Instead of studying evolutions governed by an evolutionary system starting at a given initial state on a prescribed future time interval, finite or infinite, we tackle the problem of looking both for a past interval [T − D, T ] of aperture (or length, duration) D and for the viable evolutions arriving at a prescribed terminal state at the end of the temporal window (and thus telescoping if more...

an equitable domination has interesting application in the contextof social networks. in a network, nodes with nearly equal capacitymay interact with each other in a better way. in the societypersons with nearly equal status, tend to be friendly. in thispaper, we introduce new variant of equitable domination of agraph. basic properties and some interesting results have beenobtained.

Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In ...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

A transversal of a hypergraph is a set of vertices meeting all the hyperedges. A k-fold transversal of a hypergraph is a set of vertices such that every hyperedge has at least k elements of. In this paper, we prove that a k-fold transversal of a balanced hypergraph can be expressed as a union of k pairwise disjoint transversals and such partition can be obtained in polynomial time. We give an N...

Inclusion/exclusion and measure and conquer are two of the most important recent new developments in the field of exact exponential time algorithms. Algorithms that combine both techniques have been found very recently, but thus far always use exponential space. In this paper, we try to obtain fast exponential time algorithms for graph domination problems using only polynomial space. Using a no...