We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W−1,∞ to the ’expected’ averages and obtain a sharp W−1,∞-convergence rate of order O(ε) – the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this weak...

[1] This paper synthesizes a variety of atmospheric and oceanic data to examine the large-scale energy budget of the Arctic. Assessment of the atmospheric budget relies primarily on the ERA-40 reanalysis. The seasonal cycles of vertically integrated atmospheric energy storage and the convergence of energy transport from ERA-40, as evaluated for the polar cap (defined by the 70 N latitude circle...

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The purpose of this article is to prove strong convergence theorems for fixed points of closed hemirelatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive m...

In this paper we introduce the notion of levelwise convergence of sequence of fuzzy random variables. We derive equivalent conditions for left quasi uniform convergence of fuzzy random variables. Conditions are obtained for eventually equi-right continuity for the sequence of fuzzy random variables. A necessary and sufficient condition is obtained under which for a sequence of fuzzy random vari...

Kaminski, M. and A. Sidi, Solution of an integer programming problem related to convergence of rows of PadC approximants, Applied Numerical Mathematics 8 (1991) 217-223. The following integer programming problem arises in the convergence analysis of rows of Pade approximants for meromorphic functions: maximize Xr=r( C+J, C-I,‘), subject to the constraints C:=ro, = 7, 0 < a, < w,, 1 Q i Q r. Her...

We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2(Rn). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected...

Given a weakly convergent sequence of positive functions in W 1,p 0 (Ω), we prove the equivalence between its convergence in the sense of obstacles and the lower semicontinuity of the term by term duality product associated to (the p-Laplacian of) weakly convergent sequences of p-superharmonic functions of W 1,p 0 (Ω). This result implicitly gives new characterizations for both the convergence ...

Markov chain Monte Carlo (MCMC) algorithms are widely used in statistics, physics, and computer science, to sample from complicated high-dimensional probability distributions. A central question is how quickly the chain converges to the target (stationarity) distribution. In this paper, we consider this question for a particular class of MCMC algorithms, independence samplers (Hastings, 1970; T...