Search results for "Root"
showing 10 items of 1237 documents
On Sets of Words of Rank Two
2019
Given a (finite or infinite) subset X of the free monoid A∗ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆ F∗. A submonoid M generated by k elements of A∗ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆ A∗ primitive if it is the basis of a |X|-maximal submonoid. This extends the notion of primitive word: indeed, w is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆ Y∗. The set Y is therefore called a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive …
Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six
2017
We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.
The $q$-calculus for generic $q$ and $q$ a root of unity
1996
The $q$-calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$. By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${{\cal Z}}_n$-graded fractional supersymmetry and its natural representation.
On the computation of intersection numbers for twisted cocycles
2020
Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman integrals. With this application, the practical and efficient computation of intersection numbers of twisted cocycles becomes a topic of interest. An existing algorithm for the computation of intersection numbers of twisted cocycles requires in intermediate steps the introduction of algebraic extensions (for example square roots), although the final result may be expressed without algebraic extensions. In this article I present an improvement of this algorith…
Phenotyping plant root and their interaction with soil micro-organisms
2014
International audience
Modeling the hydrological and mechanical effect of roots on shallow landslides
2016
This study proposes a new methodology for estimating the additional shear strength (or cohesion) exerted by vegetation roots on slope stability analysis within a coupled hydrological-stability model. The mechanical root cohesion is estimated within a Fiber Bundle Model framework that allows for the evaluation of the root strength as a function of stress-strain relationships of populations of fibers. The use of such model requires the knowledge of the root architecture. A branching topology model based on Leonardo's rule is developed, providing an estimation of the amount of roots and the distribution of diameters with depth. The proposed methodology has been implemented into an existing dis…
Unemployment Hysteresis in Transition Countries: Evidence using Stationarity Panel Tests with Breaks
2008
The authors test hysteresis versus the natural rate hypothesis in unemployment using panel data for transition countries covering the period 1991:1–2003:11.The advantages of the stationarity tests applied is that they exploit the cross-section variations of the series and, additionally, allow for a different number of endogenous breakpoints in the unemployment series. They do not impose independence on the panel members, so that the critical values are simulated based on their specific panel sizes and time periods. The findings stress the importance of accounting for exogenous shocks in the series and give support to the shifting natural-rate hypothesis of unemployment for all the countries…
Mi.P.A.F. targeted project for evaluation of European and Japanese plum rootstocks in Italy: Results of six years of observations
2007
The Mi.P.A.F. (Italian Ministry of Agriculture) targeted project "National Lists of Recommended Rootstocks and Cultivars", coordinated by Prof. F. Loreti, University of Pisa, aims at evaluating the performance of fruit rootstocks introduced into the Italian nursery market. As part of this project, trials were established to compare some of the most interesting rootstocks for European and Japanese plum in 9 different locations in Italy. The rootstocks tested were: 'Citation-Zaipime', 'GF 31', 'Marianna GF 8/1', 'Ishtara-Ferciana', 'Jaspi-Fereley', 'Julior-Ferdor', 'Myrobalan 29C', 'Myrobalan B', 'MrS 2/5' and 'Myrocal'. In 1995, nine orchards were planted at 5 × 5 m spacing; in each orchard,…
Present status of Phytophthora species in the Mediterranean area, especially in relation to citrus
1990
Of the 44 currently accepted species of Phytophthora, 18 have been reported in the Mediterranean area. The status of each is briefly reviewed. On citrus, P. citrophthora and P. nicotianae var. parasitica are mainly responsible for foot rot and gummosis, and in addition P. hibernalis, P. syringae, P. cifricola and P. cactorum for brown rot of fruits. The incidence of these species is closely linked to their temperature requirements. The use of sour orange as a resistant rootstock has long provided satisfactory control of foot rot and gummosis, while chemical treatments are effective against brown rot. However, there are indications that, with changingcultural practices, the resistance of sou…