In this paper, we establish a stochastic maximum principle for a stochastic minimization problem under partial information. With the Backward stochastic differential equations (in short BSDE’s), we establish a sufficient condition of optimality to characterize and determine an optimal control. This is done instead of using the Hamiltonian which is a deterministic function. The equations translating the dynamics of the state variables of the controlled system contain an BSPDE (Backward stochastic partial differential equation) which can be the unnormalized conditional density like the Zakai equation born from a problem of passage from partial to full information.
{"title":"A Stochastic Maximum Principle for a Minimization Problem Under Partial Information","authors":"Eric.K Tatiagoum","doi":"10.31559/glm2022.12.2.3","DOIUrl":"https://doi.org/10.31559/glm2022.12.2.3","url":null,"abstract":"In this paper, we establish a stochastic maximum principle for a stochastic minimization problem under partial information. With the Backward stochastic differential equations (in short BSDE’s), we establish a sufficient condition of optimality to characterize and determine an optimal control. This is done instead of using the Hamiltonian which is a deterministic function. The equations translating the dynamics of the state variables of the controlled system contain an BSPDE (Backward stochastic partial differential equation) which can be the unnormalized conditional density like the Zakai equation born from a problem of passage from partial to full information.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49624966","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":"New search direction of steepest descent method for solving large linear systems","authors":"Ayad Ramadhan Ali, B. Fathi","doi":"10.31559/glm2022.12.2.2","DOIUrl":"https://doi.org/10.31559/glm2022.12.2.2","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46962253","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":"Soft Pre Separation Axioms and Function with Soft Pre Closed Graph","authors":"Nehmat K. Ahmed, A. Khalaf","doi":"10.31559/glm2022.12.2.4","DOIUrl":"https://doi.org/10.31559/glm2022.12.2.4","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49208622","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 solutions for fractional differential equations with the Caputo-Hadamard fractional derivative of order α ∈ ( 1,2 ] . The uniqueness result is proved via Banach’s contraction mapping principle and the existence results are established by using the Schauder’s fixed point theorem. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability of the proposed equation is employed. Some examples are given to illustrate the results
{"title":"Existence and Ulam stability of solutions for Caputo-Hadamard fractional differential equations","authors":"Abduljawad K. Anwar, S. Murad","doi":"10.31559/glm2022.12.2.5","DOIUrl":"https://doi.org/10.31559/glm2022.12.2.5","url":null,"abstract":"In this paper, we study the existence of solutions for fractional differential equations with the Caputo-Hadamard fractional derivative of order α ∈ ( 1,2 ] . The uniqueness result is proved via Banach’s contraction mapping principle and the existence results are established by using the Schauder’s fixed point theorem. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability of the proposed equation is employed. Some examples are given to illustrate the results","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48742087","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":"Epsilon-Diskcyclic Operators","authors":"Abdallah M. Abu Jahel, As’ad Y. As’ad","doi":"10.31559/glm2022.12.2.1","DOIUrl":"https://doi.org/10.31559/glm2022.12.2.1","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46925900","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":"Estimating Regression Coefficients using Bootstrap with application to Covid-19 Data","authors":"Rojeen Taha Ahmad, Shelan Saied Ismaeel","doi":"10.31559/glm2022.12.2.6","DOIUrl":"https://doi.org/10.31559/glm2022.12.2.6","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48251404","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 concept of an α − nil reversible ring is a generalization of α − reversible ring as well as an extension of nil reversible rings. We first consider basic properties of α − nil reversible rings. Then we investigate extensions of α − nil reversible, including trivial extension, Dorroh extension and Jordan extension.
{"title":"Extensions of Nil-Reversible Rings with an Endomorphism α","authors":"Iman Jalal Ali, C. A. K. Ahmed","doi":"10.31559/glm2022.12.1.2","DOIUrl":"https://doi.org/10.31559/glm2022.12.1.2","url":null,"abstract":"The concept of an α − nil reversible ring is a generalization of α − reversible ring as well as an extension of nil reversible rings. We first consider basic properties of α − nil reversible rings. Then we investigate extensions of α − nil reversible, including trivial extension, Dorroh extension and Jordan extension.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42185077","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 work is to introduce a new class of nano semi-open sets in nano topological spaces which called nano Sβ-open sets in nano topological spaces. Also, we study the relationship between some types of nano near open sets with this new class. The class of nano Sβ-open sets exactly lie between nano Sp-open sets and nano semi-open sets.
{"title":"On Nano Sβ-Open Sets In Nano Topological Spaces","authors":"Osama T. Pirbal, Nehmat K. Ahmed","doi":"10.31559/glm2022.12.1.3","DOIUrl":"https://doi.org/10.31559/glm2022.12.1.3","url":null,"abstract":"The aim of this work is to introduce a new class of nano semi-open sets in nano topological spaces which called nano Sβ-open sets in nano topological spaces. Also, we study the relationship between some types of nano near open sets with this new class. The class of nano Sβ-open sets exactly lie between nano Sp-open sets and nano semi-open sets.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47455854","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, A new accurate solutions are obtained for classes of singular two-point boundary value problems (BVPs) using a new solution procedure based on the construction of the auxiliary functions of the standard optimal homotopy asymptotic method (OHAM). This procedure give us accurate approximate solutions using only one order of approximation compared with the solutions obtained previously by the standard OHAM approximation of three order. The obtained numerical results which are displayed in tables and plotted graphically in figures leads to concluded that this procedure is efficient and of third order reliable for finding the solutions of singular two BVPs.
{"title":"A New Accurate Approximate Solution of Singular Two-Point Boundary Value Problems","authors":"N. Anakira, O. Ababneh, A. S. Heilat, I. Batiha","doi":"10.31559/glm2022.12.1.4","DOIUrl":"https://doi.org/10.31559/glm2022.12.1.4","url":null,"abstract":"In this paper, A new accurate solutions are obtained for classes of singular two-point boundary value problems (BVPs) using a new solution procedure based on the construction of the auxiliary functions of the standard optimal homotopy asymptotic method (OHAM). This procedure give us accurate approximate solutions using only one order of approximation compared with the solutions obtained previously by the standard OHAM approximation of three order. The obtained numerical results which are displayed in tables and plotted graphically in figures leads to concluded that this procedure is efficient and of third order reliable for finding the solutions of singular two BVPs.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42914202","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 new results on chaotic operators on Banach spaces. Also we study the relation between subspacechaoticity and the direct sum of two operators. In particular, we prove that if the direct sum of two operators is a subspacechaotic, then both operators are subspace-chaotic, but the converse is not true in general. We show that this is true under necessary conditions.
{"title":"On Chaotic Operators","authors":"Abdallah M. Abu Jahel, As’ad Y. As’ad","doi":"10.31559/glm2022.12.1.1","DOIUrl":"https://doi.org/10.31559/glm2022.12.1.1","url":null,"abstract":"In this paper, we present new results on chaotic operators on Banach spaces. Also we study the relation between subspacechaoticity and the direct sum of two operators. In particular, we prove that if the direct sum of two operators is a subspacechaotic, then both operators are subspace-chaotic, but the converse is not true in general. We show that this is true under necessary conditions.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45845667","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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