<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we propose to compare three a posteriori error estimators namely equilibrated, star-based and residual based for the Poisson problem and the Stokes problem with lowest-order Crouzeix-Raviart finite element discretization. The numerical results are presented to compare the performance of the three estimators in an adaptive refinement strategy.
</abstract>

U.M.R. 5208 - Camille Jordan Institute, Lyon 1 University

Laboratory of Engineering Sciences, National School of Applied Sciences

Numerical comparison of three a posteriori error estimators for nonconforming finite element method

<abstract xmlns="http://www.w3.org/1999/xhtml">

We study the existence and uniqueness of a bounded weak solution for a triply nonlinear thermistor problem in Sobolev spaces. Furthermore, we prove the existence of an absorbing set and, consequently, the universal attractor.
</abstract>

AMNEA Group, MAIS Laboratory, Faculty of Sciences and Technics

MAIS Laboratory, Faculty of Sciences and Technics

Department of Mathematics, Faculty of Sciences

R&D Unit CIDMA, Department of Mathematics

Existence result of the global attractor for a triply nonlinear thermistor problem

<abstract xmlns="http://www.w3.org/1999/xhtml">

The aim of this paper is to present the mathematical and numerical study of a nonlocal nonlinear model based on the variable exponent <italic>p</italic>(<italic>x</italic>)-Laplacian for removing Cauchy noise, which is a type of impulsive and non-Gaussian degradation. The proposed model benefits from the performance of the nonlocal approach to preserve small details and textures, and the efficiency of the variable exponent to reduce the execution time. To demonstrate the reliability of our proposed model, we provide some experimental denoising results and illustrate the comparison with some models from the literature.
</abstract>

A Nonlocal Model for Reconstructing Images Corrupted by Cauchy Noise

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this work, we study the existence of at least one non decreasing sequence of nonnegative eigenvalues for the problem:
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2023-0004_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mrow><mo>{</mo> <mrow><mtable><mtr><mtd><mrow><msup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mn>2</mn><mi>p</mi></mrow></msup><mi>u</mi><mo>=</mo><mi>λ</mi><mi>m</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mi> </mi><mi> </mi><mi> </mi><mi>i</mi><mi>n</mi><mi> </mi><mi> </mi><mi> </mi><mi mathvariant="normal">Ω</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>v</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>∂</mo><mrow><mo>(</mo><mrow><mi mathvariant="normal">Δ</mi><mi>u</mi></mrow><mo>)</mo></mrow></mrow><mrow><mo>∂</mo><mi>v</mi></mrow></mfrac><mo>=</mo><mo>…</mo><mo>=</mo><mfrac><mrow><mo>∂</mo><mrow><mo>(</mo><mrow><msup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mn>2</mn><mi>p</mi><mo>-</mo><mn>1</mn></mrow></msup><mi>u</mi></mrow><mo>)</mo></mrow></mrow><mrow><mo>∂</mo><mi>v</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mi> </mi><mi> </mi><mi> </mi><mi>o</mi><mi>n</mi><mi> </mi><mi> </mi><mi> </mi><mo>∂</mo><mi mathvariant="normal">Ω</mi><mo>.</mo></mrow></mtd></mtr></mtable></mrow> </mrow></mrow></math>
<tex-math>\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u\,\,\,in\,\,\,\Omega ,} \cr {{{\partial u} \over {\partial v}} = {{\partial \left( {\Delta u} \right)} \over {\partial v}} = \ldots = {{\partial \left( {{\Delta ^{2p - 1}}u} \right)} \over {\partial v}} = 0\,\,\,on\,\,\,\partial \Omega .} \cr } } \right.</tex-math>
</alternatives>
</disp-formula>
Where Ω is a bounded domain in ℝ<italic>N</italic> with smooth boundary ∂ Ω, <italic>p</italic> ∈ ℕ*, <italic>m</italic> ∈ <italic>L</italic>∞ (Ω), and Δ2<italic>p</italic><italic>u</italic> := Δ (Δ...( Δ<italic>u</italic>)), 2<italic>p</italic> times the operator Δ.
</abstract>

Mathematics and Computer Science Department

University Abdelmalk Essaadi, Sciences and Technologies Faculty

University Abdelmalk Essaadi, National School of Applied Sciences

University Mohamed I, Multidisciplinary Faculty

Existence of solutions for 4p-order PDES with Neumann boundary conditions

<abstract xmlns="http://www.w3.org/1999/xhtml">

In the history of option pricing, Black-Scholes model is one of the most significant models. In this paper, we present a new numerical strategy for valuing American option pricing problems governed by Black-Scholes model (BSM). Numerical computations are carried out to show the efficiency and robustness of the proposed method. We compare our numerical solution with the ones based on Finite Element Method (FEM) and the Enriched Finite Element Method (PUFEM). Our result shows the efficiency of the proposed strategy. In addition, that approach can be used to treat nonlinear evolutionary problems.
</abstract>

About the valuation of American option under Black-Scholes model : a numerical study

<abstract xmlns="http://www.w3.org/1999/xhtml">

In [Appl. Comput. Harmon. Anal., 46 (2019), 664673] O. Christensen and M. Hasannasab observed that assuming the existence of an operator <italic>T</italic> sending <italic>en</italic> to <italic>e</italic><italic>n</italic>+1 for all <italic>n</italic> ∈ ℕ (where (<italic>e</italic><italic>n</italic>)<italic>n</italic>∈ℕ is a sequence of vectors) guarantees that (<italic>e</italic><italic>n</italic>)<italic>n</italic>∈ℕ is linearly independent if and only if dim<italic>{e</italic><italic>n</italic><italic>}</italic><italic>n</italic>∈ℕ = ∞. In this article, we recover this result as a particular case of a general order-theory-based model-theoretic result. We then return to the context of vector spaces to show that, if we want to use a condition like <italic>T</italic>(<italic>e</italic><italic>i</italic>) = <italic>e</italic><italic>ϕ</italic>(<italic>i</italic>) for all <italic>i</italic> ∈ <italic>I</italic> where <italic>I</italic> is countable as a replacement of the previous one, the conclusion will only stay true if <italic>ϕ</italic> : <italic>I</italic> → <italic>I</italic> is conjugate to the successor function <italic>succ</italic> : <italic>n</italic> ↦<italic>n</italic> + 1 defined on ℕ. We finally prove a tentative generalization of the result, where we replace the condition <italic>T</italic>(<italic>e</italic><italic>i</italic>) = <italic>e</italic><italic>ϕ</italic>(<italic>i</italic>) for all <italic>i</italic> ∈ <italic>I</italic> where <italic>ϕ</italic> is conjugate to the successor function with a more sophisticated one, and to which we have not managed to find a new application yet.
</abstract>

Laboratoire d’EDP, Algbre et Gomtrie spectrale

dpartement de mathmatiques, facult des sciences

Independence, infinite dimension, and operators

<abstract xmlns="http://www.w3.org/1999/xhtml">

To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid.
The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation.
Pontryagin’s maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion.
</abstract>

LAMS, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik

Laboratory of Fundamental Mathematics and their Applications (LFMA)

Department of Mathematics, Faculty of Sciences El Jadida

Fractional optimal control problem for a mathematical modeling of African swine fever virus transmission

<abstract xmlns="http://www.w3.org/1999/xhtml">

New copulas, based on perturbation theory, are introduced to clarify a <italic>symmetrization</italic> procedure for asymmetric copulas. We give also some properties of the <italic>symmetrized</italic> copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.
</abstract>

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

<abstract xmlns="http://www.w3.org/1999/xhtml">

We propose a novel diffusion process having a mean function equal to the Pareto probability density function up to a constant of proportionality. We examine the probabilistic properties of the proposed model. Then, referring to the problem of statistical inference, we describe the approach employed to tackle the issue of obtaining parameter estimates by maximizing the likelihood function based on discrete sampling. This estimation reduces to solving a set of complex equations, that is accomplished using the simulated annealing algorithm. A simulation study is also given to validate the methodology presented. Finally, using a real-world example of the Moroccan child mortality rate, we obtain the fits and forecasts by employing the suggested stochastic process and nonlinear regression model.
</abstract>

Laboratory of Analysis and Modeling Systems for Decision Support

Hassan First University of Settat, National School of Applied Sciences

Departamento de Estadística e Investigación Operativa, Faculty of sciences, Campus de Fuentenueva

Stochastic Pareto diffusion process : Statistical analysis and computational issues. Simulation and Application

<abstract xmlns="http://www.w3.org/1999/xhtml">

In this work and in the context of PDE constrained optimization problems, we are interested in identification of a parameter in the diffusion equation proposed in [1]. We propose to identify this parameter automatically by a gradient descent algorithm to improve the restoration of a noisy image. Finally, we give numerical results to illustrate the performance of the automatic selection of this parameter and compare our numerical results with other image denoising approaches or algorithms.
</abstract>

Parameters identification for a nonlinear partial differential equation in image denoising

AHEAD OF PRINT

Volume 9 (2023): Issue 3 (September 2023)

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Moroccan Journal of Pure and Applied Analysis

 The Moroccan Journal of Pure and Applied Analysis "MJPAA" (Print ISSN: 2605-6364) is a peer-reviewed open access journal published by the "Université Sidi Mohamed Ben Abdellah" (Sidi Mohamed Ben Abdallah University), covering all main-stream branches of pure and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, numerical analysis, optimization theory, and control theory.   MJPAA is published by Sidi Mohamed Ben Abdallah University in three issues in January, May and September.   Why subscribe and read    The journal covers a wide range of branches of mathematical analysis.   Pure and applied analysis topics are intensely studied by researchers throughout the world especially in Africa, the Arab and European countries.   An edition committee of high-level and international renown.   Editorial board representing different regions of the world and various research teams.      Why submit    No publication charges for the authors or their institutions.   The journal is available to be indexed in the most important databases.   The journal is among the best in its field in Africa and the Arab world.      Rejection Rate    45%      Archiving   Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.   Plagiarism Policy   The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.   Publisher:Sidi Mohamed Ben Abdallah University (Route Imouzzer, BP 2626 Fez 30000, Morocco, Tel. : 0212 5 35 60 96 60/ 61)   Contact:Professor Youssef Akdim, Sidi Mohamed Ben Abdellah Universitymjpaa.edition1@usmba.ac.ma 