SCIENTIFIC ABSTRACT PARASYUK, O. S. - PARAUBEK, G. E.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001239210017-5
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: June 15, 2000
• Sequence Number: 17
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

AUTHORS: Farasyuk, 1~1~ t T -, ML Y a SOV/41-'0-5-13/1,~!
TITLE* The Theorem of Chellen Lehman in the Space With Indefinite
Metric (Teorema Cheliena - Lemana v prostranstve a indefinitnoy
metrikoy)
PERIODICAL% Ukrainskiy matematicheakiy zhurnal,1958,Vol 10,11r 3~
pp 344 - 7~'6 (USSR)
ABSTRACTiThe authors call attention to the close connection between
quantum theoretical questions in Hilbert spaces with indefinite
metric and the operational theory of these spaces. E.g. the
so-called "ghost states" correspond to the fact proved by
Pontryagin [Ref 41 that self-adjoint operators in conoidered
spaces may possess eigenfunctions with negative norm. Further-
more it is shown that it is possible to obtain an analogue of
the theorem of Chellen - Lehman with the aid of the methods de-
veloped by Kreyn and Jokhvidov [Ref 5,61 -
There are 9 references, 5 of which are Soviet, and 4 Ameri~an.
Card 112

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PARASYUK, O.S.
On "paired" integral equations in the clasti of generalized
functions. Dokl. AN SSSR 110 no.6:957--958 0 156. (MLRA 10:2)
1. Institut matelatiki Akademii nauk USSR. Predstavleno
akademikom B.No-Bogolyubovyn.
(Integral equations)

SATIN, G.H.; PARMYUK, O.S.
Affect of a field of Inhomogeneous stress upon the plastic zone in the
neighborhood of an aperture. Dop.AN URSR no.3:41-50 148. O"A 9:9)
I.Disniy chleft AN URSR (for S&vin).2.L'vtvskiy viddil Institutu girnichet
mekh&nW AkademiA nauk Ukrainalkel RSR.
(Strains wid stresses)

UM/Magin'earing Doc 116
Mechanics
Rhaoloey
W4
*XUatlooplastic Problem With a Nonbiharmonic Pl&s-
tic State,% 0. S. Egran k. LIVOT Sao, Inst of Mathj,
Mad P
*Dok Ak Naak Vol LXIII) No 4
PI&t infinite plate with a circalar hole of radius
I is subjected to biaxial stresses C and D at in-
finity., vbIle normal stresses a and shear 4treames
b applied along the edge of the hole produce plaaW
flow in a region around the hole. In Galin's sola-.
tion for the case b equals 0, stress function in
M 45/49PL54
UM/Engineering (Contd) Doc 48
pUstic zoos appears in biharmoaic form. When b to
not equal to 0, stress function will not be bibar-
noolo. Uses Miohliala stress distribution to solve
problem. Submitted by Acad M. A. Larreatlyar,
4 Oct 48.

Multivariate local Unit tb
Ukr.mat.zhur. (1] no.1:9-20
(Probabilities)
probabilities.
Oa-RA 7:10)

Pj~RAISMI'I. L.,.. S . ;, G . .: .
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Nau~. zap. LIviv. 12 no. 3, !~-1-4"-,.
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mayul, O.S.
Brgc)dlty of geodesic currents In certain three-dImnslonal m1tiform
variables of negative curvatures. Dcp.AN UM no,6:387-388 153.
(HLRA 7:1)
1. Inetitut mtomtlki Akadvall nank Ukrainelkot JOY4 Predstaviv diyonly
eblen Akadeall nwak Ukrainslkol RM
(Ourvatures) (Wculus of variations)

PAR RS ~ UK, () , S, ,
SUBJECT USSR/MATEMTICS/Applied mathematics CARD 1/2 PG-546/547
AUTHOR BO(;OLJ"OV N.N., PARLSnX O.S.
TITLI On the theory of multiplications of singtilar causal functions.
On a formalism of subtraction for the multiplication of
singular causal functions.
PBRIODICAL Doklady Akad.Nauk 100, 25-28 (1955)
Dol-lady Akad.Nauk 100, 429-432 (1955)
reviewed 1/1957
As a continuation of earlier papers of the authors (:Doklady Akad.Nauk 81
=-LL
nos. 5 and 6 (1951), ibid. 82 a detailed
.L no. 2 (1952)), in the first paper
treatment of the singular expressions appearing in the theory of perturbation
in given. In order to give a mathematically exact treatment, the authors
"regularize" the used "functions of propagation" and write e.g.
M2 2 2 2
i eikx 1+,Vc e-ioe( -M ict(k -n +it
reg (x) -(2?r)4 f fl i )dkdcK
0
where the auxiliary massee 9 1 and the constants c i satisfy (h+1) conditions
of the kind 2:3?lc 01 1 -0,1,...h, (In the usual applications we haTe hwl).

PARASYUK, Ostap Stepanovich.
Inst of Mechanical Engineering and Automatics Aced Sci UkSSR. Academic
degree of Doctor of Physical and Mathematical Sciences, based on his
defense, 19 May 1955, in the Council of Mathematics Inst imeni Steklov,
Acad Sci USSR., of his dissertation entitled: "Theory of the Multipli-
cation of Field Operators."
Academic degree and/or title: Doctor of Silences
SO: Decisions of VAK, List no. 15, 25 Jtme 55, Byulleten' 14VO SSSR,
No. 15, Aug 56, Moscow, pp. 5-24, Uncl. JPRS/NY-537

KARMBKO,G.V., doktor tekhnicheakikh nauk, professor, redaktor; SAYIN,Q.N.
redaktor; laPATINSEXY,Ya.B.. redaktor; ISCROT.H.Ta.. daktor fisiko-
matematicheskikh nauk, redaktor; MWffLOVSKff,V.N.. kandidat tekhni-
chesklkh nauk, redaktor; PARASTUK,,O.S., kandidat fisikoLmatesatiche-
'T"'r"Ot"dldat fisikp-matenaticheakikh.
skikh nauk, redaktor; FAMM, . ,
nauk. redaktor; ZILISM.M.S.. rodaktor; RAKRLINA,N.F., takhnicheekly
redaktor
(Some problems in the fatigue of steel with calculation of the influ-
ence of active Wnto)Nekotorye voprosy ustalostnoi prochnostl stall s
uWwtom vIllanlie. aktivnol sre4. Kiev, Izd-vo Akadeall muk UM. 1955.
48 p. (XUU 9:3)
Aka&emiya nauk URM, Kiyev. Ins%itut masbinoznavetva i avtomatiti.
De7stvItsl'W chlen AN USSR (for Savin) 3. Chlen-korrespondent
AN USSR (for Lopatlankly) (Steel-Fatig")

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777

I'ARL
6 A ~h~PAP&Apli~
wN*xst&tI*&n;ry processes in wn-linearz vibrational sy'stemB.' N.A.
MitropollskII.Reviewed by O.B.Paramiuk. Ukr.w&t.zhur.8 no.1.112-114(XLBA 9:7)
956. (Differential equations) (Vibrittion) (NItr*pol'mkII.'IU.A.)-

PAR&SYUK, O.S.
-,;a
Multiplication of causality functions in connection with nonaoincident
argurienta. Izv. All SSSR.Ser.mat. 20 no.6:843-852 N-D 156,
(KLIIA 10: 1)
1. Predstavlano alcademikom N.B. Bogolyubovym.
(Qxxantnm theory) (Functions)

Z
SUBJECT USSR/MATB=TICS/Theory of functions CARD 1/2 PG - 678
AUTHOR BOGOLJUBOV N.N., pARAsjuK o.s.
TITLE On the analytio eDntinuation of generaliied functions.
PERIODIC11 Doklady Akad.Nauk 109, 717-719 (1956)
reviewed 4/1957 '
For complex-valued functions ~ (13) of a real argument E, -oo e-9