Variation of the first Hilbert coefficients of parameters with a common integral closure

A problem posed by Wolmer V. Vasconcelos on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well

A key to selected rockfishes (Sebastes spp.) based on mitochondrial DNA restriction fragment analysis

Larval and juvenile rockfishes (Sebastes spp.) are difficult to identify using morphological characters. We developed a key based on sizes of restriction endonuclease fragments of the NADH dehydrogenase-3 and -4 (ND3/ND4) and 12S and 16S ribosomal RNA (12S/16S) mitochondrial regions. The key makes use of variation in the ND3/ND4 region. Restriction endonuclease Dde I variation can corroborate identifications, as can 12S/16S variation. The key, based on 71 species, includes most North American taxa, several Asian species, and Sebastolobus alascanus and Helicolenus hilgendorfi that are closely related to rockfishes. Fifty-eight of 71 rockfish species in our database can be distinguished unequivocally, using one to five restriction enzymes; identities of the remaining species are narrowed to small groups: 1) S. polyspinis, S. crameri, and S. ciliatus or variabilis (the two species could not be distinguished and were considered as a single species) ; 2) S. chlorostictus, S. eos, and S. rosenblatti; 3) S. entomelas and S. mystinus; 4)S. emphaeus, S. variegatus, and S. wilsoni; and 5) S. carnatus and S. chrysomelas

Effect of Anharmonicity on the Kondo Phenomena of a Magnetic Ion Vibrating in a Confinement Potential

Effect of anharmonicity of a cage potential for a magnetic ion vibrating in a metal is investigated by the numerical renormalization group method. The cage potential is assumed to be one-dimensional and of the double-well type. In the absence of the Coulomb interaction, we find continuous crossover among the three limiting cases: Yu-Anderson-type Kondo regime, the double-well-type Kondo one, and the renormalized Fermi chain one. In the entire parameter space of the double-well potential, the ground state is described by a local Fermi liquid. In the Yu-Anderson-type Kondo regime, a quantum phase transition to the ground state with odd parity takes place passing through the two-channel Kondo fixed point when the Coulomb interaction increases. Therefore, the vibration of a magnetic ion in an oversized cage structure is a promising route to the two-channel Kondo effect.Comment: 6 pages, 3 figures, accepted for JPS