Notes for a talk in Stanford’s Arithmetic Dynamics Seminar, Apr. 29, 2014. This talk is an introduction to the theory of heights on projective varieties over local and global fields. I will also say something about canonical heights for a dynamical system, and a local-global formula for these. This material is from Chapters 1-2 of the book by Bombieri and Gubler on heights [BG]; also Silverman’...

A new proof is given for the explicit formulae for the non archime dean canonical height on an elliptic curve This arises as a direct calculation of the Haar integral in the elliptic Jensen formula

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...

2 Derived p-adic heights 2.1 Derived heights for cyclic groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Comparison of pairings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Compatibility of the derived heights . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Derived p-adic heights . . . . . . . . . . . . . . . . . . . . . . . . . ....

vibration cutting (vc), elliptical vibration cutting (evc) and ordinary cutting (oc) of in738 work-pieces have been experimentally investigated in the present research. the experiments were carried out by using single crystal diamond tool and ultra-precision cnc lathe. vibration frequency is 36.16khz and the amplitude is . the influence of various cutting parameters including cutting speed, fee...

crops and agricultural products are subject to natural loading during growth. different mechanical forces are also exerted on them during harvest. one product, sugar cane, experiences large shear forces are during harvest. an examination of the crop properties and machine parameters of sugar cane are necessary to develop appropriate cutting tools and the optimization and design of harvesting ma...

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.