We show that the number of renewals up to time t exhibits distributional fluctuations as t→∞ if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the asymptotics of insertion depth in random trees generated by a bit-comparison strategy from uniform input; we also obtain a representation for the resulting family of l...

In this paper, we prove that every F ∗ space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by means of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms P, the concepts of P-bounded set and γ-maxpseudo-norm-subadditive operator in F ∗ space are introduced. The uniform boundedness princ...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...

Particle swarm optimization comes under lot of changes after James Kennedy and Russell Eberhart first proposes the idea in 1995. The changes has been done mainly on Inertia parameters in velocity updating equation so that the convergence rate will be higher. We are proposing a novel approach where particle’s movement will not be depend on its velocity rather it will be decided by constrained bi...

We denote N, R, C the sets of natural, real and complex numbers respectively. Let (λn), n ∈ N be an unbounded sequence numbers. Costakis has proved following result. There exists entire function f with property: for every x, y R 0 , θ ∈(0,1) a there is subsequence natural (mn), such that, compact subset L ⊆ In present paper we show that constant cannot replaced by any non-constant G. This so ev...