Pub Date : 2017-03-23DOI: 10.5666/KMJ.2017.57.1.99
K. So, Young-Hee Kim
In this paper we construct quadratic β-algebras on a field, and we discuss both linear-quadratic β-algebras and quadratic-linear β-algebras in a field. Moreover, we discuss some relations of binary operations in β-algebras.
{"title":"On the Construction of Polynomial β-algebras over a Field","authors":"K. So, Young-Hee Kim","doi":"10.5666/KMJ.2017.57.1.99","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.1.99","url":null,"abstract":"In this paper we construct quadratic β-algebras on a field, and we discuss both linear-quadratic β-algebras and quadratic-linear β-algebras in a field. Moreover, we discuss some relations of binary operations in β-algebras.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45261313","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 : 2017-03-23DOI: 10.5666/KMJ.2017.57.1.85
G. Muhiuddin, C. Park, Y. Jun
{"title":"Relations between Regular Uni-soft Filters and Uni-soft MV - filters in Residuated Lattices","authors":"G. Muhiuddin, C. Park, Y. Jun","doi":"10.5666/KMJ.2017.57.1.85","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.1.85","url":null,"abstract":"","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42721879","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 : 2017-03-23DOI: 10.5666/KMJ.2017.57.1.145
Myeong-Ju Jeong, Chan-Young Park, M. Park
. If a virtual knot diagram can be transformed to another virtual one by a finite sequence of crossing changes, Reidemeister moves and virtual moves then the two virtual knot diagrams are said to be homotopic . There are infinitely many homotopy classes of virtual knot diagrams. We give necessary conditions by using polynomial invariants of virtual knots for two virtual knots to be homotopic. For a sequence S of crossing changes, Reidemeister moves and virtual moves between two homotopic virtual knot diagrams, we give a lower bound for the number of crossing changes in S by using the affine index polynomial introduced in [13]. In [10], the first author gave the q -polynomial of a virtual knot diagram to find Reidemeister moves of virtually isotopic virtual knot diagrams. We find how to apply Reidemeister moves by using the q -polynomial to show homotopy of two virtual knot diagrams. 57M25, 57M27.
{"title":"Polynomials and Homotopy of Virtual Knot Diagrams","authors":"Myeong-Ju Jeong, Chan-Young Park, M. Park","doi":"10.5666/KMJ.2017.57.1.145","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.1.145","url":null,"abstract":". If a virtual knot diagram can be transformed to another virtual one by a finite sequence of crossing changes, Reidemeister moves and virtual moves then the two virtual knot diagrams are said to be homotopic . There are infinitely many homotopy classes of virtual knot diagrams. We give necessary conditions by using polynomial invariants of virtual knots for two virtual knots to be homotopic. For a sequence S of crossing changes, Reidemeister moves and virtual moves between two homotopic virtual knot diagrams, we give a lower bound for the number of crossing changes in S by using the affine index polynomial introduced in [13]. In [10], the first author gave the q -polynomial of a virtual knot diagram to find Reidemeister moves of virtually isotopic virtual knot diagrams. We find how to apply Reidemeister moves by using the q -polynomial to show homotopy of two virtual knot diagrams. 57M25, 57M27.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46778956","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 : 2017-03-23DOI: 10.5666/KMJ.2017.57.1.133
Young Ho Kim, N. Turgay
In this paper, we study ruled surfaces in 3-dimensional Euclidean and Minkowski space in terms of their Gauss map. We obtain classification theorems for these type of surfaces whose Gauss map G satisfying G = f(G+C) for a constant vector C ∈ E and a smooth function f, where denotes the Cheng-Yau operator.
{"title":"On the Ruled Surfaces with L1-Pointwise 1-Type Gauss Map","authors":"Young Ho Kim, N. Turgay","doi":"10.5666/KMJ.2017.57.1.133","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.1.133","url":null,"abstract":"In this paper, we study ruled surfaces in 3-dimensional Euclidean and Minkowski space in terms of their Gauss map. We obtain classification theorems for these type of surfaces whose Gauss map G satisfying G = f(G+C) for a constant vector C ∈ E and a smooth function f, where denotes the Cheng-Yau operator.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45698168","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 : 2017-03-23DOI: 10.5666/KMJ.2017.57.1.109
K. Noor, R. Murtaza, J. Sokół
. In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator L αa,λ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.
{"title":"Some New Subclasses of Analytic Functions defined by Srivastava-Owa-Ruscheweyh Fractional Derivative Operator","authors":"K. Noor, R. Murtaza, J. Sokół","doi":"10.5666/KMJ.2017.57.1.109","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.1.109","url":null,"abstract":". In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator L αa,λ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45874989","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 : 2017-01-01DOI: 10.5666/KMJ.2017.57.2.251
M. Gümüş, R. Abo-Zeid, Ö. Öcalan
{"title":"Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers","authors":"M. Gümüş, R. Abo-Zeid, Ö. Öcalan","doi":"10.5666/KMJ.2017.57.2.251","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.2.251","url":null,"abstract":"","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849635","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 : 2017-01-01DOI: 10.5666/KMJ.2017.57.3.457
I. Jung, M. H. Mortad, J. Stochel
A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A,B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.
{"title":"On normal products of selfadjoint operators","authors":"I. Jung, M. H. Mortad, J. Stochel","doi":"10.5666/KMJ.2017.57.3.457","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.3.457","url":null,"abstract":"A necessary and sufficient condition for the product AB of a selfadjoint operator A and a bounded selfadjoint operator B to be normal is given. Various properties of the factors of the unitary polar decompositions of A and B are obtained in the case when the product AB is normal. A block operator model for pairs (A,B) of selfadjoint operators such that B is bounded and AB is normal is established. The case when both operators A and B are bounded is discussed. In addition, the example due to Rehder is reexamined from this point of view.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849681","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 : 2017-01-01DOI: 10.5666/KMJ.2017.57.3.473
R. Ali, Virendra Kumar, V. Ravichandran, Shanmugam Sivaprasad Kumar
Sharp radius constants for certain classes of normalized analytic functions with fixed second coefficient, to be in the classes of starlike functions of positive order, parabolic starlike functions, and Sokó l-Stankiewicz starlike functions are obtained. Our results extend several earlier works.
{"title":"Radius of Starlikeness for Analytic Functions with Fixed Second Coefficient","authors":"R. Ali, Virendra Kumar, V. Ravichandran, Shanmugam Sivaprasad Kumar","doi":"10.5666/KMJ.2017.57.3.473","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.3.473","url":null,"abstract":"Sharp radius constants for certain classes of normalized analytic functions with fixed second coefficient, to be in the classes of starlike functions of positive order, parabolic starlike functions, and Sokó l-Stankiewicz starlike functions are obtained. Our results extend several earlier works.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849695","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 : 2017-01-01DOI: 10.5666/KMJ.2017.57.3.503
R. Sachdeva, Rakesh Kumar, S. S. Bhatia
In this paper, we study totally umbilical slant lightlike submanifolds of indefinite Kaehler manifolds. We prove that there do not exist totally umbilical proper slant lightlike submanifolds in indefinite Kaehler manifolds other than totally geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally umbilical proper slant lightlike submanifolds of indefinite Kaehler space forms. Finally, we give a characterization theorem on minimal slant lightlike submanifolds.
{"title":"Totally Umbilical Slant Lightlike Submanifolds of Indefinite Kaehler Manifolds","authors":"R. Sachdeva, Rakesh Kumar, S. S. Bhatia","doi":"10.5666/KMJ.2017.57.3.503","DOIUrl":"https://doi.org/10.5666/KMJ.2017.57.3.503","url":null,"abstract":"In this paper, we study totally umbilical slant lightlike submanifolds of indefinite Kaehler manifolds. We prove that there do not exist totally umbilical proper slant lightlike submanifolds in indefinite Kaehler manifolds other than totally geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally umbilical proper slant lightlike submanifolds of indefinite Kaehler space forms. Finally, we give a characterization theorem on minimal slant lightlike submanifolds.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849751","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.2016.56.4.1191
Sukyung Kwon, Y. Choi, H. Baek
. The emergence of various Internet worms, including the stand-alone Code Red worm that caused a distributed denial of service (DDoS), has prompted many studies on their propagation speed to minimize potential damages. Many studies, however, assume the same probabilities for initially infected nodes to infect each node during their propagation, which do not reflect accurate Internet worm propagation modelling. Thus, this paper analyzes how Internet worm propagation speed varies according to the number of vulnerable hosts directly connected to infected hosts as well as the link costs between infected and vulnerable hosts. A mathematical model based on centrality theory is proposed to analyze and simulate the effects of degree centrality values and closeness centrality values representing the connectivity of nodes in a large-scale network environment on Internet worm propagation speed.
{"title":"Internet Worm Propagation Model Using Centrality Theory","authors":"Sukyung Kwon, Y. Choi, H. Baek","doi":"10.5666/KMJ.2016.56.4.1191","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1191","url":null,"abstract":". The emergence of various Internet worms, including the stand-alone Code Red worm that caused a distributed denial of service (DDoS), has prompted many studies on their propagation speed to minimize potential damages. Many studies, however, assume the same probabilities for initially infected nodes to infect each node during their propagation, which do not reflect accurate Internet worm propagation modelling. Thus, this paper analyzes how Internet worm propagation speed varies according to the number of vulnerable hosts directly connected to infected hosts as well as the link costs between infected and vulnerable hosts. A mathematical model based on centrality theory is proposed to analyze and simulate the effects of degree centrality values and closeness centrality values representing the connectivity of nodes in a large-scale network environment on Internet worm propagation speed.","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":"70849523","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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