Let I be an open bounded interval of R and W a non-negative continuous function vanishing only at α, β ∈ R. We investigate the asymptotic behaviour in terms of Γ-convergence of the following functional Gε(u) := ε p−2 ∫∫ I×I ∣∣∣∣u(x)− u(y) x− y ∣∣∣∣pdxdy + 1ε ∫ I W (u) dx (p > 2), as ε→ 0. Mathematics Subject Classification (2000). Primary 82B26, 49J45 ; Secondary 49Q20.

In this paper we study approximation properties for the class of general integral operators of the form (Twf)(s) = ∫ Hw Kw(s, t, f(t))dμHw(t) s ∈ G, w > 0 where G is a locally compact Hausdorff topological space, (Hw)w>0 is a net of closed subsets of G with suitable properties and, for every w > 0, μHw is a regular measure on Hw. We give pointwise, uniform and modular convergence theorems in ab...

In this paper, we prove convergence of a sticky particle method for the modified Camassa–Holm equation (mCH) with cubic nonlinearity in one dimension. As a byproduct, we prove global existence of weak solutions u with regularity: u and ux are space-time BV functions. The total variation of m(·, t) = u(·, t)− uxx(·, t) is bounded by the total variation of the initial data m0. We also obtain W 1,...

We present an algorithm for solving stochastic heat equations, whose key ingredient is a non-uniform time discretization of the driving Brownian motion W . For this algorithm we derive an error bound in terms of its number of evaluations of onedimensional components of W . The rate of convergence depends on the spatial dimension of the heat equation and on the decay of the eigenfunctions of the...

We discuss the nonparametric Nadaraya-Watson (N-W) estimator of the drift function for ergodic stochastic processes driven by α-stable noises and observed at discrete instants. Under geometrical mixing condition, we derive consistency and rate of convergence of the N-W estimator of the drift function. Furthermore, we obtain a central limit theorem for stable stochastic integrals. The central li...

The authors examined the construct of psychopathy as applied to 103 female offenders, using the multitrait-multimethod matrix proposed by D. T. Campbell and D. W. Fiske (1959). Instruments used in the study included the following: (a) Antisocial Scale of the Personality Assessment Inventory (L. C. Morey, 1991); (b) Psychopathy Checklist--Revised (R. D. Hare, 1990); and (c) Antisocial scale of t...

We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform mesh on a unit interval, the explicit representation of B-spline basis functions for a fixed mesh size h is given for p = 2, 3, 4 and for C 0-and C ...

*Correspondence: [email protected] 1Faculty of Education, Harran University, Şanlıurfa, Turkey Full list of author information is available at the end of the article Abstract New concepts of fλ,μ-statistical convergence for double sequences of order α̃ and strong fλ,μ-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we giv...

The rate of subduction is larger than the convergence rate along W-directed subduction zones, whereas it is smaller along Eor NE-directed subduction zones. Along Wdirected slabs, the subduction rate is the convergence rate plus the slab retreat rate, which tends to equal the backarc extension rate. Along Eor NE-directed slabs, the subduction rate is decreased by the shortening in the upper plat...