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Moroccan Journal of Pure and Applied Analysis最新文献

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Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations 具有离散对偶有限体积离散的完全各向异性扩散的一般Ventcell传输条件下的优化Schwarz方法
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-12-28 DOI: 10.2478/mjpaa-2021-0014
M. Gander, L. Halpern, F. Hubert, Stella Krell
{"title":"Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations","authors":"M. Gander, L. Halpern, F. Hubert, Stella Krell","doi":"10.2478/mjpaa-2021-0014","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0014","url":null,"abstract":"Abstract We introduce a new non-overlapping optimized Schwarz method for fully anisotropic diffusion problems. Optimized Schwarz methods take into account the underlying physical properties of the problem at hand in the transmission conditions, and are thus ideally suited for solving anisotropic diffusion problems. We first study the new method at the continuous level for two subdomains, prove its convergence for general transmission conditions of Ventcell type using energy estimates, and also derive convergence factors to determine the optimal choice of parameters in the transmission conditions. We then derive optimized Robin and Ventcell parameters at the continuous level for fully anisotropic diffusion, both for the case of unbounded and bounded domains. We next present a discretization of the algorithm using discrete duality finite volumes, which are ideally suited for fully anisotropic diffusion on very general meshes. We prove a new convergence result for the discretized optimized Schwarz method with two subdomains using energy estimates for general Ventcell transmission conditions. We finally study the convergence of the new optimized Schwarz method numerically using parameters obtained from the continuous analysis. We find that the predicted optimized parameters work very well in practice, and that for certain anisotropies which we characterize, our new bounded domain analysis is important.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"182 - 213"},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48806709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Domination and Kwapień’s factorization theorems for positive Cohen p–nuclear m–linear operators 正Cohen p–核m–线性算子的控制和Kwapień因子分解定理
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-12-14 DOI: 10.2478/mjpaa-2021-0010
A. Bougoutaia, A. Belacel, H. Hamdi
{"title":"Domination and Kwapień’s factorization theorems for positive Cohen p–nuclear m–linear operators","authors":"A. Bougoutaia, A. Belacel, H. Hamdi","doi":"10.2478/mjpaa-2021-0010","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0010","url":null,"abstract":"Abstract In this paper, we introduce and study the concept of positive Cohen p-nuclear multilinear operators between Banach lattice spaces. We prove a natural analog to the Pietsch domination theorem for this class. Moreover, we give like the Kwapień’s factorization theorem. Finally, we investigate some relations with another known classes.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"100 - 115"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49492558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A look at nonexpansive mappings in non-Archimedean vector spaces 关于非阿基米德向量空间中的非扩张映射
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-12-14 DOI: 10.2478/mjpaa-2021-0013
S. Lazaiz
{"title":"A look at nonexpansive mappings in non-Archimedean vector spaces","authors":"S. Lazaiz","doi":"10.2478/mjpaa-2021-0013","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0013","url":null,"abstract":"Abstract In a spherically complete ultrametric space every nonexpansive self-mapping T has a fixed point ̄x or a minimal invariant ball B(̄x, d(̄x, T(̄x)). We show how we can approximate this fixed center ̄x in a non-Archimedean vector space. And, we give a synthetic study for increasing mapping in non-Archimedean local fields.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"173 - 181"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46775866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost Somewhat Near Continuity and Near Regularity 几乎某种近似连续性和近似正则性
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-12-14 DOI: 10.2478/mjpaa-2021-0009
Z. Ameen
{"title":"Almost Somewhat Near Continuity and Near Regularity","authors":"Z. Ameen","doi":"10.2478/mjpaa-2021-0009","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0009","url":null,"abstract":"Abstract The notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"88 - 99"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49165682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Complete Approximations by Multivariate Generalized Gauss-Weierstrass Singular Integrals 多元广义Gauss-Weierstrass奇异积分的完全逼近
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-12-14 DOI: 10.2478/mjpaa-2021-0012
G. Anastassiou
{"title":"Complete Approximations by Multivariate Generalized Gauss-Weierstrass Singular Integrals","authors":"G. Anastassiou","doi":"10.2478/mjpaa-2021-0012","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0012","url":null,"abstract":"Abstract This research and survey article deals exclusively with the study of the approximation of generalized multivariate Gauss-Weierstrass singular integrals to the identity-unit operator. Here we study quantitatively most of their approximation properties. The multivariate generalized Gauss-Weierstrass operators are not in general positive linear operators. In particular we study the rate of convergence of these operators to the unit operator, as well as the related simultaneous approximation. These are given via Jackson type inequalities and by the use of multivariate high order modulus of smoothness of the high order partial derivatives of the involved function. Also we study the global smoothness preservation properties of these operators. These multivariate inequalities are nearly sharp and in one case the inequality is attained, that is sharp. Furthermore we give asymptotic expansions of Voronovskaya type for the error of multivariate approximation. The above properties are studied with respect to Lpnorm, 1 ≤ p ≤ ∞.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"134 - 172"},"PeriodicalIF":0.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47844255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Sigmoid functions for the smooth approximation to the absolute value function 绝对值函数光滑逼近的Sigmoid函数
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI: 10.2478/mjpaa-2021-0002
Yogesh J. Bagul, C. Chesneau
{"title":"Sigmoid functions for the smooth approximation to the absolute value function","authors":"Yogesh J. Bagul, C. Chesneau","doi":"10.2478/mjpaa-2021-0002","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0002","url":null,"abstract":"Abstract We present smooth approximations to the absolute value function |x| using sigmoid functions. In particular, x erf(x/μ) is proved to be a better smooth approximation for |x| than x tanh(x/μ) and x2+μ sqrt {{x^2} + mu } with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for the error function.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"12 - 19"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49133952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent 变指数Sobolev空间中一个非线性椭圆型问题拓扑度的存在性结果
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI: 10.2478/mjpaa-2021-0006
M. Ait Hammou, E. Azroul
{"title":"Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent","authors":"M. Ait Hammou, E. Azroul","doi":"10.2478/mjpaa-2021-0006","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0006","url":null,"abstract":"Abstract The aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form { A(u)=finΩu=0on∂Ω left{ {matrix{{Aleft( u right) = f} hfill & {in} hfill & Omega hfill cr {u = 0} hfill & {on} hfill & {partial Omega } hfill cr } } right. where A(u) = −diva(x, u, ∇u) is a Leray-Lions operator and f ∈ W−1,p′ (.)(Ω) with p(x) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"50 - 65"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47056749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A new conjugate gradient method for acceleration of gradient descent algorithms 一种新的加速梯度下降算法的共轭梯度法
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI: 10.2478/mjpaa-2021-0001
Noureddine Rahali, M. Belloufi, R. Benzine
{"title":"A new conjugate gradient method for acceleration of gradient descent algorithms","authors":"Noureddine Rahali, M. Belloufi, R. Benzine","doi":"10.2478/mjpaa-2021-0001","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0001","url":null,"abstract":"Abstract An accelerated of the steepest descent method for solving unconstrained optimization problems is presented. which propose a fundamentally different conjugate gradient method, in which the well-known parameter βk is computed by an new formula. Under common assumptions, by using a modified Wolfe line search, descent property and global convergence results were established for the new method. Experimental results provide evidence that our proposed method is in general superior to the classical steepest descent method and has a potential to significantly enhance the computational efficiency and robustness of the training process.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"1 - 11"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46878282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Optimal control strategy of COVID-19 spread in Morocco using SEIRD model 基于SEIRD模型的摩洛哥COVID-19传播最优控制策略
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI: 10.2478/mjpaa-2021-0007
H. Ferjouchia, A. Kouidere, O. Zakary, M. Rachik
{"title":"Optimal control strategy of COVID-19 spread in Morocco using SEIRD model","authors":"H. Ferjouchia, A. Kouidere, O. Zakary, M. Rachik","doi":"10.2478/mjpaa-2021-0007","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0007","url":null,"abstract":"Abstract This paper aims to predict the development of the COVID-19 pandemic in Morocco from a mathematical approach. Based on the reliability of the data and the nature of confirmed cases, the SEIRD model is employed to provide a theoretical framework to forecast COVID-19 ongoing epidemic. Findings suggest that the structure and parameters of the proposed model give insights into the dynamics of the virus. Hence, this study contributes to the conceptual areas of knowledge on COVID-19 in proposing an optimal control plan to help decrease the number of confirmed cases by applying preventive measures such as social distancing, wearing facial masks. Matlab/Simulink TM simulations are used to illustrate the findings.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"66 - 79"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41700545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales 时间尺度上二阶非线性中立型动力方程正解的存在性
Moroccan Journal of Pure and Applied Analysis Pub Date : 2020-11-22 DOI: 10.2478/mjpaa-2021-0003
F. Bouchelaghem, A. Ardjouni, A. Djoudi
{"title":"Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales","authors":"F. Bouchelaghem, A. Ardjouni, A. Djoudi","doi":"10.2478/mjpaa-2021-0003","DOIUrl":"https://doi.org/10.2478/mjpaa-2021-0003","url":null,"abstract":"Abstract In this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.","PeriodicalId":36270,"journal":{"name":"Moroccan Journal of Pure and Applied Analysis","volume":"7 1","pages":"20 - 29"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48817956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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