Uniqueness and existence results for ordinary differential equations

We establish some uniqueness and existence results for first-order ordinary differential equations with constant-signed discontinuous nonlinear parts. Several examples are given to illustrate the applicability of our work.     

The vertex separator problem: a polyhedral investigation

The vertex separator (VS) problem in a graph G=(V,E) asks for a partition of V into nonempty subsets A, B, C such that there is no edge between A and B, and |C| is minimized subject to a bound on max{|A|,|B|}. We give a mixed integer programming formulation of the problem and investigate the vertex separator polytope (VSP), the convex hull of incidence vectors of vertex separators. Necessary and sufficient conditions are given for the VSP to be full dimensional. Central to our investigation is the relationship between separators and dominators. Several classes of valid inequalities are investigated, along with the conditions under which they are facet defining for the VSP. Some of our proofs combine in new ways projection with lifting.In a companion paper we develop a branch-and-cut algorithm for the (VS) problem based on the inequalities discussed here, and report on computational experience with a wide variety of (VS) problems drawn from the literature and inspired by various applications.Research supported by the National Science Foundation through grant #DMI-0098427 and by the Office of Naval Research through contract N00014-97-1-0196Research supported by the Brazilian agencies FAPESP (grant 01/14205–6), CAPES (grant BEX 04444/02–2) and CNPq (grants 302588/02–7 and Pronex 664107/97–4)     

Acyl‐Directed ortho‐Borylation of Anilines and C7 Borylation of Indoles using just BBr3

Indoles are privileged heterocycles found in many biologically active pharmaceuticals and natural products. However, the selective functionalization of the benzenoid moiety in indoles in preference to the more reactive pyrrolic unit is a significant challenge. Herein we report that N‐acyl directing groups enable the C7‐selective C?H borylation of indoles using just BBr₃. This transformation shows some functional‐group tolerance and notably proceeds with C6 substituted indoles. The directing group can be readily removed in situ and the products isolated as the pinacol boronate esters. Acyl‐directed electrophilic borylation can be extended to carbazoles and anilines with excellent ortho selectivity. 4‐amino‐indoles are amenable to this process, with acyl group installation and directed electrophilic C?H borylation enabling selective formation of C5‐BPin‐indoles.     

A Study of Graphene‐Based Copper Catalysts: Copper(I) Nanoplatelets for Batch and Continuous‐Flow Applications

The use of graphene derivatives as supports improves the properties of heterogeneous catalysts, with graphene oxide (GO) being the most frequently employed. To explore greener possibilities as well as to get some insights into the role of the different graphenic supports (GO, rGO, carbon black, and graphite nanoplatelets), we prepared, under the same standard conditions, a variety of heterogeneous Cu catalysts and systematically evaluated their composition and catalytic activity in azide–alkyne cycloadditions as a model reaction. The use of sustainable graphite nanoplatelets (GNPs) afforded a stable Cu^I catalyst with good recyclability properties, which are compatible with flow conditions, and able to catalyze other reactions such as the regio‐ and stereoselective sulfonylation of alkynes (addition reaction) and the Meerwein arylation (single electron transfer process).     

Synthesis of 2-N,N-dimethylaminomethyl-2,3,3a,12b-tetrahydrodibenzo-[b,f]furo[2,3-d]oxepin derivatives as potential anxiolytic agents

New synthesis approaches that have led to a series of novel tetrahydrodibenzo[b,f]furo[2,3-d]oxepin derivatives are described. According to preliminary data these novel tetracycles can be useful intermediates for the preparation of potential new therapeutic agents.     

Fluorescent Photoinduced Electron Transfer (PET) Sensors for Anions; From Design to Potential Application

This mini review highlights the synthesis and photophysical evaluation of anion sensors, for nonaqueous solutions, that have been developed in our laboratories over the last few years. We have focused our research mainly on developing fluorescent photoinduced electron transfer (PET) sensors based on the fluorophore-spacer-anion receptor principle using several anthracene (emitting in the blue) and 1,8-naphthalimide (emitting in the green) fluorophores, with the aim of targeting biologically and industrially relevant anions such as acetates, phosphate and amino acids, as well as halides such as fluoride. The receptors and the fluorophore are separated by a short methyl or ethyl spacer, where the charge neutral anion receptors are either aliphatic or aromatic urea (or thiourea) moieties. For these, the anion recognition is through hydrogen bonding, yielding anion:receptor complexes. Such bonding gives rise to enhanced reduction potential in the receptor moieties which causes enhancement in the rate of PET quenching of the fluorophore excited state from the anion:receptor moiety. This design can be further elaborated on by incorporating either two fluorophores, or urea/thiourea receptors into the sensor structures, using anthracene as a fluorophore. For the latter design, the sensors were designed to achieve sensing of bis-anions, such as di-carboxylates or pyrophosphate, where the anion bridged the anthracene moiety. In the case of the naphthalimide based mono-receptor based PET sensors, it was discovered that in DMSO the sensors were also susceptible to deprotonation by anions such as F⁻ at high concentrations. This led to substantial changes in the absorption spectra of these sensors, where the solution changed colour from yellow/green to deep blue, which was clearly visible to the naked eye. Hence, some of the examples presented can act as dual fluorescent-colorimetric sensors for anions. Further investigations into this phenomenon led to the development of simple colorimetric sensors for fluorides, which upon exposure to air, were shown to fix carbon dioxide as bicarbonate.     

Light scattering by magnetic excitons in (FeMn)F2

The transitions between the low lying crystal field split states A_1g and B_1g of the Fe²⁺ ions in pure FeF₂ and in the mixed antiferromagnet Fe_1-xMn_xF₂ have been investigated with Raman light scattering. From the Raman polarization rules the lines have been identified as arising from the magnetic excitons associated with the transitions. The energy and the line-width of the strongest line are studied as a function of the concentration x. From the energy measurement we estimate that the single ion anisotropy parameter D of the Fe²⁺ ions varies from 6.46 cm^-1 in pure FeF₂ to 8.03 cm^-1 in MnF₂: Fe.     

Asymmetric aza-Henry reactions from N-p-tolylsulfinylimines

[reaction: see text] N-Sulfinylimines derived from aromatic or aliphatic aldehydes and ketones react with nitromethane and NaOH in a highly diastereoselective manner under mild conditions. In the presence of TBAF, the reaction rates are strongly increased and the stereoselectivity is inverted. This method provides enantiomerically pure beta-nitroamines derived from enolizable aldimines and ketimines, which so far are hardly accessible by aza-Henry reactions.