Abdullah Açikel, Amrouche Said, H. Belbachir, N. Irmak
: In this paper, we investigate several identities of k -generalized Lucas numbers with k -generalized Fibonacci numbers. We also establish a link between generalized s -Lucas triangle and bi s nomial coefficients given by the coefficients of the development of a power of (1 + x + x 2 + · · · + x s ) , with s ∈ N
{"title":"On $k$-generalized Lucas sequence with its triangle","authors":"Abdullah Açikel, Amrouche Said, H. Belbachir, N. Irmak","doi":"10.55730/1300-0098.3416","DOIUrl":"https://doi.org/10.55730/1300-0098.3416","url":null,"abstract":": In this paper, we investigate several identities of k -generalized Lucas numbers with k -generalized Fibonacci numbers. We also establish a link between generalized s -Lucas triangle and bi s nomial coefficients given by the coefficients of the development of a power of (1 + x + x 2 + · · · + x s ) , with s ∈ N","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":"49326343","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}
In this present study, we pay attention to a class of nonlinear neutral type systems (NNSs) with periodic coefficients and construct some assumptions guaranteeing the exponential stability (ES) of the trivial solutions of the system considered. To get specific conditions guaranteeing the ES, we use a modified Lyapunov functional. In conclusion, we get some estimates for the exponential decay of the solutions at infinity with the constructed sufficient conditions. We give two examples to demonstrate the applicability of the results obtained with the constructed assumptions.
{"title":"Some estimates on the exponential stability of solutions of nonlinear neutral type systems with periodic coefficients","authors":"Y. Altun","doi":"10.55730/1300-0098.3444","DOIUrl":"https://doi.org/10.55730/1300-0098.3444","url":null,"abstract":"In this present study, we pay attention to a class of nonlinear neutral type systems (NNSs) with periodic coefficients and construct some assumptions guaranteeing the exponential stability (ES) of the trivial solutions of the system considered. To get specific conditions guaranteeing the ES, we use a modified Lyapunov functional. In conclusion, we get some estimates for the exponential decay of the solutions at infinity with the constructed sufficient conditions. We give two examples to demonstrate the applicability of the results obtained with the constructed assumptions.","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":"45249099","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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