University of Diyala-College of Science organize a West Asia Mathematical School (WAMS: http://www.rnta.eu/WAMS/) school in cooperation with Nesin Mathematics Village-Izmir-Turkey, Laboratoire de Mathéatiques-Jean Leray-Universit de Nantes-France and CIMPA
entitled
“Mathematics and their interactions”
Coordinators
- Abdeljalil Nachaoui, Laboratoire de Mathéatiques-Jean Leray, Universit de Nantes, France
E-mail : Abdeljalil.Nachaoui@univ-nantes.fr
- Fatima M. Aboud, Department of mathematics, College of Sciences, University of Diyala.
E-mail : Fatima.Aboud@sciences.uodiyala.edu.iq
Sponsord by: Diyala University, Nesin Mathematics Village, Laboratoire de Mathéatiques-Jean Leray-Universit de Nantes, CIMPA, IMU and University of Tikrit.
General Information
1. Title : Mathematics and their interactions
2. Location Nesin Mathematics Village-Izmir-Turkey
3. Hosting institution Nesin Mathematics Village-Izmir-Turkey
4. Dates (starting date-ending date) October 27-November 3, 2019
5. Scientific Committee (including affiliation and emails)
- Abdeljalil Nachaoui, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France Abdeljalil.Nachaoui@univ-nantes.fr
- Yusif S. Gasimov, Azerbaijan University, Azerbaijan yusif.gasimov@au.edu.az
- Abdelhalim Larhlimi, Département Informatique, Université de Nantes, France Abdelhalim.Larhlimi@univ-nantes.fr
- Tahseen H. Moubarak, College of Sciences, University of Diyala, Iraq dean@sciences.uodiyala.edu.iq
- Tamaz Tadumdaze, Institute of Applied Mathematics, Tbilisi State University, Tbilisi,Georgia, tamaz.tadumadze@tsu.ge
- Francois Jauberteau, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France Francois.Jauberteau@univ-nantes.fr
6. Local Organizing Committee (including affiliation and emails and please specify the person in charge)
- The person in charge: M. Aboud, Department of mathematics, College of Sciences, University of Diyala, Iraq ( Fatima.Aboud@sciences.uodiyala.edu.iq)
- Karzan A. Berdawood, College of Sciences, Department of Mathematics, University of Salahaddin-Erbil, Iraq ( karzan.ahmad@yahoo.com)
- Burcu Gürbüz, Department of Computer Engineering, Faculty of Engineering and Natural Sciences, Üsküdar University, Turkey(burcu.gurbuz@uskudar.edu.tr).
- Ali NESİN, Istanbul Bilgi University, Department of Mathematics and Nesin Mathematics Village, Turkey ( anesin@nesinvakfi.org)
- Aslı Can Korkmaz, Nesin Mathematics Village, Turkey (aslicankorkmaz@nesinvakfi.org)
- Aycan Sahin, Nesin Mathematics Village, Turkey (aycansahin@nesinvakfi.org)
- Lieth A Majeed, Department of mathematics, College of Sciences, University of Diyala, Iraq ( Majed@sciences.uodiyala.edu.iq)
Scientific content
1. Description of the program
The objective of this school is to offer a fairly complete offer of courses in the modeling field, ranging from theoretical approaches to concrete developments (modeling and numerical simulations). The implementation and development of numerical approximation methods requires, first and foremost, a good knowledge of mathematical equations (differential equations, partial differential equations) but also the phenomena they account for. Finally, the efficient implementation of the associated approximation algorithms can not be conceived without an introduction to computer skills.
These courses are intended for students, researchers or teaching researchers wishing to acquire an introduction to modern training in the field of mathematics and their applications
2. Lecturers and courses
- Abdeljalil Nachaoui, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France Abdeljalil.Nachaoui@univ-nantes.fr A mathematical procedure for detecting osteoarthritis-induced cartilage degeneration
- Fatima M. Aboud, Department of mathematics, College of Sciences, University of Diyala, Iraq Fatima.Aboud@sciences.uodiyala.edu.iq Mathematical tools for partial differential equations analysis
- Yusif S. Gasimov, Azerbaijan University, Azerbaijan yusif.gasimov@au.edu.az Inverse Eigenvalue Problems with Applications to Some Mechanical Systems.
- Abdelhalim Larhlimi, Département Informatique, Université de Nantes, France Abdelhalim.Larhlimi@univ-nantes.fr Mathematical methods in metabolic engineering for strain design
- Amine Laghrib, Department of Mathematics, University of Sultan Moulay Sliman Beni Mellal, Morocco, laghrib.amine@gmail.com Introduction to Image processing and image restoration
- Tahseen H. Moubarak, College of Sciences, University of Diyala, Iraq assistprof.tahseen@sciences.uodiyala.edu.iq Concepts and methods of Mathematical physics and some of there applications
3. Description of each course
- Mathematical tools for partial differential equations analysis
Partial differential equations and their numerical simulation are essential tools in both industry and research. The objective of this course is to provide some essential tools for the analysis of partial differential equations (PDEs). The content brings together notions and results from the functional analysis, and the study of some PDEs using these tools.
- A mathematical procedure for detecting osteoarthritis-induced cartilage degeneration
We introduce the inverse problem of the determination of the electrical potential on the cartilage from electrical potentials measured on the surface of the knee. The knee is modeled as a volume conductor composed of different regions characterized by specific electrical conductivities. We describe iterative methods developed for a class of bioelectrical field problems that arise in electrocardiography (ECG) and electroencephalography (EEG). The finite-element method is used to compute the potential distribution in the sequence of knee models (direct problems) induced by the algorithm of the inverse problem. We show how the non homogeneity of the electrical conductivities can be handeled by a nonoverlaping domain decomposition method. The implementation of the sequence the discret problems is done using FreeFem.
- Inverse Eigenvalue Problems with Applications to Some Mechanical Systems
In this course, eigenvalue problems are considered for the elliptic operators with variable domain. Eigenvalues of these operators are taken as functional of the domain. Using the one to one correspondence between bounded convex domains and their support functions variation of the domain is expressed by the variation of its support function and calculate the first variation of this functional. Using the obtained formulas behavior of the eigenvalues is investigated when the domain varies. Then shape optimization problems are considered for the eigenvalues. The necessary conditions of optimality are proved, an algorithm is offered for the numerical solution of the considered problems.
In this course, we consider an eigenvalue problem for the biharmonic operator that describes the transverse vibrations of the plate. Under the imposed boundary conditions, the eigenvalues of this operator are indeed eigenfrequencies of the clamped plate. The domain of the plate is taken variable and the domain functional, involving an eigenfrequency, is studied. A formula for an eigenfrequency is proved, the first variation of the functional with respect to the domain is calculated, and the necessary condition for an optimal shape is derived. Explicit formulas are obtained for the eigenfrequency in the optimal domain in some particular cases.
- Mathematical methods in metabolic engineering for strain design
Metabolic reactions play a fundamental role in sustaining cell growth. They import nutrients from the environment and they convert them into molecules needed by the living organism. Metabolic reactions do not operate in isolation; they form large-scale metabolic networks. In this lecture, we will introduce the main mathematical methods that are mandatory for predicting the behaviour of metabolic networks using constraint-based modeling. We will then present some methods that are used in metabolic engineering to design new strains.
- Introduction to Image processing and image restoration
In the last decade of the past century a great interest has been established by the mathematicians in the development of digital image processing as a science. The aim of this course is to introduce the image processing aspects and tools. Especially, we will focus on the image denoising and deconvolution techniques. Before presenting the main basic techniques for filtering images, we briefly recall the principle of one-dimensional filtering. We will see in the following that most filters act selectively on high frequencies to select them, in order to amplify or reduce them just as in the one-dimensional case. Based on the effect of filtering, we will introduce some partial differential equations (PDE's), such as Heat equation, which are used to reduce the noise. Finally, an implementation of different linear filters and PDE's will be investigated using the Matlab software.
- Concepts and methods of Mathematical physics and some of there applications
In this course we give some applications of Mathematical physics in some of real life problems like complex electrical resistivity (which can be considered as a link between insolating material in physics and its variation during the use of the material with frequency and specialy its applications at high frequency.
Also we study the effect of the energy in thermodynamics field by using integration to threat this subject. In addition we talk about the relation between Mathematics and quantum mechanics and its quantum dot applications.
4. Tentative schedule
- Introduction.
- Motivation : examples from industry
- A review of analysis
- Basic function spaces
- Definitions Properties of Hilbert space
- Green formula and its applications
- variational formulation
- A mathematical procedure for detecting osteoarthritis-induced cartilage degeneration
- Modellisation of the knee
- Iterative methods for solving the inverse Cauchy problems
- Finite-element method
- Implementation, freeFem
- Inverse Eigenvalue Problems with Applications to Some Mechanical Systems
- Eigenvalue problems in mechanics modelisation
- Shape optimization problems
- Support functions and variation of the domain
- Numerical implementation
- Mathematical methods in metabolic engineering for strain design
- Introduction to constraint-based modeling of metabolic networks
- Polyhedral theory and duality theory and their applications in metabolic engineering (minimal cut sets, objective prediction and strain design)
- Introduction to Image processing and image restoration
- Introduction to image processing
- Image restoration-Denoising
- Image restoration-Deconvolution
- Practical work using Matlab
- Concepts and methods of Mathematical physics and some of there applications
- Example of applications of Mathematical physics
- Electrical resistivity .
- Effect of the energy in thermodynamics field
- Mathematics and quantum mechanics
Participant information
Please send the following information in a word file with a CV in pdf form and the scann of your passeport to the following emails :
Fatima.Aboud@sciences.uodiyala.edu.iq
fatimaaboud@yahoo.com
For registration please visit:
https://www.math.sciences.univ-nantes.fr/WAMS-CIMPA-IZMIR19/
Note: A financial support by the WAMS can be accorded for a restricted number of participants after studying the CV and the above informations.