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