Optimization of the first Steklov eigenvalue in domains with holes: a shape derivative approach

The best Sobolev trace constant is given by the first eigenvalue of a Steklov-like problem. We deal with minimizers of the Rayleigh quotient ‖u‖² _H ¹ _(Ω) ²/‖u‖² _L ² _(∂Ω) for functions that vanish in a subset A⊂ Ω, which we call the hole. We look for holes that minimize the best Sobolev trace constant among subsets of Ω with prescribed volume. First, we find a formula for the first variation of the first eigenvalue with respect to the hole. As a consequence of this formula, we prove that when Ω is a ball the symmetric hole (a centered ball) is critical when we consider deformations that preserves volume but is not optimal. Finally, we prove that by the Finite Element Method we can approximate the optimal configuration and, by means of the shape derivative, we design an algorithm to compute the discrete optimal holes. Mathematics Subject Classification (2000) 35P15, 49K20, 49M25, 49Q10     

费-托合成Fe1-xO基熔铁催化剂的研究

 采用高温熔融法制备了用于费-托合成的Fe1-xO基熔铁催化剂,考察了其在n(H2)/n(CO)=2,温度573 K,压力1.4 MPa和空速为12?600 h-1下的催化性能. 结果表明,与Fe3O4基熔铁催化剂相比,Fe1-xO基熔铁催化剂具有较高的催化F-T合成反应的活性、较低的WGS反应选择性和较强的加氢能力. XRD结果表明,经F-T反应后的熔铁催化剂存在Fe5C2和Fe3O4两种物相,但Fe1-xO基熔铁催化剂中Fe5C2的晶粒尺寸小于Fe3O4基熔铁催化剂中Fe5C2的晶粒尺寸.     

Structural analysis of chiral complexes of palladium(0) with 15-membered triolefinic macrocyclic ligands

The complete structural analysis of the palladium complexes of the triolefinic macrocycles (E,E,E)-1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3,8,13-trienes, which featured from three identical to three different aryl groups, was achieved by performing X-ray diffraction studies, NMR spectroscopy, and other calculations. The stereochemical complexity is determined by the different isomers formed through complexation of the metal to one or other face of each of the three olefins involved. The palladacyclopropane formulation of the palladium-olefin interaction offers a clear picture of the stereogenicity of the olefin carbon atoms that are complexed to the metal. The energetically favorable isomers were identified in the solid-state and in solution by performing X-ray diffraction and NMR spectroscopic analysis, respectively.     

Argue to agree: A case-based argumentation approach

The capability of reaching agreements is a necessary feature that large computer systems where agents interoperate must include. In these systems, agents represent self-motivated entities that have a social context, including dependency relations among them, and different preferences and beliefs. Without agreement there is no cooperation and thus, complex tasks which require the interaction of agents with different points of view cannot be performed. In this work, we propose a case-based argumentation approach for Multi-Agent Systems where agents reach agreements by arguing and improve their argumentation skills from experience. A set of knowledge resources and a reasoning process that agents can use to manage their positions and arguments are presented. These elements are implemented and validated in a customer support application.     

Reducing power of simple polyphenols by electron-transfer reactions using a new stable radical of the PTM series, tris(2,3,5,6-tetrachloro-4-nitrophenyl)methyl radical

The synthesis and characterization of a new radical and its use for testing the antioxidant activity of polyphenols by electron transfer are reported. This new and stable species of magnetic nature, tris(2,3,5,6-tetrachloro-4-nitrophenyl)methyl (TNPTM) radical, has been characterized by electron paramagnetic resonance and its molecular structure determined by X-ray analysis. This new radical of the PTM (perchlorotriphenylmethyl) series, unlike 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical, is stable in conditions of hydrogen abstraction reactions. TNPTM radical is able to discriminate between the antioxidant activities of catechol and pyrogallol in hydroxylated solvent mixtures such as chloroform/methanol (2:1). These features determine the antioxidant/pro-oxidant character and the biological activities of natural and synthetic flavonoids.     

Identification of dimeric anthocyanins and new oligomeric pigments in red wine by means of HPLC-DAD-ESI/MSn

High-pressure liquid chromatography-diode array detector-electrospray ionisation/ion trap mass spectrometry (HPLC-DAD-ESI/MS(n)) analyses carried out in red wine fractions revealed the existence of dimeric anthocyanins (A-A(+)), previously detected in grape skin, and allowed the detection and identification, for the first time, of other derived oligomers. The structure of these compounds was characterised according to their MS(n)(n = 1-4) fragmentation patterns. The newly detected oligomers consisted of a flavanol, (epi)catechin or (epi)gallocatechin, linked through its C(4) position to the nucleophilic positions of the upper unit of a dimeric anthocyanin (F-A-A(+)). All the compounds contained malvidin as one of the anthocyanin subunits, whereas the other anthocyanin moiety could be either delphinidin, cyanidin, petunidin, peonidin or malvidin. With the fractionation method employed, the dimeric anthocyanins eluted in the same fractions as the monomeric anthocyanins. However, the new F-A-A(+) oligomers were found in the same fractions as F-A(+) dimers, which might indicate a structural similarity between both types of compounds. ESI/MS(n) analyses, coupled or not to HPLC, showed to be a useful and powerful tool for detecting and identifying these oligomers in wines, which usually elute from reversed-phase columns as humps and/or are overlapped by the peaks of other compounds. The detection of these oligomeric pigments in wine has provided more information about the complex pigments responsible for the elevation of the base line observed in the chromatograms of wines and has also revealed that oligomeric anthocyanins can take part in the reactions usually undergone by monomeric anthocyanins.     

Ligand-free copper-catalyzed regioselective C-2 arylation of imidazo[2,1-b]thiazoles

An effective, regioselective C-2 arylation of imidazo[2,1-b]thiazoles catalyzed by Cu(I) has been developed. This arylation proceeded smoothly without promotion of the ligands, and various functional (22 samples) groups were well tolerated. Preliminary mechanistic studies of this arylation are also reported.     

Multivariate analysis of the polyphenol composition of Tempranillo and Graciano red wines

Vitis vinifera L. cv Graciano is often used as a blending partner of Tempranillo based wines because it is considered to contribute significantly to the quality. The aim of this study is to discriminate between Tempranillo and Graciano monovarietal wines, and those made by the incorporation of 20% of Graciano variety in two different stages (at the end of malolactic fermentation and mixing the two grape varieties in the pre-fermentative maceration stage) of the winemaking process of the Tempranillo variety. To achieve this, supervised and unsupervised pattern recognition tools were applied to the data obtained in the study of the detailed polyphenolic composition, colour and other oenological parameters (143 variables). Patterns related to stages in the winemaking and ageing process, different wines and vintages can be observed using principal component analyses. Furthermore, linear discriminant analysis has been applied in order to characterise the wine samples. From the 143 variables, flavan-3-ols have exerted a profound influence on wine differentiation.