KAMOUCHE Somia

Specialty: 
Applied Mathematics
Department: 
Faculty: 
Campus: Ancien Campus
  • kamouche.somia@univ-guelma.dz
  • soumia.kamouche@gmail.com
Doctoral advisor: 
Google Scholar Link: 
Rersearchgate Link: 
ORCID: 

Thesis title

Doctoral thesis title: 
On the Generalized Quadratic Spectrum of Bounded Operators

Thesis title (Ar)

Doctoral thesis title (Ar): 
حول الطيف التربيعي العام للعوامل المقيدة

Thesis title (Fr)

Doctoral thesis title (Fr): 
Sur le spectre quadratique généralisé des opérateurs bornés

keywords

Keywords: 
Generalized Spectrum-Generalized Resolvent-Quadratic Spectrum-Spectral Approximation

keywords (Ar)

Key words (Ar): 
طيف عام - حلا عام - طيف تربيعي - تقريب طيفي

keywords (Fr)

Key words (Fr): 
Spectre généralisé-Résolvante généralisée-Spectre quadratique-Approximation Spectrale

Abstract

Abstract: 

Recently, Khellaf, Lemita, Aissaoui, and Guebbai demonstrated the utility of the generalized spectrum of two bounded operators to approximate the spectrum of an unbounded operator and address the issue of spectral pollution. They developed several numerical methods based on projection techniques derived from the theory of integral equations. Through this thesis, we aim to further extend their generalization and provide both analytical and numerical meaning to the generalization of the generalized quadratic spectrum of bounded operators, initially defined for matrices

 

Abstract (Ar)

Abstract (Ar): 

مؤخرًا، قد أظهر خلاف، لميتا، عيساوي، وقباعي فائدة طيف التعميم لمشغلين محدودين في تقريب طيف المشغل غير المحدود وحل مشكلة التلوث الطيفي. قاموا بتطوير العديد من الطرق العددية استنادًا إلى تقنيات الإسقاط المستمدة من نظرية المعادلات التكاملية. من خلال هذه الرسالة، نسعى إلى دفع التعميم الذي قاموا به بعيدًا أكثر وتوفير معنى تحليليًا وعدديًا لتعميم الطيف التربيعي العام للمشغلين المحدودين المعرفة أصلاً للمصفوفات.

Abstract (Fr)

Abstract (Fr): 

Récemment Khellaf, Lemita, Aissaoui et Guebbai ont montré l’utilité du spectre généralisé de deux opérateurs bornés pour approcher le spectre d’un opérateur non borné et résoudre le problème de la pollution spectrale. Ils ont construit plusieurs méthodes numériques basées sur les techniques de projections issues de la théorie des équations intégrales. Nous cherchons à travers cette thèse à pousser la généralisation effectuée par ces derniers plus loin et donné un sens analytique et numérique pour la généralisation du spectre quadratique généralisé des opérateurs bornés définie initialement pour des matrices.

Scientific publications

Scientific publications : 

Publications internationales:

  1.  Generalized quadratic spectrum approximation in bounded and unbounded cases, Probl. Anal. Issues Anal. 10 (28)(3), 53-70 (2021)
  2.  The Kantorovich projection method in the generalized quadratic spectrum approximation, Numerical Methods and Programming. 23 (3), 240-247 (2022)
  3.  New convergence mode for the generalized spectrum approximation, Numer. Analys. Appl. 15, 336342 (2022).
  4. Block-by-block method for solving non-linear Volterra integral equation of the first kind, Comp.  App. Math. 42, 67 (2023).
  5. On a system of Volterra integral equations with a weakly singular kernel, Journal of Mathematical Sciences (2021).
     

Scientific conferences

Scientific conferences: 

Conférences scientifiques internationales :

  1.   LECTURES DE KOLMOGOROV - IX. Problèmes de contrôle généraux et leurs applications (GCP-2020), Tambov State University- Russia , The generalized quadratic spectrum approximation.
  2. The 6th International Workshop on Applied Mathematics and Modelling. Transformation of the quadratic eigenvalues problem into a linear eigenvalues problem, Guelma, Algeria, 16-27 October 2022,  
  3. The 6th International Conference on Mathematics, An Istanbul Meeting for World Mathematicians, Weak Conditions To Approach The Generalized Quadratic Spectrum, Istanbul, Turkey. 21.06.2022,  
  4. The First Online International Conference on Pure and Applied Mathematics, Ouargla University, Algeria, May 26-27, 2021, About spectral approximation of the generalized quadratic spectrum.
  5. 8th International Congress on Fundamental and Applied Sciences 2021 (ICFAS2021), Antalya Bilim University, Antalya, Turkey. October 19 to 21, 2021, Kantorovich projection method to compute the generalized quadratic spectrum.
  6. The International Voronezh Spring Mathematical School 'Modern Methods of Boundary Problem Theory. Pontryagin Readings - XXX', May 3rd – May 9th, 2019, Voronezh, Russia, Analytical study of a system of non-linear Volterra integral equations with weakly singular kernels.

Conférences scientifiques nationales: 

  1. 3rd National Seminaire of Mathematics, Mentouri University Constantine 1, Algeria. ON THE QUADRATIC EIGENVALUES COMPUTATION OF SCHRODINGER’S OPERATORS, Constantine, Algeria. 26.05.2022.
  2. The 2nd National Conference on Mathematics and its Applications, On The Quadratic Pencil Related To Three Bounded Operators, 17-18 September 2022, Bordj Bou Arréridj University, Algeria,  
  3. Conférence Nationale Nouvelles Tendances en Mathématiques Théoriques et Computationnelles 08-09 novembre 2022, Université Amine Elokkal El Hadj Moussa de Tamanrasset, Algeria.The spectrum of an operator generated by a differential problem with boundary conditions.
  4. Rencontre Nationale sur les Mathématiques Appliquées (RNMA’2022) 15-16 Novembre 2022, Annaba, Algeria, Sur le problème spectral quadratique associé aux trois opérateurs bornés.