Uniqueness of non-negative solutions for a semipositone problem with concave nonlinearity

We study a semilinear Dirichlet problem where the nonlinearlity is monotone, negative at zero (Semipositone), and concave. We assume that the outer boundary of the region is convex and show that for large values of a parameter there can be only one non-negative solution. We show that such a solution is positive in the region.     

Chiral polycyclic ketones via desymmetrization of dihaloolefins

3-Chloronorbornenone (R)-1a (98% ee) was obtained from trichloronorbornene 5 in two steps by the in situ generation of dichloronorbornadiene 2a with t-BuOK and desymmetrization with (-)-ephedrine, followed by hydrolysis with PPTS. The generality of this desymmetrization with (-)-ephedrine was tested with dibromonorbornadiene 2c and other substituted dichloronorbornadienes.     

Molecular rotors as simple models to study amide NH-aromatic interactions and their role in the folding of peptide-like structures

The conformational behavior of designed macrocyclic naphthalenophanes (1a,b and 2a,b) derived from amino acids (Phe and Val) has been used for studying NH...pi interactions. The cycles having 16- and 17-membered rings showed a dynamic process within the NMR time scale, produced by the flipping of the aromatic naphthalene moiety with respect to the macrocyclic main plane. We used the temperature dependence of 1H NMR to obtain activation parameters of the energetic barrier for the process (variable temperature NMR and line shape analysis). The rate of the movement clearly depends on the macrocyclic ring size and, more interestingly, on the nature of the peptidomimetic side chain, the energetic barrier being higher for the compounds bearing aromatic side chains. A largely negative entropic contribution to the free energy of activation was observed, with clear differences due to the side chain nature. Molecular modeling studies suggest that the aromatic rings interact with intramolecularly H-bonded amide NH groups, protecting them from solvation and thus leading to a larger unfavorable activation entropy. This NH...pi interaction has been exploited for the preparation of new systems (1c and meso-1b) with designed conformational preferences, in which aromatic rings tend to fold over amide NH groups. Thus, these minimalistic molecular rotors have served us as simple model systems for the study of NH...pi interactions and their implication in the folding of peptide-like molecules.     

Novel approaches for the synthesis and activation of thio- and selenoglycoside donors

Alkyl thio-, phenyl seleno-, and phenyl thioglycosides can be prepared through short synthetic sequences based on the generation of glycosyl iodides as versatile intermediates. In addition, a novel cheap combined system (stoichiometric NBS and catalytic Bi(OTf)3) has been developed for rapid and efficient activation of a wide variety of thio- and selenoglycoside donors.     

The first entry to 5,6-dihydroxy-3-mercaptoindole, 5-hydroxy-3-mercaptoindole and their 2-carbomethoxy derivatives by a mild thiocyanation/reduction methodology

The hitherto unknown 5,6-dihydroxy-3-mercaptoindole (4a) and its 2-carbomethoxy derivative (4b), as well as the analogous 5-hydroxy 3-mercaptoindoles, have been conveniently obtained as O,S-acetyl derivatives 3a-d by thiocyanation of the corresponding acetoxyindoles 1a-d with the NH₄SCN/oxone system followed by SmI₂ reduction and acetylation.     

Direct stereocontrolled synthesis of polyoxygenated hydrobenzofurans and hydrobenzopyrans from p-peroxy quinols

An acidic-basic tandem catalytic process on p-peroxy quinols with hydroxy alkyl chains at C-4 allowed the one-pot synthesis of hydrobenzofuran and hydrobenzopyran tricyclic epoxides. In this transformation, two new cycles and four new stereogenic centers are created in a highly stereocontrolled manner. The usefulness of the strategy is illustrated with the first total synthesis and structural revision of natural product Cleroindicin D.     

Photocatalytic patterning and modification of graphene

TiO(2)-based photocatalysis has been widely used to decompose various organic pollutants for the purpose of environmental protection. Such a "green" photochemical process can ultimately degrade organic compounds into CO(2) and H(2)O under ambient conditions. We demonstrate here its extended application on the engineering of single- or few-layer graphene. Using a patterned TiO(2) photomask, we have achieved various photochemical tailorings of graphene, including ribbon cutting, arbitrary patterning on any substrate, layer-by-layer thinning, and localized graphene to graphene oxide conversion. UV-visible spectroscopic studies indicate that the photogenerated, highly reactive ·OH radicals work as sharp chemical scissors. Being a solution-free, cost-effective, scalable, and easy handling technique, the presented photocatalytic patterning and modification approach allows for the versatile design and fabrication of graphene-based devices and circuits, compatible with current microelectronic technology, as demonstrated by this fabricated all-carbon field effect transistor (FET) array.     

A bisferrocene-benzobisimidazole triad as a multichannel ditopic receptor for selective sensing of hydrogen sulfate and mercury ions

The bisferrocene-benzobisimidazole triad behaves as a selective redox and fluorescent chemosensor for HSO(4)(-) and Hg(2+) ions, exhibiting an easily detectable signal change in both the redox potential of the ferrocene/ferrocinium redox couple and in the emission band which is red-shifted (Δλ = 10-13 nm) and enhanced in intensity (Chelation Enhanced Fluorescence, CHEF = 486-225) upon complexation with these ions, in EtOH solutions.     

Stochastic comparisons of distorted variability measures

In this paper, we consider the dispersive order and the excess wealth order to compare the variability of distorted distributions. We know from Sordo (2009a) that the excess wealth order can be characterized in terms of a class of variability measures associated to the tail conditional distribution which includes, as a particular measure, the tail variance. Given that the tail conditional distribution is a particular distorted distribution, a natural question is whether this result can be extended to include other classes of variability measures associated to general distorted distributions. As we show in this paper, the answer is yes, by focusing on distorted distributions associated to concave distortion functions. For distorted distributions associated to more general distortions, the characterizations are stated in terms of the stronger dispersive order.