An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic height is expressed as an integral average of the logarithmic distance to the closure of the periodic points of the underlying morphism. The results may be though...

Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to problems involving the Weil height. The height appears as a solution to a certain extremal problem involving polynomials. We further generalize the above techniques...

We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus > 1, it is impractical to apply Hilbert’s Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrar...

Sagebrush (Artemisia spp.) communities constitute the largest temperate semidesert in North America and provide important rangelands for livestock and habitat for wildlife. Remote sensing methods might provide an efficient method to monitor sagebrush communities. This study used airborne LiDAR and field data to measure vegetation heights in five different community types at the Reynolds Creek E...

The ultimate goal of our multi-article series is to demonstrate the Allometric Scaling and Resource Limitation (ASRL) approach for mapping tree heights and biomass. This third article tests the feasibility of the optimized ASRL model over China at both site (14 meteorological stations) and continental scales. Tree heights from the Geoscience Laser Altimeter System (GLAS) waveform data are used ...

We construct canonical heights of subvarieties for dynamical systems of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems over C. Introduction Let X be a projective variety over a field K and fi : X → X (i = 1, · · · , k) morphisms over K. Let L be a line bundle on X, and d > k a ...

to be observed, if time is not to be needlessly wasted. One is that a writer should make himself acquainted with what has been previously said for and against the subject in discussion, to save his opponent the necessity of repeating himself, and another is that when he quotes his opponent, he ought to do so accurately and not draw inferences which, with careful perusal, it would be seen the wo...