Bernstein-type operators on a triangle with all curved sides

We construct and analyze Bernstein-type operators on triangles with curved sides, their product and Boolean sum. We study the interpolation properties and approximation accuracy. Using the modulus of continuity we also study the remainders of the corresponding approximation formulas. Finally, there are given some particular cases and numerical examples.     

Competition between Birch reduction and fluorine abstraction in reactions of hydrated electrons (H2O)n(-) with the isomers of di- and trifluorobenzene

The reactions of the isomers of di- and trifluorobenzene with hydrated electrons (H(2)O)(n)(-), n = 19-70, have been studied by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. While Birch reduction, i.e. H atom transfer to the aromatic ring, was observed for all studied isomers, a strong dependence on the substitution pattern was observed for fluorine abstraction. Nanocalorimetry combined with G3 calculations are used to analyze the thermochemistry of the reactions. Fluorine abstraction is at least 100 kJ mol(-1) more exothermic than Birch reduction, yet the latter is the dominant reaction pathway for all three difluorobenzene isomers. Fluorine abstraction and Birch reduction face activation barriers of comparable magnitude. The relative barrier height is sensitive to the substitution pattern. Birch reduction occurs selectively with 1,3- and 1,4-difluorobenzene in a nanoscale aqueous environment.     

Identifying Codes in Line Graphs

An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbors within the code. We study the edge‐identifying code problem, i.e. the identifying code problem in line graphs. If denotes the size of a minimum identifying code of an identifiable graph G, we show that the usual bound , where n denotes the order of G, can be improved to in the class of line graphs. Moreover, this bound is tight. We also prove that the upper bound , where is the line graph of G, holds (with two exceptions). This implies that a conjecture of R. Klasing, A. Kosowski, A. Raspaud, and the first author holds for a subclass of line graphs. Finally, we show that the edge‐identifying code problem is NP‐complete, even for the class of planar bipartite graphs of maximum degree 3 and arbitrarily large girth.     

MPQ-trees for the Orthogonal Packing Problem

Given a set of rectangular items of different sizes and a rectangular container, the aim of the bi-dimensional Orthogonal Packing Problem (OPP-2 for short) is to decide whether there exists a non-overlapping packing of the items in this container. The rotation of items is not allowed. In this paper we present a new exact algorithm for solving OPP-2, based upon the characterization of solutions using interval graphs proposed by Fekete and Schepers. The algorithm uses MPQ-trees, which were introduced by Korte and M?hring to recognize interval graphs.     

Bernstein-type Operators on a Triangle with One Curved Side

We construct Bernstein-type operators on a triangle with one curved side. We study univariate operators, their product and Boolean sum, as well as their interpolation properties, the order of accuracy (degree of exactness, precision set) and the remainder of the corresponding approximation formulas. We also give some illustrative examples.     

Adaptive wavelet methods for the stochastic Poisson equation

We study the Besov regularity as well as linear and nonlinear approximation of random functions on bounded Lipschitz domains in ? ^d . The random functions are given either (i) explicitly in terms of a wavelet expansion or (ii) as the solution of a Poisson equation with a right-hand side in terms of a wavelet expansion. In the case (ii) we derive an adaptive wavelet algorithm that achieves the nonlinear approximation rate at a computational cost that is proportional to the degrees of freedom. These results are matched by computational experiments.     

Fixed point results for multivalued contractions on ordered gauge spaces

The purpose of this article is to present fixed point results for multivalued E _≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].      

Spectroscopic mode mapping of resonant plasmon nanoantennas

We present spatially resolved spectral mode mapping of resonant plasmon gap antennas using two-photon luminescence microspectroscopy. The obtained maps are in good agreement with 3D calculations of the antenna modes. The evolution of the modal field with wavelength, both in the gap and along the two coupled gold nanowires forming the antenna, is directly visualized. At resonance, the luminescence for the gap area is enhanced at least 80 times and a comparison with the antenna extremities shows a dynamical charge redistribution due to the near-field coupling between the two arms.