In this paper, we study the large deviations principle textbf{(LDP)} of the Volterra process with reflection in H"olderian norm by using the Azencott method. As an application, we obtain the large deviations principle textbf{(LDP)} of a perturbed reflected diffusion process driven by the Fractional Brownian Motion with Hurst parameter $H in [frac{1}{2},1)$.
本文利用Azencott方法研究了Hölderian范数反射的Volterra过程的大偏差原理textbf{(ldp)}。作为应用，我们得到了具有Hurst参数$H in [frac{1}{2},1)$的分数阶布朗运动驱动的微扰反射扩散过程的大偏差原理textbf{(ldp)}。
{"title":"LARGE DEVIATIONS FOR STOCHASTIC VOLTERRA EQUATIONS WITH REFLECTION IN HÖLDERIAN NORM","authors":"R. A. Randrianomenjanahary, T. Rabeherimanana","doi":"10.37418/amsj.12.8.4","DOIUrl":"https://doi.org/10.37418/amsj.12.8.4","url":null,"abstract":"In this paper, we study the large deviations principle textbf{(LDP)} of the Volterra process with reflection in H\"olderian norm by using the Azencott method. As an application, we obtain the large deviations principle textbf{(LDP)} of a perturbed reflected diffusion process driven by the Fractional Brownian Motion with Hurst parameter $H in [frac{1}{2},1)$.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121703924","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}
Our aim in this paper is to study the existence and the uniqueness of the Caginalp phase-field system based on the Cattaneo Law,with initial conditions,Dirichlet Boundary Conditions and Regular Potentiels.
{"title":"EXISTENCE AND UNIQUENESS OF THE CAGINALP PHASE-FIELD SYSTEM BASED ON THE CATTANEO LAW","authors":"Cyr Seraphin, Ngamouyih Moussata, Narcisse Batangouna, Urbain Cyriaque Mavoungou","doi":"10.37418/amsj.12.8.2","DOIUrl":"https://doi.org/10.37418/amsj.12.8.2","url":null,"abstract":"Our aim in this paper is to study the existence and the uniqueness of the Caginalp phase-field system based on the Cattaneo Law,with initial conditions,Dirichlet Boundary Conditions and Regular Potentiels.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116477301","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}
C. Moussata, Deryl Nathan, Bonazebi Yindoula, B. Mampassi
In this paper we have placed a particular emphasis on the construction of the algorithmic scheme leading to the codes to identify the parameters of the silting of the banks of the rivers. To overcome the lack of real field data, we generated experimental data by solving a carefully chosen partial differential equation . All the codes obtained were executed on the Matlab 7.14(R2012 a) interface and the results of the simulation were satisfactory.
{"title":"NUMERICAL SIMULATION OF A PHENOMENON OF SILTING UP OF RIVER BANKS","authors":"C. Moussata, Deryl Nathan, Bonazebi Yindoula, B. Mampassi","doi":"10.37418/amsj.12.8.3","DOIUrl":"https://doi.org/10.37418/amsj.12.8.3","url":null,"abstract":"In this paper we have placed a particular emphasis on the construction of the algorithmic scheme leading to the codes to identify the parameters of the silting of the banks of the rivers. To overcome the lack of real field data, we generated experimental data by solving a carefully chosen partial differential equation . All the codes obtained were executed on the Matlab 7.14(R2012 a) interface and the results of the simulation were satisfactory.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122809806","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}
We propose in this article a hybridization of the algorithm of the MOMA-Plus method and that of the Differential Evolution method. This hybridization consists of defining a simplex around an efficient solution generated by MOMA-plus and applying the Differential Evolution algorithm to find a better solution than that obtained by MOMA-plus. The results interpreted through a performance study of the solutions obtained on multiobjective optimization test problems show that this hybridization improves the convergence of the basic MOMA-plus algorithm. Moreover, a better complexity than that of basic MOMA-plus is obtained.
{"title":"A NEW HYBRIDIZATION FOR IMPROVING THE CONVERGENCE OF THE MOMA-PLUS METHOD","authors":"A. Compaoré, Alexandre Som, K. Somé","doi":"10.37418/amsj.12.8.1","DOIUrl":"https://doi.org/10.37418/amsj.12.8.1","url":null,"abstract":"We propose in this article a hybridization of the algorithm of the MOMA-Plus method and that of the Differential Evolution method. This hybridization consists of defining a simplex around an efficient solution generated by MOMA-plus and applying the Differential Evolution algorithm to find a better solution than that obtained by MOMA-plus. The results interpreted through a performance study of the solutions obtained on multiobjective optimization test problems show that this hybridization improves the convergence of the basic MOMA-plus algorithm. Moreover, a better complexity than that of basic MOMA-plus is obtained.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114777253","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 work, we consider a hyperbolic fractional problem with non-degenerate integral boundary conditions. By using the method of Faedo-Galerkin, we demonstrate the existence of a solution of the considered problem by passing to the limit. A new result is given by proving the uniqueness of the solution based on assumptions for a similar problem.
{"title":"PROBLEM FOR A HYPERBOLIC FRACTIONAL EQUATION WITH THE NON-DEGENERATE INTEGRAL BOUNDARY CONDITIONS","authors":"A. Koulinté, A. Edoh, S. Bangan, D. M. Zakari","doi":"10.37418/amsj.12.7.4","DOIUrl":"https://doi.org/10.37418/amsj.12.7.4","url":null,"abstract":"In this work, we consider a hyperbolic fractional problem with non-degenerate integral boundary conditions. By using the method of Faedo-Galerkin, we demonstrate the existence of a solution of the considered problem by passing to the limit. A new result is given by proving the uniqueness of the solution based on assumptions for a similar problem.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122201262","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}
The mathematical model adopted in this work is based on the discretization of the conservation equations of mass, momentum and energy in 3 dimensions using the finite element method with appropriate initial and boundary conditions. In this numerical simulation work, we are interested in the testing of the influence of carbon nanotubes and in studying the effect of turbidity on solar ponds. The results show that an injection of the carbon nanotubes in a clear salt water solution in the storage zone clearly yields an improvement in thermal performance and generates a higher natural convection
{"title":"MATHEMATICAL MODELING OF A SALINITY GRADIENT SOLAR POND CONTAINING CARBON NANOTUBES WITH DIFFERENT LEVELS OF TURBIDITY","authors":"A. Ammar, B. Oussama, H. Sissaoui","doi":"10.37418/amsj.12.7.2","DOIUrl":"https://doi.org/10.37418/amsj.12.7.2","url":null,"abstract":"The mathematical model adopted in this work is based on the discretization of the conservation equations of mass, momentum and energy in 3 dimensions using the finite element method with appropriate initial and boundary conditions. In this numerical simulation work, we are interested in the testing of the influence of carbon nanotubes and in studying the effect of turbidity on solar ponds. The results show that an injection of the carbon nanotubes in a clear salt water solution in the storage zone clearly yields an improvement in thermal performance and generates a higher natural convection","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129710001","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}
R. Loko, C. Vouvoungui, R. Koukouatikissa, R. Bidounga, D. Barro
Whatever the sample size, the Galambos copula does not change. It remains constant. This is quite singular. To demonstrate this, we'll show that the generalized Galambos copula is completely independent of sample size. Unlike the copula of Gumbel, Ali-Michael and Haq, and certainly others, whose generalization depends on sample size, the Galambos copula is special. Unlike Gumbel's, Galambos's generalized copula is not size-dependent.
{"title":"A SINGULAR PROPERTY OF GALAMBOS COPULA","authors":"R. Loko, C. Vouvoungui, R. Koukouatikissa, R. Bidounga, D. Barro","doi":"10.37418/amsj.12.7.3","DOIUrl":"https://doi.org/10.37418/amsj.12.7.3","url":null,"abstract":"Whatever the sample size, the Galambos copula does not change. It remains constant. This is quite singular. To demonstrate this, we'll show that the generalized Galambos copula is completely independent of sample size. Unlike the copula of Gumbel, Ali-Michael and Haq, and certainly others, whose generalization depends on sample size, the Galambos copula is special. Unlike Gumbel's, Galambos's generalized copula is not size-dependent.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126244458","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 investigate the properties of the Schwarz matrix, a specific type of matrix that appears in the stability analysis of discrete-time linear time-invariant systems. We derive a formula for the determinant of the Schwarz matrix and a formula for its permanent. We also provide conditions on the entries of the Schwarz matrix that ensure the system described by the state update equation $x_{k+1} = Bx_k$ is stable, as well as conditions that guarantee the eigenvalues of the Schwarz matrix are real. These findings provide insights into the stability properties of systems characterized by Schwarz matrices and offer new tools for the analysis of interconnected subsystems in a cascaded structure.
{"title":"PROPERTIES OF SCHWARZ MATRICES IN DISCRETE-TIME LINEAR SYSTEMS","authors":"C.D. Lee, S. Koyuncu","doi":"10.37418/amsj.12.7.1","DOIUrl":"https://doi.org/10.37418/amsj.12.7.1","url":null,"abstract":"In this paper, we investigate the properties of the Schwarz matrix, a specific type of matrix that appears in the stability analysis of discrete-time linear time-invariant systems. We derive a formula for the determinant of the Schwarz matrix and a formula for its permanent. We also provide conditions on the entries of the Schwarz matrix that ensure the system described by the state update equation $x_{k+1} = Bx_k$ is stable, as well as conditions that guarantee the eigenvalues of the Schwarz matrix are real. These findings provide insights into the stability properties of systems characterized by Schwarz matrices and offer new tools for the analysis of interconnected subsystems in a cascaded structure.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124005982","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}
The aim of this paper is to propose a polynomial that we call ''characteristic polynomial'' of an integer convex polytope of dimension $d$ $(dgeq1)$. This polynomial makes it possible to count the number of vertices of an integer convex polytope without using the Schl"afli symbol. We give after that the algebraic characteristics of this polynomial.
{"title":"ON THE NUMBER OF VERTICES OF INTEGER CONVEX POLYTOPES","authors":"H. Ravelonirina, J. J. Rakoto","doi":"10.37418/amsj.12.6.4","DOIUrl":"https://doi.org/10.37418/amsj.12.6.4","url":null,"abstract":"The aim of this paper is to propose a polynomial that we call ''characteristic polynomial'' of an integer convex polytope of dimension $d$ $(dgeq1)$. This polynomial makes it possible to count the number of vertices of an integer convex polytope without using the Schl\"afli symbol. We give after that the algebraic characteristics of this polynomial.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122750459","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}
We present in this paper the new Branch and Bound method with new quadratic approach over a boxed set (a rectangle) of $mathbb{R}^{n}$. We construct an approximate convex quadratics functions of the objective function to fined a lower bound of the global optimal value of the original non convex quadratic problem (NQP) over each subset of this boxed set. We applied a partition and technical reducing on the domain of (NQP) to accelerate the convergence of the proposed algorithm. Finally,we study the convergence of the proposed algorithm and we give a simple comparison between this method and another methods wish have the same principle.
{"title":"NEW BRANCH AND BOUND METHOD OVER A BOXED SET OF $mathbb{R}^{n}$","authors":"B. Gasmi, R. Benacer","doi":"10.37418/amsj.12.6.3","DOIUrl":"https://doi.org/10.37418/amsj.12.6.3","url":null,"abstract":"We present in this paper the new Branch and Bound method with new quadratic approach over a boxed set (a rectangle) of $mathbb{R}^{n}$. We construct an approximate convex quadratics functions of the objective function to fined a lower bound of the global optimal value of the original non convex quadratic problem (NQP) over each subset of this boxed set. We applied a partition and technical reducing on the domain of (NQP) to accelerate the convergence of the proposed algorithm. Finally,we study the convergence of the proposed algorithm and we give a simple comparison between this method and another methods wish have the same principle.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116005395","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：