In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.
本文给出了一类微分-差分方程有限阶亚纯解f的唯一性定理，使得解f由其极点和两个不同的值唯一确定。
{"title":"ON UNICITY OF MEROMORPHIC SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS","authors":"P. Hu, Qiongyan Wang","doi":"10.4134/JKMS.J170387","DOIUrl":"https://doi.org/10.4134/JKMS.J170387","url":null,"abstract":"In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"785-795"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509534","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":"INFINITELY MANY SMALL ENERGY SOLUTIONS FOR EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN IN ℝ N","authors":"Yun-Ho Kim","doi":"10.4134/JKMS.J170681","DOIUrl":"https://doi.org/10.4134/JKMS.J170681","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"1269-1283"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509719","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 matrix equation Xp + A∗XA = Q has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton’s method for finding the matrix p-th root. From these two considerations, we will use the NewtonSchulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.
在一些研究中，研究了矩阵方程Xp + A * XA = Q的正定解。本文考虑了求矩阵p次根的不动点迭代和牛顿法。从这两个方面考虑，我们将使用牛顿-舒尔茨算法(n.s.a.)。我们将证明不动点迭代的残差关系和局部收敛性。局部收敛性保证了nsa算法的收敛性，并通过数值实验验证了nsa算法显著降低了cpu时间。
{"title":"NEWTON SCHULZ METHOD FOR SOLVING NONLINEAR MATRIX EQUATION X p + A ⁎ XA = Q","authors":"Hyun Min Kim, Young Jin Kim, Jie Meng","doi":"10.4134/JKMS.J170809","DOIUrl":"https://doi.org/10.4134/JKMS.J170809","url":null,"abstract":"The matrix equation Xp + A∗XA = Q has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton’s method for finding the matrix p-th root. From these two considerations, we will use the NewtonSchulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"1529-1540"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509771","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 form the basis of the abstract theory for con-structing the K¨unneth spectral sequence for a complex of Banach spaces. As the category of Banach spaces is not abelian, several difficulties occur and hinder us from applying the usual method of homological algebra directly. The most notable facts are the image of a morphism of Banach spaces is not necessarily a Banach space, and also the closed summand of a Banach space need not be a topological direct summand. So, we consider some conditions and categorical terms that fit the category of Banach spaces to modify the familiar method of homological algebra.
{"title":"THE KÜNNETH SPECTRAL SEQUENCE FOR COMPLEXES OF BANACH SPACES","authors":"Heesook Park","doi":"10.4134/JKMS.J170464","DOIUrl":"https://doi.org/10.4134/JKMS.J170464","url":null,"abstract":". In this paper, we form the basis of the abstract theory for con-structing the K¨unneth spectral sequence for a complex of Banach spaces. As the category of Banach spaces is not abelian, several difficulties occur and hinder us from applying the usual method of homological algebra directly. The most notable facts are the image of a morphism of Banach spaces is not necessarily a Banach space, and also the closed summand of a Banach space need not be a topological direct summand. So, we consider some conditions and categorical terms that fit the category of Banach spaces to modify the familiar method of homological algebra.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"809-832"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70510072","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 study harmonic maps and biharmonic maps on the principal G -bundle in Kobayashi and Nomizu [22] and also the warped product P = M × f F for a C ∞ ( M ) function f on M studied by Bishop and O’Neill [4], and Ejiri [11].
． 本文研究了Kobayashi和Nomizu[22]中主G束上的调和映射和双调和映射，以及Bishop和O 'Neill[4]和Ejiri[11]研究的C∞(M)函数f在M上的弯曲积P = M × f。
{"title":"HARMONIC MAPS AND BIHARMONIC MAPS ON PRINCIPAL BUNDLES AND WARPED PRODUCTS","authors":"H. Urakawa","doi":"10.4134/JKMS.J170251","DOIUrl":"https://doi.org/10.4134/JKMS.J170251","url":null,"abstract":". In this paper, we study harmonic maps and biharmonic maps on the principal G -bundle in Kobayashi and Nomizu [22] and also the warped product P = M × f F for a C ∞ ( M ) function f on M studied by Bishop and O’Neill [4], and Ejiri [11].","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"553-574"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509433","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":"PETTIS CONDITIONAL EXPECTATION OF CLOSED CONVEX RANDOM SETS IN A BANACH SPACE WITHOUT RNP","authors":"Fattah Akhiat, M. E. Harami, F. Ezzaki","doi":"10.4134/JKMS.J170490","DOIUrl":"https://doi.org/10.4134/JKMS.J170490","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"833-848"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509697","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 Σ g,n,b denote the orientable surface obtained from the closed orientable surface Σ g of genus g ≥ 2 by deleting the interior of n ≥ 1 distinct topological disks and b ≥ 1 points. Using the notion of symplectic chain complex, the present paper establishes a formula for computing Reidemeister torsion of the surface Σ g,n,b in terms of Reide- meister torsion of the closed surface Σ g , Reidemeister torsion of disk, and Reidemeister torsion of punctured disk.
{"title":"REIDEMEISTER TORSION AND ORIENTABLE PUNCTURED SURFACES","authors":"E. Dirican, Y. Sozen","doi":"10.4134/JKMS.J170595","DOIUrl":"https://doi.org/10.4134/JKMS.J170595","url":null,"abstract":". Let Σ g,n,b denote the orientable surface obtained from the closed orientable surface Σ g of genus g ≥ 2 by deleting the interior of n ≥ 1 distinct topological disks and b ≥ 1 points. Using the notion of symplectic chain complex, the present paper establishes a formula for computing Reidemeister torsion of the surface Σ g,n,b in terms of Reide- meister torsion of the closed surface Σ g , Reidemeister torsion of disk, and Reidemeister torsion of punctured disk.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"1005-1018"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509811","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":"Small data scattering of hartree type fractional schrödinger equations in dimension 2 and 3","authors":"Yonggeun Cho, T. Ozawa","doi":"10.4134/JKMS.J170224","DOIUrl":"https://doi.org/10.4134/JKMS.J170224","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"55 1","pages":"373-390"},"PeriodicalIF":0.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509329","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 ( n 1 ,n 2 ,...,n k )-colored permutation is a permutation of n 1 + n 2 + ··· + n k in which 1 , 2 ,...,n 1 have color 1, and n 1 + 1, n 1 + 2, ...,n 1 + n 2 have color 2, and so on. We give a bijective proof of Stein- hardt’s result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first n 1 elements, the next n 2 element, and so on, in ascending order. We then find the generating function for colored per- mutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.
{"title":"COLORED PERMUTATIONS WITH NO MONOCHROMATIC CYCLES","authors":"Dongsu Kim, J. Kim, Seunghyun Seo","doi":"10.4134/JKMS.J160392","DOIUrl":"https://doi.org/10.4134/JKMS.J160392","url":null,"abstract":". An ( n 1 ,n 2 ,...,n k )-colored permutation is a permutation of n 1 + n 2 + ··· + n k in which 1 , 2 ,...,n 1 have color 1, and n 1 + 1, n 1 + 2, ...,n 1 + n 2 have color 2, and so on. We give a bijective proof of Stein- hardt’s result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first n 1 elements, the next n 2 element, and so on, in ascending order. We then find the generating function for colored per- mutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"54 1","pages":"1149-1161"},"PeriodicalIF":0.6,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46347297","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}
. This paper is concerned with the following Klein-Gordon-Maxwell system: where ω > 0 is a constant and λ is the parameter. Under some suitable assumptions on V ( x ) and f ( x,u ), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition. 35B38.
{"title":"EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR KLEIN-GORDON-MAXWELL SYSTEM WITH A PARAMETER","authors":"Guofeng Che, Haibo Chen","doi":"10.4134/JKMS.J160344","DOIUrl":"https://doi.org/10.4134/JKMS.J160344","url":null,"abstract":". This paper is concerned with the following Klein-Gordon-Maxwell system: where ω > 0 is a constant and λ is the parameter. Under some suitable assumptions on V ( x ) and f ( x,u ), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition. 35B38.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"54 1","pages":"1015-1030"},"PeriodicalIF":0.6,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49270785","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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