SCIENTIFIC ABSTRACT BOLTYANSKAYA, E.V. - BOLTYANSKIY, V. G.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000206210003-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 9, 2000
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

ACC NRs APS029259
11000,cn
The starting material used was ethyl's -(2-pyrimidyl)pyruvate
(11), which reacted
with hydroxylamine to form ethylO4,
-oximino-p-(2-pyrimidyl)prcpJonate (III). The
latter is then reacted with stannous chloride in an acid medium;
this single step
accomplishes the reduct-ion of the kettoxime fragMent and the
saponification of the
ester group, and yieldsA -(2-pyrimidyl)alaane M. This new
pyrimidylamino acid
has very.definite amphoteric properties. Authors thank Prof. M.
A.-ProkoEfycvfor
his interebt and attention to this Ork, and are als'o deeply
grateful to 'k. P. -5-5
Skoldinov for the tetraethoxypropane which he kindly supplied.
Orig. art. has:14..,,- -
SUB CODE: 07 / SUBM DATE:' llJan65 / ORIG REP: 001 / OTH REF: 004
jw

N.A.; BOLTIANISKAYA, .1E.V.; A.A.; '-ZLFC'ITYA~I, -Zh.
F I I Vorm oittirruwt.~s In D(.k 1 . A;'.' 1 :4
933 0 '! 5. (M--Mli 18:10
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(--Ii (t-or Kratit lnllj~)V).
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A

TEPENTIYEVA, I.V.; BOLYAK, V.A.
Spectrophotomptric determination of "brevikollin".
Izv. LN Mold. SSR
no.10:71-74 162. (MIRA 17:12)

KOTELINIKOV, Boris Pavlovich; AQUANOVS. "IY
-Dnitriy-14jkhaya-o~hi-
AGEYEV, P.M., red.; GONCHAROVA, Ye.A., telft. red.
(First in the country; story of the Shebekino
Combine of
Synthetic Fatty Acids and Aliphatic
Alcohols]Pervyi v strane;
rasskaz f: Fhebekinskom korbinate sinteticheskikh
zhirrykh kis-
lot i zhii-Wkh spirtov. Belgorod, Belgorodskoe
Imizhnoe iz~-
vo, lo,61. 49 p. (MIRA 15;8)
1. Direktor Shebekinskogo
naucYno-.issledovatellskogo instituts.
sinteticheskikh zhirozameniteley i moyushchilc:-
sredsty (for
Kotellnikov). 2. GlavrWy inzhener kombinata
sinteticheskikh
zhirnykh kis--)t i zhirrorkh spirtov (for
Dolyanovskiy)*
(Shebekino--Oils and fats)

BOLTLINSKIY, A.
[Problems of vocialist organization of labor and wages in
assembly-line
production] Voprosy sotsialisticheskoi organizataii trada 1
-arabotnoi platy
v potochnom proiZTodate. [Moskva] Gas. ird-TO polit.lit-ry.
1953. 159 P.
(MLU 6:8 )
(Industrial management) (Wages)

,BOLTYANSKIY, A. ----
Comprehensive utilization of hidden potentialities in
the growth
of labor Droductivity. Sots. trad no.10:104-112 0 156.
(MIRA 9:11)
(Iabor productivity)

AUTHOR: Boltyanskiy, A. 50V-2-58-8-3/12
TITLE: The Study of Mechanization and Automation of Industry
(Ob
izuchenii mekhanizatsii i avtomatizatsii v promyshlennosti)
PERIODICAL: Vestnik statistiki, 1958, Nr 8, pp 20 - 29 (USSR)
ABSTRACT: Many questions on the characteristics of
mechanization and
automation of industrial production have not been complete-
ly worked out theoretically and are interpreted in practice
in different ways. Such initial concepts as partial and
complete mechanization or complex mechanization are without
a definite content and clearly outlined limits. The pre-
sent --article examines some of these questions, taking the
work in foundries of machine construction plants as an ex-
ample. A proper evaluation of the engineering-economic
degree of mechanization and automation can only be given
provided the following four basic indices are thoroughly exa-
mined: 1) the extent of mechanization and automation of
individual operations; 2) the extent of the complexity of
Card 1/3 mechanization and automation in a section, a
workshop or

'The Study of Mechanization and Automation of Industry
SOV-2-58-8-3/12
in the enterprise as a whole; 3) the engineering degree
of the adopted means of mechanization and automation; 4)
the effectiveness of mechanization and automation. The
author quotes generally accepted definitions for stages of
development of partial and complete mechanization and auto-
mation with which he does not entirely concur. He examines
the difference of opinion by examples~quoting in this con-
nection a table which shows the expenditure of time in mold-
ing one machine part. He tries to prove that an increase
in the degree of mechanization and automation is accompan-
ied by a relative augmentation of the share of manual labor
if all or most of the labor-consuming operations are not
simultaneously mechanized. A higher form of mechanization
Card 2/3 should be regarded as that in which basic
operations are

The Study of Mechanization and Automation of Industry
SOV-2-58-8-3/12
completely mechanized, and only auxiliary work is performed
by hand. The lower stage of mechanization is the one where
only a part of the basic operations are mechanized. Turn-
ing to the complexity of automation, the author maintains
that none of the existing definitions are sufficiently
clear. He illustrates this by particulars on the operat-
ion of a continuous conveyer section of a foundry. To
characterize the degree of mechanization (automation) of an
area, workshop or enterprise, the author suggests consider-
ing several symptoms and comments on them. Dealing with
indices of effeotivenese of mechanization, he states that
effectiveness is not characterized by any single index but
by the total of indices. Thore are 6 tabloa and 5 Soviet
references.
Card 3/3

INVENTOR: Bol-'.Yanskiy, A. A.; Pshenichnikov, Yu. V.
ORG: None'
TITLE: Measurement attachment to fit on an automatic machine for
multiple-range
;.sorting according to deviation of some parameter from standard.
Class 42, No. 182898
(announced by the Kuyliyshev Aviation Institute (Kuybyshevskiy
aviatsionnyy inatitut)]
SOURCE: izobretniya, promyshlennyye obraztsy, tovarnyye znaki, no.
12, 1966, 89
TOPIC TAGSi. analog digital converter, digital analog converter,
sorter, parameter
.ABSTRACT: This Author's Certificate introduces a measurement
attachment to 'Lit on
&r. automatic machine for multiple-range sorting according to
deviation of some para-
P-eter from standard. The device contiiins an industrial-frequency
induction trans-
ducer for converting this deviation to AC voltage. Measurement
accuracy is improved
and sorting speed is increased by equipping the instrument with
magnets, a decoder
and a converter with feedback which includes a device for
comparing AC input voltage' ~1
of industrial frequency with the output-voltage of the converter.
The converter alsol-
incorporates a generator null indicator connected to the output of
the comparator
and generating pulses if the'amplitude of the AC input voltage in
the comparator is
-greater than the oVtPut voltage of the converter. Counters
convert the pulses from
..Card 1/2 UDC; 531-T:621.3-078.3

output ofthe generator null indicator to binary code. A controlled
Yoltage divider
converts this binary code to DC -voltage which is fed to the
comparator for checking
against the AC input voltage. ' The sorting command is given by
the magneto 'which are
connected by the decoder to the converter counters.
1-4.-agnets; 2--decoder; 3-generator null
ind-Acator; 4--counters; 5-voltage divider
SUB CODE; 09, 13/ SUBY, DATE; 3lMay65
Card

ACCESSION M AR4042171
8/0272/64/C)OO/005/0024/0024
SOURCE, Ref. th. Metrologlya I ismerit. tokhn, Otd. vy4p.9 Abse
5032*138
AUTHOR: Boltyanakiye A. A.
TITLE: Inductive multirange motor of small displacements
CITED SOURCE#. Nauchn. tr. vuzov Pbvolzhlya, vy4p. 1, 1963, 180-186
ITOPId TAGS: Inductive multirange motor, d2splacoment
ITRANSLATION: A differential sfultirange Inductive pickup with
linear scale (non-
~linearity within 2%) is described.' Limits of measuremento 4 30;
130; 1~00i and
+60 and + 300A& Meneuring force 100-150 goo Eight 171luatrationso
Bibliogra-
1�30, -
lphye. 4 refevinces.
sue CoDet =9 1z EMCM 00
:Card 3-A
-- - - - -------

B 0 LI-ITYI AIIN~ k,Ae. ~. ~ a/a A )- I-
. ekon. nauk.
os of assembly line operations in foundries. MS-
shinostrottell no.1:11-14 A 158. (xiRA na)
(Foundries) (Assembly line methods)

117-`18-7-10/25
AUTHOR: Boltyanskiy, A.I., Candidate of zconoriiic iciences
TITLE: Production Reserves on a Poundry Conveyer Line (Rezervy
pro-
izvodstva na konveyernoy linii v liteynom tsekhe)
PLKODIGAL: Mashinostroitell, 10,58, Nr 7, pp 30 - 32
ABSTRACT: The work of the conv 10 '4
of the "KATEK" Plant, a foundry inkuybyshev, is here stati- ti-
cally analyzed. 1'BotFF_Pr.Lr-_rks1' Lormin.-- on the line are
explained
by incomplete mechan*4:,tion. Only the preparation of molding
mix is nearly fully Of 27 different operations on-'.A
10 are mechanized, air, 103 workers of the 133 working on the
line are occupied by manual work which includes the pouring.
The mechanization of the line is illustrated in table 3 showing
the situation in 1950 and after re-mechanization in 1957. The
author stresses the J~& ovitut of continuous rhythmic work. The
ChetvUrtyy Gosudarsta"N Ordena Lenina Kuybyshevskiy pod-
shipnikovyy zavod (0s StateOrder of Lenin Kuybyshev Bearing
Plant) nd the plani.~ "Avtopribor" in Leningrad are mentioned
as plants where single, "advanced", sections and shops do such
Card 1/2 rhythmic work. There-, are 3 tables.
rl: M193

Production Reserves on a Foundry Conveyer Line
117-58-7-10/25
1. Conveyer system-4W&lyzim
Card 212

SOV-3-58-1%--15/23
AUTHOR: Boltyanskiy, A.I., Candidate of Economic Sciences,
Docent
TITLE: To Cultivate an Economic Way of Thinking (Vospityvat'
eko-
nomicheskoye myshleniye),
PERIODICAL: Vestnik vysshey shkoly, 1958, Ur 10, PP 74 - 77
(USSR)
ABSTRACT: An increase in the economic training of proppective
engineers
can only be attained with the active cooperation of all the
chairs of a vtuz. The problems which the various chairs hnva
to face in this connection must be -differentiated. For this
purpose the Kuybyshev Aeronautical Institute has divided en-
gineering subjects into 3 categories'- general theoretical,
applied, and specialized. The autho; states which subjects
Dertain to the different categories and that the possibili-
ties of furthering the students' economic thinking mount as
they transfer from the first to the third group. He describes
how the connection between the subject (mathematics, drawing,
Card 1/2 engineering) and economics can be established by the
instruc-

To Cultivate an Economic Way of Thinkin ',0V-3-5B-l0-15/23
tor during the lesson. Other methodical means to cultivate
economic thinking are also given: the preparation of
special
questions on the economics and organization of production
during laboratory and other exercises. The article contains
1 table.
ASSOCIATION: Kuybyshevskiy aviatsionnyy institut
(Kuybyshev Aeronautical
Institute)
Card 212

SOV/122-59-4-23/28
AUTHOR: Boltyanskiyj A.I.7 Candidate of Economic Sciences,
Doce-RT-
TITLE: On the Planned and Actual Effectiveness of Technical
Organisation Measures (0 raschetnoy i deystvitellnoy
effektivnosti organizatsionno-tekhnichoskikh meropriyatiy)
PERIODICAL: Vestnik Mashinostroyeniya, 1959, Nr 1+1 PP
78-80 (USSR)
ABSTRACT; Organisational and technical measures are judged
by the
predicted annual savings and the period during which they
pay for themselves. The difference between measures such
as design improvements or new production methods which
have an integrated effect composed of savings throughout
the chain of manufacture and those which have a localised
effect, is emphasised. The computation of the actual
economies arising from improvements is discussed and
illustrated with examples. Again, the effect of
improvements in one stage on the total cost must be
considered. Some localised improvements yield no
overall savings, mostly because of poor coordination with
the complete prod-action process. Improvements at
Card 1/2 different stages should be complementary. In a
factory
of electrical automotive equipment7 a sand blasting

SOV/122-59-4-23/28
On the Planned and Actual Effectiveness of Technical
Organisation
Measures
installation was replaced with a shot peening plant.
The predicted productivity was higher but, owing to the
absence of spare parts and an excessive hourly output
without accompanying organisational measures to utilise
the released time of the operatives, no actual economies
were achieved. An automatic machine for assembling
roller chains did not yield an overall saving in the
absence of measures to speed up preceding operations.
Other examples are given showing individual improvements
yielding only a fraction of the predicted saving through
poor coordination. Reduced machining times led to under-
loading of machines. The conception of an "implementation
factor" for organisational and technical production
Card 2/2 improvements is introduced.
There is 1 table.

BOLTYANSKIYP A.I. (Assist.Prof-Cand.Econ.Sc.) I
"On certain Processes of DeteminiriF Effectiveness of
Industrial Improvement."
report presented at the 13th Scientific Technical
Conference of the Kuybyshev
Aviation Institute, March 1959,

MOCHALOVA, A.; BOUTYANSKIT, A.; THISHIN, G.
State Bank control over the delivery of goods in
the trade
system. DenA I-tred. 18 no.2:6o-63 F 16o. (MIRh
13:1)
(Russia-Commerce) (Credit)

lie
0
An emimple
fBLJ~ ~as 'I~V
hose topoLogical '5-ffft~ three-~Cri
' ' rDo ,,ad Wh(
Dokl~dy ALA Nau-' SSSR (N.S.) 67, S97-S99
(U- 4'1;
19,V
y
(jt~ _
.~ian
(Russiari)
T
Let p be an arbitrary. but fvxed,~ prinie
and ~let be an~
Le
_t P bc
!q-
A, posst;ve integ , Tlis-'authorconstructs.,
arbitrary, but rj% eir,
arbitrary. I
a space P (lying, in
fotir-ditreit--.~onal';Eiiclideiii gpace)k
P = P(p, h). such that dirm P - 2-but d.im
(P XP) J. - -6
follows. Begin with an minulus, 1C. Uith
edges ey and
0 ldenti~"- as a siflq!e 'mil:t. cacti sset-
~af ~ Points -of 'a tvI 1"'Ch
rlivide ir into P ell,--al ~Lrcs
and:.:~niiiarl~ jl~entify' 4!3'Cfl se''t of
pk poirit, Of [I (liVi,.!' drcs. 'The
reWfting.- :'C' 1:',.'
into P"
ln~
iedron is ciffled a Zeaf -of nedcr"k. a t
polyl d is
P J:
I C.", which iesult.fr6m ~a bind
Its edgms a:atid b ard t ip "circl
CWIon~s~ \'Oi~ if a 6Iar:Jxo16_"
rerpectively afttr the ific-atift
is cut out of some two-cell, and
the'~~dgC'411, Of ri, Isn"latched"" 1
vit:% the e thelhol~ of th ~t'
edge of this fuile, ih n 'IS
o -Aid to be overlaid %vi-h the leaf;il'.
:"qc-,t One dchiles-i
~~)Wer fli,.i dependint, e~n die ~ntegcrs
4'.and 1" ag, fallowi., i:
r~cart with a kaf Ili, e edges.
0t 3 h6le~ in it" note touching
cf the leaf, and ove&iy this, hole'. "vith
a~ leaf rTA,,-. in tbaC i... ~:_i 1
leaf evt our a linle not m&t.ting
its.:Ldgeii and ovtrLY th'
hole with a leaf Crintinue this
leaf-upon-leaf to the Ith
1~tage. The resulting p;-jfyi-_-dron is t1k,
t'de,,~ired totV6--
Let S' 1)4L a triangulated two-#A imensional
Sphere, In each
i-implex, cut out a ficloy arW overl ; wi h
the leaf. TT*. Let
t
IP&A, denote the reStilitril, space, -and
-suppose m6w tha
t
iomehow there i~~ conmructed a tmanruLted
surface Pa,.
1~flad- Sphere an d overizid le--ts I
11~k) consisting of r if,
of respective order:,, k, A, 4- 1. No-, ctit
a hole in each'
nging to S' are to b~ overlaid
-'irnplex of -Pt. 1. The llolct i-~60
g eaf n.
-11, b"t the hnles.bclonr;ng to
...,ith (k, 'rhis c!ims the poly
The construc
hedron of the n-t ~',C-T'Oted by P1.14.1
tions can be tholi%ht (;f -,-5 carried out
in a four-nparcc. dic''
simplexe'~ of sormAlve surfzces
arpprcrzlcllm~
s-,Irfk 5 P
'illii is
it (o a h1fiti-- -~"Tfacc fjem'~)tcd by P
desired qjace P. The Pr(v. :.F~ Skutclmd i-1
some dc';~i'
L. Z_iPPIM

7~_
7-1i6ityansm, V. on the ~!Mnsloxud
trklady _Akid._Natik,SSSR- tq.S.)_67,17
_~XA
Tbe~ cQ=P-' elia !f talled dimcn~)Qnalj
9461131) if, forevery compact Y, thol iss6ciatedili
P
(1) dim (XXT)Z_dim X.+dim-Y.
The abblor aratelizes this v tai MIAng an
priklemdue,toT.
1-238 (193 2), problem-XIIIi it. is known. tha hca4r;a
t all liy
and 01 Dne-dinjcnAlonal Compacta Wong to 6e A I I wt
let P.,, for each prime p,-denote the compatturn constructed
f by the authmin a previous mte (s4ine val., 59?-;-5S4.0949);:-
thesv~Rm 11,45 not' belonging, to ibc 4ass in, tlue&;
],and
tion, thrn the first theorem is as follbiwis., in -Ordefthat-X~
':betap6logi~~lydirri-cn--~ionallyfull-valuediiisnece---qaryancl
t is
sliffident that rela6sn (3) hold whenever, Y=mPi, for an- en,40nallly
full-valued, i
be dim
ior every
primess p. The cornpacturn X is algebraically Then in order that X'
that dir, X' = DP(X%),
sufficient
full-vulued -if dim X= v. for some 7j. and if for every prime P
DereS53'ry ?,ndprools appm to b. qjjite detailed.
P pji,, (Flushing, N~ Y.).
there e.,xists a rdalive cyde 7, mod p in X which ii'not pnrne
cally divmble-by p. The author chows: that ~ them',
hornolcgi
algebraic and topologic defin ions ar~ equivalent Let Q,,
denbte the additi V719' gioup of ratianals of: the form. m1P,
p a fixed prime-red6ced mod L Let D,(X) denote the
homolojjy V-dimosim: of X, with Qi. ~as cmfficient group.
Ma
Vol
no

UWR/kathematics - Dimension Theory,
May/Jun 51
"0 Topology
11concerning a Theorem on the Addition of
Dimen...
sions," V. Boltyanskiy
"UsPekh Matemat Nauk" 'Vol VI, No 3 (434),
PP 99-128
Considers the construction of compacta Fmy
Pm and
their linglutination'; dimensions of
phi-compactumo.
Pontryagin's compactum; topological
product (pro-
duction) of structured compacta; relative
cycles
of complexes Ki; relative cycles of
complexes
K xL - 2-dimensionality of compacts, Fm;
dimen-
sloniallity of the product FmxFn; relative
cycles
1188T56
USSR /Mathematics Dimension, Theory,
KaY/Juz 51
Topology (Contd)
of couplexes.Kk 1; relative cycles of
complexes
30~111 '; 2-dimensionality of compacta P ;
dimen-
a I
501dEity 6f the product P xPmP additivity
oi dimen-
sions, vith respect to pri;Te modulus.
18ft56

BOLTIYANSKTY, V. G.
"Construction of a Two-Dimensional Compactum Possessing a
'Mree-Dimensional
Topological Square," Usp. Mat. Nauk Vol. 6 No. 4 (44), PP
193-220, 1951.
u-1635, 16 Jan 52

BOLTYANTSKTY, V.G.
"Vector Fielcla in P Manifold." Sub 27 Jun 51, Sci Pee Ine, of
Mec;, niccc- ani Mr,"rer-A.-
v p
tl,cti, Mo~,now Order Lopin Stpte U imeni M. V. Lomonosov
.4, :4. 14,LtlL,-u - /v .
Diqairtstions nresented for actence and engineoring dol-,rees In
Moscow anring. 3.951.
SO: Sum. No. 4SO, 9 liny 55

USSIRMathematico - Dimensions 3lov/Dec 51
"Neir Geometric Characteristics of
Uryson's Dimen-
sions," V. G. Boltyanskiy, Moscov
"Matemat Sbor" Vol IXIX (71), No 3, pp
603-614
Gives a new definition of the Uryson
dimensions,
which to a certain extent is similar to
the homolog-
'Leal definition of dimensions, differing
however
from the latter in that thert~ are
neither groups,
coeffs, nor orientations in the cited
definition.-
Calls dimensions thus obtained by the
name geomet!ric.
The theorem that geometric dimensions
coincide with
UxWon dimexisions. iseasily deduced from
the fun-
damental results of the homological
theory of 198T42
USSR/Mathematics - Dimensions Nov/Dec 51
(Contd)
dimensions. However, the demonstration of
these re-
sate was c6nducted by algebraic means
whereas the
author's de~wnztration here is completely
geometrical.
Siamitted 16 May 51.
198T42

USSR/J0&themtIcs - Modern Algebra, 1 jul-52
Secant Surfaces
"Secant Surfaces of Diagonal Products," V.
Boltyanskiy
"Dok Ak Nauk bBSR" Vol 100M, No 1, PP 17-20
Gives the condition for the possibility of
construct-
ing secant surfaces on Brtp. Designates P
as the dia-
gonal product whose basis is the complex B
and whose
layer is the manifold C admitting
transitive compact
group (Lie) G of transf ormat ions, which
basis enters
into the detn of the diagonal product (as
a group of
homeomorphisms of the layer). This means
that to
each point a in B corresponds a certain
subset (layer)
C& in P homeomorphic C; here if a and b
are different
2-24T81
points of B, then C& and Cb do not
intersect; more-
over, if T is a Bimplex,of complex B and a
is a point
of simplex T, then the definitely
homeomorphic re-
flection xT,a of manifold C on C. depends
continuously
on a in T. Submitted by Acad A.-N.
Kolmogorov 23 Apr
52.

USSRA-Tathematics - Topology
Card 1/1 Pub. 22 - 1/56
AuthOr'D I Boltyanskiy, VJaJ,,A'R-
Title IThe problem of taking off a secant surface from a subproduct
FerlodiCal IDok. AN SSSR 99/59 669-672, Dec i1,' 1954
-Abstract iA solution of a problem is g:Xven which deals with finding
the conditions-under -
which a secant surface G.,-. B-)P of the slant product P can be
talmn. off from,
a subproduat d?, othervisep under which conditions, the secant
surface 9. can be
transformed into such a secant surfaceg of the product P , thata 'B)C
P/Q
The symbols B~ P., Q and P & Q are defineod. Two references 1-USSR
~1'947 and
1950).
Institution Mathenatical Ins-Atate im. A. V. Steklov of ths Acad. of
Sea. of the USSR -
Presented by: Academician P. S. Alexandroff, September 28, 1954

. . . . . . . . . . . .

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MR

5

LT*,Ai,;.-;~iY, Vlaclivir Griporlyevich
POLTYANSMY. Vladimir G-igorlyevich, Academic Degree of Doctor of
Physico-Mathematical
Sciences, based-o-n-ni-Rdefense, 26 May 1955, in tbe Council of the
Mathanatics Inst imeni Steklov of t~e Acad Sci ussr, of his
dissert~ltion
entitled: "Research on the homotopic theory of intersecting
surfaced
of oblioue works". For the Academic Title of Doctor of Sciences.
SO: Byulleten' Ministerstva, Vysshego Obrazovaniya SSSR, List No
19, 2h Sept. 1955,
Decision of Higher Certification Corvds3ion Concerning Academic
Degrees and Titles.

BOIeTYANSKIY, v. [G--- )
Infinite-dimensional homologies and cohomologies.
D*kl.AN SSSR 105
n9.6:1141-1143 D '55. (MLRA 9:4)
1.P~redstavleno akademikom A.N.Kalmogorevym.
(Topology)

V.G-
SUBJECT USSR/MATHEMATICS/Geometry CARD 1/1 PG - 592
AUTHOR BOLTJANSKIJ V.G.
TITLE Equally large ani decomposition-equal figures.
PERIODICAL Moscow: State pi-.ol-ination for
technical-theoretical literature
64p- (1956) (Pol.ular lectures on mathematics No. 22).
reviewed 2/1957
The present book gives an introduction to the theory of the
contents, where
especially the modern results of Hadwiger's school are
considered. At first
it is shown that for plane polygons the equality of
decomposition is equi-
valent to their equality of contents. Then the theorem of
Hadwiger and Glur
is shown that the equal polygons can be decomposed such that
the correspond-
ing parts are congruent only by means of shiftings and point
refleotions.
Purthermoer it is proved that the group of shiftings and
point reflections
is also the smallest with respect to which all equal
polygons can be de-
composed into equival;~nt parts. In the second part the
well-known theorem
of Dehn is proved that in the R 3 there exist volume-equal
but not decompo-
sition-equal or completi'on-equal polyhedra, e.g. cubes and
tetrahedra. The
proof for this is given in modern form by aid of a lemma of
Hadwiger on
additive functions of the angles of edges. After a short
discussion of the
possibilities to define contents by limit values, the
theorem of Siedler on
the equivalence of decomposition- and comPletion-equality of
polyhedra is
proved.

ABRAKOV. A.A.,, rodakt or-, Pq~~44KIY, - VASILIYEV,
A.M..
radaktor,
redaktor; MEDVNMV. A.D., redaktor;
NIKOLISKIY, S.M., ot7etB:vennyy redaktor; FWTNIKOV,
A.G., redaktor;
nOXHOROV, Yu.V., redaictor; MNIKOV, K.A., redaktor;
UL'YANOV. P.L.,
redaktor; USPUSKIY, V.A.. redaktor; CHETAYEV, N.G.,
redattor;
SHILOV, G.Ye., redaktor; SHIRSHOV, A.L. redaktor;
SIMKINA, Te.H.,
takhatcheakikh redaktor
(Proceedings of the third All-Union mathematical
congress] Trudy
tretlego vessoiusnogo matematichaskogo sOesda. Moskva,
Izd-vo
Abwdemii nauk SSSR. Vol.l. [Reports of the sections]
Bektaionnye
'doklady. 1956. 236 P. (MLRA 9-7)
1. Voesoyuznyy matematicheskiy slyead-3rd Moscow, 1956.
(Mathematics)

ABRAMOV, A.A., redaktor; redaktor; VABILIYBV, A.M..
redaktor: %WVZ)NV,*B.V.. redaktor; KYSHKIS, A.D..
redaktor;
NIKOLISKIY, S.M., otvetstvennyy redaktor; POSTNIKOV,
A.-I., redaktor;
PROKHCIROV,,Yu.V., reclaktor; RYBNIKOV, K.A.,
reclaktor; ULIYANOV, P.1..
redaktor; USPANSKIY, V.A., redaktor; CHETAYET, N.G.,
redaktor;
SHILOV, G.Ye., redaktor; SHIRSHOV, A.I., radaktor;
SIMKINA. Ye.R.,
tekhnichaskly re(laktor
[Proceedings of the all-Union Mathematical Congress]
Trudy trettego
vassoiuznogo Matematicheskogo s8ezda; Moskva
iiunl-iiull 1956.
Moskva. Xzd-vo Akademii nauk SSSR. Vol.2. [Brief
summaries of
reports] Kratkoe soderzhanis obzornykh i saklusionnykh
dokladov.
1956. 166 p. (MI3A 9:9)
1. Vaesoyuznyy matematicheskiy 8*yezd. 3, Moscow, 1956.
(gathematics)

M. Z-5 - ~7-

.
Amf
"

5'
119-
6). 2

~ontraacfiblk'
Lct- S ba paea-ruormccUd, lomfly c,
-6 lop
&Dup~-G- Operate effectivoy
Le S A, I r b the staMliityi
et

he Projection P: G-->-S, given bl

illtur~ of tht- lm,;', ~Pacc oi

'Ai
lo,--~l
iutim witb

su xvcc, al; all
-.NbO r a sp

"o

be a oompact Bau-sdorlfspacc; ar-, 01 a closcd sub- I
Lat A

bejhe subspaLc maj~., w,
~d let Bc~(-S,

Ilia"- C-C,
s usw~

316 9 be- giveT
po wg

~,Dd let 0 he L:
te t7 ac

tc

5
1

7
~
fi bi e C

J -s sin Z!prT; ck~~, a,

2.1

The remm-'Ung remift::are wntMned irt'five'lem

~ -1 1A
'i f
acV about I
The first 06 Msu-t elemelma"t
N

-
Dpm to y for whith tbe I iiAbor S w rpnetes-
_pobg, give,

I
nYs. Lemma 3.-It
br

-4i
ii ielAivejo 9. L li C iE; L11 s

velatili ta~ g, th~i hg, &hiverzal
cover is t`d- -T-Spate

rel, tivc t6 Am'G is the space ol. Pa6s 6 V
issuing

L t,'te~ient,- -van t~,- ob,4u4s structure
Lng -1,

I
I~Tollp R, cohylected

.

'stnichire. of- a,,
a a t-n ii b I s4paceille,luthor i1c.Kwolill -

',(VfesI that~
tllis:iesult - is due ~ to FWkrfAnn,' pf tJ
"All

M (Mi~),2M426--IAR B,i,64

BDLTTANSKIY, V.G.
"Son-elementary problems in elementary formulation."
A.K.Ikglom,
I.K.IAglo-m. Reviewed by T.G.Boltianskii. Usp.mat.nauk
11 Do.1:
266-268 J&-F 156. (KLRk 9:6)
(Kathematica--Problems, exercises, etc.)(IAglom.
A.M.)(IAglom.I.K.)

T
__7 k -
SUBJECT USS~/MLTHKMATICS/Topology CARD 1/2 PG
-AUTHOR BOLTJANSKIJ V,G,
TITLE The second impediments for intersection Bvrfaoes.
MRIODICAL Izvestija Alcad. Nauk, Ser. mat. 20, ~9-136 (1956)
reviewed 5/1956
Let P be a fibre bundle with a complex B as basis, with a
fibre 0 being
aspherical.in the dimensions< r (r-p2) and with a connecting
structure group
G operating effectively and transitively on C which possesses
a local inter--
section surface (e.g. a Lie group). Further let the isotropy
group r 9'G be
cont.inuous-connecting and the characteristic class of
cohomologies
Y r+I E V r+'(Bv7e(C)) of the bundle B be equal zero. Then
there exists an
intersection surface T of P over r+1 . The author determines
the second
impediment Zr+2( 4,) F q7r+2 (D9 Ic r+1 (C)) against the
continuation of Ton Br+2.
r+2(ef) _ Zr+2( %~) + Rr+2 r) + ~r,-2
We have Z (D Y There V is an arbitrary
To 0
intersection surface over B r+1 , Dr6c is the r-aifference
of'U',
and T9 R r+2 (Dr) in the impediment aLgaInst the continuation
on B r+2 for EL 0
mapping fs Br+1 C which, compared with the constant mapping of
Br , has a
difference cocycle E Dr in 0. For the term ,r+2 (,r) explicit
expressions are

SUBJECT USSR/NAMMATICS/Differential equations CARD 1/3 PG - 707
AUTHOR ZOLTJANSKIJ V.a., GAMMLIIDZI R.V., PONTRJA91N L.S.
TITLE On the theory of optimal processes.
PERIODICAL Doklady Akad.Nauk 111101? 7-10 (1956)
reviewed 4/1957
Vie problem of the quality of control being actual in the theory of
automatic
control in represented in general form and in considered.
Let be given the,system i i'. ri(x Xa1 1910 ... 'U r) . fi (xvu)9
4-19 ... on),
is the image point in tho n-d6monsional phase space
and u (.1,...'ur) in the"controlling vector". If u(t) is piecowise
smooth
and continuous and if it belongs to a fixed olos*d region A of the
variables
ul p-purp v&ere fl has a piecovise smooth (n-l)-dimenuional
boundary, than
u(t) is called permissible. 1 n
Parmulation of the problem; In the phase space x x two points EO and
are given. A Permissible control vector u(t) is to be choeon in
such a way
that the point of the phase space comes from the position ~c to the
position
in minimal time. Assuming the existence of a solution and if u(t)
is the
optimal "'otor and x(t) the corresponding optimal path, then to the
somewhat
deviating vector u(t)+ Su(t) there corresponds the path x+ Ex. In
linear
approximation we have
and ir lot N(X')~'u) - 'rot f (x,u) have a maximum A( a, i~) in u
if u changes inQ.

Doklady Akad-Nauk 110, 7-10 (1956) CARD 3/3 FG - 707
'If the 2n-dimensional vector (X,-W) is a solution of the system
i
fl(xtu)
(2) Wi
fat
where.the pieoewiss continuous vector u(t) always satisfies the
condition
then u(t) is the optimal control and
x t) is the corresponding locally optimal path.
Starting from a fixed initi&l condition x(t 0) -7~0 and changing
the condition
-~(t ) . I , then (2) with thee* conditions and the condition
R(x(t),t?(t)Pu(t))-
M N(x(t),'Y(t))?-O determines the set of all"locally optimal
paths throu h
the point 10 M X(t 0) and the corresponding optimal control
mechanisms u~t)-
INSTITUTION: Math.Inst.Aoad.Sci.

BOLTYANSKIY, V.G. 'Moscow); YrJ'REr-j0VjCjj,V.A. kIvanovo)
Outlining tho basic idnns of topolop_y. Met. pros.no.2:3-34
'57.
(MER-A 11-7)
(To-pology)

IOLTTA!i,SKIT, VIG., red.; DTITKIhR, Te.B., rfd.;
POSTIIIKOV, M.M., red.;
--, -~&P!-T-,NTSUV, TP.D., red.; IOVLI.,7.k, R.L.,
tekhn.rad.
[Fiber spaces and tboir applications; collection of
tranalationg]
Rmnsloannye prostranetva i Ikb prilozheniim; nbornIV
pprevoapv.
Mlonkvn, I7d-vo innstr.lit-rr, 1958. 1,60 p. (mi-ah
1?:l)
(TOI)VICt-'r)

NIKO.-,ISKIY, S.M., otv.red.; ABRAHOV, A.A.. red.;
BOLTTANSKIT#- red.;
VASILOYET, 'A.M., red.; MEDVEM, BJOP IS, A.D., red.;
POSTRIKOV, A.G.. red.; PROKHORDT. Tu.T.. red.; RTBNIKOV.
K.A.,
red.; ULITANOT, P.L.. red.; USPRISKIT, V.A., 'Ted.;
CHETAMIT, N.G.,
red.; SHILOT. G.Te., red@; SHIRSHOT, 1,I,', red.; GUSIVA,
1.N'9
tokha.red.
[Proceed a of thoo Third All-Union Mathematical GonogTess]
Trudy
I tretlegolzesoiusnogo matemtichaskogo swazda. Vol-3
16Ynoptic
papers) Obzornye doklady. Moskva, Izd-vo Akad.usuk SSSR.
1958. ~96 p.
(MIRA 12:2)
1. Tsesoyuznyy matematicheskiy s'Oyozd. 3d, Moscow, 19569
(Mathematics--Congresses)

BOLTYANSKIY, V.G. (14oskva); YEMII)VICH, V.A.
(Ivanova)
Outlining the basic ideas of topology (continued).
Mat. pros.
no-3:5-40 '58. (14IRA. 11:9)
(Topology)

AUTHOR-
s0ow) SOV39-46-1-5/6
TITLEg
Homotopic Classification of
the Secant Surfaces (Gomotopiches-

kaya llassifikatsiya
sekushchilch poverkhnostey)
PERIODICAL:
Matematichaskiy
sbornik,1958, Vol 469Nr 1. pp 91-124 (USSR)
ABSTRACT%
The
paper izonsists of six paragraphs. The first five contain,

partially with and partially without proof, well-known
results

of Ste-enrod~ Pontryagin and Postnikov and form the
basis for

the last paragraph, in which the General
classification theorem

for secant surfaces of an oblique
product is proved (necessary

and sufficient conditions for
the homotopy). From this general

criterion the classification
theorems of Steenrod, Pontryagin

and Postnikov can be
concluded. The proofs for some results of

Postnikov [Ref 5,6]
which have not been published till nowp

seem to be of
interest.

There are '15 references, 10 of which are Soviet, 4
American,

and i Siviss.
SUBMITTEDs
March 26, 1957
Card '/-I

'P6
AUTHOR:
BOLTYARSKIY, V.G. 20-118-1-2/58
TITLE:
Homotopic
Classification of Vector Fields (Gomotopichesltaya

klassifikatsiya vektornvkh poley)
M
PERIODICAL:
Doklady Akademii Nauk/rM:Vol 116,Nr I Pp 13-16
(Usmq)
ABSTRACTt
The author gives a hoi~otopic classification of
the vect-

fields on n-dimensional manifolds. In the case n - n k + n + k .
There are 7 references, 3 of which are Soviet, and 4 German.
PRESENTED: by P.S. Aleksandrov, Academician
SUBMITTEDs January 3, 1959 blc--
Card 2/2

ANTONOVSKIY, M.Ya.; BOLTYAASKIY, V.G.;
SARYMSAKOV, T.A.;
SIRAZHDINO red.
[Topological semifields]Topologicheskie
polupolia. Tash
kent, Izd-vo SamGU. 1960. 48 p. (MIRA 16:4)
(Topology)

rv T-N
Hl
t: i f

FOLWAVISYN, V. G. ~P~L V. C-,); JFFIR-P-MVIC, V. A. (Tefrer-ovich,
V. A,)
I ~Y-q ~n~ku--
, y mat fyz astr 5 no. 1:7-27. 160
on topology. Pol-rol,
q

V.G.; ISS11.1.0Vp Yv.
"ar irnbguddinL::~ lic-tion to t---2 t. ec.-..*y of
-o--in-ticn of fi.: I ra-L.k 15 1 o. .':121: 132
- . a
14i.2)

16(1) B/03a/60/024/01/001/006
AUTHORSz DU.L !Z anskiy,V. Q,.,,..G=krelidze.R.V
And"'Fontryagin, 1.S.
TITLE- Theory of Optimal Processes. I Maximum Principle
PERIODICAL: Izvestiya Akademii nauk SSSR. Seriya
matematicheskaya, 1960,
Vol 24, Nr 1, PP 3-42 (USSR)
ABSTRACT: The paper contains a detailed representation of the
results
published by the authors in fRef 1-6, 10_7. At the
Mathematical Congress in Edinburgh L.S.Pontryagin has
reported about the most essential results.
There are 10 referencess 7 of which are Soviet, 1 German,
and 2 American.
SUBMITTED: MaY 14, 1959
Card 1/1

AUTHORS: Boltyanskiyq_V.G., Poetnikov, M.M.
36463
S/020/60/133/004/032/040 AX
C111/C333
TITLE; , On Principal Notions of Algebretic Topology. Axiomatic
Definition
of Cohomology Groupe
PERIODICAL: Do.klady Akademii nfiuk SSSR, 1960, Vol. 133, No. 4,
PP. 745 - 747
TEXT-. The objects of a category 66 are assumed to be
topological spaces
0
with marked points, the mappings of ()C0 are assumed to be
continuous and
to transfer marked points into marked points. Let 0x be a marked
point of
the space X. Let IX be the topological product 10,11 x X in
which [0,I]xOX
is drawn together into the point 0 - 01X. Let the mapping X-3-IX
defined by
x-->(t,x) be denoted by qt. For every f.- X--,-Y let If denote
the mapping
IX--,IY defined by qt(x)->qt(f(x)).
Card 1/4

86463
On Principal Notions of Algebraic Topology.
S1020160"133100410321(140 XX
Axiomatic Definition of Cohomology Groups C111/C33/3
fi-1 fi
The sequence .... X i_1 xi+,---> .... is called exact, if
for every 3.
the image Im f i-1 . fi_1 (Xi_,) coincides with the kernel
Ker fi= f
f g
of f The exact sequence X -> Y--> Z ->a is called cof ibring
(with respect
to a subcategory L of Lt 0) if for every- space Q from L and
arbitrary A:
IX->Q , / Y->Q from Or, 0 for which A 0 qo /- Of , there
exists a
mapping It: IY-~Q such that it- = 11 0 q 0and .~ h! 0 1 f .
X is called
cobasis, Y the space of the cofibring, Z the cofibre.
Let L OT, . The subcategory Ot of - is called admissible, if
1. R,-
0 Uk 0
0
contains the zero-dimensional sphere S 9 2. '(1 with X also
contains IX and
qo , q, a X->IX ; furthermore-if M with every mapping f
contains- If too.
f g
3- If in (110 X - ~-' Y- Z X,Y belong to also Z is to belong
to if
in (t) X,Z belong to !4jf., then also Y is to belong to if
X,Y,Z belong
Card 2/ 4

6 116.3
On PrinciDal Notions of' Algebraic Topology. S/02
60/133/004/03cn/040 XX
Axiomatic-Defi-nition of Cohomology Groups C111YC333
to ~'ien also the mappings f,g are to belong to
Let :a admissible and fixed. Spaces and mappings of then are
called
admil:~-- e too. The cofibrings (4) with admissible X,Y,Z are
called admissible
too. ~,.-.Iissible mappings f0, fi: X-+Y are called homotopic
(in if
thero -:exists an F: IX->Y such that P oqi- fil i = 011.
n
Let every integer n a contravariant functor H be given which
is defined
in and attains values in the category of the abelian groups
and their bo-
n n n
momcrDhisms. Then three functors H I # HIi 0-1~11 are defined
on the category
Ift
of admissible cofibrings (and of their admissible mappings).
JE~' makes
-,pond the group Hn(X) to the cofibring (*), H(n) the group
Hn(Z).
corr;.1~ n III
The functors H form the gropp theory of the cohomologies, if
for every n
a natural transformation gn from n into H n+1 is given and if
the following
axiom8 are satisfied:
H
1 . The groups Hn(So) are trivial for n ~ 0
Card 15,~l

86463
On Principal Notions of Algebraic Topology.
S/020/60/133/004/032/040 XX
Axiomatic Definition of Cohomology Groups C11I/C333
H
2 . For arbitrary admissible mappings f,g i X--),Y which are
mutually homo-
topic the homemarphisme-H n(f), H(n)(g) , lln(y)_-.,Hn(X) are
identical.
H f g
3 F*-r every admissible cof ibring X Y ---,Io-Z it holds the
rigorous sequence
e(g) n(Y) e(f) n(X) n n+1
Z) H - *> H ------ 31. H(z)
HQ(So" is called group of coefficients of the theory
considered.
j
The same axioms (correspondingly changed) describe the
homolopy groups.
There are 2 American references,
ASSOCIATION: Matematicheskiy institut imeni V.A. Steklova
Akademii nauk SSSR
(Mathematical Inatitute imeni V.A. Stekloy of the Academy of
Sciences USSR)
PRESENTED: May 10, 1950, by I.M. Vinogradov, Academician
SUBMITTED- May 9, 1960
Card 4/4

ANTONOVSKIYs, M.Yao; BOLTYANSXIY,, V.G.; SARYMSAKOV9 T.A.;
SIRAZRDINOV, S-Kh. prol,
otv. red.
[149tric spaces above half-fieldd) Metricheskie proctranstva nad
polupoliami. Tashkent, 1961. 70 p. (Tashkent. Universitet.
Trudy, no.191). (MIRA 15:5)
(Topology)

BOLTYANSKIY, Vladimir Grigor'yevich; CHERMSIEVA,
L.Yu., red.; LIKHACREVA,
L.V.
, tekhn, re
[Envelopes] Ogibaiushobaia. Moskva., Gos. izd-vo
fiziko-natem. lit-
ry, 1961. 75 P. (Populiarnye lektsii po matematike,
no.36)
(MIU 14: 10)
(Envelopes (Geometry))
4a i
R",

PONTRYAGIN, Lev Semenovich;,BOLTYANSKIYI V.G., red.;
BAYEVAp A.P., red.;
YE104AKCYVA, Ye.A.,
(Ordinary differential equations) Obyknovennyo
differentsial'up
uravneniia. Moskva, Gos. izd-vo fiziko-matem. lit-ry
1961. 331 P.
IMIRA 114-:7)
(Differential equations)

PHASE IBOOK EXPLOITATION SOV15883
,eontryagin, Lev Semenovich Vladimir Grigorlyevich Boltyanskiy,
Revaz
Valarianavich
Matematicheskaya teoriya optiniallafth protsessov (Mathematical
Theory of Optimum
Processes) Moscow, Fizmatgizp 1961. 391 p. 10,000 copies
printed.
'FA-8 N. Kh. Rozov; Tech. Fd.s K. F..Brudno.
PURPOSEa This book is intended*.for specialists concerned with
the mathematical
theory of optimum control prodesses.
tOVERAGE2 The book contains a systematic presentation of
results on,*69". theory
'of optimum control processes obtained by the authors during
the years 1956-1961.
Sone data obtained from other scientists are also included. The
authorsl so-
iaall6d "Principle of Maximum" suikaB possible the solution af
a considerable
number of variational problem of nonclassical type associdted
with the opti-
mization of controlled processes. The principle is presented in
detail and is
.compared with Bellman's principle of dynamic programming. A
series of problems
on optimuta processes is studied on the basis of general
methods of the Principle
Card

30556
S/56 61/002/UUO/UO2/UO8
1~.kooo (1,931, 113 2 D298YD302
AUTHORS: Boltyanskiyo V.G.0 Gamkrelidze R.V., iAishchenko, Ye.
F-9 and FMMryagtny L.S. (USSR~
TITLE: Principle of maximum in the theory of optimal
processes
SOURCE: 1FA0'P, let Uongressp Moscow 1960. Teoriya diskretnykh,
optimallnykh i SaMOnaBtraivayushikheya sistem.
Trudy, v. 2, 1961, 457 -,~ 470
TE)LT% The general optimum problem is formulatedp as well as
the
basic results obtained by the authors. The n-dimensional phase-
space )01 is considered, and the controlled object (plant) is
des-
cribed by the vector equation
1 = f(xp U), f = (fl, .... n); (2)
is the class of allowed controller's is defined as the class
of pie-
cewise linear functions u(t)p t Ig!5: t t!!;:- t2' The optimum
proolem. is
formulated as follows: The two points It,, ~2 are given in Xn;
it
Card 1/6

30556
S/569/ "61/002/000/UO2/008
Principle of maximum in the theory ... D296/D302
is required to chooseq among the allowed controllers, a
controller
u(t), so that the corresponding trajectory x(%) of Eq. k2),
defined
on the entire interval t -_ t --__-t2' connects the points ~iv
�~29
kx(-u,) X(t and the integral
2) = ~2)1
t2
S f O(x(t), u(t))dt (3)
t1 X
is minimized. Any allowed controller which satisfies the above
con-
ditions, is called the optimal controllerg and the corresponding
11rajectory -- optimal trajectory. Depending on the choice of
the
funcTion fO(x, u) integral (3) may represent the time elapsed,
the
fuel, energy, etc. spent during the process. Tne necessary
condi-
tions which any optimal controller and its corresponding
irajectu-
ry satisfies, are expressed by the following basic theorem 1p
cal-
led the principle of maximum. Preliminarilyp The vector 3E of
(n +
+ I)-dimensional space Xn+l is introducedt as well as the
covari-
ant vector ~p- and the scalar function
Oard 2/6

8/569/61/002/000/U02/008
Prinoiple of waximum in the theory ... D298/002
H(Tv x. u) vaf,(X, U)
Thereupon the Hamiltonian system of equations
H 0. X. U) p 1 0 n (6)
9H x u) r-i Or n (7)
9x
is set up. The notation
M(Tf x) sup H(7pp xp u)
is used. Theorem I (principle of maximum): Let u(t) be the
optimum
controller and x(t) -- the corresponding optimum' trajectory
of (2).
Then the nonzero, covar-Jent, continuous function V(t) cnn be
found
Card )/6
n

(&/0
2~y
S/569/61/00 0 021008
erinciple of maximum in the theory 1)298/D302
so that the coordinates x 1 and xo satisfy on the interval t t
tP the Hamiltonian system
jH X _.-')
Xi
i ~H u)
Oxi
and the condition of maximum
H(T(t)t x(t)v u(t)).= 1,1(f(t), x(t)); (8)
thereby M, x E Ot and.14) const-_~-- 0. It is noted that the prine',
0
ple of maximum holds also under more general assumptions than aboyQ
Under certain conditionsp the problem is equivalent to Lagranget,5
problem of variational calculus, whereby the principle of maxiu-A~-.
coincides with Weierstrass's criterion. The basic difference bet-
ween both formulations consists in the arbitrariness of the set
(of the v~Llues of u) in the case of the principle of maximum.
optimum problem for the case of limited phase coordinates me~jns
Uard 4/6

30556
8/569/61/002/000/002/008
Principle of maximum in the theory ... D298/D302
that only such allowed controllers can be chosen, for which the
corresponding phase trajectory of (2) belQYLgB entirely to a
fixed,
closed region U of n-dimensional phase space Xn. In this case
the
functional (3) is minimized. Further, a theorem is formulated
for
optimal trajectories which lie at the boundaries of the region
G.
In order to uniquely determine the optimum trajectoryp a
further
condition has to be satisfied by the -trajectory when it
passes from
the inte=r of G to its boundary; this condition is called
discon-
tinuity (jump) condition (as the covariant function V may
undergo
a discontinuity). Points of the boundary g(x) = 0, which
satisfy
certain conditionsp are called point of contiguity (junction)&
A
theorem is formulated which relates the discontinuiij
conditions to
the points of contiguity. Furtherp a statistical problem is
stated.
The significancet for optimization theoryg of the obtained
result,
has yet to be ascertained. It is noted, that it led already to
the
solution of a new problem "small parameter" for parabolic
equations.
The phaee-coordinates are denoted by z. In additionp the point
Q
with probability distribution in the space R, is considered.
It is
required to select the controiler u(t) of z so that the
funciional
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30556
3/569/61/'002/000/'002/008
krinciple of maximum in the Theory D~98/D.)02
Co r
h( 'r) (x , d p 'r) j d r (15)
is minimized. The author obtained an effective formula for
calcula-
Tin -uhe prooabiiity function 14),u . A discussion followed,
A.I. Lurl-
ye NSR), Sun-Tayan' (People's Republic of China) were Taking
part. There are 16 references: 14 Soviet-bloc and 4
non-boviet-bloo
The references to the B'nglish-language publications read as
follows:
R.B. Bellmang G.I. Glicksberg O.A. Gross, Some aspects of the
ma-
ihematical iheory of control pro7resses. U.S.Air Force Projeci
RAND,
RAND Corporation, California, 1958; J.P. La Oalle, Time optimal
control systems. Proc. Nato Ac. Scia, vo 45, no, 4, 19589 573
- 577
D.W. Bushawq Experimental towing tank. 6tevens Institute of Te
chnO-
logy, heporT N 469, Hoboken, N.Y., 1953.
Card 6/6

BOLTYANSKIY,- V.G. LMoskva); YEFREHOVICH, V.A. (Moskva)
17-~
Outline of the b4sic ideae of topology (conclusion).
Me,.pros. no.6s
107-139 16L ' (KIRA 1533)
(Topology)

BOLTYANSKIY, V.Q. (Moskva); ROZENDOIRII, E.R. (YzBkva)
The 21st Natbematics Olympiad for the schools of
Moscow. Mat.proso
no.6001-309 161. (MIRA 15:3)
(Moscow--Mathematies-4ompotitions)

29896
S/517/61/060/000/OC2/009
L) Bl]2/B!25
AUTHOR: Boltyanskiy, V.. G.
TITLE- Application of the theory of optimal. processes to
appiox-I-ma-
tion problems of function,.;
SOURCE, Akadelzmiya nau-Ic SSSR. Matematicheskiy :nsti-tut, Tr
u dy
v. 60, 1961, 82
- 95
TEM The author considers the following "fundamental problem":
Fcr th.-;-
b
n f, e. L-ra IP(-(t). y(IL))dt (P(x.,y) and y(t) are given
continuous f,,.:n,,,-
a
tions), an extremal function x(t) is sought, whi,,-h satisfies
n Lipschitz
conditions with a given constant. a >,O. The existence of a
solution and
i's uniqueness for the special case P(X*Y) = (x _ Y)2 are
demonstrat,ed..
Then, the author reduces the fundamental problem to the
followinG problem
of the theory of optimal processes: k function u(+-) (Iu(t)I is
sougth, which has such a form that the system of differ-eniial
equations
1 - 9. R2 . 11 ~ Y141, ef! , u 1 . n (n)
k = x X3 .... ic x W (X w (I X
Card

29896
S/51 7/61/060/000/d 0 2 1009
Application of the theory of .... B112/B125
I
X which Is ,Ln extremal function of the J11*1Q'~-"'-a1
fF(x'. y(t))dt for given boundary values x'(a) and x'(b)
In order to solve this problem, the author applies some
theorems of his
(et al~) earlier pa-per "Teoriya optiira2'nykh protsessov
(Theory of optimall
p.rocesse Izv. AN SSSR, ser. matem., 1960. 2-4. 3 - 12). The
prLneipal result is the following: If x(t) is a solution of the
fundamer-
tal problem,, one of the relations
t, , S t) ~F(xl YT )
f df = 0,
)n aF(.(1).. Y(S)l df
X sign
Ot a x
a
w -- 1-1 be fulf-Liled in the interval 1a,b] . Several examples
Illus-.rate tl-e
theoretica-.. -jart of this paper. The author refers to Liip
follo-afngpapers:
V~ G Bol4yansKiLy, R. V, Gamkrelidze, L, S. Poritryagin- D.
SSSR, 1956.
1 10, No 7 - 10, , V. Boltyanskiy. DAN SSSR, 191~8-. i;o. 6,
'070
F., 'i G ar-, k r - 1 i dz eDAN SSSR, 123, No, 2, 227 - 226-,
1958.
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29896
S/517/61/060/00O./002/009
Application cf the theory of - B112/B125
L S. Pontryagin,. UMN, 1959, 14, No. 1, 3 - 20.. N~ V
Yefi.,uov,
S. B. Stechkin, DAN SSSR, 191,)8, 118, No. 1, 17 - 1c) - 1,14-
V. Yei-i'llov.
S B Stechkin DAN SSSR, 1958, 121, No- 4. 582 - ~,55 N V,
Yefamov,
S: B. Stechkin. DAN SSSR, 1959, 127, No. 2, 254 - 2'--,?-
There are
61 fi,-,ures and 9 Soviet references,
Card 3/11

2,9 3 / 1/.2 // / 3 It 4t) 25772
It' S/020/61/!39/002/002/017
C111/C333
AUTHORs Boltyanskiy, V. G.
-----------------------------
TITLE: Modelling of optimal linear high9peed operations by
means of relay circuits
PERIODICAL: Akademiya nauk SSSR. Doklady, v. 139, no. 2,
19619
275-278
TEXT: The author considers an object with the equations of
motion
n r
X a x- + b u n
where the control variable u = (U".,., U'2 is a point of
the convex
closed bounded polyhedron U in the space E' with the
~.oordinateq
111'111.~ u r. Find an u(t) C- U so that the system comes
from the
position x 0into the position x, wi-,.hi-n shortest time3.
In vector form ('.) has the form
Card 1/1

25772
S/020/6!/!39/002/002/01,'j
Modelling of optimal Iinear C111/C333
x = Ax + Bu, (2)
where A s X-4 X (X--. phase space(x X')) and B ; E' X
are
n
linear operaturs defined in the ~-,nnrd-Jnates x and
u',.-... la
by the matrices (a-) and(b-).
i k
Let the following condition be satisfieds If the
vector w Is paral 1
with one of the edges of U, then the vectors Bw,
ABw,..., A U.-I BW
are linearly independent in X.
The author introduces the auxiliary system
A (3)
where the operator A* is described by the matrix
tranAposed to (a
For an arbitrary vector Lp. 4/n assume that e(41)
denotes
the set of all u 61J for which
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25772
S/020/6'/139/002/002/017
Modelling of optimal linear CI11/C333
Y,Bu (4)
C4 1 3
as function of u 6, U attains its maximum,
Theorem is For an arbitrary nontrivial solution T (t) of
(3) the set
e(Y (Q) is a corner of the polyhedron U for all values t
except a
finite number. I. e. the relation
u(+.' = e(If (t)) (5)
(which is meaningless in a finite number of points) defines
a piece-
wise constant function u(t) with values in the corne= of U.
Such func-
tions are denoted as extremal controls.
Theorem 2s Every optimal control is extremal,. Conversely.
assume that
the origin of E" i,s an interior point of U and that all
eigen values
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25772
S/020/61/139/002/002/017
Modelling of optimal linear C111/C333
of (a possess negative real parts. Then, for every point x
n 6, X.~
there exists one and only one(Up to time translation)
eitremall control
u(*) transferring the phase point from the position x. into
the
origin 0 of the space X, This extremal control is
simull+anecus'-Y
optimal ..
The extremal trajectory is uniquely determined by the chcice
of the
initial value The author proposes a modelling plant. which
allows
to determine the corresponding extremal trajectory x(-t) for
given
Figure 1 shows the scheme of the plant,. "Vo -
Card 44

2577
3/020/
Yodelling of optimal linear C111/c
b E: hy
T
Jr-
Here i t holds
n r
04
I I I ~- . . . f-
Bw )V. b w J 1,2
0/.j
he. r e
(6)
Wil w2t ... Wff
Card 5/7

E~Ivgzll !.WR

25772

i3/020/61/139/002/002/017

Modelling of optimal linear
.
0111/0333

are vectors parallel with the edges of
r
U, w W are the components

. Then
.of w.. Purthermor.e sgnj

j

+
(8)
`%
~

J-
J

where b. 1 or -1,, if the -Vector w or-iV beginning in the'Orner

Ij

e
of.U lies in one of the edges of TJ;
otherwise, 8
is not defined

,j

and is not considered. Then t
w
are
in the direction of the edges

ij
j
.

beginning in the corner ei; the number
of these edges is lie Finally

we have

q

Us
? e
(9)

,,,,
2

r
where e e are the coordinates

of the corner e of U and q ih

Card 6/7

2`772
S~02Y6`/- ',~/002/002/017
,533
Modelling of optimal linear VIII
the number of corners.
Theorem 13: The scheme shown on -r-~gure I (see also (7)1 (8),
(0j.)
feali-s a moti-onn of the object, (2) a2ong 'the extremal
tralec.-,nry
(Iror arbitrary ini+--al values of the variables Y i and xi)"
A simpler scheme is obtainea in the case where U is a
xectang,.ilar
paradlelepilped so that the u? in (1) are independent from each
other.
L. S. Pentryagin and R,. V. Gamkrelidze are mentfoned,, There
are 2
fi&-ires and 5 Szviet-bloc references.
ASSOCIATIONx Ma,..emaIIichesk:.y J, -;ti--ut imen't V, A,
Steklova Akadem4li
nauk SSSR (Institute of MathemaTics imeni V- A. Steklov
of the A.oademy of Sciences USSR)
PRESENTED?. March 196`, ty L- S.. Pontryagin, Academiclar,
SUBMITTED5 Mar?h 9. ':96,
Card 7/7
Mt.
;MW,H
IN

29108
0 C) (/01 S/020/61/140/005/003/02?
C11111C222
AUTHOR: Bo 1 ty~~naki3L~g
TITLE- Sufficient conditions 'or optimal-ity
I - I
PERIODICAL: Akademiya nauk SSSR. Doklady, v 140, no. 5,
196!~
994-997
TEXT! The author gives sufficient conditions for the
optimality of a
process on the base of the dynamic programmin6 by Bellman
as wellas or
the base of the maximum principle by Pontryagin whereby a
conne--tion
between these two methods is found.
In the phase space X of the variable x = (x i.X 2. Xn) the
author
considers
i. n
X (X1 ...... X ,U)~ n.
The piecewi.se continuous control u(t), to 19 t .4 t14 with
values in a
topological space U is called admissible with respect to x
E V~- X if
for a substitution of u into (1) the solution of (1) with
The -initial
value x(t 0) = X0 for t 0-< t :5-- t 1lies in V. Let the fI
and ',)f-J13Xj
e inuous on V x U.
araoV15
8

291 U,8
S/020/ul/140/005/003/022
Sufficient conditions for optimality C!11/C222
Problem; Among the admissible u = u(t) that one shall be
determined
which transfers the phase point from the position x in a
given other
position x 1 in the shortest time (optimal control).,o
Let K be a,-bounded closed s-dimensional n) convex
polyhedron in
th " sPce t,,: L~ of tb 9 vari.abl e a On an open se-, N
Of [-Eli containinc K lot be given a differentiable
mappip& N -) X
so that. the functional matrix (axl/alj) in every K has
the r,-,-,,k s
and that to different points of K there correspond
dif-ferent points of
X,. The image L -IF(K) of K is called a curvilinear
s-dimensional
pelyhedron in X, Every set MC. V being representable as
a union of all
at most countable number of curvilinear polyhedra of the
damensions-~!' n
is called a piecewise smooth set in V if these polyhedra
lie so that
in every closed bounded set in V there intersect at
most. a coiin t ab]
set of these polyhedra
Theorem I: Let a C:.V be a fixed point., In V let be
giver, a real con-,:-
nuous function Cc (x) so that a) U~ (a) - 0, W (x) -:: 0
for x a; b) i n
V there exists a piecowise smooth set M so that C., (x)
on V M
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29108
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Sufficient conditions for optimality C11'/C222
1 2 n
continuously differentiable with respect to x ,X x , and
satis
fies the condition
n
sup 22C24 f'~'~X,U) = 1 for x r~ V\ M - (2)
UEU ~)X 0~1
Then for every x G V and every control admissible with
respect to x
0
which transfers the phase space from the position x into the
qr
a, the time of transferring from x0 to a is not smaTler than
- -
Theorem 2: Theorem 1 is valid also then if instead of the
piecewise
smoothness of M it is demanded: Al is closed in V and
contains no
innar points; besides, G3 (x) satisfies locally the
Lipschitz condit:.on
~in the neighborhood of each x(L V)..
Conclusion! If the assumptions of theorem 1 (or theorem 2)
are satis-
fied and for every x. C V there exists a control admissible
with respect
to x which transforms x to a in the time then all these
Card 3/,S

2 C 1 8
S/020/61/1-40/005/005/022
Sufficient conditions for optimality CI1I/C222
controls are o 1) t i nia 1 ,
Theorem ~; _i sdevoted to the maximum princ.,ple. be~
n
P P -V
P P P
whexe all P are piecewise smooth; let. v(x) be F1 function
vvith vallies
in U given in V, Under numerous assumptions on the
structu-re cf the
sets Pi and on the course of the trF-,jectories of
i(xi
x f (-x)
with the aid of the sets and the function -,,Ix) the author
in*roduces the notion of the regular synthesis for 1) In V..
Ther., il.
-is proved. that certain trajectories appearing in the
definition of Alit?
regular synthesis which sat.iE;fy tho maximuui principle are
Mal (theorem 3),
There are ? Sov-iet--Won iind 1 non.-Soviet-bloo refrence
The reference
Card 4/5

29' 1.08
S/020/61/140/005/003/022
Sufficient conditi.ons for opti-mality Clil/C2122
to the E'r,-lish-language publication reads as follows:
R. Bellman,
Danamiche-c':oy~, r=C-rammirovamiye (Dynamic
programming). jL, 1960
ASSOC12,TION: Yatertaticheskiy institut imeni V A
Stiklova Akademi=14
nauk M;SR (Mathematical Institute jmeni V A, Steklov of
the Academy of Sciences USSR)
PRESENTED- J~aq !g, 19611, by L, S. Pontryagin,
Academl-cian
SUBMITTED: YaY 17, !961
Cai-d 5A