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Symmetry Webinar | Different Approaches for the Solutions of Differential Equations

13 Jan 2023, 10:00 (CET)

Radial Kernels, Heun Equations, Grad Shafranov Equations, ODE, PDE
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Welcome from the Chair

9th Symmetry Webinar

Different Approaches for the Solutions of Differential Equations

Many important and significant problems in mathematics and in general in applied sciences are formulated through differential equations. In this webinar, we would like to combine an approach to the recent theory on some classes of differential equations, with considerable material and methods of solutions that have proved useful to a wide variety of applications, to methods have a systematic and orderly structure and not merely a miscellaneous collection of unrelated mathematical tricks.

Solving a difficult problem in differential equations often requires the use of a variety of tools, both analytical and numerical: the implementation of an efficient numerical procedure typically rest on a good deal of preliminary analysis, to determine the qualitative features of the solution of the solution as a guide to computation, to test limiting or special cases, and so forth.

Gaining an understanding of a complex natural process is often accomplished by combining or building upon simpler and more basic models.

In this webinar will be presented recent results regarding some relevant differential equations, as the Heun equations, where will review the current state of the theory of these equations, focusing on the expansion of solutions in simpler mathematical functions, primarily of the hypergeometric class and the Grad-Shafranov plasma equilibrium equation, in toroidal geometry, that has been the fundamental step towards the realization of the Tokamak configurations and, consequently on the route towards the achievements of the Fusion energy production, furthermore will be presented adaptive schemes for solving radial basis function collocation problems, which involve elliptic partial differential equations.

Date: 13 January 2023

Time: 10:00 am CET | 4:00 am EST | 5:00 pm CST Asia | 1:00 pm AMT (Armenia Time)

Webinar ID: 874 4552 9212

Webinar Secretariat: symmetry.webinar@mdpi.com

Chair

Section of Mathematics, Uninettuno University, Roma, Italy

DETAILS
Bio
Clemente Cesarano is associate professor of Numerical Analysis at the Section of Mathematics -Uninettuno University, Rome Italy; he is the coordinator of the doctoral college in Technological Innovation Engineering, coordinator of the Section of Mathematics, vice-dean of the Faculty of Engineering, president of the Degree Course in Management Engineering, director of the Master in Project Management Techniques, and coordinator of the Master in Applied and Industrial Mathematics. He is also a member of the Research Project “Modeling and Simulation of the Fractionary and Medical Center”, Complutense University of Madrid (Spain) and head of the national group from 2015, member of the Research Project (Serbian Ministry of Education and Science) “Approximation of Integral and Differential Operators and Applications”, University of Belgrade (Serbia) and coordinator of the national group from 2011-), a member of the Doctoral College in Mathematics at the Department of Mathematics of the University of Mazandaran (Iran), expert (Reprise) at the Ministry of Education, University and Research, for the ERC sectors: Analysis, Operator algebras and functional analysis, Numerical analysis. Clemente Cesarano is Honorary Fellows of the Australian Institute of High Energetic Materials, affiliated with the National Institute of High Mathematics (INdAM), is affiliated with the International Research Center for the “Mathematics & Mechanics of Complex Systems” (MEMOCS) - University of L’Aquila, associate of the CNR at the Institute of Complex Systems (ISC), affiliated with the “Research ITalian network on Approximation (RITA)” network as the head of the Uninettuno office, UMI member, SIMAI member.

Invited Speakers

Department of Mathematics, University of Turin, Italy

DETAILS
Bio
Alessandra De Rossi got a degree in Mathematics, Università di Torino, Italy, 7/7/92, with honors and a Ph. D. in Computational Mathematics, Università di Milano, Italy, 9/17/97, dissertation title: Metodi numerici gerarchici per l’approssimazione di equazioni differenziali alle derivate parziali, advisor Professor C. Canuto. Positions held: October 1999-May 2018 Assistant Professor in Numerical Analysis, Department of Mathematics, Università di Torino; June 2018-present Associate Professor in Numerical Analysis, Department of Mathematics, Università di Torino; August 2018 National Scientific Qualification Full Professor National Committees and Membership in Professional Societies. She is member of the doctoral panel in Pure and Applied Mathematics, University of Torino up to 2019-present, member of GNCS-INDAM (National Group for the Scientific Computing), RITA (Research ITalian network on Approximation) and to SIMAI (Italian Society of Industrial and Applied Mathematics), UMI (Italian Mathematical Union) and of UMI's group TAA (Approximation Theory and Applications). Co-Coordinator RITA 3/1/2020-2/28/2022. Alessandra De Rosso has published more than 80 papers on referred journals, proceedings or volumes.

University of Tuscia/DTT, Viterbo, Italy

DETAILS
Bio
From 1982 up to 2021 I have been working in the ENEA Frascati centrum. Along these years I have worked on several quite different research field, i. e. plasma equilibrium, plasma control, plasma turbulence… I have also spent large part of these years working in the European JET Experiment, leading different groups and as responsible of some enhancements. On the late ENEA period I have been one of the key people on the new Divertor Tokamak Test (DTT) facility proposal, presently under realisation in Frascati. On the 2021 I left ENEA and I became full professor in the Tuscia University.

Institute for Physical Research, Armenian Academy of Sciences, Ashtarak, Armenia

DETAILS
Bio
Artur Ishkhanyan got the Ph.D. in Theoretical and Mathematical Physics, at Institute for Problems in Mechanics, Moscow, Russia and Dr. of Sci. at Yerevan State University, Yerevan, Armenia with a thesis on Selected problems of coherent interaction of model quantum systems with light. He was Assoc. Prof. at Yerevan State University, Yerevan, Armenia, doing courses in Quantum mechanics, Laser physics, oscillations and waives, degenerate quantum gases. From August 2007 to present is the Head of research group, Institute for Physical Research NAS of Armenia (Ashtarak, 0203 Armenia). His main field of specializations are Exact solutions of wave equations, Quantum mechanics, Dynamics of few-level quantum systems, Non-linear dynamics, Theoretical atomic, molecular and optical physics, Laser physics and in particular the Theory of Heun differential equations.

Webinar Content

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Program

Speaker/Presentation

Time in CET

Prof. Dr. Clemente Cesarano

Chair Introduction

10:00 - 10:10 am

Prof. Dr. Alessandra De Rossi

Adaptive Procedures for RBF Collocation Methods

10:10 - 10:30 am

Prof. Dr. Flavio Crisanti

The Grad-Shafranov Equation in Plasma Physics: Exact Solutions and Reconstruction of Physical Parameters

10:30 - 10:50 am

Prof. Dr. Artur Ishkhanyan

A Survey on Heun Equations

10:50 - 11:10 am

Q&A Session

11:10 - 11:25 am

Closing of Webinar
Prof. Dr. Clemente Cesarano

11:25 - 11:30 am

Relevant SI

Guest Editor: Prof. Dr. Clemente Cesarano
Deadline for manuscript submissions: 28 February 2023

Sponsors and Partners

Organizers

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