Besov regularization,thresholding and wavelets for smoothing data

Smoothing of data is a problem very important for many applications ranging from 1-D signals (e.g., speech) to 2-D and 3-D signals (e.g., images). Many methods exist in the literature for facing the problem; in the present paper we point our attention on regularization. We shall treat regularization methods in a general framework which is well suited for wavelet analysis; in particular we shall investigate on the relation existing between thresholding methods and regularization. We shall also introduce a new regularization method (Besov regularization), which includes some known regularization and thresholding methods as particular cases. Numerical experiments based on some test problems will be performed in order to compare the performance of some methods of smoothing data.

AMS (MOS) Subject Classifications: 65R30, 41A60.     

New Results on Rational Approximation

Results in Mathematics - First asymptotic relations of Voronovskaya-type for rational operators of Shepard-type are shown. A positive answer in some senses to a problem on the pointwise...     

Synthesis and conformational studies of peptidomimetics containing a new bifunctional diketopiperazine scaffold acting as a beta-hairpin inducer

A practical synthesis of a new bifunctional diketopiperazine (DKP) scaffold 1, formally derived from the cyclization of L-aspartic acid and (S)-2,3-diaminopropionic acid, is reported. DKP-1 bears a carboxylic acid and an amino functionalities in a cis relationship, which have been used to grow peptide sequences. Tetra-, penta-, and hexapeptidomimetic sequences were prepared by solution-phase peptide synthesis (Boc strategy). Conformational analysis of these derivatives was carried out by a combination of 1H NMR spectroscopy, IR spectroscopy, CD spectroscopy, and computer modeling, and reveals the formation of beta-hairpin mimics involving 10-membered and 18-membered H-bonded rings and a reverse turn of the growing peptide chain.     

The Revival of Enantioselective Perfluoroalkylation – Update of New Synthetic Approaches from 2015–2022

Over the last years, methods devoted to the synthesis of asymmetric molecules bearing a perfluoroalkylated chain have been limited in number. Among them, only a few can be used on a large variety of scaffolds. This microreview aims at summarizing these recent advances in enantioselective perfluoroalkylation (−CF₃, −CF₂H, −C_nF_2n+1) and highlights the need for new enantioselective methods to easily synthesize chiral fluorinated molecules which would be useful for the pharmaceutical and agrochemical industries. Some perspectives are also mentioned.     

Silica nanoparticles for fluorescence sensing of Zn(II): exploring the covalent strategy

Silica nanoparticles (about 15 nm diameters), which contain a derivative of 6-methoxy-8-(p-toluensulfonamido)-quinoline (TSQ) as a Zn(II) fluorescent probe covalently linked to the silica network, were prepared and studied as Zn(II) fluorescent chemosensors. The systems selectively detect Zn(II) ions in water rich solutions with a submicromolar sensitivity: 0.13 microM concentrations of Zn(II) can be measured with the only interference of Cu(II) and Cd(II) ions. Compared with free TSQ, the nanoparticles based systems have the advantage that they can be employed in aqueous solutions without aggregation problems while at the same time, they maintain a similar Zn(II) affinity and sensing ability. Addition of a second, substrate insensitive, fluorophore to the particles leads to the realization of a ratiometric sensor.     

The role of different soil sample digestion methods on trace elements analysis: a comparison of ICP-MS and INAA measurement results

The measurement of trace-element concentration in soil, sediment and waste, is generally a combination of a digestion procedure for dissolution of elements and a subsequent measurement of the dissolved elements. “Partial” and “total” digestion methods can be used in environmental monitoring activities. To compare measurement results obtained by different methods, it is crucial to determine and to maintain control of the bias of the results obtained by these methods. In this paper, ICP-MS results obtained after matrix digestion with modified aqua regia (HCl+HNO₃+H₂O₂) method and two “total” digestion methods (microwave aqua regia+HF and HNO₃+HF) are compared with those obtained by instrumental neutron activation analysis, a non-destructive analytical method for the determination of the total mass concentrations of inorganic components in environmental matrices. The comparison was carried out on eight agricultural soil samples collected in one test area and measured by k₀-INAA and ICP-MS to determine As, Co, Cr, Sb and Zn mass concentration. The bias of results for As, Cd, Co, Cr, Cu, Ni, Pb, Sb and Zn of the three digestion methods were assessed using selected measurement standards. This paper highlights that the digestion procedure is an integral part of the measurement and can affect the measurement result in environmental analysis.     

Analysis of Composites with Infrared Thermography

The aim of this study was a non-destructive evaluation of composites through their behaviour under thermal stimulation. Such behaviour was monitored by infrared thermography. Several specimens were fabricated involving: glass/epoxy with inclusion of foreign materials; carbon/epoxy with backdrilled holes; carbon/epoxy with impact damage; Glare^® failed in bearing way. The obtained results prove that infrared thermography is capable of detecting the materials inhomogeneities and/or damage listed above. In particular, lock-in thermography is capable of supplying useful information about: the distribution of the adhesive thickness in composite structures; the distribution of the paint thickness; the behaviour under load of aluminium layers and glass fibres in Glare^®.