A Modular Class of Fluorescent Difluoroboranes: Synthesis,Structure, Optical Properties,Theoretical Calculations and Applications for Biological Imaging

Ten borylated bipyridines (BOBIPYs) have been synthesized and selected structural modifications have been made that allow useful structure–optical property relationships to be gathered. These systems have been further investigated using DFT calculations and spectroscopic measurements, showing blue to green fluorescence with quantum yields up to 41 %. They allow full mapping of the structure to determine where selected functionalities can be implemented, to tune the optical properties or to incorporate linking groups. The best derivative was thus functionalised with an alkyne linker, which would enable further applications through click chemistry and in this optic, the stability of the fluorophores has been evaluated.     

Abstract Riemann integrability and measurability

We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be computed as an improper classical Riemann integral of the measures of its spectral sets under some weak continuity conditions which in fact characterize the integral representation.     

Organocatalytic asymmetric michael addition of aldehydes to beta-nitroacroleine dimethyl acetal

[Structure: see text] The organocatalytic asymmetric Michael addition of aldehydes to beta-nitroacroleine dimethyl acetal has been studied in detail. The reaction took place with excellent yields and high stereoselectivities when a chiral beta-amino alcohol such as L-prolinol was employed as the catalyst, leaving a formation of highly functionalized enantioenriched compounds containing two differentiated formyl groups together with a nitro moiety.     

Self‐Assembled Submonolayer of β‐Cyclodextrins on Gold Electrode for the Selective Determination of 4‐Aminobiphenyl

The formation of an inclusion complex between 4‐aminobiphenyl (4‐AB) and β‐cyclodextrin molecules (β‐CD), allows the use of thiolated β‐CDs as chemi‐adsorbed material on a Au electrode as a self‐assembled submonolayer for the selective square wave voltammetric determination of 4‐AB. The submonolayer was characterized by reductive desorption and an association constant of 1.2×10⁴ L/mol was obtained. The optimization of variables yielded a linear dependence of ip/4‐AB concentration in the range of 10^?5 to 10^?4 mol/L. The selectivity of the method was evaluated in the presence of other aromatic amines obtaining better results with the modified electrode. This methodology was applied to the voltammetric determination of 4‐AB in wastewater samples.     

The averaging method and the persistence of attractors

The theorems that are presented in this paper, are a contribution to the foundations of the averaging method for ordinary differential equations. They involve the study of the persistent features of vector fields, under non autonomous perturbations of mean value zero. The problem of obtain ing qualitative information from the study of the averaged equation is considered and theorems that give new conditions to guarantee the uniform validitv of the approximation over the time interval [ 0.∞), are proved. A general icsult on the persistence of attractors is presented. The analysis uses in a fundamental way, a generalization of the notion of a solution stable under persistent disturbances. The proofs do not require special behavior of the linearized system and the results obtained are not only local, but give relevant information about the persistence of domains of attraction.     

Determination of brominated diphenyl ethers (from mono- to hexa- congeners) in indoor dust by pressurised liquid extraction with in-cell clean-up and gas chromatography–mass spectrometry

This study presents a selective pressurised liquid extraction (PLE) and gas chromatography–mass spectrometry/mass spectrometry method for the determination of brominated diphenyl ethers (BDEs) in indoor dust. Selective PLE consisted of the addition of Florisil mixed with the sample in order to perform an in-cell clean-up. This approach provided a cleaner and almost colourless extract, ready to be injected in the gas chromatograph. The PLE conditions were studied using an experimental design, firstly a 4 × 3 × 2 multifactor categorical design to screen sorbent, solvent and temperature and then a central composite design to optimise sorbent mass, temperature and time. Finally, the number of extraction cycles was studied. The selected conditions were 4 g of Florisil all mixed with the sample and no additional clean-up sorbent layer, 1:1 n-hexane-dichloromethane, 60% flush volume, 40 °C, 1,500 psi, 2-min static time and one cycle. The proposed method allowed accurate determination of BDEs, with recovery values between 82% and 101% and detection limits between 0.06 and 0.24 ng g⁻¹. It also has advantages over other existing methods in terms of simplicity, automation, analysis time and solvent consumption.     

Influence of polarity on the scalability and reproducibility of solvent-free microwave-assisted reactions

Organic reactions performed in the absence of solvent in domestic ovens without appropriate temperature control are generally considered as not reproducible, particularly when different instruments are used. For this reason, reproducibility has historically been one of the major issues associated with Microwave-Assisted Organic Synthesis (MAOS) especially when domestic ovens are involved. The lack of reproducibility limits the general applicability and the scale up of these reactions. In this work several solvent-free reactions previously carried out in domestic ovens have been translated into a single-mode microwave reactor and then scaled up in a multimode oven. The results show that most of these reactions, although not considered as reproducible, can be easily updated and applied in microwave reactors using temperature-controlled conditions. Furthermore, computational calculations can assist to explain and/or predict whether a reaction will be reproducible or not.     

A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron

A study was made of the global minimization of a general quasiconcave function on a convex polyhedron. This nonconvex problem arises in economies of scale environments and in alternative formulations of other well-known problems, as in the case of bilinear programming.Although not very important in our final results, a local minimum can be easily obtained. However, a major aspect is the existence of two families of lower bounds on the optimal functional value: one is provided by non-linear programming duality, the other is derived from a lexicographic ordering of basic solutions which allows the use of relaxation concepts. These results were exploited in a finite algorithm for obtaining the global minimum whose initial implementation has had encouraging performance.     

An approximate functional Radon-Nikodym theorem

We prove that for two linear and positive functionals (not necessarily Daniell)J andI on a lattice unitary algebraB of functions such thatJ is absolutely continuous with respect toI, one can expressJ as follows: , where (v _m)m is a fixed sequence inB, for allf inB. This result is the “functional” similar of a previous deep result due to C. Fefferman. The comments and the counterexamples which we are introducing show that the main result (i.e sequential approximation) cannot be improved.