1 1 INTRODUCTION 2 1 Introduction Classical calculus is a basic tool in analysis. We use it so often that we forget that its construction needed considerable time and effort. Especially in the last decade, the progresses made in the field of analysis in metric spaces make us reconsider this calculus. Along this line of thought, all started with the definition of Pansu derivative [24] and its ve...

In the best practices, planning of urban green spaces is managed in such a way that it follows the key principles such as meeting per capita standards and providing accessible and balanced distribution of these spaces all across the city. In the context of emerging economy, these principles are unfortunately not followed strictly all times. In this study, it is attempted to investigate Tabriz c...

This report describes the two-hour mini-course given by myself at the Pretty Structures 2011 workshop (http://www.lix.polytechnique.fr/~liberti/pretty_structures). This work is due to a research team also including Carlile Lavor, Jon Lee, Benoıt Masson and Antonio Mucherino. The proofs and mistakes in this presentations are, however, entirely mine. The problem I treat here is the Distance Geome...

For this example, 19/40=47.5% of the columns have a carry of 1. Holte shows that if the binary digits are chosen at random, uniformly, in the limit 50% of all the carries are zero. This holds no matter what the base. More generally, if one adds n integers (base b) that are produced by choosing their digits uniformly at random in {0, 1, . . . , b− 1}, the sequence of carries κ0 = 0, κ1, κ2, . . ...

Kleene states the theorem with V = N, relative to specific φ, S n , supplied by his Enumeration Theorem, m = 0 (no parameters ~y) and n ≥ 1, i.e., not allowing nullary partial functions. And most of the time, this is all we need; but there are a few important applications where choosing “the right” φ, S n , restricting the values to a proper V ( N or allowing m > 0 or n = 0 simplifies the proof...