Synthesis of lupeol derivatives and their antileishmanial and antitrypanosomal activities

The natural product lupeol 1 was isolated from aerial parts of Vernonia scorpioides with satisfactory yield, which made it viable to be used as starting material in semisynthetic approach. Ten lupeol derivatives 2–11 were prepared by classical procedures. Including, five new esters derivatives 7–11, which were obtained by structural modifications in the isopropylidene fragment. All semisynthetic compounds and lupeol 1–11 were confirmed by ¹H NMR, ¹³C NMR and HRMS. Their antiprotozoal activity was evaluated in vitro against L. amazonensis and T. cruzi. Derivative 6 showed the best antitrypanosomal activity (IC₅₀ = 12.48 μg/mL) and the lowest cytotoxic derivative (CC₅₀ = 161.50 μg/mL). The mechanism of action of the most active derivatives (4, 6 and 11) is not dependent from the enzyme trypanothione reductase.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

A characterization of adding machine maps

Let f :X→X be a continuous map of a compact metric space to itself. We prove that f is topologically conjugate to an adding machine map if and only if X is an infinite minimal set for f and each point of X is regularly recurrent. Moreover, if X is an infinite minimal set for f and one point of X is regularly recurrent, then f is semiconjugate to an adding machine map.     

Searching for extensible Korobov rules

Extensible lattice sequences have been proposed and studied in [F.J. Hickernell, H.S. Hong, Computing multivariate normal probabilities using rank-1 lattice sequences, in: G.H. Golub, S.H. Lui, F.T. Luk, R.J. Plemmons (Eds.), Proceedings of the Workshop on Scientific Computing (Hong Kong), Singapore, Springer, Berlin, 1997, pp. 209–215; F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138; F.J. Hickernell, H.Niederreiter, The existence of good extensible rank-1 lattices, J. Complexity 19 (2003) 286–300]. For the special case of extensible Korobov sequences, parameters can be found in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C.Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138]. The searches made to obtain these parameters were based on quality measures that look at several projections of the lattice. Because it is often the case in practice that low-dimensional projections are very important, it is of interest to find parameters for these sequences based on measures that look more closely at these projections. In this paper, we prove the existence of “good” extensible Korobov rules with respect to a quality measure that considers two-dimensional projections. We also report results of experiments made on different problems where the newly obtained parameters compare favorably with those given in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138].     

Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

Incomplete data problems in X-ray computerized tomography

Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4     

Braids on surfaces and finite type invariants

We prove that there is no functorial universal finite type invariant for braids in Σ×I if the genus of Σ is positive. To cite this article: P. Bellingeri, L. Funar, C. R. Acad. Sci. Paris, Ser. I 338 (2004).