Pub Date : 2017-01-24DOI: 10.11648/J.PAMJ.20170601.11
Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria
Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.
{"title":"Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets","authors":"Gikunju David Muriuki, Nyaga Lewis Namu, Rimberia Jane Kagwiria","doi":"10.11648/J.PAMJ.20170601.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20170601.11","url":null,"abstract":"Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"9 1","pages":"1"},"PeriodicalIF":0.2,"publicationDate":"2017-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81892225","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 : 2017-01-01DOI: 10.11648/j.pamj.20170606.13
Tanjima Akhter, J. Hossain, Salma Jahan
Uncontrolled human population growth has been posing a threat to the resources and habitats of Bangladesh. Population of different region of Bangladesh has been increasing dramatically. As a thriving country Bangladesh should artistically deal with this issue. This work is all about to estimate the population projection of the districts Noakhali, Feni, Lakhshmipur and Comilla, Bangladesh. By considering logistic growth model and making use of least square method and MATLAB to compute population growth rate and carrying capacity and the year when population will be nearly half of its carrying capacity and shown population projection for the above mentioned districts and give a comparison with actual population for the same time period. Also estimate future picture of population for these districts.
{"title":"Population Projection of the Districts Noakhali, Feni, Lakhshmipur and Comilla, Bangladesh by Using Logistic Growth Model","authors":"Tanjima Akhter, J. Hossain, Salma Jahan","doi":"10.11648/j.pamj.20170606.13","DOIUrl":"https://doi.org/10.11648/j.pamj.20170606.13","url":null,"abstract":"Uncontrolled human population growth has been posing a threat to the resources and habitats of Bangladesh. Population of different region of Bangladesh has been increasing dramatically. As a thriving country Bangladesh should artistically deal with this issue. This work is all about to estimate the population projection of the districts Noakhali, Feni, Lakhshmipur and Comilla, Bangladesh. By considering logistic growth model and making use of least square method and MATLAB to compute population growth rate and carrying capacity and the year when population will be nearly half of its carrying capacity and shown population projection for the above mentioned districts and give a comparison with actual population for the same time period. Also estimate future picture of population for these districts.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"132 1","pages":"164"},"PeriodicalIF":0.2,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89429232","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 : 2017-01-01DOI: 10.11648/j.pamj.20170606.14
Bello Olalekan Akanji, S. Ibrahim, Awodutire Phillip Oluwatobi, Olapade Akintayo Kehinde
In this paper, we obtained a generalized half logistic distribution which is called a five-parameter type I generalized half logistic distribution. The distributional properties of the model such as the cumulative distribution function (cdf), moment, skewness, kurtosis, the median and the mode of the generalized distribution were established and finally a theorem that relate the distribution to pareto distribution was stated and proved.
{"title":"A Study of Five Parameter Type I Generalized Half Logistic Distribution","authors":"Bello Olalekan Akanji, S. Ibrahim, Awodutire Phillip Oluwatobi, Olapade Akintayo Kehinde","doi":"10.11648/j.pamj.20170606.14","DOIUrl":"https://doi.org/10.11648/j.pamj.20170606.14","url":null,"abstract":"In this paper, we obtained a generalized half logistic distribution which is called a five-parameter type I generalized half logistic distribution. The distributional properties of the model such as the cumulative distribution function (cdf), moment, skewness, kurtosis, the median and the mode of the generalized distribution were established and finally a theorem that relate the distribution to pareto distribution was stated and proved.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"97 1","pages":"177"},"PeriodicalIF":0.2,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85910594","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 : 2016-12-26DOI: 10.11648/J.PAMJ.20160506.16
Teshome Bayleyegn Matebie
In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.
{"title":"The Method of Successive Approximations (Neumann’s Series) of Volterra Integral Equation of the Second Kind","authors":"Teshome Bayleyegn Matebie","doi":"10.11648/J.PAMJ.20160506.16","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20160506.16","url":null,"abstract":"In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"21 1","pages":"211"},"PeriodicalIF":0.2,"publicationDate":"2016-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88591028","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 : 2016-11-15DOI: 10.11648/J.PAMJ.20160506.15
S. I. Hamidov
The model of economic dynamics of the Leontief type is considered. The problem of determining the equilibrium state of the model with a fixed budget is investigated. It is proved that the state of equilibrium exists, if the trajectory model is a solution to the consumer problem.
{"title":"On a Consumer Problem","authors":"S. I. Hamidov","doi":"10.11648/J.PAMJ.20160506.15","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20160506.15","url":null,"abstract":"The model of economic dynamics of the Leontief type is considered. The problem of determining the equilibrium state of the model with a fixed budget is investigated. It is proved that the state of equilibrium exists, if the trajectory model is a solution to the consumer problem.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"190 1","pages":"205"},"PeriodicalIF":0.2,"publicationDate":"2016-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83058436","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 : 2016-11-11DOI: 10.11648/J.PAMJ.20160506.14
M. Elliotis
In this study the Singular Function Boundary Integral Method (SFBIM) is implemented in the case of a planar elliptic boundary value problem in Mechanics, with a point boundary singularity. The method is also extended in the case of a typical problem of Solid Mechanics, concerning the Laplace equation problem in three dimensions, defined in a domain with a straight edge singularity on the surface boundary. In both the 2-D and 3-D cases, the general solution of the Laplace equation is approximated by the leading terms (which contain the singular functions) of the local asymptotic solution expansion. The singular functions are used to weight the governing equation in the Galerkin sense. For the 2-D Laplacian model problem of this study, which is defined over a domain with a re-entrant corner, the resulting discretized equations are reduced to boundary integrals by means of Green’s second identity. For the 3-D model problem of this work, the volume integrals of the discretized equations are reduced to surface integrals by implementing Gauss’ divergence theorem. The Dirichlet boundary conditions are then weakly enforced by means of Lagrange multipliers. The values of the latter are calculated together with the singular coefficients, in the 2-D case or the Edge Flux Intensity Functions (EFIFs), in the 3-D model problem, which appear in the local solution expansion. For the planar problem, the numerical results are favorably compared with the analytic solution. Especially for the extension of the method in three dimensions, the preliminary numerical results compare favorably with available post-processed finite element results.
{"title":"The Singular Function Boundary Integral Method for the 2-D and 3-D Laplace Equation Problems in Mechanics, with a Boundary Singularity","authors":"M. Elliotis","doi":"10.11648/J.PAMJ.20160506.14","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20160506.14","url":null,"abstract":"In this study the Singular Function Boundary Integral Method (SFBIM) is implemented in the case of a planar elliptic boundary value problem in Mechanics, with a point boundary singularity. The method is also extended in the case of a typical problem of Solid Mechanics, concerning the Laplace equation problem in three dimensions, defined in a domain with a straight edge singularity on the surface boundary. In both the 2-D and 3-D cases, the general solution of the Laplace equation is approximated by the leading terms (which contain the singular functions) of the local asymptotic solution expansion. The singular functions are used to weight the governing equation in the Galerkin sense. For the 2-D Laplacian model problem of this study, which is defined over a domain with a re-entrant corner, the resulting discretized equations are reduced to boundary integrals by means of Green’s second identity. For the 3-D model problem of this work, the volume integrals of the discretized equations are reduced to surface integrals by implementing Gauss’ divergence theorem. The Dirichlet boundary conditions are then weakly enforced by means of Lagrange multipliers. The values of the latter are calculated together with the singular coefficients, in the 2-D case or the Edge Flux Intensity Functions (EFIFs), in the 3-D model problem, which appear in the local solution expansion. For the planar problem, the numerical results are favorably compared with the analytic solution. Especially for the extension of the method in three dimensions, the preliminary numerical results compare favorably with available post-processed finite element results.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"18 1","pages":"192"},"PeriodicalIF":0.2,"publicationDate":"2016-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87344605","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 : 2016-11-08DOI: 10.11648/j.pamj.20160506.12
Lanping Li
The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.
{"title":"Bayesian Test for Lifetime Performance Index of Ailamujia Distribution Under Squared Error Loss Function","authors":"Lanping Li","doi":"10.11648/j.pamj.20160506.12","DOIUrl":"https://doi.org/10.11648/j.pamj.20160506.12","url":null,"abstract":"The aim of this paper is to estimate the lifetime performance index of Ailamujia distribution. A Bayesian test procedure is developed under squared error loss function. Firstly, Bayes estimation of life performance index is derived, then a Bayesian test procedure for lifetime performance index using posteriori probability ratio test method. Finally, an example is used to illustrate the effectiveness and feasibility of the method.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"20 1","pages":"181"},"PeriodicalIF":0.2,"publicationDate":"2016-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72706342","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 : 2016-11-08DOI: 10.11648/J.PAMJ.20160506.13
Guobing Fan
The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.
{"title":"Admissibility Estimation of Pareto Distribution Under Entropy Loss Function Based on Progressive Type-II Censored Sample","authors":"Guobing Fan","doi":"10.11648/J.PAMJ.20160506.13","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20160506.13","url":null,"abstract":"The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using maximum likelihood on the basis of Bayes estimator. Finally, the admissibility of a class of inverse linear estimators are discussed under suitable conditions.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"52 1","pages":"186"},"PeriodicalIF":0.2,"publicationDate":"2016-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88750776","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 : 2016-10-17DOI: 10.11648/J.PAMJ.20160506.11
Baodan Tian, Yanhong Qiu
In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.
{"title":"Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water","authors":"Baodan Tian, Yanhong Qiu","doi":"10.11648/J.PAMJ.20160506.11","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20160506.11","url":null,"abstract":"In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear Whitham- Broer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"18 1","pages":"174"},"PeriodicalIF":0.2,"publicationDate":"2016-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77687172","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 : 2016-10-13DOI: 10.11648/J.PAMJ.20160505.15
Ahmad Salehi Zarrin Ghabaei, S. Azami
Let be a graph on n vertices and let be the degree of vertex A graph is defined to be harmonic if is an eigenvector of the -adjacency matrix of We now show that there are 4 regular and 45 non-regular connected pentacyclic harmonic graphs and determine their structure. In the end we conclude that all of c-cyclic harmonic graphs for are planar graphs.
{"title":"Pentacyclic Harmonic Graph","authors":"Ahmad Salehi Zarrin Ghabaei, S. Azami","doi":"10.11648/J.PAMJ.20160505.15","DOIUrl":"https://doi.org/10.11648/J.PAMJ.20160505.15","url":null,"abstract":"Let be a graph on n vertices and let be the degree of vertex A graph is defined to be harmonic if is an eigenvector of the -adjacency matrix of We now show that there are 4 regular and 45 non-regular connected pentacyclic harmonic graphs and determine their structure. In the end we conclude that all of c-cyclic harmonic graphs for are planar graphs.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"389 1","pages":"165"},"PeriodicalIF":0.2,"publicationDate":"2016-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80721621","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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