In this paper, we introduce a D -isometric deformation of almost contact metric manifold where we give some new results of this type of deformation, the harmonicity and the biharmonicity of the identity map are characterized by using this deformation.
{"title":"On the $D$-isometric deformation of Kenmotsu manifolds and biharmonic maps","authors":"Smail Chemikh, D. Behloul, S. Ouakkas","doi":"10.21915/bimas.2022204","DOIUrl":"https://doi.org/10.21915/bimas.2022204","url":null,"abstract":"In this paper, we introduce a D -isometric deformation of almost contact metric manifold where we give some new results of this type of deformation, the harmonicity and the biharmonicity of the identity map are characterized by using this deformation.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"5 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74764401","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}
In this paper, we use the mean squared relative error as a loss function to construct a local linear estimator of the regression operator. More precisely, we consider n pairs of independent random variables ( X i , Y i ) for i = 1 , . . . , n that we assume drawn from the pair ( X, Y ), which is valued in ( F , R ), where F is a semi-metric space equipped with the semi-metric d . Under some standard assumptions, we give the convergence rate in mean square of the constructed estimator. The usefulness of the estimator is highlighted through the exact expression involved in the leading terms of the quadratic error. Notice that this method is useful in analyzing data with positive responses, such as life times.
本文用均方相对误差作为损失函数，构造了回归算子的局部线性估计。更准确地说，我们考虑n对独立随机变量(X i, Y i)，对于i = 1，…。， n，我们假设从(X, Y)对中得到，它的值在(F, R)中，其中F是一个半度量空间，具有半度量d。在一些标准假设下，给出了构造估计量的均方收敛速率。通过在二次误差的前导项中所涉及的精确表达式，突出了估计器的有用性。请注意，此方法在分析具有积极响应的数据(如生命周期)时非常有用。
{"title":"High dimensional statistics: Quadratic error in the local linear estimation of the relative regression","authors":"Oussama Bouanani, Mustapha Rachdi, Saâdia Rahmani","doi":"10.21915/bimas.2022206","DOIUrl":"https://doi.org/10.21915/bimas.2022206","url":null,"abstract":"In this paper, we use the mean squared relative error as a loss function to construct a local linear estimator of the regression operator. More precisely, we consider n pairs of independent random variables ( X i , Y i ) for i = 1 , . . . , n that we assume drawn from the pair ( X, Y ), which is valued in ( F , R ), where F is a semi-metric space equipped with the semi-metric d . Under some standard assumptions, we give the convergence rate in mean square of the constructed estimator. The usefulness of the estimator is highlighted through the exact expression involved in the leading terms of the quadratic error. Notice that this method is useful in analyzing data with positive responses, such as life times.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"13 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84342415","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}
{"title":"Consistency result of recursive conditional distribution estimate for dependent data under left truncation, with applications to the conditional quantile","authors":"Fatima Benziadi, I. Bouazza","doi":"10.21915/bimas.2022102","DOIUrl":"https://doi.org/10.21915/bimas.2022102","url":null,"abstract":"","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"49 22 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79767640","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}
{"title":"Solvability of solution of singular and degenerate fractional nonlinear parabolic Dirichlet problems","authors":"Bourabta Ahmed, Oussaeif Taki-Eddine, Rezzoug Imad, Chebana Zainouba","doi":"10.21915/bimas.2022104","DOIUrl":"https://doi.org/10.21915/bimas.2022104","url":null,"abstract":"","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"17 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87170581","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}
{"title":"Asymptotic expansion of the Bergman kernel via semi-classical symbolic calculus","authors":"Yuanyuan Hou","doi":"10.21915/bimas.2022101","DOIUrl":"https://doi.org/10.21915/bimas.2022101","url":null,"abstract":"","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"56 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82095343","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}
{"title":"A priori estimate and numerical study of solution for a parabolic equation with nonlinear integral condition","authors":"Chebana Zainouba, Oussaeif Taki-Eddine, Dehilis Sofiane, Leila Benaoua","doi":"10.21915/bimas.2022103","DOIUrl":"https://doi.org/10.21915/bimas.2022103","url":null,"abstract":"","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"27 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77043765","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}
In this paper, we study under refined Lipschitz hypothesis, the question of existence and uniqueness of solution of controlled neutral stochastic functional differential equations driven by G -Brownian motion ( G -NSFDEs in short). An existence of a relaxed optimal control where the neutral and diffusion terms do not depend on the control variable was the main result of the article. The latter is done by using tightness techniques and the weak convergence techniques for each probability measure in the set of all possible probabilities of our dynamic. A motivation of our work is presented and a numerical analysis for the uncontrolled G -NSFDE is given.
{"title":"Existence of relaxed optimal control for $G$-neutral stochastic functional differential equations with uncontrolled diffusion","authors":"Nabil Elgroud, H. Boutabia, A. Redjil, O. Kebiri","doi":"10.21915/bimas.2022202","DOIUrl":"https://doi.org/10.21915/bimas.2022202","url":null,"abstract":"In this paper, we study under refined Lipschitz hypothesis, the question of existence and uniqueness of solution of controlled neutral stochastic functional differential equations driven by G -Brownian motion ( G -NSFDEs in short). An existence of a relaxed optimal control where the neutral and diffusion terms do not depend on the control variable was the main result of the article. The latter is done by using tightness techniques and the weak convergence techniques for each probability measure in the set of all possible probabilities of our dynamic. A motivation of our work is presented and a numerical analysis for the uncontrolled G -NSFDE is given.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"238 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74696931","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}
{"title":"A New Approach to Stochastic Integration with Respect to Fractional Brownian Motion for No Adapted Processes","authors":"Bachir Cherif Khalida, Kandouci Abdeldjebbar","doi":"10.21915/bimas.2021403","DOIUrl":"https://doi.org/10.21915/bimas.2021403","url":null,"abstract":"","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"44 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74800958","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}
{"title":"Existence results for higher order fractional differential equations with integral boundary conditions via Kuratowski measure of noncompactnes","authors":"Adel Lachouri, A. Ardjouni, N. Gouri, K. Khelil","doi":"10.21915/bimas.2021401","DOIUrl":"https://doi.org/10.21915/bimas.2021401","url":null,"abstract":"","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"47 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79872376","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}
In this paper, we study the existence of periodic and asymptotically periodic solutions of neutral nonlinear coupled Volterra integro-differential systems. We furnish sufficient conditions for the existence of such solutions. Krasnoselskii’s fixed point theorem is used in this analysis.
{"title":"Periodic and Asymptotically Periodic Solutions for Neutral Nonlinear Coupled Volterra Integro-Differential Systems with Two Variable Delays","authors":"Bouzid Mansouri, A. Ardjouni, A. Djoudi","doi":"10.21915/bimas.2021404","DOIUrl":"https://doi.org/10.21915/bimas.2021404","url":null,"abstract":"In this paper, we study the existence of periodic and asymptotically periodic solutions of neutral nonlinear coupled Volterra integro-differential systems. We furnish sufficient conditions for the existence of such solutions. Krasnoselskii’s fixed point theorem is used in this analysis.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"15 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74124343","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}
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