Upper semi-continuity of the Royden-Kobayashi pseudo-norm, a counterexample for H\"olderian almost complex structures

If $X$ is an almost complex manifold, with an almost complex structure $J$ of class \CC^\alpha, for some $\alpha >0$, for every point $p\in X$ and every tangent vector $V$ at $p$, there exists a germ of $J$-holomorphic disc through $p$ with this prescribed tangent vector. This existence result goes back to Nijenhuis-Woolf. All the $J$ 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 $J$ is enough. Here we show the following: Theorem. There exists an almost complex structure $J$ 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

Clean milk : essential requirements from production to consumption

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New Classes of Potentials for which the Radial Schrodinger Equation can be solved at Zero Energy

Given two spherically symmetric and short range potentials $V_0$ and V_1 for which the radial Schrodinger equation can be solved explicitely at zero energy, we show how to construct a new potential $V$ 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 $L^n$ 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 $\sum_{j=1}^nL^j$) for the class of systems under consideration. In certain situations, including Pomeau-Manneville intermittency maps, we obtain higher order expansions for $L^n$ 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