In this note, the (p, q) outer generalized inverse in Banach algebra is considered, a new representation based on the (1, 5) inverse is presented. Also, we construct an iterative method for computing the (p, q) outer generalized inverse in Banach algebra. 2000 Mathematics Subject Classification: 15A09

This paper considers the block selection problem for a block bootstrap variance estimator applied to spatial data on a regular grid. We develop precise formulae for the optimal block sizes that minimize the mean squared error of the bootstrap variance estimator. We then describe practical methods for estimating these spatial block sizes and prove the consistency of a block selection method by H...

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we develop a method for obtaining uniform asymptotics, with respect to the spectral parameter, of the generalized eigenvectors. Our technique can be applied to a w...

We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal invariants of Lie groups endowed with a certain type of Jacobi structures. We also propose a method to obtain generalized Lie bialgebras. It is a generalization of t...

In this paper, we discuss the concept of the expected opportunity cost of a potentially incorrect selection as a measure of selection quality on a new selection procedure that is used to selecting the top m systems for large scale problems. This procedure is used the ordinal optimization method to reduce the size of the search space, and then it is used the idea of computing budget allocation O...