A 2 XB 2 = C 2 , there are some valuable efforts on solving a pair of the matrix equations with certain linear constraints on solution. For instance, Khatri and Mitra [7] derived the Hermitian solution of the consistent matrix equations AX = C, XB = D. Deng et al. [8] studied the consistent conditions and the general expressions about the Hermitian solutions of the matrix equations (AX,XB) = (C...

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

It is well known that the Chern classes ci of a rank n vector bundle on P N , generated by global sections, are non-negative if i ≤ n and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers ci with i ≥ 4 can be arbitrarily negative for reflexive sheaves of any rank; on the contrary fo...

The generalized inverse has numerous important applications in aspects of the theoretic research matrices and statistics. One core problems is finding necessary sufficient conditions for reverse (or forward) order laws matrix products. In this paper, by using extremal ranks Schur complement, some are given forward law A1{1,2}A2{1,2}…An{1,2}⊆(A1A2…An){1,2}.

and Applied Analysis 3 to a class of complex matrix equations with conjugate and transpose of the unknowns. Jonsson and Kågström 24, 25 proposed recursive block algorithms for solving the coupled Sylvester matrix equations and the generalized Sylvester and Lyapunov Matrix equations. Very recently, Huang et al. 26 presented a finite iterative algorithms for the one-sided and generalized coupled ...