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The theory of 'minus partial order' on the class of matrices over a field is well studied in the literature, and it is known that the rank additive property 'ρ(A) = ρ(B)+ρ(A− B)'holds whenever B is lesser than A under the minus partial order. The rank additive property fails in the class of regular matrices over a commutative ring, though several other characterizations of minus partial order relation known for the class of matrices over a field are easily extended. So, an extension of rank additive property in the class of regular matrices is further investigated. In the process, Rao-Mitra's theorem on invariance of B A − C is further probed and a general condition for such invariance is obtained for matrices over a commutative ring.

The cross sections for the 93 Nb(n,2n) 92m Nb, 93 Nb(n,α) 90m Y and the 92 Mo(n,p) 92m Nb reactions have been measured with respect to the 197 Au(n,2n) 196 Au monitor reaction at the incident neutron energy of 14.78 ± 0.19 MeV by employing methods of activation and off-line γ-ray spectrometry. The covariance analysis was carried out by taking into consideration of partial uncertainties in different attributes and correlation among the attributes. The present data have been compared with the literature data available in EXFOR, evaluated data of different libraries and theoretical values based on TALYS-1.8 code. Keywords 93 Nb(n,2n) 92m Nb, 93 Nb(n,α) 90m Y and 92 Mo(n,p) 92m Nb reactions • Cross sections • 3 H(d,n) 4 He reaction neutron • Activation and off line γ-ray spectrometry • Covariance analysis • TALYS-1.8

In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.