SCIENTIFIC ABSTRACT MAKHOVER, M. - MAKHOVIKOV, V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001031610002-7
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Sequence Number: 2
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

~~"Mmovwt M,
,:7~0~A't--t-he shores of Africa.0 lr&uJm i sidsn' 28 n0*1873 Ja 161*
.1 , (MIM 2411)
(Coamograybic revearah)

Minna Vladi ... -i r9 vna
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f the quest-4,-)n (sullfonaraidny'kh) ;:repari-A' ns ~n un-icallulbr
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Dissertation for candidate -)f a '*cdAcLl Science Lel-ree.
Chair -)i' General Uol-)gy (h--, ,: I r--)l'. ',unt.r-.) Sarat-)v Institute, 1944

L- MAKHOVNI. H.V.
Intravital changes in nerve calls of the entire body. under the
influence of novocaine. TSitologiia 1 no.2:195-201 Mr-hp '59.
(MIRA 12:9)
1. Kafedra, obshche~, biologit Leningradskogo sanitarno-gigiyeni-
cheskago meditsinskogo inatituta.
(UHRUS) (ITOVOCLI113) (RhINS AND STAINING (MICROSCOPY))

MAIMOTM.
Qytochsmistr7 of oogenesis In the house fly. Trudy LSOKI 43t69-75
159. (KM 130)
(m35) (Ocrgimsis)

MAKHOVF.R,, M.,V-.'. - ~ I
Cytochemical and cy-tological study of the hepatic cellB in
human embryo. Arkh. anat., gist. I embr. 49 no.9-3P-" Ag 165.
(MIRA l8t9)
1. Kafedra obahchey biologil (nauchnyy rukovoditell- chlen-
korrespondent AMN SSSR prof. F.V. Makarov) Leningradakogo
sanitarno-gigiyenicheskago meditsinskogo instituta.

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KMOM, YO.S.
Protection.of underground gas pipelines frdii external corrosion.
Gaxeprow.no.3M-25 Kr 156, (KLRA )-,N:1)
(Gas pipes) (Electrolytic corrosion)

/'~ IIr Z- .-)
MAKHOV M, -e,S.; ~UMOVSKATA, V.V,
f4easuring votentials in uaderi-round gas pinellnes. Gaz.prom,
no.8-14-18 Ag 156. (14LRA 10-?)
(Electrodes) (Blectrolytic corroslor,.; as pipes)

SLADKOV, S.P., inzbener'. =M--Te inzhener.
~IWWSI , , "; ". Iii, 01 WO
Automatic draft signal for gas flues of water heaters
activated by rarification. Gar. khoz. Mosk. 30 no-7:
13-15 J1 156. (,%URA 9: 10)
1. Institut "Mospodzemproyekt."
(Gas appliances)

MMTIY3[7, I.M.; KAMOM. Ta.S.; ALMSANDR0710H. A.I.
Sanitary suglueeriog pipes made of plastic materials. Gor. khm.
Houk. 32 n0.7.'5-8 JI '58. ()WA 11:6)
1, Direktor Instituta, "Nospodsamproyakt" (for Mmmvlyev). 2. RmjmTo-
ditell materskor 16.9 instituta Nospodzemproyekb" (for Makhover),
3, Glavmyy Inshener materskoy 16.9 instituta "Rospodsemproyekta
(for AlsksandLrovich).
(pipe. Plastic)

f
AL&SMEDROVICII, A.I.; HAKHOVER, Ye.S.; SLAMOV. S.P.; TTRCITSKAYA,
F.B.
"Oe,nnek," an automatic, gaa-operated air heater. Gaz.prom.
5 n0-1:25-30 Ja 160. (14IRiL 13:4)
(Gas-Roatir)g and cooking)

Z-UOO -Y"i AMONAD-ROVICH, A.I.
IAP~ NVER
Over-al-I aut=iluion of heating-oystem boiler rooms of all types.
.Gor. khoz. MoA. 35 no.2~22-31 F 161. 041~~
1. Pulkovoditell ma-sterskoy No.9 Institute "Mosinzliproyeictll (-)j-
Mi::hover). 2. GlavnTj inzhener 7asterskoY No.c, Instituta "MuAnzh-
proyekt"'(for AlQksandrovicb).
(Auto~iatic control) (Hot-water heating)

ALEKSANDROVICH, A.!.; MAKE"ER. Ye.S.
Plastio undergroLuici gas plpelin6s. Gaz. pron. 9 ni.5-,16--2-2 164.
(M I-RA 17. 6)

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K ffO V,& RYi V,
124-11-13062
Translation from: Referativryy Zhurnal, Mekhanika, 1957, Nr 11, p 112 (USSR)
AUTHOR: Makhover, Y;.
TITLE: Bending of a Plate Having Variable Thickness and a Sharp Edge.
(izgib plastinki peremennoy tolshchiny s ostrym krayem)
PERIODICAL: Uch. zap. Leningr. gos. ped. in-ta, 1957, valij, -ply-28-39
ABSTRACT: Investigation of the equation of the bending of a plate with variable
thickness and a sharp edge for specified boundary conditions. The
quartic differential equation obtained appears to degenerate on part
of the contour, and in its study the Author took his point of departure
from the theory of degenerate second-order elliptical equations as
developed in the works of S. G. Mikhlin and others. He clarifies the
condi'.'ons of discreteness of the operators in the equation.
(P. M. Varvak)
Card 1/1

HMOTj Yea Vep inzh.
- - --------- -- ---
Change in the light distribution of a point sou:,ce of light
when submerged in vxter. Svetotekhnika 9 no.2:19-21 F 163.
(MIRA 164)
(S-AMMing pools-Lighting)

-MAKHOVAt Yu.V,; TROSHKINA, U.S.
Results of the study of the layering and banding of Elbrus
glaciers, based on spore-pollen analysin data. Infom.sbor,
o rab.Geog.fak.Kosk.goo.un.po Mezhdunat.goofiz.godu no.9:126-
138 #62. (MM 16:2)
(Elbrus,, Mount-Glaciers) (Elbrus, Mount-Palynology)
(N

ALEMANDROVICH, A.1.9 inzh.; WKWVER, Ye.S., inzh.; KHAYKIN, M.M., inzh.
The "Progress:~ flush tank. Gor.kboz.Hook. 36 no.7i2lV Jl
062. (HIR& 16t1)
(water closets)

MAKHOVER, YO.V.
Spectrum of the fundamental frequencies of a pla!~~- with a sharp
edge. Uch sap. Ped inst Gerts. 197:113-118 '58. (AURA 16:9)
(Differential equations)
(Frequencies of oscillating systems)

CMUBO W.Ta.-t lnzb.l KAKIIOV m 9 Ingib.
study of the performwe of' a loadIng bucket
tomWor. Trudy LIVT no.6808-64 064. (MIPA 18in)

3OPI)DATOV, V.A., kand.biolog.nauk; DMIDOV, V.F.; DUKWIN, A.N.; ZMKOVA,
Asale, KADMINIKOV. Tu.T.; KAMCHMO. Yu.L.; KORZKOVA, Tu.A.-,
KM V , Z.I.; PSTROV, G.P.; PROSYDWV, U.S.; WJLXT, N-N-; SOKO-
S-PICHAK, M.K.; KEaWKOV, N.S.; S11M, V.I., red.; FOFMA-
LM, Ye.A., teklm.red.
(Study of tuna fish and sardinea in the eastern part of the Atlantic
Ocean; report on the cruise of the scientific fishery survey
expedition of 19571 Issledovaniia tuntsa i sardiny v vostochnoi
chasti Atlantichaskogo oksana; relsovyi otabot nanchno-poiskovoi
skapeditsii, 1957 g. Kosk7a, 1959. 158 p. (KIRA 13:6)
1. Koacow. Voesoyuznyy nauchno-isaledovatellskiy Inatitut morskogo
r7bnogo khozyaystva i okeenoRrafii.
(Atlantic Ocean--Tuns fish) (Atlantic Ocean--Sardines)
(Pish, CAnned)

KAUOUR. Z.H.
Tornado in the vicinity of Toronash. Priroda 43 no.5:113-114 Ky 154.
(mm 7:5)
1. Toroneshakoys Gldrowtbyuro. (Toronesh-Tornadoes)
(Tornadoes-Toronesh)

r\ U Y
UM/Pbysics of the Atmosohere - Dynamic Meteorology, M-2
Abst Journal: Referat Zhur - Fiziks., No 12p 1956P 36082
Author: Antanov, V. S., Bexanov, N. P., Makhover, Z. M.
Institutions None
Titles Certain Results of Applying the Suggestions by K. L Kashin and
M..*V. Griteerko to the Prediction of the ftaergence of Caspian
Cy~lones
Orlid 1
Peri(~Ucal: Meteerol. i gidrologiya, 1955, No 6, 34-35
Abstracts For the sake of verification, an analysis was made ~~f 32 aero~
logically-interpreted cyclones in the regions of the northern
Caucasus., the Caspian, and the Povolzh'ye. In 30 cases the
cyclones moved parallel to the axis of the tongue of heat on the
500 mb isobaric surface thus, ccifirming the qQXrectness of the
above statement. An example iliustrating the motion of the
cyclone in accordance with the above assumption is given.
Card 1/1

ANTOROV, V.S.; MAKHOM, Z.H.
What do isotherm charts reflect at the 500 miUibar level? Katear.j
gidrol. no.g:)2 S '56. (MLRA 9:11)
(Atmospheric temperatue)

ANTONOV, V.S.; BAHANOV, M.P., -HAXHOM, Z. H.
Forecasting the aMmarance of Caspian cyclones in the southeastern
Nuropean region of the U.S.S.R. Trudy TSIP no.42:3-10 '56.
(WBA 9:11)
1. Voroneshokoye gidrometbyuro.
(Russia, Southern--Cyclones)

14MOVER, Z.14.; K&LYMM, A.S.
Thunderstorms in winter. Friroda 45 no.2:126 F 156. (MI-RA 9:5)
1. Nachal'nik Voronezhakogo Gidrometbyuro (for Kakhover); 2. Star-
shiy inzhoner-sinoptik Rostovskogo-aa-Donu byuro pogody. (for
KalyuzhW)-
(Thunderstorms)

A i< J4 G, Q
AUBM: Makhover., Za M.
TITIZ: Servibing the National Econonq organizations by the Voronezh
Hydrometeorological Bureau(Obsluzhivaniye narodnokhozyays tvenrUkh
organizatsiy gidrometeorologichaskIm Lyuro, Voronezh)
PMIODICALt Meteorologlya i Gidrologiya, 1957, No. 1, pp. 42-43 (U.S.S.R.)
ABSMACT: The daily activities of the Voronezh Uydromateorological Bureau in its
functions of servicing the city of Voronezh and the Voronezh region am
described. Weather forecasts are transmitted over radio, telephone and
bulletins twice daily at 0700 and 1400 hours. In contrast to other such
bureaus,, the Voronezh Office also publishes early morning bydrological
bulletins for regional agricultural and other organizations interested
in weather forecasts. The radio operators of the Office have learned bow
to prepare weather cards (prepared at 0300 and 1500 hours) on the baeJA of
data receivecl by radio. The daily weather bulletin carries weather fore-
casts for 24-hour periods from 10 o'clock of one day to 10 o'clock of the
following day,, weather forecasts for the following 2 days., weather reviews
for the days past and meteorological data. Every day., at 1400 hours., the
Bureau compiles weather prognoses from 1900 hours of the current day to
1900 hours of the day following, These forecasts are telephoned to
Card 1/2 service organizations for futher dissemination. The Office employs the

Servicing the National Economy Organizations by the
Voronezh Fqdrometeorological Bureau
newest methods in preparing isothermal charts which are used in preparing
weather forecasts. Senior engineer-synoptician V. S. Antonov introduced
a special system for the calculation of vertical currents by the wind
field. Precipitations are computed by the L, A. Bachurina method, The
Office has a detailed climatic description of the territory serviced.
Agriculture is furnished data regarding early fall radiation frosts and
weather phenomena dangerous to agriculture. Regularly twice yearly
d=d.ng fall and spring the office conducts synoptic investigations of
processes and phenomena for winter and summer. Spring weather forecasts
also include data about soil temperature at a depth of 10 cm. The impor-
tance of these services to farming and industry is amalyzed.
ASSOCIATIDN:
PRESENTED BY.-
S'UB' XTTED:
AVA31ABLE:
Card 2/2

MAKHOVAR -alman KoiseZgLv ~ch- PERVAKOV, I.L., red.; ZORKIn, G.P.,
-- _--&-jL
mladshly red,; VIMSKATA, E.N., tekhn.red.
[On African shores] U beregov Afriki. Koakva. Gos.izd-vo
geogr.lit-ry, 19,30. 89 p. (KIM 101: 9)
(Afrim-Description and travel)

MAIMOVER, Z. K
Distribution of si- r precipitation over s-I I areas. Sbor.
rab.Kursk.gidromet.obaer, nool:66-73 160, (MIRA 14-8)
(Precipitation (Meteorology))

AUTHOR: Makhover, Z. U. S/05q/6O/OOO/O3/O05/02O
- - ---- ------- \Y B007/BOO2
TITLE: Comparison of the Mean Tropospheric Temperature
With the Temperature at the 500 mb Level
PERIODICAL: Meteorologiya i gidroiLogiya,.1960, Nr 3, pp 29 - 30 (USSR)
ABSTRACT: On the basis of analyses of 1034 probings of the atmosphere made
in Kursk and Tambov, the author showed in the paper of reference 1
that the isothermal lines at the 500 mb level yielded the mean
tropospheric temperature. In the present paper, the mean values of
tropospheric temperatures are compared with the temperatures at
the 500 mb level on 27 stations in the northern and central region
of the European part of the USSR. For this purpose, the correspond-
ing temperatures and their altitudes were computed,as well as the
difference between.the mean-tropospherio temperature and that of
the 500 mb level. The mean tropospheric temperature (t T.) was de-
termined as the arithmetic mean from the values of the r.ir tqm-,
perature at the earth's surface or at the upper level of the ground
inversion, and from the temperature at the tropopause levels The
hight (h tTr ) at which the mean tropospheric temperature had been
found, was also determined by extrapolation of the temperature of
Card 1/2 di-fferent levels. The determination of the temperature of the TI)

Comparison of the Kean Tropospheric Temperature With 8/050J60/000/03/005/02C
thia Temperature at the 500 mb Level B007/BO02
500 mb level (t 500 ) and the height of this level (h 500 ) did ncz
involve any difficulties. On the basis of the data obtained, the
diagrams for the tTr and t 500 courses shown in figure 1, and also
the diagrams for the changes in h tTr and h500 were constructed. By
means of these diagrams it is shown that the maps of isothermal
lines for the 500 mb level reproduce the distribution of the mean
tropospheric temperature. rt is noted that the winter temperature
gradients are slightly larger on the maps of the temperature of
the 500 mb level than the gradients on the maps of the mean tropos-
pheric temperature. There are I figure and 3 Soviet references.
Card 2/2

mu'ROVE!K~.
Hicrosynoptic distribLtion of ovmier in flizhnedevitak
District, Voronezh Province. Sbor. rab. po sinop. no.5:67-86 $60.
(MIRA 14:8)*
1. Gidrometeobyuro Voronezh.
(Nizhnedevitsh District-RaiL and rainfall)

IMMOVERV Z.M.; SMIRNOVA, M.I.
Winter flooda in the upper courae of the Don River. Trudy TSIF
no,100-.92-201 160. (KM 14:5)
(Don Rivetio-Flooda)

MARHOVER, Z.M.
A.I.Voeikov at the 9th Congress of Naturalists and Physicians. izv.
Vses. geog. ob-va 93 no.6:541-543 N-D '61. (MIRA 15:1)
(Voeikov, Aleksandr Ivanovich, 1842-1916)

MAKHOVER, Z.14. (Voronezh)
Hurricane in Voronezh. Priroda 51 no.3:69-71 fir 162.
(Voronezh Province-Hurricanes) (KLR-k 15:3)

MAKHOVYI, Z.M.
microc-limatir -!-,arac~eristl7a or ,-- nomoer cf says wick '.,~
procipl.l.ations n.-id lurat'on c[ Tue'r fall. Sbor - r a*r,, ~ mr ~,~ ,
gldromet.obzerv nc,,.2';4-2-0 IImi-iAl. 1--').

GORDSM. G.S.. prof.; YAKTSHKIN, D.I.. Prinimali uchastiye: GORSKAYA, H.V.;
GRANOVSKAYA. A.Ye.; YEVSTIGNEYZVA, Tu.G.; KRYLOV, M.V.; LEYKIN. D.I.:
ROMOVETSKIY, V.A.; MEYMMORP, A.L.; HAZ 0, V.I.; RICH M RUX.
O.K:T_FA_VWV, L.I.; RUMYANTSEVA. N.V.; SOSENSKIT. I.I.; CHMMVSKIY.
Yu.V.,, TULUFNIKOV, A.I.. red.; SOLOVOYEV, A.T., prof., red.;
RAITINA, Te.D., red.; ZDBPJLRU. Z.P., takhn.red.
(Agriculture in capitalist countries; a statistical manual] Sal'skoe
khoziaistvo kapitalisticheakikh stran; fftatisitcheakil sbornik.
Moskva, Goo.izd-vo ee- khoz.lit-ry, 1958. 247 p. (MIRA 12:5)
l. Moscow. Vaeooyuznyy nouchno-iseledovatellskiy institut ekonomiki
sel'skogo khozyayastva. 2. Otdol nauchnoy informateli po ekonomike i
organizatsii sel'skogo khozyayastva zarnbeshnykh stran Vaesoyuznogo
nauchno-iseledovatellskogo Inatituta ekonomiki sel'skogo khozyaystva
(for all except Tulupnikov, Solov'yev, Rakitina. Zubrilina). 3.
Direktor Veasovuznogo nouchno-tooledovatellskogo Inatituta ekonomiki
sellskogo khozynystva (for Tulupnikov). 4. Zamestitell direktora
Voesoyuznogo nauchno-issledovatellskogo instituta ekonomiki sel'skogo
khozyaystva (for Solovlyev).
(Agriculture--Statistics)

MAMRIOVIGH A-18A0111- T-Uolofol-,-nwich; TABUNINA, V.A.J, red.
['afety. mannal for workers employed at buil-ding-site
Anortar-making plants] Fardatka po tekhriike bazopasnosti
dlia rabochikri, obsluzhivaiushchikh rastvorrqe uzly na
otroitellnol plozhchadko. VoLkva, ',Lroiizdat, 1964. 26 p.
(MIRA 18:8)

MAKHOVICH. S.D.; BALABAN N.I.
.9
Rasult of centralized bookkeeping. Zdravookhranenie 5 no.5.
47-48 S-0162. (MMA 16:7)
1, Iz Leovskoy rayomoy bollnitay (glavnyy vrach - S.Ds
Makhovich), ~bldavskaya SSR.
(LEOVO.-DISTRICT-HOSPITALS--ACCOUNTING)

Aqfitl#~6'vlcllz~ 1,14
CZECHOSLOVAKLV.Amlytical Chemistry - Analysis of Organic Sub- E-3
stances
AbB Jour : Ref Zhur - Khiuiya) No 3) 1958) HO 7723
Author :_~24hovicheva
Inst ~ oi- ~Given
Title The Separation of Reserpine, Reserpinic .cid and YohiLibine
by Paper Chromatography.
Orig Pub Ceskosl. farmc., 1957, 6, No 6, 310-311
Abstract For the separation of reserpine (I) from reserpinic acid
(II) and yohimbine (III) the solvent systems of the Zctfaroni
type are suitable (Zaffaroni A. J. Biol. Chem., 1951, 188,
763)
II and III remain on the spot where a drop is introduced
and I has a sufficiently great R value. Mie.method is suit-
able for the identification of I in tablets. For the separa-
tion of II from III basic and n-butanol containing systems are
suitable. In this case I is displaced together with the sol-
vent front. By, combining both chromatographic methods I, III
and III are separated. The alkaloid spots are observed under
Card 1/1 ultra-violet light.

ACCESSION MRz AP4o?-s467 5/0181/64/006/(R4/124911251'
AUTHORS: Trubitsy*n, A. M.,; Kabanov, A. A.; Boldy*rev, V.V.;-Xi%khawik,,-A. K.
TItLE: The nature of electrical conductivity in the permanganates of alkali metals
SOURCEt Fizika tverdogo tela, Y. 6, no. 4,1964, 1249-1251
TOPIC TAGS: electric conductivity, alkali'permangarate, thermoe .leotromotive force,
transference number
ABSTRAUTT; The type of conductivity in ionic cry3tals of permanganate type was
established by inVestigating the elect--ical conduoti t
vi,y, the transference numbers,
and the thermoelectromotive force.. The samples *ere prepared from chemically pure'
materials pressed at room temperature under a pressure of 104 kdcm 2 for 4 M#Utes-
It was found that the electrical oonductivity is practically the same at high
temperatures for KMh04, RbMn04, and CaMnO 4' but that the activation energies are
.different for each. The VhO- is much larger than the cationsp and this, . with the
experimental data# Indicates &
4that the eleoti-ical conductivity of the indi6ated
*compounds is noniozLic and that the cations are nckt reffousible Tor the electrical
conductivity. In all these permanganates the ihdrmoelectmaotive force proved.to be
Card 1/2

ACCESSIOM,NRs AP4028467
negative, indicating an electron mechanism or elsotrical oanductivity. Orig. art.
hans 1 figure.
ASSOCIATIONS Tomskiy inatitat radioeloktronixi i elek 0-M-Ay W&Aki (Tomsk
Institute of Radio Bleatronias and Electronic Engineering)
SMWTTEDs O6Dec63 DATE ACQ2 27Apr64 ENCLs 00
So CODES ICP EK go REP SOVt 004
OrM 005
Card 2/2

GORN, Vasilty Nikolayevich; - TIKOV DmItr,- Ivanovich: ZAVITALOV,
G.N., redaktor; VXU c so edaktor.
[Semiautomatic brake release accelerator] Poluavtomatichookii
uskoritell otpuska tormozov. Moakwa, Gas.transportnoe zhel-.dor.
izd-vo. 1954. 22 p. (MLRA 8:9)
(Brakes)

MAKHOVIKOV, V.I.
Solution of the heat conduction problem for a plate. Dokl.
AN BSSR 7 n6.9:602-605 S 163. (MIRA 17:1)
1. Predstavleno akademikom AN BBSR A.V. Lykovym.

MAKHOV1KPV,_.Y.!jc (MakhovykQv, V.I.j (Kharlkov)
Shift of a cyl-indgr having a multiply connected lateral CrOBB
section. Prykh.mekh. 9 no.5:544-551 163. (MEIRA 16:10)
1. Kharll,,.,)vskoye vysshe.~a voyennoye aviatsionnoye uchil-ishche
letchikov.

KAKMVIMV V., I. (Kharkiv)
Approxime.te conformal mappings and their application In the
theory of elasticity [with summary in ftglish]. Prykl. mekh.
3 no.1:20-37 '57. OCRA 10:5)
1. Kharkivalkiy "tomobilino-ohlyakhoviy inatitut.
(Conformal mapping) (Ilasticity)

AUTHOR: __~~~~~akhovykov, V.I.) 21-5-2/26
TITLE: Two Compound Problems for Analytical Functions (Dve smeshanyye
zadachi dlya analiticheskikh funktsiy)
PERIODICAL: Dopovidi Akademii Nauk Ukrains1koi RSH, 1957, Nr 5, P 431-435
(USSR)
ABSTRLCTs The author proposes a method for solving boundary problems in
two cases. The first case jeals with a unit circle contain-
ing the points e~q' and e-E), and the area epv , (v,tv = 1,2,...m).
The problem consists of finding an analytical function T(~
in the circle, if the boundary conditions are as follows
(formulas 1 in the article):
(0)+P, (0) in the area 1,2 .... mE e
~p (&)+If P
A (9) CP (0+A (0) Y (E)~J-L (8) P, (04A (0) R (e) In the arco C',
where Po (0), P, (0) A (0) are f r4gmen t- continuous and period-
Card 1/3 io functions of 0 . The bar over the function means a

Two Compound Problems for Analytical Functions 21-5-2/26
conjugated function. The methods consists in the construct-
Ion of the function
in the area (2)
141L (19 ) in the arcs ",I
whore G), and w2.~ E are values of"analytical-in-the-
circleo functioniq w, f _and us,( 6 ) in the unit circle.
The systems of aquatione (1) is then reduced to one equation
And this equation Is solved with respect to the unknown funct-
ion 1P ( C ). In the second problem there is a region D
which is mapped conformally on the circle. The problem con-
sists in the finding"analytical-ir,-the-unit-circld functions
1P ( C ) and (P if the boundary conditions are as
follows:
(E) + -~t--Awl Y (E) + T (0 - PO (0) in the arcal, (12)
(E)+ --,wJ7F(EET) (P'(E)+6A)(P (E) -'Pi (0) in the area t J,
Card 2/3 where PC (0). R (% dl (0) are given functions. By making use

MAKHOVIKOV.9 V. i., Candidate of Tech Sci (diss) -- "Approximate conformal repoo-
sentatiom and their auplication to the theox-j of eLasticity". 11-IarIkov, 1q,- .
,)9
9 Pp (Acad Sci Wcr SSj, Inst of Structural Moch), 150 coplos (KL, No 20, 1.05~, 113)

20
67511
14(-14 16. -7 S o o SOV/155-59-1-16/30
AUTHOR: Makhovikov, V I.
TITLE: On the Solution of the Problem of Elasticity,for a Cylinder
PBRIODICALt NF-ucbnyye doklady vysshey shkoly. Fiziko-matrma-ticheskiye naukig
1959,Nr 1, pp 102-109 (USSR)
ABSTRACT: Given a right cylinder the crots section of which is a certain
domain D the boundary of which may be an arbitrary plane curve.
The diameter of the domain D is sufficiently smaller than the
height of the cylinder. The author proposes a solution of the
equations of equilibrium in shifts (equations of Lame') which
permits to satisfy completely the boundary conditions at the
lateral face of the cylinder for certain loads. The boundary
conditions at the bases are not satisfied; but the author
points out that by averaged consideration of the boundary con-
ditions (compare Z-Ref 1-7) at the bases it always can be
reached that in agreement with the principle of Saint-Venant
the obtained 6tate of tension distinguishes from the real one
only in the neighborhood of the bases. Papkovich and Galerkin
Card 1/2 are mentioned. <

675,_1
On the Solution of the Problem of Elasticity SOV/155-59-1-16/30
for a Cylinder
There are 2 Soviet references.
ASSOCIATION: Kharlkovskiy avtomobillno-dorozhnyy institut (Khar-cov
Automobile Road Institute)
SUBMITTED: December 7, 1956 V1(
Card 2/2

KAKMTIKOV. V. I.
Solving the elasticity problem for a plate. Nixuch.dokl-778,
shkoly; strol. no.2:63-70 159. NIRA 13:4)
1. Rekomendovana kafedroy stroitol'noy mokhaniki Khar'kovskogo
avtodorozhnogo Instituta.
(Elastic plates and shells)

7.1.
//2 r
lixej Pro'ble., C-r~fo,-- ~.l Mapping (Smeshan-
n~iya :(-"I 01-anoye L;reobrazo,,-.i.1Yi_;
-;_'7,P1O-1ICAL: Dopovidi Akademii nauk Ukrains'lkoi
pp 125-129 (UbbR)
ABSTRACT: Usin~; the data contained 4:- --ference 3, the authcr
prove-s, that by using the:_esullm ~~f a mixed
examined in that reference, 1T, is, nossible to a;)-
proximately construct conformal mapping functions.
This article contains an examination o~L' o~ie
problem for analytical furictions (peripheral rroble:..~
and a way of repreoenting the inside of a square
nrea -~-!ith rounded-up corners. Desi-YLOttions are Pt;-.nd-
a-rd mathematical, The agreed-upon designRtions are
E~s followq- Ile" (with po,,-i(-__s) are poiritn ori
ivo circle "1" -aith indices and powers, are
1 is a circle, Re F is real part of L'unction
Card 112 u((~) and v(~) are values on a circled,,; e, e( ) are

The Mixed Problem -L.,,d Cor--formal Mapping
functions, Po is ri-iction of parai-e'-~:r, r
end roints of an Iq o cut(~. ol, ,I
circle, Therp FLre 2
AS80CIATION: Kharlkovskiy -tvto;:iobilli-,.o-',.Iorozi,,iyj- inst, i~t (Kli-ir
kov Automobile and Road Inntitute)
PRESENTED: By F. - . Member
SUBMITM: June 17, 1958
Card 212

68785
24 (8) S/170J59/009/12/018/021
AUTHOR. Makhovikov, V. I~ B014/BO14
TITLEs Determination of Thermal Stresses in a Cylinder

PERIODICALt -IU851i)
Inzhenerno-f izicheskiy zhurnal, 1959 i Vol N
ABSTRACTs The author studied a cylinder of arbitrary cross section, the
height of which is great compared to its diameter. The beat
equation was solved by fully satisfying of the boundary condition
on the surface of the cylinder. This was achieved by the appli-
cation of equation (1) by Dubammel-fieuman. Proceeding from equation
(1) and the stress equations (2) the author investigated the dis-
placement problem for which purpose he derived formulas (10). Equa-
tions (12) describe the surface of the cylinder. On the basis of the
boundary conditions (14) the author deduced equation (19) for the
case in which the surface tensions are given. Equation (26) offers a
solution for the case in which the temperature along the cylinder
variso linearly. There are I figure and 7 Soviet references.
ASSOCIATIOM Avtomobillno-dorozhnyy institut, g. Khar1kov (Highways Institute,
City of Kharlkov)
Card 1/1

16(l) 80V/21-59-3-5/27
AUTHOR: MakhoV4kov, V.I.
TITLE: Some Problems for LaPlace?s Equation (Neskollko
zadach dlya uravneniya Laplasa)
PERIODICAL,- Dopovidi Akademii nauk Ukrainolkoi RSR, 1959, Nr 3,
pp 245-251 (USSR)
,ABSTRACT: The author presentr his contribution to the use of
la Place equation for the solution of problems in
the field of mechanics. Three solutions of the
equation are presented. One solution (15) makes
it possible to fully satisfy the boundary conditions
on a cylindrical surface and at several points at
the ends of the cylinder. A s�multaneous applica-
tion of the function (13) and (15) solves the prob-
lem for a plate with given polyharmonics from x,y
functions on the end faces, when the boundary con-
ditions on the cylindrical surface are satisfied
Card 1/2 by several lines z = const. Another solution (22)

Some Problems for La Place's Equation SOV/21-59-71--5/27
makes it possible to reduce the space boundary
problem for a body obtained at rotation of plane
region D around axis z, to plain boundary problems
on the boundary of region D.
ASSOCIATION: Kharlkovskiy avto-doroz)inyy institut (Khar1kov
Auto-Road Institute)
PRESENTED: June 17, 1958, by F.P. Belyankin, Member of the
AS UkrSSR
Card 2/2

MLMVIM)V, V.I. LYakhovykor. T.I.J (Kharliwv)
Approximate methods of conformal mapping of double-connected areas.
Pr7k1. nekh. 5 z)o.3;237-275 '59. (MIRA 13:2)
1.Khar1kovskly avtomobillno-doroshAyy institut.
(Conformal mapping) (Blastic plates and shells)

- MAKWV IKOV. V.I.
Determination of thermal atresso,; In a cylinder. Inzh.-fiz.
zhur. no.12:97-104 D '59. (MIRA 13-4)
1. Avtnmobil'nn-dorozhnVy institut, Kharlkov.
(Thermal strenees)

8 Vs
a
AV noz, a3la ri
Ail 1
All H I
2 A,
cc :1 ~S

-Xt
84270
S/170/60/003/010/016/023
B010054
AUTHOR: Makhovikov, V. I,
TITL13: The Problem of Heat Conduction Concerning Bodies of
Rotation
PERIODICAL: Inzhenerno-fizi-'cheskiy zhurnal, 1960, Vol. 3, No. 10,
PP. 103-105
TEXT; The author proceeds from Laplace equation (1) in cylindrical
coordinates, and by the substitution 1) -PQ he obtains the differential
24) = a24)/az2 + a2,~/aQ2 + I (a2(p/ag2 + '5/4)
equation V 1 2 0.
Q
This differential equation (2) has the solution (3), and by introducing
the solution in the differential equation, the author obtains a very
extensive expression. If the temperature distribution on the surface of
the body of rotation is given by
Card 1/2

Bbzo
The Ptoblem of Heat Conduction Concerning 3/17 60/003/010/016/023
Bodies of Rotation B019YB054
n
T = I os.~jf(2n-2k) (Q)p + si Q (2n-2k+l) (Q)qk (6),
VQ" ~: [ 2 k n~f
k-0
the boundazy conditions are fulfilled with the aid of the function
T = 1 4). v
Y'Q1
ASSOCIATION: Avtomobillno-doroshnyy institut, g. Khar1kov
(Highway Institute, Khar1kov)
SUBMITTED: March 22, 1960
Card 212

Sum
15
85930
3/140/60/000/003/009/011
C111/0222
AUTHORS:- Makho' vikov, V.1 and Ishchenko, I.M.
TITLE:: The Dettrmination of'Tensions in a Space of an-Orthotropio Medium
With a Cylindric.Cavity
PERIODIC,AL-. Izvestiya vysshikh uchebnykh zavedeniy. Matematika, 1960,
Nr-3, PP-205-212
TEXT.. The authors consider an elastic orthotropic body with a cylindric
cavit:r, the generators of which are pArallel to the z-axis, while the body
is bounded by the planes z - h, z - -h. The directrix of the cylinder is an
arbitrary curve L.. At first the authors give the conditions of equilibrium
~;in the shifts u, v, w, according to (Ref.1). Then the following arrangement
is ma-le for the shiftst
Card 1 C

85930
S/140/qO/000/003/009/011
Gill/0222
The betermination of Tensions in a Space of an Orthotropic Medium With a
Cylindric Cavity
X,
(2) U 2 Re [J (z) (r, + w +f, (z) ('Pj + ~j + PI P34) +
dEs
9241 + *2 72
Xids + a _f )] ..
+ + + f
v 2 Re [AZ) (4073 + Poll) +f' (Z) (00111 + Poff + X24.,)
(Z) (COTo + Polo + cgoXj f
f di. f p.A + al f d12 f ~242+ f X14)].
cg,
2Re[~(z)12+.r(z);Xj+,xjf 2A 42) +
W
41
+r W + sif q'14fil + f td 2 + M. f WE.)].
where 'ReE I means the real part of the bracket, f(z) is(a polynomial of
-degree 8-0,1,2) are
seco d. 9 \Ps Ts YS(52), 3
Card7T4__7Xjp

85930
S/140/60/000/003/009/011
Clll/C222
The Datermination of Tensions in a Space of an Orthotropic Medium With a
Cylindric Cavity
analytic functions of the Ile 12P 13 (~j - x+t-jy, j-1,2,3) and OLV *-i' Pe
are conotants. By substituting (2) in the conditions of equilibrium the
authors obtain three expressions of the type
Ile lf(z).Cli+fl(z)C2i.f"(Z)C 31 ] - 0, iml,2,3.
Now the unknown constants are obtained from the claims C,i - 0 (j,i.i,2,3).
The functions P,,-W,, A., are then found from the boundary conditions, if
the shifts on the cylindrical surface are given in the form
u - 2 Re f(z
% )P2+f'(7-)Pl+f"(z)po '
(13) v - 2 Re f(z)q IL (z)q P
2+"' (z) q I +f "0
w - 2 Re -A*(Z)t2 +ff(z)ti+f"(Z)to f
where pj, qjP t i are given functions of the arc of L.
The performance of this method is discussed with the example of a cavity
Card 3/4

85930
S/140/60/000/003/009/011
C1111C222
The Detexmination of Tensions in a Space of an Orthotropic Medium With a
Cylindrit) Cavity
for which L is an ellipse, where the boundary conditions are chosen as if
at two mutually symmetrical equal pieces of arcs of the ellipse two dies
were impressed in it, while the remaining are of the ellipse is tightly
ola.nped.
There art) 2 figures, 1 table and 4 Soviet references.
(Abstracter's notei (Ref.1) concerns S.G.Lekhnitskiy, Theory of Elasticity
of the ]Ulisotropio Body, 19501
ASSOCIATION. Kharlkovskiy avtomobillno-dorozhnyy institut (Kharlkov
Highway Construction Institute)
SUBMITTED: April 28, 1958
Card 4/4

MMOVIKOVO V. I.
0 Several theme-slaaticity problems for a space having an infinite
number of cylindrical iperhik szv
Report presented at the let All-Union Conference on Heat- and Mass-
ftchange3, Hinsk, BSSR, 5-9 June 1961.

25157
S/021/61/000/004/009/013
D213/D303
AUTHORS: Rakivnenko, V.M., and Makho kov, V.ri'.
Vy
TITLE: Concentration around a circular hole in a square plate
PERIODICAL: Akademiya nauk Ukrayinslkoyi RSR, Dopovidi, no.
1961, 464 - 468
-TEXT: This paper gives an wialytical solution for the stress.dis-
tribution of the load on the square and the-hole. The following
transformat-ion function,was obtained
0,00815 + 0,0346
0,948,,, 1 -t- 0,550t4
Here a 1 0.057, a2 0.0143, a 3 0.00-51, a 4 0.0016. Funo-
tion (1) describes a square for 0 < E) < 2 X/ 'and it
describes very nearly a circle Ae for i e. w(Ae-) ;k.e-(I+ n)
Card 1/7

251~.7
/0
S/021/61/000/004/009 13
Concentration around a ... -D2!3/D303
The error n is small, and for A 1/V3*it i6 less thain 0.01165,
and,decreasing markedly with decreasing Ai. The problem to be sol-
ved was represented by the plane boundary equations
COW +
(1) + ;T(T) qp,(C) Xj~ (8) (Do (6), Q6S) -t- (2)
(2)
Here are required anAlytical functions in the annulus
of ;t', are given constants; ~0(0), ~1(0) are given
functions which can be expanded
4
a,,, (0) -(b'ka + b%-e'), O~ (9) -E(b,,e" + b'-k-P- (3)
k-0 k-0
0 0
b b b b being constants. Eq. (2) was solved by the'me-
k -k k -k
thod of V.I. Makhovikov (Ref. 2: Pribilizhennyye konformnye ot9bra-
zheniya i ikh prilozheniya v teorii uprugosti (Approximate Confor-
Card 2/7

25157
Concentration around a ...
S/021/61/000/004/009/013
D213/D303
mal.Representations and their Application to the Strain Theorj)
Diss., K., 1959) for the case:
(8) = p W-T7F-, PJW(AE), -X0 =,X, gal
~
o 0
to give
21t
TO(V CA + C A ,C4k C4 A, + A~ + Pow
V 0,5
(I+ 0,948c 50C4 1 + X0
k-I
att4k+l + P02
I+Z C-k
0
14-0
2n cc
kt4f, + B-AC-4k E b,-,4/+c,('4-4-0,948)-I+cil(;1+0,550)-'+
B
VO (C)
h-0 /-2"+l
Card 3/7

'25157
S/02 61/000/004/0d9/013
Concentration around a ... D213Y.D303
( C5 +
+ [c, + 0,948)-l + c, + 0,550)-1 +
to' + 0,948
c8 I ak ~-O (4i +
+ -0,550
k-I k-n+S
ff
4k+l
k-0
where Akp Ao, Act Bir c are certain constants and b
.11 029 `9 c6 k
are the coefficients of expansion
cc
I+
Card 4/7

25157
Concentration around a
S/02 L /6-L/000/004/009/013
D213/D303
For real p 0 and p, constant precsure results of magnitude p. and
p, on the square and the circular opening, respectively. Function
(11) satisfies accuralely the boundary equat--on for the -sojare and
very nearly for the circular opening, Table 1 givf:s the first few
coefficients Gf the expansion of function (11) for the case n = 4,
0.0625a. ;(o I,
VT
and p Is p 0 " PIO The stresses on the opening were zalculated from
-Hh,o f ri r m ~ i I -A
where o'p p, . Table
I
on the opening (for
square is --atis;fIL-d
for the op,7--ning the
a
2 gives the
1/
exact-.L,,-, the
error is les6
f? e [ cf,
-I~a. ,es of c f,:.r positions
As -he bound,--ry equa-i--on for the
I
rt-mainder error i-3 -'~,-o. whi'Le
than 0,021~ p, which Igives a sa-
C a r d

25157
S/021 `61/000,. "15041 /009/013
Concentration around a D213YD303
tisfactory --olution to the problem- T.r.ere are 2 ta~,'Les, 1 figure,
and 3 Soviet-bloe references.
ASSOCIATIONi Ukray-'nslkyy zaochnyy r-.,.,.tekhnichnyy in--ty?'--t (Ukrai-
nijar, Polytelchnic InEitlt-l-v)
PRESENTED, H.ML Savin, Member AS UxrSSF
SUBMITTED: june .7, 1960
Card 6/7

S/170/61/004/"001/013/020
9 C) 6) 0 BO19/BOc6
AUTHORt -1.
TITLE: Problems of Heat Conduction and Thermo-elaz)ticit;~ ~f
Plane With an Infinite Number of Groups of openir~;s
PERIODICAL: Inzhenerno-fizi--heskiy zhurnal, 1961, Vol. N3. 1,
pp. 82-91
TEXT: A steady, two-dimensional heat problem is analytically investigated,
where the plane (space) investicated is assumed to contain an infinitp
number of similar groups of circular openings, each of these gr("L1j'-S
the same temperature field. In 'the course of a complex investi~;atl-"'I' the
first part deals with the problem of heat conduction. The bour.&-_'-'.
is solved with the aid of special, functions, which reduce the prcl:lc~r.: t-,
a plane, single-connected problem for ~he i-th opening. Ccr.,esp0r.1`1r'L;
the steady conditions, *he temperature T is a harmonic functlion, -In'l
composed of an analyt4zal 1,arf ri complex which ~:;
hereto. This f,'inctic;n j~_ o~ta_"nerl by means -f b~-_zrAary prDbl~:M
above. The boundanj problem ~;f them the z-- la6'_ -M s
Card 112

Proble=- of Heat, Conduction -in] Thz~-rm'--- -S/117C/61/GO4/G0:/O--
elasticit y of a Plane With an Inf-4n-l'.e N-,,rjb~r (,f 301,,,/B01~(
Groups of Openings
reduction ,nd
'tions 1,y analy
of the hounclar~ - "cal
-
-
There are 1 figure and 4 S.DviEtt refe-rpn--es.
ASSOCIATIO114 Avtomobillnodor-ozimyy instit,~~, g. Kll:...-Ikov (Institate -~*L'
E'otor Roads, Kharlkov)'
SUBIMITTED; July 12, 19(0
Card 2/2

22829
/61/004/005/015/015
S/176
B111/B214
AUTHOR: Makhovikovt V. 1.
-TITLE:' -The problem ofheat conduction in a cylinder
PERIODICAL: Ihzhenerno-fizicheskiy zhurnal, 5, 1961, 118-124
v. 4, no
TEXT: Two solutions of the heat conduction equation (without initial
Values) are given. ' The cylinder is considered to.lie parallel to the. z-axis
a.nd have an arbiti-ary cro.ss'section. For'the solution of the heat equation:
X(T) = 4 ae~Ta~ + O'T 1 8T (1) (T - t ,he desired tempera-
72 -a 7t 0
z
ture inside the cylinder; t time; x - iy) the
n ~Tix,+iaxt 'Y;
auxiliarj function Ti e. 5_7 f(n'.k) (z)~$TC(E) (x' material constant;
K-O
f(s)(*,) 9-th derivative of f with respect to z) is first inserted in Eq. (11
and
Card 1/8

22 9
S/170/6 004/005/015/015
The problem ... B111/B214
4- 1'(z) + 2 T-- 0. 41 + 114+11 (Z) 00 +
(Z) (3)
+ 1(--') (z) 10, + 2 V1 0.
obtained* This equation is certainly satisfied when f is a polynomial of
the nth degree and
?.di 0,, (E),
2
(4)
d [Ok+. (t) + 2 111 'A -Pk+~(Qj d Z.
0k 4'A (t) 4
k n - 2, n - 3.....0.
holds. It is seen that the'solution of (1) can be written as:
Card 2A

22829
S/ITO/61/004/005/015/015
The problem ... B111/B214
ffs 4. lit d%1 f~-k) (Z) I-Ok +
-T Rei e wk ce)
"-0
-2
(6)
IV,, -~j dtj[t Vk+, CE) + 2 VIT Wk+,(f d
-n-2.' a-3, 0.
At the surface of the cylinder, the temperature is Eiven in the form:
T= Re e N-
(Z)Pk
k-0
Card 3/8
j

L
The problem ...
22629
3/170/61/004/005/015/015
B111/B214
(Pk - function of the are of the c.ontour K limitingthe cross section of the
cylinder). The boundary condition (5) is satisfied by (7) and so it is
sufficient to obtain a solution along the contour:
V9 + Pk;"k-.' n ' a-'. 0. From this the functions q n, Tno
Yn-11 7n-l' etc. may be successivily determined according to the method of
solution of a surface ham6nic problem. The bc`uifdbLry donditions on the plane
surfaces of the cylinder remain unsatisfied. For a unique solution,it is
necessary to add to the function (5) the solution of varnishing boundary
condition at the cylindrical 'surface and given boundary values at the plane
eurfALces of the cylinder. Initial v&lues were neglected.' This is valid for
timbs far removed from the time of switching on. Second solution: If the
expression
T eaz-cos ( 1~z + xat)Re*~ is eubstitute~ in (1),
2a
ago
U(O) =-I&0- 0.
(Hat
IL
421.
and
Card 4/8

22829
S/170/61/004/005/015/015
The problem Blll~B214
+ 00 d 2E.
are obtained'where is..,an analytic function;
V'(E) d 1.
(12)
holds. It is shown that 6 can beneglected. for sufficiently large n. If
the temperature is given in the form
T - eaz Cos ( 1'-z +' xat).f(x,y) at a cylindrical surface, the
2a
following eT-iation holds at the croas sectional boundary of the cylinder:
Reb - f(x,y). A hollow cylinder is considered as an example. The cylinder
is bounded by an external circular area K 0 and internal circular area
K' (s =-. 1, 2, m). The equations for the circles are:
s
Card 5/8

228
S/lTOf6f/00.4/005/015/015
T4e.problem B111/B214
0 0 2 E. + H$,
(14)
If the function is written in the* form
k (tj d', (16)
ki
k--O
it satisfies Eq.,(11.) exactly to within expression.
Tv(tv)dt.
n!
After a longer cd Iculaiion one obtains for
Card 6/6

22829
S/1 70/61/004/005/015/015.
.'The problem BI I I /B214
(P. (1, cs. (ti 08, + a. (1). (21)
o~--Jot-
Upit k > I and
k-1
ek (t)
pI (k - I)I
P.0
apk +
(k 01 pf (k -i-p)l pl (k + p)l (22)
t t)P
I+ kf 1] (P (in + tA Ift) In t,
kI (k - I)l P-1 p1 (k + p)l
coo W
P-0 P, (in t -ag), s 6 0., IL
Card 7/8 a2 0;.al + I - afj= arl 4- k + P
P tAl

22829
/61/004/005/015/015
S/170
The problem B111/B214
It is shown -in the&foliowing that.at the boundary purves K (s 1, 2, .. m)
the function f(xty) Pan be written in the form
f(x,Y Re_~ the p' 'being real constants.'
There are
k k
K-0
2 Soviet-bloc refer6noes.*
SUBMITTED: January 16, 1961
Card 8/8

25560
S/170J61/004/008/010/016.
B125/B201
AlUTHOR% Makhovikov, V. 1.
TITLE: Solution of problems of heat oonduction and thermoelasticity
for a cylinder with multiply connected cross section
PERIODICAL: Inzhenerno-fizicheski-y zhurnal, v. 4, no. 6, 1961, 9.9. 106
TEXT: The method of conformal mapping has been used to study the
tempetature field and thermoelastio stresses in multiply connected
cylinders under a steady-state behavior, with temperature remaining
constant along the cylinder elements. The cylinder cross section is
a multiply connected region D', bounded by m + 1 contours V; ('.'= 0,1'...' M).
In addition, the.conformal mapping )r- + JY of region D, on-
to the region D bounded by m + 1 circles K"j is assil~ed to be known. KV
are defined by the equations r~o = E eiE; E_ + H Tro ?"(1
where are real and H' complex constants. "Moreover,
)-I --: Hi I < 1. Hit = H1 _'H" j = 1, M, t R1, t 9~- (2)
Card 1/10 Hit > 4/ + ).t ~j 1)., z + Hit < 1, Xj Hi 1< 1,

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Solution oh.. B125YB201
and T W) + Tr_(t7, where F(k' is a function being analytic in DI,'
and r is a function that i~ conjugate complex-to it. Since
also F-f ~Q) is valid, where ~(f) denotes a function
being analytic in D. Problem of heat conduction:' The-temperature on
the boundary surfaces of the cylinder is assumed to be given as a function
of the respective arcs of the contours K.I., Then, the boundary conditions
in the region DI will pass over into the boundary conditions in the
region D because of the conformal mapping (,_)(1):
TV (3), -'- 071, ... m (3)s where TI)(6) are given func`
V) +
tions. Equations (3) are-solved by the formulation
V [0, H,) ,In(.-HJ, -,O=Ho~o,
(7),
-0
where the functions forl'~ are analytic.
0
On the boundary circumferences K and K ...,m), this function (7)
0 n
_k
+ 71, A~ + 7 0
has the properties Tl~ rjlnE + 'o (12) and
k-1 j=1
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2 6/0 10/0 16
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B125 B201
Solution of ... n
k
~(~j) ~j(/Aj&) + yjlnF- + 6 + ~f (16), re;pectively, where
rz
a T so
S/ k
k = 1, (17) is valid.
M nj
A' 11 In k/+ Tt In Hit + 3,11, -.,,Hs
0 1 1 Hit,
t-1 S-1
nt
Z10 I I x/Y -11.1 '31,
I I [ I't
k=ni-I t=1 Hit k
By substituting (12) 'and (16) in (3) one obtains'an equation of the
Dirichlet type:
Card 3/10

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Solution of... B1 253201
no
Re 4),,(3) + A,' a-L
0. 2Rer'Dl()./z)+ V'A'
L k-.0
3) + 0' 0. (18)
with the approximate solution
I n
(PI (C) = ff (C) )k_ af,
(MC) (C) Ck, 0 (19).
k-I k-1
The latter formula is accurate to within 5v on the circumference Kv.
For sufficiently large n is valid. Problem of thermoelasticity:
The shifts u and v of space, which are parallel to the axes x and y.,
re3pectively, must satisfy the thermoelastic equation by Duhamel anew
Neumann: + 2--L- (u - iv) - (3 "T (22)'. The atreasea (L're given
1 2
by C, + - y 2G~~' - -' t,' - 'i-C- AG -' - i,) ~23) ith
Ci-y 2 (u
x 'I - 2 ":L XY
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Solution of... B125/B201
Me-4:. ( u iv), 2a' + o~,is the coefficient of thei?mail
expansion, ~L is Po~ssonls ratio, and G is the shear modulus. Since
T - F(f) + Yq7, equation (22) is also satisfied by the shifts
U - iv
Y;~eclb + A (24)
A 0. - q (z 7;7'+ (T- F'(,') + 1) 1 E E-P(E) +S 4-)); (25).
are functions being analytic in the region D'
Here, v, U), ana
4 3; q + The combination of the edge stresses
2 1 T-:7 - F Pn' tn
can be represented in the form
2 0 + M + + S (p,, iij d f'+ c, (26)
aw?CL z q -' f'T F'(Z)f (27),
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Solution of... 3125/3201
Here, p and t denote the components of external stresses being,
n n
rebpect.ively,perpendicular and tan ential to.the edge. The formulas
for the stresses assume, after (241 is introduced, the form
-
+ 8 G Re M + z q
V M
z q("c t')12F'(~) 4 (28).
Y-2
P(M)
Applying the conformal mapping w(f) of the region DI to the refion D,
the following boundary conditions of the problem.are obtained from 24) Dr
(26) (expressed in shifts or stresses):
Y., (0) + c, 0. (29),
Here, and f,)(-O) are functions given on K;',, being
piecewise continuous said -periodic with respect to c.,. are arbitrary
constants and Zz/are given constants. From these equations (29) and vith
-the function
Card 6~0

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Solution of.*. B125y3B201
I?
1-0
(30)
+
and the.series expansion
00 00
Tom AN, PO c*
la' a0 -J k
k-I
(3 V)
k-1
one obtains the equations
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Solution of... B125IB201
.~o (a) + 40) T: (a) + x- -0(c) No (0) - rT,
0 , (34T
0.10) -F-'1-1 (0) ?; (XI -) + -1 T/ (XI s) - NI (0) - n, M.
3Aecb 0603UMHO
no -k
NO (0) (0) - -V, IB2 (0) kBok + xxk gk.
k-1
al + co,
NI (0) fl (0) - B,, sk + BI + X, 'bi -k 50
tL, (0) + ci
U5
+ 136 d Bv + %v OV -0, 1, M. (36),
Card 6/1 o dXvz

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Y
Solution of... B201
B! 25

If V Of equations (34) are solved with
respect to the functions Yv(f) ~c
and %VV(f) for each J.separately. This is done by the well-known method
used to solve a singly. eonnected problem. In this connection, it is
*
easy to obtain \,D (0) = 0, kf
(oo) = 0. In the therm
oelastic problem for
10
j
alspace with three circular, cylindrical o Irl
penings,-5 = w(f) and
the temperature is given by T - 1,F) (1) + V71, where (21'\ holds for
The edge stresses*at the openings Ki, x X are equal to zero.
2 f 3
Then, the desired functions be-ng-analytic outside the three openings
read
,p q (C) + y-2 h) - f,
q [~j (C) -1 ~. (C h) h)),
The errors of TFJ 7 are estimated from
2 the inequalities
/
< 10-5( 1 + t
U
1) q, 1-1
1