Pub Date : 2022-01-01DOI: 10.11648/j.pamj.20221102.12
Aideyan Donald Osaro, Usman Suleiman
{"title":"Frequency Domain Analysis of Nigeria All Share and Capital Index from 1989-2010 (A Case Study of Nigerian Stock Market)","authors":"Aideyan Donald Osaro, Usman Suleiman","doi":"10.11648/j.pamj.20221102.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20221102.12","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"49 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82208305","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 : 2022-01-01DOI: 10.11648/j.pamj.20221101.11
Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles
{"title":"A Mathematical Analysis for the Preservation of Forestry Biomass Using the Laplace Decomposition Method","authors":"Bazuaye Frank Etin-Osa, Omoregbe Osahon Charles","doi":"10.11648/j.pamj.20221101.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20221101.11","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80380467","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 : 2022-01-01DOI: 10.11648/j.pamj.20221102.11
Zaheer Kareem Ansari, A. Kumar Singh, Priyesh Kumar, Jay Prakash Patel
{"title":"Fixed Point Result on Generalized Cone b-Metric Spaces","authors":"Zaheer Kareem Ansari, A. Kumar Singh, Priyesh Kumar, Jay Prakash Patel","doi":"10.11648/j.pamj.20221102.11","DOIUrl":"https://doi.org/10.11648/j.pamj.20221102.11","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78846104","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 : 2022-01-01DOI: 10.11648/j.pamj.20221101.12
Ganesan Thangaraj, Ayyavu Vinothkumar
{"title":"On Fuzzy Semi-P-spaces and Related Concepts","authors":"Ganesan Thangaraj, Ayyavu Vinothkumar","doi":"10.11648/j.pamj.20221101.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20221101.12","url":null,"abstract":"","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"40 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78023638","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 : 2021-10-12DOI: 10.11648/J.PAMJ.20211005.11
Yang Liu
In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic structure on the tangent bundle of a Riemannian manifold.
{"title":"On Geodesic Flow and Energy Functional on Riemannian Manifolds","authors":"Yang Liu","doi":"10.11648/J.PAMJ.20211005.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211005.11","url":null,"abstract":"In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic structure on the tangent bundle of a Riemannian manifold.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75285248","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 : 2021-08-04DOI: 10.11648/J.PAMJ.20211003.13
Nadia Khan, Munazza Shamus, Fauzia Ghulam Hussain, Mansoor Iqbal
Let G be a connected graph with n vertices. Then the class of connected graphs having n vertices is denoted by Gn. The subclass of connected graphs with 5 cycles are denoted by Gn5. The classification of graph G∈Gn5 depends on the number of edges and the sum of the degrees of the vertices of the graph. Any graph in Gn5 contains five linearly independent cycles having at least n+3 edges and the sum of degrees of vertices of 5-cyclic must be equal to twice of n+4. In this paper, minimum degree distance of class of five cyclic connected graph is investigated. To find minimum degree distance of a graph some transformations T have been defined. These transformation have been applied on the graph G∈Gn5 in such a way that the resultant graph belongs to Gn5 and also degree distance of T(G) is always must be less than G. For n=5, the five 5-cyclic graph has minimum degree distance 78 and the minimum degree distance of 5-cyclic graphs having six vertices is 124. In case of n greater than 6, a general formula for minimum degree distance is investigated. In this paper, we proved that the minimum degree distance of connected 5 cyclic graphs is 3n2+13n-62 by using transformations, for n≥7.
{"title":"Minimum Degree Distance of Five Cyclic Graphs","authors":"Nadia Khan, Munazza Shamus, Fauzia Ghulam Hussain, Mansoor Iqbal","doi":"10.11648/J.PAMJ.20211003.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211003.13","url":null,"abstract":"Let G be a connected graph with n vertices. Then the class of connected graphs having n vertices is denoted by Gn. The subclass of connected graphs with 5 cycles are denoted by Gn5. The classification of graph G∈Gn5 depends on the number of edges and the sum of the degrees of the vertices of the graph. Any graph in Gn5 contains five linearly independent cycles having at least n+3 edges and the sum of degrees of vertices of 5-cyclic must be equal to twice of n+4. In this paper, minimum degree distance of class of five cyclic connected graph is investigated. To find minimum degree distance of a graph some transformations T have been defined. These transformation have been applied on the graph G∈Gn5 in such a way that the resultant graph belongs to Gn5 and also degree distance of T(G) is always must be less than G. For n=5, the five 5-cyclic graph has minimum degree distance 78 and the minimum degree distance of 5-cyclic graphs having six vertices is 124. In case of n greater than 6, a general formula for minimum degree distance is investigated. In this paper, we proved that the minimum degree distance of connected 5 cyclic graphs is 3n2+13n-62 by using transformations, for n≥7.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"95 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75416218","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 : 2021-08-04DOI: 10.11648/J.PAMJ.20211004.11
Ezequias Adolfo Domingas Cassela Adolfo Cassela, Amado Leonardo André
This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of Rene Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an "if...then" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.
{"title":"From Pure Geomatics for Algebraic Procedures with a View to Obtaining Equations from Ellipse from the Perspective of René Descartes","authors":"Ezequias Adolfo Domingas Cassela Adolfo Cassela, Amado Leonardo André","doi":"10.11648/J.PAMJ.20211004.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211004.11","url":null,"abstract":"This article aims to study the ellipse from the perspective of pure or synthetic geometry to the representation of points on a plane through the use of real numbers, as well as the representation and classification of this conic curve through the use of equations. The perspective developed in this article is based on the view of Rene Descartes, in considering that “the algebraic steps in a demonstration should really correspond to a geometric representation.” The relevance of this article is to bring a reflection that eliminates the study of Analytical Geometry through ready-made and finished formulas, without satisfactory justification and without a logical chain that gives a greater meaning to the studied concepts. In general, the study developed in this article emphasizes the demonstration of results based on propositions adapted a priori, whose ability to be developed is aimed at establishing an \"if...then\" type of reasoning, making conjectures involving various knowledge already acquired and confirming such truths from a logical system, using definitions and propositions. Therefore, the demonstrations made in the scope of Synthetic Geometry will help to establish a connection with the equations obtained from the perspective of Analytical Geometry, serving as a consultation for students and professors of Analytical Geometry, thus avoiding sudden transitions between contents of degrees of distinct difficulties.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79504854","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 : 2021-07-27DOI: 10.11648/J.PAMJ.20211003.12
Lemi Moges Mengesha, Solomon Zerfu Degefa
This paper was intended to examine mathematics teacher’s practices of assessment techniques used in secondary schools in Guraghe Zone and attempt to explore methods of assessment used by mathematics teachers, nature of feedback provided to student and the support provided by school authorities to enable them undertake assessment effectively. For this study, mixed research approach, inferential statistics and descriptive survey method would be employed; both quantitative and qualitative data were gathered through questionnaire, document analysis, FGD and interviews. The total sample sizes of the study were 377 students and all mathematics teachers in the selected schools. In addition thirteen school principals were interviewed. In the selection of the sample population, stratified sampling, systematic random sampling and purposive samplings were used. Thus, the findings indicate that, the overall respondents’ perception towards practices of continuous assessment has mean 3.630 and standard deviation 1.063 which is medium perception. In addition to this, the result showed that the first challenging step to implement Continuous assessment is large class size; the second is lack of in-services training, the third is it takes time and the last challenging step is shortage of teaching materials. Study showed that most of the teachers use the traditional feedback mechanism for continuous assessment which is not recommendable and had to use the enhanced feedback to encourage the learners’ capacity. So, concerned bodies of the zone education office and schools should give support by providing teaching materials and giving training for teachers in order to increase and develop their assessment practices in theimplementation Continuous assessment.
{"title":"Assessment Practices of Secondary School Mathematics Teachers in Guraghe Zone","authors":"Lemi Moges Mengesha, Solomon Zerfu Degefa","doi":"10.11648/J.PAMJ.20211003.12","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211003.12","url":null,"abstract":"This paper was intended to examine mathematics teacher’s practices of assessment techniques used in secondary schools in Guraghe Zone and attempt to explore methods of assessment used by mathematics teachers, nature of feedback provided to student and the support provided by school authorities to enable them undertake assessment effectively. For this study, mixed research approach, inferential statistics and descriptive survey method would be employed; both quantitative and qualitative data were gathered through questionnaire, document analysis, FGD and interviews. The total sample sizes of the study were 377 students and all mathematics teachers in the selected schools. In addition thirteen school principals were interviewed. In the selection of the sample population, stratified sampling, systematic random sampling and purposive samplings were used. Thus, the findings indicate that, the overall respondents’ perception towards practices of continuous assessment has mean 3.630 and standard deviation 1.063 which is medium perception. In addition to this, the result showed that the first challenging step to implement Continuous assessment is large class size; the second is lack of in-services training, the third is it takes time and the last challenging step is shortage of teaching materials. Study showed that most of the teachers use the traditional feedback mechanism for continuous assessment which is not recommendable and had to use the enhanced feedback to encourage the learners’ capacity. So, concerned bodies of the zone education office and schools should give support by providing teaching materials and giving training for teachers in order to increase and develop their assessment practices in theimplementation Continuous assessment.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"130 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77643623","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 : 2021-07-09DOI: 10.11648/J.PAMJ.20211003.11
G. Duressa, T. A. Bullo
In this paper, a higher-order numerical method is presented for solving the singularly perturbed delay differential equations. Such kind of equations have a delay parameter on reaction term and exhibits twin boundary layers or oscillatory behavior. Recently, different numerical methods have been developed to solve the singularly perturbed delay reaction-diffusion problems. However, the obtained accuracy and its rate of convergence are satisfactory. Thus, to solve the considered problem with more satisfactory accuracy and a higher rate of convergence, the higher-order numerical method is presented. First, the given singularly perturbed delay differential equation is transformed to asymptotically equivalent singularly perturbed two-point boundary value convection-diffusion differential equation by using Taylor series approximations. Then, the constructed singularly perturbed boundary value differential equation is replaced by three-term recurrence relation finite difference approximations. The Richardson extrapolation technique is applied to accelerate the fourth-order convergent of the developed method to the sixth-order convergent. The consistency and stability of the formulated method have been investigated very well to guarantee the convergence of the method. The rate of convergence for both the theoretical and numerical have been proven and are observed to be in accord with each other. To demonstrate the efficiency of the method, different model examples have been considered and simulation of numerical results have been presented by using MATLAB software. Numerical experimentation has been done and the results are presented for different values of the parameters. Further, The obtained numerical results described that the finding of the present method is more accurate than the findings of some methods discussed in the literature.
{"title":"Higher-Order Numerical Method for Singularly Perturbed Delay Reaction-Diffusion Problems","authors":"G. Duressa, T. A. Bullo","doi":"10.11648/J.PAMJ.20211003.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211003.11","url":null,"abstract":"In this paper, a higher-order numerical method is presented for solving the singularly perturbed delay differential equations. Such kind of equations have a delay parameter on reaction term and exhibits twin boundary layers or oscillatory behavior. Recently, different numerical methods have been developed to solve the singularly perturbed delay reaction-diffusion problems. However, the obtained accuracy and its rate of convergence are satisfactory. Thus, to solve the considered problem with more satisfactory accuracy and a higher rate of convergence, the higher-order numerical method is presented. First, the given singularly perturbed delay differential equation is transformed to asymptotically equivalent singularly perturbed two-point boundary value convection-diffusion differential equation by using Taylor series approximations. Then, the constructed singularly perturbed boundary value differential equation is replaced by three-term recurrence relation finite difference approximations. The Richardson extrapolation technique is applied to accelerate the fourth-order convergent of the developed method to the sixth-order convergent. The consistency and stability of the formulated method have been investigated very well to guarantee the convergence of the method. The rate of convergence for both the theoretical and numerical have been proven and are observed to be in accord with each other. To demonstrate the efficiency of the method, different model examples have been considered and simulation of numerical results have been presented by using MATLAB software. Numerical experimentation has been done and the results are presented for different values of the parameters. Further, The obtained numerical results described that the finding of the present method is more accurate than the findings of some methods discussed in the literature.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"76 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80721877","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 : 2021-05-14DOI: 10.11648/J.PAMJ.20211002.13
Jean-Max Coranson-Beaudu
In this paper we show that Riemann's function (xi), involving the Riemann’s (zeta) function, is holomorphic and is expressed as a convergent infinite polynomial product in relation to their zeros and their conjugates. Our work will be done on the critical band in which non-trivial zeros exist. Our approach is to use the properties of power series and infinite product decomposition of holomorphic functions. We take inspiration from the Weierstrass method to construct an infinite product model which is convergent and whose zeros are the zeros of the zeta function. By applying the symetric functional equation of the xi function we deduce a relation between each zero of the function xi and its conjugate. Because of the convergence of the infinite product, and that the elementary polynomials of the second degree of this same product are irreducible into the complex set, then this relation is well determined. The apparent simplicity of the reasoning is based on the fundamental theorems of Hadamard and Mittag-Leffler. We obtain the sought result: the real part of all zeros is equal to ½. This article proves that the Riemann’ hypothesis is true. Our perspectives for a next article are to apply this method to Dirichlet series, as a generalization of the Riemann function.
{"title":"A Speedy New Proof of the Riemann's Hypothesis","authors":"Jean-Max Coranson-Beaudu","doi":"10.11648/J.PAMJ.20211002.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20211002.13","url":null,"abstract":"In this paper we show that Riemann's function (xi), involving the Riemann’s (zeta) function, is holomorphic and is expressed as a convergent infinite polynomial product in relation to their zeros and their conjugates. Our work will be done on the critical band in which non-trivial zeros exist. Our approach is to use the properties of power series and infinite product decomposition of holomorphic functions. We take inspiration from the Weierstrass method to construct an infinite product model which is convergent and whose zeros are the zeros of the zeta function. By applying the symetric functional equation of the xi function we deduce a relation between each zero of the function xi and its conjugate. Because of the convergence of the infinite product, and that the elementary polynomials of the second degree of this same product are irreducible into the complex set, then this relation is well determined. The apparent simplicity of the reasoning is based on the fundamental theorems of Hadamard and Mittag-Leffler. We obtain the sought result: the real part of all zeros is equal to ½. This article proves that the Riemann’ hypothesis is true. Our perspectives for a next article are to apply this method to Dirichlet series, as a generalization of the Riemann function.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"10 1","pages":"62"},"PeriodicalIF":0.2,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78550560","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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