Diamond module for the Lie algebra so(2n+1,C)\mathfrak{so}(2n+1,\mathbb C)

The diamond cone is a combinatorial description for a basis of an indecomposable module for the nilpotent factor $\mathfrak n$ of a semi simple Lie algebra. After N. J. Wildberger who introduced this notion, this description was achevied for $\mathfrak{sl}(n)$, the rank 2 semi-simple Lie algebras and $\mathfrak{sp}(2n)$. In the present work, we generalize these constructions to the Lie algebras $\mathfrak{so}(2n+1)$. The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they form a basis for the shape algebra of $\mathfrak{so}(2n+1)$. Defining the notion of orthogonal quasistandard Young tableaux, we prove these tableaux give a basis for the diamond module for $\mathfrak{so}(2n+1)$

DESIGN OF SMART VERTICAL HYDROPONIC SYSTEM

ABSTRACT All horticultural regions of the world have fundamentally developed in the programmatic era through farmer impact and imaginative development practices. The methods described are used to monitor satisfaction and crop yields. Because of the quality of the soil and the nourishment of the land, their cultivation has improved and created more money. The disadvantage is that it took them a long speculation to acquire the crops, and the level of nutrition was not usually put at its obvious level. In addition, many areas were devoted to production, which required a lot of work to treat the whole area. In order to control the time and methods well, the majority of the regions switched to careful development principles with IoT structures. Growing on water is the most progressive strategy to grow natural plants, vegetables and fruits without using land. The use of Rockwool in agricultural strategies where water contamination is possible for a certain period will result in huge yields and the requirement of longer growing times will be waived. Most of the countries that have practiced smart and economic development with little external intervention. IoT sensors are used in the water cultivation development system to test the situation and quality of yields continuously. They will effectively provide information to the whole system when the water or nutrient level has dropped. In the beginning, the development of hydroponics was done horizontally in small spaces in order to maintain the water flow. Today, it is applied on a vertical structure to save space and water flows when needed. With this method, yields are likely to be achieved even more space-efficiently and with little external intervention. Vertical hydroponics performs better than previous conventional approaches; perhaps the farmers in the extension unit have considered the cost of the total layout. This evaluation paper describes the use of procedures and development of automated methods using IoT platforms. Many reference materials can be used big data

Some constructions of multiplicative n-ary Hom-Nambu algebras

We show that given a Hom-Lie algebra one can construct the n-ary Hom-Lie bracket by means of an (n-2)-cochain of given Hom-Lie algebra and find the conditions under which this n-ary bracket satisfies the Filippov-Jacobi identity, there by inducing the structure of n-Hom-Lie algebra. We introduce the notion of Hom-Lie n-uplet system which is the generalization of Hom-Lie triple system. We construct Hom-Lie n-uplet system using a Hom-Lie algebra

Jeu de Taquin and Diamond Cone for so(2n+1, C)

International audienceThe diamond cone is a combinatorial description for a basis of a natural indecomposable n-module, where n is the nilpotent factor of a complex semisimple Lie algebra g. After N. J. Wildberger who introduced this notion, this description was achieved for g = sl(n) , the rank 2 semisimple Lie algebras and g = sp (2n).In this work, we generalize these constructions to the Lie algebra g = so(2n + 1). The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they index a basis for the shape algebra of so(2n + 1). Defining the notion of orthogonal quasistandard Young tableaux, we prove that these tableaux describe a basis for a quotient of the shape algebra, the reduced shape algebra of so(2n + 1)

Effet d’un traitement électrocinétique sur la structure d’une kaolinite mélangée au carbonate

International audienceThe aim of this work is to study the structure evolution of kaolinite + carbonate mixture after an electrokinetic treatment. The aim is to understand how an electrokinetic treatment can change the mechanical properties of the samples. The X-rays diffraction analysis show that the orientation of the particles and their size depend on the composition of the samples and to the presence of lead. The mercury intrusion tests show that the porosity vary slightly after the electrokinetic treatment.Le but de ce travail est d’étudier l’évolution de la structure de mélange de kaolinite + carbonate après un traitement électrocinétique. Le but étant d’appréhender les éventuelles variations des propriétés mécaniques des sols après l’électrocinétique. La diffraction des rayons X montre que l’orientation des particules et leur taille dépend de la composition du sol et de la présence du plomb. La porosimétrie au mercure a montré une faible variation de la porosité