Mohammed Shakir Mahdi Zabiba

In this work, we consider the fuzzy stochastic differential delay equation and study the numerical solution of backward fuzzy stochas- tic differential delay equations (FSDDEs). Finally, we examine nu- merical convergence for FSDDEs.

Minimal partition problems consist in finding a partition of a domain into a given number of components in order to minimize a geometric criterion. In applicative fields such as image processing or continuum mechanics, it is standard to incorporate in this objective an interface energy that accounts for the lengths of the interfaces between components. The present work is focused on the theoretical and numerical treatment of minimal partition problems with such interface energies. The considered approach is based on a Γ-convergence approximation combined with convex analysis techniques.

Minimal partition problems consist in finding a partition of a domain into a given number of components in order to minimize a geometric criterion. In applicative fields such as image processing or continuum mechanics, it is standard to incorporate in this objective an interface energy that accounts for the lengths of the interfaces between components. The present work is focused on the theoretical and numerical treatment of minimal partition problems with interface energies. The considered approach is based on a

For fixed positive integer n³3 ,let Dn be the dihedral group, Dnh= Dn ÏC2 and cf(Dnh,Z) be the abelian group of Z-valued class functions of the group Dnh .The intersection of cf(Dnh,Z) with the group of all generalized characters of Dnh , R(Dnh) is a normal subgroup of cf(Dnh,Z) denoted by R (Dnh),then cf(Dnh,Z)/ R (Dnh) is a finite abelian factor group which is denoted by K(Dnh). I n this paper ,we determine the cyclic decomposition of the finite abelian factor group cf(Dnh,Z)/R(Dnh) when n is an odd number, we find that the cyclic decomposition of K(Dnh) depends on the elementary divisor ofn ,if n= p 11a.p 22 a..p mmawhere p1 ,p 2 ,…, p m are distinct primes and 1 a , 2 a ,.., m a are positive integers, then ; K(Dnh)= 2 1 = Å i K(Dn) ( )( ) ( )2 1 1 1 1 1+ × 2 + + - = Å m i a a L a C2 Å K(C4). And we find the rational valued characters table of the group Dnh.