Quantum affine transformation group and covariant differential calculus

We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of the group is achieved by using the adjoint representation. The elements of quantum matrix form a Hopf algebra. Furthermore, we construct a differential calculus which is covariant with respect to the action of the quantum matrix.Comment: LaTeX 22 pages OS-GE-34-94 RCNP-05

Laughlin states on the sphere as representations of Uq(sl(2))

We discuss quantum algebraic structures of the systems of electrons or quasiparticles on a sphere of which center a magnetic monople is located on. We verify that the deformation parameter is related to the filling ratio of the particles in each case.Comment: 8 pages, Late

Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are described by infinite measure dynamical systems.We show that the time average of the observation function which is not the $L^1(m)$ function, whose average with respect to the invariant measure $m$ is finite, converges to the generalized arcsine distribution. This result leads to the novel view that the correlation function is intrinsically random and does not decay. Moreover, it is also numerically shown that the time average of the observation function converges to the stable distribution when the observation function has the infinite mean.Comment: 8 pages, 8 figure

Enhancement of the incretin pathway in response to bariatric surgery is important for restoration of beta cell function

ArticleDIABETOLOGIA. 52(2):374-375 (2009)journal articl

Regularized Renormalization Group Reduction of Symplectic Map

By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the symplectic symmetry and fails to describe a long-time behaviour. In order to preserve the symplectic symmetry, we present a regularization procedure, which gives a regularized symplectic RG map describing an approximate long-time behaviour succesfully

Isospectral Hamiltonians and W1+∞W_{1+\infty} algebra

We discuss a spectrum generating algebra in the supersymmetric quantum mechanical system which is defined as a series of solutions to a specific differential equation. All Hamiltonians have equally spaced eigenvalues, and we realize both positive and negative mode generators of a subalgebra of $W_{1+\infty}$ without use of negative power of raising/lowering operators of the system. All features in the supersymmetric case are generalized to the parasupersymmetric systems of order 2.Comment: 15 pages, LaTeX, one postscript figure available by request version appearing in Prog. Theore. Phy

Neutrino Mass Textures with Maximal CP Violation

We have found three types of neutrino mass textures, which give maximal CP-violation as well as maximal atmospheric neutrino mixing. These textures are described by six real mass parameters: one specified by two complex flavor neutrino masses and two constrained ones and the others specified by three complex flavor neutrino masses. In each texture, we calculate mixing angles and masses as well as Majorana CP phases.Comment: 10 pages, RevTex, no figures, references updated, version to appear in Phys. Rev.

Chiral symmetry analysis and rigid rotational invariance for the lattice dynamics of single-wall carbon nanotubes

In this paper, we provide a detailed expression of the vibrational potential for the lattice dynamics of the single-wall carbon nanotubes (SWCNT) satisfying the requirements of the exact rigid translational as well as rotational symmetries, which is a nontrivial generalization of the valence force model for the planar graphene sheet. With the model, the low frequency behavior of the dispersion of the acoustic modes as well as the flexure mode can be precisely calculated. Based upon a comprehensive chiral symmetry analysis, the calculated mode frequencies (including all the Raman and infrared active modes), velocities of acoustic modes and the polarization vectors are systematically fitted in terms of the chiral angle and radius, where the restrictions of various symmetry operations of the SWCNT are fulfilled

Raman and Infra-red properties and layer dependence of the phonon dispersions in multi-layered graphene

The symmetry group analysis is applied to classify the phonon modes of $N$-stacked graphene layers (NSGL's) with AB- and AA-stacking, particularly their infra-red and Raman properties. The dispersions of various phonon modes are calculated in a multi-layer vibrational model, which is generalized from the lattice vibrational potentials of graphene to including the inter-layer interactions in NSGL's. The experimentally reported red shift phenomena in the layer number dependence of the intra-layer optical C-C stretching mode frequencies are interpreted. An interesting low frequency inter-layer optical mode is revealed to be Raman or Infra-red active in even or odd NSGL's respectively. Its frequency shift is sensitive to the layer number and saturated at about 10 layers.Comment: enlarged versio