On the convergence of a local third order shock capturing method for hyperbolic conservation laws

The Piecewise Polynomial Harmonic Method (PPHM) is a local third order accurate shock capturing method for hyperbolic conservation laws. In this paper, theoretical stability properties are presented. Using these properties, the convergence of the scheme for scalar conservation laws is obtained. A direct adaptation of these results should be used to derive the convergence of the PHM (Marquina, SIAM J. Sci. Comput. 15(4), 892–915, 1994). Finally, the method is tested in several classical problems in order to explore its numerical behavior.     

On an algorithm to adapt spline approximations to the presence of discontinuities

Numerical Algorithms - Interpolatory splines are usually useful to reconstruct data that present certain regularity. This paper is devoted to the construction and analysis of a new technique that...     

Access to Enantiopure Advanced Intermediates en Route to Madangamines

The synthesis of enantiopure ABCE and ABCD tetracyclic advanced intermediates en route to madangamine alkaloids and studies for the construction of the triunsaturated 15-membered D ring of madangamine B and the saturated 13-membered D ring of madangamine E are reported.     

Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms

This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms. As soon as a nonlinear scheme can be written as a specific perturbation of a linear and convergent subdivision scheme, we show that if some contractivity properties are satisfied, then stability and convergence can be achieved. This approach is applied to various schemes, which give different new results. More precisely, we study uncentered Lagrange interpolatory linear schemes, WENO scheme (Liu et al., J Comput Phys 115:200–212, 1994), PPH and Power-P schemes (Amat and Liandrat, Appl Comput Harmon Anal 18(2):198–206, 2005; Serna and Marquina, J Comput Phys 194:632–658, 2004) and a nonlinear scheme using local spherical coordinates (Aspert et al., Comput Aided Geom Des 20:165–187, 2003). Finally, a stability proof is given for the multiresolution transform associated to a nonlinear scheme of Marinov et al. (2005).     

Kinetic studies on the oxidation of ascorbic acid by technetium(VII)

The pertechnetate ion oxidizes ascorbic acid in strong acid medium to form red species. A reaction mechanism has been developed which correctly predicts all the experimental facts. The results obtained support the postulate according to which the red species corresponds to a complex formed between Tc(V) and dehydroascorbic acid. The rate constants and Arrhenius parameters have been investigated.     

Anion Directed Self‐Assembly of One‐Dimensional and Two‐Dimensional Coordination Polymers Containing Bridging Diphosphine Ligands

The reactions of 1,2‐bis(diphenylphosphanyl)ethane (dppe) with different silver(I) salts facilitated the formation of 1D and 2D coordination polymers, [Ag(dppe)(OAc)]_n · nH₂O ( 1 ) and [Ag₂(dppe)_1.5(NO₃)₂]_n ( 2 ), respectively. The complexes were characterized by elemental analysis, ATR‐IR spectroscopy, ¹H NMR, ¹³C NMR, and ³¹P NMR spectroscopy, and single‐crystal X‐ray diffraction. Structural analysis revealed that complex 1 exhibits a 1D infinite wavy structure, in which each silver(I) ion is bridged by dppe ligands. Structure 2 has a 2D topologically promising architecture that displays a 6.6.6 graphitic net, which corresponds to hnd topology. The nitrate ions and dppe ligands are in a μ₂ bridging mode and support the formation of this net. Moreover, significant π–π interactions between the phenyl rings in the apertures of (6,3) grid stabilized complex 2 .     

A general synthetic route to enantiopure cis-fused perhydrocycloalka[c]pyridines from phenylglycinol-derived lactams

A synthetic route to enantiopure piperidines bearing a five-, six-, or seven-membered carbocyclic ring cis-fused on the c side of the heterocycle from a common phenylglycinol-derived δ-lactam is reported. Key steps are (i) a cyclocondensation reaction of (R)-phenylglycinol with a racemic γ-oxoester in a process that involves a dynamic kinetic resolution; (ii) a highly stereoselective conjugate addition of an organocuprate to an unsaturated δ-lactam; and (iii) a ring-closing olefin metathesis.     

A new synthetic entry to pentacyclic Strychnos indole alkaloids

Cyclization of the thionium ion generated by DMTSF treatment of dithioacetal 15 constitutes a new synthetic entry to the pentacyclic ring system of Strychnos indole alkaloids.