Localized electropolymerization on oxidized boron-doped diamond electrodes modified with pyrrolyl units

This paper describes the functionalization of oxidized boron-doped diamond (BDD) electrodes with N-(3-trimethoxysilylpropyl)pyrrole (TMPP) and the influence of this layer on the electrochemical transfer kinetics as well as on the possibility of forming strongly adhesive polypyrrole films on the BDD interface through electropolymerization. Furthermore, localized polymer formation was achieved on the TMPP-modified BDD interface using the direct mode of a scanning electrochemical microscope (SECM) as well as an electrochemical scanning near-field optical microscope (E-SNOM). Depending on the method used polypyrrole dots with diameters in the range of 1-250 microm are electrogenerated.     

Blind separation of piecewise stationary non-Gaussian sources

We address independent component analysis (ICA) of piecewise stationary and non-Gaussian signals and propose a novel ICA algorithm called Block EFICA that is based on this generalized model of signals. The method is a further extension of the popular non-Gaussianity-based FastICA algorithm and of its recently optimized variant called EFICA. In contrast to these methods, Block EFICA is developed to effectively exploit varying distribution of signals, thus, also their varying variance in time (nonstationarity) or, more precisely, in time-intervals (piecewise stationarity). In theory, the accuracy of the method asymptotically approaches Cramér–Rao lower bound (CRLB) under common assumptions when variance of the signals is constant. On the other hand, the performance is practically close to the CRLB even when variance of the signals is changing. This is demonstrated by comparing our algorithm with various methods that are asymptotically efficient within ICA models based either on the non-Gaussianity or the nonstationarity. The benefit of our algorithm is demonstrated by examples with real-world audio signals.     

A fractional isoperimetric problem in the Wiener space

We introduce a notion of fractional perimeter in an abstract Wiener space and show that half-spaces are the only volume-constrained minimisers.     

On Well-Posedness of 2D Dissipative Quasi-Geostrophic Equation in Critical Mixed Norm Lebesgue Spaces

We establish local and global well-posedness of the 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces. The result demonstrates the persistence of the anisotropic behavior of the initial data under the evolution of the 2D dissipative quasi-geostrophic equation. The phenomenon is a priori nontrivial due to the nonlocal structure of the equation. Our approach is based on Kato's method using Picard's iteration, which can be adapted to the multi-dimensional case and other nonlinear non-local equations. We develop time decay estimates for solutions of fractional heat equation in mixed norm Lebesgue spaces that could be useful for other problems.     

Singular solutions for the constant Q-curvature problem

This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature.     

Hyperpositive non-linear effects: enantiodivergence and modelling

The chiral ligand N-methylephedrine (NME) was found to catalyse the addition of dimethylzinc to benzaldehyde in an enantiodivergent way, with a monomeric and a homochiral dimeric complex both catalysing the reaction at a steady state and giving opposite product enantiomers. A change in the sign of the enantiomeric product was thus possible by simply varying the catalyst loading or the ligand ee, giving rise to an enantiodivergent non-linear effect. Simulations using a mathematical model confirmed the possibility of such behaviour and showed that this can lead to situations where a reaction gives racemic products, although the system is composed only of highly enantioselective individual catalysts. Furthermore, depending on the dimer''s degree of participation in the catalytic conversion, enantiodivergence may or may not be observed experimentally, which raises questions about the possibility of enantiodivergence in other monomer/dimer-catalysed systems. Simulations of the reaction kinetics showed that the observed kinetic constant k_obs is highly dependent on user-controlled parameters, such as the catalyst concentration and the ligand ee, and may thus vary in a distinct way from one experimental setup to another. This unusual dependency of k_obs allowed us to confirm that a previously observed U-shaped catalyst order vs. catalyst loading-plot is linked to the simultaneous catalytic activity of both monomeric and dimeric complexes.

An asymmetric reaction consisting of competing monomeric and dimeric catalysts may explain enantiodivergent non-linear effects.     

A Preorganized Hydrogen-Bonding Motif for the Molecular Recognition of Carbohydrates

The choice between adaptive and preorganized architectures, or of the most effective hydrogen bonding groups to be selected, are dilemmas that supramolecular chemists must address in designing synthetic receptors for such a challenging guest as carbohydrates. In this paper, structurally related architectures featuring two alternative hydrogen bonding motifs were compared to ascertain the structural and functional origin of their binding differences and the advantages that can be expected in monosaccharide recognition. A set of structurally related macrocyclic receptors were prepared, and their binding properties were measured by NMR and ITC techniques in chloroform vs a common saccharidic target, namely, the β-octyl glycoside of D-glucose. Results showed that the diaminocarbazolic motif, recently reported as the constituting unit of highly effective receptors for saccharides in water, is a superior hydrogen bonding motif compared to the previously described diaminopyrrolic motif, which was successfully employed in molecular recognition of carbohydrates in polar organic solvents, due to intrinsic structural and functional factors, rather than to hydrophobic contributions. In addition, the occurrence of a rare example of a thermodynamic template effect exerted by the beta-glucoside has been ascertained, enhancing the synthesis outcome of the otherwise low yielding preparation of the described macrocyclic receptors.     

Computational insights about the dynamic behavior for the inclusion process of deprotonated and neutral aspirin in β-cyclodextrin

A high-efficiency microwave irradiation (MW) assisted protocol was proposed to synthesize series SPE-β-CD with specific degree of substitution (DS) in the sodium hydroxide solution. This protocol provided an eco-friendly way to modify the cyclodextrins with bulky sulfopropyl substituent on the purpose of avoiding organic solvents and high quantities of thermal energy. Temperature and energy distribution became more uniform under the new method accordingly. Therefore, not only the reaction time reduced significantly from over 20 h to a few hours, but also the DS increased up according to ¹H NMR spectroscopy, MS and elemental analysis results. Most importantly, the effects of reaction parameters on DS were compared both under MW method and conventional heating method, and were sufficiently studied to guarantee the aforementioned results could be better reproduced and DS of products could become more specific through the synthesis process. Products structures were characterized by FT-IR, DSC, and ¹³C NMR spectroscopy.     

A second-order blind source separation method for bilinear mixtures

In this paper, we are interested in the problem of Blind Source Separation using a Second-order Statistics (SOS) method in order to separate autocorrelated and mutually independent sources mixed according to a bilinear (BL) model. In this context, we propose a new approach called Bilinear Second-order Blind Source Separation, which is an extension of linear SOS methods, devoted to separate sources present in BL mixtures. These sources, called extended sources, include the actual sources and their products. We first study the statistical properties of the different extended sources, in order to verify the assumption of identifiability when the actual sources are zero-mean and when they are not. Then, we present the different steps performed in order to estimate these actual centred sources and to extract the actual mixing parameters. The obtained results using artificial mixtures of synthetic and real sources confirm the effectiveness of the new proposed approach.     

Modulating the electronic properties of porphyrinoids: a voyage from the violet to the infrared regions of the electromagnetic spectrum

This paper examines the preparation of tailor-made azaporphyrins and analogues exhibiting their Q-bands in several particular and predetermined regions of the electromagnetic spectrum. The applications of phthalocyanines, the possibility of preparing novel related porphyrinoids with different colour properties and, consequently, new emerging applications, are discussed.