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.     

A new technique for fluid velocimetry based on near field scattering

We show that the time evolution of near-field scattering speckles, originated by a fluid suspension of particles, provides information about the velocity field in the fluid. This information can be extracted from a statistical analysis of speckle fields taken at different times, either by measuring their cross-correlation function or by recovering the power spectrum corresponding to the difference between the two speckle fields. Experimental data are in accordance to the expected behaviors. The results are independent of the scatterer's size, allowing one to exploit the technique also with sub-wavelength tracking particles.     

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.     

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.     

Second-generation mimics of ganglioside GM1 oligosaccharide: a three-dimensional view of their interactions with bacterial enterotoxins by NMR and computational methods

As a step to delineate a strategy of ligand design for cholera toxin (CT), NMR studies were performed on several mimics of the GM1 ganglioside oligosaccharide. The conformation of these analogues was investigated first in solution and then upon binding to cholera toxin by transferred nuclear Overhauser effect (TR-NOE) measurements. It was demonstrated that CT selects a conformation similar to the global minima of the free saccharides from the ensemble of presented conformations. No evidence of major conformational distortions was obtained, but one or two of the available conformers of the hydroxyacid side chain appear to be selected in the bound state. The NMR data were interpreted with the aid of computer models, generated and analyzed by using a combination of different approaches (MacroModels' MC/EM and MC/SD, Autodock, and GRID). Analysis of the NMR data supported by computational studies allowed us to interpret the experimental observations and to derive workable models of the ligand:toxin complexes. These models suggest that the higher affinity of the (R)-lactic acid derivative 3 may stem from lipophilic interactions with a hydrophobic area in the toxin binding site located in the vicinity of the sialic acid side chain binding region of the CT:GM1 complex, and formed by the side chain of Ile-58 and Lys-34. Thus, the models obtained have allowed us to make useful design suggestions for the improvement of ligand affinity.