The relative volume growth of minimal submanifolds

The volume growth of certain well-defined subsets of minimal submanifolds in riemannian spaces are compared with the volume growth of balls and spheres in space forms of constant curvature. Work partially supported by a DGICYT Grant No. PB97-1425 and Fundacio Caixa Castello Grant No. 0I027.     

Spin-canting and transverse relaxation in maghemite nanoparticles and in tin-doped maghemite

The magnetic properties of maghemite nanoparticles and tin-doped maghemite have been studied by ⁵⁷Fe and ¹¹⁹Sn Mössbauer spectroscopy at temperatures from 6 to 300 K with and without applied magnetic fields. The low-temperature ⁵⁷Fe spectra of both samples, obtained in a field of 4 T, can be described in terms of A-site and B-site components with perfect ferrimagnetic order and a strongly canted component, which seems to have its main contribution from B-site ions. At higher temperatures, the components with strong canting are influenced by transverse relaxation, which results in significant line broadening, a reduction of the magnetic hyperfine splitting and a reduction in the relative areas of lines 2 and 5. The ¹¹⁹Sn spectra show a very broad distribution of magnetic hyperfine fields at low temperatures. When the sample was exposed to applied magnetic fields the distribution became narrower. The spectra show that the direction of the hyperfine field of a large fraction of the tin ions in maghemite is antiparallel to the applied field, but a minor fraction of the tin ions have canted hyperfine fields.     

Mössbauer effect in small particles

Mössbauer spectroscopy is very sensitive to the special magnetic properties of ultrafine particles. Studies of particles in the superparamagnetic state allow determination of the particle size and the magnetic anisotropy energy constant A strong magnetic interaction between the particles may result in ordering of the magnetic moments of particles which would be superparamagnetic if they were non-interacting. This so-called superferromagnetic state can also be characterized by Mössbauer spectroscopy measurements. Furthermore, because a large fraction of the atoms in very small particles are in the surface layer, Mössbauer spectroscopy can be applied for studies of surface magnetism in small particles.     

Spectral pairs in cartesian coordinates

Let ^d have finite positive Lebesgue measure, and let () be the corresponding Hilbert space of -functions on . We shall consider the exponential functionse on given bye (x)=e ^i2·x . If these functions form an orthogonal basis for (), when ranges over some subset in ^d , then we say that (, ) is a spectral pair, and that is a spectrum. We conjecture that (, ) is a spectral pair if and only if the translates of some set by the vectors of tile ^d. In the special case of =I^d, the d-dimensional unit cube, we prove this conjecture, with =I^d, for d3, describing all the tilings by I^d, and for all d when is a discrete periodic set. In an appendix we generalize the notion of spectral pair to measures on a locally compact abelian group and its dual.Acknowledgements and Notes, Work supported by the National Science Foundation.Dedicated to the memory of Irving E. Segal     

On the product of two generalized derivations

Two elements and in a ring determine a generalized derivation on by setting for any in . We characterize when the product is a generalized derivation in the cases when the ring is the algebra of all bounded operators on a Banach space , and when is a -algebra . We use these characterizations to compute the commutant of the range of .

     

Recent applications of microemulsion electrokinetic chromatography

Microemulsions are used in a similar way as micellar solutions are used for separations in capillary electrophoresis. Within the last approximately six years, a number of papers have appeared in the literature in which the separation characteristics of microemulsion electrokinetic chromatography (MEEKC) have been investigated. The total number of papers dealing with MEEKC is now close to 100. One of the major fields of application for MEEKC has been the characterization of the lipophilicity of chemical substances but the technique has also been applied for the analysis of substances within the fields of natural products, pharmaceuticals, vitamins, peptides, proteins, and nucleic acid bases as well as nucleosides. An overview of the applications is given together with the microemulsions used for each application.     

The human keratinocyte two-dimensional gel protein database (update 1992): towards an integrated approach to the study of cell proliferation, differentiation and skin diseases.

The master two-dimensional gel database of human keratinocytes currently lists 2980 cellular proteins (2098 isoelectric focusing, IEF; and 882 nonequilibrium pH gradient electrophoresis, NEPHGE) many of which correspond to posttranslational modifications. About 20% of all recorded proteins have been identified (protein name, organelle components, etc.) and they are listed in alphabetical order together with their M(r), pI, cellular localization and credit to the investigator(s) that aided in the identification. Also, we have listed 145 microsequenced proteins that are recorded in this database. As an aid in localizing the polypeptides we have included blow-ups of the master images (IEF, NEPHGE) displaying all the protein numbers. In the long run, the master keratinocyte database is expected to link protein and DNA sequencing and mapping information (Human Genome Program) and to provide an integrated picture of the expression levels and properties of the thousands of proteins that orchestrate various keratinocyte functions both in health and disease.     

Time-dependence of the isotope effects in the unimolecular dissociation of tertiary amine molecular ions

The intramolecular secondary isotope effects on the α-cleavage of deuterium-labelled N-methyldipentylamine radical cations have been studied as a function of ion lifetime by field ionization kinetics. The isotope effects observed are all normal and increase in magnitude with increasing ion lifetime, with the exception of the δ-labelled compound which shows an inverse effect (predominant loss of the labelled radical) at times shorter than 10^?9 s, and a normal effect at longer times. The isotope effects reflect differences in zero-point energies of the transition states as well as the influence of slight reductions of isotope-dependent frequencies on the state sums–a statistical weight effect. The latter is particularly important at high ion energies and is the primary reason for the occurrence of the inverse isotope effect. The time dependence of the normal and inverse isotope effect is reproduced by QET/RRKM calculations.