Synthesis and crystal structure of hexakis(N-methylimidazole) iron(II) pyridine-2-sulfonate

The compound [Fe(C₄H₆N₂)₆][C₅H₄NSO₃]₂ crystallized in the monoclinic space group, P2₁/n with unit cell parameters: a = 13.676(3), b = 8.345(2), c = 18.663(4) Å, = 106.40(3)° and Z = 2. The title compound consists of a [Fe(C₄H₆N₂)₆]⁺² hexacoordinated iron(II) cation and two C₅H₄NSO^– ₃ anions. In the cation the iron atom is coordinated to six N-methylimidazole imine nitrogen atoms in a distorted octahedral arrangement. The N1,N5,N1ⁱ,N5ⁱ atoms are coplanar and the iron lies in this plane.     

New proof of the Calabi-Bernstein theorem

By means of a local integral formula on a maximal surface, which involves the hyperbolic angle between the unit normal vector field and a fixed timelike direction, we give a new proof of the parametric Calabi-Bernstein theorem. A suitable modification of the integral formula gives an independent proof to the non-parametric case of this result.     

A method for obtaining transitive approximations of a binary relation

A binary relation R does not always possess the desirable property of transitivity. Consequently, this needs to be imposed artificially by deviating as little as possible from R. In this paper, three approaches to transitive approximation are analyzed within a common distance-based framework: exterior (transitive closure), interior (openings or maximal transitive sub-relations contained in R) and mixed (transitive fittings) approximation. Additionally, we propose a method for obtaining all these transitive approximations. The method is based on a distance function optimization framework that leads to straightforward goal programming models.     

Nonminimal gravitational coupling: The spectrum of cosmic solutions

We present a complete analysis of the set of homogeneous and isotropic cosmological solutions generated by a vector field coupled nonminimally to gravity. As a consequence of this analysis we can interpret our universe as (classical) fluctuations in the infinite past of unstable Minkowskian space-time.     

Mass spectrometry guided in situ proteolysis to obtain crystals for X-ray structure determination

A strategy for increasing the efficiency of protein crystallization/structure determination with mass spectrometry has been developed. This approach combines insights from limited proteolysis/mass spectrometry and crystallization via in situ proteolysis. The procedure seeks to identify protease-resistant polypeptide chain segments from purified proteins on the time-scale of crystal formation, and subsequently crystallizing the target protein in the presence of the optimal protease at the right relative concentration. We report our experience with 10 proteins of unknown structure, two of which yielded high-resolution X-ray structures. The advantage of this approach comes from its ability to select only those structure determination candidates that are likely to benefit from application of in situ proteolysis, using conditions most likely to result in formation of a stable proteolytic digestion product suitable for crystallization.     

Forecasting cancellation rates for services booking revenue management using data mining

Revenue management (RM) enhances the revenues of a company by means of demand-management decisions. An RM system must take into account the possibility that a booking may be canceled, or that a booked customer may fail to show up at the time of service (no-show). We review the Passenger Name Record data mining based cancellation rate forecasting models proposed in the literature, which mainly address the no-show case. Using a real-world dataset, we illustrate how the set of relevant variables to describe cancellation behavior is very different in different stages of the booking horizon, which not only confirms the dynamic aspect of this problem, but will also help revenue managers better understand the drivers of cancellation. Finally, we examine the performance of the state-of-the-art data mining methods when applied to Passenger Name Record based cancellation rate forecasting.     

Uranium and phosphate behavior in the vadose zone of a fertilized corn field

Phosphate fertilizers contain approximately 200 mg^.kg^-1 of uranium. The uranium and phosphate can move through the vadose zone and reach groundwater. Therefore, the knowledge of the ways in which these two elements are distributed, their partition relationships and their mobility behavior is of great interest. In order to study the latter, suction cup samplers, intended to collect soil water at different depths, were installed in an experimental site in a high plain of Mexico, where corn is cultivated and phosphate fertilizers are systematically applied. It was observed that the vadose zone contains high concentrations of uranium (1-50 mg^.kg^-1) and phosphates (22-33 mg^.kg^-1), which decrease at greater depths. Uranium concentration in the soil water varies between 10 and 3 mg^.l^-1 and phosphates between 1 and 0.3 mg^.l^-1. Their evolution throughout the profile of the vadose zone is determined by the decrease in concentrations, due to the physico-chemical processes involved.     

Thermo‐oxidative degradation of HDPE as a function of its crystalline content

The composition, the thermal properties, and the kinetics of the thermo‐oxidative degradation of high‐density polyethylene (HDPE) were studied as a function of the increasing crystalline fraction, which resulted from the selective extraction of the amorphous part, through digestion by immersion in fuming nitric acid (HNO₃) for different periods of time. The chemical and thermodynamic changes in HDPE, brought about by digestion in nitric acid for different periods of time, are discussed. Changes in the chemistry and microstructure of the HDPE, as a function of acid treatment for different periods of time, were studied using infra‐red spectroscopy (FTIR), gel permeation chromatography (GPC), and thermal analysis (DSC and TGA), as well as scanning electron microscopy (SEM). These studies were carried out as a function of the extracted amorphous fraction of HDPE samples via digestion in HNO₃. These studies showed that in the first stages of the acid chemical attack, the amorphous part first undergoes a chemical modification and then dissolves into the strong acid medium. The total crystalline fraction apparently decreases during the first stages of the chemical attack and then increases as the amorphous part is extracted. TGA results show that as the selective extraction of the amorphous part occurs, there is a displacement of the thermo‐oxidative degradation toward higher temperatures. The kinetics of the thermo‐oxidative degradation as a function of the extraction of the amorphous part was followed according to the Horowitz‐Metzger method, and it was found that as the concentration of the crystalline fraction increases, the activation energy for the thermo‐oxidative degradation increases. SEM studies show that the extraction of the amorphous part does not affect the size of the crystalline lamellar thickness of HDPE. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1906–1915, 2009