589 research outputs found
Upper semi-continuity of the Royden-Kobayashi pseudo-norm, a counterexample for H\"olderian almost complex structures
If is an almost complex manifold, with an almost complex structure of
class \CC^\alpha, for some , for every point and every
tangent vector at , there exists a germ of -holomorphic disc through
with this prescribed tangent vector. This existence result goes back to
Nijenhuis-Woolf. All the holomorphic curves are of class \CC^{1,\alpha}
in this case.
Then, exactly as for complex manifolds one can define the Royden-Kobayashi
pseudo-norm of tangent vectors. The question arises whether this pseudo-norm is
an upper semi-continuous function on the tangent bundle. For complex manifolds
it is the crucial point in Royden's proof of the equivalence of the two
standard definitions of the Kobayashi pseudo-metric. The upper semi-continuity
of the Royden-Kobayashi pseudo-norm has been established by Kruglikov for
structures that are smooth enough. In [I-R], it is shown that \CC^{1,\alpha}
regularity of is enough.
Here we show the following:
Theorem. There exists an almost complex structure of class \CC^{1\over
2} on the unit bidisc \D^2\subset \C^2, such that the Royden-Kobayashi
seudo-norm is not an upper semi-continuous function on the tangent bundle.Comment: 5 page
The Impact of Access Roads on Spontaneous Colonization Chane-Piray Area Department of Santa Cruz Bolivia
The purpose of this study was to investigate the impact of access roads on the process of spontaneous colonization of virgin forest land in the tropical lowlands of Bolivia. An access road in the Department of Santa Cruz serving an area opened up by spontaneous colonization was studied. The interpretation of aerial photographs and data collected in the area were used to illustrate the importance of access roads for successful spontaneous colonization. General conclusions were drawn with regard to the role that spontaneous colonization as a dynamic force was playing in the development of Bolivia\u27s tropical lowlands
The spectrum of the random environment and localization of noise
We consider random walk on a mildly random environment on finite transitive
d- regular graphs of increasing girth. After scaling and centering, the
analytic spectrum of the transition matrix converges in distribution to a
Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph
changes from a regular tree to the integers, the noise becomes localized.Comment: 18 pages, 1 figur
The Absence of Positive Energy Bound States for a Class of Nonlocal Potentials
We generalize in this paper a theorem of Titchmarsh for the positivity of
Fourier sine integrals. We apply then the theorem to derive simple conditions
for the absence of positive energy bound states (bound states embedded in the
continuum) for the radial Schr\"odinger equation with nonlocal potentials which
are superposition of a local potential and separable potentials.Comment: 23 page
New Classes of Potentials for which the Radial Schrodinger Equation can be solved at Zero Energy
Given two spherically symmetric and short range potentials and V_1 for
which the radial Schrodinger equation can be solved explicitely at zero energy,
we show how to construct a new potential for which the radial equation can
again be solved explicitely at zero energy. The new potential and its
corresponding wave function are given explicitely in terms of V_0 and V_1, and
their corresponding wave functions \phi_0 and \phi_1. V_0 must be such that it
sustains no bound states (either repulsive, or attractive but weak). However,
V_1 can sustain any (finite) number of bound states. The new potential V has
the same number of bound states, by construction, but the corresponding
(negative) energies are, of course, different. Once this is achieved, one can
start then from V_0 and V, and construct a new potential \bar{V} for which the
radial equation is again solvable explicitely. And the process can be repeated
indefinitely. We exhibit first the construction, and the proof of its validity,
for regular short range potentials, i.e. those for which rV_0(r) and rV_1(r)
are L^1 at the origin. It is then seen that the construction extends
automatically to potentials which are singular at r= 0. It can also be extended
to V_0 long range (Coulomb, etc.). We give finally several explicit examples.Comment: 26 pages, 3 figure
Plant poisonings in livestock in Brazil and South Africa
Information on intoxication of livestock by plants in Brazil, in terms of cause, clinical signs and
pathology, is compared with information on livestock poisoning by plants in South Africa.
Plant poisoning, including mycotoxicosis, is considered to be one of three major causes of
death in livestock in Brazil, which is one of the top beef producing countries in the world,
with a cattle population of more than 200 million. Cattle production in South Africa is on a
more modest scale, but with some 600 species of plants and fungi known to cause toxicity
in livestock, as opposed to some 130 species in Brazil, the risk to livestock in South Africa
appears to be much greater. The comparisons discussed in this communication are largely
restricted to ruminants.http://www.jsava.co.zaam201
Barycentric decomposition of quantum measurements in finite dimensions
We analyze the convex structure of the set of positive operator valued
measures (POVMs) representing quantum measurements on a given finite
dimensional quantum system, with outcomes in a given locally compact Hausdorff
space. The extreme points of the convex set are operator valued measures
concentrated on a finite set of k \le d^2 points of the outcome space, d<
\infty being the dimension of the Hilbert space. We prove that for second
countable outcome spaces any POVM admits a Choquet representation as the
barycenter of the set of extreme points with respect to a suitable probability
measure. In the general case, Krein-Milman theorem is invoked to represent
POVMs as barycenters of a certain set of POVMs concentrated on k \le d^2 points
of the outcome space.Comment: !5 pages, no figure
Operator renewal theory and mixing rates for dynamical systems with infinite measure
We develop a theory of operator renewal sequences in the context of infinite
ergodic theory. For large classes of dynamical systems preserving an infinite
measure, we determine the asymptotic behaviour of iterates of the
transfer operator. This was previously an intractable problem.
Examples of systems covered by our results include (i) parabolic rational
maps of the complex plane and (ii) (not necessarily Markovian) nonuniformly
expanding interval maps with indifferent fixed points.
In addition, we give a particularly simple proof of pointwise dual ergodicity
(asymptotic behaviour of ) for the class of systems under
consideration.
In certain situations, including Pomeau-Manneville intermittency maps, we
obtain higher order expansions for and rates of mixing. Also, we obtain
error estimates in the associated Dynkin-Lamperti arcsine laws.Comment: Preprint, August 2010. Revised August 2011. After publication, a
minor error was pointed out by Kautzsch et al, arXiv:1404.5857. The updated
version includes minor corrections in Sections 10 and 11, and corresponding
modifications of certain statements in Section 1. All main results are
unaffected. In particular, Sections 2-9 are unchanged from the published
versio
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