Ample canonical heights for endomorphisms on projective varieties

We define an "ample canonical height" for an endomorphism on a projective variety, which is essentially a generalization of the canonical heights for polarized endomorphisms introduced by Call--Silverman. We formulate a dynamical analogue of the Northcott finiteness theorem for ample canonical heights as a conjecture, and prove it for endomorphisms on varieties of small Picard numbers, abelian varieties, and surfaces. As applications, for the endomorphisms which satisfy the conjecture, we show the non-density of the set of preperiodic points over a fixed number field, and obtain a dynamical Mordell--Lang type result on the intersection of two Zariski dense orbits of two endomorphisms on a common variety.Comment: 41 pages. The previous version has a serious mistake on the proof of the main conjecture for simple abelian varieties, but the present version gives a renewed proof that works for arbitrary abelian varietie

The classification of smooth quotients of abelian surfaces

We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.Comment: 12 page

Black Hole Perturbation

We present analytic calculations of gravitational waves from a particle orbiting a black hole. We first review the Teukolsky formalism for dealing with the gravitational perturbation of a black hole. Then we develop a systematic method to calculate higher order post-Newtonian corrections to the gravitational waves emitted by an orbiting particle. As applications of this method, we consider orbits that are nearly circular, including exactly circular ones, slightly eccentric ones and slightly inclined orbits off the equatorial plane of a Kerr black hole and give the energy flux and angular momentum flux formulas at infinity with higher order post-Newtonian corrections. Using a different method that makes use of an analytic series representation of the solution of the Teukolsky equation, we also give a post-Newtonian expanded formula for the energy flux absorbed by a Kerr black hole for a circular orbit.Comment: 120 pages ptptex file. To appear in Progress of Theoretical Physics Supplement No.128 (1997) `Perturbative and Numerical Approaches to Gravitational Radiation

Comparison of Verbal and Emotional Responses of Elderly People with Mild/Moderate Dementia and Those with Severe Dementia in Responses to Seal Robot, PARO

Introduction: The differences in verbal and emotional responses to a baby seal robot, PARO, of elderly people with dementia residing at an elderly nursing care facility were analyzed. There were two groups of elderly people: one was with mild/moderate dementia (M-group) that consisted with 19 elderly residents in the general ward, and the other was with severe dementia (S-group) that consisted with 11 elderly residents in the dementia ward. Method: Each elderly resident in both groups interacted with either PARO or a control (stuffed lion toy: Lion) brought by a staff at each resident’s private room. Their responses were recorded on video. Behavioral analysis of the initial 6 min of the interaction was conducted using a time sampling method. Results: In both groups, subjects talked more frequently to PARO than to Lion, showed more positive changes in emotional expression with PARO than with Lion, and laughed more frequently with PARO than with Lion. Subjects in M-group even showed more negative emotional expressions with Lion than with PARO. Furthermore, subjects in S-group showed neutral expression more frequently with Lion than with PARO, suggesting more active interaction with PARO. For subjects in M-group, frequencies of touching and stroking, frequencies of talking to staff member, and frequencies of talking initiated by staff member were significantly higher with Lion than with PARO. Conclusion: The elderly people both with mild/moderate dementia and with severe dementia showed greater interest in PARO than in Lion. The results suggest that introducing PARO may increase willingness of the staff members to communicate and work with elderly people with dementia, especially those with mild/moderate dementia who express their demand of communication more than those with severe dementia

The Acceleration Mechanism of Resistive MHD Jets Launched from Accretion Disks

We analyzed the results of non-linear resistive magnetohydrodynamical (MHD) simulations of jet formation to study the acceleration mechanism of axisymmetric, resistive MHD jets. The initial state is a constant angular momentum, polytropic torus threaded by weak uniform vertical magnetic fields. The time evolution of the torus is simulated by applying the CIP-MOCCT scheme extended for resistive MHD equations. We carried out simulations up to 50 rotation period at the innermost radius of the disk created by accretion from the torus. The acceleration forces and the characteristics of resistive jets were studied by computing forces acting on Lagrangian test particles. Since the angle between the rotation axis of the disk and magnetic field lines is smaller in resistive models than in ideal MHD models, magnetocentrifugal acceleration is smaller. The effective potential along a magnetic field line has maximum around $z \sim 0.5r_0$ in resistive models, where $r_0$ is the radius where the density of the initial torus is maximum. Jets are launched after the disk material is lifted to this height by pressure gradient force. Even in this case, the main acceleration force around the slow magnetosonic point is the magnetocentrifugal force. The power of the resistive MHD jet is comparable to the mechanical energy liberated in the disk by mass accretion. Joule heating is not essential for the formation of jets.Comment: 15 pages, 15 figures, 1 table, accepted for publication in Ap

General Relativistic Simulations of Jet Formation in a Rapidly Rotating Black Hole Magnetosphere

To investigate the formation mechanism of relativistic jets in active galactic nuclei and micro-quasars, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of jet formation in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We study cases in which the Keplerian accretion disk is both co-rotating and counter-rotating with respect to the black hole rotation. In the co-rotating disk case, our results are almost the same as those in Schwarzschild black hole cases: a gas pressure-driven jet is formed by a shock in the disk, and a weaker magnetically-driven jet is also generated outside the gas pressure-driven jet. On the other hand, in the counter-rotating disk case, a new powerful magnetically-driven jet is formed inside the gas pressure-driven jet. The newly found magnetically-driven jet in the latter case is accelerated by a strong magnetic field created by frame dragging in the ergosphere. Through this process, the magnetic field extracts the energy of the black hole rotation.Comment: Co-rotating and counter-rotating disks; 8 pages; submitted to ApJ letter