Supremum metric and relatively compact sets of fuzzy sets

The supremum metric D between fuzzy subsets of a metric space is the supremum of the Hausdorff distances of the corresponding level sets. In this paper some new criteria of compactness with respect to the distance D are given; they concern arbitrary fuzzy sets (see Theorem 7), fuzzy sets having no proper local maximum points (see Theorem 12) and, finally, fuzzy sets with convex sendograph (see Theorem 13). In order to compare results with a previous characterization of compactness of Diamond–Kloeden, the criteria will be expressed by equi-(left/right)-continuity. In the proofs a first author's purely topological criterion of D  -compactness and a variational convergence (called Γ-convergence) which was introduced by De Giorgi and Franzoni, are fundamental.     

An optimization of Chebyshev’s method

From Chebyshev’s method, new third-order multipoint iterations are constructed with their efficiency close to that of Newton’s method and the same region of accessibility.     

Smale’s point estimate theory for Newton’s method on Lie groups

We introduce the notion of the (one-parameter subgroup) γ-condition for a map f from a Lie group to its Lie algebra and establish α-theory and γ-theory for Newton’s method for a map f satisfying this condition. Applications to analytic maps are provided, and Smale’s α-theory and γ-theory are extended and developed. Examples arising from initial value problems on Lie group are presented to illustrate applications of our results.     

First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂ and CuGaSe₂, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂ and p-type Cu_1−xV_CuxAlS₂ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂-based PVSCs.