For 0 < p < ∞, the optimal Lp rate of convergence of a nonparametric estimate of m is of order n −k 2k+d when m is assumed to be a k-times differentiable function and for p = ∞, the optimal rate is (n−1 log n) k 2k+d (see, Stone (1985)). This rate of convergence which depends on the dimension d of the covariable X becomes worse as the dimensionality of the problem increases. In the literature, ...

For n particles di using throughout R or Rd let n t A A B t be the random measure that counts the number of particles in A at time t It is shown that for some basic models Brownian particles with or without branching and di usion with a simple interaction the processes f n t E n t p n t M C L R g n N converge in law uniformly in t Previous results consider only convergence in law uniform in t b...

1. Elementary limit formulas We consider the classical orthogonal polynomials as monic polynomials pn(x) = x + terms of degree less than n. We have • Jacobi polynomials p (α,β) n (x) with respect to weight function (1 − x) (1 + x) on (−1, 1); • Laguerre polynomials ln(x) with respect to weight function e −x x on (0,∞); • Hermite polynomials hn(x) with respect to weight function e −x on (−∞,∞). ...

We compare the two most common types of success criteria for learning processes. The (;) criterion employed in the PAC model and its many variants and extensions, and the identiication in the limit criterion that is used in inductive inference models. By applying common techniques from the theory of Probability, and a stochastic variant of Rissanen's MDL principle, we demonstrate close connecti...

the combination of graphene (gr) and nickel oxide nanoparticles (nio nps) yields nanostructured electrochemical sensor formed a novel kind of structurally uniform and electrocatalytic activity material. in cyclic voltammetry (cv) studies, in the presence of ep, nio/gr composite modified electrode shows a significantly higher current response for ep oxidation. based on differential pulse voltamm...

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit sets, but are not convex cocompact.