Pub Date : 2020-01-01DOI: 10.1080/25742558.2020.1829277
T. Mekonnen, G. Duressa
Abstract This paper deals with the numerical solution of singularly perturbed parabolic convection-diffusion problems with two small positive parameters multiplying the convection and diffusion terms. A parameter-uniform computational method is developed to solve these problems. The stability and consistency of the method are well established. Numerical experimentation is done and it is observed that the formulated method is stable, consistent and gives more accurate results than some methods exist in the literature.
{"title":"Computational method for singularly perturbed two-parameter parabolic convection-diffusion problems","authors":"T. Mekonnen, G. Duressa","doi":"10.1080/25742558.2020.1829277","DOIUrl":"https://doi.org/10.1080/25742558.2020.1829277","url":null,"abstract":"Abstract This paper deals with the numerical solution of singularly perturbed parabolic convection-diffusion problems with two small positive parameters multiplying the convection and diffusion terms. A parameter-uniform computational method is developed to solve these problems. The stability and consistency of the method are well established. Numerical experimentation is done and it is observed that the formulated method is stable, consistent and gives more accurate results than some methods exist in the literature.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1829277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44566028","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 : 2020-01-01DOI: 10.1080/25742558.2020.1750878
Jiabu Ye, D. Lai
Abstract Nonparametric tests are commonly used tests for two sample comparison in clinical studies. However, the estimation of treatment effects associated with the tests may not be obvious, especially under the covariate adjustment. In this article, we evaluated the effect of covariate adjustment on estimating treatment effects based on the Wilcoxon Rank Sum test, the van Elteren test, aligned rank test, and Jaeckel, Hettmansperger-McKean test through Monte Carlo simulations via mean square error and coverage probability. Based on the simulation, commonly used ANCOVA-based approach do not have good estimation of treatment effect when the covariate imbalance is severe. Aligned rank test seems perform well across most scenarios.
{"title":"Estimations of treatment effects based on covariate adjusted nonparametric methods","authors":"Jiabu Ye, D. Lai","doi":"10.1080/25742558.2020.1750878","DOIUrl":"https://doi.org/10.1080/25742558.2020.1750878","url":null,"abstract":"Abstract Nonparametric tests are commonly used tests for two sample comparison in clinical studies. However, the estimation of treatment effects associated with the tests may not be obvious, especially under the covariate adjustment. In this article, we evaluated the effect of covariate adjustment on estimating treatment effects based on the Wilcoxon Rank Sum test, the van Elteren test, aligned rank test, and Jaeckel, Hettmansperger-McKean test through Monte Carlo simulations via mean square error and coverage probability. Based on the simulation, commonly used ANCOVA-based approach do not have good estimation of treatment effect when the covariate imbalance is severe. Aligned rank test seems perform well across most scenarios.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1750878","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44594725","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 : 2020-01-01DOI: 10.1080/25742558.2020.1761001
Giangiacomo Gerla, A. Miranda
Abstract Researches in “point-free geometry”, aiming to found geometry without using points as primitive entities, have always paid attention only to the logical aspects. In this paper, we propose a point-free axiomatization of geometry taking into account not only the logical value of this approach but also, for the first time, its educational potentialities. We introduce primitive entities and axioms, as a sort of theoretical guise that is grafted onto intuition, looking at the educational value of the deriving theory. In our approach the notions of convexity and half-planes play a crucial role. Indeed, starting from the Boolean algebra of regular closed subsets of ℝn , representing, in an excellent natural way, the idea of region, we introduce an n-dimensional prototype of point-free geometry by using the primitive notion of convexity. This enable us to define Re-half-planes, Re-lines, Re-points, polygons, and to introduce axioms making not only meaningful all the given definitions but also providing adequate tools from a didactic point of view. The result is a theory, or a seed of theory, suitable to improve the teaching and the learning of geometry.
{"title":"Point-free foundation of geometry looking at laboratory activities","authors":"Giangiacomo Gerla, A. Miranda","doi":"10.1080/25742558.2020.1761001","DOIUrl":"https://doi.org/10.1080/25742558.2020.1761001","url":null,"abstract":"Abstract Researches in “point-free geometry”, aiming to found geometry without using points as primitive entities, have always paid attention only to the logical aspects. In this paper, we propose a point-free axiomatization of geometry taking into account not only the logical value of this approach but also, for the first time, its educational potentialities. We introduce primitive entities and axioms, as a sort of theoretical guise that is grafted onto intuition, looking at the educational value of the deriving theory. In our approach the notions of convexity and half-planes play a crucial role. Indeed, starting from the Boolean algebra of regular closed subsets of ℝn , representing, in an excellent natural way, the idea of region, we introduce an n-dimensional prototype of point-free geometry by using the primitive notion of convexity. This enable us to define Re-half-planes, Re-lines, Re-points, polygons, and to introduce axioms making not only meaningful all the given definitions but also providing adequate tools from a didactic point of view. The result is a theory, or a seed of theory, suitable to improve the teaching and the learning of geometry.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1761001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45152127","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 : 2020-01-01DOI: 10.1080/25742558.2020.1813961
S. Thota, P. Shanmugasundaram
Abstract In this paper, we present a new symbolic method for solving neutral functional-differential equations with proportional delays having variable coefficients via homotopy perturbation method. The proposed symbolic method is also applicable to solve the multi-pantograph equations with variable coefficients. Several numerical examples are given to illustrate the proposed method and the results show that the proposed symbolic method is very effective.
{"title":"On a symbolic method for neutral functional-differential equations with proportional delays","authors":"S. Thota, P. Shanmugasundaram","doi":"10.1080/25742558.2020.1813961","DOIUrl":"https://doi.org/10.1080/25742558.2020.1813961","url":null,"abstract":"Abstract In this paper, we present a new symbolic method for solving neutral functional-differential equations with proportional delays having variable coefficients via homotopy perturbation method. The proposed symbolic method is also applicable to solve the multi-pantograph equations with variable coefficients. Several numerical examples are given to illustrate the proposed method and the results show that the proposed symbolic method is very effective.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1813961","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45322495","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 : 2020-01-01DOI: 10.1080/25742558.2020.1805092
Patrick Rakotomarolahy
Abstract Encompassing test has been well developed for fully parametric modeling. In this study, we are interested on encompassing test for parametric and nonparametric regression methods. We consider linear regression for parametric modeling and nearest neighbor regression for nonparametric methods. We establish asymptotic normality of encompassing statistic associated to the encompassing hypotheses for the linear parametric method and the nonparametric nearest neighbor regression estimate. We also obtain convergence rate depending only on the number of neighbors while it depends on the number of observation and the bandwidth for kernel method. We achieve the same convergence rate when . Moreover, asymptotic variance of the encompassing statistic associated to kernel regression depends on the density, this is not the case for nearest neighbor regression estimate.
{"title":"Asymptotic behavior of encompassing test for independent processes: Case of linear and nearest neighbor regressions","authors":"Patrick Rakotomarolahy","doi":"10.1080/25742558.2020.1805092","DOIUrl":"https://doi.org/10.1080/25742558.2020.1805092","url":null,"abstract":"Abstract Encompassing test has been well developed for fully parametric modeling. In this study, we are interested on encompassing test for parametric and nonparametric regression methods. We consider linear regression for parametric modeling and nearest neighbor regression for nonparametric methods. We establish asymptotic normality of encompassing statistic associated to the encompassing hypotheses for the linear parametric method and the nonparametric nearest neighbor regression estimate. We also obtain convergence rate depending only on the number of neighbors while it depends on the number of observation and the bandwidth for kernel method. We achieve the same convergence rate when . Moreover, asymptotic variance of the encompassing statistic associated to kernel regression depends on the density, this is not the case for nearest neighbor regression estimate.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1805092","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45876293","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 : 2020-01-01DOI: 10.1080/25742558.2020.1858560
E. Vatandoost, Athena Shaminezhad
Abstract Let be a graph and be a function where for every vertex with there is a vertex where Then is a Roman dominating function or a of The weight of is The minimum weight of all is called the Roman domination number of denoted by Let be a graph with and G' be a copy of with Then a functigraph with function is denoted by its vertices and edges are and respectively. This paper deals with the Roman domination number of the functigraph and its complement. We present a general bound where is a permutation. Also, the Roman domination number of some special graphs are considered. We obtain a general bound of and we show that this bound is sharp.
{"title":"On roman domination number of functigraph and its complement","authors":"E. Vatandoost, Athena Shaminezhad","doi":"10.1080/25742558.2020.1858560","DOIUrl":"https://doi.org/10.1080/25742558.2020.1858560","url":null,"abstract":"Abstract Let be a graph and be a function where for every vertex with there is a vertex where Then is a Roman dominating function or a of The weight of is The minimum weight of all is called the Roman domination number of denoted by Let be a graph with and G' be a copy of with Then a functigraph with function is denoted by its vertices and edges are and respectively. This paper deals with the Roman domination number of the functigraph and its complement. We present a general bound where is a permutation. Also, the Roman domination number of some special graphs are considered. We obtain a general bound of and we show that this bound is sharp.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1858560","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41373226","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 : 2020-01-01DOI: 10.1080/25742558.2020.1781505
R. Ghanam, G. Thompson
Abstract For each of the six-dimensional indecomposable nilpotent Lie algebras, the geodesic equations of the associated canonical Lie group connection are given. In each case, a basis for the associated Lie algebra of symmetries is constructed and analyzed.
{"title":"Lie symmetries of the canonical geodesic equations for six-dimensional nilpotent lie groups","authors":"R. Ghanam, G. Thompson","doi":"10.1080/25742558.2020.1781505","DOIUrl":"https://doi.org/10.1080/25742558.2020.1781505","url":null,"abstract":"Abstract For each of the six-dimensional indecomposable nilpotent Lie algebras, the geodesic equations of the associated canonical Lie group connection are given. In each case, a basis for the associated Lie algebra of symmetries is constructed and analyzed.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1781505","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46688489","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 : 2020-01-01DOI: 10.1080/25742558.2020.1758361
A. Salem, M. Alnegga
Abstract In this paper, we investigate a non-linear Langevin equation with periodic, multi-point and non-local fractional integral boundary conditions. The contraction mapping theorem is employed to determine sufficient conditions for the uniqueness of the solution. Also, different results in the existence of solution are demonstrated by using Krasnoselskii and Leray-Schauder theorems. Finally, some examples are provided as applications of the theorems in order to support the main outcomes of this paper.
{"title":"Fractional Langevin equations with multi-point and non-local integral boundary conditions","authors":"A. Salem, M. Alnegga","doi":"10.1080/25742558.2020.1758361","DOIUrl":"https://doi.org/10.1080/25742558.2020.1758361","url":null,"abstract":"Abstract In this paper, we investigate a non-linear Langevin equation with periodic, multi-point and non-local fractional integral boundary conditions. The contraction mapping theorem is employed to determine sufficient conditions for the uniqueness of the solution. Also, different results in the existence of solution are demonstrated by using Krasnoselskii and Leray-Schauder theorems. Finally, some examples are provided as applications of the theorems in order to support the main outcomes of this paper.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1758361","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44856221","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 : 2020-01-01DOI: 10.1080/25742558.2020.1833427
Reza Babaei, H. Rahimi, G. Soleimani Rad
Abstract In this paper, we consider weakly compatible mappings with respect to a generalized -distance in cone -metric spaces and obtain new common fixed-point theorems. Our results provide a more general statement, since we need not to nor the continuity of mappings and nor the normality of cone. In particular, we refer to the results of M. Abbas and G. Jungck [Common fixed point results for non-commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008) 416–420]. Some corollaries and examples are presented to support the main result proved herein.
{"title":"Weakly compatible mappings with respect to a generalized c-distance and common fixed point results","authors":"Reza Babaei, H. Rahimi, G. Soleimani Rad","doi":"10.1080/25742558.2020.1833427","DOIUrl":"https://doi.org/10.1080/25742558.2020.1833427","url":null,"abstract":"Abstract In this paper, we consider weakly compatible mappings with respect to a generalized -distance in cone -metric spaces and obtain new common fixed-point theorems. Our results provide a more general statement, since we need not to nor the continuity of mappings and nor the normality of cone. In particular, we refer to the results of M. Abbas and G. Jungck [Common fixed point results for non-commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008) 416–420]. Some corollaries and examples are presented to support the main result proved herein.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1833427","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41458899","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 : 2020-01-01DOI: 10.1080/25742558.2020.1788298
Abednego Orobosa Isere
Abstract Natural rhotrix refers to the rhotrix whose elements are all natural numbers, arrayed in their natural order. This type of rhotrix has just recently been introduced in literature. Therefore, this work is taking a further look at its properties. It introduces the concept of diagonal function of a natural rhotrix and examines its properties. It is found that the diagonal function of a natural rhotrix is given as . Furthermore, it presents the sum of the other elements outside its diagonals as where is the set of elements along any of its diagonals, , and are the complement of , the index and the heart of respectively. These properties are all peculiar to this beautiful set of rhotrix called the natural rhotrix.
{"title":"Diagonal function of natural rhotrix","authors":"Abednego Orobosa Isere","doi":"10.1080/25742558.2020.1788298","DOIUrl":"https://doi.org/10.1080/25742558.2020.1788298","url":null,"abstract":"Abstract Natural rhotrix refers to the rhotrix whose elements are all natural numbers, arrayed in their natural order. This type of rhotrix has just recently been introduced in literature. Therefore, this work is taking a further look at its properties. It introduces the concept of diagonal function of a natural rhotrix and examines its properties. It is found that the diagonal function of a natural rhotrix is given as . Furthermore, it presents the sum of the other elements outside its diagonals as where is the set of elements along any of its diagonals, , and are the complement of , the index and the heart of respectively. These properties are all peculiar to this beautiful set of rhotrix called the natural rhotrix.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2020.1788298","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45233625","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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