SCIENTIFIC ABSTRACT FEDOROV, F.I. - FEDOROVA, G.A.

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• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000412620007-9
• Release Decision: RIF
• Original Classification: S
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• Document Creation Date: November 2, 2016
• Document Release Date: March 20, 2001
• Sequence Number: 7
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

GRDSalT, T.K., I.
10,patic properties of a particle with spin 3/2. Dokl.AJr SSSR
4 no.7:278-283 J1 160o (KIRA, 13: 8)
1. Institut fisiki AN BSSR.
(Particles (Nuclear pbysice)-Magnatic proportion)
. ~-:I-'.1.'-,-!I z
11" -, ?,-

BOKUTI. B.V.; FMOROV, F.I.
Reflection and refraction of light in optic*Ujv isotropic active
media. Opt* I spektr. 9 no.5:635-639 N 16o. (KIRA 13:11)
(PoMrization (TAght)) (Reflection (Optics))
(Refraction)

MOROZ. L.G.; FZDOROV, 791.
Taking Paull interabtion into account in a scattering matrix.
Zhur. ekep. i teor. fix. 39 no.2:293-303 Ag 160. (MIRA 13:9)
1. Institat fiziki Akademii nauk Belorusekoy SSR.
(Particles (Nuclear physics)) (Field theory)

9 &a
Parametric deocription of a Lorento group. Dokl. AN BSSR 3 not3dol-104
Mr 161. (MU 24:3)
Is Institut, fiziki AN BSSRs
(Tranaformations~Mathematioe))

One generalization of Iappo-Danilevskiila triterion. Dokl.AX BBSR
4 no. 11:454-455 N 1600 (MEU 13:12)
1. Institut fisiki AN BSSR.
(Differential equationa, Linear)

3/058/62/000/003/028/092
A061/A101
AUTHOR: Fedorov, F. 1.
TITLE: Some properties of the Lorentz matrix
PERIODICAL: Referativnyy zhurnal, Fizika, no. 3, 1962, 34, abstract 3A323 (Dokl.
AN BSSR, 1961, V. 5, no. 5, 194 - 198)
TM: It is shown that any matrix of proper Lorentz transformation can be
parametrized using the complex tridimensional vector q - a + ib (the parametriza-'
tion method is decribed in -another paper b,.- the author [WbFiz, 1961, 1OA108]).
The change of velocity of a particle in a constant and homogeneous electromagnetic
field Is examined as an example.
[Abstracter's note: Complete translation]
liCard 1/1

S/053/6Z/000/003/019/092
64-11 740 A06IIA101
AtYMORS.- Bogush, A. A., Fedorov, F. 1.
TIM: An invariant expression for a Lorentz matrix transforming one vector
into another
PERIODICALI Referativnyy zhurnal, Fizika, no. 3, 1962, 34, abstract 3A324 (Dokl.
AN BSSR, 1961, v. 5, no. 6, 241 - 244)
TM: A formula is obtained for the parameters of the Lorentz transformation,
Pf 4-vector p into pl (using the parametrization of the Lorentz transformation)
considered by Fedorov [RZhFiz, 1961, IOA108]).
[Abstracterls~notet Complete translation]
JC
Card-1/1'

./6. '56-av S/058/6Z/000/003/020/092
dy'LI600 A051/A101
AUTHORS: Bogush, A. A.,-Fedorov, F. I.
Tl=-: General transformation of the Lorentz group representation In the
bi-spinor space
PERIODICAL: Referativnyy zhurnal, Fizika, no. 3, 1962, 34, abstract 3A325 (Doia.
AN BSSR, 1961, V. 5, no. 8, 327 - 330)
TEXT: Formulas are obtained for the transformation of bi-spinors in an ar-
bitrary Lorentz transformation, if the latter is given by the complex vector q
(see.RZbFiz, IOA108).
[Abstracterts notel Complete translation)

YELIYASHEVICII N.A.1 TOrMILICHIK, L.14.; Fx'JXROV, F.I.
mCritique of the foundations of the relativity theory* by
A.Ke 14azeev, Reviewed by M.A. Elliashevich, L*111* To-
milichikp FJ, Fedorove Uape fizo.nauk 74,no.4:757-759
Ag 161. .1"o, (Physics)) (Y-M 14-.8)
:'taneevp AOKI)

S/250/621006/00201JOD7
1028/1228
AUTHOR: Hogush, A. A. and Fedorov, ~F, 1.
TITLE: On the properties of the matrices of Daffin-Kemmer
PERIODICAL* Akademiya nauk Bclaruskaya SSR. Doklady, v. 6, no. 2, 1962, 81-85
TEXT: The most important properties of the Daffin-Kemmer matrices are obtained on the basis of general
considerations. The following representation of the matrix P,, with the aid of the projective operations P"' and
PW (separating respectively the scalar and vector (tensor) part of the Wimensional space: k = 5, 10) is
used as starting point:
A, = PA. P + PA. P (3)
The rules of commutation are obtained from here:
A-P + P18. = fl..; A-P + JA. (5)
Thegeneralform of the projective operators Pond Pis then obtained:
P'-al P P-a2
a2--al a,-a2 (10)
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on the properties of the... S/250/62/006/002/001/007
1028/1228
where P2 a 113) = 4, a3(5) ~ I ; a vo) . 3. *a2('O) - 2112" Lastly, a general expression for the spur of
the product of any number of 10-dimensional Daffin-Kemmer matrices is cictermintd, The mo.'a important
English-language reference read as follows: Harich-Chandra, Proc. Roy. Soc., 18, 502, 1946. M. Neuman,
E. H. Fwry, Phys. Rev. 76, 1677, 1949.
ASSOCIATION: Institut fiziki AN BSSR (institute of Physics of AS BSSR)
SUBMITTED: November 3, 1961
Card 2/2

S/07o/62/007/oo6/oll/020'
E132/E435
AUTHORS: Fedorov, F.I., Bokut', B.V., Konstan.tinova, A,F,
TITLE: The optical activity of crystals of the classes of
intermediate symmetry having planos of symmetry
PERIODICAL;'Kristallografiya,,V-7, no.6, 1962, 910-915
TEXT: The classes in question. L66P; L44P and L33P (6 mm, 4 mm,
3mm) having a plane of symmetry parallel to their axes of'
highest order have hitherto been thought'to-be optically inactive.
There are.few crystals representative of these classes but
tourmaline is one.- Rotation of the plane of polarization cannot
occur for any direction of propagation but optical activity can
manifest itself by other phenomena, as in.optically active
crystals of other classes, for propagation along directions other
than the optic- axis, It is shown that the phenomenon of the
elliptic polarization of the reflected Wave In a unique symptom
of optical activity ;-5. It in, however, normally extremely small
of the order of 1 in quartz. An experimental arrangement
for making observations under the beat conditions is suggested.
The surface of the crystal is immersed in a liquid of carefully
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C

FFWROV, F.I.;. KOrTYASIL.. T.L.
Passage of light through a plate made from a trarmparent
uniaxiallrystal. Opt, i opektr. 12 no.2:298-)03 F 162o
(MIRA 15:2)
(Crystalo--Optical properties)

S/051/62/ol2/003/008/016
E202/E192
AUTHORS: Fedorov, F.I., and Konstantinova, A.F.
TITLE: Passage of light through plates of uniaxial active
crystals belonging to axial classes
PERIODICAL; Optika i spektroskopiya, v.12, no.3, 1962, 407-411
TEXT: An exact solution to the passage of light through
a plane parallel plate cut out from an optically active crystal
is given. The s6lution takes intoaccount the refraction at
both edges of the plate. It is based on the earlier work of
F.I. Fedorov and T.L. Kotyash (Ref.2. Opt. i spektx-. v.12, 1962,
298) in which the same problem was solved for an uniaxial not
(optically) active crystal. The accuracy in the present solution
was particularly stressed since the anisotropi.c property is weak
and could easily be masked or exceeded by the effect of the
,refraction at both edges of the plate polarising the emergent
wave* The solution is applicable to a normal incidence of light
at any orientation of optical axis. The exprossions for
amplitudes of the emergent wave are given in terms of the
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J-
37221
s/o5i/62/Ol2/oo4/oo6/ol5
E039/E:485
AUTHORS. Fedorov, F.I., Konstantinova,'A.F.
TITLE: The passage of light through plates of uniaxial
optically active crystals. II. Plates, parallel to
optical axis
PERIODICAL: Optika i spektroskopiya, v.12, no.4, 1962, 505-509
TEXT: In a previous paper a general expression was obtained for
the amplitude of.waves passing perpendicular to plane parallel
plates with arbitrarily orientated optical axes cut from
uniaxial optically active'crystals. In this paper is considered
the case when the optical axis is parallel to the faces of the
plate. When linearly polarized light passes through non-active
uniaxial crystals the polarization is unchanged, but in the case
considered here the linear polarization is converted into
elliptic al. Calculations are made which show that the magnitude
of this 'effect is small in the case of quartz. It is also shown
that the polarization parameters for waves passing through two
crossed plates have approximately the same value as for one plate.
It is concluded'that the plane of polarization of linearly
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B/020/62/143/001/008/030
11'~,3000 Zj~, L/300 B I 12/B 102
AVTHORs Fedorov, F. X.
TITLEs Composition of the parameters of the Lorentz-group
PERIODICAL; Akademiya nauk SSSR. Doklady, v. 143, no. 1, 1962, 56 59
TEXT: The author considers quaternions J. The composition rule is
q*~ +
written in the form (q q1) + q q qql). The compositiow
and -il) are shown to be equivalent to the relitions
q (n,iu n,
V'2 11 + q2~2/(j + jqj ~)20 where 3* o 21U/ ( I + u2 ), end
T
n' + q q + + +
General considerations concerning the Lorentz group are based on these
main formulas. There are 5 Soviet references.
ASSOCIATIONj Institut fiziki Akademii nauk BSSR (Institute of Physics of'
the Academy of Scienoes,BBSR)
Card 1/2

B/020/62/143/001/008/030
Composition of the parameterSea. B112/BIO2
PRESENTEDt October 28, 1961, by V. L. Pok, koademician
SUBMITTEDt October 71 1961
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s/o5i/63/oi4/ool/ol6/031
E032/9311I.::
AUTHORS: Fedorov, and Gonchatenko% A%M%'i
TITLE: f
Propagation of light'along circular optic axes o
absorbing-crystAIS
PERIODICAL-.- Optika spektroskopiyat v. '14, no. 1, 1963,
100 - 105
rEXT: A general theory of propagation of*.eleetromagnetic
rbing crystals, baged 6n
pves along circulat optic axes of abso
an invariant methodl is described. General solutions are
d'rived of the Maxw I equations for an arbitrary absorbing
c3~ystal, including refraction and reflection at normal incidenc 8JJ1
atIan arbitrary absorbing crystal surface,and a;plane-parallel
plate, cut from such a crystal with the circular axis pej~pen-,
dicular to the reflecting face. Explicit expressions are
'The present
obtained for the- wave amplitudes in each caso
analysis of A*P* Khapa,146ik (Opt. i spektrd
results include the
12, 106, 1962) as a special cases
SUBMITT M- December 19, ~9611
Card 1/1

s1o5216310 14/0 02/0.12/026
E039/E120
,AUTHORSi Fedorov, F#I,j and Petrov, N.S.
~TITLE: A special case of non-uniform electromagnetic waves
in transparent crystals
PERIODICALs Optika i spektroakoplya, v.14, no.2, 1963, 256-261
TEXT. It in shown that with complete reflection of a normal
..plane electromagnetic wave from a transparent crystal:non-uniform
-waves of a special form may arise, the field of which contains not
.only an exponential factor but also a linear polynomial.
Maxwell's equations are solved for waves of the form:
i(~ - Wt)
E a Q, + f e (3)
-2
re is the normal to the surface boundary directed
!,ache kqr (q
;;-from the firsT-med-lum to the second). The equations for the scalar
0 fo
;:Iparameters At,, P1, f are derived and are as followas
2
0
E f m c + f0 d (21)
e
2
d 1/2
Lca~r_ ------

OWN%
s/o5i/63/014/002/012,(026
iA special case of non-uniform E039/E120
0 + I I
(23Y:
~fo ~'Mrm c 1-1 + f 6 Tmo
2 -0
1
I ~[2a2 2 2 2 2
'A' (71-in ME q+in n )+O(con -n n )jAi2n nqel V1 -v0
0 0 0 0 0
(3.0),
1 JL212 2 2 2 2
B1 q+in Me TI-in n )+cl(coq _non )jBt2n nqr, A/co A3
0
0 01 0
0 2 2
f ~2i (C q in n )+e' C iql Alnone- Ale' BI
0
1 A n 0 0 0
0 0
(31):
f!; 21a2 q
f9 n
2 Tcon + in 0 (A in q/Co (q + in 0
rvrc- L
0
-It is shown that when the solution has the form of Eq.(3) the
bo 'dary condition problem in Oolved more easily.
un
SUBMITTED: February 19, 1962
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_T1 EWIPW/EWT(m)/M~ AFM./ASD/ESD-3 WNW/Mi~JG
ACCESSIUN NR-. AF3000,772 3/0070/63/008/003/0398/0404
AUTHOR: Fedorov, F. I
MILE: Approximaticn, theory of ..quasilongitudinal, waves in crystals
SOURCE: KristaUografiya, v. So to. 3, 1963,, 398-404
-TOPIC TAGS: elastic constantsl anisotropy, cubic system,, hexagonal system, alums
All Mo2 Pbl Ni. KBrp CuZn, Lil wave-velocity, uave displacement
ABSTRACT: The author has t&
ken published,data expressing an equation for propa-
gation of elastic waves~in orysta2ahnd from this has developed equations for approx-
imating values of velocity and displacement of quasilongitudinal elastic Waves in
crystals. A similar derivation was made by P.Materman (Phys. Rev. 113, 1240, 1959),
but only for directions along and near the symmetry axes. This paper offers's
general solution for any direction. --From-.the developed eqiiations- on the basis of
recurrent relationag. the author his computed the elastic constants of a numbbr of
materialsi alum Mb Pb Ni KBrl CuZno and Li. He finds that the first approx-
_P L=
MaNk "& A"" # wu
izationp even or "IrM 0 ic crystals (lithi=) j has
- - W/,-ub
IV?
wer hadlonsh Gotropi"
an average error of ies t one h9aWof one per canto The second approximation
gives an error on the order of 10 sup -3, which is within the limits of error of
measuring the alaatio constants. The author concludes that for practically all

GONCHARENKOO A*M.,-
Optical proportion of crystalline plates,
94-9.1Y ;at 63. (Cz7st&l OPtics)
OptA spektr. 14 no.l:
(KRA 16-15)

FEDOROV..I.J~. GONCHARENKO, A.H.
.Light propagation along the ciroule:r optical axes of absorbing
crystals. Opt. i spe~tr. 14 no.1:100-105 Ja 163.
(Crystal optics) (MIRA 16:5)

FEDOROT F.I.; FETROVp N.S.
k special case of nonunifo= electroZ tic waves in trans;arent
.4
crystals.' Opt* i'spektr. 14 no.2:25 g F 1639 (KIRA 160)
6pn
(Cryotals-Optical properties) ectromagnetic waves)

,%CC17S.'3101 hit- AMU0040 S/0051/63/Ok5/006/0792/0704-
AUTHOR: tj
Petrov,N.S.,, Fedorov, F.1,
TIT12: Now form of plane electromagnetic waves in absorbing crystals
SOURCE: Optika i spaktroskopiya, v.15, no.6, 1063, 702-706
TOPIC TAGS: electromagnetic wave , plane wave: .nonuniform wave,., crystal absorp-
,,tion, Maxwell equation, refraction
ABSTRACT: It was shown earlier (F.I.Fedorov, Optika anizotropny*kh srocl [Optics of
anisotropic media) Minsk,1958) that in the case of oblique incidence of light on m
absorbing crystal of the one of the middle crystallographic systems birefringence
will be absent on condition that Cmoc]2.. 0, where mo is the refraction vector of
the refracted nonuniform wave, and a is the unit optical axis vector. When this
condition is fulfilled the ordinary and extraordinary waves are indistinguishable;
hence there is propagated through the crystallionly one purely exponential wave
with circular polarization. The purpose of the present work was to solve the Max-
well equations and the boundary problem for the above described particular case of
absorption in middle-system crystals. Equations are written for mo and c, and the
L
Cardl/2

ACC.KR: AP4009463
Maxwell equations,are solved, using these expressions to find the electric and mag-
notic field vectors. The boundary problem In susceptible of solution only for a
particular form of the electromagnetic wave given by the solution of the Maxwell
equations. The characteristics of the waves propagating in the crystal are des-
cribed; they are non-uniform plane waves with exponentially decreasing amplitudc.
The conditions when such waves may appear are discussed. it in noted that waves
of this now distinctive typo can also appear incident to oblique incidence of light
on absorbing crystals of lower symmetry systems. Orig.art.has: 50 formulas.
ASSOCIATION: none
SUBMITTED: lOJan63 ACQ.DATE: 03,Tan64 ENCL: 00
SUB-CODE: PH NR REP SOV: ~004 OTIUM: 001
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ACCESSION NHV AP4009464 8/0051/82/015/0()0/0797/0802
ts
AUT11ORt Boku B.V.; Fedorov, r,I,
TITLE: Reflection and refraction of'3.jjftt-. by optically active crystals
SOURCE: Optikal spelctroskopiya, v.15, no.6, 1063, 797-802
TOPIC TAGS; reflection, refraction, polari;ation, Maxwell equation-', optically ac-
/-tive crystal ,tatragonal crystal,, nonmagnetic crystal-
ABSTRACT: T6 date the properties of optically active crystals have not been ade-
quately Investigated. Accordingly, in the present paper there is solved in gener-
al form the problom of reflection and refraction of plane electromagnetic waves at
the surface of an arbitrarily oriented, transparent, isotropic medium with a given
index of refraction, the magnetic proportiestof which are neglected. In view of
the cumbersome character of the calculations'in tho ordinary coordLnato representa-
tion, some simplifying assumptions are made and the results are obtained in covar-
iant torm. The analysis is started with thelMaxwell equations for plans waves in
an optically, active medium, written taking into account the dielectric constant,
the electric optical activity tensor., the refraction vector, the wavenumber, the
Cardl/2

ACC. NR: AP4009464
index of refraction, and the ways normal. The results of the rather lengthy and
involved calc-ulations are applied to crystals of the inversion-planar class of
tetragonal symmetry. It is concluded that when the wave normals of the retracted
waves coincide in direction with the optical c axing the ellipticity will be nil:
that is, in this case the inversion-planar crystal will not differ. an regards its
optical properties from an inactive uniaxial crystal. Orig.art.has: 81 formulas.
ASSOCIATION: none
SUBMITTED- 24Mar63 DATE ACQ: 03Jan64 EXCL: 00
SUB CODE: PH HR REF SOVt 004 0MRz 003
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Misory of qymi-tromm4ree elastic waves in crystals Dokl*
AN SSSR 149 no.5:1060-1063 Ap 163. iMM 160)
1. Predstavl6no akademikom A,.V*Shubn:Lkovym.
(Elastic waves) (CMta3.s)

'J P
NT (1'11/' !
Fed=-
-'-'1.E: Reflection and refraction of light by optj_ca'11,
vp_~rsion-p~~mjr crystals
Optika i spektroskopiya, v. 17, no. 1964,
MOPIC TAGS: crystal lattice eymmetry, crystal syngony, light re-
flection, light refraction, opti.cal activity
ABSTIMCT: The results of an earlier investigation by authcrs
(Opt. i spektr. v. 15, 798, 1964) to
,;aves reflected and refracted by -i:
aT~ai class of tetri,i-
a-=_ In-
paraliei or perpendicular to Lhe bi-_
Ccsr~l
1/12

- -T)L I a
I -Q .
I tk: :
A. "
, v ;~ -.'I ~
) 1) , -S S Np PRo-,

FFDOROV) F.1,
.1 , - ~- , ~'-i...-
Generalized approximate theory of elastic waves in crystals.
Dokl. AN SSSR 155 no. 4z792-794 Ap 164. (MIJA 17:5)
1. Institut Miki AN BSSSR. Predetavleno akademikom AS.
Shubnikovym.

GONCIIARENKO, A.M.; GfWM-GRZHIMAYLO, S.V.; FEDOROV, F.I.
,r
Light absorption surfaces of crystals of various systems.
Kristallografila 9 no-4:589-598 JI-Ag 161,.
(MIRA 17:11)
1. Institut fiziki AN BSSR i Institut kristallografii AN SSSR.

I)ution t the theerv o' ir
I t r;- ri 5 .. e r 9 FI- I S Ot r,)p me
EI: Mo8cow. Universitet. Vestn k. S-ri%-j
1965, 9-16
-,PIC TAC-q: crystal syngony, crystal a-
elastic constant
This is i of an
p R
-roparjar- Lon of eiast,, waveg
co n,., e n j- etfor approximwite pi
t
/3

ACCESS~'GN NR: AP5005144
describing the propagation of elastic waves in a crystal urith the
a
l I
'd o' a tensor characterizing the isotropic medium and a deviation
frotr this tensor. Whereas in the earlier article only twc parameters
were avallable for the determination of the comparison tersor, in
article, to attain better aDuroxi-matior a,,.(j make the
P t-ensor depend on a larger number o f p r-,r ant et e r-,;, zne medium
Is assumed to be tranaversely-isotropic, possessing a rotational
sy-tavietry about a fixed direction with raspect to E certair. property.
For example, all uniaxial crystals are tranovereelv-isotrooic with
zi p to optical properties. With respect to eiasL-Ic Pr,oerties.
-xagonal crystalB are of this type. rhe -a~kthor- --.en :12-
t-eimiiies the elastic constant tensor of a modium whnn-
ut-vLdte ieast in. the mean from a specir-,ed crystai. The con-
cept of transverse anisotropy of the elastic properties of the crys-
ta-I is introduced. The results obtained are applied to crrstails with--'
tetragonal and trigonal syngonies. Of the former, tin and barium
titanate have very low transverse anisotropy, and of the I,ttter, the
Z:I

,L 32787-65
ACCESSION NR: APS005144
'M I
lowest transverse anisotropcy is possessed by hematite and touL a ine,
fii Ffi-r litUe in their elast.-c- propertle-:, from.
;I The max imum. t r ar --e r 9 e i
I~V ca'citte, and quartz.
t a-- i e s
Kafedra fiz'ka kristallov Wmko-vs-kGgo tfni-rsiteta
(Depext=nt of Crystal PbVeics Moscow Udiversity)
SUP241 7rED: 25Feb63 ENCL: 00 S U B ~O D'E' -,S, GP
004 OTRER: 000
.7, 7777777~71

:~ ~: , - - -1 t:, I I': , ". - -
- ..

SIBHTTT-t,D: i6May64
-a,-) izrr sov- -004

,
Theory of elastic waves in crystals on a comparison with a
tranaversally isotropic medium. Vast. Moak, un. Ser. 3t Fiz.f
astron. 20 no.10-16 Ja-F 165. (MIRA 1823)
1. Kafedra fiziki kristallov Moskovskogo universiteta.

MOROV, Fedor Ivanovich; VIRKO, I.G., red.
--fl.
[Theory of elastic waves in crystals) Teorlia uprugikh
voln v kristallakh. Moskvao Nauka, .1965. 386 p
(VJRA 18: i)

AR' AP5017492
URJOW/65jai~/666/052j/05i3l
1 AUTHOR2 43
TITLEs Covariant descripi
pro1wrties of JJAt beWa
i a0twEs Zburnal priklAdnoy spektroskopil.# v. 2., We 61,
TOPIC TAGSt light poUrlastion# light theory# tensor
JMSTRACT: After first pointing out acme difficulties connected with the c
veed method of Stokes parameters for determining the change in polarization of a
3igbt beam Interacting with a mediuia,, the author introduces t~e corelt of the ten..:
ESE% 8) -E 5) over an tbi
sor of the light beamj, 00 defiried as the am 9f dyads 0 = a
noncoberent simple vaves in the given beara I(MG) Is the projection of the complex
electric field Intensity on the coordinate axis). All the quantities determining
t"he polarization of the light are then expressed through iiwariants of this tensor.',
Tae tensor 0 can be represented in various mathematical forms corresponding to the
rapresent
ation of the beam as a am of two polarized mutually orthogonal beaas or
to the resolution of the beam into a sum of natural and coeLpletely polarized llght.~
It in shown that the tensor 0 can be determined by means of three intensity meamn-
mentai, two of vhich are made with a linear analyzer and one vith a circular wVL-
:*zer. A great advantage of this method In that it can be extended to the case or
Card

.rLDCRCVj, F.I.; BARKOVSKII, L.N.
Phenomenolcgt,!al theory of the linear olectre.;-nFtl~al affect
in uniaxial errjt&ls. Zhur. prikl. sF,--kt. 3 no.1:82-91 Jl
165. (MIRA 184.9)

MMMMS LJuL_=_T&A4!_
Ran raUUme In U&M moftli&ttcn with -the WA of the
14 elenigo A % OfrOCt, ZhUr,WM. spektr. 3
tut'Imm 16~._
W
.5 N WRA l8tn)

FEDOROVI-F.Itj LOBKOI S.I.
Magnetic moment of a particle with variable spin 1/2-3/2.
Dokl. AN BSSR 9 no.3:147-151 Mr 165.
(MIM 18-- 6)
1. Belor-uoskiy gosudarstvennyy universitet imeni 1pnina.

FEDOROV F.I.
Debys temperature of crystals, Kriotallograftia 10 no.2:
167-173 Mr-AP 165. (MMA 18-.7)
1. Institut fiziki AN BSSR.

BARKOVSKIYj L.M.; FEDOROV, F.I.
Covariani form of the dieiectric tensor in crystals of hi$7-er
.and medium syngony under vector action. Kristallografiia 10
no,2:171+-180 Mr-Ap 165. O-ORA 18:7)
ls Belorueskiy gosudaratvennyy universitat imeni V.I. Lenina.

L 2822-66 EWT (I )/T IJP(C) GG
~ACCESSION NR.- AP5016178 UR/0051/65/018/006/1047/1052'
348.o:533.001.1
iAUTHOR: Fedorov, F. I. 4~;49Dk
TITLE: Stimulated optical anisotropy of ~i~anspa~ent uni~~al,_cry!tals
;SOURCE: Optika L spektroskopiya, Y. 18, no. 6, 1965, 1047-1052
!TOPIC TAGS: crystal anisotropy, dielectric constant, uniaxial-crystal, teusorj re-,
!fractive index, light transmission
~ABSTRACT: The authors develop in covariant form an approximate theory for the pro-1
I
:pagation of light in transparent uniaxial crystals subjected to external orienting i
:'artion of arbitrary character. The eigenvalues and the eiSenvectors of the die-
:1ectric constant tensor of ouch crystals are determined. General expressions are
..derived for -the refractive indices and for the orientations of the field vectors ofl
;the light waves propagating in the crystal under these conditions. The results arell
independent of the cause of the stimulated anisotropy, provided the change -in the
;dielectric teneor is symmetrical. Orig, art. has: 45 formulas.
ASSOCIAMON., None
Card. .......
-:~l r;

Card 2/2

L 2821-66 EWTI(1-)/T,-. -IIJP(~c-)----IGGI-.-~.I..----..
ACCESSIOX NRt 'AP5016IT9
UR/0051165/018/006/1053/1056
548.o:535.001.1
AUTHOR: Petrov. N. 80 Fedoroy F
TITLE: On the conditions for the absence of birefringence in absorbiq cmtal
of medium syngonies
SOURCE: Uptike, i spektroskopiya,, Y. 18, no. 6, 1965, 1053-1056
TOPIC TAGS: crystal structure, crystal symmetry, crystal absorption, light
absorption, double refraction, light refraction
ABSTRACT: The authors consider the case of absence of birefringence (and double
absorption) in absorbing crystals of medium syngonies for oblique incidence of the
light. It is shown that for a specified orientation of the optical axis of the
crystal the inhomogeneous waves experience no birefringence for two different dir-
ections of the normal of the incident wave, unlike the special case of total re-
'i flection in transparent crystals# If the aosorption is weak, the absorbing crystad-
does not differ in this respect from a transparent crystal. Orig. art. hasi 14
formulaB.
ASSOCU210H i None
fi Cqrd

FEDOROV, F.I.
Generpl. formla for the Debye temperature of m7rstals. D,-;1,1. AN
SSSR 164 noe4#804-806 0 165. (MIRA 18:10)
1. Institut fizikt AN BSSR.

UMOVIO T,Oo flystmal IsHoll Ommal F.I. triodam,, Yr,l
lbotlo propmUoo.of cubic c"t4am, V"tslAN ESSR.
afrorlso-wtousys nools$5.40 165. (HIPA 1911)

~M!
ROMANOVAR I.S. fft=iamp T.fQ;.-nDO'lWf F.1, (Flodarsup M.)
SWations vith highest derivatives -for an eleatromVoUo
flold. Ventel AN MR. Bar, fls,wAnstnavo noo2W.57 1165.
(HIPA 19, 1)

MIMS Ross) FEDMMS polf-
CorxUlAwa ftw the abnnoo of birefrin(pnee in oxpt&U
vith oentria O=OU7* OPto I spektra 28 noo6lW53-20%
Jo 165o (HrPA 28#22)

FEDOROVS.F.I.; BARKOVSKIY, L.M.
Liduced optical wilvotropy of tritimpnrant uld4xiltl C1710tiklme
Opt. i spektr. 18 no.01047-1052 Jre 165.
(MIRA 18:12)

NRi
AUTHOR: Barkoveldy, L. M. Fedorov, Y. L
ORG: none
TITLE: Phase, relationships In light modulation by means of the linear clectrooptic effect
SOURM Zhurnal prikladnoy spektrookopil, v. 3, no. 5, 1965, 449-455
TOPIC TAGS- electrooptio effect, light modulation, optic crystal, untaxial crystal, light
polarization, crystal orlentatlon~llght modulator
ABSTRACT- The authors employ the covariant method in the case of the linear &'C465*
4c
effect to study the phase relationships between light waves of arbitrary dr-ection of the elec-
tric field and light waves normal to symmetry elements In awl crystal In an average system.
General expressions are found for the phases of both light waves propagating In a direction In
unlaxial electrooptio crystals located In a linearly polarized high frequency field of arbitrary
direction. The expressions presented In this article and elsewhere (ZhPS, 3, 83, 1965) m.,dw
possible the most general investigation of the phase, amplitude, aud polarization modulation
of light by means of electroaptic modulators. Orig. art. has: 18 formulas.
SUB CODE: 20 SUBM DATE: 16Dec64 ORIG REF: 003 OTH REF: 007
~rd

L 1016-66 ZWT(1) GGAW
J!jK9Y
ACC NRI AP600547~ SOURCE CODE: UR/0368166/004/001/0058/0063
'AUTHOR:
ORG: none
24,441
TITLE: -imma.when Aight interacts w
Tranj=ion..0f a ith matter
SOURCE: Zhurnal prikladnoy spektroskopiis v. 4$ no. 1$ 19669 58-63
TOPIC TAGS: light scattering, mathematic anakysis, Rayleigh scattering, luminescent
materia Optics,
,ABSTRACT: The author considers the linear trExisformation'of the electric,field of a
;light wave-which takes place during interacti(ni with a medium due to the linearity
,!and homogeneity of electrodynamic equations mid boundary conditions. A formula is
;derived for transformation of the tensor of a light beam for the case of Rayleigh
,~scattering, as well as for diffusion by a volume element of a luminescent material
by a luminescent crystal and for the case of rresnel reflection and refraction 0t
o
r
:light. It is shown that the proposed covaritint method gives the required results I
with considerably fewer and simpler steps than when Stokes parameters are used.
'-Card 1/2 UDC.-. .535.51.

25782-66 EPF(n),~~EWT(d)/EWT(1)/T IJP(c) GGM
ACC NRj AP6016361 SOURCE com tl-R/oo2o[65/i64/oo-476RVo8-o6~i
AUTHOR: Fodorov, F,16
ORG., Institute of Physics, AN BSSR (Institut fiziki AN BM)
TITLE: General formda for Debye ta4
of,
SOURCE: AN SSSR. Doklady, v. 3.64, na. 4, 1965, 804-806
TOPIC TAGS: Debyo temperature, crystal, tensor
ABSTRACT: Because of'great computntionAl difficulties the-'Debye-
temperature 9 has hitherto-been "loulated for only a very few
crystals (excluding the cubic aftd*hexAgonal systems). Tn earlier:''
articles the author suggested a method of computing the Debye
temperature which was suitable, In principle, for nny crystals
,and permitted'a significant deorease In calculations no comnared
,to all.previous methods. The present article presents a further
'development of this method "lending to even more significant
Isimplifications." Tho author formulates several correlations
which are of a universal character and suitable for crystals of
any symmetry. To obtain formulas for a certain type of crystal
,the corresponding expressions for tensor A must be substituted
into these corroldtiones An.-IllustratIon -1s..gly-en u-sing cubic -------

L 2518-2-66
ACC NR, AP6016361 0
cryst,als, and the rosultant. formu.1as are used to compute the Debye temperature for
pro
certain cub!.c crystals (Al, Au, LiF, Ag, NaCl, Cu, KBr, Li). This paper was
sented. by Academician Ao Vo Shubnikovon Z4 February 1963o Orige artq. has; 17
formalas and 1 tablo. rjPM7
SUB CODS 20 MJM DATE: 04Feb65 ORIG REFt 005 OTH REF: 001
Coo

-:A P6 0-3 03-71 SOU RCECODE: UR/0428/66/C-00/001/0099/0106i;
AUTHOR: Bolsun, A. I.; Fedorov, F. I.
,CRG: none
I TITLE: Pseudoscalar matrix beta sub 5 and the electrical dipole moment of the W-Wson
SOURCE: AN BSSR. Vestsi. Seryya fizika-matematychnykh navuk, no. 1, 1966, 99-106~
TOPIC TAGS: meson, dipole moment
ABSTRACT: This paper, which was discussed at a seminar at-the Theoretical Physics
Laboratory, Institute of Physics, Academy of Sciences BSSR, shows that the4 matrix
. 5
is necessary for the introduction of pseudovector interactions related to the internal
electrical dipole moment (EDM) of a W-meson. The matrix and its properties, the EDM
of the W-meson, and the effect of the latter on the processes e++ e- 4+ W_
are discussed in detail. The authors thank all who participated in the seminar at
the Theoretical Physics Laboratory, Institute of Physics, BSSR_ for the valuable
discussions. Orig. art. has: 1 figure and 35 formulas. LJTKS-: 35,6681
SUB CODE: 20 / SUBM DATE: 20Dec65 / CRIG REF: 007 / ME REF: 010
Card

A I-Q.
I.' , Ajp6Gv-Z62
Mic
AUTHOR: Sotskayap Kh* N.; FedoroypF. Io
ORG: none
Singular points of the cross section curves of the surfaces of elastic waves
in crystau
SOURCE: AN BSSR. Veirtsio Serlya, fitika-matmatychnykh navuk,, no. 3.. 10t 3DT-116
TOPIC TAGS: elastic wave., elastic modulus., crystal lattice structure, crystal Sym-
metry
ABSTRACT: The autbors obtain equations for the sections of the' wave surfaces by the
symmetry planes for rhombico hexagonal., tetragona., add cubic crystals in a parametric
formp and for arbitrary crystals in an Implicit form,' and investigate the singu3Ar
points of these sections. All the calculations are based on the fact that the see-
tions of pure3y transverse waves by the symmetry planes are ellipses.,and the equa--
tions for'the different symmetries are obtained by substituting the proper moduli of
elasticity and other constants. The investigation of the singular points, which has
not been carried out by anyone before, is based on eliminating the angle variable - -
from the parametric equations by means of a coordinate transformation. It is shown,.
In agreement with earlier results by one of the authors (Fedorov, Teoriya, upurgikh
voln v krisULUA& (Theory of Elastic Waves In Crystals], Nauka, M. 1965) that the
equation for the section of the ways surftce by the rjmwtry plane in any crystal has

-ALC--14K, AFW-~3002-
a degree not hi r than twelve. The positions of the turning points and other
.9he
singular points are.determined. with particular attention to the plans perpendicular
to the fourfold axis,, and the conditions under which the singular point in a turning
point are established. Orig,art. has.- 55 formulas-
am CME: 2D/ AM Unt IONeya/ OPM MW: 007/-. OTH'MW:
001

-:1 7 i i f T
ACC NR: A~7000753 "'OU111CE CODE: Uii/C)25()/66/010/',-;C)5/0301/03C4
FEDOROV, F. I. Institute of Physics, AN BSSR (Institut
"Beam Surfaces for Elastic Waves In Crystals"
45
'Minsk, Doklady Akadewit Nauk DSSR (Reports of the Academy of Sciences BSSR),
!No 5, 66, pp 301-304
ZABSTRACT: The beam surface (wave surface) is an important indicator of the
I'vronagatign _Wj ;hn crystals, since it describes the real movement
-of eja&US~ Ug
0#1 the wave -en~i`gj If fux_,~_he6 the wave normal is oriented In various directions.
On the basis of methods suggested fit a previous study (FEDOROV, F. I., Teorlya
UpruglIch Voln v Kristallakh, Izd-vo Nauka, 1965), the author derives in an
explicit, form an equation for the curve of.the section of wave surfaces by any
plane of symmetry in crystals with hexagonal, tetragonal, cubic, and rhombic
16yngony. It is shown that in the case of hexagonal crystals this equation ac-
tvnll,y determines the total beninsurface, which thus turns out to be a 12-th
lorder rather than 150-th order-surface. The corresponding formulas are derived
with the assumption that the equation for the section of wave. surfaces is ob-
:taincd by excluding components of the unitary displacement vector u (ul, uz)
,(u2 from the. system A abcdubucud - 0 (d, b, c, d - 1, 2), where /_ abcd is'
a two-dimensional fourth-rank tensor. Orig. art. hat;: 14 formulas. IJFf-.3: 37,33,01
TOPIC TAGS% elastic wave, cry.,3tallography
SUB CODE: 20 SUBM DATE,: 1'/Jan66 ORIG IEF: C02
Curd 1/1 -jot-

-EWT+"WTfWZ-WT(MVT/ZT.PW/ET1 =(C) JD/W-W
ACC N"
AP6018764 SOURCE CODE: UR/0070/66/011/003/0368/037
hUTHOR*. Fedorovp F. 1,,j Bystrovs, T. G.
ORO : Institute of Physics, AN BSSR Mwtitut fiziki AN BSSR)
TITLE: Dabye temperatures for cubic crystals
3OURCE: Kristallografi-yag v, lls no, 3. 1966# 368-374
rOPIC TAGS: Dabye temperature, cubic crystal
ABSTRACT: Using generalized formulas, the artic presents calculations
of the Debe* tomperSturo 9 for 82 oubio oustalsilhose elastic constants
are known. These results are compared with experimental data and with
tbe'.results of calculations by other authors, with good agreement. In
general, the characteristic Debye temperatures close to absolute zero
depend only on the elastic constants of the crystals and can be written
in the form:
0 C(1V4)-%1 M
where G is expressed in terms of the Boltzmann and Planck.elastic
constants - - - j
C h 135,78, (2)
k
'0
Card 1/2 UDC: 5k8.0

ACC NR- AP6018764
The method of calculation used starts with the approximate expression
],==a--'/, 2+rrb o,irl(i-qoor.)+57,2-8,4r.1-0,48n
1001 -11 +
+ C-V1 rbr.- ,7,2 (t - rx) + 0,5rb - r., (7,2 - 6,7r2)] (3)
1001
If we limit ourselves to terms not higher than the 4tb order with
respect to the elastic anisotropy, we got
11 + jalh (0,17r, + 0,26r,* + 4,18r,3 + 5,72ril) -
toot
(4)
c-V-(0,17rj + 0,7rit + 5,8643 - 5,28rzl) I
Here r = o /a; rb Yb; r o /c- r = b/a; r2 b/c; a = c + 0.203;
b =:02 a+ 0,9, 3; c = ab; oo c2 3 Zd I are expressed in terml of the
usual elastic constants of tie auha cryhols, and the density in the
following manner: C" C12 + C" Cif - CL2 - 2c"
CS
P P (5)
Results of calculation with Equation (3) and (4) are shown in extensive
tables. Orig, art* has: 5formul&B and 2 tables,
1 20/ SUBM DAM 11Apr65/ ORIG REP: 012/ OTH REP: 037

SGURRICE
AUTHOR: Fedorov, F. I.j Barkovskiy, L. M.
ORG: Belorussian State University (Beloruaskiy gosudarotvennyy universitet)
TITLE: Effects of stimulated optical anisotropy in biaxial crystals
SOURCE: Kristallografiya, v. 11, no. 5, 1966, 766-770
TOPIC TAGS: optic crystal, cr7stal property, dielectric constant, tensor,
electrooptic effectp piezoelectricity,
ABSTRACT: This is a continuation of earlier work (Optika i spektroskoplya v. 18,
1047, 1965). where a simple method was proposed for approximately determining the
parameters of the reciprocal dielectric tensor of a transparent uniaxial crysta unar
the influence of an external action. The present paper is devoted to a similar pro-
blem for the case of a biaxial crystal. A covariant method is used, in which the
changes to the tensor are determined in the form of small increments to the initial
values of its components. It in assumed that the natural anisotropy of the crystal i
much larger than the artificial anisotropy produced by the-external action. The meth,
od yields the directions of the optical axes and the principal vilues of the dielec-
tric tensor for the disturbed crystal. The method is -also used to determine the lin-
ear electrooptic effect in a Rochelle salt crystal. Covariant expressions are pre-
Card
UDC', S4F.%O;535-34
ACC NRt Ap6o3296,
sented for the tensor of the electroo ptic constants in biaxial crystals. An interest-,
ing result in the case of Rochelle salt is that the scattering indicatrix is rotated,
as a whole under the influence of an external field of arbitrary direction, without
changing forms and dimensions. Orig. art- has: 18 formulas a 1 table.
SUB CODE: 20/ SUBK DATE: 2-V(ar65/ ORIG REFt 008/ OTH REP: 003

AA5 01519 DO
Fedorov,,. Fed?i~jv_anovich
Theory of -glactic Wavo in crystals (Toorlya uprugikh voln T kristallalch) Moscow,,
lzd-vo ONauka"s 1965o 386 po illusq~ biblioas indox# 4500 coP103 printed* Editorl
Is Go Virko; Technical editor& L. Ao Pyzhovaj Proofreaders Le Ot Sechelko,
TOPIC TAGS: Cvystal physics, crystal theory, elastic NaTej elasticity theory,
linear operator, tensor analysis
rURPCGS AND COVEWGS: Thin book will be of use to scientiate',and engine"ra apeciali-
zing in the practical utilization of -elastic waires in crystals and also may be used as
a textboOk for otudents- and aspirants specializing in the physics of crystals. The
basic lawn of the propagation of two-4imensional elActic vraves in crystals of differeni
aynnstry are proaantode In diatinction fr*,q uoual rothodis of preaentation, linaar
(noncoordinate) mathoda of vector and terisor calculus are utilized hero$ Special atm
tontion is paid to inyestigation of general methods of solying portinqnt problems;
however, at the same time, the methodology of real computations in Irecented in de-
tail. The book Is based on a course of lectures presented in thg fall of 1962 to Stu-
donto and aspirants specializingm in the physics of or7stals at MGU* The author thanks
Ve, A. Noptalk and To.G, Byetrova for their assistance in preparing the manuscript for
publication*
TABIZ OF Gai=St
Card 3,/2. UDC : Z3'1. 2/

NRt
Foreword
Cho I* Conoral equations of the tb9ory of elasticity ?
Ch. 2. F.Iongnts of linear algebra and or linear tonsor calculus o- - 45
Ch, 39 General laws or propagation of two-dimensional elastic waves in crystals . 98
Ch. 4. Energ)r flux and ways surfaces . - 136
Cho So General theory of elastic waves In c ryatals- on tho basis of compariaoa wiu
an isotropic medium - - 189
Ch. 6o Elastic waves In tranzveraely isotropic media 230
Cho 7& Elastic waves in crystals of cubic and central iyngouy-- o- 261
Ch. Oo Rarlection and refraction of elastic wavas 299
Cho 9o Elastic waves and specific beat of crystals 332,
Appendixes &.379
Literature a- 38Z
SubJect index 384
SUB CCM: 20 /.UBM DAM 25Jan65 /ORM M.7i 0 28 /OTH MWt 023

CE OUR UUR A "b0/w-VW-i
AP6024334---- I ~
AVM01ts Fedorovp F# 1.
ORGI none
TITLEs Formula for the 1)2~Xe tem-perature for tranoveree-isotropio media
SOMCEt AN BSSR. Veetsi, Seriyya finika-matematychnykh navukq no. it 1966, 91-98
TOPIC TLOSi Debye temperatureq orystalp cry3tal lattice, crystal vibration
ABSTRACTs A formula for the Debye- temperature for tranaveree-iootropia media has
been derived* This derivation is an extension of an easion for the Debye tempera;-
ture derived by the present author in wi earlier paper7p. I# Fedorov, LU 8SMj 164j,
0049 1965)o In the first ap~roximationj the formula assumes the form
"(As + SAI + ij Aj + q2 co-MI (As -rs'
5AI
jar
3 1.4\
A#'m y* ko -- 2 + 181, Is + 6P4),~
105(2112
3
rAf ii,X.; 0) kt 4.
14 AL P I
33 1287
.,.Y
Card IL2
--7

AMN&-A260243
3
-As (ok 2 1 239 43
I PS + *-~- PS It +to P4, +- R
105 -6 T43
.4 165
15
-A; A4 --L5 19P4
1r
8
70 16
As
8 3 4-7 16
`7
36
2 19
As -70