Mixed integer nonlinear programming tools: a practical overview

We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties.     

Formation of copper(I)-templated [2]rotaxanes using ��click�� methodology: influence of the base, the thread and the catalyst

Three new copper(I)-assembled [2]rotaxanes incorporating the same macrocycle and different axes containing a bipy, a phen or a terpy have been synthesized thanks to CuAAC reaction for attaching the stoppers. The influence of the nature of the base used for the stoppering reaction was investigated on the formation of the bipy-containing rotaxane. The yield of the [2]rotaxane synthesis was increased when using a phen as a coordinating unit in the thread with [Cu(CH₃CN)₄](PF₆) as catalyst. The strong influence of the nature of the catalyst was clearly evidenced for the formation of the terpy rotaxane, increasing the yield of the stoppering reaction from 0 to 95% by just substituting the Cu(I) catalyst. Finally, the best conditions found for our systems are the use of Na₂CO₃ as a base and Cu(tren??)Br as a catalyst.     

Indirect Study of the 2H(d,p)3H and 2H(d,n)3He Reactions at Astrophysical Energies via the Trojan Horse Method

The ²H(d,p)³H and ²H(d,n)³He reactions have been indirectly studied by means of the Trojan Horse Method applied to the quasi-free ²H(³He, p³H)¹H?²H(³He, n³He)¹H reaction at 18?MeV of beam energy. This is the first experiment where the spectator (here ¹H) has been detected in coincidence with the charged participant, avoiding the limitations of standard neutron detectors. The d ? d relative energy has been measured from 1.5?MeV down to 2?keV, at center of mass angles from 40° to 170°. Indirect angular distributions are compared with the direct behaviour in the overlapping regions.     

Aromaticity and electronic delocalization in all-metal clusters with single, double, and triple aromatic character

A series of monocyclic planar inorganic compounds with single, double, and triple (anti)aromatic character has been studied. The electron delocalization and aromaticity of these compounds have been assessed by means of two-center and multicenter electronic delocalization indices and their ??-, ??-, and ??-components. Results show that these indices are excellent predictors of the ??-, ??-, and ??-aromatic character of all-metal and semimetal clusters.     

Ochres from rituals of prehistoric human funerals at the Toca do Enoque site, Piau��, Brazil

The archaeological site known as Toca do Enoque (geographical coordinates, 09° 14?? 65.3?? S 43° 55?? 62.5?? W) is a rock shelter located in the Serra das Andorinhas (Serra das Confusões National Park), rural area of the city of Guaribas, state of Piauí, Brazil. Several rupestrian paintings (anthropomorphic and zoomorphic motifs along with some pure graphisms), predominantly in red, are found on the sandstone walls. Charcoals, lithic materials, necklaces with teeth, animal bones, gastropod shells, ochres and human skeletons (dated from 6,220 ± 40 to 6,610 ± 40 years before present, BP) were identified in recent excavations in this shelter. Red and yellow ochre samples were collected from prehistoric funeral structures and analyzed with powder X-ray diffractometry, Fourier-transform infrared spectroscopy and ⁵⁷Fe transmission Mössbauer spectroscopy at 298 K and 80 K. Mössbauer data indicate that the red ochre do contain predominantly hematite (??-Fe₂O₃) whereas goethite (??-FeOOH) is the major mineral in the yellow ochre.     

Hereditary quasirandom properties of hypergraphs

Thomason and Chung, Graham and Wilson were the first to systematically investigate properties of quasirandom graphs. They have stated several quite disparate graph properties — such as having uniform edge distribution or containing a prescribed number of certain subgraphs — and proved that these properties are equivalent in a deterministic sense.     

The constructive characterization of (��,?)-edge-connected digraphs

We give a constructive characterization for (??, ?)-edge-connected digraphs, proving a conjecture of Frank.