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.

     

An unusual dimer of camptothecin-7-aldehyde

An intermolecular aldol reaction of 20S-camptothecin-7-aldehyde in the presence of strong bases affords an unusual dimeric compound, the structure and stereochemistry of which was assigned on the basis of NMR analysis and MM2 calculations.     

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.     

On deformations of Hamiltonian actions

In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the symplectic form on the manifold. Received: 21 March 2006     

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.     

Rigidity of codimension two indefinite spheres

We describe all isometric immersions f:S _n ^s S _s ⁿ +2/S _s ⁿ n–s4, whenever the set of totally geodesic points does not disconnect S _s ⁿ , where S _n ^s denotes the complete n-dimensional indefinite Riemannian space form of constant positive curvature 1 and signature s.     

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.     

Gas chromatographic/mass spectrometric determination of vinyl acetate levels in air

The determination of vinyl acetate at parts per 10⁹ by volume (ppbv) levels in air by gas chromatography/mass spectrometry (GC/MS) was achieved by optimizing the GC conditions and choosing specific extraction solvents that are sufficiently pure. The ideal solvent should not give rise to fragment ions at m/z 43, in order to rule out any possible interference during the monitoring of the same vinyl acetate ion. Traces of acetone and butan-2-one in solvents suitable for this GC/MS determination may also mislead the detection of vinyl acetate. A 440 μl volume of a mixture of tetrachloroethylene containing 9% acetonitrile allowed the recovery of more than 90% of the ester with a detection limit of 1.5 ppbv in air together with a good linearity of response.     

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.