SCIENTIFIC ABSTRACT LEBEDEV, N.N. - LEBEDEV, O.A.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000929020010-8
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 31, 2001
• Sequence Number: 10
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

3/057/62/032/003/018/019
The force acting on a conducting... BliqlBir.4
C = -E a 2@ (2). a2@@-1.64E a 2- The force actinc upon the sphere is:
0 6 0 0
e co
2 2 2 x 3dx 1 2 2 1;2 2
F = E a 2. a 'N3) +-'!@-1.37 a . There are 2 Soviet
- ' 0 6 ,0
0 h
0
references.
.t*%SSOCIA.TIOlE: Fiziko-tekhnicheskiy institut im. i,. r. lofr'fe AN. S'S'SIR
LeninCrad (Physicotechnical Institute imeni A. F. Ioffe
AN USSR LeninGrad)
SUMiITTED: November 9, 1961
Card 2/2

LEBEDBV@ Nikolay Nikolayevi,h5 AKILOVI G.P., red.; j,UK'YANOV, A.A.,
tekhn. red- -ation^ I Spetsial'nYO
ctions and their applic dop. Mo-
[Special fun zd.2., perer. i
funktsii i ikh prilozhenila. (mim 16:11)
skva, FizmatgiZ, 1963. 358 P-
(Functions)

S/0057/64/034/005/0801/0808
:ACCESSION NR: AP4035686
AUTHOR: Lebedev, N.N.,; Skallskaya, I. P.
TITLE: Some problems of the theory of heat conductivity in wedge-shaped bodies. 1.
SOURCE: Zhurnal tekhnicheskoy fiziki, v.34, no.5, 1964, 801-808
"TOPIC TAGS: thermal conductivity, wedge heat conductivity, Laplace transformation,
Kontorovich Lebedev transformation
#BSTRACT: The temperature distribution is calculated within an infinite wedge-
shaped body of arbitrary vertex angle, that was initially at the temperature To
throughout, and the two faces of which have been subsequently held at the tempera-
ture T1. The calculation is performed by subjecting the temperature to a Laplace
transf6rmation with respect to time and a Kontorovich-Lebedev transformation (M.I.
Kontorovich and N.N.Lebedev, ZhE77j8111920 1938) with respect to the distance from
the certex of the wedge. The heat transfer equation is thereby transformed to an
ordinary differential equation. This is solved, and the temperature is obtained
with the aid of inversion formulas for the Laplace and Kontorovich-Lebedev transfor-
mations. This leads to an expression for the temperature in the form of a contour
Card 1/2
0

ACCESSION NH: AP4035686
integral. For a wedge with the vertex angle T(/n, where n is an integer, this expres-
sion is simplified and the temperature is expressed as the sum of n terms. 'When n
is odd, the terms of this sum are error functions of appropriate argumcnLs; when n
is even, the terms of the sum can be expressed by mpans of the function T(h,a) in-
troduced by D.B.Owen (The bivariate no'-mal probability distribution, Sandia Corpora-
tion, Res.rop.,March,1957) and tabul-it-,d by N.V,Smirnov and L.N.13ol'shev (Tablitsy-
dlya vy*chisleniya funl@tsii dvumernogo normalnogo raspredeloniya, Izd.AN SSSR,N1. ,
1962). The integral transformation method employed in this calculation Is also suit-
able for treating boundary value problems in which a linear relation between the un-
known function and its normal derivative is specified on the boundary (boundary con-
ditions of the third kind). Orig.art,has: 40 formulas and 1 figure.
ASSOCIATION: Fizilco-teldinicheskiy institut im.A.F.Ioffe AN SSSR,Loningrad (Physico-
technical Institute, AN SSSR)
SUBMITTED: MuM DATE AOQ: 20May64 ENCL: 00
SUB CODE: TD NR REF SM 008 OMERt 002
Cora '912
It

L i2MI-455--k. por(i )/pPA(s)_2/EPF (v)/'F FeIA (I Pe-5 F-,' -7-
ACCESSXOX XR: AP4045264 S/0057/64/034/009/1556/1565
AVrHOR: Lebedev, X.M.; Skallskaya. I.P.
TITLE: some problemo of the theory of beat conductioa@n wedge-shaped bodies. U-1
v.34, no.9, 1964, 1556-1665
TOPIC TAGS* orrQa@fjon__
Cauchy problem, he t conduction equation,
ABSTRACT: Cauchy's problem for the heat conduction equation is solved for the
wedge-shaped region bounded by the planes (P w �7 (rg,z are cylindrical coordinates,
2 y is the vertex angle of the wedge) with the Initial ccadition that the tempera-
ture be uniform throughout the re.-ion and the boundary conditions that the tempera-
ture gradient at the boundary planes be in the direction of the outward normal and
proportional to the temperature. The solution of this proble= describes the cooling
ol a homogeneous wedge-shaped body of initially uniform temperature immersed in a
medius of which the temperature remains constant at a value that is arbitrarily set
equal to zero. The solution is effected by successively performing a Laplace trans-
formation with respect to time and a Kontorovich-Lebodev transformation (M.I.Konto-
rovich and U.N.-Lebadev,7=7 8,1192,1938; N.N.Lebcdev,MM 13,465,1949) with respeot
1/2

L 12001-65
ACcES-SION hn- AIP4045294
to r. The transformed temperature is found to satisfy a functional equation of a
type previously disouzsed by the authors (ZhTF 32,1174,1962). The solution of this
functional equation to discus"- , and in the special cases 2 7 - rjn, where a is an
integer, it is effected. The corresponding solutions of the heat flow equation are
then obtained by performing inverse Kontorovich-Lebedev and Laplace trans f ormat ions.
When n is odd the aolution is obtained as a finite sum. of products of exponential
and error functions; when n is even the solution is more involved, arZ the general
for even a Is not written. The solution obtained reduces for a to I to the
falm,-liar solution for a plane boutidary, an@d for n - 2 to a previously kno-wn solu-
tion ;or a rectangular wedge. It Is suggested that similar methods -may prove to be
applicable to other problems. Orlg.art.has: 63 formulita and I figure.
ASSOCIATION: Fiziko-takhnicheskiy institut im.A.F.loffe AN S-3SR,Leningr&d (Physico-
-teclinical -Insvitute. AN GGER
SUBUITTED: IlDecO EWL: 00
Sun CODE-. N-R REP SOV: 004 GMR-.000
2/2

L 30378-66 EWT (d
ACC'NR, AP6012544
(m)/EVIP(w) IJP(c) BI
SOURCE CODE:
AUTHORS: Lebedev, N. N. (Leningrad); Skallskaya, 1. F. (Leningrad)
ORG: none
0252/0_2%
'@6 1
TITLE: An expansion for an arbitrary function in integrals of spherical functions
SOURCEt Prikladnaya matematika i mekhanika, v. 30, no. 2, 1966, 252-258
TOPIC TAGS: Legendre polynomial, asymptotic expansion, boundary value problem,
elasticity, J'C'VA/C;r/0A/_, pw@@/C@T
ABSTRACT: A mathematical method is outlined for the ution of a boundary value
problem in mathematical physics and-elasticity-theoryffor a hyperboloid of r-evolution
of one sheet. The problem consists of showing the existence of an expansion of the
arbitrary function f(x)which is defined by a Mehler-Pok type integral or,
00 P (ix) P_jj'J'(iY)+P
/(.)=@Ilh,- (Y) @ % @ 0 -,/,+f,(-,Y) d. +
ob nT 2
P-,/.,,, (fx) - P-./,,,, ix) j, (io - P-./"f, iY). dy) d-r
+ 2i N
C-0 00)
The following theorem is proved; Let f(x) be a given'function defined in the domain
Ccrd 1

L 30378-66
ACC NR. AP 012544 is piecewise continuous and has
(-001 00) and satisfying the conditions; 1 f(X)
bounded variation in the interval ko, co@,and 2)
I(z)jxj-'I-In(I+jXj)C=-L(-oo, -a)
/(x)x-'/-In(1+x)c-L(a, (1>0)f
then there exists the expansion 0)] < <
0" P (- iY) dy +
00 P + -11" 1, YO +
th 3%T (Y)
2
0
P P,/,+,, (iy) - P-./,Ti; (- ly d d-r
(Y) 2i Y1 J
arat.ely after several values and
The proof is given for even and odd functions sep ave been investigated.
ymptotic characteristics of the above spherical functions h
as ed. The first defines f(x) as
Two examples are consider I
.1 W 10.
and thesecondt (at - x3)-,/, 1 X I < h
M Fd 0 IzI>a
Orig. art. has: 42 equations.
SUB COM 12/ SUBhj DATEt 02Nov65/ ORIG RU, 005/ WH RU' 003
Card @@14 CL@-

AtC.@NR: AP6033204 SOURCE CODE: UR/0040/66/030/005/0889/0896
AUTHOR:,,Lebcdav, N..N. (Leningrad).- Skal'skaya, 1. P. (Leningrad)
ORG- none
TITLE: Certain boundary value problems in mathematical physics and elasticity theory
for a .hyperboloid of rotation of one sheet
SOURCE; Frikladnaya matematika i mekhanika, v. 30, no. 5, 1966, 889-896
TOPIC TAGS: rotation hyperboloid, boundary value problem, elasticity theory,
Dirichlet problem
ABSTRIkCT: This paper studies a technique of solving boundary value problems in po-
tential theory and elasticity theory for one-sheet hyperboloids of rotation which is
based on use of an integral presentation. Boundary value problems for hyperboloids of@l
-revolution and the'problems in elasticity theory leading to these boundary value
problems belong to the class of problems with separable variables and their solution
presents no fundamental difficulties. Despite this, the literature studies in detail
only the case of two-sheet hyperboloids, while the corresponding problems referring
to regions delimited by the surface of a single-sheet hyperboloid have not in fact
been studied. @he reason for this is apparently the inadequate development of the
mathematical apparatus involved in solving problems of this type. A substantialpart I
of this apparatus is comprised of the theorem of expansion of an arbitrary function
ccr@

ACC NR. AP6033204
:E(x) (determined in the interval from minus infinity to plus infinity) into an in-
tegral with spherical functions
P LX
'T tb nTr dy +!
2
2 -40
M P-JI.1,100 - d dv
+
21