PATRÍCIA DAMAS BEITES, ALEJANDRO PIÑERA NICOLÁS, JOSÉ DA SILVA LOURENÇO VITÓRIA
Motivated by circular complex interval arithmetic, some operations on closed balls in $mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n in {3, 7}$, are studied. In addition, certain equations involving the defined multiplications are solved.
基于循环复区间算法，考虑了$mathbb{C}^n$中闭球的若干运算。本质上，研究了$mathbb{C}^n$中闭球的可能乘法的性质，这些性质与向量的Hadamard积有关，与$n in {3,7 }$时的$2$-fold向量叉积有关。此外，还求解了涉及定义乘法的某些方程。
{"title":"Multiplication of closed balls in $mathbb{C}^n$","authors":"PATRÍCIA DAMAS BEITES, ALEJANDRO PIÑERA NICOLÁS, JOSÉ DA SILVA LOURENÇO VITÓRIA","doi":"10.55730/1300-0098.3471","DOIUrl":"https://doi.org/10.55730/1300-0098.3471","url":null,"abstract":"Motivated by circular complex interval arithmetic, some operations on closed balls in $mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n in {3, 7}$, are studied. In addition, certain equations involving the defined multiplications are solved.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating y ′ ( u ) using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to several numerical problems. All calculations in this method have been performed using the computer program MATLAB R2021a.
{"title":"A new approaching method for linear neutral delay differential equations by using Clique polynomials","authors":"ŞUAYİP YÜZBAŞI, MEHMET EMİN TAMAR","doi":"10.55730/1300-0098.3483","DOIUrl":"https://doi.org/10.55730/1300-0098.3483","url":null,"abstract":": This article presents an efficient method for obtaining approximations for the solutions of linear neutral delay differential equations. This numerical matrix method, based on collocation points, begins by approximating y ′ ( u ) using a truncated series expansion of Clique polynomials. This method is constructed using some basic matrix relations, integral operations, and collocation points. Through this method, the neutral delay problem is transformed into a system of linear algebraic equations. The solution of this algebraic system determines the coefficients of the approximate solution obtained by this method. The efficiency, accuracy, and error analysis of this method are demonstrated by applying it to several numerical problems. All calculations in this method have been performed using the computer program MATLAB R2021a.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Assume that ( G n ) n ∈ Z is an arbitrary real linear recurrence of order k . In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by ( t, G t ) ( n 0 ≤ t ≤ n 1 ). The main result is an explicit formula depends on the explicit formula of G n and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of ( G n ) . During the investigations, we developed certain formulae related to the finite differences
{"title":"Interpolation polynomials associated to linear recurrences","authors":"MUHAMMAD SYIFA'UL MUFID, LASZLO SZALAY","doi":"10.55730/1300-0098.3473","DOIUrl":"https://doi.org/10.55730/1300-0098.3473","url":null,"abstract":": Assume that ( G n ) n ∈ Z is an arbitrary real linear recurrence of order k . In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by ( t, G t ) ( n 0 ≤ t ≤ n 1 ). The main result is an explicit formula depends on the explicit formula of G n and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of ( G n ) . During the investigations, we developed certain formulae related to the finite differences","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Let Q = ( a,b R ) denote the quaternion algebra over the reals which is by the Frobenius Theorem either split or the division algebra H of Hamilton’s quaternions. We have presented explicitly in [4] the matrix of a typical derivation of Q . Given a derivation d ∈ Der ( H ) , we show that the matrix D ∈ M 3 ( R ) that represents d on the linear subspace H 0 ≃ R 3 of pure quaternions provides a pair of idempotent matrices AdjD and − D 2 that correspond bijectively to the involutary matrix Σ of a quaternion involution σ and present several equations involving these matrices. In particular, we deal with commuting derivations of H and introduce some results to guarantee commutativity. We also mention briefly eigenspace decomposition of a derivation.
{"title":"Involutive automorphisms and derivations of the quaternions","authors":"EYÜP KIZIL, ADRIANO DA SILVA, OKAN DUMAN","doi":"10.55730/1300-0098.3474","DOIUrl":"https://doi.org/10.55730/1300-0098.3474","url":null,"abstract":": Let Q = ( a,b R ) denote the quaternion algebra over the reals which is by the Frobenius Theorem either split or the division algebra H of Hamilton’s quaternions. We have presented explicitly in [4] the matrix of a typical derivation of Q . Given a derivation d ∈ Der ( H ) , we show that the matrix D ∈ M 3 ( R ) that represents d on the linear subspace H 0 ≃ R 3 of pure quaternions provides a pair of idempotent matrices AdjD and − D 2 that correspond bijectively to the involutary matrix Σ of a quaternion involution σ and present several equations involving these matrices. In particular, we deal with commuting derivations of H and introduce some results to guarantee commutativity. We also mention briefly eigenspace decomposition of a derivation.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Best proximity for proximal operators on $b$-metric spaces","authors":"ARIANA PITEA, MONICA STANCIU","doi":"10.55730/1300-0098.3469","DOIUrl":"https://doi.org/10.55730/1300-0098.3469","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, generalized Pell graphs $Pi _{n,k}$, $kge 2$, are introduced. The special case of $k=2$ are the Pell graphs $Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $Pi _{n,k}$ and the generating function of its cube polynomial are determined. The center of $Pi _{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $Gamma_{n}$. It is also shown that $Pi _{n,k}$ is a median graph, and that $Pi _{n,k}$ embeds into a Fibonacci cube.
{"title":"Generalized Pell graphs","authors":"VESNA IRSİC, SANDI KLAVZAR, ELİF TAN","doi":"10.55730/1300-0098.3475","DOIUrl":"https://doi.org/10.55730/1300-0098.3475","url":null,"abstract":"In this paper, generalized Pell graphs $Pi _{n,k}$, $kge 2$, are introduced. The special case of $k=2$ are the Pell graphs $Pi _{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $Pi _{n,k}$ and the generating function of its cube polynomial are determined. The center of $Pi _{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $Gamma_{n}$. It is also shown that $Pi _{n,k}$ is a median graph, and that $Pi _{n,k}$ embeds into a Fibonacci cube.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: The Berezin symbol ˜ A of an operator A on the reproducing kernel Hilbert space H (Ω) over some set Ω with the reproducing kernel k λ is defined by
{"title":"Invariant subspaces of operators via Berezin symbols and Duhamel product","authors":"MÜBARİZ T. GARAYEV","doi":"10.55730/1300-0098.3485","DOIUrl":"https://doi.org/10.55730/1300-0098.3485","url":null,"abstract":": The Berezin symbol ˜ A of an operator A on the reproducing kernel Hilbert space H (Ω) over some set Ω with the reproducing kernel k λ is defined by","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose of the present work is to offer a complete mathematical analysis of the effect that the refuge brings about.
{"title":"Dynamical complexity of a predator-prey model with a prey refuge and Allee effect","authors":"JIANPING GAO, JIANGHONG ZHANG, WENYAN LIAN","doi":"10.55730/1300-0098.3481","DOIUrl":"https://doi.org/10.55730/1300-0098.3481","url":null,"abstract":"We consider a predator-prey model with a non-monotonic functional response encompassing a prey refuge and a strong Allee effect on the prey. The multiple existence and stability of interior equilibria are investigated. The bifurcation analysis shows this model can exhibit numerous kinds of bifurcations (e.g., saddle-node, Hopf-Andronov and Bogdanov-Takens bifurcations). It is found that there exist diverse parameter values for which the model exhibits a limit cycle, a homoclinic orbit, and even many heteroclinic curves. The results obtained reveal the prey refuge in the model brings rich dynamics and makes the system more sensitive to parameter values. The main purpose of the present work is to offer a complete mathematical analysis of the effect that the refuge brings about.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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