696 research outputs found
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 in resistive models, where 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
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