Immersed disks, slicing numbers and concordance unknotting numbers

We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number, which is the minimal number of crossing changes to a slice knot; and the concordance unknotting number, which is the minimal unknotting number in a smooth concordance class. Using Heegaard Floer homology we obtain bounds that can be used to determine two of these invariants for all prime knots with crossing number ten or less, and to determine the concordance unknotting number for all but thirteen of these knots. As a further application we obtain some new bounds on Gordian distance between torus knots. We also give a strengthened version of Ozsvath and Szabo's obstruction to unknotting number one.Comment: 24 pages, 5 figures. V2: added section on Gordian distances between torus knots. V3: Improved exposition incorporating referees' suggestions. Accepted for publication in Comm. Anal. Geo

Self-consistent perturbational study of insulator-to-metal transition in Kondo insulators due to strong magnetic field

In order to study the effects of strong magnetic field on Kondo insulators, we calculate magnetization curves and single-particle excitation spectra of the periodic Anderson model at half-filling under finite magnetic field by using the self-consistent second-order perturbation theory combined with the local approximation which becomes exact in the limit of infinite spatial dimensions. Without magnetic field, the system behaves as an insulator with an energy gap, describing the Kondo insulators. By applying magnetic field to f-electrons, we found that the energy gap closes and the first order transition from insulator to metal takes place at a critical field $H_c$. The magnetization curve shows a jump at $H_c$. These are consistent with our previous study in terms of the exact diagonalization. Relationship to the experiments on YbB$_{12}$ and some other Kondo insulators is discussed.Comment: 5 pages, LaTeX, 7 PS figures included, uses jsps.st

Iterative Perturbation Theory for Strongly Correlated Electron Systems with Orbital Degeneracy

A new scheme of the iterative perturbation theory is proposed for the strongly correlated electron systems with orbital degeneracy. The method is based on the modified self-energy of Yeyati, et al. which interpolates between the weak and the strong correlation limits, but a much simpler scheme is proposed which is useful in the case of the strong correlation with orbital degeneracy. It will be also useful in the study of the electronic structures combined with the band calculations.Comment: 6 pages, 3 Postscript figures, to appear in J. Phys. Cond. Matte

Detection of reactive oxygen and nitrogen species by electron paramagnetic resonance (EPR) technique

During the last decade there has been growing interest in physical-chemical oxidation processes and the behavior of free radicals in living systems. Radicals are known as intermediate species in a variety of biochemical reactions. Numerous techniques, assays and biomarkers have been used to measure reactive oxygen and nitrogen species (ROS and RNS), and to examine oxidative stress. However, many of these assays are not entirely satisfactory or are used inappropriately. The purpose of this chapter is to review current EPR (Electron Paramagnetic Resonance) spectroscopy methods for measuring ROS, RNS, and their secondary products, and to discuss the strengths and limitations of specific methodological approaches