Pub Date : 2023-08-18DOI: 10.56947/gjom.v15i1.1060
Manzoor Ahmad, Rajshree Mishra, R. Jain
There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black-Scholes model on a single asset is a partial differential equation characterizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of the regular Black-Scholes model. Explicit solution of the problem has been obtained with the help of generalized Mittag-Leffer function. The numerical analysis prove that this method is efficacious in solving various problems of financial theory.
{"title":"Analytical solution of time fractional Black-Scholes equation with two assets through new Sumudu Transform iterative method","authors":"Manzoor Ahmad, Rajshree Mishra, R. Jain","doi":"10.56947/gjom.v15i1.1060","DOIUrl":"https://doi.org/10.56947/gjom.v15i1.1060","url":null,"abstract":"There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black-Scholes model on a single asset is a partial differential equation characterizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of the regular Black-Scholes model. Explicit solution of the problem has been obtained with the help of generalized Mittag-Leffer function. The numerical analysis prove that this method is efficacious in solving various problems of financial theory.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128335485","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}
Pub Date : 2023-04-15DOI: 10.56947/gjom.v14i2.1177
Issa Cherif Geraldo
The aim of this paper is to prove the existence, uniqueness and strong consistency (i.e. almost sure convergence to the true unknown value) of the maximum likelihood estimator (MLE) of the vector parameter for a statistical model used in statistics applied to road safety. In the general case, the strong consistency of the MLE may be established by using the well-known result by Abraham Wald (in 1949) or its variants under a set of conditions. However, for the model considered in this paper, all these conditions are very difficult to verify because of the great dimension of the parameter space and the rather complex expression of the log-likelihood function. To circumvent these difficulties, we first demonstrate that the MLE exists and is unique afterwards we demonstrate the strong consistency of the MLE using the properties of the model and some theorems of mathematical analysis.
{"title":"Existence, uniqueness and strong consistency of the maximum likelihood estimator for a model of accidents frequencies","authors":"Issa Cherif Geraldo","doi":"10.56947/gjom.v14i2.1177","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1177","url":null,"abstract":"The aim of this paper is to prove the existence, uniqueness and strong consistency (i.e. almost sure convergence to the true unknown value) of the maximum likelihood estimator (MLE) of the vector parameter for a statistical model used in statistics applied to road safety. In the general case, the strong consistency of the MLE may be established by using the well-known result by Abraham Wald (in 1949) or its variants under a set of conditions. However, for the model considered in this paper, all these conditions are very difficult to verify because of the great dimension of the parameter space and the rather complex expression of the log-likelihood function. To circumvent these difficulties, we first demonstrate that the MLE exists and is unique afterwards we demonstrate the strong consistency of the MLE using the properties of the model and some theorems of mathematical analysis.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115119064","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}
Pub Date : 2023-04-15DOI: 10.56947/gjom.v14i2.1179
Tuğba Mert, M. Atc̣eken, Pakize Uygun
In this article, semi-symmetry of almost C(α)-manifold is investigated on some special curvature tensors. First, the behavior of the almost C(α)-manifold is investigated when the special curvature tensors discussed are flat. Then, for these special curvature tensors, the behavior of the manifold in the semi-symmetric condition is observed and for some special curvature tensors, important properties such as the semi-symmetric almost C(α)-manifold being Einstein and η-Einstein manifold are obtained.
{"title":"Semi-symmetric almost C(α)-manifold on some curvature tensors","authors":"Tuğba Mert, M. Atc̣eken, Pakize Uygun","doi":"10.56947/gjom.v14i2.1179","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1179","url":null,"abstract":"In this article, semi-symmetry of almost C(α)-manifold is investigated on some special curvature tensors. First, the behavior of the almost C(α)-manifold is investigated when the special curvature tensors discussed are flat. Then, for these special curvature tensors, the behavior of the manifold in the semi-symmetric condition is observed and for some special curvature tensors, important properties such as the semi-symmetric almost C(α)-manifold being Einstein and η-Einstein manifold are obtained.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"453 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125787698","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}
Pub Date : 2023-04-15DOI: 10.56947/gjom.v14i2.1176
Hiren D. Patel
Let R be a commutative ring with non-zero identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r∈R 0 such that Ir=(0). Let A(R) denote the set of all annihilating ideals of R and A(R)∗=A(R){(0)}. In this article, we introduce and investigate the weakly annihilating-ideal graph of R denoted by WAG(R). It is the undirected graph whose vertex set is A(R)∗ and two distinct vertices I, J are adjacent in this graph if and only if there exist non-zero ideals A, B of R with A ⊆ ann(I) and B ⊆ ann(J) such that AB=(0). The aim of this article is to study the interplay between the ring-theoretic properties of R and the graph-theoretic properties of WAG(R). We discuss some results regarding the connectedness of WAG(R) and determine its diameter and girth. Moreover, we provide some conditions under which WAG(R) and AG(R) are identical.
{"title":"The weakly annihilating-ideal graph of a commutative ring","authors":"Hiren D. Patel","doi":"10.56947/gjom.v14i2.1176","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1176","url":null,"abstract":"Let R be a commutative ring with non-zero identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r∈R 0 such that Ir=(0). Let A(R) denote the set of all annihilating ideals of R and A(R)∗=A(R){(0)}. In this article, we introduce and investigate the weakly annihilating-ideal graph of R denoted by WAG(R). It is the undirected graph whose vertex set is A(R)∗ and two distinct vertices I, J are adjacent in this graph if and only if there exist non-zero ideals A, B of R with A ⊆ ann(I) and B ⊆ ann(J) such that AB=(0). The aim of this article is to study the interplay between the ring-theoretic properties of R and the graph-theoretic properties of WAG(R). We discuss some results regarding the connectedness of WAG(R) and determine its diameter and girth. Moreover, we provide some conditions under which WAG(R) and AG(R) are identical.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"05 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127191598","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}
Pub Date : 2023-04-15DOI: 10.56947/gjom.v14i2.1178
S. Sarkar, S. Pahan, A. Bhattacharyya
The aim of the present paper is to study the critical point equation (shortly CPE) conjecture within the framework of various contact metric manifolds. First we establish that Kenmotsu manifold satisfying the CPE either becomes an Einstein manifold or the derivative of potential function along characteristic vector field satisfy a certain relation on the distribution of η. Next we study CPE on (κ, μ)'-almost Kenmotsu manifold and obtain that the manifold is Einstein. Later in case of 3-dimensional trans-Sasakian manifold, we get that either the manifold becomes α-Sasakian or it becomes Einstein. Finally we give examples of 3-dimensional trans-Sasakian manifold and (κ ,μ)'-almost Kenmotsu manifold to verify our outcomes.
{"title":"Critical point equation within the framework of various contact metric manifolds","authors":"S. Sarkar, S. Pahan, A. Bhattacharyya","doi":"10.56947/gjom.v14i2.1178","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1178","url":null,"abstract":"The aim of the present paper is to study the critical point equation (shortly CPE) conjecture within the framework of various contact metric manifolds. First we establish that Kenmotsu manifold satisfying the CPE either becomes an Einstein manifold or the derivative of potential function along characteristic vector field satisfy a certain relation on the distribution of η. Next we study CPE on (κ, μ)'-almost Kenmotsu manifold and obtain that the manifold is Einstein. Later in case of 3-dimensional trans-Sasakian manifold, we get that either the manifold becomes α-Sasakian or it becomes Einstein. Finally we give examples of 3-dimensional trans-Sasakian manifold and (κ ,μ)'-almost Kenmotsu manifold to verify our outcomes.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127616905","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}
Pub Date : 2023-04-04DOI: 10.56947/gjom.v14i2.1042
Mounir El Ouarrachi, Abdelmonaim Bouchikhi
Let f : A → B be a ring homomorphism and J be an ideal of B. In this note, we investigate the transfer of the weak McCoy property to the amalgamation of A with B along J with respect to f (denoted by A⋈fJ) introduced and studied by D’Anna, Finocchiaro and Fontana in 2009. Our aim is to provide conditions under which A⋈fJ is a left weak McCoy (resp. right weak McCoy, McCoy) ring. Our results enrich the literature with new families of left weak McCoy (resp. right weak McCoy, weak McCoy) rings.
{"title":"Weak McCoy property in amalgamated algebra along ideal","authors":"Mounir El Ouarrachi, Abdelmonaim Bouchikhi","doi":"10.56947/gjom.v14i2.1042","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1042","url":null,"abstract":"Let f : A → B be a ring homomorphism and J be an ideal of B. In this note, we investigate the transfer of the weak McCoy property to the amalgamation of A with B along J with respect to f (denoted by A⋈fJ) introduced and studied by D’Anna, Finocchiaro and Fontana in 2009. Our aim is to provide conditions under which A⋈fJ is a left weak McCoy (resp. right weak McCoy, McCoy) ring. Our results enrich the literature with new families of left weak McCoy (resp. right weak McCoy, weak McCoy) rings.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131866584","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}
Pub Date : 2023-04-04DOI: 10.56947/gjom.v14i2.1107
M. Altunbaş
In this paper, we investigate Ricci solitons on tangent bundles with respect to the complete lift of a projective semi-symmetric connection using vertical and complete lifts of torqued vector fields.
本文利用力矩矢量场的垂直和完全提升，研究了切束上关于射影半对称连接的完全提升的Ricci孤子。
{"title":"Ricci solitons on tangent bundles with the complete lift of a projective semi-symmetric connection","authors":"M. Altunbaş","doi":"10.56947/gjom.v14i2.1107","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1107","url":null,"abstract":"In this paper, we investigate Ricci solitons on tangent bundles with respect to the complete lift of a projective semi-symmetric connection using vertical and complete lifts of torqued vector fields.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121832357","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 objective of the present paper is to study conformal η-Ricci soliton on Lorentzian Para-Kenmotsu manifolds with some curvature conditions. We study Concircular curvature tensor, Quasi conformal curvature tensor, Codazi type of Ricci tensor and cyclic parallel Ricci tensor in Lorentzian Para-Kenmotsu manifolds. At last we give examples of such manifolds.
{"title":"Conformal η-Ricci soliton in Lorentzian para Kenmotsu manifolds","authors":"R. Prasad, Vinay Kumar","doi":"10.56947/gjom.v14i2.931","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.931","url":null,"abstract":"The objective of the present paper is to study conformal η-Ricci soliton on Lorentzian Para-Kenmotsu manifolds with some curvature conditions. We study Concircular curvature tensor, Quasi conformal curvature tensor, Codazi type of Ricci tensor and cyclic parallel Ricci tensor in Lorentzian Para-Kenmotsu manifolds. At last we give examples of such manifolds.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131071750","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}
Pub Date : 2023-04-04DOI: 10.56947/gjom.v14i2.1000
M. Dadhwal, G. Devi
In this paper, the notion of multiplicative generalized (α, β)-reverse derivations associated with (α, β)-reverse derivations of *-prime rings is characterized. The action of these derivations on *-Lie ideals of *-prime rings is also investigated. Moreover, the commutativity of *-prime rings admitting multiplicative generalized (α, β)-reverse derivations associated with (α, β)-reverse derivations satisfying certain algebraic identities on *-Lie ideals is explored.
{"title":"On Lie ideals and multiplicative generalized (α, β)-reverse derivations of *-prime rings","authors":"M. Dadhwal, G. Devi","doi":"10.56947/gjom.v14i2.1000","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.1000","url":null,"abstract":"In this paper, the notion of multiplicative generalized (α, β)-reverse derivations associated with (α, β)-reverse derivations of *-prime rings is characterized. The action of these derivations on *-Lie ideals of *-prime rings is also investigated. Moreover, the commutativity of *-prime rings admitting multiplicative generalized (α, β)-reverse derivations associated with (α, β)-reverse derivations satisfying certain algebraic identities on *-Lie ideals is explored.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126274464","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 class Gη_1,η_2β(α,t), consisting of Bazilevic functions of type α and involving a certain generalized differential operator is defined by means of Gegenbauer polynomials. Initial coefficient bounds and Fekete-Szego estimates for functions belonging to this class are obtained. Furthermore, upon varying the involving parameters in our main results, a number of known and new results are stated as corollaries.
{"title":"Gegenbauer polynomials for certain subclasses of Bazilevic functions associated with a generalized operator defined by convolution","authors":"E. Oyekan","doi":"10.56947/gjom.v14i2.967","DOIUrl":"https://doi.org/10.56947/gjom.v14i2.967","url":null,"abstract":"In this paper, a class Gη_1,η_2β(α,t), consisting of Bazilevic functions of type α and involving a certain generalized differential operator is defined by means of Gegenbauer polynomials. Initial coefficient bounds and Fekete-Szego estimates for functions belonging to this class are obtained. Furthermore, upon varying the involving parameters in our main results, a number of known and new results are stated as corollaries. ","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129314676","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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