In 1994, A. Okabe and R. Matsuda introduced the notion of a semistar operation in [OM] as a generalization of the notion of a star operation which was introduced in 1936 by W. Krull and was developed in [G] by R. Gilmer. In 2000, M. Fontana and J.A. Huckaba investigated the relation between semistar operations and localizing systems and they associated the semistar operation ∗F for each localizing system F on D and the localizing system F∗ for each semistar operation ∗ on D. Using these correspondences, they established a very natural bridge between semistar operations and localizing systems which has been proven to be a very important and essential tool in the study of semistar operation theory. Let D be an integral domain with quotient field K and let D[X] be the ring of polynomials over D in indeterminate X. We shall denote the set of all semistar operations on D (resp. D[X]) by SS(D) (resp. SS(D[X])) as in [O5]. We have much interest in considering the relation between SS(D) and SS(D[X]). First, in [OM], a correspondence ∗ 7→ ∗′ from SS(D[X]) into SS(D) was given by setting E∗ ′ = (ED[X])∗ ⋂ K for each nonzero D-submodule E of K. In this paper, this semistar operation ∗′ is called the polynomial descent semistar operation associated to ∗ and is denoted by ∗. Next, in [P3], G. Picozza defined a reverse correspondence ∗ 7→ ∗′ from SS(D) into SS(D[X]) by setting ∗′ = ∗F∗[X] for each ∗ ∈ SS(D). In this paper, this semistar operation ∗′ is called the polynomial ascent semistar operation associated to ∗ and is denoted by ∗. Thus we have two correspondences between SS(D) and SS(D[X]). The purpose of this paper is to investigate the relation between SS(D) and SS(D[X]) using these two semistar operations ∗ and ∗. In Section 1, we first recall some well-known results on semistar operations and localizing systems on an integral domain D which will be used in sequel and we shall show some new results concerning semistar operations [∗] and ∗a which were introduced in [FL1]. In Section 2, we shall prove some important properties of semistar operations ∗ and ∗. In Theorem 27, we show that (∗) = ∗̄ for each semistar operation ∗ on D
{"title":"On polynomial ascent and descent semistar operations on an integral domain","authors":"A. Okabe","doi":"10.5036/MJIU.42.3","DOIUrl":"https://doi.org/10.5036/MJIU.42.3","url":null,"abstract":"In 1994, A. Okabe and R. Matsuda introduced the notion of a semistar operation in [OM] as a generalization of the notion of a star operation which was introduced in 1936 by W. Krull and was developed in [G] by R. Gilmer. In 2000, M. Fontana and J.A. Huckaba investigated the relation between semistar operations and localizing systems and they associated the semistar operation ∗F for each localizing system F on D and the localizing system F∗ for each semistar operation ∗ on D. Using these correspondences, they established a very natural bridge between semistar operations and localizing systems which has been proven to be a very important and essential tool in the study of semistar operation theory. Let D be an integral domain with quotient field K and let D[X] be the ring of polynomials over D in indeterminate X. We shall denote the set of all semistar operations on D (resp. D[X]) by SS(D) (resp. SS(D[X])) as in [O5]. We have much interest in considering the relation between SS(D) and SS(D[X]). First, in [OM], a correspondence ∗ 7→ ∗′ from SS(D[X]) into SS(D) was given by setting E∗ ′ = (ED[X])∗ ⋂ K for each nonzero D-submodule E of K. In this paper, this semistar operation ∗′ is called the polynomial descent semistar operation associated to ∗ and is denoted by ∗. Next, in [P3], G. Picozza defined a reverse correspondence ∗ 7→ ∗′ from SS(D) into SS(D[X]) by setting ∗′ = ∗F∗[X] for each ∗ ∈ SS(D). In this paper, this semistar operation ∗′ is called the polynomial ascent semistar operation associated to ∗ and is denoted by ∗. Thus we have two correspondences between SS(D) and SS(D[X]). The purpose of this paper is to investigate the relation between SS(D) and SS(D[X]) using these two semistar operations ∗ and ∗. In Section 1, we first recall some well-known results on semistar operations and localizing systems on an integral domain D which will be used in sequel and we shall show some new results concerning semistar operations [∗] and ∗a which were introduced in [FL1]. In Section 2, we shall prove some important properties of semistar operations ∗ and ∗. In Theorem 27, we show that (∗) = ∗̄ for each semistar operation ∗ on D","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"89 1","pages":"3-16"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80921575","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}
Throughout this paper the letter D denotes an integral domain with quotient field K. We shall denote the set of all nonzero D-submodules of K by K(D) and we shall call each element of K(D) a Kaplansky fractional ideal (for short, K-fractional ideal ) of D as in [O3]. Let F(D) be the set of all nonzero fractional ideals of D, that is, all elements E ∈ K(D) such that there exists a nonzero element d ∈ D with dE ⊆ D. The set of finitely generated K-fractional ideals of D is denoted by f(D). It is evident that f(D) ⊆ F(D) ⊆ K(D). An ideal of D means an integral ideal of D and the set of all nonzero integral ideals of D is denoted by I(D). If D is a quasi-local domain with maximal ideal M , then we say that (D,M) is a quasi-local domain. In [HHP], a nonzero ideal I of D is called an m-canonical ideal of D if I : (I : J) = J for each nonzero ideal J of D. In [HHP, Proposition 6.2] it was shown that if (D,M) is an integrally closed qausi-local domain, then M is an m-canonical ideal of D if and only if D is a valuation domain. In [BHLP, Proposition 4.1], it was proved that the integrally closed hypothesis in the above result can be eliminated, that is, if (D,M) is a quasi-local domain, then D is a valuation domain if and only if M is an m-canonical ideal of D. Recently, in [B2, Corollary 2.15], it was proved that if a quasi-local integral domain (D,M) admits a proper m-canonical ideal I of D, then the following statements are equivalent: (1) D is a valuation domain. (2) I is a divided m-canonical ideal of D. (3) cM = I for some nonzero element c ∈ D. (4) I : M is a principal ideal of D. (5) I : M is an invertible ideal of D. (6) D is an integrally closed domain and I : M is a finitely generated ideal of D. (7) M : M = D and I : M is a finitely generated ideal of D. (8) If J = I : M , then J is a finitely generated ideal of D and J : J = D. Let I be a nonzero ideal of D such that I : I = D. Then in [HHP, Proposition 3.2], it was proved that the map J 7−→ I : (I : J) of F(D) into F(D) is a star operation
{"title":"On generalized divisorial semistar operations on integral domains","authors":"A. Okabe","doi":"10.5036/MJIU.41.1","DOIUrl":"https://doi.org/10.5036/MJIU.41.1","url":null,"abstract":"Throughout this paper the letter D denotes an integral domain with quotient field K. We shall denote the set of all nonzero D-submodules of K by K(D) and we shall call each element of K(D) a Kaplansky fractional ideal (for short, K-fractional ideal ) of D as in [O3]. Let F(D) be the set of all nonzero fractional ideals of D, that is, all elements E ∈ K(D) such that there exists a nonzero element d ∈ D with dE ⊆ D. The set of finitely generated K-fractional ideals of D is denoted by f(D). It is evident that f(D) ⊆ F(D) ⊆ K(D). An ideal of D means an integral ideal of D and the set of all nonzero integral ideals of D is denoted by I(D). If D is a quasi-local domain with maximal ideal M , then we say that (D,M) is a quasi-local domain. In [HHP], a nonzero ideal I of D is called an m-canonical ideal of D if I : (I : J) = J for each nonzero ideal J of D. In [HHP, Proposition 6.2] it was shown that if (D,M) is an integrally closed qausi-local domain, then M is an m-canonical ideal of D if and only if D is a valuation domain. In [BHLP, Proposition 4.1], it was proved that the integrally closed hypothesis in the above result can be eliminated, that is, if (D,M) is a quasi-local domain, then D is a valuation domain if and only if M is an m-canonical ideal of D. Recently, in [B2, Corollary 2.15], it was proved that if a quasi-local integral domain (D,M) admits a proper m-canonical ideal I of D, then the following statements are equivalent: (1) D is a valuation domain. (2) I is a divided m-canonical ideal of D. (3) cM = I for some nonzero element c ∈ D. (4) I : M is a principal ideal of D. (5) I : M is an invertible ideal of D. (6) D is an integrally closed domain and I : M is a finitely generated ideal of D. (7) M : M = D and I : M is a finitely generated ideal of D. (8) If J = I : M , then J is a finitely generated ideal of D and J : J = D. Let I be a nonzero ideal of D such that I : I = D. Then in [HHP, Proposition 3.2], it was proved that the map J 7−→ I : (I : J) of F(D) into F(D) is a star operation","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"61 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72760294","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}
We study the results of M. Fontana and J. Huckaba [FHu] on localizing systems and semistar operations, and give a couple of remarks for them. After M. Fontana and K.A. Loper [FL3], we study also Nagata rings, Kronecker function rings, and related semistar operations on semigroups.
{"title":"Note on localizing systems and Kronecker function rings of semistar operations","authors":"Ryuki Matsuda","doi":"10.5036/MJIU.41.15","DOIUrl":"https://doi.org/10.5036/MJIU.41.15","url":null,"abstract":"We study the results of M. Fontana and J. Huckaba [FHu] on localizing systems and semistar operations, and give a couple of remarks for them. After M. Fontana and K.A. Loper [FL3], we study also Nagata rings, Kronecker function rings, and related semistar operations on semigroups.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"21 1","pages":"15-38"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91078883","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}
Let D be an integral domain with quotient field K. Then it is easily seen that every invertible fractional ideal of D is finitely generated. An integral domain D is called a Prufer domain if each nonzero finitely generated ideal of D is invertible. A Prufer domain may be an example of an integral domain which would have the maximum number of characterizations in all the classes of integral domains which have been already defined in commutative algebra. The number of characterizations of a Prufer domain is already over eighty now. In this paper, we continue to study a Prufer domain and we shall give some new characterizations of a Prufer domain. In Section 1, we first collect a family of well-known characterizations of a Prufer domain which is only a part of the known characterizations of a Prufer domain and we recall some definitions and preliminary results on semistar operations and localizing systemes which will be uscd in Section 2. In Section 2, we shall give some new semistar-theoretical characterizations of a Prufer domain by the use of properties of a semistar operation and a localizing system.
{"title":"On characterizations of a Prüfer domain","authors":"A. Okabe, Ryuki Matsuda","doi":"10.5036/MJIU.39.1","DOIUrl":"https://doi.org/10.5036/MJIU.39.1","url":null,"abstract":"Let D be an integral domain with quotient field K. Then it is easily seen that every invertible fractional ideal of D is finitely generated. An integral domain D is called a Prufer domain if each nonzero finitely generated ideal of D is invertible. A Prufer domain may be an example of an integral domain which would have the maximum number of characterizations in all the classes of integral domains which have been already defined in commutative algebra. The number of characterizations of a Prufer domain is already over eighty now. In this paper, we continue to study a Prufer domain and we shall give some new characterizations of a Prufer domain. In Section 1, we first collect a family of well-known characterizations of a Prufer domain which is only a part of the known characterizations of a Prufer domain and we recall some definitions and preliminary results on semistar operations and localizing systemes which will be uscd in Section 2. In Section 2, we shall give some new semistar-theoretical characterizations of a Prufer domain by the use of properties of a semistar operation and a localizing system.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"1 1","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2007-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89643344","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}
{"title":"Caloric morphisms with respect to radial metrics on semi-euclidean spaces","authors":"Katsunori Shimomura","doi":"10.5036/MJIU.37.81","DOIUrl":"https://doi.org/10.5036/MJIU.37.81","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"1 1","pages":"81-103"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78033011","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}
In this paper we discuss some properties of rigid analytic functions related to the p-adic Mellin transform and the p-adic Laplace transform.
本文讨论了刚性解析函数与p进梅林变换和p进拉普拉斯变换有关的一些性质。
{"title":"On Krasner analytic functions and the p-adic Mellin transform","authors":"M. Vâjâitu, A. Zaharescu","doi":"10.5036/MJIU.37.23","DOIUrl":"https://doi.org/10.5036/MJIU.37.23","url":null,"abstract":"In this paper we discuss some properties of rigid analytic functions related to the p-adic Mellin transform and the p-adic Laplace transform.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"51 1","pages":"23-33"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77377987","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}
We define a Kronecker function ring for any L-semistar operation, and study ascents and descents of L-semistar operations.
定义了任意l -半星运算的Kronecker函数环，并研究了l -半星运算的上升和下降。
{"title":"On generalized Kronecker function rings","authors":"A. Okabe","doi":"10.5036/MJIU.44.7","DOIUrl":"https://doi.org/10.5036/MJIU.44.7","url":null,"abstract":"We define a Kronecker function ring for any L-semistar operation, and study ascents and descents of L-semistar operations.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"158 1","pages":"1-22"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76813529","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}
The object of our research is a piecewise Riemannian 2-polyhedron which is a combinatorial 2-polyhedron such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. In the previous paper [4], which is a joint work with J. Itoh, we have introduced the concept of total curvature for piecewise Riemannian 2-polyhedra and proved a generalized Gauss-Bonnet theorem and a generalized Cohn-Vossen theorem. In this paper, we shall give a definition of flatness of piecewise Riemannian 2polyhedra and characterize them. §1.Introduction. "Curvature" is one of the most important tools to investigate "Geometry" of manifolds. For our research object "polyhedra," the concept of "Curvature" has been introduced and remarkable results are obtained by Banchoff [3] for any dimensional compact piecewise linear polyhedra, and by Ballman-Brin [1] and Ballman-Buyalo [2] for 2-dimensional cocompact piecewise Riemannian polyhedra. My interest is based particularly on the study of noncompact case from the view point of total curvature. In our previous paper [4] with J. Itoh, we have defined two kinds of total curvature for noncompact piecewise Riemannian 2-polyhedra, total curvature and weak total curvature, which both coincide with the usual definitions for Riemannian manifolds or compact 2-polyhedra. It is naturally and easily seen that a generalized Gauss-Bonnet theorem holds under these total curvatures. Furthermore, in [4], we have shown the difference between the geometric meanings of these two kinds of total curvature, and under the assumption of admitting total curvature (not weak total curvature) we have proved a generalized Cohn-Vossen theorem. The aim of my research is to clarify the meaning of "Curvature" of polyhedra and characterize them in terms of curvature. In this paper, as a first step of this research direction, we shall define the flatness of polyhedra and classify Partially supported by Grant-in-aid for Scientific Research (C) No. 13640060, Japan Society for the Promotion of Science. Received May 11, 2004. 2000 Mathematics Subject Classification. Primary: 53C23, Secondary: 57M20.
{"title":"Erratum to: “Structures of flat piecewise Riemannian 2-polyhedra”","authors":"Fumiko Ohtsuka","doi":"10.5036/MJIU.37.107","DOIUrl":"https://doi.org/10.5036/MJIU.37.107","url":null,"abstract":"The object of our research is a piecewise Riemannian 2-polyhedron which is a combinatorial 2-polyhedron such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. In the previous paper [4], which is a joint work with J. Itoh, we have introduced the concept of total curvature for piecewise Riemannian 2-polyhedra and proved a generalized Gauss-Bonnet theorem and a generalized Cohn-Vossen theorem. In this paper, we shall give a definition of flatness of piecewise Riemannian 2polyhedra and characterize them. §1.Introduction. \"Curvature\" is one of the most important tools to investigate \"Geometry\" of manifolds. For our research object \"polyhedra,\" the concept of \"Curvature\" has been introduced and remarkable results are obtained by Banchoff [3] for any dimensional compact piecewise linear polyhedra, and by Ballman-Brin [1] and Ballman-Buyalo [2] for 2-dimensional cocompact piecewise Riemannian polyhedra. My interest is based particularly on the study of noncompact case from the view point of total curvature. In our previous paper [4] with J. Itoh, we have defined two kinds of total curvature for noncompact piecewise Riemannian 2-polyhedra, total curvature and weak total curvature, which both coincide with the usual definitions for Riemannian manifolds or compact 2-polyhedra. It is naturally and easily seen that a generalized Gauss-Bonnet theorem holds under these total curvatures. Furthermore, in [4], we have shown the difference between the geometric meanings of these two kinds of total curvature, and under the assumption of admitting total curvature (not weak total curvature) we have proved a generalized Cohn-Vossen theorem. The aim of my research is to clarify the meaning of \"Curvature\" of polyhedra and characterize them in terms of curvature. In this paper, as a first step of this research direction, we shall define the flatness of polyhedra and classify Partially supported by Grant-in-aid for Scientific Research (C) No. 13640060, Japan Society for the Promotion of Science. Received May 11, 2004. 2000 Mathematics Subject Classification. Primary: 53C23, Secondary: 57M20.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"1 1","pages":"107-114"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79299451","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}
We determine the index and co-index of the twisted tangent bundle of projective spaces. We also discuss the stabilty of them, and determine the set of integers that can be realized as the stable co-index of a vector bundle over the projective space.
{"title":"The index and co-index of the twisted tangent bundle over projective spaces","authors":"Ryuichi Tanaka","doi":"10.5036/MJIU.37.35","DOIUrl":"https://doi.org/10.5036/MJIU.37.35","url":null,"abstract":"We determine the index and co-index of the twisted tangent bundle of projective spaces. We also discuss the stabilty of them, and determine the set of integers that can be realized as the stable co-index of a vector bundle over the projective space.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"44 1","pages":"35-38"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74121289","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}
In this paper we shall prove the existence of sharp remainder terms involving singular weight (logR/|x|)-2 for Hardy-Sobolev inequalities of the following type:∫Ω|∇u(x)|2dx≥(n-2/2)2∫Ω|u(x)|2/|(x)|2dx for any u∈W1, 20(Ω), Ω is a bounded domain in Rn, n>2, with 0∈Ω. Here the number of remainder terms depends on the choice of R.
{"title":"Sharp remainder terms of Hardy-Sobolev inequalities","authors":"Alnar Detalla, T. Horiuchi, Hiroshi Ando","doi":"10.5036/MJIU.37.39","DOIUrl":"https://doi.org/10.5036/MJIU.37.39","url":null,"abstract":"In this paper we shall prove the existence of sharp remainder terms involving singular weight (logR/|x|)-2 for Hardy-Sobolev inequalities of the following type:∫Ω|∇u(x)|2dx≥(n-2/2)2∫Ω|u(x)|2/|(x)|2dx for any u∈W1, 20(Ω), Ω is a bounded domain in Rn, n>2, with 0∈Ω. Here the number of remainder terms depends on the choice of R.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"10 1","pages":"39-52"},"PeriodicalIF":0.0,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79363941","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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