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In this paper we consider the classical system of matrix equationsover R, an arbitrary regular ring with identity. Necessary and sufficient conditions for the existence and the expression of the general solution to the system are derived. As an application, the linear matrix equation AXB + CY D = E over R is considered.

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We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show that nonlocality induces an attractive force in the otherwise repulsive soliton interaction.

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