Kakutani Dichotomy on Free States

Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.Comment: 12 page

Mean-field approach to superdeformed high-spin states in 40Ca and neutron-rich 50S regions

With the use of the symmetry-unrestricted cranked SHF method in the 3D coordinate-mesh representation, a systematic search for the SD and HD rotational bands in the N=Z nuclei from 32S to 48Cr has been done, and SD and HD solutions have been found in 32S, 36Ar, 40Ca, 44Ti, and in 36Ar, 40Ca, 44Ti, 48Cr, respectively. The SD band in 40Ca is found to be extremely soft against both the axially symmetric (Y30) and asymmetric (Y31) octupole deformations. Possible presense of SD states in neutron-rich sulfur isotopes from 46S to 52S has also been investigated, and deformation properties of neutron skins both in the ground and SD states are discussed.Comment: 10 pages including 9 ps figures, Talk at International Symposium on "Frontiers of Collective Motion 2002", November 6-9, 2002, Univ. of Aizu, Japa

Pairing effects on the collectivity of quadrupole states around 32Mg

The first 2+ states in N=20 isotones including neutron-rich nuclei 32Mg and 30Ne are studied by the Hartree-Fock-Bogoliubov plus quasiparticle random phase approximation method based on the Green's function approach. The residual interaction between the quasiparticles is consistently derived from the hamiltonian density of Skyrme interactions with explicit velocity dependence. The B(E2) transition probabilities and the excitation energies of the first 2+ states are well described within a single framework. We conclude that pairing effects account largely for the anomalously large B(E2) value and the very low excitation energy in 32Mg.Comment: 14 pages, 9 figure

Superdeformed bands in neutron-rich Sulfur isotopes suggested by cranked Skyrme-Hartree-Fock calculations

On the basis of the cranked Skyrme-Hartree-Fock calculations in the three-dimensional coordinate-mesh representation, we suggest that, in addition to the well-known candidate 32S, the neutron-rich nucleus 36S and the drip-line nuclei,48S and 50S, are also good candidates for finding superdeformed rotational bands in Sulfur isotopes. Calculated density distributions for the superdeformed states in 48S and 50S exhibit superdeformed neutron skinsComment: 18 pages including 10 ps figure

Nuclear Tetrahedral Symmetry: Possibly Present Throughout the Periodic Table

More than half a century after the fundamental, spherical shell structure in nuclei has been established, theoretical predictions indicate that the shell-gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the $T_d^D$ ('double-tetrahedral') group of symmetry, exact or approximate. The corresponding strong shell-gap structure is markedly enhanced by the existence of the 4-dimensional irreducible representations of the group in question and consequently it can be seen as a geometrical effect that does not depend on a particular realization of the mean-field. Possibilities of discovering the corresponding symmetry in experiment are discussed.Comment: 4 pages in LaTeX and 4 figures in eps forma

Lymph node removal enhances corneal graft survival in mice at high risk of rejection

Peer reviewedPublisher PD

On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change