5,281 research outputs found
Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve
For a projective variety X defined over a field K, there is a special class
of self-morphisms of X called algebraic dynamical systems. In this paper we
take K to be the function field of a smooth curve and prove that at each place
of K, subvarieties of X of dynamically small height are equidistributed on the
associated Berkovich analytic space. We carefully develop all of the arithmetic
intersection theory needed to state and prove this theorem, and we present
several applications on the non-Zariski density of preperiodic points and of
points of small height in field extensions of bounded degree.Comment: v2: Various typos fixed; statement and proof of auxiliary Prop. 6.1
corrected. During the process of preparing this manuscript for submission, it
came to the author's attention that Walter Gubler has recently proved many of
the same results. See arXiv:0801.4508v3. v3: References updated and a few
more typos corrected. To appear in Acta Arithmetic
A Remark on the Effective Mordell Conjecture and Rational Pre-Images under Quadratic Dynamical Systems
Fix a rational basepoint b and a rational number c. For the quadratic
dynamical system f_c(x) = x^2+c, it has been shown that the number of rational
points in the backward orbit of b is bounded independent of the choice of
rational parameter c. In this short note we investigate the dependence of the
bound on the basepoint b, assuming a strong form of the Mordell Conjecture.Comment: 5 pages; Final version to appear in Comptes Rendus Mathematiqu
Sensing with FETs - once, now and future
In this paper a short overview is given of the several FET-based sensor devices and the operational principle of the ISFET is summarized. Some of the shortcomings of the FET sensors were circumvented by an alternative operational mode, resulting in a device capable of acid/base concentration determination by coulometric titrant generation as well as in an original pH-static enzyme sensor. A more recent example is presented in which the ISFET is used for the on-line monitoring of fermentation processes. Future research is directed towards direct covalent coupling of organic monolayers on the silicon itself. In addition, the field-effect can be applied to the so-called semiconducting nanowire devices, ultimately making single molecule detection of charged species possible
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