SCIENTIFIC ABSTRACT BOROVIKOV, L. I. - BOROVICKOVA, B.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000206510020-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 9, 2000
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENCEAB

15-57-8-10386
In Appreciation of the Life and Scientific Activity (Cont.)
study of the territory along the Murmansk railroad; during 1918-1924
he carried out a geological survey of the Kirov district, the results
of which are found rmstly on Sheet 107 of the ten-verst geological
map; for this he received the przhevallski Great Gold Medal in 1930.
In 1925 KaS31n devised a paleontologically oriented stratigraphic
system for the structure of Central Kazakhstan. A group of geo-
logists working under his supervision was the first to establish the
paleontological characteristics of the Cambrian and Ordovician
deposits, the complex of extrusive formations of the Silurian-
Devonian, and also of the pre-Paleocene deposits in northeastern
Kazakhstan. Kassin's investigations in IJugodzhary established that
~ significant part of the section, which had been formerly considered
~ member of the coal-bearing layer of the Lower Carboniferous, was
actually pre-Paleozoic. A number of important metallogenic problems
were solved as a result of Kassin's work on determining the age of
different intrusions in Central Kazakhstan. He established the lac1:
of congruity in the total scheme of the Caledonian and the Hercynian
structures in Central Kazakhstan and clarified the part played by
ancient blocks ("platforms" or "masses") in the development of the
Card 2/3

~o I nn! ;_,n an-11 tho, 1-1ti-c Is I ons n" t~~,e d" trio 1
ed
n, ,I ol.'Sorv ntl u I ~,ll ('n I. vuo t C t~ I C
--Pay flexiarE tnerit j .,ijt-st
rl,~! t Lle 1. 1'l
Lc nticm ;Ll oL 'r,, eca, t e rl, e 1 L. t
!between rretLllor-runesis t~ni Ric s tlzdli ed the KF4 z Vic ns T'D r.
water resources and tlhe of trio KnrauLndin Caftoniferous
s i r.
Card 3/3 D. 1. Gor"eyev

WROVIKOV, L.I.
Fossil organism remains in ancient "barren" strata in Xazakhstan.
Biul*VSEGEI no,,1:71-81 158, (MIRA 1445)
(Kazakhstan-Paleontology)

BOROVIZOV, L.I.
Middle Jurassic sediments in the northeastern part of the Caspian
Depression. Izvil Uzakh.SM.Ser.gsol. no*3;44-51 '58.
(NM 32: 1)
(Caspian Depression-Geo'logy, Stratigraphic)

--- BOROVIXUL-JA-L---
Phosphorites of the Atasu region in central lazakhstan*
Rasved.i okh.nedr 26 no.6:11-13 MV 16o. (MIRA 13:7)
1. Vsesovusnyy geologicheskiy nauchno-iseledovateliskiy
Institut.
(Atasu region(Xazakhotan)-Phosphorites)

ABDULKABIROVA, Jj.A.; ALEY.SANDROVA, I.I.I.; jUTNICHEV, N.A.; BlINDALSTOV,
S.M.; B-61111LOV, V.F.; BOGDANOV, A.A.; DOIRSUK,
D.I.; BORUKAYEV, R.A.; DUVALKIN, A.K.; BYKOVA, 14.S.; DVORTSOVA,
R.I.; DI-11DO, T.M.; ZHUOV, M.A.; ZVONTSOV,- V.S.; IVSHIN, N.K.;
KOPYATUVICH, R.A.; KOSTEIFO, N.N.; KUMPAN, A.S.; KWIDYUKOV,
K.V.; LJXROV, V.V.; LYAPICHEV, G.F.; lw/,URK~WICH, M.V.;
14I1Q1AyL0V$ A.Ya.; MMIAYLOV, N.P.; MYCHNIK, M.B.; NIDLL110, Ye.N.;
PI11'.1TIN,, I.F.; NIKIFOROVA, K.V.; NIKOLAYEV, N.I.; PUPYSEW, N.A.;
IVISKATOV, G.I.; WENGARTEN, P.A.; SAVICW.VA, A.Ye.; SALIN, B.A.;
SEVRI'UG.114, N.A.; SU-2NOV, A.I.; CHERNYAKNOVSKIY) A.G.; 01HUYNOV-111
V.G.; SHLYGIN, Ye.D.; SHULIGh, V.M.; ELIGME, E.S.; YAGOVYIN, V.I.;
I-,TA-LIVKI'.,,T, D.V., alcademik, red.; PMUROV, S.V., red.; 1-Uj2:.USHIN,
V.A., telchn.red.
[Geological structure of central and southern Kazuhhstan]
Geologicheskoe stroenie TSentrallnogo i Hzhnogo Kazakhstana.
Leningracl, Otdel nauchno-tokn.informatsii, 1961. 496 p.
(Leningrad. Vsesoiuznyi geologicheskii institut.Materialy, no.41)
t? (Kazakhstan-Geology) (MIHA 14:7)

BMOVIKOV, L.I.; KRYSIKOV, L.N.
Cambrian sediments in the Kendyktas Mountains (southern Kazakhstan).
Dokl. AN SSSR 151 no.3t644-647 J1 163. (MMA 16:9)
1. Vsesoyuznyy nauchno-issledovatel'skiy geologicheskiy institut.
Predstavlano akademikom A.L.Yanshinym.
(Kenduktas Mountains--Geology, Stratigraphic)

BORMIKOVY L.I.; KIMIUV) L.N.
r~arnb~-Ian sedim6nts in Uie Krindyktas Il vmtains (souUern
-to Kazakha L"
Trudy WSWEI 94:20'*&-260 '(")3. (Ml%4 YI. 6)

SPT;,HARS.-,J':Y.. -%7i,~ uomrw, Yll.'Ya.; prinlinaill uchnollya* L.I.;
T. ; ."',"1011, L. Str~ XL
map, -und inc-
(MIRA 18:6)

_7",ZqARL"~*ly, "..
BOROVTRY,j I L,I.- 1~1_ ,. i N.
1
Frine.;iples of the division and oorrelation of Pre.-Cambrian
sedf-itents. Geol. 1 geofiz. no.1421-229 165. (MIRA 19-6)
1. Vsp.3oyuzriyy nauchno- i s s led It f3kiy geologiclieskiy instiltut,
Leningrad.

SAVC4~KO~ (eiyev); KORSHUN, A. (s.Gagino, Gorlkovskaya oblast');
DOIXATOY, P. (XoskTa); DOROSHINKO, A. (g.Rikolayev); YBYSEYEV, G.
(Simferor.Poll); SHIROIOV, 1. (Vollak, Saratovskaya oblast');
BORDT-MIL-K-., Minsk); USHAKDV, B. (Moskovskaya oblasti);
-SIUMAK, I. (Xaraganda); NECHIPORIMED, I. (Sumy).
At the fighting stand. Posh.delo 3 no.10:22-23 0 '57. (MIRA 10:11)
(Firemen)

A
CC NR- AR6029293 SOURCE CODE: UR/0271/66/0(1"1"006/AO24/AO24
AUTHOR: Borovikov, M. A.
TITLE: Some problems in the design of electric drives according to 0e YIUS-D system
SOURCE! Ref. zh. Avtomatika, telemekhanika i vychislitel'naya tekhnika, Abs. 6A189
REF SOURCE: Izv. Tomskogo politekhn. in-ta, v. 153, 1965, 131-141
TOPIC TAGS: electric motor, motor generator, magnetic amplifier
ABSTRACT: The problems associated with the design of regulated drives using standard
magnetic amplifiers and dc motors are analyzed. The motor is selected according to
the waveshape coefficient of the current in the armature circuit. For single-phase
circuits it is 1.25 -- 1.3 and 1.01 -- 1.04 for the three-phase circuits. The
magnetic amplifiers are chosen according to the rectifier circuit and the desired load;
current. Recommendations are made for the selection of standard magneLiC amplifier
parameters: supply voltages, working winding current, etc. The recommiendation for
the selection of rectifiers contains formulas for the determination ot the average
current passing through the gate and the inverse voltage. If the regulation range is
to be extended to 1:50 the rate feedback should be replaced by voltage and current
feedback and the intermediate amplifier should be magnetic. Its parameters are
selected from the mechanical characteristics. It is shown that the use of the inter-
mediate magnetic amplifier with a few control windings easily solves the problem of
Lqord 1/2 UDC: 62-83

ACC NR: AR6029293
current limiting. The methods of analysis and design of the recommended current
i limiting circuits are given. [Translation of abstract] 5 illustrations and bi'Aio-
graphy of'10 titles. Ya. R.
SUB CODE: 09

--80�OVIKOV,.Mikha.il Alekseyevich, starshiy prepodavatell
Transiente, of a d.c. motor operating in a 14US-D 3ystem. Izv.vys.ucbeb.
zav.; qlek.tr.=2~_b. 7 no.1:53-759 64. (MIRA 17-9)
1. Kafedra elektrifikatsii promyshlennykh predprlyatiy Tomskogo
politakhnicheskogo instituta.

BCalUVTKMT M K ~ - GEYZENBLAZ , V.A.
Device for determining the level of :ietal in the ladle. Lit.
proizv. no.307 Mr 164. (NIRA 28:9)

L 32947-66 EWT(1) SCTB L
ACC NRs AN6015750
SOURCE CODE: UR/9023/66/000/043/0003/0003
AUTHOR: Borovikov,.P. Associate)
ORG: Institute of Oceanology. Academy of Sciences SSSR -Cinstitut okeanologii. Akademii,
nauk SSSR)
TITLE: Man lives at the bottom of the ocean
SOURCE: Sovetskiy patriot, 29 May 66, p. 3, col. 1-4
TOPIC TAGS: underwater clothing, underwater comunication, underwater sound equipment
V k -4
ABSTRACT: Problems encountered by aquanauts working in the lower reaches of the ocean
are discussed and means of overcoming these problems are suggested. The use of under-
water chambers fed by mixtures of oxygen, nitrogen and helium is discussed. A mixture
of 4% oxygen, 16% nitrogen, and 80% helium was found to distort voice communication
to the point of incomprehensibility. Tests have shown that some 100 gases and vapors
(all of which must be removed) accumulate in the chamber. Air purification systems
used on submarines are not adequate for the task. Battery powered heating elements
for diving suits are suggested as a means of protecting the aquanaut against the cold.
It is suggested that dolphins may provide a means nf protecting aquanauts against
sharks. The use of underwater chambers for aquanauts is recoomended for shortening
time spent on undaiwater work. In 2Y2 months, eight divers working from an underwater

ACC NRs M6015750
chniber at a depth of 55-60 a werv able to omplete repair wm* which would havo rv-
quLzed at least a yew using tz-aditional methods.
$M CODE: 06913/ SUN DAM

VEFISHINSWITI Nbv.; DMOVMVI POAO
Calculation of statlerm vith autoratically variable depth,
Trudy Inst. akeen. 74s85.89 165. (YVA IN12)

RCE CODE: OR/2566/65/074/000/0085/0089
AUTHOR: Vershinskiyj__1!. _V-. Borovikov, P. A.
ORG : none+,'
TITLE: Design of gtations'w'ith automatically controlled depth
SOURCE.,AAN SSSR. Ins-titut-DUanalogii. Trudy, v. 74, 1965. Elektronnyye pribory diva
okeanolog-i-&e-sWirVh-issledovaniy (Electronic instruments for oceanological research)',
as-89
TOPIC TAGS: measuring apparatus, oceanographic instrument
ABSTRACT: An automatic device for the continuous collection of o~~~ ~c da--'a is
described. The device is based on a work by R. A. Zlotky ("A Concept for a Remotely
Interrogated Synoptic Oceanographic Data Sampling Buoy," Marine Sci. Instnenentation,
1961, 1). The station consists of a signal buoy with a radar device and a signal light,
a cable with an anchor at one end and a submerged lift buoy, and an instrument package
which moves up'and down the cable at programmed intervals. Data are stored in the me-
morylof the measuring device and transmitted to a receiver when the device is near the
ocean surface. The electric power required to move the package up and down the cable
is calculated and a solution for a particular case is given. The design of a new elec-
tramechanical device with a considerably reduced power consumption is reported. Orig.
art. has.- 4 figures, 13 formulas.
SEM CODE: 08014/ SUBM DATE., none/ ORIG REF: 003/ OTH REF: 003
Card 1/1 vmb

15-57-7-9856
Translation from: Referativnyy zhurnal, Geologiya, 1957, Nr 7,
pp 161-162 (USSR)
AUTHOR: Borovikov, P. P.
TITLE: Prospecting Methods in the Northwestern Mica-Bearing
Areas of the USSR (0 napravlen-Ji i metodike poisko-vykh
rabot v severo-zapadnykh slyudonosnykh rayonakh SSSR)
PERIODICAL: Inform. sb. Vses. n.-i. geol. in-t, 1956, Nr 4,
pp 124-128
ABSTRACT: Present methods of prospecting for mica-bearing pe,7ma-
tites in the northwestern areas of the country are
based on general geological premises and obvious indi-
cations of the presence of the minerals. These
methods do not guarantee effective exploratory work.
The necessity of preliminary study of fissure tectonics
and structure of the pegmatites and the host rock is
Card 1/3 indicated. Study of the relation between the ore

15-57-7-9856
Prospecting Methods (Cont. )
mineralization and muscovite makes it possible to determine more
precisely the tectonic phenomena which are detrimental to the mica.
Three types of formation of industrial mica are distinguished:
1) Uniform micatization. The muscovite is genetically associated
with quartz of an essentially plagioclase pegmatite; the muscovite
content of 10 to 50 kg/cu m usually decreases with depth until the
veins taper out completely. 2) Zonal micatization. The muscovite
is associated with pegmatites of plagio-microcline composition; the
content of muscovite varies from 10 to 200 kp_/cu m and over. The
zones of micatization are spread throughout the entire extent of the
vein; since the muscovite is not associated with a specific structure
or composition of the pegmatite, actual excavations are necessary
for evaluating; the industrial potential of deposits of this type,.
3) Pocket micatization. The muscovite is associated with pegmat'.tes
of essentially microcline composition, having a coarse pegmatoid
structure. The content of muscovite varies from a few kilograms to
300 to 500 kg/cu m and over. The content of mica is extremely
Card 2/3

prospecting ME!thods (Cont.) 15-57-7-9856
irregular. This type of micatization is quantitatively the most
unfavorable for industrial purposes.
Card 3/3 V. A. Vollfson

BOROVIKOV p F. 11. ---
Muse(wite formation in pegmatites of the Kola series. Inform.
Sbor. VSEGEI no. 201U-28 159. (MIRA 1411)
(Kola Peninsula-Pagmatites)

BOROVIKOV, Fetr. Favlovich, lmnd.geologo-mineral.nauk; KUZIIETSOV, S.S.,
'd~ktor goologo-mineral.nauk, nauchnyy red.; HANNOV, A.V., red.
izd-va; GURDZHITIVA. A.M.. takhn.red.
(Formation of mountains and mineral resources] Obrazovanis gor
i poleznykh iskopaemykh. Leningrad, O-vo po raBprostraneniiu
polit. i nauchn.inanii RSYM. Loningr.otd-nie, 1960. 51 p.
(MIRA 13:6)
(Geology. leonomic)

BOROVIKOV, P.1).
Magmatic and structural control of pegmatitic deposits, Trudy
VSEGIU 57:5-44 161. (KRA 15~4)
(Pegmatites)

BOROVIKOVP F.P.; L'VOVA, I.A.
TYPes of vermiculite deposits, their commerciAl Sighificance,
and ALrther prospecting trends. Zakonom. razm. polezn. iskop.
6.-470-A,88 162. (MIRA 16:6)
L Vse,soyuznyy geologicheskiy institut.
(Vermiculite)

BORGVIK(JV., F'r 10
New commercial type of vermiculite deposits. Trudy VSBGEI
83971-81 162. (WRA 16.9)

UNKSOV, V.A.; pLROVIKOV,_P Zj RUNDKVIST, D.V.9- PAVLOVA, I.G.;
ALYAVDIN, V.F.; VOLOSTNYKH, G.T.; ROZINOV, M.I.,- SHCHEGLOV, A.D.~
IVANOVA A.A.; KORMILITSYN, V.S.; SHCHEGLOV, A.D.; ARTEMOV, V.R.t
RYTSK, 'ru.Ye.; GINZBURG, A.I.; DORTMAN, N.B.; TOPORETS, S.A.;
TRUNINA, V.Ya.; YAKOVLEV, ~.K.-, BOGDANOVA, L.A.- SARBEYEVA, L.M.
Y
Problems of the geology and characteristics of the distribution
of mineral dePosits- LTrudy) VSEGEI 92.53-89 163. (MIRA 17.-4)

BOROVIKGV, F. P.
Motasomatic nature of micas, Trudy VSEGEI 108:5-22 164, (MIRA 18:2)

BABOSHINJ V.A.; BOROVIKC'r P.P.; ZAKHARCHENKO, A.I.; IVANOV, A.A.; NIKANOROV,
A.S. - NIgNMIK: V.D.; -RYTSK, Yu.Ye.; SMIMOVA, V.S.; SOKOLOV, Ya.N.;
p I
SOLOVIYEVY A.T.; TSEKHOMSKIY, A.M.
In memary of Daniil Timofeevich Misharev. Trudy VSEGEI 108:169-191
164. (MIRA 18:2)

40ROVIKOV S.I. [Borovvkov S.I.]; GERASECRENKO, O.A. [Herashchenko, O.A.]:-
- - .9
- ~UHDONVP V.G.':'IFedorov, V.H.]
gediation furnace. Zbir. prate, Inst. topl, AN URSR no.24:12S-132 162,
(Electric furnaces) (MIII 1633:1

BOROVIZOV, V.A.., inthener; SOBOLIV. M.I., insheiker.
A~M-Wwffftldl
Uss, of' reactors in chubers of iumdficitint *its.
no.6:24-25 Js 156.
(Blectric reactor&)
Inergetik 4
(" 9:8)

BOROVIKOV, V. A.; SOBOLEV, Il. I.
Electric Machinery - 4tintenance and Repair
Installing and repairing synchronous compensators without Et gentry crane.
Rab. energ. 2, No. 9, 1952.
9. Monthl List of I-iussian Accessions, Library of ~~ongress, December 1952. UNCIA&5IFIED.

WAqYAQVp V.A., gorW inzh.; KARPUNOV, Ye.G., gornyy --'nzl,.; TI~TIYANOV,
YU.K., gorny-y in2h.
lmprovement of boring and blasting operations in breaking
down shale in longwall chambers. Vzry-v. delo no.54/11:
374-379 164. (MJ.RA 17i9)
1. Leningradskiy gornyy institut (for Borovikov, Karpunov).
2. Shakhta No-3 kombinata Leningradslanets (for Tretlyakov).

L 13826-63 FWT(J)'/BDS M~~TC/ASDJSSD Pi-4
ACCEMION NRs AP300545 S/OD.-b/63/1.1il/%)02/1)252/0254
AUTHDRI Dorovikov
t,V,, A.
TITLEs Green's function for problem of diffractio4 ova polyhedral angle
ISOVIRCEs AN SM. Doklady*2 V. 1511'n'o. 2# 19639 251-254
TOPIC TAGSs Greents functions diffraction, polyheftal amgle
AWRACT v - The asympdate of the Gresn' a function for a stationary diffraction prob-;
left on the polyhodroil S in completely deternined by the sinqularities (occurring In
a neighborhood of vaire fronts) of the Green's function for the non-stationary dif-
1fraction problem, Tito construction of the Green's function for the noao;-stationary
diffraction problem reduces to the construction of this flinction for a di-hodral
anale and for a polyhedral ang 1. G.
je. The paper was prosented by Academician
Petrovakiy on 30 January 1963. Orig. art. hazz 7 formulas.
ASSOCIATIONt none
SUBMITTED: 2Man63 DATR ACQ: 3OJul63 INCL: OD
ISUB CODE: MM NO REP SOVS 004 OTHER: 001
C-0
-
1. rd- 1/1

BOINVIKOV) V.
PA 2413TB2
USSR/Mathematics - Modern Algebra ]NOV/Dec 52
"Intersection of a Sequence of Simplexes," V, Borovi-
kov -
"Usp Matemat Nauk" Vol 7, No 6 (52)) PP 17951,80
Article is devoted to a demonstration of the follov-
ing theorem, in reply to a question posed by A. N.
Kolmogorov: The intersection of a decreasing se-
quence of simplexes is a simpl.6x. Thanks V. G. Bolt-
yanskiy, who considerably simplified the author's
original demonstration and edited article. Submitted
9 Sep 52
243T82

7TTTV7VT-
VV.L1,V, )
USSR/Mathematics - Set theory n-454
I
~Iard 1/1 : Pub. 64 - 6/11
Author : Borovikov, V. A. (Moscow)
Title : Constructing a zero-dimensional compactum, of metric order n
Periodical : Mat. sbor., 34 (76), 279-288, Mar/Apr 1954
Abstract : States that the concept "metric order ofcompacta" was introduced in
1928 by P. S. Aleksandrov, when he posed the problem of the metric
regularity of compacta lying in a Euclidean space. This problem was
solved in 1949 by K. Sitnikov. 1, natural. question now arises: do
all curved polyhedra, in particulai all simple arcs, possess the
property of metric regularity? In this vork the answer is shown to
be in the negative. Thanks Acad F. S. Aleksanarov for guidance.
institution :
Submitted : March 24J. 1953

V
V
V
Category : USSR/7heoretical Physics - quantum Electrodynamics B-5
Abs Jour ; Ref Zhur - Fizika, No 2, 1957 No 2950
Author : Borovikov, V.Ao'
Title T. One Topological Problem Connected vith Problems in Quantum
Electroaynamics
Orig Pub : Uspekhi matem. nauk, 1956, 11, No 3, ~.13-118
Abstract : The author investigates, from the topological point of view, the
structure of the Feynman diagrams and solves the topological problem
of the unique determinateness of the equivalent irreducible diagrant.
The conditions under vhich an equivalent irreducible diagram exists
for a given diagram are formulated, and a. suitable theorem is proven.
Card 1/1

SUBJECT USSR/UATHEMATICS/Differential equations CARD 1/2 PG - -,25
AUTHOR BOROVIKOV V.A.
". 6- - eral'o- A,
TITLE iza' ion of the formula of Herglotz-Petrovskii and
the diffusion of waves.
PERIODICAL Doklady Akad. Nauk 106, 587-590 (1956)
reviewed 10/1956
The author gives a solution formula for the Cauchy problem
M ult-0 -~a U/ ra tI t--0 ,... . ry,-2 Itwo W 09 U-lu/~ tn-1 It.O-f(X,.)
relative to the hyperbolic equation
(2) A ( 1~ V Q )u M 0,
7t- a xi
whereAM, Ji) is a homogeneous polynomial of a-th degree such that tho
equation A(IC, Ej) - 0 for all 1 12> 0 has n. different (real) rootzrC I
i
the last condition in not essential but serves for simplicity. The author's
formula is of the type
(3) u(t,x,) . I K(t,3C,- t i)f ( Ji) d Ji

Doklady Akad. Nauk 106. 567-590 (1956) CARD 2/2 PG - 325
where the kernel K(t'Xi) is an ordinary function fox, njpp, a generalized
function for n-4p. The determination of X in an explicite form in the
case n> p coincides with those given by Herglotz-Petrovskij. The formula
obtained by the author is used to show that the surface of the equation
A (1, Ii) n 0 is bounded, and for p being odd, in order that the equation
(2) has the form of the equation of the diffusion of waves it is necessary
and sufficient that n - p - 140.

'~~C)P C) V 6 Ll
RUMA-I'VEA/Dieoretical Physics 7) %2aatum Electrodynamics B-5
Abs Jour : Ref Zhur - Fizika, No 4., 1958.. 140 7585
Author : BoroviMX,,,,V, A. -
Inst :-Yo-i Given
Title : One Topological Problem Connected with Problers in Quantum
Electrodynamics
Drig Pub : An. Rom,-Sov. Ser. mat.-fiz., 1957., 11j, No 21 31-37
Abstract : See Referat Zhur Fizikaj, 1957., No 2p 2950
Card : 1/1

BCRGVIVCV, V.A. I Grnd Phy*-Lath '-CJ- -- solutionr of
p4x~ - _T
line,.r e~mf~tians in deriv,.tives vith lit
11'.0ri, 1 58- 8 -PT) (11.1os Order of Le-l-lin ind oL L7.7,'Ibor Red 3--nnor Univ
1C0 co-pies
im WeV.Loric-nosov. Lechw&-Ilath Faculty
-2-

AUTHOR% Borovikov, V.A. 20-119-3-1/65
TITLEz Fundamental Solution of a Linear Partial Equation With
Constant Coefficients (Fundamentallnoye resheniye lineynogo
uravneniya v chastnykh proizvodnykh s postoyannymi koeffit-
siyentami)
PERIODICALs Doklady Akademii Naukq 19589 Vol 119, Nr 3, PP 407-410 (USSR)
ABSTRACTs Let L( be a homogeneous polynomial of n-th, de-
M 2
greet Let for L 0 and L > 0 be grad L> 0. Let the
equation
L( 4_ u (x1tx2'-'xm) - f(xl""'xm)
M
be given, its solution is obtained from
U(119*~.P~M)' ...f K(Xlg.*,Xm)f(,Cl-xl,.., ~m _xm)dx1dx 2 ... dx m
where K(xi, ... 9xm) is a generalized solution of
Card 1/ 2

Fundamental Solution of a Linear Partial Equation 20-119-3-1/65
With Constant Coefficients
PRESENTED:
SUBMITTED:
a 4D
L f jox ... 9 TX_ (X19 ... fxm) = Pxj'..'Xm)
4_1 2 ' M
The author investigates the behavior of the fundamental so-
lution K(Xl, ... 9xm) in the neighborhood of the character-
istic cone (i.e. of that cone on which K(x i,*,*,Xm) possesses
singalarities). A series expansion of K (xl,...,x m ) in terms
of powers of the distance from the characteristic cone is
given, whereby the point, in the neighborhood of which this
series expansion holds, is assumed to be not singular. For
the case of a hyperbolic operator L the author obtains an in-
tegral representation of K~x 1 ...,xm) by Cauchy-regularization.
There are 2 Soviet references.
November 2,1957, by
I.G. Petrovskiy, Academician
October 30, 1957
Card 2/2

BOROVIKOV, V.A.
Basic solutions of linear partial equations with constant
coefficients. Trudy Mosk.mat.ob-va 8:199-258 159.
(Differential equations, Partial) (MIRA 13:2)

RTABKOV, Aleksandr Takovlevich-Edeceasedj;,~OV ~,OV T A - XOSMY,
V.K.; XHODOT. G.A.; KARPOV, F.F.. red.; IIORUH(*: i:i., tekha.red.
[Electric note and systems] Blektricheskie seti i sisteaq. llzd*411
perer. i dop. T.A.Borovikovym. T.X.Kosarevymp G.A.Khodotom.
Moskva, Goo.energ.isd-vo, 1960. 511 P. (MM 13:2)
(Electric networks)

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W/OY61/055/00(5/00/004
0 j 1*4VII D304
AUTHONs j0rAV1kGV,-VA, (MOSCOW)
TITLE: On sufficient conditions for absence of gaps
PERIODICAL; Matematicheskiy abornik, v. S5# no. 5, 1961, 237-254
TEXT: The author proves that AsNo Davydova'B condition (Ref. 7P
Candidate's thesis, MGU, 1945), as well an those formulated bY
himself in an earlier workt are sufficient conditions for the ab-
sence of gaps, i.e. of domains, in which the fundamental solution
of linear hyperbolic equations vanishes identically. In addition,
an example is given which illustrates that these conditions are
not necessary ones. The fundamental solution of Cauchy's problem
7t' W, 0' (1)
Ij 11.0 1 11=0 ,on-il 1,
Ut t 0,
(M-2? -0 =
fit NXI, xt)
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On sufficient conditions for ... 1)299/D304
is defined as the generalized function K(Tp i,~), for which
U(ti P Xi A K(t, , X, - ~j X, - ~: Z.
L :.l) f(5;19
d'i .00 d~r
is ~i
Purther, the concepts of characteristic cone and characteristic
surface are defined. A.M. Davydoya's condition io formulated as a
theorem. In modified form, this condition is as follove: let k be
the number.of positive elements of a diagonal matrix (similar to
the matrix related to the equation of the characteristic surface).
Then, if k is oddt the considered domain cannot be a gap (lacuna).
The validity of this statement follows from formulas (obtained by
the author in an earlier work)v involving the expansion of the fun-
damental solution along the normal at the regular point of thecha-
racteristic cone. The condition is stated, under which no wave dif-
fusion occurs for Eq. (1). The absence of wave diffusion (as defi-
ned by the author) is equivalent to the existence of gaps contain-
ing the origin of coordinates. Theorem 2. If the surface H('5";:'jl
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On sufficient conditions for D299/D304
0 is bounded, then the neighborhood olf-the origin of coordi-
nates is-a gap for m -- I + 1 and odd 1, and no gap otherv.,ise. This
theorem is proved. The absence of gaps between a series of con-cen-
tirc ovals is also discussed.. Let L(8/6t, 6/8xj, 8/8xl) be an ope-
rator of the fourth order and the suface HH11 consist of
two convex ovals; 1 = 5. Then Herglotz-Petrovskiyls formula beco-
mes
I--- r 6' ff" X, + () d,
K V, X,.... I X")C ell (10)
lgradHI-sign
Fig. -4 shows the surface H(~,) = 0, and Fig. 3 the characteristic
surface for this equation. It is proved that A cannot be a gap.
Further, the general case is considered: the surface H = 0 consists
of m/2 ovals and (if m is odd) of an additional component. Denot-
ing by Ak the set of points ~'xj' ...' x 1, 1, for which the Diane
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On sufficient conditions for ... D2997D304
Zxi ~i + t = 0 does not intersect the first k ovals, and by :k
the complementary surface (related to the surface, dual to GO
which contains the point at infinityp one obtains Theorem 3: For 1y,
even 1, the intersection of A k and Bk is never a gap. For odd 1,
the intersection of Ak and Bk is no gap if the polynomial H(!~Zi)
cannot.be expressed as the product of two polynomials H = Hi ' H2
for one of which the surface F1 j(~i) = 0 (j equals either 1 or 2)
coincides with Gk. (Gk denotes the set of complementary ovals~
This theorem is proved in several steps. A further theorem is zta-
ted. An example is constructed which shows that even with none of
the foregoing conditions (Theorems 1 - 4) satisfied, there are no
lacunas. There are 6 figures and 8 references: 7 Soviet-bloc and
1 non-Soviet-bloc.
SUBMITTED: December 7, 1961
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- - - Ae_ X,
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AUTHOR: Borovikov, V. A.
Pi 12
S/020/62/144/003/010/030
BIOB/B102
TITLE: Reduction of some three-dimensional diffraction problems to
a Dirichlet problem for the Laplacian equation
PERIODICAL: Akademiya nauk SSSR. Doklady, v. 144, no- 3, 19062, 527-530
TEXT: The diffraction of a plane wave f(t - x) on a conical,obstacle S
is considered. It is shown that when the form of the incident wave is
properly chosen, the problem
-2 -2 2 2
0 U 13 U a u a u
- 2 0 with 0 at t