SCIENTIFIC ABSTRACT B.F. DIKIY - N.R. DIKIY

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000410330009-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 12, 2000
• Sequence Number: 9
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

DIKIY, B.F., inzhener.
Electrical scheme for controlling a lamp or signal from two points.
Energetik I no.2:21-22 Jl 153. (MLRA 6:8)
(Electric wiring)

AUTHOR; Rikiy, B.F., Ivashchenko, B.P. 32-9-27/43
TITLEs A Photorefractometer for the Automation of Control Processes
(Fotorefraktometr dlya avtom&tizatnii protsessov kontrolya)
IWIODICAL: Zavodskaya Laboratoriya, 1957, Vol. 23, Nr 9, pp.il24-1125 (USSR)
ABSTRACT: A ref motometer, which can be mounted in a production apparatus
and which can be used in order to obtain signals for the automaL-
tion of control in the technical production of tomato pulp is
constructed. In the case of the photorefractometer developed here
the light does not pass from the solution to the prism, but, un-
like what is the case with other refractometers, through the prism
into the solution. The apparatus is then described. From the dia-
graxm obtained it may be seen that, with a reduced angle of iuoi-
denoe of light down to a certain amount which depends on the con-
centration of tomatoes, the signal increases considerably. The
maximam of the ratio of signal amounts produced in the case of
different degrees of concentration of tomatoes, is attained at a
certain angle of incidence of light. By using the diagrams the
device is adjusted for a maxinum degree of sensitivity for
Card 1/2 changes of tomato concentration within the limits of the given

A Photorefractometer for the Automation oft'jontrol Processes
32-9-27/43
domain. The device makes it possible to determine the per-
oentile content of dry substances Ath an accuracy of + OA% abs.
There are 2 figures.
ASSOCIATIONt Technological Institute of the Food and Refrigeration Industry of
Odessa (Odesskiy tokbnologiohaskiy institut pishohevoy i kholo-
dill noy promyehlannosti)
AMIABLE: Librar7 of Congress
Card 2/2

DIKIS, 14.7a.; XALIZIKIT, A.N.; SDIDIOV, &.11ra., doktor tekhnicheskikh nauk,
`font.
[Canning plant machinery] Takhnologlaheekoe oborudovanis konservnykh
zavodov. Moskva, Pishchopromisdat, 1953. 540 p. (NISA 7:8)
(Canning industry)

DIKIS, M. YA.
Dikis. H. Ya., "An Automatic Regulator for the Concentration of Tomato-
Paste in the Final Vessel of a Vacuum-evaporation Installation,"
Traktaty odesskogo tekhnologicheskogo institute pishchevoy i kholodill-
lioy pron7shlennosti 5ra~sactions of the Odessa Food and Refrigeration
Technological Institutt7, 1953, Volume V, Issue 2, Pages 151-164;
bibliography, 7 items.

DIXIS M.Ya. kandidat tekhaicheakikh nank, dotsent; KOGAN.L.L., inzhe-
'61R.Miedaktor; LMA,V.I., inshener, redaktor; RUDINSK:[T.Ya.V..
te;;nicheskiy redaktor
[Automatic machines for hermetically sealing canned goods] Mashiny-
avtomaty dlia. germetizataii I-onservuoi tary. Kiev, Gos.nauchno-
tekhn.izd-vo mashinostroit. lit-ry, 1955 205 P- (WRA 9:2)
(Canning and preserving-Apparatus and supplies)

DIKIS, Mikhail Yakovlevich -- aAarded sci degree of Doe Tech Sci for the
10 May 57 defense of dissertation: "Technological equipment of canning
factories and the basic problems in improving it" at the Council, Kiev
Technolog Inst of Food Ind imeni Mikoyan; Prot No 111 10 May 58.
(BMV01 10-58920)

DIKIS, M.Ta.
Regulating the operation of continuous vacuum evaporators on the
basis of the consumption of bnating otnam. Izv. vys. ucbeb. zav.;
plabcb. takh. no-3:132-135 '58. (MIRA 11:9)
1. Odeaskiy tekhnologichnakiy institut pishcbevoy i kholodill-
nny promyshlnnnnati, Kafedra tokhnologicbeekogo oborudovaniya
pishcherykb proizvodstv.
(Evaporating applioances)

DIKISO M.Ya.
-
Improving heat exchange in oteam-hented f27ars. Xons. i ov. -or4O=,
13 no,7tl( --:W JI 158, (HUA lltO
1. Odeaskiy tokhnologiaheakiy institut piahchevoy i kholadillnoy-
pror7ohlennosti
(;00d industry~Jqui~)ment and supplies)

*414, DW3 ,p
. ~- ~
isa" MW* .
Nomogram for power calculationo for iiaaming machines. Kona. i ov.
prom. 13 no.1.0:19-21 0 158. (MIRA 11:10)
1.0deaskly takhnalogichookiy inatitut pishchevoy i kholodillnoy
promyehlennosti.
.(Container industry-Iquipmont and supplies)

Bills, M.Ya.
Continuous sterilizers with a automatic thermally actuated bellows
sealing device for glass jars. Kons. i ov. prom. 13 n;.12:17-19
D '5 8. . (MIn 1-1: 12)
1.0deaskiy tekhnologicheskly institut pishchevoy i kholodillnoy
promyahlonnesti.
(Canning industry-lquipment and supplies)

GERNET) M.M., doktor tekhn.nauk,prof.; DIKIS2 M.Ya., doktor tekhn.nauk)
prof.; LUKIYANOV, V.V.9 doktor--Te-Z-m.n--aurc, rof.fdeceasedl: POPOV,
V.I., doktor tekhn. nauk, prof.; SOKOLOV, A.Ya. doktor tokhn.nauk,prof.;
SOKOLOV V.1.,eloktor tekhn.nauk, prof.; MRKOV,~.D,,doktor tekh.vKuk, prof.;
BAIMOVS,HYs N.V., knd.tekhn.nauJc, dots.; BROYDO, B.Ye.,, kand,tajain.
nauk,, dots.; BUZYK01, N.A.., kand.tekhn.nauk, dots.; GOROSWKO) M.K.,
kand.tekhn.nauk, dots.; GORTINSKIY, V.V., kand.tekhn.nauk, dots.;
GREWINYUK) S.H., kand.takhn.nauk, dots.; GUSIKOV, K.P., kand.toklm.
nauk, dots.; DEKIDOV~ A.R., kand.tekhn.nauk., dots.; ZHISLIN, Ya.M.,
kand.teldni.nauk, dots.; KARPIN, Ye.B.,, kand.tekhn.nauk, dots.;
KOSITSYN, I.A., kando tekba.nauk, dots..(deceased]; GEYSHTOR, V.S.,
kandatelchn.nauk, dots.; MARSHALKIN, G.A., kand.tekhn.nauk, dots.;
MOLDUSMY, G.Ye.t kand.tekhn.nauk, dots.; ODESSKIY, D.A., kand.
tekhn.nauk, dots.; PELEM, A.I., karKI.tekhn.nauk, dots.,- RUB, D.M.,,
kand.tekhn.nailk, dots.; SKOBLO, D.I., kand.tekhn.nauk, dots.;
SHUVALOV, V.34.# kand.tekhn'naulc.. dots.; M-ELINITSKAYA, A.Z., red.;
SOKOLOVA, I.A., tekhn. red:
[Principles of the desi and constniction of machinery and apparatus
for the food industriesrOanovy rascheta i konstruirovaniia mashin i
apparatov pishchevykh proizvodstv. Moskva, Pishchepromizdat, 1960.
741 P. (Food industry-Equipment and supp3ies) (MIRA 14-:12)

DIKIS S M.Ya,
More about the sterilizer of continuous action. Kons.i ov. prom.
16 no.2sl3-14 F 161. (NIRA 14:4)
1. Odesskiy tekhnologichesldy institut pishchevoy i kholodilinoy
promyshlennosti.
(Food., Canned--Steril-ization)

DIKIS) Mikhail Takovlevich, prof.; MALISM , Aleksandr Nikolayevichp
dots.-- -SOKOMV7-A-.Ya*.q doktor tekhn. nauk, prof., retsenzent;
BU21KIN, N.A., kand. tekbn. nauk) dotEients retsenzwt; SKOBW,
D.I., kand. tekbn. nauk, dots.0 retserizent; BIMLINITSKAYA, A.Z.,
red.; KISINA, 79.1., tekhn. red.
[Machinery and equipment for canneries] Tekbnologicheskoe obora-
dovanie konservzwkh F*vodov. lzd*3,, dop, i perer. Moskva, Pi-
shchopromizdat., 1961. 539 P. (MIRA 15:1)
(Cinning industry-Equipment and suppligs)

PIKISI M.Ya.; MOLDAVSKIYj G.Kh.
Urgent objectives of the MA can manufacture. Kons.i av.prom. 16
(MIRA 14*-5)
no.5:19-22 My 161. 1
1. Odeaskiy tekhnologioheakiy institut pisholievoy ikholodillnoy
promy-ohlennosti. (Tin cans)

DIKIS, M.Ya.; MDROZOV, N.V.; A.KNOV, H.S.
Air as heat carrier for the sterilization of canned food in
glass containers. Izv.vys.ucheb.zav.; pishch.tekh. no.4:
128-132 162. (KRA 15- 11)
1. Odesskiy tekhnologicheskiy institut pishchevoy, i kholodillnoy
promyshlennosti, kafedra tekhnologicheskago oborudovaniya
pishchevykh proizvodstv.
(Heat--Transmission)
(Food, Canned--Sterilization)

DIKIS, M Ya.- AMINOV, M.S.
Vacuum deep-frying of vegetables. Kons.i ov.prom. 17 no.5:12-15
My 162. (MIRA 15.5)
1. Odesskiy tekhnologicheskiy institut pishchevoy i
kholodilinoy promyshlennosti.
(Canning and preserving)

g%IS,.HikhaIl-,UKoy1evicb; M&LISKIY, Aleksandr Nikolayevich; RABINER,
N.Ya., kand. tekhn. nauk, retsenzent; STEPANOV, N.V., inzh.,
retsenzent; KHRELINITSKAYA, A.Z., red.; SATAROVA, A.M.,
tekhn. red.
[Equipment of canning plants] Oborudovanie konservnykh zavo-
dov. Izd.3., dop. i perer. Moskva., Fishchopromizdat, 1962.
468 p. (MIRA 16-4)
(Canning industry-Equipment and supplies)
1%4-

DIKIS, M.YM.
------- :-
Basia requirements for machinery and &pparatus of mechanised
production lings in the canning industry. Kons. i ov.prom. 18
no.30-5 Mr 163. (MIRA 16:3)
1. Odesskiy tekhnologicheskiy institut pishchevoy i kholodiltnoy
pronyshlennosti.
(Canning industry-.-Equipment,and supplies)
jAssembly-line methc4s)

DIKIS, M.Ya.; ROMATOVSKAYA, T.L.
-:11 -1-11- ...... ---.
Calculating the cooling time of fried fish in a liquid canling medium.
Izv.vys.ucheb.zav.; pishch.tekh. no.5:83-86 163. (MIRA 16:12)
1. Odosskiy tokhnologichoskiy institut pishchevoy i kholodiltnoy
promyshlennosti, kafedra takhnologlebaskogo oborudovaniya
pishchevykh proizvodstv.

DIKIS M.Ya,; GLADUSHNYAK, A.K.
Effect of the angle of inclination cif the jet on the area
of the washed-out soiled surface of glass containers. Izv,
vys. ucheb. zav.; pishch. tekh. no.6j:121-124 163.
(MIRA 17:3)
1. Odeaskly takhnologicheskiy institut pishchevoy i kholodill-
noy promyshlennosti,-kafedra tekhno3.ogicheskogo oborudovaniYa
pishchevykh proizvodstv.

DIKIS, M. Ya.; CHERNIGOV, A. R.
Contact heating of liquid food products by water vapor. Izv.vys.
.1
ucheb.zav.; pishch.tekh.no. 2:84-87 164. (MIRA 17:5)
1. Odesskiy tekhnologicheskiy institut pishchevoy i kholodillnoy
prom7shlennosti, kafedra tekhnologicheskogo oborudovaniya
pishchevykh proizvodstv.

PHASE I BOOK EXPLOITATION sov/4518
Dik-4y., Aleksandr Danilovich, Candidate of Technical Scienees., and
fv_~-~IffiUr_e-y e-VTc-F-Y_6M_ t-oN
Feredatchiki radiotekhnicheskikh sredstv (Radio Transmitters)
Moscow, Voyenizdat,, 1960'. 367 P. 'No. of copies printed not
given.
Ed.: V. L. Sterligov, Engineer, Major; Tech. Ed.: N. Ir. Sribnis.
FURPOM- This is a textbook intended for students in higher
military engineering schools and can also be used.by those
studiA.ng the theory of-transmitting systems in schools of
higher'education.
COVERAGE: The textbook sets forth the fundamentals of the theory
of transmitting systems,, the principles of circuit ' design,and
the elements of their computation, with special emphasis on
rada.- systems. A. D. Dikiy wrote the introduction and Chapters
1. VI, VII, VIII., IX,and XIi I. A. 3oldatov wrote Chapters II,
4.
I.L1, iv,, VAr~d VU; Chapter X was wrl"tten by I. Ye. Khvatovker,

Radio Transmitters
SPV/4518
Candlde,e of Technical Sciences. No personalities are.mentioned.
There wre 14 ref erenees, all Soviet (int.,luding 2 translations).
TABLE OF CONTEWIPS-.
t
Introduotion 3
1 Subje4t, problems, and signifi,,.,,ame of the course 3
2: Hiatory in brief of the development of radio tans-
mitting syetems 3
Ch. 1. Gener-al Information on Radio Tiansmitte.-a 8
I. Claasification of radio transmittez,3 8
2. Basi^_ teohni,:!_9.1 requirements of radic. tramsmitters 8
3. Block dia,grzmg of radio transmitters 12
Ch. II. Fundamentals of the Theory of Ossillatora 15
1. Basic definitions and primAple of aaction of osoillators
w.-Lth sepaz-ate exaltation 15
2. kpplir~ation of quasi-linear t7heory to osaillators 20
3. Analysis of the atatl.-_ charaat-ertst-'Aas of osoillatlor
tubes 22

S/781/62/000/000/035/036
j.
AU-Tl-'.O'RS: Silenok4el'ski~, G. A.v-Dikiv A. G., Scilodovchenko, S. I.
TITIZ: Plasma electron concentration measurement with a resonator
SOURCE: pla-viy. i problemy.-upravlyay~-zmgo:te--Troyader4nogo sinteza-
dol-clady I konferentsii po fizLke, plazmy i pr6ble-ne upravlyaye.-iykh
te2.7royadeY-nykh reaktsiy..J~.z~-tekh. inst. AIN Ukr. SSR. Kiev, 1zd-vc,
A24 Ukr. SSR, 1962..167-169
TEXT4 A method is proposed'foxv.,neasur-ing plasna electron-concentration by,
datex'mining the, change in the': dispersion propertieis of a waveguide system in which
g
-Che pla--.ra is placed, since the phase velocity of ~wave propaggation in a wave-
gui de syste-n. fillied with plasma depends not only. on the gemetry of the sys-Lem,
the boundar"i conditions, ~nd the frequency, but also on the electron concentration,
as i'lell as the regretic fields the collision frequency, and the type of gas. The
affect of the 7)lasma on the -phasevelocity in a wmvegui& with a helix partl
y
"led with ~ pla-sma was -rive-sti ated exreriTrantally. The ap us and experL-,
parat
ental* conditions are brief3lydescribed. : The extex-iments were carried out witIh-
out, a nz-gnetic field, andlit is indicated:that application of the field would
d 1/2
__car

ACC SOURCE CODE: UR/0185/66/011/012/1341/13"
AUTHOR: Borovyk, Ye. S.- Borovik, Ye. S.; Dykyy, A. P.-.-Di-ki.y, A...P.;
14amaluy, Yu. 0'-Mamaluy,, Yu, A,
VkG - Khar1kovj State University iftO.M. Gorlkiy (Kharkivalkyy
4e'rz~lniversyte~)
A
TITLE: Magnetostriction of ferroxplans
I
SOURCF: Ukraylnolkyy zhurnal., v. 11, no. 12, 1966, 11-41-1344
,TOPIC TAGS: m~gnetogtriction, magnetic permeability, ferromagnetic
material, cobalt containing alloy, nickel c6fitaining alloy
ABSTRACT: Theimagnetostriction of mixed ferroxplans of the type
Co Ni W ('here W,,-BaOe6Fe2O3), and of some pure ferroxplans of
y Z-y Va V
thin- W type 'was-measlAre The measuretenta vere made on polycrystalline
samples with values*'of y = 0, 0.2, 0.4, 0-7, 1, 1.5, and 2. The
ferroxplans-in*estigated were in the form of solid solutions having
different signg of the first anisotropy constant K1. Investigation of
the anisotropy-energy and the magnetic permeabili-ty of such systems of
mixed ferroxplans showed that, for given composition, a minimum of
anisotropic energy and a maximum permeability exist. The value of the
Card

ACC NRI AP7003614
i - small because with the given concentration of Co
anisotrcw enerp
ions in ferroxplan the first misotropy constant changes its sip, i.e.
K1-0 for this composition. Measurements of magnetostrictio.n showed
that saturation magnetostriction of-,all investigated ferroxplans has a
negative valuii Orig. art. has: -3 figures and 1 formula.
S.UB'CODE% 20/, SUBM DATE-. 3lMar66/ ORIG REF: 005/ OTH REFt oo4

WKIY, B.F. kand.teldin.nauk
Disconnecting and blocking device contotining a mechanism for signaling
the fault of an electric motor on cont uous production lines.
Rnergetik 9 no-5:27-29 My 161. It (MIRA 14:5)
11*-, (Automatic control) j
:-,J, (Electric driving)
(Assembly"line methods)

DIKIY, B.F., kand.takhn.nauk, dotsent; IVASHCHLNM, B.P., assistant; S2NMTM,,
starshiy laborant
Now submersible photorefractometer for the automatic control of
evaporation. Trudy OTIPiKhP 9 no.2:143-148 159. (MIRA 13-9)
(Refractometer) (Densitometers)

DIKIY, B.F. [Dykyi, B.F.]; LOMAKIN, V.F.
I
Conductophotometric transducer for wine flow control. Kharch.promo' no,
4:63 O-D 163. (Iffap, -17:3.)

DIKIY B F - KHAYUTINY Yu.D.
Continuous control of the concentration of homogenized
tomato Pulp. Izv. vys. uchebe zav,; piahch. takho no.6;
136-138 163. (MIRA 17:3)
1. Odeaskiy tekhpologichaskiy institut pishchavoy i
kholodillnoy pzopyahlannosti~ kafedra avtomatiki,

JIUK11, -Boris ~W o.rovi c h; LOMM4, V-Ladimir F.lippovich; DREVS1,
G.V., dote,., retsenzent; ZAYCHIK, TS.R., dnzh.,
retsenzent.; Yll,'.~ODKHINA, N.V. , red.
[Automation. of The processes in wine making] Avtomati-
zatsiia protsessov vinodel-iia. Moskva, Fishchew:ia pro-
mys-demiost', 11964. 365 p. L
?:%))

-Y
IKI _~ G.F.; BUTIMO, B.M.; IVASHKEVICH, YU.K.; IVASI]CMIKO,
D
LOMIAKIN, V.F.
[Automation of production processes in the wine and
brandy making factory in Tiraspoll Avtomatizatsiia pro-
izvodstvenrykh protsessov na Tiraspollskom V=D-
konliachnom zavode. Moskva, TSentr. in-t nauchno-
tekhn. informatsii, pishchevoi promyshl., 1964. 32 p.
(MDA 17:11)

ACC NRI AP6034905 SOURCE CODE: LTR/0.382/66/000/002/0032/0038
'AUTHOR...Pj4iX._.,2,',,, P. ; Kostenko, P. P. : Selivanov. V. G. Frolov. S. D.
ORG: none
TITLE: Conducting gas flow in an annular duct in the presence of an axial magneticl
field
SOURCE: Magnitnaya gidrodinamika, no. 2, 1966, 32-38
TOPIC TAGS: axial magnetic field, gas flow, laminar flow, annular duct,
magnetohydrodynamic generator
ABSTRACT: The authors attempt an analytical calculation of the influence of
azimuth currents on the electrical efficiency of an MHD converter.~' Approximate
values of the radial-velocity component and the gras temperature are simultaneous
calculated and given. The paper examines the laminar flow of a conducting gas in
an annular duct of an MHD converter in the presence of an axial magnetic field.
The above-mentioned influence of azimuth currents on the efficiency of the
generator was found. Orig. art. has: 8 formulas.
SUB CODE: 20/SUBM DATE: 09Jun65/ ORIG REF: 003/ OTH REF: 002/
ill UDC:-533.95:538.4

L, ?211
S/057j62/032/011/003/014
B104/BIO2
AUTHORS: Dikiy, G. P., and Tarapov, I* Ye.
TITLE: Somw~ self-similation problems of magnetohydrodynamics with
I axial symmetry
PERIODICAL: Zhurnal takhnicheakdy fiziki, v- 32, no- lit 1962, 1302-1312
TEXT: The nonstationary equations of magneitohydrodynamics for an
incompressible viscous fluid of finite conductivity are given by Eq. (1)
and (2) if axial symmetry is assumed and cylindrical coordinates are used:
allr -+-Vr allr = H, a
at ar a" -a -, (rHr))
OHp =H, a"
at ar r Or 1. dr r 6r
OH, H a
Vr -!- ra -4--,.-L-~L r r ~(rHr) 0.
at H 1*
r dr r dr
Card 1/6

Some self-similation problems see
S/057/62/032/011/003/014
B104/B102
I JP" I jH,. _ H,
-t- Vr -!!!I- - - = - - -i-in? H, or r
t Or r or
Or r dr.
av, OH, HH,
O 479
0 Or
r r pr
P
?
L L
-+-V-
Or -
(rv)
Or
av,
-L 'p-
L"
-
1 -j-V av,
-L-L ~
(r
. -Ot -
-
-,I-Vr-
ar P ds 4rp Or or
r Or
a H2
--v, (rvr)=O; P.=P-+--i-
r x
(L. D- Landau and Ye. Me Lifshits, Elektrodinamika sploshnykh ared
Electrodynamics of continuous medial GITTLt Meg 1957)-' From these
equations follows
(2)
Card 2/6

Some self-similation problems
S/057/62/032/011/003/014
BI(A/B102
P. = P, (11 r) -4- A W - (3),
Vr=Q(t); H,='-"
2% 2r. r
where Q(t) is the quantity of fluid passing through the cylindrical
nurface, and a,(t) is the magnetic flux. ~(t) is constant and.Q(t) is
assumed to be constant. P 2(t) is assumed known and Pl(t,r) is obtained
by integrating the first equation of (2). -rhe problem is thus reduced to
the determination of v , v R and H froz the system
T z 'T 2
ON _4_ Q _!Hv 1, dv, Q

-
-
-+-- v
(rH
- M-
-
2
))
(
at 2rr Or ,
77-
2r.r
P i-
P Or
7
,
01-T -
-
q
( OvT
t I- V,
1
L
-
v (

t _
_
.I
2nr. -
.
-
-4-
rv,
(
Or 7 0
pr Or r Or r Or
OH, W, _~L 6-, _L _L (4)-
21%r Or 2nr dr r Or
Ov,
- Q

-
-*- av,

- P2 (1) 0 dH,

-
- -I- -~- v
0t r
W dr P Bu2pr Or r Or or
Card 3/6

S/057/62/032/011/003/014
Some self-similation problems ... B104/B102
The solution of (4) AS soughi in the form
H T=H,/g(C), H,==HrPh(C)9
vT= v,==v,,r,YPI1 (5)
P2 (f) - PO
where R~09 Hzo P VJ,O , Vzoo P20 and 0 are donistants and the dimenjionless
funct ns 9. ho f, and V are functions of 'the dimensionless variable
~Avt- Assuming the form (5) the system:
Vg-+--~~ [(a - 1) ff-4- 2C4 =OVVI I(- Xf]-i--
2nv -i?-CIIH~
VO
V
Vf -9- [(a -1- 1) f-~- %fj 1)g -i~ Zg] (7)
2r.v 87t?PVVo
I)f--i- 4 (m -+- 1) tf -+- Vjv,
2,xv 2%vHo
VV
Vm [PlIt -*- 4 (P -+- 1) W -+- 4M9,
V
Card 4/6

5/057/62/032/011/003/014
Some self-similation problems B104/B102
41~` -4- Q~ Zfl P20V-';'
2nv (4v)V-1
4'H,o
Sr.2p%Vo
is obtained which cannot be solved in general. For the following special
cases (7) is solved: (1) In an irivestigation of'the vortex sources in
the usual hydrodyn&mica (H 0) it is shown that an initial vortex source
of the form vr a Q/2ur, v 1,/2Ar, does not change its configuration and
that sources or sinks alter the diffusion velocity of the vortex in the
fluid. (2) The diffusion of the vortex of the magnetic field: The
problem leads to the solution of the first eq4ation of (7) with
a - -1 + Q/2. (3) The damping of a magnetic vortex field in a rotating vl~
fluid in the presence of a radial magnetic field: The functions and
f( ) are determined from the first two equations of the system Mg
(4~ The damping of the axial magnetic field in the presence of a sink:
Hz is determined as a function of time from the function h(T) which
satisfies the third equation of the system ONI with 0 - Q/2. (5) The
damping of the axial magnetic field and the axial motion of the fluid in
Card 5/6

Some self-similation problems ...
S/057/62/032/011/003/014
B104/B102
the presence of a constant radial field: The solution of the nonstationaxy
problem has the form:
H. 0, r) =0Cr-1 h
2nv,
v. (t, r) = XGr-1
where h(j) and Yqj) satisfy the last two equations of (7) with
P - -A. There are 5 figures.
ASSOCIATION: Kharlkovskiy gosudarstvannyy universitet im. A. M. Gor'kogo
(Kharlkov State University imeni A. M. Gor'kiy)
PRESENTED. June 26, 1961 (initially)
SUBMITTED: December 15, 1961 (after revision)
Card 616

)")gig
S/057/6VO32/011/004/014
B100102
AUTHORS; Dikiy, G._P,,--and Tarapov, I. Ye.
TITLE: Some stationary problems of magnetohydrodynamics with
axial symmetry
PERIODICAL: Zhurnal tekhnicheskoy fiziki, V. 32, no. 11, 1962, 1333-1341
TEXT: The stationary motion of an incompilessible visc_9us fluid with
.4
finite conductivity is considered assuming that v and H are independent
of the coordinates -,Q and z. In this case the general magnetohydro-
dynamics in cylindrical coordinates lead ;o:-
d.,
dr = H, dr fir dr
M. v H du JY V, d
Vr = H yr (rH-))
r r dr r dr Y
.~H, v' (r 'H'
vr Hr �-
dr fir r dr dr
1. d
7 W (r Hr) = 0.
Card 1/6

S/057/62/032/011/0(),1/014
Some stationary problems of B104/B102
6p
dv, I (H, -d
dr dr r dr r jr
H, dHI -i- H H (2)
dr r 4-.? dr dr r dr
dv, I op.
vr- - -i- -L H,
dr ~z 4-,? dr r dr dr
d H2
W-(rv,)=O; P.=p4---r-
(L. D. Landau and Ye. M. Lifshits, '-'lektrodinamika sploshnykh sred,
Elec.trodynainics of continuous media., GITTL, M., 1957). From these
eqi,,-
,,~.ions and the assumed axial symmetry it follows that
P. P~ P" - Z; (3)9
2-
r r
bard 2/6'-

5/057/62/032/011/004/014
Some stationary problems of ... B104/B102
where Q is the quantity of liquid flowing through the cylindrical surface
and 9- is the magnetic flux. The constant gradient of pressure P M along
the axis of symmetry is assumed to be known, P,(r) is obtained by the
integration of the first equation of (2). Thus the problem is reduced to
determining v , v , H,, and H fr6m the system
z z
d Q- d H I d
-4- "' - = 0;
Yr r dr -2.,. 77- (-r 2nv. dr r
If Q I d III I d (4)
v 7. -j- (r v,,) (rHv) 0
7r r dr r
d dH,)_ Q -.&Hx VII/
_L_: dv. == 0;
ar dr 2rv,, dr 2r.-"" j'-
d "' �'L=P'--r.
Yr dr 2rv up 2r2?v dr. PV
whose general solution ist
Card 3/6

Some stationary problems of
S/057/62/032/D11/004/014
B104/BI02
H (C,r"-+-C,,")-+-4-pQC3r-4-(DC4 1
2 r
V Q C'r'. -,-,Dc"r -I--
QC, I;
r
H, (Cr's Qr") -i- C7 r2;
2rv. Q)
Q
V, Cr C,r"' Q
r2
(5)
4r. 4-.. v
-4- -L) =t (.L -.L
4r v V. Y V J, 16-0" 6).
?,V
The following special cases are discussed: (1) Stationary vortex eouroes
Card 4/6

S/057/62/032/011/004/014
some stationary problems of B104/B102
V, = C12" -4- Cr
Wrr
in the usual hydrodynamics (H - 0); (2) magnetic vortex fivid and
hydrodynamic sources
(7);
H,=Cjr-4-C2r_I.#_'.':
(3) hydrodynamic vortex in a radial magnetic'field
(C~~'-4-C'J~A)_+_Ci Hr
2%v. P
V,P "2
(9);
(4) the motion of the fluid along the z axis in a radial-axial magnetic
field-
Card 5/6

S/057/62/052/011/004/014
Some otationary problems of B100102
Q
H,=i" Vr yrr
jjE2qe P, 2
H. (ca". ce".) -'-- C7-
21tv. 4n? Wtv - Q) (4nv. - Q) - 01
2 X,) Cr:k. Q - X,) ~'Gr). -I- C. -4-
21 v. 2nv.
40 (4xv. - Q) A (5a)-
Op (41:v - Q) (4xv, - Q)
ASSOCIATION: Kharlkovikiy ilosudarstvennyy universitet im. A. hi. Gor,kogo
(Khar1kov State University ivieni A. M. Gorlkiy)
SUBMITTED: June 26, 196*1 (initially)
December 15, 1961 (after revision)
Card 6/6

DIKIY., G.P..; TARAPOV, I.Ye.
,Same auto4c4d problems in magnetohrirodynamicsI given axial
symmetry. Zhur. tokh. fiz. 32 no.'.11:1302-d= N 162.
(MIRA 15: 11)
1. Kharlkovskiy gosudarstvennyy univorsitet imeni. A.M.Gortkogo.
(Magnatohydrodynamice)

DIKIY G P TARAPOV, I.Ye.
Some stationary problems in magnetohydrodynamics, given axial
symetry. Zhur, tekh, fiz. 32 no.13-:1333-1341 N 162. (MM 15:11)
1. KharIkovskiy goeudtLrstvennyy universitet imeni A.M.GorIkogo.
(Mapetohydrodynamics)

DIKIY) G.P.
Sources of spherical eddies in magnetohydrodynamics. Zhur. tekh.
fiz. 33 no.11-12115-1289 N 163. (MIRA 16sU)
1. Kharlkovskiy aviatsionnyy institut.

'1111CIV, T
V . - F.
' ' ("' 6. Ly .1 ~ L
,.4 1 DIIKI~ , 1. 1". Ra~ryl, a,icvri,-,my Sele:,snochncy I -~jlezenki 'Iri
Vo,,il Md-mcisytichnov D..rcinennostl. Vracheb, Delo, 19/,3, Nc 11, ic!5,16-
SC -. L.-tol Is I "hurral Inyl-I SU,tey, 74., 1949
a .6

DIKIY, 1. F.
DIKIY, 1. F. "Petri fication of the fetlia In abOonjinal six-.morth rjret:-
mancy", Vratheb. delo, 19LL8, I~o. 12, paragrarhs 1105-08.
SO: U-3042, 11 March 53, (-'etopis Inykh Statey, Eo. 10, 1949).

T
USSR/Mathematuics - Eigenvalue
11,_'oncernering, a "'ertain Gellfand-Levitan 0:)naula,, 11 L. 1L. ijiL-iy
Usp. -at. ..auk, Iol 8:1 Ao 2 ("15)~ Pp 119-123
Discusses the significance of the theorem of I. vi. Gellfand and i). v.. Levitan
(IIA Simple Identilty for Licencalues of a 3e~,,ond-Order erential -Dr)erator,'!
DAIN 33SIR, Vol M, -,,o h, 1953); nauely, Lae folloidn_- t',-I..Dorc-jr,: if- ar e
N
ei,~-,!envalues of the OPE!rabor -d2 + p(x) on the int_~rval (o,)r) wiv-, zero "Doundary
yp t2
P
cond -ions, wftere'fL,(x)dx 0, then the Loll.owin,- subjEct fora,ula holds
OD
(k (p(O)+p(YT) Ilizmansion in Eigenfuncidors," (_-_tazlo!';hen_J"3,e no
4
,Joustvenijym I`unks~iyam), B) ri. Levitan) -,Aed. Imitate iuWi Pr(-s, 1-i-L, j.*,;5C).
IDubidttud 26 J-,ec 1952.

DIKIY, L. A.
DIKIY, L. A.: "The zeta-function of the Sturm-Louisville operator and its
application to spectrum investigation". Moscow., 1955 Moscow State U imeni
M. V. Lomonosov. (Dissertation for the Degree of CILndidate of PHYSICOMATIMIATICAL
SCIE11CES)
SO: Knizhnitya Letopial No 51, 10 Deccmber 19555

r)IK\Ny, L'.f~
SUBJECT USSR/MATHEMATI-.S/Differen-tial. equations CARD 1/3 PG -108
AUTHOR DIKIJ I.A.
TITIE Zeta.function.9 of an ordinary differential equation on a
finite interval.
PERIODICAL -Izvestija Akad. Nauk j.L 187-200 (1955)
reviewed 611956
M
The author considers the zeta function Z(S) - 2" Vs where An are the
eigenvalues of the differential operator
Au d u P(X)u U (0) .11(-M) - 0.
If the function p(x) with all its derivatives vanishes at the ends of the
interval [0,1ZI , then Z(s) can be oontinued on the whole complex s-plane.
It has only simge poles in -the points s - 1P - 1 1 - 3 r - 1) , .#o * The
1 .1 1 2 2 2 2
Tesidue in 1 is but in -k it is 1: L (k- x)d3:. There the
2jr 2k
functions A., are defined as followni
s
e(s,x) B1 m(x) ( 1+m k k%'
M-- 0 2 2

Izvestija Akad. Nauk 19. 1137-200 (1955) CARD 2/3 Pa - 108
ELad the B1'm (x) are given by the recuxrence formulas:
I -
3o'o(X) M4, Bl'm (x) S 0 for m >1
131+2,m(x) = p(x).B lpm (z) - B!,'9m(x).+,'-'Bl'+j 'M-1 (x).
In the genral case (P(x) does not vanish as alove) the situation of the
poles remains the same, for the residues a sumAzi. the A and their derivatives
is given. If C, '4
2 2
'-A
n + c + - +
n 0 . n2 XL4
is an asymptotic decomposition cf A (existence is not proved), then
Z(a) (2s) - soo
where ~; is the Riemannian I>- -function. A combination of the obtained
expressions for residues and this dave2opment leads to a recurrent system
of equations for the de-termination of the eY e.g.
Ir
.30 p(x) dx
ir IV
( P(x)dx)2 1 1 _ -p 1 (0)
0 P2(x) ft
2 -" -41r_ 121C

Izvestija Akad. Nauk 1,9t lel'-200 (1955) CARD 3/3 PG - 108
After the continuation of Z(s) on the whole plane, Z(-J)tZ(-2),Z(-3) are
and forinally denoted as the au -A 2, y
Me , \n3 In
the special case whe Kk p(x) with all derivati,res vanishes at the ends of
[0,-Mi , we have 7 - 0., In the general case holds a long formula (series
in A and derivatives). J?kk or Z(-k) can be denoted as the sum of the
1 x k 11
numbers (except of those terms of the advalopment of A k *bich
n n
disturb the convergence). 1~7om the sum there must be subtracted the half
of the free term of the asynptotic development.
These results for Z(s) are-extended to' the fune-tiouB
CO
I )~
Z(s;:kvy) ;Cjj 8
Mgt 1
where n(x) are normalizea eigenfunctions of the operator.

IY
J

Piz- i; AIL L Mies 40CI:ertain Identiffec;
,
L'
t jiuwIIe
qperator,,
ifor the -cpecw fouctku"of 4 15
687-690..
Niult; SSSR f]
DAL Alj~ad.
1 jT9 s),
1 -

'Re. bouiid. piobi~'in
dry-valm

_4 ere it is i'ssurned that p i
!6, 6considered, wh I S
_
- -
iw
h
l
o
d
A
6
h
l
s ait
Jimi
e
e Ccase prevai
h
iab
t
ififthlitelit
if
re
t P I
p
i..iIIIIi4y, alid 1:hO.Spectfurn 1--positivei-L'[Pt 0.=9(x,yII) ba
_
~:
ct* f
ion or thd blcn~11~: and let Af be
the cpectjt,
J:Iun
.,pro
clefi~ed j(1)64. Then Ihi:re exist nurnbeni
r, supblhi~jbuz, y~AO, -

A~*-~icond iesult is Iii6vedi Which states that
A,
T, -n+ijIdt 0
rj~

r 10 ingivW (co ~e
f
X" E. A, C dd nhageil

A.1

XUTHORs .-DIKIY L.A. 20-1-2/u
Tf TLE: A N*wApprcodmition blethod for the, Caloalation of the Eig-suvalwas
of the. Sturm-Ifouville's Problem-(Movyy &yomob---pribI:Lzhenr%ogo
vyehis1eniy&..sobetvenuykh chisel zadachi..Shturna-Liuvillya)
PERIODICILt Doklady, Almd. If Nauk SSSR, 1957,701-116, Ir. 1 , pp. 12-14 (USSR)
A13STRALCT: For -tha. ealculation. of the eigenvalues of the Sturm-LiouTille I a
problemi.
_Ulf + P(x)u -Aut u(0) - u(Ir) - 0
the! -given in -an. -earli*r- p"er. flef .41
which..-*o-6mbine-. the. smms. of -positive- powers. of. the eigenvalues. -with
the funation,P(x), e.g.
OD 4 _R~O t2(1C_) P,. (0) P,.
n - 2.2) - c +
2 5 8
n-1
,Fhere c 1- P2 1,:r)dx. Eere p(x) is raplaoed by a -trigonometric
2 'Zr f
N 0
Card 1/2 sum: P(x) - T. a nocis n x and, beclause of the diTergence, the
n-1

A New t0pradmatIm..Method for: the. Oalcu_bttion of the ligenvalues 20-1-2/44)
of- the Sturm-LiouvJ-lle I a Problem.
appwarin&.-Ser~i 9 mr- -are- xwgulawi~xwt- 1~y, -MLbArruatiau.. For the
de.tarxinAtion ~of , the-- thivd~Approximation -the Auihor obtains the
algabraic system: + -4 + A2 + -N2 + -A 2 P-B;
1 2 1 2
-A 3~ )~3 + 3
1 _+ 2 3 f,-C, -whare A,:B,C -are conistants depending on
P(O), P(-T)p P"(O)f P"("r)q I? IV (0)q P'V(it*) and on the integrals
of the function p and their deriTatives.
ASSOCIATIONtInati-Lute of.-Atmospheric Phyvios,Aoad.Sc..USSR (Institut fiziki
-atmesfery'.Alt SSSR)
PFMBWM BY: A. A. Doroiluitsyn, Academician, April 8, 1957-
SUBMITTED' Dec. 21, 1956
AVAILA13IR: Library of Congress
Card 2/2

AUTHOR: Dikiy, L.A. SOV/42-13-3-2/41
TITLE: Formu-la-s-M7tra
,R~Eof the Differential Operators of Sturm-Liouville
(Formuly sledov/differentsial.Inykh operatorov Shturma-Liuvillya)
PERIODICAL: Uspekhi Matematicheskikh Nauk, 1958, Vol 13, Nr 3, PP 111-143 (USSR)
ABSTRACT: Gellfard and Levitan recently discovered a nev -roup of problems which
arc someiihat, different, and more ELIgebrlLiC in character. The Sturm-
Liouville self-ad,~oint problem may be stated thus:
-utl + p(X)U - Xu, u(0) - u(-K) = 0.
In the mean time the author, Gellfand and DorodnaMyn have published
several papers in this direction. The present paper gives a
summary of tie results. Shortly sketched the following problem is
treated; Defining the traces of the differential operators
2
(1) 'A
Z: '/ n SP dx 2 + P(x))
(2) 2 Sp d2 _ + p (x) ) 2
n dx2
etc, then these expressions at first are senseless since at the
left hand side there are divergent slaries. Now the general methods
of regularization J� 2) are used, especially an elementary method
Card 1/2. of Gellfand /Ref 21 is described (� 3-4). � 5 contains some

SOV
For-,ulas for Traces of the Differential Operators of Sturm-Liouville /42-13-3-2/41
generalizations. In � 6 the obtained trace formulas are used in
order to calculate the asymptotics of the eigenvalues and the
first eigenvalues. The contents of � 7 is new. Here the trace
formulas are combined with the theory of perturbation. In (1) the
differential operator is comprehended as an operator of the
highest derivative which is superposed by the "disturbance
operator" (operator with the remaining lower derivatives). Then
the author obtains approximate values for eigennumbers with the
aid of methods of the theory of perturbation. It is asserted
that the trace formulas are equivalent to the statement that
the mean deviation of the approximate vales for the eigennumbers
from the real values equals zero. The author conjectures that
this fact (which is proved in the present paper for differential
operators) is valid more general.
There are 21 references, 12 of which are Soviet, 5 American,
1 Indian, 1 Hungarian, 1 German and 1 French.
CarO 2/2

'3.'7000 67051
AUTHOR: Dikiy, L. A. sov/49-59-8-11/27
TITLE: On Acoustic and Gravitational Vibrations in the Atmosphere
PERIODICAL: Izvestiya Akademii nauk SSSR, Seriya geofizicheskaya,
1959, Nr 8, pp 1186-1194 (USSR)
ABSTRACT: The.waving motions in the polytropic atmosphere were
investigated by the author. The motions were classified
into two different types: acoustic and gravitational,
similar to those observed in the isothermic. The
general formula, Eq (1), is considered for the two-
dimensional waving motion along the horizontal axis Ox.
This formula -can be presented in a simplified form as
shown in the transformation Eqs (2) to (4). In the
case of a polytropic atmosphere, where T = T 0 - YZI
the formulae (10) to (12) can be applied. These
become Eqs (10a) to (12a) in the case of Y ~ 0. In
order to find the solution, the function
,(0
wx) = _10-, I
can be introduced. Fig I shows that both functions/
Card 1/2 MW and N(h) bave two joined intersection points. It

67051
SOV/49-59-8-il/27
on Acoustic and Gravitational Vibrations in the Atmosphere
can be shown that the frequency w2 related to t e
upper point can be considered a s acoustic (Wak and
the one corresponqing to the lower point as a
gravitational (w lip ) frequency of vibration. In order
to define the physical characteristics of both frequencies,
the formulae
W2 -> k y) gxR and w 2 k y) gxR
ak ~(Ya - PP I (Ya
the functions U(P (Fig 2) and yQ,%) (Fig 3) were
analysedo Thus, It is shoim that in the isothermic
atmosphere all the gravitational frequencies for any k
are smaller than all the acoustic ones and a
vibrationless interval can be distinguished. In the
polytropic atmosphere there is no such interval.
There are 3 figures and 4 Soviet references.
ASSOCIATION: Akademiya nauk SSSR Institut fiziki atmosfery
(Institute of Physics of the Atmosphere, Ac.Sc., USS
SUBMITTED: October 18, 1958
Card 2/2

!)Day) T,. A. (Mogeav)
"On the Stability of the Plane Parallel Flow of a Nonhomogeneaus Iluid. "
report presented at the First ALI-Union Cong-ess on Theoretical and Applied
Mechanics, Moscow, 27 Jan - 3 Feb 1960.

.16-3400
AUTHOlli A.
TITLE: On Baundary Condition:3 D:~poncllii~" on EIE~;c-nva-11110
PERIODICAL: Uspeklil matematichoskilch nauk, 196o, voi vir 1,
pp 1.95-198 (USSR)
ABSTRA,~T: The auchor conslders a bo~ictdary value pro'blem where
the eigenvalue appears both in t-lie equation and in
the boundary conditlon. Tne problem I.,;:
-u U(x)u - 'Xit; u 1(0) lt(o) = 11(a) 0 (a.)
where U~x) Is a contl!!,tous ILlnCt-iOl-I O!'t 411KI ~AJ'le--val
o" t'
fart(:t
Z -0,
N(
_7
a t,- o I r,. ~
1. 11
-
-,lvt~ii
and
eigenvalue of the
equation ,.-mLlsVying at th-'-~
Card 1/11 0. Let

On B-Dundury ConclItIono JYq-I,en(JIInr~ ol)
Eigenvalue
m(
is differentiation v,,-JIAh respec'u, to
tion is sinrrle valued fo::, all fo-
which the denorainator t!",
elgenvalues o.L' the probl,:~ni ~iith cond.1-t- ID!II
u(0) u(aL) = 0. Each One -IL3 lar-Tei, t-,-ian 'LJ . -
MILI,
-)b" em.,
The A o which M. = 0 are eigrenvalues o-*," ~Uiie orc
with conditiom-, 1-i 1 (0) = LI (a) =0. They are alt,.lo
.larger then U Tn o s c., or - 'AIch 1VI -1-e
lu&I n V011 -
IN" (I ") > 0
the eigenva 21 of problein 1 0 k
N C!,
-arid f ar large
(.x a), M C 7, a
Aj
zand M L
Card 2A an, *X-,> - - 1, then the system of eigen
f UnCtions of problem (1) is complete. Theorem 1*1S
somewhat generalizable, i.e., a finite set of' X ~
L
can be replaced by arbitrarily distributed points as
long as after some i the 1-th point belongs to the i-th
branch of M( A). If N( /A) is analytic con~tinuable
into the complex plane, t],.en there may be also complex
Card 3/4

On Boundary Conditions Depending on
Elgenvalue
SUBMITTEM
elLcl,envalues. There iS 1 fIgUre.
September 2, 1958
778011
SOV/) 12 --.1
card 4/4

80244
S/040/60/024/02/07/032
AUTHOR:-.Dikiy, L. A. (Moscow)
TITLE. On'~~e- Sta'biliity of Plane Parallel Flows of an Inhomogeneous
Fluid
PERIODICAL: Prikladnaya matematika i mekhanika, 1960, Vol. 24, Eo. 2,
pp. 249-257
TEXT: In the infinite half space the author considers a two-dimensio-
nal horizontal flow, the velocity V of which increases linearly with
the height, while2the density S, decreases exponentially: V(z) = k(z),
Fo = const - e-j'- . This flow was investigated by the Yxve -..I(.thod
of Taylor (Ref -5) who stated that, if the Richardson number is
R there occur neutral waves, while for R < -111 there are
no raves at all. From this itIwas concluded in (Ref.6,7) that the
flow is stable only for R > it . The author shows that stability
holds for all R > 0. Here a motion is called-stable if an arbitrary
initia2 i)erturbation remains bounded in a finite region under in-
creasing time. At first the considered problem is formulated as a
linearized Cauchy problem; this is solved v.,ith the aid of the Laplace
Card 1/2

80244
3/040/60/024/02/07/032
On the Stability of Plane Parallel Flows of an Inhomogeneous Fluid
transformation, where the solution contains a certain function which-
must be determined from a Volterra integral equation of first order,
The investigation of this integral equation leads to the above-mentioned
statement of stability.
V... Kelqysh is mentioned in the paper.
There are ? :ri6ures, and 8 references; I Soviet, 2 American, 3.German,
1 English and 1 Norwegian,
SUBMITTED: September 25, 1959
Card 2/2

S/03 0/0 24/0,3 6/0"1 4/03 4
C1 1 1X333
AUTHORz Dikiy, L.A - --------
TITLE: On the Zeros of the Whittaker Function and the Macdonald Function
With Complex Index
PERIODICALt Izvestiya Akademii nauk SSSR, Seriya matematicheakaya, 1960,
Vol. 24, No. 6,pp. 943-954
TEXTs The Whittaker function W At/, (z) is defined as solution of the
differential equation 1 2
(1) W11 + .1 + + -4 W - 0
(- 4 112
which shows the asymptotic behavior
z
(2) W (Z) r%.~ e- z
for z oo arg z
2
For 0 it is expressed by the cylindric Macdonald function
Card 1/3

C 111 YC333
On the Zeros of the Whittaker Function and the Macdonald Function With
Complex Index
z
P:1 K ", ( Z )
(3) V0~~t(z) - / 4, / 2'
The author proves s
Theorem I s If A and " are real, A !,= 0 and then WA, _(z)
possesses no zeros in the sector I&rg zj!E~ IL
Theorem 2 s If A t!~ 0, IA,- complex and I Re IA-4-1 1, Im -/-Oq then WA,/, (z)
possesses no zeros in the sector -T,!~ arg zz!S 0 .
Corollary s If /4, satisfies the conditions of thearem 2, then the statement
of the theorem holds for the function K,.(Z).
Theorem 3 : If A is real, /t4purely imaginary, thell WA ~' (z) possesses a
denumerable set of positive zeros in the sector larg zj-,'- it and possesses
no further zeros.
Corollary a K"' (z) possesses no zeros in 0 < I arg n 1:55,- -1C for a purely
imaginary /tv .
Theorem 4 t For A >~- 0 , 0