Pub Date : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.927
H. Goda, Masaaki Suzuki
In this note, we study a monodromy map of a fibered 2-bridge knot. We show the monodromy map of a fibered 2-bridge knot as an element in the automorphism group of a free group.
在这篇文章中，我们研究了一种纤维双桥结的单构图。在自由群的自同构群中给出了纤维2桥结的单构映射。
{"title":"Monodromy Maps of Fibered 2-Bridge Knots as Elements in Automorphism Groups of Free Groups","authors":"H. Goda, Masaaki Suzuki","doi":"10.5666/KMJ.2016.56.3.927","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.927","url":null,"abstract":"In this note, we study a monodromy map of a fibered 2-bridge knot. We show the monodromy map of a fibered 2-bridge knot as an element in the automorphism group of a free group.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849422","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 : 2016-07-12DOI: 10.5666/KMJ.2016.56.3.683
M. Afkhami, K. A. Javaheri, K. Khashyarmanesh
. In this paper we investigate the toroidality of the comaximal graph of a finite lattice.
． 本文研究了有限格的极大图的环向性。
{"title":"When the comaximal graph of a lattice is toroidal","authors":"M. Afkhami, K. A. Javaheri, K. Khashyarmanesh","doi":"10.5666/KMJ.2016.56.3.683","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.683","url":null,"abstract":". In this paper we investigate the toroidality of the comaximal graph of a finite lattice.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849369","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.349
S. Bang, Yan-Quan Feng, Jaeun Lee
For any integer n ≥ 2, each palindrome of n induces a circulant graph of order n. It is known that for each integer n ≥ 2, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes σ with gcd(σ) = 1 to the connected circulant graphs. It was also shown that the number of palindromes σ of n with gcd(σ) = 1 is the same number of aperiodic palindromes of n. Let an (resp. bn) be the number of aperiodic palindromes σ of n with gcd(σ) = 1 (resp. gcd(σ) ̸= 1). Let cn (resp. dn) be the number of periodic palindromes σ of n with gcd(σ) = 1 (resp. gcd(σ) ̸= 1). In this paper, we calculate the numbers an, bn, cn, dn in two ways. In Theorem 2.3, we find recurrence relations for an, bn, cn, dn in terms of ad for d|n and d ̸= n. Afterwards, we find formulae for an, bn, cn, dn explicitly in Theorem 2.5.
{"title":"On the Numbers of Palindromes","authors":"S. Bang, Yan-Quan Feng, Jaeun Lee","doi":"10.5666/KMJ.2016.56.2.349","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.349","url":null,"abstract":"For any integer n ≥ 2, each palindrome of n induces a circulant graph of order n. It is known that for each integer n ≥ 2, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes σ with gcd(σ) = 1 to the connected circulant graphs. It was also shown that the number of palindromes σ of n with gcd(σ) = 1 is the same number of aperiodic palindromes of n. Let an (resp. bn) be the number of aperiodic palindromes σ of n with gcd(σ) = 1 (resp. gcd(σ) ̸= 1). Let cn (resp. dn) be the number of periodic palindromes σ of n with gcd(σ) = 1 (resp. gcd(σ) ̸= 1). In this paper, we calculate the numbers an, bn, cn, dn in two ways. In Theorem 2.3, we find recurrence relations for an, bn, cn, dn in terms of ad for d|n and d ̸= n. Afterwards, we find formulae for an, bn, cn, dn explicitly in Theorem 2.5.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848530","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.387
Huanyin Chen, H. Kose, Y. Kurtulmaz
An n×n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) ∈ Mn ( R[[x]] ) . We prove, in this note, that A(x) ∈ Mn ( R[[x]] ) is strongly clean if and only if A(0) ∈ Mn(R) is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.
{"title":"Strongly Clean Matrices Over Power Series","authors":"Huanyin Chen, H. Kose, Y. Kurtulmaz","doi":"10.5666/KMJ.2016.56.2.387","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.387","url":null,"abstract":"An n×n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) ∈ Mn ( R[[x]] ) . We prove, in this note, that A(x) ∈ Mn ( R[[x]] ) is strongly clean if and only if A(0) ∈ Mn(R) is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848657","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.507
R. Abo-Zeid
Difference equations have played an important role in analysis of mathematical models of biology, physics and engineering. Recently, there has been a great interest in studying properties of nonlinear and rational difference equations. One can see [3, 7, 9, 10, 11, 12, 13, 14, 16, 17] and the references therein. In [8], E.M. Elsayed determined the solutions to some difference equations. He obtained the solution to the difference equation
{"title":"Behavior of Solutions of a Fourth Order Difference Equation","authors":"R. Abo-Zeid","doi":"10.5666/KMJ.2016.56.2.507","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.507","url":null,"abstract":"Difference equations have played an important role in analysis of mathematical models of biology, physics and engineering. Recently, there has been a great interest in studying properties of nonlinear and rational difference equations. One can see [3, 7, 9, 10, 11, 12, 13, 14, 16, 17] and the references therein. In [8], E.M. Elsayed determined the solutions to some difference equations. He obtained the solution to the difference equation","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848764","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.541
U. Ki, Soo-Jin Kim, Hiroyuki Kurihara
Let M be a real hypersurface of a complex space form with almost contact metric structure (φ, ξ, η, g). In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor φ, then M is a homogeneous real hypersurface of Type A provided that TrRξ is constant.
{"title":"Jacobi Operators with Respect to the Reeb Vector Fields on Real Hypersurfaces in a Nonflat Complex Space Form","authors":"U. Ki, Soo-Jin Kim, Hiroyuki Kurihara","doi":"10.5666/KMJ.2016.56.2.541","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.541","url":null,"abstract":"Let M be a real hypersurface of a complex space form with almost contact metric structure (φ, ξ, η, g). In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor φ, then M is a homogeneous real hypersurface of Type A provided that TrRξ is constant.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848836","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.343
M. Ashraf, Mohammad Aslam Siddeeque
Posner’s first theorem states that if R is a prime ring of characteristic different from two, d1 and d2 are derivations on R such that the iterate d1d2 is also a derivation of R, then at least one of d1, d2 is zero. In the present paper we extend this result to ∗-prime rings of characteristic different from two.
{"title":"Posner's First Theorem for *-ideals in Prime Rings with Involution","authors":"M. Ashraf, Mohammad Aslam Siddeeque","doi":"10.5666/KMJ.2016.56.2.343","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.343","url":null,"abstract":"Posner’s first theorem states that if R is a prime ring of characteristic different from two, d1 and d2 are derivations on R such that the iterate d1d2 is also a derivation of R, then at least one of d1, d2 is zero. In the present paper we extend this result to ∗-prime rings of characteristic different from two.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848521","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.367
A. Suvarnamani
In this paper, we consider the generalized Lucas sequence which is the (p, q) Lucas sequence. Then we used the Binet’s formula to show some properties of the (p, q) Lucas number. We get some generalized identities of the (p, q) Lucas number.
{"title":"Some Properties of (p, q) - Lucas Number","authors":"A. Suvarnamani","doi":"10.5666/KMJ.2016.56.2.367","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.367","url":null,"abstract":"In this paper, we consider the generalized Lucas sequence which is the (p, q) Lucas sequence. Then we used the Binet’s formula to show some properties of the (p, q) Lucas number. We get some generalized identities of the (p, q) Lucas number.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848590","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.451
Nan Li, Lian-Zhong Yang, Kai Liu
In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R. .
{"title":"A Further Result Related to a Conjecture of R. Brück","authors":"Nan Li, Lian-Zhong Yang, Kai Liu","doi":"10.5666/KMJ.2016.56.2.451","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.451","url":null,"abstract":"In this paper, we investigate the uniqueness problem of a meromorphic function sharing one small function with its differential polynomial, and give a result which is related to a conjecture of R. .","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848689","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 : 2016-06-23DOI: 10.5666/KMJ.2016.56.2.583
Dong-Soo Kim, Dong Seo Kim, Young Ho Kim, H. Bae
Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle . It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane , these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S
{"title":"Areas associated with a Strictly Locally Convex Curve","authors":"Dong-Soo Kim, Dong Seo Kim, Young Ho Kim, H. Bae","doi":"10.5666/KMJ.2016.56.2.583","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.2.583","url":null,"abstract":"Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle . It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane , these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70848869","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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