: We consider an initial value problem related to the equation
我们考虑一个与方程有关的初值问题
{"title":"Blow-up of solutions for wave equation with multiple ?(x)-Laplacian and variable exponent nonlinearities","authors":"A. Khaldi, Amar Ouaoua, M. Maouni","doi":"10.55730/1300-0098.3409","DOIUrl":"https://doi.org/10.55730/1300-0098.3409","url":null,"abstract":": We consider an initial value problem related to the equation","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43943490","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 the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the efficiency and reliability of the presented method. The error norms L 2 and L ∞ with mass, energy, and momentum conservation constants I 1 , I 2 and I 3 , respectively, are computed. To do a comparison with the other studies in the literature, the newly found approximate solutions are exhibited in both tabular and graphical formats. Also, stability analysis of numerical approach by the von Neumann method is researched.
：在本手稿中，Benjamin Bona Mahony Burgers（BBMB）方程将通过Strang时间分裂技术进行数值处理。在应用该技术的同时，采用了基于五次B样条基函数的配置方法。根据我们的目的，在将具有适当初始边界条件的BBM-Burgers方程分解为包含时间导数的两个子方程后，将基于五次B样条的配置有限元方法（FEM）用于空间离散化，并将合适的有限差分方法用于时间离散化，从而获得两个不同的代数方程组。利用四个测试问题来测试所提出方法的有效性和可靠性。计算了质量、能量和动量守恒常数分别为I1、I2和I3的误差范数L2和L∞。为了与文献中的其他研究进行比较，新发现的近似解以表格和图形形式显示。此外，还研究了冯-诺依曼方法数值逼近的稳定性分析。
{"title":"Numerical solution for Benjamin-Bona-Mahony-Burgers equation with Strang time-splitting technique","authors":"Melike Karta","doi":"10.55730/1300-0098.3377","DOIUrl":"https://doi.org/10.55730/1300-0098.3377","url":null,"abstract":": In the present manuscript, the Benjamin-Bona-Mahony-Burgers (BBMB) equation will be handled numerically by Strang time-splitting technique. While applying this technique, collocation method based on quintic B-spline basis functions is applied. In line with our purpose, after splitting the BBM-Burgers equation given with appropriate initial boundary conditions into two subequations containing the derivative in terms of time, the quintic B-spline based collocation finite element method (FEM) for spatial discretization and the suitable finite difference approaches for time discretization is applied to each subequation and hereby two different systems of algebraic equations are obtained. Four test problems are utilized to test the efficiency and reliability of the presented method. The error norms L 2 and L ∞ with mass, energy, and momentum conservation constants I 1 , I 2 and I 3 , respectively, are computed. To do a comparison with the other studies in the literature, the newly found approximate solutions are exhibited in both tabular and graphical formats. Also, stability analysis of numerical approach by the von Neumann method is researched.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42273138","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":"Some remarks on parameterized inequalities involving conformable fractional operators","authors":"Cihan Ünal, F. Hezenci, H. Budak","doi":"10.55730/1300-0098.3381","DOIUrl":"https://doi.org/10.55730/1300-0098.3381","url":null,"abstract":"","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42379221","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 introduce ⊕ calculus and ⊗ calculus for intuitionistic fuzzy values and prove some basic theorems by using multiplicative calculus which has useful tools to represent the concepts of introduced calculi. Besides, we construct some isomorphic mappings to interpret the relationships between ⊕ calculus and ⊗ calculus. This paper reveals also new calculi for fuzzy sets in particular.
{"title":"A calculus for intuitionistic fuzzy values","authors":"E. Yavuz","doi":"10.55730/1300-0098.3392","DOIUrl":"https://doi.org/10.55730/1300-0098.3392","url":null,"abstract":"We introduce ⊕ calculus and ⊗ calculus for intuitionistic fuzzy values and prove some basic theorems by using multiplicative calculus which has useful tools to represent the concepts of introduced calculi. Besides, we construct some isomorphic mappings to interpret the relationships between ⊕ calculus and ⊗ calculus. This paper reveals also new calculi for fuzzy sets in particular.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43601070","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 ( H 3 , g 1 ) and ( H 3 , g 2 ) be the Lorentzian-Heisenberg spaces with nonflat metrics g 1 and g 2 , and ( TH 3 , g s 1 ) , ( TH 3 , g s 2 ) be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold H 3 . We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold H 3 . We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.
{"title":"Geodesics and isocline distributions in tangent bundles of nonflat Lorentzian-Heisenberg spaces","authors":"M. Altunbaş","doi":"10.55730/1300-0098.3356","DOIUrl":"https://doi.org/10.55730/1300-0098.3356","url":null,"abstract":": Let ( H 3 , g 1 ) and ( H 3 , g 2 ) be the Lorentzian-Heisenberg spaces with nonflat metrics g 1 and g 2 , and ( TH 3 , g s 1 ) , ( TH 3 , g s 2 ) be their tangent bundles with the Sasaki metric, respectively. In the present paper, we find nontotally geodesic distributions in tangent bundles by using lifts of contact forms from the base manifold H 3 . We give examples for totally geodesic but not isocline distributions. We study the geodesics of tangent bundles by considering horizontal and natural lifts of geodesics of the base manifold H 3 . We also investigate more general classes of geodesics which are not obtained from horizontal and natural lifts of geodesics.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41817007","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, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system
{"title":"Qualitative study of a second order difference equation","authors":"Messaoud Berkal, J. F. Navarro","doi":"10.55730/1300-0098.3375","DOIUrl":"https://doi.org/10.55730/1300-0098.3375","url":null,"abstract":": In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44379203","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}
Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft rough approximation operator have been presented. Moreover, a new kind of bipolar approximation space via two ideals, called bipolar soft biideal approximation space, was introduced and studied by two different methods. Their properties are discussed and the relationships between these methods and the previous ones are proposed. The importance of these methods is reducing the vagueness of uncertainty areas by increasing the bipolar lower approximations and decreasing the bipolar upper approximations. Also, the bipolar soft biideal rough sets represent two opinions instead of one opinion. Finally, an application in multicriteria group decision making (MCGDM) in COVID-19 by using bipolar soft ideal rough sets is suggested by using two methods. [ FROM AUTHOR]
{"title":"Bipolar soft ideal rough set with applications in COVID-19","authors":"H. Mustafa","doi":"10.55730/1300-0098.3343","DOIUrl":"https://doi.org/10.55730/1300-0098.3343","url":null,"abstract":"Bipolar soft rough set represents an important mathematical model to deal with uncertainty. This theory represents a link between bipolar soft set and rough set theories. This study introduced the concept of topological bipolar soft set by combining a bipolar soft set with topologies. Also, the topological structure of bipolar soft rough set has been discussed by defining the bipolar soft rough topology. The main objective of this paper is to present some solutions to develop and modify the approach of the bipolar soft rough sets. Two kinds of bipolar soft ideal approximation operators which represent extensions of bipolar soft rough approximation operator have been presented. Moreover, a new kind of bipolar approximation space via two ideals, called bipolar soft biideal approximation space, was introduced and studied by two different methods. Their properties are discussed and the relationships between these methods and the previous ones are proposed. The importance of these methods is reducing the vagueness of uncertainty areas by increasing the bipolar lower approximations and decreasing the bipolar upper approximations. Also, the bipolar soft biideal rough sets represent two opinions instead of one opinion. Finally, an application in multicriteria group decision making (MCGDM) in COVID-19 by using bipolar soft ideal rough sets is suggested by using two methods. [ FROM AUTHOR]","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47713588","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 note, we describe a way to study local regularity of a weak solution to the Navier-Stokes equations, satisfying the simplest scale-invariant restriction, with the help of zooming and duality approach to the corresponding mild bounded ancient solution
{"title":"Duality Approach to the Regularity Problems for the Navier-Stokes Equations","authors":"G. Seregin","doi":"10.55730/1300-0098.3402","DOIUrl":"https://doi.org/10.55730/1300-0098.3402","url":null,"abstract":": In this note, we describe a way to study local regularity of a weak solution to the Navier-Stokes equations, satisfying the simplest scale-invariant restriction, with the help of zooming and duality approach to the corresponding mild bounded ancient solution","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44899877","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 work we will show that if $F$ is a positive integer, then the set ${mathrm{Arf}}(F)={Smid S mbox{ is an Arf numerical semigroup with Frobenius number } F}$ verifies the following conditions: 1) $Delta(F)={0,F+1,rightarrow}$ is the minimum of ${mathrm{Arf}}(F),$ 2) if ${S, T} subseteq {mathrm{Arf}}(F)$, then $S cap T in {mathrm{Arf}}(F),$ 3) if $S in {mathrm{Arf}}(F),$ $Sneq Delta(F)$ and ${mathrm m}(S)=min (S backslash {0})$, then $Sbackslash {{mathrm m}(S)} in {mathrm{Arf}}(F)$. The previous results will be used to give an algorithm which calculates the set ${mathrm{Arf}}(F).$ Also we will see that if $Xsubseteq Sbackslash Delta(F)$ for some $Sin {mathrm{Arf}}(F),$ then there is the smallest element of ${mathrm{Arf}}(F)$ containing $X.$
在这项工作中，我们将证明如果$F$是一个正整数，那么集合${mathrm{Arf}}(F)={Smid S mbox{ is an Arf numerical semigroup with Frobenius number } F}$验证了以下条件:1)$Delta(F)={0,F+1,rightarrow}$是${mathrm{Arf}}(F),$的最小值;2)如果${S, T} subseteq {mathrm{Arf}}(F)$，则$S cap T in {mathrm{Arf}}(F),$; 3)如果$S in {mathrm{Arf}}(F),$，则$Sneq Delta(F)$和${mathrm m}(S)=min (S backslash {0})$，则$Sbackslash {{mathrm m}(S)} in {mathrm{Arf}}(F)$。前面的结果将用于给出计算集合${mathrm{Arf}}(F).$的算法，我们还将看到，如果$Xsubseteq Sbackslash Delta(F)$对于某些$Sin {mathrm{Arf}}(F),$，那么${mathrm{Arf}}(F)$包含的最小元素 $X.$
{"title":"The set of Arf numerical semigroups with given Frobenius number","authors":"M. A. Moreno-Fr'ias, J. Rosales","doi":"10.55730/1300-0098.3436","DOIUrl":"https://doi.org/10.55730/1300-0098.3436","url":null,"abstract":"In this work we will show that if $F$ is a positive integer, then the set ${mathrm{Arf}}(F)={Smid S mbox{ is an Arf numerical semigroup with Frobenius number } F}$ verifies the following conditions: 1) $Delta(F)={0,F+1,rightarrow}$ is the minimum of ${mathrm{Arf}}(F),$ 2) if ${S, T} subseteq {mathrm{Arf}}(F)$, then $S cap T in {mathrm{Arf}}(F),$ 3) if $S in {mathrm{Arf}}(F),$ $Sneq Delta(F)$ and ${mathrm m}(S)=min (S backslash {0})$, then $Sbackslash {{mathrm m}(S)} in {mathrm{Arf}}(F)$. The previous results will be used to give an algorithm which calculates the set ${mathrm{Arf}}(F).$ Also we will see that if $Xsubseteq Sbackslash Delta(F)$ for some $Sin {mathrm{Arf}}(F),$ then there is the smallest element of ${mathrm{Arf}}(F)$ containing $X.$","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45030753","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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