In this paper, we have defined recurrence and symmetry of different kinds in Hsu-structure manifold. Some theorem establishing relationship between recurrent H- HSU-Structure manifold involving equivalent conditions with respect to projective, conformal, conharmonic concircular curvature tensors has been discussed parameter also studied.

Auslander and Furstenberg asked the following question in [1]: If (x, y) is recurrent for all uniformly recurrent points y, is x necessarily a distal point? We call such a point x weakly product recurrent. Haddad and Ott [4] answered the Auslander/Furstenberg question in the negative by identifying a class of weakly product recurrent points that are not distal; however, the points in this class...

a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...

in this paper, we prove a fi xed point theorem for a pair of generalized weakly contractive mappings in complete partial metric spaces. the theorems presented are generalizations of very recent fixed point theorems due to abdeljawad, karapinar and tas. to emphasize the very general nature of these results, we illustrate an example.

We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which objective function is weakly convex ambient Euclidean space. Such are ubiquitous engineering applications but still largely unexplored. present family Riemannian subgradient-type methods---namely subgradient, incremental and stochastic subgradient methods---to solve these show that they all have an iterat...

Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...

This paper concerns the dynamical behavior of weakly reversible, deterministically modeled population processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are “repelling.” It has been conjectured that any population process whose network graph is weakly reversible (has strongly connected components) is persistent. We prove thi...