Metric heights are modified height functions on the non-zero algebraic numbers Q ∗ which can be used to define a metric on certain cosets of Q ∗ . They have been defined with a view to eventually applying geometric methods to the study of Q ∗ . In this paper we discuss the construction of metric heights in general. More specifically, we study in some detail the metric height obtained from the n...

Vertical deformations of the Earth’s surface result from a host geophysical and geological processes. Identification assessment induced signals is key to addressing outstanding scientific questions, such as those related role played by changing climate on height variations. This study, focused European Mediterranean area, analyzed GPS time series 114 well-distributed stations with aim identifyi...

We prove that the two smallest values of h(α)+h( 1 1−α )+h(1− 1 α ) are 0 and 0.4218 . . . , for α any algebraic integer. Introduction For K an algebraic number field, let Kv be the completion of K at the place v and let | |v be the absolute value associated with this completion Kv (more precise definitions are given below). For α ∈ K, we define the (logarithmic) Weil height, h(α), as follows:

These notes correspond to the ALGANT Graduate course given in Bordeaux during the academic year 2009-2010 (second semester). The course intends to be as self contained as possible. The notes (in French) of the graduate course Géométrie Différentielle Complexe (Niamey, December 2009), available on line at http://www.math.u-bordeaux1.fr/~yger/Cours-Niamey.pdf will help for some eventual perequisi...

In this paper several recurrences and formulas are presented leading to an upper bound and a lower bound, both logarithmic, for the expected height of a node in a heap. These bounds are of interest for algorithms that select the kth smallest element in a heap. CR categories: E.1, F.2.2, G.2.1.

Introduction: Nowadays, excessive computer use in the workplace has raised concerns about the health status of VDT workers, particularly complaints about eye discomforts. Due to the importance of the eyelids and eye closure parameters on eye health during computer works and the direct effect of monitor height on these parameters, this study was aimed to examine the effect of different monitor h...

In this article, we prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for algebraic families of rational maps ft : P(C)→ P(C), parameterized by t in a quasi-projective complex variety. We use this to prove one implication in the if-and-only-if statement of [BD2, Conjecture 1.10] on unlikely intersections in the moduli space of rational maps; we present the co...

1) Spot heights at summits have an accuracy of about ±3.3m at all map scales, in agreement with the published figure. 2) Levelled heights from old 6-inch maps can be a few metres below the summit but are unlikely to be more than a few tenths of a metre higher. 3) The accuracy of old and new 1:50k maps is similar, but where heights have changed the old height has a tendency to be too low. 4) Spo...