Geodesic
Solutions of ultrahyperbolic equations and their application in texture analysis
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2159-2167

Voir la notice de l'article provenant de la source Math-Net.Ru

Solutions of ultrahyperbolic $2\times 2$ equations are examined. An inverse diffraction problem—the recovery of the orientation distribution function from x-ray or neutron measurements of pole figures (PFs)—is reduced to a system of integral equations on the rotation group $SO(3)$. By transforming $SO(3)$, the original problem is reduced to a well-known problem in integral geometry, namely, to the recovery of a function in three-dimensional space from known integrals along straight lines. Upon this transform, the PFs are solutions to an ultrahyperbolic equation and the solution is nonunique. 
@article{ZVMMF_2005_45_12_a5,
     author = {T. I. Savyolova},
     title = {Solutions of ultrahyperbolic equations and their application in texture analysis},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2159--2167},
     publisher = {mathdoc},
     volume = {45},
     number = {12},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a5/}
}
TY  - JOUR
AU  - T. I. Savyolova
TI  - Solutions of ultrahyperbolic equations and their application in texture analysis
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 2159
EP  - 2167
VL  - 45
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a5/
LA  - ru
ID  - ZVMMF_2005_45_12_a5
ER  - 
%0 Journal Article
%A T. I. Savyolova
%T Solutions of ultrahyperbolic equations and their application in texture analysis
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 2159-2167
%V 45
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a5/
%G ru
%F ZVMMF_2005_45_12_a5
T. I. Savyolova. Solutions of ultrahyperbolic equations and their application in texture analysis. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2159-2167. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a5/