Pub Date : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1103
P. Das
. In this paper, we study a directed simple graph Γ s ( N ) for a near-ring N , where the set V ∗ ( N ) of vertices is the set of all left N -subsets of N with nonzero left annihilators and for any two distinct vertices I, J ∈ V ∗ ( N ), I is adjacent to J if and only if IJ = 0. Here, we deal with the diameter, girth and coloring of the graph Γ s ( N ). Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring N in the left annihilator of some vertex in the strong zero-divisor graph Γ s ( N ).
． 在这篇文章里,我们研究a导演简单graphΓs (N) for a near-ring N套V∗(N)》,哪里vertices集》是所有左派N的-subsets nonzero左annihilators和为任何两个distinct vertices I, J∈V∗(N), I '是adjacent to J如果只和如果IJ = 0。这里,我们成交直径,girth》和《coloring graphΓs (N)。而且,我们证明a sufficient condition for occurrence of a常规编程元素of near-ring N》境之左者一些vertex坚强zero-divisor graphΓs (N)。
{"title":"On the Diameter, Girth and Coloring of the Strong Zero‑Divisor Graph of Near‑rings","authors":"P. Das","doi":"10.5666/KMJ.2016.56.4.1103","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1103","url":null,"abstract":". In this paper, we study a directed simple graph Γ s ( N ) for a near-ring N , where the set V ∗ ( N ) of vertices is the set of all left N -subsets of N with nonzero left annihilators and for any two distinct vertices I, J ∈ V ∗ ( N ), I is adjacent to J if and only if IJ = 0. Here, we deal with the diameter, girth and coloring of the graph Γ s ( N ). Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring N in the left annihilator of some vertex in the strong zero-divisor graph Γ s ( N ).","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849858","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1115
J. Lim, D. Y. Oh
Let D ⊆ E be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D and let H(D,E) and H(D, I) (resp., h(D,E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this paper, we show that H(D,E) satisfies the ascending chain condition on principal ideals if and only if h(D,E) satisfies the ascending chain condition on principal ideals, if and only if ∩ n≥1 a1 · · · anE = (0) for each infinite sequence (an)n≥1 consisting of nonzero nonunits of D. We also prove that H(D, I) satisfies the ascending chain condition on principal ideals if and only if h(D, I) satisfies the ascending chain condition on principal ideals, if and only if D satisfies the ascending chain condition on principal ideals.
{"title":"Composite Hurwitz Rings Satisfying the Ascending Chain Condition on Principal Ideals","authors":"J. Lim, D. Y. Oh","doi":"10.5666/KMJ.2016.56.4.1115","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1115","url":null,"abstract":"Let D ⊆ E be an extension of integral domains with characteristic zero, I be a nonzero proper ideal of D and let H(D,E) and H(D, I) (resp., h(D,E) and h(D, I)) be composite Hurwitz series rings (resp., composite Hurwitz polynomial rings). In this paper, we show that H(D,E) satisfies the ascending chain condition on principal ideals if and only if h(D,E) satisfies the ascending chain condition on principal ideals, if and only if ∩ n≥1 a1 · · · anE = (0) for each infinite sequence (an)n≥1 consisting of nonzero nonunits of D. We also prove that H(D, I) satisfies the ascending chain condition on principal ideals if and only if h(D, I) satisfies the ascending chain condition on principal ideals, if and only if D satisfies the ascending chain condition on principal ideals.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849899","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1259
A. Mukharjee, Kallol Bhandhu Bagchi
. In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.
{"title":"On Mean Open and Closed Sets","authors":"A. Mukharjee, Kallol Bhandhu Bagchi","doi":"10.5666/KMJ.2016.56.4.1259","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1259","url":null,"abstract":". In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849618","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1069
V. T. Le, Hong Tin Phan
In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M :
本文研究了e-局部模的结构和通过本质小的模的类。我们证明了下列条件对于模M是等价的:
{"title":"Some Characterizations of Modules via Essentially Small Submodules","authors":"V. T. Le, Hong Tin Phan","doi":"10.5666/KMJ.2016.56.4.1069","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1069","url":null,"abstract":"In this paper, the structure of e-local modules and classes of modules via essentially small are investigated. We show that the following conditions are equivalent for a module M :","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849845","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1179
Yong Hun Lee, Sang Dong Kim
{"title":"Note on a Classical Conservative Method for Scalar Hyperbolic Equations","authors":"Yong Hun Lee, Sang Dong Kim","doi":"10.5666/KMJ.2016.56.4.1179","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1179","url":null,"abstract":"","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849510","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1141
S. Thota, D. Kumar
In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coefficients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green’s operator and the vector Green’s function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.
{"title":"Symbolic Algorithm for a System of Differential-Algebraic Equations","authors":"S. Thota, D. Kumar","doi":"10.5666/KMJ.2016.56.4.1141","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1141","url":null,"abstract":"In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coefficients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green’s operator and the vector Green’s function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849533","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1237
A. E. Dehkordy
In this paper we study some properties of submanifolds of a Riemannian manifold equipped with a generalized connection ▽̂. We also consider almost Hermitian manifolds that admits a special case of this generalized connection and derive some results about the behavior of this manifolds.
{"title":"On Some Properties of Riemannian Manifolds with a Generalized Connection","authors":"A. E. Dehkordy","doi":"10.5666/KMJ.2016.56.4.1237","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1237","url":null,"abstract":"In this paper we study some properties of submanifolds of a Riemannian manifold equipped with a generalized connection ▽̂. We also consider almost Hermitian manifolds that admits a special case of this generalized connection and derive some results about the behavior of this manifolds.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849583","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1135
Hyunsuk Moon
Let A be an abelian variety over a global field K. We know [6, 7] that, in many cases, the average number of n-torsion points of A over various residue fields of K, takes the minimal possible value. In this article, we study several defect cases by calculating the number of Galois orbits.
{"title":"On the Calculation of the Number of Galois Orbits","authors":"Hyunsuk Moon","doi":"10.5666/KMJ.2016.56.4.1135","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1135","url":null,"abstract":"Let A be an abelian variety over a global field K. We know [6, 7] that, in many cases, the average number of n-torsion points of A over various residue fields of K, takes the minimal possible value. In this article, we study several defect cases by calculating the number of Galois orbits.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849495","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1047
B. Kethesan
. In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denoted by −→ D r,s ( x ) ; where r; s ∈ N and x is an indeterminate are introduced. A presentation of walled signed Brauer algebras in terms of generators and relations is given. The cellularity of a walled signed Brauer algebra is established. Finally, −→ D r,s ( x ) ; is quasi- hereditary if either the characteristic of a (cid:12)eld, say p; p = 0 or p > max ( r; s ) and either x ̸ = 0 or x = 0 and r ̸ = s:
{"title":"The Structure of Walled Signed Brauer Algebras","authors":"B. Kethesan","doi":"10.5666/KMJ.2016.56.4.1047","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1047","url":null,"abstract":". In this paper, a new class of diagram algebras which are subalgebras of signed brauer algebras, called the Walled Signed Brauer algebras denoted by −→ D r,s ( x ) ; where r; s ∈ N and x is an indeterminate are introduced. A presentation of walled signed Brauer algebras in terms of generators and relations is given. The cellularity of a walled signed Brauer algebra is established. Finally, −→ D r,s ( x ) ; is quasi- hereditary if either the characteristic of a (cid:12)eld, say p; p = 0 or p > max ( r; s ) and either x ̸ = 0 or x = 0 and r ̸ = s:","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849830","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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