions of statistical methodology
in studying the productivity of labor. It lasted from 24 - 27
December 1956, with a participation of 390 persons.
Favorable results were achieved in the collaboration of the
TsSU with the Institute of Economics of the USSR Academy of
Sciences, the Scientific Conjuncture Research Institute of the
Ministry of Foreign Trade, the Nutrition Institute of the USSR
Academy of Medical Science, and with other scientific organiza-
tions. An example of fruitful cooperation was seen in the
October 1956 conference of statisticians of countries which are
partners in the Council of Mutual Economic Assistance, where
census questions were discussed.
The report of V.N. Starovskiy was followed by debates in
which a number of persons participated. B.T. Kolpakov, Chief
of the RSFSR Statistical Administration, stated that it was
Card 3/7 necessary to increase sharply the standard of economic work

The All-Union Conference of Statisticians 2-4-2/7
of the statistical administrations and of the district and city
inspection offices. Professor V.S. Novikov of the Moscow
Thstitute of Economics and Sbatistics de,%It with the question of
development of statistical science. D.S. Shemetun,.Chief of the
Statistical Administration of the Drogobych Oblast', Ukrainian
SSR, stressed the necessity for submitting correct and authentic
data. A.G. Pervukhin, Chief of Planning Administration of the
Ministry of Coal Industry, paid special attention to questions
connected with the reduction, simplification and unification of
records. Doctor of Economics, A.Ya. Boyarskiy, Professor of the
Moscow Thatitute of Zconmics that the level
of work of all the TsSU offices should be raised considerably.
M.S. Markin, Chief of Ukrainian SSR Statistical Administration,
stated that 11 administrative economic districts are being
established in the Ukraine. The established Sovnarkhozes are
large economic productive associations. Academician V.S.
Nemchinov spoke about mechanization in the processing of atatis-
tical materials. While giving his approval of analytical comput-
ing machineap he recommends that electronic computers be intro-
duced in the large economic districts and centers of the USSR
Republics. He proposed that an Institute of Statistical Metho-
dology be established and attached to the TsSU and the USSR
Card 4/7 Academy of Sciences, and that an All-Union Statistical
Society

The All-Union Conference of Statisticians 2-4-2/7
be founded. L*K. Volodarskiyt,Deputy Chief of the TsSU; V.V.
Doroshenko, Chief of the Statistical Administration, Mogilev
Oblast'; V.P. Perspelkin, Chief.of the'planning section of a
machine construction plant; V.I. Pereslegin, Chief of Book-
keeping and Accounting Administration of the USSR Finance
Ministry; NeV. Toogoyev, Chief of the Stavropol' Kray
Statisti-
cal Administration, and T.U. Uvashev, Chief of the KazaMbL Sa
Statistical Aaministration; participated in further
discussions.
T.Y. Ryabushkin, Chief of the Statistical section, Institute
of Ecohomice of the USSR Academy of Sciences, welcomes the
actions directed toward the development of a system of
central-
ized state statistics# Academician S.G. Strumilin, considering
Soviet statistics as the beat in the world, indicates a number
of deficiencies especially in the field of agricultural
statis-
tics. V.E. Ovsiyenko, Director of the Moscow Institute of p4m-
ordes and Statistics # dealt with the question of training
cadres
for mechanization of accounting and statistical work.
The article mentions a number of other scientists who parti-
cipated in the debate and summarizes the reporter's concluding
speech. The resolution adopted by the Conference thereafter
Card 5/7 aims at a substantial improvement in the management
of the

The All-Union Conference of Statisticians 2-4-2/7
building trade and at a removal of the numerous departmental
barriers. The reconstruction of the administration of industry
and building trade on territorial principles will create the
necessary conditions for eliminating superfluous recording and
accounting.
The resolution itself is broken up into 5 parts. The first
part' deals with the centralization of recording and statistics
which will eliminate parallelism, and considerably reduce the
recording system.
The second part deals with the simplification in recording
and accountingo th6 mechanization of the statistical work and
computer stations.
The third part emphasizes the improvement of the analysis
of the statistical material. It is also recommended that
account-
ing balances of the income and expenditures of the population,
of labor, of production and distribution of the different kinds
of production be compiled regularly on a territorial basis.
Part four of the resolution deals with the further develop-
ment of statistical science and the improvement of
methodological
work on statistices Among the problems which the conference
considered wares a) questions of classification of industrial
branches, b) questions of working out territorial indexes, a)
Card 6/7 working out methodological foundations for
inter-district com-

The All-Union Conference of Statisticians 2-4-2/7
parisone for a number of indices for the development of in-
dustry and construction trade.
,The resolution also emphasizes the necessity to increase the
participation of scientific institutions in solving problems
of statistics. The establishment of an All-Union scientific-
research institute on statistics is also demanded. It requests
that the USSR Academy of Sciences and the TsSU create an All-
Union Statistical Society as an organization of USSR statisti-
oians, that a bulletin containing the results of statistical
works be published, that the journal I'Vestnik Statiatiki" be
issued on a monthly basis instead of bimonthly, and that the
printing of statistical literatur* be increased.
The last part deals with the necessity of training personnel
for mechanization of accounting and statistical work.
AVAILABLE: Library of Congress
Card 7/7

BOYARSKIY, A. I.
"An Experiment in the Theory of.a Census with Control Bounds."
paper submitted at 31st International Statistical Institute,
Brussels, 2-8 Sep '58-

AUTHORs __Boyaroklyp A. 2-2-7/12
TITLEt Categories of Population to be Usted in.. a
Census (0 kattgoriyakh naseleniya, uchityvayemogo pri perepi-
eyakh)
PXRIODICALs Vestnik 3tatistlkig 19589 # 2g py 61 - 66 (usn)
ABSTRACTs The author given some rooommendations supposed to
ensure a
proper census taking in 1959e~
The census takers will have to register either present
or constant population. The first consists of all permanent
residents# excluding those temporarily absent, but including
those temporarily present, The constant population in-
cludes all persons temporarily absent, but does not include
persons temporarily present. It depends on the census taker
whether a man will be put into the right category or not.
Af ter giving instructions tothe census-taking personnel, the
author points out that the uniformity of regulations and their
strictest observation in the first rule in carrying out stati-
stical investigations. Every mistake made in determining -the
statistical category of a man will lead inevitably to false
Card 1/2 results.

Categories oflopulation to be Listed In a Census~"- . .
There is one sketch.
AVAIUBLZI Library of Cc W ess
9
Card 2/2
2-2-7/12

KHOTIKSKIY, Valentin Ivanovich, mtootistik-kommmist; BOYARSKIT.
I.Ya.,
rodeo, PTATAKOVA# I*D*9 tokhuered,
[Aligning statistical series by the wthod of least square@
(Chmbyehav's mthod) and tables for the derivation of
equations for parabolic curves] Tyravnivanie statiatichookikh
riadov po mtodu'nalmn'shikh kwadratov (sposob Chabyahave)
I tablitey dlIa nakhoshdonlia uravnenii parabolichookikh
krivykh. Isd.2. Koskva, Goo.stat.isd-vot 1959. 85 p.
(KIU 12:6)
(Hathassitical statistics)
.!L~k

A R S .-AjA
17
d H,
ip
l

YEZIIOV Anatoliy Ivanovich; BOTARSKIY A.7a.,,, red.; SHENTSIS, Ye.N.s
red.; PONOMAREVA, ix-,~ ~-V
[Flattening and calculation of distribution series) Vy
ravnivanie i vychislenie riadov raspredelenii. Moskva#
Gosstatizdat, 1961. .335 P. (MIRA 150)
(Mathematical statistics)

HIKBALEVSKIYO B.N.; NENCHINOV., V.S.., akad., otv. red.;
BDIARSM
,, prof., doktor ekon. nauk, red.; DOERUSMN, R.L., kand.
A.Ya
fiz.-mat. nauk, red.; YSTISUVSKIY, P.S., kand. ekon. nauk,,
red.; KHOWAKOV, A.I., red.izd-va; TIKHO14IROVAj, S.G.,
tekbn.
red.
[Transactions of.the Conference on the Application of
Mathematical Methods in Economic Research and Planning)
Trudy
Nauchnogo sovesbchaniya o primenenii matematicheskikh
metodov v
ekonomicheskikh issledovarilakh i planirovanii, Moscow,
1960.
Moskva, Izd-vo Akad. nauk SSSR. Vol.2. [Mathematical
analysis
of expanded production] 1-tatematicheskii analiz
rasshirennogo
vosproizvodstva. 1962. 266 P. Vol-3-[Interbranch balance of
the means.of production and its distribution in the national
econony] Mezhotraslevoi balans proizvodstya i raspredeleniia
produktsii v narodnom khoziaistve. 1962. 342 p-.
Vol.7.[Mathe-
matical statistics] Matematicheskaia statistika. 1962. 232
p.
(MIRA 15: 5)
(Continued on next card)

MIKHALEVSKIY, B.N.-- (continued) Card 2.
1. Nauchnoye soveshchaniye o primenenii matematicheskikh
matodov v ekonordchaskikh isoledovaniyakh i planirovanii,
ra
Moscow, 1960. 2. Labo toriya po prlmeneniyu
matematicheskikh
metodov v ekonomicheakikh issledovaniyakh i planirovanii
Akademii nauk SW (kor Mikhalevskiy)- 3. Moskovskiy gosudar-
stvennyy universitat irk. MiV.Lomonosova (for Boyarskiy),,

BOYARSKIY, Aron Yakovlevich; SIMTSIS, Ye.M.., red.;
PYATAKOVA, N.D.,
[Studies on mathematical
economics]Matematiko-ekonorAcheskie
ocherki. Moskva,, Gosstatizdat, 1962. 399 p. (MIRA 15-.9)
.(Economics, Mathematical)

SAVINSKiY, D.V., prof.; NX~~JY ~AYa.; PODVARKOV,
G.A.; CHEKANSKIY,
N.A.; GROMYKOj, G.L..: TRUDDVA9.M.G.j- ITVWVIAL~~-~r"4
'-KOZWVA, T.A., tekbne red,
[Economic statistieslEkonoxicheskaia statistika; kurs
lektsii.
Pod red. D.V.Savinskogo. Moskva, Izd-,Yo Hoak. univs,
1962. Z70 P.
(MIRA 16:2)
1. Moscov. Universitet. Wedra statiatiki.
(statistics),

.ISE Illy& Grigorlyevich; KILIDISHEV, q4gpriy Semenovighi
1. &L, nattahnyy red.; PREVEWTSEVA, A.G., red.;
PI&BUIX,Aj
n'TU$HENKOVA, T.P., tek)m. red.
fBasic priie'ip:len of math6matical statistical onnovy matma-
ticheskoV. statistikia, Mokya, Gonstatisdat, 1963. 307 p..
(MIRA 16t6)
(Mathweatical statistics)

LANGE, Oskar; MARSHY, A.Ya.., red.; ZAYTSEV, N.V., red.
[Introduction to econometrics! Vvedenie v ekonometriku.
Pod obshchei red. i a predisl. A.IA.Boiarskogo. Moskva,
lzd-vo "Progress," 1964. 294 P. (MIn 17:5)

YAsTREMKIN, Boris Sergeyevieh, zasl. deyatelf nauki,,prof"`b
BWARSKTY k.Ya.,, pro'
[Selected works] lzbramiye tnidy. Sost. i nauchn. red.
A.IA.Boiarskii. Moskva, Statistika, 1964. .389 P.
(,maRA 17: 10)

BOYARSKIY, B.,, kand. biolog. nauk
Plant Protection Experiment Station. Zashch. rast.
ot vred.
i bol-. 10 no.12:13-15 165. (IMM 19:1)
1. Direktor stantsii. zashchity rasteniy Moskovskoy
ordena Lenina.
sellskokhozyaystvennoy akademii im. Timiryazova.

BOYARSM 2 G aspi rant
Methods of preserving Xwrirus antigens (with summary in
Englisb].
I-zv. TSKhA no.2:221-223 161. (MIRA 14:8)
.(Virus diseases of Plants)
(Antigens and antibodies)

BOYARSKIY. B PLOTNIKOV, V.F.; SOBDIEVA-DOKUCHAYEVA., I.I.; TSVETI N.N.;
AEMRA NKOp V.V.
Information and brief news, Zas6she rest. ot vred, i bol, 8-:
no.41.56-59 Ap 163. (KMA 16t10)
(Plants, Protection of)

BOYARSKIY, B.G., kand. biolog. nauk.
Serodiagnosis in-plant protection. Zashch. rast, ot vred. i bol.
9 no.12:36-37 164. (MBA 1814)
1. Opytneya stantsiya zaahchity rasteniy Moikovskoy ordena
TAnina seltakokhozyaystvannoy akademil imoni K.A.Timiryazeva,

BOYARSKIY, B. V.
*Somoi Boundary Value Probl6im for an Elliptic System Idth Two
Independent
Variables." Cand PhFs4&th Soi, Moscow State U,, Moscow, 1954. (KL, No
2, Jan 55)
Survey of Scientific and Technical Dissertations Defended at USSR Higher
Iducational Instiutions (12)
SOs Sm. No. 5561, 24 Jun 55

lip
disc and
n
'Idf'T crnd,
:'or" At lh~

~: 14, 11, !-. ~,-, - - .11 ~ -, - - -
. I ~ .. ~ ~ Z~,- .! ., i~;, I "it l'i : " ~
I . . . -
I - . , .

VC.
~t,
AUTHOR: 130YARSKIY,. 3.V.- (Warsirwa) ic-f-'43-4-3/4
TITLES Generalized Solutions of a System of Differential Equations
of Elliptic Type of First Order With Discontinuous Coeffi-
cients (Obobshchennyr resheniya, sistemy differentsiallnykh
uravneniy pervogo pc--yadka ellipticheskogo tips, s razryvnymi
koeffitsjyeitami)
PERIODICAL: Matematichoskiy Sbornikfl957,Vol 43,Nr 4,PP 451-503
(USSR)
ABSTRACTS The author considers linear systems
v = 4u + BU + au + bv + e
VX = r2 x + S Uy + cu. + dv + f
whereot, B, ~,E are measurable functions and satisfy the
condition 03+~)2>
,,k0> 0 . By introduction of the
complex variable w(z) = u + i v (1) is brought into the
form
(2) w- - ql(z)w, - q w = Aw + Bi + C
z 2(z) z
Then this equation is investigated whereby it is supposed
Card 1/3 that the equation is defined in a bounded domain G , that
qj(z) and -q2( z) are measurable,lql(z)l+lq 2(z)11< Qo 2
Just like in his former publications ef.2, 31- the author
applies a method proposed by Vekua [Ref.11 which is based
on an inequality of Calderon and Zygmund TRef.4] allowing
a much simplified treatment of the subject in L , p> 2 .
At first Beltramils system wi - q(z)wz = 0 ispoonsidered,
V = Aw + B; and
then the more complicated one w- - q(z)W"
z
finally (2) . The structure of the generalized solutions is
investigated, different representations of the solutions
are obtained and from these a series of properties and exact
estimations is derived. In particular it follows that the
solutions of are closely connected with analytic funz-
tions of a complex variable. A general theorem of existence
is set up which in many cases allows an immediate construc-
tion of the solution. For a=b=c=d=e-f=O and otherwise con-
tinuous coefficients the generalized solutions of (1) are
identical with the quasi-conformal mappings according to
Lavrentlev. With the aid of the developed theory the unique-
ness of the quasi-conformal mapping of a simply connected do-
main onto the unit circle is proved. Some examples of appli-
Card 2/3 cation are considereds the Diriehlet problem for the
circle,

Generalized Solutions of a System of Differential Equations
39-43-4.-3/4
of Elliptic Type of First Order With Discontinuous Coefficients
correctness of the Cauchy problem etc. 25 theorems and nume-
rous lemmata and consequences are presented. A small part of
the very comprehensive paper was already published as an-
nouncement [Ref.2) . 18 Soviet and 13 foreign references are
quoted.
SUBMITTED: 21 January 1957
AVAILABIX-i Library of Congress
1. Differential cquationa-Theory
Card 3/3

WTARk9Iv-&,Vv-
Ronotopic clasess of matrix functions. $00b. AN G=z*SSR 21
no.3:263-269 8 '58. (Min 12:4)
1, AN SSSR9 Pat smatichookly - lust Itut Ine VeAe Steklove,
Mcmkva.
Prodstawleno akad*mIkM I~N-F Toknas
(AmtIonal analysis)

BOYARS.11Y. B.V. ,
of the gllb*A probleu f or a holomorphic vector.
Boob. AN Gras. SSR 21 : no.4:391-398 0 '58. (MIRA 3-2:4)
1. Ali SSSR, Katematiaheskly Institut in. V.A. Steklovs,
Moskva.
Predstawleno akademikm I.S. Tekmae
(Functional analysis)

AUTHOR:
Boyarskiyo,Mi 20-119-2-1/60

TITLE:

On a Boundary Pr"o tions (0b
kez of the Theor of Pane odnoy

granichnoy zadache teorii funkt97
PERIODICAL:
Doklady Akadenii NauT, R1958, Vol 119, Nr 2, pp 199-202
(USSR)
ABSTRLCTt
Lot G be an (M+1)'-tuply connected domain of the
x-plane being

, where ri are closed non
bounded by r
4: r,+...+ r

.
o
intersecting curves and r encloses all other rip
0

Let Oidenote the class of functions holomorphic in G and

continuous
in G + r

Problem 1: Find all pairs of functions ot, yro 01,

satisfying
the boundary condition *+ x f on r, where f

aAd X are given complex
functions of the point t r and on r

being continuous with respect to
H81der.

Problem IIS kn
11 -*) p qC- Ot 9 AFC- Ot , satisfying the
k
L
fj

.
t
condition %f + W
0 on ro where t - t(s) is the
j,

equation of r a are length.

Theorem: Every solution of I is
continuous with respect to

Hblder in G +

Card 1/2
Theorem: For n 4 arg .4 0 the homogeneous problem I
21C

r

On a Boundary Problem of the Theory of Functions
20-119-2-1/60
(f !69) has no solution different from zero.
Theoremi If n>-2(m-1), then the nonhomogeneous probl*s I
always can be solved, while the homogen*ous problem ban
exactly 2n-2(m-l) linear independent solutions. If a-40,
then the inhomogeneous problem is solvable only then if
1* - 2(M-1) - 2n conditions of the type I -fjf dt - 0 are
r
satisfied. Then the solution is unique. The %P, are the
complete system of solutions of II. Beside of the
mentioned
three theorems the author formulates four further similar
(partially more special) theorems.
There are 5 Soviet reforences.
PRESENTIDs October 16, 1957, by S.L.Sobolev, Academician
SUBRITTZDs Octoberr 14. 1957
Card i/2'

AUTHOR: Boyarskiy, B.V. and Vekua, I.N. 38-22-2-2/8
- _~Y,~~e _ __
TITLEs Proo 0 Rigidity of Piecewise-Regular Closed Convex Sur-
faces of Nonnegative Curvature (Dokazatellstvo zhestkosti ku-
sochno-regulyarnykh zamknutykh vypuklykh poverkhnostey neot-
.ritsatellnoy krivizny)
PERIODICALs Izvestlft Ak&d=1I 'nm* S38R.,-.3erlyt M&temtIChegkaY&
aq
Nr 2, pp 7 6 T4SARI 221
ABSTRAM Let X , X (u,v) be the equation of a regular surface S
which
in limited by a-finite number of pi-%Ce *se smooth simple qurves
L09 L19 so@, L m e Furthermore let Y =WY (u,v) and T = 7(ugv)
be the fields of.displacement and of rotation which correspond
to an infinitely small deformation of the surface. Then it is
dY , Z)(dY , dXed - 0 , from which Blaschke [Ref 11 with the
aid of the Ostrogradsky-formula obtains the following relations
(1) 2 ~JX Zu ZV dudv X Z di*
L
where L denotes the totality of theL
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Proof of the Rigidity of Piecevise-Regular Closed Convex 38-22-2-2/8
Surfaces of ITonnegative Curvature
The authors consider closed convex surfaces which are com-,
bined together from a finite number of regular surface ele-
ments with nonnegative Gauss curvature. By application of
(1) (in a somewhat varied form) to each regular part of the
surface and by addition the rigidity is proved at first for
the case that the limiting contours of the single partial
pieces are Jordan curves and then for the general case. At
first conical points are excluded. Then it is shown by a li-
mit passage that the proof even holds in presence of conical
points. There are 2 references, 1 of which is Soviet, and
1 German.
SUBMITTEDs April 1, 1957
AVAILABLEs Library of Congress
3Wfaees_4ktb=&tt"I emdYsIs
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BOYARSKIY, B.V.
A boundary problem in the theory of functions. Doki. AN SSSR
119 no.2:199-202 Mr. 158. (MIRA 11:5)
1. Predstavleno akademikom S.L. Sobolevym.
(Punctions. Analytic)

AUTHORs Boyarskiyv B.V. 20-119-3-2/65
TITLEt On a'Speci *&I Case of the.Riemann-Hilbert Problem (Ob
osobom
sluchaye zadachi Rimana Gillberta)
PERIODICALs Doklady Akadexii Nauk, 19589 Vol 119, Nr 3, PP
411-414 (USSR)
ABSTRACTs In an (m+l)-fold connected domain G with the boundary
r -
-r +r + ..* + r ri (I r - o r. smooth, functions
0 1 a i i
%f(z) are to be determined which #re holomorphio in G, con-
tinuous in a + r and for which Re(A - 09 whereby A is a
function of the point t c- F, Pa .= As a special case of
this Riemann-Hilbert prgblem the case is denoted, where the
so6alled index n a 1/21r.6 r arg A satisfies the inequality
OKn 4a - I. Since only the question of the solubility of
tble special case is investigatedg the author reducen the
problem to a qualitatively equivalent simpler one ( r 0 unit
circle, r circles etc). Four theorems are proved* As the
main result the author states that even in the considered
special case the formula of Vekua [Ref 21 a
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On a Speoial Case of the Hismann-Hilbert Problem
20-119-3-2165e
1 M max (0,2n - m + 1)
holds in general for the number of linearly independent so-
lutions, The validity holds in a certain sense for the "pre-
ponderant majority' of the cases. There are 4 references,
3 of which are Soviet, and I American.
PRESENTEDs October 169 19571,
by S.L. Sobolevp Academician
SUBMITTEDs October 14, 1957

IUTHORs Boyarskiy, B.V. SOV20-122-4-1/57
TITLEs The General Representation of the Solutions of an Elliptic
System of 2u_E4uations in the Plane (Obshcheye predstavleniye
resheniy ellipticheskoy sistemy 2n uravneniy na ploskosti)
PERIODICALs Doklady Akademii nauk SSSR,1958sVol 122,Nr 4,PP
543-546 (USSR)
ABSTRACTs The author considers the system
(1) WY - QwZ W Aw + BW + F,
where w(z) is the sought n-dimensional complex vector, A and B
are given quadratic complex matrioes, F is a complex vector and
Q= tQVQ29"'PQp~ a quaai-diagonal matrix. Here Q i- t qlk,il
are quadratic matricesp q lk,imo for k~plj qll,ioq, a,d q lk,io
=Bl-k for k