Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.

Let E,F,G,D be infinite complex Banach spaces and B(F,E) the Banach space of all bounded linear operators from F into E. Consider A1,A2∈B(F,E), B1,B2∈B(D,G)B1,B2∈B(D,G). Let MA1,B1:X→A1XB1 be the multiplication operator on B(G,F) induced by A1,B1. In particular, LA1=MA1,I and RB1=MI,B1, where I is the identity operator are the left and the right multiplication operators, respectively. The elementary operator Ψ defined on B(G,F)B(G,F) is the sum of two multiplication operators Ψ=MA1,B1+MA2,B2. This paper gives necessary and sufficient conditions for the existence of a common solution of the operator equations MA1,B1(X)=C1 and MA2,B2(X)=C2 and derive a new representation of the general common solution via the inner inverse of the elementary operator Ψ; we apply this result to determine new necessary and sufficient conditions for the existence of a Hermitian solution and a representation of the general Hermitian solution to the operator equation MA,B(X)=C. As a consequence, we obtain well-known results of Dajic´ and Koliha.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.

The magnetohydrodynamics (MHD) is an important interdisciplinary field. It is the interaction between an electromagnetic field and an electrically conducting fluid. Electromagnetic pumps are widely used for the transportation of the fluids in a variety of technological processes. The advantage of these devices is that permits the pumping of liquids without moving parts. The design of the pump is considered as an optimization problem where the objective function is the minimum of the MHD pump mass with both geometrical and electromagnetic contraints type. The obtained optimization results using the finite volume method with Matlab software show the performances of the used stochastic simulated annealing method.