Transfinite interpolation on the medians of a triangle and best L 1-approximation

Let be a triangle in and let be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on The interpolants are of type f(₁)+g(₂)+h(₃), where (₁,₂,₃) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L¹-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C³().Received: 17 December 2003     

Localization of the electromagnetic field in the vicinity of gold nanoparticles: Surface modification of different substrates

Theoretical predictions and experimental results for nanosized modification of metal (Au), semiconductor (Si), or dielectric (soda lime glass) substrates using near-electromagnetic field enhancement in the vicinity of gold nanoparticles are presented. The near field properties for the system consisting of an isolated gold nanoparticle or nanoparticle aggregate deposited on the substrates, which is irradiated by electromagnetic wave, are investigated using Finite Difference Time Domain Simulation technique. The influence of the substrate material on the near field distribution characteristics is predicted. The results reveal that the field on the substrate surface is enhanced in the three investigated cases, but its spatial distribution and magnitude depend on the substrate material. In the case of the metal and semiconductor substrate the enhanced near field is strongly localized in the vicinity of the contact point with the particle, in an area with diameter smaller than the particle's one. The intensity of the enhanced field on the glass is more than an order of magnitude lower than the case of using silicon substrate. The properties of the near field on the substrate surface also depend on the particle arrangement. For a two-dimensional gold nanoparticle array, when the particles are closely arrayed, the intensity of the enhanced field on the substrate surface is minimal. With the increase of the interparticle distance the near field intensity increases. The validity of the obtained theoretical results is confirmed experimentally.     

On the Convexity of the KdV Hamiltonian

Motivated by perturbation theory, we prove that the nonlinear part \({H^{*}}\) of the KdV Hamiltonian \({H^{kdv}}\), when expressed in action variables \({I = (I_{n})_{n \geqslant 1}}\), extends to a real analytic function on the positive quadrant \({\ell^{2}_{+}(\mathbb{N})}\) of \({\ell^{2}(\mathbb{N})}\) and is strictly concave near \({0}\). As a consequence, the differential of \({H^{*}}\) defines a local diffeomorphism near 0 of \({\ell_{\mathbb{C}}^{2}(\mathbb{N})}\). Furthermore, we prove that the Fourier-Lebesgue spaces \({\mathcal{F}\mathcal{L}^{s,p}}\) with \({-1/2 \leqslant s \leqslant 0}\) and \({2 \leqslant p < \infty}\), admit global KdV-Birkhoff coordinates. In particular, it means that \({\ell^{2}_+(\mathbb{N})}\) is the space of action variables of the underlying phase space \({\mathcal{F}\mathcal{L}^{-1/2,4}}\) and that the KdV equation is globally in time \({C^{0}}\)-well-posed on \({\mathcal{F}\mathcal{L}^{-1/2,4}}\).     

Repeated passing principle for propagation in optical resonators

In this paper we make comparison between a well-known theoretical model of light propagation through racetrack resonator and experimentally obtained results. Observed differences are studied and some original modifications are made in the existing model so as to achieve better alignment with experiment. The influence of several geometric parameters on racetrack’s response is used for further adjustments to be performed. This procedure opens up the possibility to estimate the free spectral range and resonant wavelength for different geometric parameters and consequently to predict resonator functionality and working conditions, as well as functionality of complex photonic devices based on resonant structures.     

INTERPOLATION WITH RESTRICTED ARC LENGTH

AbstractFor given data (t_i,y_i),i=0, 1,…,n,0=t_0相似文献   

PAMAMOS: The first commercial silicon‐containing dendrimers and their applications

The world of dendrimers presently encompasses several thousands of publications, including scientific papers and patents, several hundreds of different compositions, but only a few commercially available families of products (i.e. polyamidoamines (PAMAMs), until recently polypropyleneimines, and phosphorus‐containing dendrimers) This is the story of PAMAMOS, which recently became the first commercially available silicon‐containing dendrimers, and how we journeyed from our initial idea to the point of their commercialization. It focuses on three unique features of these new dendrimers: their ability to form precisely defined nano‐structured, honeycomb‐like, 2D or 3D networks; the amazing usefulness of these networks for the preparation of a variety of nanocomplexes and nancomposites; and some of the new vistas that these materials open up for engineering nanotechnology applications. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2755–2773, 2006     

A contribution to the elemental profile of the leaf samples of newly developed Cabernet Franc varieties

The elemental profile of the leaf samples of three Cabernet Franc clone candidates recently developed in Serbia (Nos. 02, 010 and 012) obtained in the last phase of clonal selection was examined within this study by ICP-OES. Optimal content of Al, Fe, Cu and Zn, the metals well known for their links with a number of neurodegenerative disorders including Alzheimer’s disease, has actually highlighted the potential of the leaf sample No. 10 to afford a novel food supplement of natural origin possessing well balanced metal ingredients. Furthermore, lower content of some other elements (Cr, Mn, Ni and Pb) thoroughly supports such a claiming. Finally, the most favourable K/Na ratio observed for the aforementioned sample points out its likely cardioprotectivity. However, two other Cabernet Franc clone candidates might also be recommended for breeding in the same or similar viticultural conditions, since all obtained values were below toxic ones for human consumption.     

DNA binding and antitumor activities of zinc(II) complexes with some S-alkenyl derivatives of thiosalicylic acid

Transition Metal Chemistry - Two zinc(II) complexes with S-alkenyl derivatives of thiosalicylic acid as ligands have been synthesized and characterized by microanalysis, IR, 1H and 13C NMR...     

Stable isotopes of H,C and N in mice bone collagen as a reflection of isotopically controlled food and water intake*

²H/¹H ratios in animal biomass reflect isotopic input from food and water. A 10-week controlled laboratory study raised 48 mice divided in two generations (8 mothers Mus musculus and their offspring). The mice were divided into four groups based on the combination of ²H, ¹³C, ¹⁵N-enriched and non-enriched food and water. Glycine, the most common amino acid in bone collagen, carried the ²H, ¹³C, ¹⁵N-isotopic spike in food. ANOVA data analysis indicated that hydrogen in food accounted for ～81?% of the hydrogen isotope inventory in collagen whereas drinking water hydrogen contributed ～17?%. Air humidity contributed an unspecified amount. Additionally, we monitored ¹³C and ¹⁵N-enrichment in bone collagen and found strong linear correlations with the ²H-enrichment. The experiments with food and water indicate two biosynthetic pathways, namely (i) de novo creation of non-essential amino acids using hydrogen from water, and (ii) the integration of essential and non-essential amino acids from food. The lower rate of isotope uptake in mothers’ collagen relative to their offspring indicates incomplete bone collagen turnover after ten weeks. The variance of hydrogen stable isotope ratios within the same cohort may limit its usefulness as a single sample proxy for archaeological or palaeoenvironmental research.