In this study, using a system of delay nonlinear ordinary differential equations, we introduce a new compartmental epidemic model considered effect of filiation (contamination) control strategy to the spread of Covid-19. Firstly, the formulation of this new SI u I a QR epidemic model with delay process and the parameters arised from isolation and filiation is formed. Then the disease-free and endemic equilibrium points of the model is obtained. Also, the basic reproduction number R 0 is found by using the next generation matrix method and the results on stabilities of the disease-free and endemic equilibrium points are investigated. Finally some examples are presented to show the effect of filiation control strategy.
{"title":"Stability analysis of a mathematical model SI_{u}I_{a}QR for COVID-19 with the effect of contamination control (filiation) strategy","authors":"Ü. Çakan","doi":"10.33401/FUJMA.863224","DOIUrl":"https://doi.org/10.33401/FUJMA.863224","url":null,"abstract":"In this study, using a system of delay nonlinear ordinary differential equations, we introduce a new compartmental epidemic model considered effect of filiation (contamination) control strategy to the spread of Covid-19. Firstly, the formulation of this new SI u I a QR epidemic model with delay process and the parameters arised from isolation and filiation is formed. Then the disease-free and endemic equilibrium points of the model is obtained. Also, the basic reproduction number R 0 is found by using the next generation matrix method and the results on stabilities of the disease-free and endemic equilibrium points are investigated. Finally some examples are presented to show the effect of filiation control strategy.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123442753","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 study, we deal with an $m$ banded circulant matrix, generally called circulant $m$-diagonal matrix. This special family of circulant matrices arise in many applications such as prediction, time series analysis, spline approximation, difference solution of partial differential equations, and so on. We firstly obtain the statements of eigenvalues and eigenvectors of circulant $m$-diagonal matrix based on the Chebyshev polynomials of the first and second kind. Then we present an efficient formula for the integer powers of this matrix family depending on the polynomials mentioned above. Finally, some illustrative examples are given by using maple software, one of computer algebra systems (CAS).
{"title":"Circulant $m$-diagonal matrices associated with Chebyshev polynomials","authors":"Ahmet Öteles","doi":"10.33401/FUJMA.809913","DOIUrl":"https://doi.org/10.33401/FUJMA.809913","url":null,"abstract":"In this study, we deal with an $m$ banded circulant matrix, generally called circulant $m$-diagonal matrix. This special family of circulant matrices arise in many applications such as prediction, time series analysis, spline approximation, difference solution of partial differential equations, and so on. We firstly obtain the statements of eigenvalues and eigenvectors of circulant $m$-diagonal matrix based on the Chebyshev polynomials of the first and second kind. Then we present an efficient formula for the integer powers of this matrix family depending on the polynomials mentioned above. Finally, some illustrative examples are given by using maple software, one of computer algebra systems (CAS).","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"8 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125001795","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 : 2020-12-19DOI: 10.22541/au.160837765.56795844/v1
Mehmet Solgun
In this work, we apply the notion of D-homothetic deformation on an almost paracontact metric manifolds and show that the structure after the deformation is also almost paracontact metric structure. Also, we state the classes of almost paracontact metric structures having parallel characteristic vector field and get some results about D- homothetic deformations on these classes.
{"title":"Some Results on D-Homothetic Deformation On Almost Paracontact Metric Manifolds","authors":"Mehmet Solgun","doi":"10.22541/au.160837765.56795844/v1","DOIUrl":"https://doi.org/10.22541/au.160837765.56795844/v1","url":null,"abstract":"In this work, we apply the notion of D-homothetic deformation on an\u0000almost paracontact metric manifolds and show that the structure after\u0000the deformation is also almost paracontact metric structure. Also, we\u0000state the classes of almost paracontact metric structures having\u0000parallel characteristic vector field and get some results about D-\u0000homothetic deformations on these classes.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132654141","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}
This study is devoted to give solvability conditions and solutions of the Robin boundary problem with constant coefficients for the homogeneous and the inhomogeneous Cauchy-Riemann equation in an annular domain. In order to get results, known representations and theorems in the literature are used. The representations for the solutions and solvability conditions are given in explicit form and here only a special Robin problem is considered. At the end of the paper, it is concluded that with some choices, boundary value problems for the Cauchy-Riemann equation reduce to some basic boundary problems in the ring domain.
{"title":"Robin Boundary Value Problem Depending on Parameters in a Ring Domain","authors":"İlker Gençtürk","doi":"10.33401/fujma.795538","DOIUrl":"https://doi.org/10.33401/fujma.795538","url":null,"abstract":"This study is devoted to give solvability conditions and solutions of the Robin boundary problem with constant coefficients for the homogeneous and the inhomogeneous Cauchy-Riemann equation in an annular domain. In order to get results, known representations and theorems in the literature are used. The representations for the solutions and solvability conditions are given in explicit form and here only a special Robin problem is considered. At the end of the paper, it is concluded that with some choices, boundary value problems for the Cauchy-Riemann equation reduce to some basic boundary problems in the ring domain.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114879019","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}
Higher order differential equations (ODE) has an important role in the modelling process. It is also much significant which the method is used for the solution. In this study, in order to get the approximate solution of a nonhomogeneous initial value problem, reproducing kernel Hilbert space method is used. Reproducing kernel functions have been obtained and the given problem transformed to the homogeneous form. The results have been presented with the graphics. Absolute errors and relative errors have been given in the tables.
{"title":"On Solutions of a Higher Order Nonhomogeneous Ordinary Differential Equation","authors":"Elif Nuray Yildirim, A. Akgul","doi":"10.33401/fujma.795418","DOIUrl":"https://doi.org/10.33401/fujma.795418","url":null,"abstract":"Higher order differential equations (ODE) has an important role in the modelling process. It is also much significant which the method is used for the solution. In this study, in order to get the approximate solution of a nonhomogeneous initial value problem, reproducing kernel Hilbert space method is used. Reproducing kernel functions have been obtained and the given problem transformed to the homogeneous form. The results have been presented with the graphics. Absolute errors and relative errors have been given in the tables.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126952620","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}
We shall determine the coding matrix of the semi-direct product group $ G = C_{n} rtimes_{phi} C_{m} $ ; $ phi : C_{m} longrightarrow Aut(C_{n}) $ of two cyclic groups in order to generalize the known result for the dihedral group $D_{2n}$, which is known to be a semi-direct of the two cyclic groups $C_{n} , C_{2}$.
{"title":"Coding Matrices for the Semi-Direct Product Groups","authors":"Amnah Alkinani, Ahmed A. Khammash","doi":"10.33401/fujma.690424","DOIUrl":"https://doi.org/10.33401/fujma.690424","url":null,"abstract":"We shall determine the coding matrix of the semi-direct product group $ G = C_{n} rtimes_{phi} C_{m} $ ; $ phi : C_{m} longrightarrow Aut(C_{n}) $ of two cyclic groups in order to generalize the known result for the dihedral group $D_{2n}$, which is known to be a semi-direct of the two cyclic groups $C_{n} , C_{2}$.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116030027","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 numerical methods for solving a nonlinear reaction-diffusion model for the polarization phenomena in ionic conductors. In particular, we propose three types of numerical methods, including the finite difference, cubic B-spline collocation, and local discontinuous Galerkin method, to approximate the quenching time of the model. We prove the conservation properties for all three numerical methods and compare their numerical performance.
{"title":"A Comparative Study of the Numerical Approximations of the Quenching Time for a Nonlinear Reaction-Diffusion Equation","authors":"F. Jones, He Yang","doi":"10.33401/fujma.755721","DOIUrl":"https://doi.org/10.33401/fujma.755721","url":null,"abstract":"In this paper, we study the numerical methods for solving a nonlinear reaction-diffusion model for the polarization phenomena in ionic conductors. In particular, we propose three types of numerical methods, including the finite difference, cubic B-spline collocation, and local discontinuous Galerkin method, to approximate the quenching time of the model. We prove the conservation properties for all three numerical methods and compare their numerical performance.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"2013 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114810375","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}
Let $ G $ be a graph having vertex set $ V(G) $. For $ Ssubseteq V(G) $, if each vertex is adjacent to a vertex in $ S $ or has at least two vertices in $ S $ at distance two from it, then the set $ S $ is a disjunctive total dominating set of $ G $. The disjunctive total domination number is the minimum cardinality of such a set. In this work, we discuss the disjunctive total domination of shadow distance graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.
设$ G $是一个顶点集$ V(G) $的图。对于$ Ssubseteq V(G) $，如果每个顶点与$ S $中的一个顶点相邻，或者在$ S $中至少有两个与它的距离为2的顶点，则集合$ S $是$ G $的析取总支配集。析取的总支配数是这样一个集合的最小基数。本文讨论了循环图、路径图、星图、完全二部图和轮图的阴影距离图的析取全支配性。
{"title":"Disjunctive Total Domination of Some Shadow Distance Graphs","authors":"C. Çiftçi","doi":"10.33401/fujma.790046","DOIUrl":"https://doi.org/10.33401/fujma.790046","url":null,"abstract":"Let $ G $ be a graph having vertex set $ V(G) $. For $ Ssubseteq V(G) $, if each vertex is adjacent to a vertex in $ S $ or has at least two vertices in $ S $ at distance two from it, then the set $ S $ is a disjunctive total dominating set of $ G $. The disjunctive total domination number is the minimum cardinality of such a set. In this work, we discuss the disjunctive total domination of shadow distance graphs of some graphs such as cycle, path, star, complete bipartite and wheel graphs.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132177981","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 classify warped translation surfaces being invariant surfaces of i-type, that is, the generating curve has formed by the intersection of the surface with the isotropic xz-plane in the three-dimensional simply isotropic space $mathbb I^3$ under the condi tio n $Delta^{J}x_i=lambda_i x_i,$ w ith J=I,II . Here, $Delta^{J}$ is the Laplace operator with respect to first and second fundamental form and $lambda_i$, $i=1,2,3$ are some real numbers. Also, as an application, we give some examples for these surfaces and also some explicit graphics of them. All graphics have been plotted with Maple14.
{"title":"Warped Translation Surfaces of Finite Type in Simply Isotropic 3-Spaces","authors":"Alev Kelleci","doi":"10.33401/fujma.785781","DOIUrl":"https://doi.org/10.33401/fujma.785781","url":null,"abstract":"In this paper, we classify warped translation surfaces being invariant surfaces of i-type, that is, the generating curve has formed by the intersection of the surface with the isotropic xz-plane in the three-dimensional simply isotropic space $mathbb I^3$ under the condi tio n $Delta^{J}x_i=lambda_i x_i,$ w ith J=I,II . Here, $Delta^{J}$ is the Laplace operator with respect to first and second fundamental form and $lambda_i$, $i=1,2,3$ are some real numbers. Also, as an application, we give some examples for these surfaces and also some explicit graphics of them. All graphics have been plotted with Maple14.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128083693","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 manuscript, almost para-contact metric structures on 5 dimensional nilpotent Lie algebras are studied. Some examples of para-Sasakian and para-contact structures on five-dimensional nilpotent Lie algebras are given.
{"title":"Almost Para-Contact Metric Structures on 5-dimensional Nilpotent Lie Algebras","authors":"N. Özdemir, Mehmet Solgun, S. Aktay","doi":"10.33401/fujma.800222","DOIUrl":"https://doi.org/10.33401/fujma.800222","url":null,"abstract":"In this manuscript, almost para-contact metric structures on 5 dimensional nilpotent Lie algebras are studied. Some examples of para-Sasakian and para-contact structures on five-dimensional nilpotent Lie algebras are given.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121191014","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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