Pub Date : 2017-12-01DOI: 10.21099/tkbjm/1521597625
M. Nunokawa, J. Sokół
{"title":"On multivalent functions in the unit disc","authors":"M. Nunokawa, J. Sokół","doi":"10.21099/tkbjm/1521597625","DOIUrl":"https://doi.org/10.21099/tkbjm/1521597625","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"41 1","pages":"251-263"},"PeriodicalIF":0.7,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/tkbjm/1521597625","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47068969","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}
Pub Date : 2017-12-01DOI: 10.21099/TKBJM/1521597626
P. Mrozik
{"title":"Extending functors from the category of strict morphisms of inverse systems to the associated pro-category with applications to the first derived limit","authors":"P. Mrozik","doi":"10.21099/TKBJM/1521597626","DOIUrl":"https://doi.org/10.21099/TKBJM/1521597626","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"41 1","pages":"265-296"},"PeriodicalIF":0.7,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/TKBJM/1521597626","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47320744","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}
Pub Date : 2017-12-01DOI: 10.21099/tkbjm/1521597621
Soichi Ikeda, I. Kiuchi, Kaneaki Matsuoka
{"title":"The mean values of the double zeta-function","authors":"Soichi Ikeda, I. Kiuchi, Kaneaki Matsuoka","doi":"10.21099/tkbjm/1521597621","DOIUrl":"https://doi.org/10.21099/tkbjm/1521597621","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"41 1","pages":"169-187"},"PeriodicalIF":0.7,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/tkbjm/1521597621","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43625116","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}
Pub Date : 2017-12-01DOI: 10.21099/TKBJM/1521597622
H. Kikyo, M. Sawa
{"title":"Köhler theory for countable quadruple systems","authors":"H. Kikyo, M. Sawa","doi":"10.21099/TKBJM/1521597622","DOIUrl":"https://doi.org/10.21099/TKBJM/1521597622","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"41 1","pages":"189-213"},"PeriodicalIF":0.7,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/TKBJM/1521597622","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41963368","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}
Pub Date : 2017-08-01DOI: 10.21099/tkbjm/20224601145
A. Patkowski
We present new relationships between the work of H. Davenport and A. I. Popov. A new general formula involving the Von Mangoldt function is presented, as well as a criteria for the Riemann Hypothesis.
{"title":"On arithmetic series involving the fractional part function","authors":"A. Patkowski","doi":"10.21099/tkbjm/20224601145","DOIUrl":"https://doi.org/10.21099/tkbjm/20224601145","url":null,"abstract":"We present new relationships between the work of H. Davenport and A. I. Popov. A new general formula involving the Von Mangoldt function is presented, as well as a criteria for the Riemann Hypothesis.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42724664","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}
Pub Date : 2017-07-01DOI: 10.21099/tkbjm/1506353557
D. Buhagiar, V. Gutev
{"title":"Selections and deleted symmetric products","authors":"D. Buhagiar, V. Gutev","doi":"10.21099/tkbjm/1506353557","DOIUrl":"https://doi.org/10.21099/tkbjm/1506353557","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"41 1","pages":"1-20"},"PeriodicalIF":0.7,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43887325","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}
Pub Date : 2017-07-01DOI: 10.21099/tkbjm/1506353562
Michio Amano
{"title":"Corrigendum to “On the Cartier duality of certain finite group schemes of order $p^n$, II” [Tsukuba J. Math. 37 (2) (2013) 259-269]","authors":"Michio Amano","doi":"10.21099/tkbjm/1506353562","DOIUrl":"https://doi.org/10.21099/tkbjm/1506353562","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":"41 1","pages":"167-168"},"PeriodicalIF":0.7,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.21099/tkbjm/1506353562","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49438428","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}
Pub Date : 2017-07-01DOI: 10.21099/TKBJM/1571968818
Toshikazu Miyashita
The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{e}nez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $tilde{gamma}$ of order four on $G$ and $H$ is a fixed points subgroup $G^gamma$ of $G$. According to the classification by J.A. Jim{e}nez, there exist seven compact simply connected Riemannian 4-symmetric spaces $ G/H $ in the case where $ G $ is of type $ E_8 $. In the present article, %as Part II continuing from Part I, for the connected compact %exceptional Lie group $E_8$, we give the explicit form of automorphisms $tilde{w}_{{}_4} tilde{upsilon}_{{}_4}$ and $tilde{mu}_{{}_4}$ of order four on $E_8$ induced by the $C$-linear transformations $w_{{}_4}, upsilon_{{}_4}$ and $mu_{{}_4}$ of the 248-dimensional vector space ${mathfrak{e}_8}^{C}$, respectively. Further, we determine the structure of these fixed points subgroups $(E_8)^{w_{{}_4}}, (E_8)^{{}_{upsilon_{{}_4}}}$ and $(E_8)^{{} _{mu_{{}_4}}}$ of $ E_8 $. These amount to the global realizations of three spaces among seven Riemannian 4-symmetric spaces $ G/H $ above corresponding to the Lie algebras $ mathfrak{h}=ibm{R} oplus mathfrak{su}(8), ibm{R} oplus mathfrak{e}_7$ and $mathfrak{h}= mathfrak{su}(2) oplus mathfrak{su}(8)$, where $ mathfrak{h}={rm Lie}(H) $.
{"title":"Realizations of inner automorphisms of order four and fixed points subgroups by them on the connected compact exceptional Lie group $E_8$, Part II","authors":"Toshikazu Miyashita","doi":"10.21099/TKBJM/1571968818","DOIUrl":"https://doi.org/10.21099/TKBJM/1571968818","url":null,"abstract":"The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{e}nez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $tilde{gamma}$ of order four on $G$ and $H$ is a fixed points subgroup $G^gamma$ of $G$. According to the classification by J.A. Jim{e}nez, there exist seven compact simply connected Riemannian 4-symmetric spaces $ G/H $ in the case where $ G $ is of type $ E_8 $. In the present article, %as Part II continuing from Part I, for the connected compact %exceptional Lie group $E_8$, we give the explicit form of automorphisms $tilde{w}_{{}_4} tilde{upsilon}_{{}_4}$ and $tilde{mu}_{{}_4}$ of order four on $E_8$ induced by the $C$-linear transformations $w_{{}_4}, upsilon_{{}_4}$ and $mu_{{}_4}$ of the 248-dimensional vector space ${mathfrak{e}_8}^{C}$, respectively. Further, we determine the structure of these fixed points subgroups $(E_8)^{w_{{}_4}}, (E_8)^{{}_{upsilon_{{}_4}}}$ and $(E_8)^{{} _{mu_{{}_4}}}$ of $ E_8 $. These amount to the global realizations of three spaces among seven Riemannian 4-symmetric spaces $ G/H $ above corresponding to the Lie algebras $ mathfrak{h}=ibm{R} oplus mathfrak{su}(8), ibm{R} oplus mathfrak{e}_7$ and $mathfrak{h}= mathfrak{su}(2) oplus mathfrak{su}(8)$, where $ mathfrak{h}={rm Lie}(H) $.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45020721","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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