On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta

The infinite number of particles limit in the dual to elliptic Ruijsenaars model (coordinate trigonometric degeneration of quantum double elliptic model) is proposed using the Nazarov-Sklyanin approach. For this purpose we describe double-elliptization of the Cherednik construction. Namely, we derive explicit expression in terms of the Cherednik operators, which reduces to the generating function of Dell commuting Hamiltonians on the space of symmetric functions. Although the double elliptic Cherednik operators do not commute, they can be used for construction of the N → ∞ limit.

Modelling Sessile Droplet Profile Using Asymmetrical Ellipses

Modelling the profile of a liquid droplet has been a mainstream technique for researchers to study the physical properties of a liquid. This study proposes a facile modelling approach using an elliptic model to generate the profile of sessile droplets, with MATLAB as the simulation environment. The concept of the elliptic method is simple and easy to use. Only three specific points on the droplet are needed to generate the complete theoretical droplet profile along with its critical parameters such as volume, surface area, height, and contact radius. In addition, we introduced fitting coefficients to accurately determine the contact angle and surface tension of a droplet. Droplet volumes ranging from 1 to 300 µL were chosen for this investigation, with contact angles ranging from 90° to 180°. Our proposed method was also applied to images of actual water droplets with good results. This study demonstrates that the elliptic method is in excellent agreement with the Young–Laplace equation and can be used for rapid and accurate approximation of liquid droplet profiles to determine the surface tension and contact angle.

Handwriting Quality Analysis using Online-Offline Models

This work is part of an innovative e-learning project allowing the development of an advanced digital educational tool that provides feedback during the process of learning handwriting for young school children (three to eight years old). In this paper, we describe a new method for children handwriting quality analysis. It automatically detects mistakes, gives real-time on-line feedback for children’s writing, and helps teachers comprehend and evaluate children’s writing skills. The proposed method adjudges five main criteria: shape, direction, stroke order, position respect to the reference lines, and kinematics of the trace. It analyzes the handwriting quality and automatically gives feedback based on the combination of three extracted models: Beta-Elliptic Model (BEM) using similarity detection (SD) and dissimilarity distance (DD) measure, Fourier<br>Descriptor Model (FDM), and perceptive Convolutional Neural Network (CNN) with Support Vector Machine (SVM) comparison engine. The originality of our work lies partly in the system architecture which apprehends complementary dynamic, geometric, and visual representation of the examined handwritten scripts and in the efficient selected features<br>adapted to various handwriting styles and multiple script languages such as Arabic, Latin, digits, and symbol drawing. The application offers two interactive interfaces respectively dedicated to learners, educators, experts or teachers and allows them to adapt it easily to the specificity of their disciples. The evaluation of our framework is enhanced by a database collected in Tunisia primary school with 400 children. Experimental results show the efficiency and robustness of our suggested framework that helps teachers and children by offering positive feedback throughout the handwriting learning process using tactile digital devices.<br>

Partitioning of Molecular Weight - An Elliptic Model for Isomers

Partitioning of any real number has been achieved based on an elliptic model introduced. Then, it has been adopted to isomeric molecules including optically active ones. Certain angles and bounds are defined. A bivariant regression model has been proposed for a set of isomeric molecules and discussed.

A Semi-Linear Elliptic Model for a Circular Membrane MEMS Device Considering the Effect of the Fringing Field

In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller–Box scheme, and the III/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.

Workbook for e-Education: Children’s Online Handwriting Quality Analysis.

<div>This paper describes an innovative e-learning project which is the development of a digital workbook that helps teaching handwriting at school. In this work, we propose a new qualitative and quantitative analysis process of cursive handwriting. This process detects automatically mistakes, gives a real-time feedback and helps teachers evaluate children’s writing skills. The main aim of this digital workbook is to help children learn how to write correctly. The proposed process is composed of five main criteria: shape,direction, stroke order, position respect to the reference lines and kinematics of the trace. It analyzes the handwriting quality and gives automatically feedback based on the Beta-Elliptic Model using similarity detection (SD) and dissimilarity distance (DD) measure. Our work apprehends dynamic and visual representation of the acquired traces and selects efficient features adapted to various handwriting styles and multiple script languages such as Arabic, Latin, digits, and symbols drawing. It demonstrates that beta-elliptic is not only a model for segmentation and recognition but also a tool to evaluate handwriting. Our application offers two interactive interfaces respectively dedicated to learners, and experts or teachers who can adapt it easily to the specificity of each child. The validation of the proposed system is done on a database collected in Tunisia primary schools with 400 children. Experimental results show that the efficiency and robustness of our suggested framework that do help teachers and children by offering positive feedback throughout the handwriting learning process using tactile digital devices.</div>

Workbook for e-Education: Children’s Online Handwriting Quality Analysis.

<div>This paper describes an innovative e-learning project which is the development of a digital workbook that helps teaching handwriting at school. In this work, we propose a new qualitative and quantitative analysis process of cursive handwriting. This process detects automatically mistakes, gives a real-time feedback and helps teachers evaluate children’s writing skills. The main aim of this digital workbook is to help children learn how to write correctly. The proposed process is composed of five main criteria: shape,direction, stroke order, position respect to the reference lines and kinematics of the trace. It analyzes the handwriting quality and gives automatically feedback based on the Beta-Elliptic Model using similarity detection (SD) and dissimilarity distance (DD) measure. Our work apprehends dynamic and visual representation of the acquired traces and selects efficient features adapted to various handwriting styles and multiple script languages such as Arabic, Latin, digits, and symbols drawing. It demonstrates that beta-elliptic is not only a model for segmentation and recognition but also a tool to evaluate handwriting. Our application offers two interactive interfaces respectively dedicated to learners, and experts or teachers who can adapt it easily to the specificity of each child. The validation of the proposed system is done on a database collected in Tunisia primary schools with 400 children. Experimental results show that the efficiency and robustness of our suggested framework that do help teachers and children by offering positive feedback throughout the handwriting learning process using tactile digital devices.</div>