Scaled-oscillation and regularity

We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.

     

Spectral operators generated by damped hyperbolic equations

We announce a series of results on the spectral analysis for a class of nonselfadjoint opeators, which are the dynamics generators for the systems governed by hyperbolic equations containing dissipative terms. Two such equations are considered: the equation of nonhomogeneous damped string and the 3-dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. Nonselfadjoint boundary conditions are imposed at the ends of a finite interval or on a sphere centered at the origin respectively. Our main result is the fact the aforementioned operators are spectral in the sense of N. Dunford. The result follows from the fact that the systems of root vectors of the above operators form Riesz bases in the corresponding energy spaces. We also give asymptotics of the spectra and state the Riesz basis property results for the nonselfadjoint operator pencils associated with these operators.     

Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter

The traditional empirical Bayes (EB) model is considered with the parameter being a location parameter, in the situation when the Bayes estimator has a finite degree of smoothness and, possibly, jump discontinuities at several points. A nonlinear wavelet EB estimator based on wavelets with bounded supports is constructed, and it is shown that a finite number of jump discontinuities in the Bayes estimator do not affect the rate of convergence of the prior risk of the EB estimator to zero. It is also demonstrated that the estimator adjusts to the degree of smoothness of the Bayes estimator, locally, so that outside the neighborhoods of the points of discontinuities, the posterior risk has a high rate of convergence to zero. Hence, the technique suggested in the paper provides estimators which are significantly superior in several respects to those constructed earlier.     

Atomic layer deposition in nanometer-level replication of cellulosic substances and preparation of photocatalytic TiO2/cellulose composites

TiO2 replicas of filter paper with nanometer-level accuracy were prepared by atomic layer deposition of thin conformal TiO2 coating, followed by a removal of the paper by air-anneal at 450 degrees C. Photocatalytic anatase TiO2/cellulose composites were also made by leaving the paper intact. The TiO2 films were deposited from Ti(OMe)4 and H2O at 150-250 degrees C. The photocatalytic activity of the TiO2/cellulose composite was verified by photocatalytic reduction of Ag(I) from an aqueous solution to Ag nanoparticles on the TiO2 surface. The TiO2/cellulose composites are mechanically more stable than the free-standing TiO2 replicas and are therefore potentially suitable as lightweight, high surface area photocatalysts.     

The measurement of radioactivity in Italian drinking waters

Drinking waters generally contain variable amounts of radioactivity. Many radionuclides, like ⁴⁰K and those belonging to the natural decay series of ²³⁸U, ²³⁵U and ²³²Th, are transferred to the water from the aquifer rocks by erosion and dissolution mechanisms.In recent years, a great interest arose towards the natural radioactivity in drinking water. The European Council Directive 98/83/EC, subsequently enforced in Italian law, pushed public authorities to organize tap water surveys. Parameter values for radioactivity levels in water are given, according to World Health Organization recommendations. Maximum concentration values for radon are separately proposed in a European Commission Recommendation.For this reason, during the latest years, the Regional Environment Protection Agency (ARPA) has been performing an extensive monitoring of tap waters in the Lombardia district of Italy. Natural radioactivity content was measured to check the compliance with recent European and Italian rules.Analyses were performed by an ultra-low level scintillation counter equipped with an alpha-beta discrimination device. Specifically arranged procedures, requiring quick and easy pre-treatments, allowed to measure gross alpha and beta activity, ²²²Rn, ²²⁶Ra, and uranium isotopes concentrations in a relatively short time. Subsequently, more complex procedures, involving radiochemical separation of radionuclides, are currently being studied for ²¹⁰Pb, ²¹⁰Po and ²²⁸Ra. Method performances were carefully tested by both internal validation procedures and international intercomparison exercises.These procedures have been employed for a wide range screening in the Lombardia district in Italy. Obtained results showed that in most cases gross alpha activity was lower than the parameter value given by the cited regulations. When these values were exceeded, a more detailed survey was planned: at present three of them, in the western and south-western part of Lombardia and in the city of Milan have been carried out.     

A new approach to phosphoserine and phosphothreonine analysis in peptides and proteins: chemical modification,enrichment via solid-phase reversible binding,and analysis by mass spectrometry

beta-Elimination of the phosphate group on phosphoserine and phosphothreonine residues and addition of an alkyldithiol is a useful tool for analysis of the phosphorylation states of proteins and peptides. We have explored the influence of several conditions on the efficiency of this PO(4)(3-) elimination reaction upon addition of propanedithiol. In addition to the described influence of different bases, the solvent composition was also found to have a major effect on the yield of the reaction. In particular, an increase in the percentage of DMSO enhances the conversion rate, whereas a higher amount of protic polar solvents, such as water or isopropanol, induces the opposite effect. We have also developed a protocol for enrichment of the modified peptides, which is based on solid-phase covalent capture/release with a dithiopyridino-resin. The procedure for beta-elimination and isolation of phosphorylated peptides by solid-phase capture/release was developed with commercially available alpha-casein. Enriched peptide fragments were characterized by MALDI-TOF mass spectrometric analysis before and after alkylation with iodoacetamide, which allowed rapid confirmation of the purposely introduced thiol moiety. Sensitivity studies, carried out in order to determine the detection limit, demonstrated that samples could be detected even in the low picomolar range by mass spectrometry. The developed solid-phase enrichment procedure based on reversible covalent binding of the modified peptides is more effective and significantly simpler than methods based on the interaction between biotin and avidin, which require additional steps such as tagging the modified peptides and work-up of the samples prior to the affinity capture step.     

In situ enzymatic digestion of oligopeptides on a direct insertion probe tip combined with fast atom bombardment and tandem mass spectrometry

The applicability of an approach to establish the sequence of oligopeptides involving on-probe-tip enzymatic fragmentation and subsequent direct fast atom bombardment (FAB) mass spectrometry (MS) and FAB-MS/MS of the subpeptide mixture was tested using two model peptides consisting of 19 and 25 amino acid residues. The method was found to be both time and sample sparing and flexible enough to use even subsequent digests, if necessary, with enzymes of different specificity. It provided in both cases complete information, not only for the sequence of enzymic fragments but also for their order in the original oligopeptide. Consequently, this approach to the sequence analysis of oligopeptides can be a method of choice when the FAB-MS/MS technique itself is unsuitable for obtaining detailed structural information. The method seems to be applicable to enzymically digestible peptides with an upper mass limit of about 3500.     

Mass spectrometric studies on azidomorphine derivatives

The mass spectrometric behaviour of nine azidomorphine derivatives have been studied. These compounds proved to have surprisingly specific and selective fragmentation under electron-impact. For 6-deoxy-6-azido-dihydro-isomorphine derivatives (I to V) the main decomposition pathway involves the loss of an N₂ molecule followed by a very rapid and selective fragmentation process. On the other hand, the molecular ions of 6-deoxy-8-azido-pseudomorphine derivatives (VI to VIII) and 6-deoxy-6-azido-14-hydroxy-isocodein (IX) primarily decompose by loss of the N₃ radical. This is due to the allylic effect of the double bond in ring C, corresponding to the chemical behaviour of these compounds.     

First chemical study of anaspidean Syphonota geographica: structure of degraded sterols aplykurodinone-1 and -2

Two unprecedented degraded sterols, aplykurodinone-1 (1) and -2 (2), have been isolated from the skin of the marine anaspidean Syphonota geographica, collected along the coasts of Greece. The structures and the relative stereochemistry were established by spectroscopic analysis and confirmed by chemical correlation with related known compounds.