We present some equivalent conditions of the reverse order law for the Moore–Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore-Penrose inverse in C∗-algebras.

Moore’s paradox is the fact that assertions or beliefs such as Bangkok is the capital of Thailand but I do not believe that Bangkok is the capital of Thailand

Spatial and temporal aberration detection methods for disease outbreaks in syndromic surveillance systems Dongmei Chen a , John Cunningham b , Kieran Moore c & Jie Tian d a Department of Geography, Queen's University, Kingston, ON, Canada b Leeds, Grenville & Lanark District Health Unit, ON, Canada c Department of Family Medicine, Queen's University, Kingston, Canada d Department of Geology & G...

In this paper, a link between the Hyers–Ulam stability and the Moore–Penrose inverse is established, that is, a closed operator has the Hyers–Ulam stability if and only if it has a bounded Moore–Penrose inverse. Meanwhile, the stability constant can be determined in terms of the Moore– Penrose inverse. Based on this result, some conditions for the perturbed operators having the Hyers– Ulam stab...

Given a set Un = {0, 1, ..., n−1}, a collectionM of subsets of Un that is closed under intersection and contains Un is known as a Moore family. The set of Moore families for a given n, denoted by Mn, increases very quickly with n, thus |M3| is 61 and |M4| is 2480. In [1] the authors determined the number for n = 6 and stated a 24hcomputation-time. Thus, the number for n = 7 can be considered as...

We investigate the probabilistic behavior of a string-matching heuristic used for searching for the occurrences of a pattern in a random text. Our investigation covers the two cases when the pattern itself is xed or random. Under suitable normalization we show that the total search time is asymptotically normally distributed in the case of xed pattern, whereas in the case of random pattern the ...

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

In this paper, some new representations of the Moore-Penrose inverse of a complex m × n matrix of rank r in terms of (s × t)-constrained submatrices with m ≥ s ≥ r, n ≥ t ≥ r are presented.