We characterize the pointwise multipliers from a weak Orlicz space to another weak Orlicz space.
我们刻画了从一个弱Orlicz空间到另一个弱Ollicz空间的逐点乘子。
{"title":"Pointwise multipliers on weak Orlicz spaces","authors":"Ryota Kawasumi, E. Nakai","doi":"10.32917/hmj/1595901625","DOIUrl":"https://doi.org/10.32917/hmj/1595901625","url":null,"abstract":"We characterize the pointwise multipliers from a weak Orlicz space to another weak Orlicz space.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43640251","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}
A bstract . The Besicovitch covering theorem is well known to be the useful tools in many fields of analysis. Federer extended the result of Besicovitch to a directionally limited metric space. In this paper, we prove the Besicovitch covering theorem for parabolic balls in Euclidean space, although the parabolic metric is not directionally limited.
{"title":"The Besicovitch covering theorem for parabolic balls in Euclidean space","authors":"Tsubasa Itoh","doi":"10.32917/HMJ/1544238028","DOIUrl":"https://doi.org/10.32917/HMJ/1544238028","url":null,"abstract":"A bstract . The Besicovitch covering theorem is well known to be the useful tools in many fields of analysis. Federer extended the result of Besicovitch to a directionally limited metric space. In this paper, we prove the Besicovitch covering theorem for parabolic balls in Euclidean space, although the parabolic metric is not directionally limited.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45633693","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":"Information geometry in a global setting","authors":"A. Mori","doi":"10.32917/HMJ/1544238029","DOIUrl":"https://doi.org/10.32917/HMJ/1544238029","url":null,"abstract":"","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49296927","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}
A bstract . In this paper we show the validity of Stein’s interpolation theorem on variable exponent Morrey spaces.
摘要。本文证明了变指数Morrey空间上Stein插值定理的有效性。
{"title":"Interpolation of an analytic family of operators on variable exponent Morrey spaces","authors":"A. Meskhi, H. Rafeiro, M. A. Zaighum","doi":"10.32917/HMJ/1544238031","DOIUrl":"https://doi.org/10.32917/HMJ/1544238031","url":null,"abstract":"A bstract . In this paper we show the validity of Stein’s interpolation theorem on variable exponent Morrey spaces.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.32917/HMJ/1544238031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47563703","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 present paper, we discuss two categorical characterizations of local fields. We first prove that a certain full subcategory of the category of finite flat coverings of the spectrum of the ring of integers of a local field equipped with coherent modules completely determines the isomorphism class of the local field. Next, we also prove that a certain full subcategory of the category of irreducible schemes which are finite over the spectrum of the ring of integers of a local field completely determines the isomorphism class of the local field.
{"title":"Two categorical characterizations of local fields","authors":"Yuichiro Hoshi","doi":"10.32917/HMJ/1544238027","DOIUrl":"https://doi.org/10.32917/HMJ/1544238027","url":null,"abstract":"— In the present paper, we discuss two categorical characterizations of local fields. We first prove that a certain full subcategory of the category of finite flat coverings of the spectrum of the ring of integers of a local field equipped with coherent modules completely determines the isomorphism class of the local field. Next, we also prove that a certain full subcategory of the category of irreducible schemes which are finite over the spectrum of the ring of integers of a local field completely determines the isomorphism class of the local field.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44109974","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 present paper considers a model selection criterion in regression models using generalized estimating equation (GEE). Using the prediction mean squared error (PMSE) normalized by the covariance matrix, we propose a new model selection criterion called PMSEG that reflects the correlation between responses. A numerical study reveals that the PMSEG has better performance than previous other criteria for model selection.
{"title":"Model selection criterion based on the prediction mean squared error in generalized estimating equations","authors":"Yu Inatsu, S. Imori","doi":"10.32917/HMJ/1544238030","DOIUrl":"https://doi.org/10.32917/HMJ/1544238030","url":null,"abstract":"The present paper considers a model selection criterion in regression models using generalized estimating equation (GEE). Using the prediction mean squared error (PMSE) normalized by the covariance matrix, we propose a new model selection criterion called PMSEG that reflects the correlation between responses. A numerical study reveals that the PMSEG has better performance than previous other criteria for model selection.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.32917/HMJ/1544238030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42931271","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}
A bstract . The existence of a‰ne resolvable block designs has been discussed since 1942 in the literature (cf. Bose (1942), Clatworthy (1973), Raghavarao (1988)). Kadowaki and Kageyama (2009, 2010, 2012) obtained a number of results on combinatorics for the existence of an a‰ne resolvable SRGD design. In this paper, a new existence result is shown as a generalization of Theorem 3.3.3 given in Kadowaki and Kageyama (2009, 2010). Furthermore, another existence result is shown as a conditional converse of Theorem 3.3.3 and also a generalization of Theorem 3.3.4, both theorems given in Kadowaki and Kageyama (2009, 2010).
{"title":"Two existence results between an affine resolvable SRGD design and a difference scheme","authors":"Satoru Kadowaki, S. Kageyama","doi":"10.32917/hmj/1544238033","DOIUrl":"https://doi.org/10.32917/hmj/1544238033","url":null,"abstract":"A bstract . The existence of a‰ne resolvable block designs has been discussed since 1942 in the literature (cf. Bose (1942), Clatworthy (1973), Raghavarao (1988)). Kadowaki and Kageyama (2009, 2010, 2012) obtained a number of results on combinatorics for the existence of an a‰ne resolvable SRGD design. In this paper, a new existence result is shown as a generalization of Theorem 3.3.3 given in Kadowaki and Kageyama (2009, 2010). Furthermore, another existence result is shown as a conditional converse of Theorem 3.3.3 and also a generalization of Theorem 3.3.4, both theorems given in Kadowaki and Kageyama (2009, 2010).","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49583019","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 classify all edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are pseudo-double wheels. For this, we characterize these spherical tilings by a quadratic equation for the cosine of an edge-length. By the classification, we see: there are indeed two non-congruent, edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are the same pseudo-double wheel and the cyclic list of the four inner angles of the tiles are the same. This contrasts with that every edge-to-edge spherical tiling by congruent 3-gons is determined by the skeleton and the inner angles of the skeleton. We show that for a particular spherical isohedral tiling over the pseudo-double wheel of twelve faces, the quadratic equation has a double solution and the copies of the tile also organize a spherical non-isohedral tiling over the same skeleton.
{"title":"Classification of spherical tilings by congruent quadrangles over pseudo-double wheels (II)—the isohedral case","authors":"Y. Akama","doi":"10.32917/hmj/1554516036","DOIUrl":"https://doi.org/10.32917/hmj/1554516036","url":null,"abstract":"We classify all edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are pseudo-double wheels. For this, we characterize these spherical tilings by a quadratic equation for the cosine of an edge-length. By the classification, we see: there are indeed two non-congruent, edge-to-edge spherical isohedral 4-gonal tilings such that the skeletons are the same pseudo-double wheel and the cyclic list of the four inner angles of the tiles are the same. This contrasts with that every edge-to-edge spherical tiling by congruent 3-gons is determined by the skeleton and the inner angles of the skeleton. We show that for a particular spherical isohedral tiling over the pseudo-double wheel of twelve faces, the quadratic equation has a double solution and the copies of the tile also organize a spherical non-isohedral tiling over the same skeleton.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69464785","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}
Given a representation of a link group, we introduce a trilinear form, as a topological invariant. We show that, if the link is either hyperbolic or a knot with malnormality, then the trilinear form equals the pairing of the (twisted) triple cup product and the fundamental relative 3-class. Further, we give some examples of the computation.
{"title":"Twisted cohomology pairings of knots III; triple cup products","authors":"Takefumi Nosaka","doi":"10.32917/hmj/1595901628","DOIUrl":"https://doi.org/10.32917/hmj/1595901628","url":null,"abstract":"Given a representation of a link group, we introduce a trilinear form, as a topological invariant. We show that, if the link is either hyperbolic or a knot with malnormality, then the trilinear form equals the pairing of the (twisted) triple cup product and the fundamental relative 3-class. Further, we give some examples of the computation.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2018-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45821216","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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