Stochastic comparisons for time transformed exponential models

Different sufficient conditions for stochastic comparisons between random vectors have been described in the literature. In particular, conditions for the comparison of random vectors having the same copula, i.e., the same dependence structure, may be found in Müller and Scarsini (2001). Here we provide conditions for the comparison, in the usual stochastic order sense and in other weaker stochastic orders, of two time transformed exponential bivariate lifetimes having different copulas. Some examples of applications are provided too.     

Analysis of Simulated Fluorescence Intensities Decays by a New Maximum Entropy Method Algorithm

A new algorithm for the Maximum Entropy Method (MEM) is proposed for recovering the lifetime distribution in time-resolved fluorescence decays. The procedure is based on seeking the distribution that maximizes the Skilling entropy function subjected to the chi-squared constraint χ ²?~?1 through iterative linear approximations, LU decomposition of the Hessian matrix of the lagrangian problem and the Golden Section Search for backtracking. The accuracy of this algorithm has been investigated through comparisons with simulated fluorescence decays both of narrow and broad lifetime distributions. The proposed approach is capable to analyse datasets of up to 4,096 points with a discretization ranging from 100 to 1,000 lifetimes. A good agreement with non linear fitting estimates has been observed when the method has been applied to multi-exponential decays. Remarkable results have been also obtained for the broad lifetime distributions where the position is recovered with high accuracy and the distribution width is estimated within 3 %. These results indicate that the procedure proposed generates MEM lifetime distributions that can be used to quantify the real heterogeneity of lifetimes in a sample.     

Solubility and Crystallizability: Facile Access to Functionalized π‐Conjugated Compounds with Chlorendylimide Protecting Groups

Functional π‐conjugated molecules are relevant for the preparation of new organic electronic materials with improved performance. However, their synthesis is often rendered difficult by their inherently low solubility, and the permanent attachment of solubilizing groups may change the properties of the material. Here, we introduced the chlorendylimidyl moiety as a new temporary protecting group for the straightforward large‐scale synthesis of protected quarter‐, sexi‐, octathiophene, and perylene bisimide diamine and dicarboxylic acid derivatives. The obtained chlorendylimides and chlorendylimidyl active esters were highly soluble in organic solvents, and optical spectroscopy confirmed the low tendency of the compounds to aggregate in solution. At the same time, they could be conveniently purified by recrystallization or precipitation. Single‐crystal X‐ray structures obtained for most compounds showed supramolecular motifs highlighting the role of the rigid, polychlorinated chlorendyl moieties in their crystallization. The obtained protected diamine and dicarboxylic acid derivatives were easily deprotected and converted into various amide‐substituted oligothiophenes and perylene bisimides that are of interest as new functional materials for organic electronic thin film or nanowire devices.     

Influence of the solvent and R groups on the structure of (carboranyl)R2PI2 compounds in solution. Crystal structure of the first iodophosphonium salt incorporating the anion [7,8-nido-C2B9H10]-

The influence of the electron-donor or electron-acceptor capacity of the R groups (R = (i)Pr, Ph, Et) and the solvent on the molecular geometry in solution of adducts of carboranylphosphanes [(carboranyl)(i)Pr2P, (carboranyl)Ph2P and (carboranyl)Et2P] with I2 in 1 : 1 ratios, has been studied in detail by 31P{1H} and 11B{1H} NMR spectroscopies. The more electron-accepting Ph groups make the (carboranyl)Ph2P less nucleophilic, thus stabilizing the I2 encapsulated neutral biscarboranylphosphane-diiodine adducts in solution, such as (carboranyl)Ph2PI-IPPh2(carboranyl), generating P---I-I---P motifs. Even in a polar solvent, such as EtOH, the arrangement is preserved. The expected basicity of these carboranylphosphanes is: (carboranyl)(i)Pr2P > (carboranyl)Et2P > (carboranyl)Ph2P. Thus, the comparatively higher basicity of (carboranyl)Et2P vs. (carboranyl)Ph(2)P facilitates a higher transfer of electron density to the I2 sigma*, generating the ionic species, [(carboranyl)Et2PI]+I-, even in low polar solvents, such as CH2Cl2 and toluene, with no degradation of the cluster. However, in EtOH, the formation of the anionic [7,8-nido-C2B(9)H10]- cluster takes place by removal of one boron atom from the closo cluster. The basicity of (carboranyl)(i)Pr(2)P should be the highest, superior to (carboranyl)Et2P. This is observed in the reaction of these carboranylphosphanes with I(2) in EtOH. Whereas the formation of P four-coordinated molecular "spoke" charge-transfer complexes, (carboranyl)(i)Pr2P-I-I, are suggested for (carboranyl)(i)Pr2P in low polarity solvents, ionic species are formed in ethanolic solutions, which deboronate in a few days, faster than (carboranyl)Et2P, to yield the zwitterionic species. This is attributed to the higher basicity of (carboranyl)(i)Pr2P vs. (carboranyl)Et2P. The X-ray crystal structure of [7-PI(i)Pr2-8-Ph-7,8-nido-C2B9H10], 2c, obtained from the reaction of 1-P(i)Pr2-2-Ph-closo-1,2-closo-C2B10H10 with I(2) in EtOH, confirms the formation of the zwitterion. These results prove that minor changes in the nature of the R substituents on the P atom in carboranylphosphanes, along with the solvent in which the reaction takes place, produce major alterations in the geometry of the (carboranyl)R2P-I-I species in solution, and in their possible further reactivity.     

Stereoselective NaN3-catalyzed halonitroaldol-type reaction of azetidine-2,3-diones in aqueous media

Azetidine-2,3-diones (alpha-oxo-beta-lactams) and bromonitromethane undergo coupling in aqueous media in the presence of catalytic amounts of sodium azide. The stereoselectivity of the process was generally good, proceeding with reasonable anti : syn ratios under substrate control. On this basis, a simple and fast protocol for the synthesis of the potentially bioactive 3-substituted 3-hydroxy-beta-lactam moiety has been developed. Besides, 2-azetidinone-tethered 1-halo-1-nitroalkan-2-ols are quite useful building blocks; for example, reactions of the above nitrobromohydrins provided spiranic and fused bicyclic-beta-lactams.     

Catalytic behavior of supported Pd catalysts in the selective hydrogenation of campholenic aldehyde to naturanol

Selective catalytic reduction of campholenic aldehyde to naturanol was investigated over Sn-and Fe-doped SiO₂, and Fe₂O₃-supported Pd catalysts. On Pd/SiO₂ and Pd-Sn/SiO₂ only saturated campholenic aldehyde is formed. Addition of Fe increases the C=O hydrogenation rate producing the corresponding unsaturated alcohol with a good selectivity. Also Fe₂O₃-supported catalysts were found to be more selective towards carbonyl hydrogenation. Addition of tin to Pd/Fe₂O₃ contributes to a further selectivity enhancement towards naturanol.     

Totally regio- and stereoselective behavior of mono- and diactivated cyclic alkenes in the Lu reaction: synthesis of enantiopure functionalized cyclopentanes

5-Alkoxyfuran-2(5H)-ones and their optically pure 3-p-tolylsulfinyl derivatives, synthetic equivalents of the acyclic esters, react with dipoles generated from allenoates and PPh(3) (Lu reaction), in a completely regioselective, pi-facial selective and endo-selective manner, yielding bicyclic adducts, which are easily converted into optically pure highly substituted cyclopentane derivatives.     

Carbonyl and nitrosyl diruthenium compounds: Crystal structure of [Ru2(O2CMe)(DPhF)3(CO)]BF4 · CH2Cl2 and its isomorphous nitrosyl analogue

The reaction of [Ru₂(O₂CMe)(DPhF)₃(H₂O)]BF₄ (DPhF = N,N′-diphenylformamidinate) with CO gas leads to [Ru₂(O₂CMe)(DPhF)₃(CO)]BF₄ (1), that is the first isolated carbonyl complex containing the Ru₂⁵⁺ unit. The nitrosyl analogue [Ru₂(O₂CMe)(DPhF)₃(NO)]BF₄ (2) is prepared by reaction of Ru₂Cl(O₂CMe)(DPhF)₃ with NOBF₄. However, the attempts to obtain the cyanide derivative by reaction of Ru₂Cl(O₂CMe)(DPhF)₃ or [Ru₂(O₂CMe)(DPhF)₃(H₂O)]BF₄ with NaCN were unsuccessful. The structure of compounds 1 · CH₂Cl₂ and 2 · CH₂Cl₂ are described. Both compounds are isomorphous. The magnetic measurements at variable temperature demonstrate that 1 is paramagnetic with one unpaired electron in all range of temperature, in contrast to the three unpaired electrons usually present in Ru₂⁵⁺ complexes. The analogous nitrosyl compound 2 is diamagnetic.     

CrCl2-promoted stereospecific and stereoselective alkyl- and silylcyclopropanation of alpha,beta-unsaturated amides

An efficient chromium-promoted alkyl- or silylcyclopropanation of alpha,beta-unsaturated amides is described. These reactions can be carried out on (E)- or (Z)-alpha,beta-enamides in which the C-C double bond is di-, or trisubstituted. This process takes place with total stereospecificity and the new stereogenic center is generated with high or total stereoselectivity. Some synthetic applications of the obtained silylcyclopropyl amides are also reported. Two mechanisms based on the generation of carbenoid or carbene complexes have been proposed to explain this cyclopropanation reaction.