Ω |∇u| N ) 1 N . The dual space is denoted W−1,N ′ , where N ′ is the Hölder conjugate of N , and has the associated norm ‖ · ‖∗. Denote strong convergence by “→”, weak convergence by “⇀” and convergence in the sense of measure (or distributions) as “⇀∗”. Unless otherwise denoted, integration is performed over the domain Ω. Specific constraints on e(x, u) and h(x) are described later, but we no...

In this paper we define the sequence space ∆v (X) = {x ∈ w : (∆v xk) ∈ X}, (m ∈ N) , where ∆v xk = ∑m i=0 (−1) ( m i ) xk+ivk+i and X is any sequence space. We give some relations related to this space. Furthermore we introduce the concept of ∆v −statistical convergence and give some inclusion relation between ∆v (wp)−convergence and ∆v −statistical convergence.

In this manuscript, we will study \({\tilde{o}}\)-convergence in (partially) ordered vector spaces and a kind of convergence space V. A V is called semi-order (in short space), if there exist an W operator T from into W. way, say that with respect to \(\{W, T\}\). net \(\{x_\alpha \}\subseteq V\) said be \({\{W,T\}}\)-order convergent \(x\in write \(x_\alpha \xrightarrow {\{W, T\}}x\)), wheneve...

We study homogenization by Γ-convergence of functionals of type Z Ω W “ x ε ,∇φ(x) ” dx, where Ω ⊂ RN is a bounded open set, φ ∈ W 1,p(Ω; Rm) and p > 1, when the 1-periodic integrand W : RN ×Mm×N → [0, +∞] is not of p-polynomial growth. Our homogenization technique can be applied when m = N and W has a singular behavior of type W (x, ξ) → +∞ as detξ → 0. However, our technique is not consistent...

Parameter tuning is a fundamental problem that has to be handled by any Big Data analytics system. Identifying the optimal model parameters is an interactive, human-in-the-loop process that requires many hours – if not days and months – even for experienced data scientists. We argue that the incapacity to evaluate multiple parameter configurations simultaneously and the lack of support to quick...

This paper presents a path-based traffic assignment algorithm for solving the static deterministic user equilibrium traffic assignment problem. It uses the concepts of the path shift-propensity factor and the sensitivity of path costs with respect to path flows in the flow update process, and is labeled as the slope-based path shift-propensity algorithm (SPSA). It seeks to enable faster converg...

In this paper, a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved without using Bruck’s result, see RE Bruck (Bruck 1981). This theorem is different from the recent strong convergence theorems due to S Matsushita and W Takahashi (Matsushita and Takahashi 2008) and HK Xu (Xu 2006).

The convergence properties of mixed-norm algorithms as i t applies to echo cancelers under general error criteria is derived for correlated and identically distributed inputs. The convergence analysis of this class of algorithms i s carried out using the linearization process of the error nonlinearities. Necessary and suficient conditions for convergence are derived for the independent input ca...

Aggregation-based multigrid with standard piecewise constant like prolongation is investigated. Unknowns are aggregated either by pairs or by quadruplets; in the latter case the grouping may be either linewise or boxwise. A Fourier analysis is developed for a model twodimensional anisotropic problem. Most of the results are stated for an arbitrary smoother (which fits with the Fourier analysis ...

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, N -dependent, choice of an optimizing parameter λ, which is an important feature of the method, the sequence of approximants ZN tends to Z with an error propor...