This paper considers the qualitative behaviour of flow in a neighbourhood closed invariant sets dynamical systems. The properties compactness, invariance, and connectivity pseudo-prolongations are investigated. A rather deep analysis vicinity compact set asymptotically phase spaces is presented. connection pseudo-prolongation with first positive prolongation T. Ura weakly elliptic points refined.

It is well known that in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with "sandwich" covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal and of asymptotic variance that is in general different than the sandwich matrix. It is shown that due to t...

The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic context of multivariate Gaussian models. And the modified likelihood ratio tests (MLRT) that are used ...

We summarize the conditions discovered for the existence of new ergodic type solutions (asymptotically almost periodic, pseudo almost periodic, . . .) of differential equations with piecewise constant arguments. Their existence is characterized by introducing a new tool, the ergodic sequences. 2000 Mathematics Subject Classification. 39-02, 34K14, 34D09.

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces. Acknowledgement. The authors A. R. Khan and M. Abbas are grateful to King Fahd University of Petroleum and Minerals for supporting research project IN 121037.