In the present paper, the SIR model tracks the numbers of susceptible, infected and recovered individuals during an epidemic with the help of ordinary differential equations (ODE). First, we give the model formulation of our phenomena. Secondly, a fully discrete difference scheme is derived for the SIR model.At the end of this aper, we give the simulation results of the model. A comparison of the obtained numerical results of both the models is performed in the absence of an exact solution.
{"title":"THE HIGHER FINITE DIFFERENCE METHOD FOR SOLVING THE DYNAMICAL MODEL OF COVID-19","authors":"Amar Megrous","doi":"10.37418/amsj.12.1.16","DOIUrl":"https://doi.org/10.37418/amsj.12.1.16","url":null,"abstract":"In the present paper, the SIR model tracks the numbers of susceptible, infected and recovered individuals during an epidemic with the help of ordinary differential equations (ODE). First, we give the model formulation of our phenomena. Secondly, a fully discrete difference scheme is derived for the SIR model.At the end of this aper, we give the simulation results of the model. A comparison of the obtained numerical results of both the models is performed in the absence of an exact solution.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127501680","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 present two New models named New-Weibull-Weibull ($NWW$) and New-Weibull-Rayleigh ($NWR$) from The New-Wei- bull-G family recently introduced that can have a variety of hazard rate shapes that allows to describe observations from different fields of study. The unknown parameters of the $NWW$ and $NWR$ models have been estimated under the maximum likelihood estimation method. Moreover, we construct a modified chi-squared goodness-of-fit test based on the textit{Nikulin– Rao–Robson} ($NRR$) statistic to verify the applicability of the proposed $NWW$ and $NWR$ models. The modified test shows that the models studied can be used as a good candidate for analyzing a large variety of real phenomena. The $NWW$ and $NWR$ models are applied upon a five different real complete and right-censored data sets in order to evaluate its practicability and flexibility.
{"title":"GOODNESS-OF-FIT TESTS FOR THE NEW WEIBULL-G FAMILY OF DISTRIBUTIONS","authors":"K.K. Meribout, N. Seddik-Ameur, H. Goual","doi":"10.37418/amsj.12.1.15","DOIUrl":"https://doi.org/10.37418/amsj.12.1.15","url":null,"abstract":"In this paper, we present two New models named New-Weibull-Weibull ($NWW$) and New-Weibull-Rayleigh ($NWR$) from The New-Wei- bull-G family recently introduced that can have a variety of hazard rate shapes that allows to describe observations from different fields of study. The unknown parameters of the $NWW$ and $NWR$ models have been estimated under the maximum likelihood estimation method. Moreover, we construct a modified chi-squared goodness-of-fit test based on the textit{Nikulin– Rao–Robson} ($NRR$) statistic to verify the applicability of the proposed $NWW$ and $NWR$ models. The modified test shows that the models studied can be used as a good candidate for analyzing a large variety of real phenomena. The $NWW$ and $NWR$ models are applied upon a five different real complete and right-censored data sets in order to evaluate its practicability and flexibility.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122332179","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}
M.N. Boukhetouta, M. Krachni, F. Yazid, F.S. Djeradi
In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ Delta ^n setminus Z $ into $ X $, where $ Z $ is an analytic subset of $Delta^n $ such that codimension of $ Z $ at least 2.
在本文中，我们证明了如果存在一个定义在复流形$ X $上的全纯的、固有的满射映射到具有可并行纤维的光滑代数曲线上，那么定义在$mathbb{C}^n$的Hartogs定域$ T $上的任何全纯映射都可以被全纯扩展。亚纯地)从$Delta^n set - Z $变成$ X $，其中$ Z $是$Delta^n $的解析子集，使得$ Z $的余维至少为2。
{"title":"HOLOMORPHIC EXTENSION","authors":"M.N. Boukhetouta, M. Krachni, F. Yazid, F.S. Djeradi","doi":"10.37418/amsj.12.1.14","DOIUrl":"https://doi.org/10.37418/amsj.12.1.14","url":null,"abstract":"In this paper, we prove that if there exists a holomorphic, proper, surjective map defined on a complex manifold $ X $ into a smooth algebraic curve with parallelizable fibers, then any holomorphic mappings defined on the Hartogs domain $ T $ of $mathbb{C}^n$ can be extended holomorphically (resp. meromorphically) from $ Delta ^n setminus Z $ into $ X $, where $ Z $ is an analytic subset of $Delta^n $ such that codimension of $ Z $ at least 2.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116599263","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 provide necessary optimality conditions for singular controlled stochastic differential equations driven by an orthogonal continuous martingale measure. The control is allowed to enter both the drift and diffusion coefficient and has two components, the first being relaxed and the second singular, the domain of the first control does not need to be convex, and for the relaxing method, we show by a counter-example that replacing the drift and diffusion coefficients by their relaxed counterparts does not define a true relaxed control problem. The maximum principle for these systems is established by means of spike variation techniques on the relaxed part of the control and a convex perturbation on the singular one. Our result is a generalization of Peng's maximum principle to singular control problems.
{"title":"MAXIMUM PRINCIPLE FOR SINGULAR CONTROL PROBLEMS OF SYSTEMS DRIVEN BY MARTINGALE MEASURES","authors":"S. Labed","doi":"10.37418/amsj.12.1.13","DOIUrl":"https://doi.org/10.37418/amsj.12.1.13","url":null,"abstract":"We provide necessary optimality conditions for singular controlled stochastic differential equations driven by an orthogonal continuous martingale measure. The control is allowed to enter both the drift and diffusion coefficient and has two components, the first being relaxed and the second singular, the domain of the first control does not need to be convex, and for the relaxing method, we show by a counter-example that replacing the drift and diffusion coefficients by their relaxed counterparts does not define a true relaxed control problem. The maximum principle for these systems is established by means of spike variation techniques on the relaxed part of the control and a convex perturbation on the singular one. Our result is a generalization of Peng's maximum principle to singular control problems.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"451 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122157187","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 remark that some stationary processes do not verify $x_infty|x_infty$ is equal to its value. To do this, we propose a new definitions to differentiate it in which a process is asymptotically stable if it verifies this property. We also remark that all processes in all financial models have missed this property. Which leads us to reexamine the models and look the impact and importance of this property.
{"title":"ASYMPTOTICALLY STABLE PROCESS AND APPLICATIONS","authors":"A. Hasina, R. Sedra, R. Raft","doi":"10.37418/amsj.12.1.10","DOIUrl":"https://doi.org/10.37418/amsj.12.1.10","url":null,"abstract":"We remark that some stationary processes do not verify $x_infty|x_infty$ is equal to its value. To do this, we propose a new definitions to differentiate it in which a process is asymptotically stable if it verifies this property. We also remark that all processes in all financial models have missed this property. Which leads us to reexamine the models and look the impact and importance of this property.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126604817","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 POISSON ALGEBRA STRUCTURE OVER THE EXTERIOR ALGEBRA OF A QUADRATIC SPACE","authors":"S. C. Gatsé, C. C. Likouka","doi":"10.37418/amsj.12.1.11","DOIUrl":"https://doi.org/10.37418/amsj.12.1.11","url":null,"abstract":"We construct a Poisson algebra structure of degree $-2$ over the exterior algebra of a quadratic space. Here we do not use Clifford algebra as in [4].","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115756947","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 give an example of locally conformally symplectic manifolds.
本文的目的是给出一个局部共形辛流形的例子。
{"title":"AN EXAMPLE OF LOCALLY CONFORMALLY SYMPLECTIC MANIFOLDS","authors":"S. C. Gatsé","doi":"10.37418/amsj.12.1.12","DOIUrl":"https://doi.org/10.37418/amsj.12.1.12","url":null,"abstract":"Our aim in this paper is to give an example of locally conformally symplectic manifolds.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114650913","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}
This article studies the problem of nonparametric estimation of the conditional model of a scalar response variable $Y$ given a functional random variable $X$. Our estimate is based on semi recursive approach. The asymptotic properties of the proposed estimators are established Under Mixing Conditions.
{"title":"SEMI RECURSIVE ESTIMATION OF CONDITIONAL CUMULATIVE DISTRIBUTION FUNCTION FOR FUNCTIONAL DATA UNDER MIXING CONDITION","authors":"Bouadjemi Abdelkader","doi":"10.37418/amsj.12.1.9","DOIUrl":"https://doi.org/10.37418/amsj.12.1.9","url":null,"abstract":"This article studies the problem of nonparametric estimation of the conditional model of a scalar response variable $Y$ given a functional random variable $X$. Our estimate is based on semi recursive approach. The asymptotic properties of the proposed estimators are established Under Mixing Conditions.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129703809","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 article, Adomian Method is applied for spatially inhomogeneous Population Balance Equation incorporating breakage and coalescence processes in both batch and continuous flow systems. It should be Note that the analytical solutions obtained using this technique are not available in the literature.
{"title":"ADOMIAN DECOMPOSITION METHOD FOR SOLVING SPATIALLY INHOMOGENUOUS POPULATION BALANCE EQUATION","authors":"I. Achour, A. Bellagoun","doi":"10.37418/amsj.12.1.8","DOIUrl":"https://doi.org/10.37418/amsj.12.1.8","url":null,"abstract":"In this article, Adomian Method is applied for spatially inhomogeneous Population Balance Equation incorporating breakage and coalescence processes in both batch and continuous flow systems. It should be Note that the analytical solutions obtained using this technique are not available in the literature.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125484984","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 2020, G. Suresh Singh and Manju V. N. cite{mvn} introduced the concept of weak join of two disjoint graphs with respect to the degrees of the given graphs and categorized them as homogeneous weak join, heterogeneous weak join and studied some of their properties. Homogeneous weak join can be splitted in to three cases namely, odd to odd degree weak join, even to even degree weak join, odd to odd and even to even degree weak join. Similarly, heterogeneous weak join includes the other three cases namely, odd to even degree weak join, even to odd degree weak join, odd to even and even to odd degree weak join. In this paper we try to find bounds for the Wiener index of odd to odd, even to even, odd to even and even to odd degree weak join of graphs.
2020年，G. Suresh Singh和Manju V. N. cite{mvn}针对给定图的度引入了两个不相交图的弱连接概念，并将其分类为齐次弱连接和异质弱连接，并研究了它们的一些性质。齐次弱连接可分为奇到奇次弱连接、偶到偶次弱连接、奇到奇和偶到偶次弱连接三种情况。类似地，异构弱连接还包括其他三种情况，即奇偶弱连接、偶奇弱连接、奇偶弱连接和偶奇弱连接。本文试图找到图的奇到奇、偶到偶、奇到偶、偶到奇次弱连接的维纳指数的界。
{"title":"SOME BOUNDS FOR THE WIENER INDEX OF WEAK JOIN OF TWO GRAPHS","authors":"V. N. Manju, T. Athul, G. Suresh Singh","doi":"10.37418/amsj.12.1.7","DOIUrl":"https://doi.org/10.37418/amsj.12.1.7","url":null,"abstract":"In 2020, G. Suresh Singh and Manju V. N. cite{mvn} introduced the concept of weak join of two disjoint graphs with respect to the degrees of the given graphs and categorized them as homogeneous weak join, heterogeneous weak join and studied some of their properties. Homogeneous weak join can be splitted in to three cases namely, odd to odd degree weak join, even to even degree weak join, odd to odd and even to even degree weak join. Similarly, heterogeneous weak join includes the other three cases namely, odd to even degree weak join, even to odd degree weak join, odd to even and even to odd degree weak join. In this paper we try to find bounds for the Wiener index of odd to odd, even to even, odd to even and even to odd degree weak join of graphs.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128708837","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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