{"title":"A NOTE ON GENERALIZED DERIVATIONS AS A JORDAN HOMOMORPHISMS","authors":"A. Chandrasekhar, S. Tiwari","doi":"10.4134/BKMS.B190429","DOIUrl":"https://doi.org/10.4134/BKMS.B190429","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"709-737"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362085","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 define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the twoparameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.
{"title":"AN AVERAGE OF SURFACES AS FUNCTIONS IN THE TWO-PARAMETER WIENER SPACE FOR A PROBABILISTIC 3D SHAPE MODEL","authors":"Jeong-Gyoo Kim","doi":"10.4134/BKMS.B190467","DOIUrl":"https://doi.org/10.4134/BKMS.B190467","url":null,"abstract":"We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the twoparameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"751-762"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362531","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":"SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p 3","authors":"M. Darafsheh, M. Shahsavaran","doi":"10.4134/BKMS.B190458","DOIUrl":"https://doi.org/10.4134/BKMS.B190458","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"739-750"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362909","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 the holomorphic curves (or derived holomorphic curves introduced by Toda in [15]) with maximal defect sum in the complex plane. Some well-known theorems on meromorphic functions of finite order with maximal sum of defects are extended to holomorphic curves in projective space.
{"title":"ON THE DEFECTS OF HOLOMORPHIC CURVES","authors":"Liu Yang, Ting Zhu","doi":"10.4134/BKMS.B190865","DOIUrl":"https://doi.org/10.4134/BKMS.B190865","url":null,"abstract":"In this paper we consider the holomorphic curves (or derived holomorphic curves introduced by Toda in [15]) with maximal defect sum in the complex plane. Some well-known theorems on meromorphic functions of finite order with maximal sum of defects are extended to holomorphic curves in projective space.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"1195-1204"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70363144","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 study the mapping property of multilinear fractional maximal operators in Lipschitz spaces. It should be pointed out that some of the techniques employed in the study of fractional integral operators do not apply to fractional maximal operators.
{"title":"ENDPOINT ESTIMATES FOR MULTILINEAR FRACTIONAL MAXIMAL OPERATORS","authors":"Suixin He, Jing Zhang","doi":"10.4134/BKMS.B190269","DOIUrl":"https://doi.org/10.4134/BKMS.B190269","url":null,"abstract":"We study the mapping property of multilinear fractional maximal operators in Lipschitz spaces. It should be pointed out that some of the techniques employed in the study of fractional integral operators do not apply to fractional maximal operators.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"28 1","pages":"383-391"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361844","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 M(X,Y ) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlettype spaces D α, M(D p−1,D q q−1) = {0}, if p 6= q, 0 < p, q < ∞. If 0 < p, q < ∞, p 6= q, 0 < s < 1 such that p + s, q + s > 1, then M(D p−2+s,D q q−2+s) = {0}. However, X ∩ D p p−1 ⊆ X ∩ D q q−1 and X ∩ D p−2+s ⊆ X ∩ D q q−2+s whenever X is a subspace of the Bloch space B and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ D p−2+s, X∩D q q−2+s) is nontrivial. In this paper, we study the multipliers M(X ∩ D p−2+s, X ∩ D q q−2+s) for distinct classical subspaces X of the Bloch space B, where X = B, BMOA or H∞.
{"title":"MULTIPLIERS OF DIRICHLET-TYPE SUBSPACES OF BLOCH SPACE","authors":"Songxiao Li, Zengjian Lou, Conghui Shen","doi":"10.4134/BKMS.B190302","DOIUrl":"https://doi.org/10.4134/BKMS.B190302","url":null,"abstract":"Let M(X,Y ) denote the space of multipliers from X to Y, where X and Y are analytic function spaces. As we known, for Dirichlettype spaces D α, M(D p−1,D q q−1) = {0}, if p 6= q, 0 < p, q < ∞. If 0 < p, q < ∞, p 6= q, 0 < s < 1 such that p + s, q + s > 1, then M(D p−2+s,D q q−2+s) = {0}. However, X ∩ D p p−1 ⊆ X ∩ D q q−1 and X ∩ D p−2+s ⊆ X ∩ D q q−2+s whenever X is a subspace of the Bloch space B and 0 < p ≤ q < ∞. This says that the set of multipliers M(X ∩ D p−2+s, X∩D q q−2+s) is nontrivial. In this paper, we study the multipliers M(X ∩ D p−2+s, X ∩ D q q−2+s) for distinct classical subspaces X of the Bloch space B, where X = B, BMOA or H∞.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"429-441"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361994","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 compute the Bergman kernel for Ωp,q,r = {(z, z′, w) ∈ C ×∆ : |z| < (1− |z′|2q)(1− |w|)}, where p, q, r > 0 in terms of multivariable hypergeometric series. As a consequence, we obtain the behavior of KΩp,q,r (z, 0, 0; z, 0, 0) when (z, 0, 0) approaches to the boundary of Ωp,q,r.
{"title":"ON THE BERGMAN KERNEL FOR SOME HARTOGS DOMAINS","authors":"Jong-Do Park","doi":"10.4134/BKMS.B190382","DOIUrl":"https://doi.org/10.4134/BKMS.B190382","url":null,"abstract":"In this paper, we compute the Bergman kernel for Ωp,q,r = {(z, z′, w) ∈ C ×∆ : |z| < (1− |z′|2q)(1− |w|)}, where p, q, r > 0 in terms of multivariable hypergeometric series. As a consequence, we obtain the behavior of KΩp,q,r (z, 0, 0; z, 0, 0) when (z, 0, 0) approaches to the boundary of Ωp,q,r.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"521-533"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362234","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":"ASYMPTOTIC EXACTNESS OF SOME BANK-WEISER ERROR ESTIMATOR FOR QUADRATIC TRIANGULAR FINITE ELEMENT","authors":"Kwang-Yeon Kim, Ju-Seong Park","doi":"10.4134/BKMS.B190278","DOIUrl":"https://doi.org/10.4134/BKMS.B190278","url":null,"abstract":"","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"393-406"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362410","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, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B∗(G)⊗̂B∗(K) is isomorphic to the bounded cohomology Ĥ∗(G×K) of G×K, which is the cohomology of B∗(G×K) as topological vector spaces, where B∗(G) is a complex of bounded cochains of G with real coefficients R. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ∗(G × K) to the seminorm in the cohomology of B∗(G)⊗̂B∗(K).
{"title":"THE KÜNNETH ISOMORPHISM IN BOUNDED COHOMOLOGY PRESERVING THE NORMS","authors":"Heesook Park","doi":"10.4134/BKMS.B190547","DOIUrl":"https://doi.org/10.4134/BKMS.B190547","url":null,"abstract":"In this paper, for discrete groups G and K, we show that the cohomology of the complex of projective tensor product B∗(G)⊗̂B∗(K) is isomorphic to the bounded cohomology Ĥ∗(G×K) of G×K, which is the cohomology of B∗(G×K) as topological vector spaces, where B∗(G) is a complex of bounded cochains of G with real coefficients R. In fact, we construct an isomorphism between these two cohomology groups that carries the canonical seminorm in Ĥ∗(G × K) to the seminorm in the cohomology of B∗(G)⊗̂B∗(K).","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"873-890"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70362727","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}
The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.
{"title":"GLOBAL SOLUTION AND BLOW-UP OF LOGARITHMIC KLEIN-GORDON EQUATION","authors":"Y. Ye","doi":"10.4134/BKMS.B190190","DOIUrl":"https://doi.org/10.4134/BKMS.B190190","url":null,"abstract":"The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"281-294"},"PeriodicalIF":0.5,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70361876","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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