Monotonic bounds in multistage mixed-integer stochastic programming

Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochastic multistage mixed integer linear programs. Chains of inequalities among the new quantities are provided in relation to the optimal objective value, the wait-and-see solution and the expected result of using the expected value solution. The computational complexity of the proposed lower and upper bounds is discussed and an algorithmic procedure to use them is provided. Numerical results on a real case transportation problem are presented.     

The infrared spectrum of DCCF in the 320–850 cm−1 region: bending states up to υ4+υ5 = 3

Infrared spectra of deuterated monofluoroacetylene, DCCF, have been recorded in the region between 320 and 850 cm^?1 at an effective resolution ranging from 0.0024 to 0.0031 cm^?1. In total, 6650 rotation vibration transitions were assigned to 37 bands involving the bending states with v₄ + v₅ and |l₄+l₅|, respectively, up to 3, allowing the characterisation of the ground state and of 18 vibrationally excited states. The vν₅ bending fundamental has been studied for the first time. In addition, the difference band v₃ ← v₄ has been detected and analysed. All the assigned transitions have been fitted simultaneously by adopting a model Hamiltonian that takes into account the vibration and rotation l?type resonances. Rotational transitions in the ground and in bending excited states reported in the literature have been included in the global analysis. The set of 57 derived spectroscopic parameters reproduces 6130 infrared and 90 microwave and millimetre?wave transitions satisfactorily with root mean square values of 5.3 × 10^?4 cm^?1 and 77 kHz, respectively.     

Enzyme-mediated synthesis of EEHP and EMHP,useful pharmaceutical intermediates of PPAR agonists

A new scaleable synthetic route to the title compounds has been developed. The reaction pathway is based on the α-chymotrypsin-catalysed hydrolysis of the racemic ethyl 2-ethoxy-3-(p-methoxyphenyl)propanoate or of the racemic ethyl 2-methoxy-3-(p-methoxyphenyl)propanoate to give the corresponding resolved (S)-esters with excellent ee. The acids were easily separated from the (S)-esters by a simple acid–base work-up. The overall yields of 1 and 2 were 16% and 17%, respectively.     

The structure of higher order C60-fullerene-γ-cyclodextrin complexes

C₆₀ inclusion complexes in γ-cyclodextrin are studied by molecular mechanics and semi-empirical methods with the aim of comparing measured and calculated induced circular dichroism (ICD) spectra. Low energy geometries of the complexes are generated by Monte Carlo simulations, also accounting for solvation effects by an aqueous environment. The ICD spectrum of the complex is then obtained from an exciton model based on semi-empirical calculations of the transition energies and the corresponding transition moments. Highly symmetric, tightly bound complexes of two γ-cyclodextrins and buckminsterfullerene are found as the most probable structures. The main bands of the experimentally derived ICD spectrum are assigned to the excitation transitions of the chromophore and are discussed in comparison to calculations on the magnetic circular dichroism (MCD) spectrum of C₆₀.     

Isotope shift in the proton magnetic resonance of deuterated methanes

The isotope shift in the proton magnetic resonance of deuteromethanes has been examined. By the use of Pople's formula for the chemical shift, it has been shown that the effect is due to vibronic coupling from the bending modes S₄. The chemical shift was evaluated under the assumption that the hydrogen population is linearly dependent on the 2S character of the bonded carbon hybrid. Satisfactory agreement between theoretical and experimental results was obtained.     

Mechanism of formation of organic carbonates from aliphatic alcohols and carbon dioxide under mild conditions promoted by carbodiimides. DFT calculation and experimental study

Dicyclohexylcarbodiimide (CyN=C=NCy, DCC) promotes the facile formation of organic carbonates from aliphatic alcohols and carbon dioxide at temperatures as low as 310 K and moderate pressure of CO2 (from 0.1 MPa) with an acceptable rate. The conversion yield of DCC is quantitative, and the reaction has a very high selectivity toward carbonates at 330 K; increasing the temperature increases the conversion rate, but lowers the selectivity. A detailed study has allowed us to isolate or identify the intermediates formed in the reaction of an alcohol with DCC in the presence or absence of carbon dioxide. The first step is the addition of alcohol to the cumulene (a known reaction) with formation of an O-alkyl isourea [RHNC(OR')=NR] that may interact with a second alcohol molecule via H-bond (a reaction never described thus far). Such an adduct can be detected by NMR. In alcohol, in absence of CO2, it converts into a carbamate and a secondary amine, while in the presence of CO2, the dialkyl carbonate, (RO)2CO, is formed together with urea [CyHN-CO-NHCy]. The reaction has been tested with various aliphatic alcohols such as methanol, ethanol, and allyl alcohol. It results in being a convenient route to the synthesis of diallyl carbonate, in particular. O-Methyl-N,N'-dicyclohexyl isourea also reacts with phenol in the presence of CO2 to directly afford for the very first time a mixed aliphatic-aromatic carbonate, (MeO)(PhO)CO. A DFT study has allowed us to estimate the energy of each intermediate and the relevant kinetic barriers in the described reactions, providing reasonable mechanistic details. Calculated data match very well the experimental results. The driving force of the reaction is the conversion of carbodiimide into the relevant urea, which is some 35 kcal/mol downhill with respect to the parent compound. The best operative conditions have been defined for achieving a quantitative yield of carbonate from carbodiimide. The role of temperature, pressure, and catalysts (Lewis acids and bases) has been established. As the urea can be reconverted into DCC, the reaction described in this article may further be developed for application to the synthesis of organic carbonates under selective and mild conditions.