Subadditive approaches in integer programming

Linear programming duality is well understood and the reduced cost of a column is frequently used in various algorithms. On the other hand, for integer programs it is not clear how to define a dual function even though the subadditive dual theory has been developed a long time ago. In this work we propose a family of computationally tractable subadditive dual functions for integer programs. We develop a solution methodology that computes an optimal primal solution and an optimal subadditive dual function. We present computational experiments, which show that the new algorithm is tractable.     

Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.     

Insights into the Catalytic Activity of Nitridated Fibrous Silica (KCC‐1) Nanocatalysts from 15N and 29Si NMR Spectroscopy Enhanced by Dynamic Nuclear Polarization

Fibrous nanosilica (KCC‐1) oxynitrides are promising solid‐base catalysts. Paradoxically, when their nitrogen content increases, their catalytic activity decreases. This counterintuitive observation is explained here for the first time using ¹⁵N‐solid‐state NMR spectroscopy enhanced by dynamic nuclear polarization.     

A Multi‐Addressable Switch Based on the Dimethyldihydropyrene Photochrome with Remarkable Proton‐Triggered Photo‐opening Efficiency

A series of photochromic derivatives based on the trans‐10b,10c‐dimethyl‐10b,10c‐dihydropyrene (DHP, “closed form”) skeleton has been synthesized and their photoisomerization leading to the corresponding cyclophanediene (CPD, “open form”) isomers has been investigated by UV/Vis and ¹H NMR spectroscopies. Substitution of the DHP core with electron‐withdrawing pyridinium groups was found to have major effects on the photoisomerization efficiency, the most remarkable examples being to enhance the quantum yield of the opening reaction and to allow fast and quantitative conversions at much lower radiant energies. This effect was rationalized by theoretical calculations. We also show that the reverse reaction, that is, going from the open form to the closed form, can be electrochemically triggered by oxidation of the CPD unit and that the photo‐opening properties of pyridine‐substituted DHPs can be efficiently tuned by protonation, the system behaving as a multi‐addressable molecular switch. These multi‐addressable photochromes show promise for the development of responsive materials.     

A Cross-Entropy Approach to the Estimation of Generalized Linear Multilevel Models

In this article, we use the cross-entropy method for noisy optimization for fitting generalized linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to the benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the article, the method is used to model the probability of firm exits in the healthcare industry in Italy. Supplemental materials are available online.     

Influence of the purification process on the stability of <Emphasis Type="Italic">Jatropha curcas</Emphasis> biodiesel

The aim of this work was to evaluate the influence of the purification process on the stability of Jatropha curcas biodiesel. The biodiesel was obtained using a variety of purification processes: three wet methods with different drying processes (vacuum oven, conventional oven and anhydrous sodium sulfate) and one dry method (purification with adsorbent magnesium silicate). Biodiesel was characterized through the analysis of carbon residue, acidity index, infrared and gas chromatography. The composition J. curcas oil indicated 56.3 % of unsaturated fatty acids and 43.7 % of saturated fatty acids. Jatropha oil presented high quantity of saturated acids, which are less susceptible at oxidation. The biodiesel sample that was chemically purified (PUsq) presented better purity, indicating be the process more efficient in remove the residues of synthesis. Thermogravimetric curves of purified biodiesel by wet method, PUsq, with chemical drying using anhydrous sodium sulfate, and PUsv, with vacuum drying, showed the highest initial decomposition temperatures, indicating higher thermal stability. The carbon residue and infrared analyses suggested that contamination by catalyst residue is a determining factor in reduction of the oxidative stability of biodiesel. The oxidative stability was evaluated using Rancimat and pressure differential scanning calorimetry. Biodiesel samples showing better oxidative stability were purified using PUsq and PUsv, which obtained stability of 6 h using the Rancimat technique, the minimum limit set by Brazilian legislation, without the addition of antioxidant, suggesting that these methods least influenced the stability of biodiesel.     

Diprotodecarboxylation Reactions of 3,4-Dialkoxythiophene-2,5-dicarboxylic Acids Mediated by Ag2CO3 and Microwaves

An efficient and rapid method is reported to obtain 3,4-dialkoxythiophenes from 3,4-dialkoxythiophene-2,5-dicarboxylic acids through a diprotodecarboxylation reaction with Ag₂CO₃/AcOH as a catalytic system and microwave heating in dimethylsulfoxide (DMSO) as solvent. This methodology lets us obtain for the first time good performance with thiophenes bearing strong electron-donating groups such as alkoxides. This methodology eliminates the usage of harmful quinoline as solvent, as well as the long reaction times typically used (12–18 h) to obtain the 3,4-dialkoxythiophenes. The reaction of 7 diacids showed good yields (60–89%) following 20 min of microwave heating in a temperature range of 120–150 °C.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Highly diastereoselective synthesis of new heterolignan-like 6,7-methylendioxy-tetrahydroquinolines using the clove bud essential oil as raw material

The diastereoselective synthesis toward novel heterolignan-like 2-aryl-4-(4-hydroxy-3-methoxyphenyl)-6,7-methylendioxy-1,2,3,4-tetrahydroquinolines using for the first time clove bud essential oil as a renewable material was carried out. The synthetic protocol consisted of the hydrodistillation of dried flower buds, the solid base-catalyzed isomerization of the obtained essential oil enriched with eugenol in order to give isoeugenol and its participation, as a chemical reagent (dienophile) in the BF₃·OEt₂-catalyzed three component Povarov reaction, without previous purification. Final products were obtained as racemic mixtures of new trans-2,4-diaryl-r-3-Me-1,2,3,4-tetrahydroquinolines in moderate to good yields.     

Synthesis of (Z)-organylthioenynes using KF/Al2O3/solvent as recyclable system

PEG-400 and glycerol were successfully used as recyclable solvents for the synthesis of several organylthioenynes in good to excellent yields and high selectivity using solid supported catalyst (KF/Al₂O₃). This easy, general and improved method furnishes the corresponding alkenyl sulfides preferentially with Z configuration. The catalytic system and the glycerol or PEG-400 can be reused up to three times without previous treatment with comparable activity.