Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Effects of Proteins from Culture Medium on Surface Property of Silanes- Functionalized Magnetic Nanoparticles

Monodisperse magnetic nanoparticles (MNPs) were synthesized by thermal decomposition of iron-oleate and functionalized with silanes bearing various functional groups such as amino group (NH2), short-chain poly(ethylene glycol) (PEG), and carboxylic group (COOH). Then, silanes-functionalized magnetic nanoparticles (silanes-MNPs) were incubated in cell culture medium plus fetal calf serum to investigate the effects of proteins from culture medium on surface property of MNPs. Zeta potential measurements showed that although surface charges of silanes-MNPs were different, they exhibited negative charges at neutral pH and approximate isoelectric points after they were incubated in cell culture medium. The reason was that silanes-MNPs could easily adsorb proteins from culture medium via non-covalent binding, resulting in the formation of protein-silanes-MNPs conjugates. Moreover, silanes-MNPs with various functional groups had different adsorption capacity to proteins, as confirmed by Coomassie blue fast staining method. The in vitro cell experiments showed that protein-silanes-MNPs had higher cellular uptake by cancer cells than silanes-MNPs

Structure and dynamics of Rh surfaces

Lattice relaxations, surface phonon spectra, surface energies, and work functions are calculated for Rh(100) and Rh(110) surfaces using density-functional theory and the full-potential linearized augmented plane wave method. Both, the local-density approximation and the generalized gradient approximation to the exchange-correlation functional are considered. The force constants are obtained from the directly calculated atomic forces, and the temperature dependence of the surface relaxation is evaluated by minimizing the free energy of the system. The anharmonicity of the atomic vibrations is taken into account within the quasiharmonic approximation. The importance of contributions from different phonons to the surface relaxation is analyzed.Comment: 9 pages, 7 figures, scheduled to appear in Phys. Rev. B, Feb. 15 (1998). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Transmission through a many-channel random waveguide with absorption

We compute the statistical distribution of the transmittance of a random waveguide with absorption in the limit of many propagating channels. We consider the average and fluctuations of the conductance T = tr t^{\dagger} t, where t is the transmission matrix, the density of transmission eigenvalues \tau (the eigenvalues of t^{\dagger} t), and the distribution of the plane-wave transmittances T_a and T_{ab}. For weak absorption (length L smaller than the exponential absorption length \xi_a), we compute moments of the distributions, while for strong absorption (L >> \xi_a), we can find the complete distributions. Our findings explain recent experiments on the transmittance of random waveguides by Stoytchev and Genack [Phys. Rev. Lett. 79, 309 (1997)].Comment: 13 pages, RevTeX; 9 figures include

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics

4-Deoxy-4-fluoro-GalNAz (4FGalNAz) is a metabolic chemical reporter of O-GlcNAc modifications, highlighting the notable substrate flexibility of O-GlcNAc transferase

Bio-orthogonal chemistries have revolutionized many fields. For example, metabolic chemical reporters (MCRs) of glycosylation are analogues of monosaccharides that contain a bio-orthogonal functionality, such as azides or alkynes. MCRs are metabolically incorporated into glycoproteins by living systems, and bio-orthogonal reactions can be subsequently employed to install visualization and enrichment tags. Unfortunately, most MCRs are not selective for one class of glycosylation (e.g., N-linked vs O-linked), complicating the types of information that can be gleaned. We and others have successfully created MCRs that are selective for intracellular O-GlcNAc modification by altering the structure of the MCR and thus biasing it to certain metabolic pathways and/or O-GlcNAc transferase (OGT). Here, we attempt to do the same for the core GalNAc residue of mucin O-linked glycosylation. The most widely applied MCR for mucin O-linked glycosylation, GalNAz, can be enzymatically epimerized at the 4-hydroxyl to give GlcNAz. This results in a mixture of cell-surface and O-GlcNAc labeling. We reasoned that replacing the 4-hydroxyl of GalNAz with a fluorine would lock the stereochemistry of this position in place, causing the MCR to be more selective. After synthesis, we found that 4FGalNAz labels a variety of proteins in mammalian cells and does not perturb endogenous glycosylation pathways unlike 4FGalNAc. However, through subsequent proteomic and biochemical characterization, we found that 4FGalNAz does not widely label cell-surface glycoproteins but instead is primarily a substrate for OGT. Although these results are somewhat unexpected, they once again highlight the large substrate flexibility of OGT, with interesting and important implications for intracellular protein modification by a potential range of abiotic and native monosaccharides

Light induced single molecule frequency shift

Alight induced frequency shift of the 0-0 line was measured in two-photon excitation spectra of single diphenyloctatetraene molecules doped in a crystal matrix. The shifts were proportional to the laser power with a slope of about 600 MHz/W when the laser beam of about 300 mW power was focused to a diameter of 2 mu m. Significantly, the observed line broadenings were an order of magnitude smaller than the shifts. The effect is ascribed mainly to a ''fast'' energy exchange between a local vibration and thermal phonons created by the third harmonic C-H band absorption in the matrix, and partially to an ac Stark shift

Energy Flow in the Hadronic Final State of Diffractive and Non-Diffractive Deep-Inelastic Scattering at HERA

An investigation of the hadronic final state in diffractive and non--diffractive deep--inelastic electron--proton scattering at HERA is presented, where diffractive data are selected experimentally by demanding a large gap in pseudo --rapidity around the proton remnant direction. The transverse energy flow in the hadronic final state is evaluated using a set of estimators which quantify topological properties. Using available Monte Carlo QCD calculations, it is demonstrated that the final state in diffractive DIS exhibits the features expected if the interaction is interpreted as the scattering of an electron off a current quark with associated effects of perturbative QCD. A model in which deep--inelastic diffraction is taken to be the exchange of a pomeron with partonic structure is found to reproduce the measurements well. Models for deep--inelastic $ep$ scattering, in which a sizeable diffractive contribution is present because of non--perturbative effects in the production of the hadronic final state, reproduce the general tendencies of the data but in all give a worse description.Comment: 22 pages, latex, 6 Figures appended as uuencoded fil