. The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some Q -polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.
{"title":"The main component of a reducible Hilbert curve of conic fibrations","authors":"M. Fania, A. Lanteri","doi":"10.4134/JKMS.J200534","DOIUrl":"https://doi.org/10.4134/JKMS.J200534","url":null,"abstract":". The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some Q -polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"1211-1226"},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47091927","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}
. Demeter [1] and Kuk and Lee [5] proved the unboundedness of the trilinear Hilbert transforms H a,b,c under the critical index 1 / 2 for some parameters a,b and c . We show the unboundedness of H a,b,c for any parameters.
{"title":"Unboundedness of the trilinear Hilbert transform under the critical index","authors":"Y. Komori‐Furuya","doi":"10.4134/JKMS.J200656","DOIUrl":"https://doi.org/10.4134/JKMS.J200656","url":null,"abstract":". Demeter [1] and Kuk and Lee [5] proved the unboundedness of the trilinear Hilbert transforms H a,b,c under the critical index 1 / 2 for some parameters a,b and c . We show the unboundedness of H a,b,c for any parameters.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"1299-1309"},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43000249","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}
An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.
{"title":"Remarks on the existence of an inertial manifold","authors":"Minkyu Kwak, Xiuxiu Sun","doi":"10.4134/JKMS.J200565","DOIUrl":"https://doi.org/10.4134/JKMS.J200565","url":null,"abstract":"An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"1261-1277"},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42551258","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}
Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.
{"title":"Estimation algorithm for physical parameters in a shallow arch","authors":"S. Gutman, J. Ha, Sudeok Shon","doi":"10.4134/JKMS.J200226","DOIUrl":"https://doi.org/10.4134/JKMS.J200226","url":null,"abstract":"Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"723-740"},"PeriodicalIF":0.6,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41706060","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":"Homotopy properties of $text{map}(Sigma^n mathbb C P^2,S^m)$","authors":"Jin-ho Lee","doi":"10.4134/JKMS.J200249","DOIUrl":"https://doi.org/10.4134/JKMS.J200249","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"761-790"},"PeriodicalIF":0.6,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45308465","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 introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.
{"title":"General iterative algorithms for monotone inclusion, variational inequality and fixed point problems","authors":"J. Jung","doi":"10.4134/JKMS.J180808","DOIUrl":"https://doi.org/10.4134/JKMS.J180808","url":null,"abstract":"In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"525-552"},"PeriodicalIF":0.6,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46215940","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 G = ( V,E ) be a connected locally finite and weighted graph, ∆ p be the p -th graph Laplacian. Consider the p -th nonlinear equation − ∆ p u + h | u | p − 2 u = f ( x,u ) on G , where p > 2, h,f satisfy certain assumptions. Grigor’yan-Lin-Yang [24] proved the existence of the solution to the above nonlinear equation in a bounded domain Ω ⊂ V . In this paper, we show that there exists a strictly positive solution on the infinite set V to the above nonlinear equation by modifying some conditions in [24]. To the m -order differential operator L m,p , we also prove the existence of the nontrivial solution to the analogous nonlinear equation.
设G=（V，E）是一个连通的局部有限和加权图，∆p是第p个图拉普拉斯算子。考虑G上的第p个非线性方程−∆p u+h | u | p−2 u=f（x，u），其中p>2，h，f满足某些假设。Grigor’yan-Lin-Yang[24]证明了上述非线性方程在有界域中解的存在性Ω ⊂ 五、在本文中，我们通过修改[24]中的一些条件，证明了上述非线性方程在有限集V上存在严格正解。对于m阶微分算子LM，p，我们还证明了类似非线性方程非平凡解的存在性。
{"title":"EXISTENCE OF GLOBAL SOLUTIONS TO SOME NONLINEAR EQUATIONS ON LOCALLY FINITE GRAPHS","authors":"Yanxun Chang, Xiaoxiao Zhang","doi":"10.4134/JKMS.J200221","DOIUrl":"https://doi.org/10.4134/JKMS.J200221","url":null,"abstract":". Let G = ( V,E ) be a connected locally finite and weighted graph, ∆ p be the p -th graph Laplacian. Consider the p -th nonlinear equation − ∆ p u + h | u | p − 2 u = f ( x,u ) on G , where p > 2, h,f satisfy certain assumptions. Grigor’yan-Lin-Yang [24] proved the existence of the solution to the above nonlinear equation in a bounded domain Ω ⊂ V . In this paper, we show that there exists a strictly positive solution on the infinite set V to the above nonlinear equation by modifying some conditions in [24]. To the m -order differential operator L m,p , we also prove the existence of the nontrivial solution to the analogous nonlinear equation.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"703-722"},"PeriodicalIF":0.6,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44031010","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 prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the k-th generalized Tanaka-Webster connection.
{"title":"Killing structure Jacobi operator of a real hypersurface in a complex projective space","authors":"J. Pérez","doi":"10.4134/JKMS.J200134","DOIUrl":"https://doi.org/10.4134/JKMS.J200134","url":null,"abstract":"We prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the k-th generalized Tanaka-Webster connection.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"473-486"},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46003199","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 aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator M ρ Ω ,b which is generated by the parameter Marcinkiwicz integral M ρ Ω and the Lipschitz function b on generalized Orlicz-Morrey space L Φ ,ϕ ( R d ) in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral M ρ Ω on the L Φ ,ϕ ( R d ), and the commutator [ b, M ρ Ω ] generated by the M ρ Ω and the space BMO on the L Φ ,ϕ ( R d ), are also obtained, respectively.
{"title":"Parameter Marcinkiewicz integral and its commutator on generalized Orlicz-Morrey spaces","authors":"G. Lu","doi":"10.4134/JKMS.J200071","DOIUrl":"https://doi.org/10.4134/JKMS.J200071","url":null,"abstract":". The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator M ρ Ω ,b which is generated by the parameter Marcinkiwicz integral M ρ Ω and the Lipschitz function b on generalized Orlicz-Morrey space L Φ ,ϕ ( R d ) in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral M ρ Ω on the L Φ ,ϕ ( R d ), and the commutator [ b, M ρ Ω ] generated by the M ρ Ω and the space BMO on the L Φ ,ϕ ( R d ), are also obtained, respectively.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"383-400"},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44847368","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 introduce the notion of strong Galois Hprogenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ∼= Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.
{"title":"MONOIDAL FUNCTORS AND EXACT SEQUENCES OF GROUPS FOR HOPF QUASIGROUPS","authors":"J. Álvarez, J. M. F. Vilaboa, R. G. Rodríguez","doi":"10.4134/JKMS.J200069","DOIUrl":"https://doi.org/10.4134/JKMS.J200069","url":null,"abstract":"In this paper we introduce the notion of strong Galois Hprogenerator object for a finite cocommutative Hopf quasigroup H in a symmetric monoidal category C. We prove that the set of isomorphism classes of strong Galois H-progenerator objects is a subgroup of the group of strong Galois H-objects introduced in [3]. Moreover, we show that strong Galois H-progenerator objects are preserved by strong symmetric monoidal functors and, as a consequence, we obtain an exact sequence involving the associated Galois groups. Finally, to the previous functors, if H is finite, we find exact sequences of Picard groups related with invertible left H-(quasi)modules and an isomorphism Pic(HMod) ∼= Pic(C)⊕G(H∗) where Pic(HMod) is the Picard group of the category of left H-modules, Pic(C) the Picard group of C, and G(H∗) the group of group-like morphisms of the dual of H.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"351-381"},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48318921","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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