In this paper we consider a free boundary problem which describes contact angle dynamics on inhomogeneous surface. We obtain an estimate on convergence rate of the free boundaries to the homogenization limit in periodic media. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.

We consider systems of n parallel edge dislocations in a single slip system, represented by points in a two-dimensional domain; the elastic medium is modelled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations, and prove several convergence results in the limit n → ∞. The main aim of the paper is to study the convergence of the evolution...

The leading term in the normal approximation to the distribution of Student’s t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form of the leading term is shown to have its origin in the way in which extreme data influence properties of the Studentized sum. The leading-term approximation...

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O(k−ρ) for some ρ ∈ (0,∞).

We consider Bayesian density estimation for compactly supported densities using Bernstein mixtures of beta-densities equipped with a Dirichlet prior on the distribution function. We derive the rate of convergence for α-smooth densities for 0 < α ≤ 2 and show that a faster rate of convergence can be obtained by using fewer terms in the mixtures than proposed before. The Bayesian procedure adapts...

Solution: Since {xn} ∞ n=1 is a bounded sequence in R, the Bolzano-Weierstrass Theorem ensures that there is at least one convergent subsequence: let L be its limit. If the entire sequence does not converge to L, then for some > 0 there must be infinitely many terms of the sequence outside the ball B = (L− , L+ ). This infinite but bounded collection of terms likewise by Bolzano-Weierstrass has...

the complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. as a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

the complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. as a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

In this paper we study the concepts of I-Cauchy and I∗-Cauchy for double sequences in a linear metric space. Also, we give the relation between I-convergence and I∗-convergence of double sequences of functions defined between linear metric spaces.

For the Lotka-Sharpe-McKendrick demographic model the rate of convergence to the persistent age distribution is estimated in terms of the age-dependent mortality and fertility. In an abstract setting the problems amounts to estimating the second largest spectral bound of a linear operator. The convergence rate is indeed characterized as the difference between the first and second spectral bound...