Approximate minima via the ekeland variational principle 1

In this paper several consequences derived by an equivalent version of the Ekeland variational principle are presented. In particular, a notion of an approximate minimum (for a function defined in a complete metric space), which improves an earlier one given by Attouch and Riahi, is discussed. This is obtained by considering truncations of the metric function     

Prediction of vicinal proton–proton coupling constants 3 J HH from density functional theory calculations

Vicinal coupling constants ³ J _HH have been calculated at the optimized geometries for a series of selected molecules with the aim of developing a practical procedure for predicting this kind of coupling. Calculations of couplings and optimizations of molecular geometries have been carried out at the DFT/B3LYP level using a moderate sized basis set. When the Fermi contact contributions to ³ J _HH calculated for 25 mono- and 23 1,1-di-substituted ethanes are multiplied by a factor of 0.904, the corresponding predicted couplings J ^pre are in good agreement with the experimental J ^exp couplings, with standard deviation σ of 0.10?Hz. When such a comparison is carried out for the remaining sets of molecules the σ deviation increases to 0.26?Hz for a dataset of 21 couplings from 11 monosubstituted cyclohexanes, to 0.19?Hz for a dataset of 40 couplings from 6 norbornane type molecules and to 0.25?Hz for a dataset of 54 couplings from 14 three-membered rings. For the complete dataset of 163 couplings the?σ?deviation amounts to 0.20?Hz. This figure is further reduced to 0.17?Hz by adding to the J ^pre coupling a small correction given by the term ?0.15cos?, depending on the dihedral angle ? between the coupled protons. A larger σ deviation of 0.31?Hz was reported for the best empirically parameterized extended Karplus equation. DFT J ^pre values could be further improved by more accurate calculations for the pertinent substituted ethane constituents of the molecule in question by applying a substituent effect model.     

Isolation and structural characterization of a non-diketopiperazine phytotoxin from a potato pathogenic Streptomyces strain

Two Streptomyces spp. strains responsible for potato common scab infections in Uruguay which do not produce diketopiperazines were identified through whole-genome sequencing, and the virulence factor produced by one of them was isolated and characterized. Phylogenetic analysis showed that both pathogenic strains can be identified as S. niveiscabiei, and the structure of the phytotoxin was elucidated as that of the polyketide desmethylmensacarcin using MS and NMR methods. The metabolite is produced in yields of ～200?mg/L of culture media, induces deep necrotic lesions on potato tubers, stuns root and shoot growth in radish seedlings, and is comparatively more aggressive than thaxtomin A. This is the first time that desmethylmensacarcin, a member of a class of compounds known for their antitumor and antibiotic activity, is associated with phytotoxicity. More importantly, it represents the discovery of a new virulence factor related to potato common scab, an economically-important disease affecting potato production worldwide.     

Characterization of mechanochemically synthesized lead selenide

Mechanochemical synthesis of lead selenide PbSe nanocrystals was performed by high-energy milling of lead and selenium powders in a planetary ball mill. The structure properties of synthesized lead selenide were characterized by XRD analysis that confirmed crystalline nature of PbSe nanocrystals. Calculated average size of PbSe crystallites was 37 nm. The methods of particle size distribution analysis, specific surface area measurement, SEM and TEM were used for the characterization of surface and morphology of PbSe nanocrystals. SEM analysis revealed agglomerates of PbSe particles. However, HRTEM analysis confirmed perfect stoichiometric PbSe cubes with NaCl structure as well. UV-VIS-NIR spectrophotometry was used to confirm the blue shift of the small particles occurring in the powder product obtained by the mechanochemical synthesis. Presented at the 8th Conference on Solid State Chemistry, Bratislava, Slovakia, 6–11 July 2008.     

On optimal stopping of multidimensional diffusions

This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the $d$-dimensional Wiener process. We first obtain some verification theorems for diffusions, based on the Green kernel representation of the value function. Specializing to the multidimensional Wiener process, we apply the Martin boundary theory to obtain a set of tractable integral equations involving only harmonic functions that characterize the stopping region of the problem in the bounded case. The approach is illustrated through the optimal stopping problem of a $d$-dimensional Wiener process with a positive definite quadratic form reward function.     

M?ssbauer study of contaminated soils by industrial activity in Paramonga city, Region Lima Provinces, Peru

In this work we characterize soils from the Paramonga city, Region Lima Provinces in Peru, which are contaminated by residual chemicals (Br, As and Sr) from sugar and paper industry in the city. Four samples were collected, labelled as S1, S2, S3 and S4 and analized by X-ray diffraction (XRD), energy-dispersive X-ray fluorescence (EDXRF) and M?ssbauer spectroscopy. For all the samples, the chemical analysis by EDXRF revealed the presence of Fe, Mn, Cu, Zn, K, Br, Sr. The XRD detected the presence of quartz as principal phase and copper sulfide and potassium magnesium as secondary phases. The M?ssbauer spectra at room temperature (RT) for all the samples exhibit sextets which reveal the presence of an iron oxide or hydroxide. The fitting M?ssbauer for both samples S1 and S4 have three doublets corresponding to iron in paramagnetic phases and a magnetic component of around 35.50?T corresponding to goethite, α-FeOOH. Sample S2 have two magnetic phases with internal fields of 37?T and 34.6?T which correspond to the goethite and other incorporated element in the structure. The sample S3 have three magnetic fields of H1?=?36.8?T, H2?=?33.6?T and H3?=?34.8?T which correspond to hydroxide iron, pyrrhotite and goethite respectively.     

Inner and outer estimates for the solution sets and their asymptotic cones in vector optimization

We use asymptotic analysis to develop finer estimates for the efficient, weak efficient and proper efficient solution sets (and for their asymptotic cones) to convex/quasiconvex vector optimization problems. We also provide a new representation for the efficient solution set without any convexity assumption, and the estimates involve the minima of the linear scalarization of the original vector problem. Some new necessary conditions for a point to be efficient or weak efficient solution for general convex vector optimization problems, as well as for the nonconvex quadratic multiobjective optimization problem, are established.     

CO2 in 1-butyl-3-methylimidazolium acetate. 2. NMR investigation of chemical reactions

The solvation of CO(2) in 1-butyl-3-methylimidazolium acetate (Bmim Ac) has been investigated by (1)H, (13)C, and (15)N NMR spectroscopy at low CO(2) molar fraction (mf) (x(CO(2)) ca. 0.27) corresponding to the reactive regime described in part 1 of this study. It is shown that a carboxylation reaction occurs between CO(2) and Bmim Ac, leading to the formation of a non-negligible amount (~16%) of 1-butyl-3-methylimidazolium-2-carboxylate. It is also found that acetic acid molecules are produced during this reaction and tend to form with elapsed time stable cyclic dimers existing in pure acid. A further series of experiments has been dedicated to characterize the influence of water traces on the carboxylation reaction. It is found that water, even at high ratio (0.15 mf), does not hamper the formation of the carboxylate species but lead to the formation of byproduct involving CO(2). The evolution with temperature of the resonance lines associated with the products of the reactions confirms that they have a different origin. The main byproduct has been assigned to bicarbonate. All these results confirm the existence of a reactive regime in the CO(2)-Bmim Ac system but different from that reported in the literature on the formation of a reversible molecular complex possibly accompanied by a minor chemical reaction. Finally, the reactive scheme interpreting the carboxylation reaction and the formation of acetic acid proposed in the literature is discussed. We found that the triggering of the carboxylation reaction is necessarily connected with the introduction of carbon dioxide in the IL. We argue that a more refined scheme is still needed to understand in details the different steps of the chemical reaction in the dense phase.     

A complete characterization of strong duality in nonconvex optimization with a single constraint

We first establish sufficient conditions ensuring strong duality for cone constrained nonconvex optimization problems under a generalized Slater-type condition. Such conditions allow us to cover situations where recent results cannot be applied. Afterwards, we provide a new complete characterization of strong duality for a problem with a single constraint: showing, in particular, that strong duality still holds without the standard Slater condition. This yields Lagrange multipliers characterizations of global optimality in case of (not necessarily convex) quadratic homogeneous functions after applying a generalized joint-range convexity result. Furthermore, a result which reduces a constrained minimization problem into one with a single constraint under generalized convexity assumptions, is also presented.