Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: C · ρ−n · n−3/...

For the problem of dividing the space originally pad tionec ~y a blurred boundary, every learning algorithm can make the probability of incorrect prediction of an individual example E decrease with the number of training examples t. We address here the question of how the asymptotic form of ~ ( t ) as well as its limit of convergence reflect the choice of learning algorithms. The error minimum ...

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: C · ρ−n · n−3/...

This article presents the analysis of the rate of convergence of a stochastic particle method for 1D viscous scalar conservation laws. The convergence rate result is O(∆t+1/ √ N), where N is the number of numerical particles and ∆t is the time step of the first order Euler scheme applied to the dynamic of the interacting particles.

In this paper, we study the equivalent conditions of complete moment convergence for sequences of identically distributed extended negatively dependent random variables. As a result, we extend and generalize some results of complete moment convergence obtained by Chow (Bull. Inst. Math. Acad. Sin. 16:177-201, 1988) and Li and Spătaru (J. Theor. Probab. 18:933-947, 2005) from the i.i.d. case to ...

We study the existence and asymptotic convergence when t→ +∞ for the trajectories generated by ∇f(u(t), (t))u̇(t) + ̇(t) ∂2f ∂ ∂x (u(t), (t)) +∇f(u(t), (t)) = 0 where {f(·, )} >0 is a parametric family of convex functions which approximates a given convex function f we want to minimize, and (t) is a parametrization such that (t) → 0 when t → +∞. This method is obtained from the following variati...

After F a s t [6] introduced the theory of statistical convergence of a real sequence, it has become popular among mathematicians ([2], [7]–[9], [17]). The ideas of statistical limit superior and limit inferior were first extensively studied by F r i d y and O r h a n [9]. After K o s t y r k o et al. [10] extended the idea of statistical convergence to I-convergence using the concept of an ide...

New comparison theorems are presented comparing the asymptotic convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The asymptotic convergence factor of the iteration matrix T is the quantity γ(T ) = max{|λ|, λ ∈ σ(T ), λ = 1}, where σ(T ) is the spectrum of T . In the new theorems, no restrictions are imposed on ...

Multi-particle Markov chains L(N) are stochastic systems consisting of M(N) noninteract-ing particles moving according to the law of some \one-particle" nite Markov chain K(N). Our goal is to nd the convergence time to equilibrium T(N) 1, 2] for the sequence of Markov chains L(N) in the situation when the number of particles M(N) tends to innnity and the \size" of the one-particle chain K(N) gr...