Limit Theorems for the Number of Maxima in Random Samples from Planar Regions

Efficient maxima-finding algorithms for random planar samples

We collect major known algorithms in the literature for finding the maxima of multi-dimensional points and provide a simple classification. Several new algorithms are proposed. In particular, we give a new maxima-finding algorithm with expected complexity n + O( √ n logn) when the input is a sequence of points uniformly chosen at random from general planar regions. We also give a sequential alg...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

Central limit theorems for correlated variables: some critical remarks

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in physics. Next, I show that there is room for new versions of central limit theorems applicable to specific classes of problems. Finally, I argue that we have insuff...

Bifurcation of limit cycles from a quadratic reversible center with the unbounded elliptic separatrix

The paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-Hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. Attention goes to the number of limit cycles produced by the period annulus under perturbations. By using the appropriate Picard...