We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.
{"title":"FREDHOLM TOEPLITZ OPERATORS ON THE DIRICHLET SPACES OF THE POLYDISK","authors":"Kyunguk Na","doi":"10.4134/BKMS.B190371","DOIUrl":"https://doi.org/10.4134/BKMS.B190371","url":null,"abstract":"We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"509-520"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362142","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":"SMOOTH POINTS OF s ( n 2","authors":"Sung Guen Kim","doi":"10.4134/BKMS.B190311","DOIUrl":"https://doi.org/10.4134/BKMS.B190311","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"443-447"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362174","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 last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multipolycyclic codes and their duals and we give some examples to illustrate the theorems.
{"title":"ON GENERALIZATIONS OF SKEW QUASI-CYCLIC CODES","authors":"Sumeyra Bedir, F. Gursoy, I. Siap","doi":"10.4134/BKMS.B190325","DOIUrl":"https://doi.org/10.4134/BKMS.B190325","url":null,"abstract":"In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multipolycyclic codes and their duals and we give some examples to illustrate the theorems.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"459-479"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362360","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}
Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module M , we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by M . We also consider the relationship between the conditions (1) M is a fully prime (semiprime) module, and (2) the endomorphism ring of M is a fully prime (semiprime) ring.
{"title":"FULLY PRIME MODULES AND FULLY SEMIPRIME MODULES","authors":"J. Beachy, M. Medina-Bárcenas","doi":"10.4134/BKMS.B190864","DOIUrl":"https://doi.org/10.4134/BKMS.B190864","url":null,"abstract":"Fully prime rings (in which every proper ideal is prime) have been studied by Blair and Tsutsui, and fully semiprime rings (in which every proper ideal is semiprime) have been studied by Courter. For a given module M , we introduce the notions of a fully prime module and a fully semiprime module, and extend certain results of Blair, Tsutsui, and Courter to the category subgenerated by M . We also consider the relationship between the conditions (1) M is a fully prime (semiprime) module, and (2) the endomorphism ring of M is a fully prime (semiprime) ring.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1177-1193"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363077","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 consider a class of inhomogeneous random intersection graphs by assigning random weight to each vertex and two vertices are adjacent if they choose some common elements. In the inhomogeneous random intersection graph model, vertices with larger weights are more likely to acquire many elements. We show the Poisson convergence of the number of induced copies of a fixed subgraph as the number of vertices n and the number of elements m, scaling as m=⌊βnα⌋ (α,β>0), tend to infinity.
{"title":"Poisson approximation of induced subgraph counts in an inhomogeneous random intersection graph model","authors":"Y. Shang","doi":"10.4134/BKMS.B180971","DOIUrl":"https://doi.org/10.4134/BKMS.B180971","url":null,"abstract":"In this paper, we consider a class of inhomogeneous random intersection graphs by assigning random weight to each vertex and two vertices are adjacent if they choose some common elements. In the inhomogeneous random intersection graph model, vertices with larger weights are more likely to acquire many elements. We show the Poisson convergence of the number of induced copies of a fixed subgraph as the number of vertices n and the number of elements m, scaling as m=⌊βnα⌋ (α,β>0), tend to infinity.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1199-1210"},"PeriodicalIF":0.5,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45221281","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 prove that for every surjective phase-isometry between the unit spheres of real atomic Lp-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.
本文证明了对于实原子lp空间单位球间的每一个满射相等距，其正齐次扩展是相等距，其相等价于线性等距。
{"title":"EXTENSION OF PHASE-ISOMETRIES BETWEEN THE UNIT SPHERES OF ATOMIC L p -SPACES FOR p > 0","authors":"Xujian Huang, Xihong Jin","doi":"10.4134/BKMS.b180561","DOIUrl":"https://doi.org/10.4134/BKMS.b180561","url":null,"abstract":"In this paper, we prove that for every surjective phase-isometry between the unit spheres of real atomic Lp-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"1377-1384"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359127","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":"Geometric characterizations of canal surfaces in Minkowski 3-space $mathbb{I}$","authors":"Xueshan Fu, S. Jung, J. Qian, Mengfei Su","doi":"10.4134/BKMS.B180643","DOIUrl":"https://doi.org/10.4134/BKMS.B180643","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"867-883"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359384","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":"ON HÖLDER ESTIMATES FOR CAUCHY TRANSFORMS ON CONVEX DOMAINS IN ℂ 2","authors":"L. Ha","doi":"10.4134/BKMS.B180684","DOIUrl":"https://doi.org/10.4134/BKMS.B180684","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"929-937"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70359588","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}
Rings in which all accessible subrings are ideals are called filial. A ring R is called fully filial if all its subrings are filial (that is rings in which the relation of being an ideal is transitive). The present paper is devoted to the study of fully filial torsion rings. We prove a classification theorem for semiprime fully filial torsion rings.
{"title":"ON FULLY FILIAL TORSION RINGS","authors":"R. Andruszkiewicz, K. Pryszczepko","doi":"10.4134/BKMS.B180030","DOIUrl":"https://doi.org/10.4134/BKMS.B180030","url":null,"abstract":"Rings in which all accessible subrings are ideals are called filial. A ring R is called fully filial if all its subrings are filial (that is rings in which the relation of being an ideal is transitive). The present paper is devoted to the study of fully filial torsion rings. We prove a classification theorem for semiprime fully filial torsion rings.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"56 1","pages":"23-29"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70358802","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}
Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann-Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann-Liouville fractional derivatives. The amazing fact here is that we do not need any boundary conditions as the classical Polya integral inequality requires. We extend our Polya inequality to Choquet integral setting.
{"title":"RIEMANN-LIOUVILLE FRACTIONAL FUNDAMENTAL THEOREM OF CALCULUS AND RIEMANN-LIOUVILLE FRACTIONAL POLYA TYPE INTEGRAL INEQUALITY AND ITS EXTENSION TO CHOQUET INTEGRAL SETTING","authors":"G. Anastassiou","doi":"10.4134/BKMS.B180934","DOIUrl":"https://doi.org/10.4134/BKMS.B180934","url":null,"abstract":"Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann-Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann-Liouville fractional derivatives. The amazing fact here is that we do not need any boundary conditions as the classical Polya integral inequality requires. We extend our Polya inequality to Choquet integral setting.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"272 1","pages":"1423-1433"},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70360276","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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