SCIENTIFIC ABSTRACT METELSKIY, A. S. - METEV, V.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001033720003-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: July 19, 2001
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

L 65086-65
ACCESSION NR: AP5021227 ENCLOSIM: 01

50
-APSOII 1227-
ACCESS-IONI-m-
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Fig. 2. Welded frame of half-roof

AYZENSHTAT, V.S,; HETELISM, A.S.
x
4, ""f - "
cmputing integrals of the type A- t' " Vestsi Art
BSSR Ser. fiz.-takhe nav. no. 1;11.9-~6 161. (MMIA 14: 4)
(Integrals) /'

LIL100
8863:L
S/ 170/6' /004;'~02/009/0'8
B019/BO6b
AUTHORS: Ayzenshtat, V. S., Metel'skiy, A. S.
TITLE: A Numerical Laplace Transformation
PERIODICAL: Inzhenerno-fizicheskiy zhurnal, 1961, Vol. 4, No. 2,
pp. 82-91
TEXT: A study has been made of the integral
00
F(p) e-pxf(x)dx (1) which is widely used in integral transfcrma-
0
tions. By the substitution px - t, this integral acquires the fcrm
so
-1 r
F(p) - P e 00 f(t/p)dt. Furthermore, this integral can be rendered ir
the form We-t T(t)dt (s >-I) (2) by the substitution
a
f(t/p) = tslf(t).~br the approximation of (2), the rellati~n
Card 1/3

8863' 1
A Numerical Laplace Transformation s/170/6!~004/OC2/009/1018
BO;9/Bo6/0
00 n
r S t r (n ts - 1
t e- T(t)dt----~ 2:AkT(tk)(3) is given, where Ak~n k
ki,
,r(s)'(t 2 k = 1,2,3,...,n (4), and
(Ln 01
L(8)(t) = (--1)"t-aet dn(ts+n a-t)/d tn , are Laguerre polynomials of rith
n
degree. This mode of calculating (1) offefs good results.The rcsts of
Laguerre polynomials of nth degree y = Lns)(t), which is kncwn tr
satisfy the differential equation ty" + (s+l-t)yt ~ ny - 0. are determined
by way of a nonlinear system, from which it may be seen that t~.e
coordinates of the ?qjilibrium points of free electric charges ccin,tide
with the roots of LnS (x). A bulky Table gives, for a = 2/3, --112, '//5.
1/3, 1/2, 2/3, 4/3, 3/2, 5/2, the values of tk and Ak for n = 4 ... 10, and
k = I ... 10. V. I. Krylov Is thanked for guidance and advicc- There are
1 table and 5 references: 3 Soviet, 1 British, and I US.
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88631
A Numerical Laplace Transformation 5/11 701161/00,410021'~C,91'0 18
B019/BO60
ASSOCIATION: Institut matemattki i vychislitellnoy tekhnik! AN BSSR,
g. Minsk (Institute of Mathematics and Compiter Technique
of the AS BSSR, Minsk)
SUBMITTED: May 28, 1960
L/
Card 3/3

AYZEVS'h?AT, V.S.; IMLOV, V.I.; VETELISKIY "AHAIWIM, Ye.,
red. izd-va; ATLAS, A., - hn. red.
(Tables of numeric,-1 Laplace transforrations and for the
0.0
calculation of integrals of the forms xse-xf(x) dx)
Tablitsy dlia chislennogo preobrazovaniia Laplasa i vychisleniia
00
integralov vida xse-x f(x) dx. Minsk, Izd-vo Akad. nauk WSH,
1962. 3?5 p. (MIRA 15:4)
(Laplace transformation) (Integrals)

Vq 6'~
1024/1224
A UTHORS: Rubanov, A. S., M Gairilova, Ya. N., and Kogan. A. Sh
TITLE: Calculation of the entropy of probability distributions of the co-ordinates and momenta
of an harmonic oscillator
PERIODICAL: Akademiya nauk Belaruskay SSR. Doklady, v. 6, no. 4, 1962, 220-222
TEXT: The purpose of the article isto check the assumption that the co-ordinate and momentum entropies
in a harmonic oscillator increase with the number of the stationary state level (Rubanov A, S., Stepanov B. I..
DAN SSSR, 140, 1, 1961). The entropy of the probability distribution of the above variables for the i)-level
is found from the expression
H' - Ina H.2(y) In H~2(y) dy (4)
/n 2'u /iz 2'u
a =~ 'U Vj for the entropy of the co-ordinate distribution and a = Iuwh for the entropy of the momcmtun
distribution, where u is the mass and to the frequency of the oscillator. In calculation, the integral taken
twice, with the lower limit of 0 and the upper limit of b was chosen so that the value of the integral re-
mained unchanged with the increase of b.
Card 1/2

Calculation of the entropy.. S/250/62,'006/0(A/001 /001
1024/1224
The integral was evaluated by the Simpson rule with a step h -0.001. on an electronic computer "Minsk I'
The coordinate and the momentum entropies were calculated for the first 12 levels of the oscillator Rtibano%,
and Stepanov found the upper limits of the coordinate and momentum entropies-
H,' - 11.0 = H; - 110