We give some new formulae relating an obstruction to the weak approximation on homogeneous spaces to the set of local and global Brauer and R-equivalence classes.
给出了局部和全局Brauer和r等价类集合在齐次空间上弱逼近的阻碍的一些新公式。
{"title":"A note on obstructions to weak approximation and Brauer and R-equivalence relations for homogeneous spaces over global fields","authors":"N. Q. Thang","doi":"10.3792/pjaa.98.016","DOIUrl":"https://doi.org/10.3792/pjaa.98.016","url":null,"abstract":"We give some new formulae relating an obstruction to the weak approximation on homogeneous spaces to the set of local and global Brauer and R-equivalence classes.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89196700","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":"Hidden symmetries of hyperbolic links","authors":"H. Yoshida","doi":"10.3792/pjaa.98.014","DOIUrl":"https://doi.org/10.3792/pjaa.98.014","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90572566","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 note, we investigate the tree-depth and tree-width in a heterogeneous random graph obtained by including each edge e ij ð i 6¼ j Þ of a complete graph K n over n vertices independently with probability p n ð e ij Þ . When the sequence of edge probabilities satisfies some density assumptions, we show both tree-depth and tree-width are of linear size with high probability. Moreover, we extend the method to random weighted graphs with non-identical edge weights and capture the conditions under which with high probability the weighted tree-depth is bounded by a constant.
在这篇文章中，我们研究了一个异构随机图的树深度和树宽度，该图是通过以概率p n ð e ij Þ独立包含K n / n个顶点的完全图的每个边e ij ð i 6¼j Þ获得的。当边缘概率序列满足一定的密度假设时，我们证明了树深和树宽都具有高概率的线性大小。此外，我们将该方法推广到具有不同边权的随机加权图中，并捕获了加权树深度有一个常数有界的高概率条件。
{"title":"On the tree-depth and tree-width in heterogeneous random graphs","authors":"Y. Shang","doi":"10.3792/pjaa.98.015","DOIUrl":"https://doi.org/10.3792/pjaa.98.015","url":null,"abstract":": In this note, we investigate the tree-depth and tree-width in a heterogeneous random graph obtained by including each edge e ij ð i 6¼ j Þ of a complete graph K n over n vertices independently with probability p n ð e ij Þ . When the sequence of edge probabilities satisfies some density assumptions, we show both tree-depth and tree-width are of linear size with high probability. Moreover, we extend the method to random weighted graphs with non-identical edge weights and capture the conditions under which with high probability the weighted tree-depth is bounded by a constant.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73442516","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 establish congruences for higher order Euler polynomials modulo 720. We apply this result for constructing analogues of Stern congruences for Euler secant numbers E 4 n (cid:3) 5 ð mod 60 Þ ; E 4 n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ to Euler tangent numbers and Genocchi numbers. We prove that Euler tangent numbers satisfy the following congruences E 4 n þ 1 (cid:3) 16 ð mod 720 Þ , and E 4 n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ . We establish 12-periodic property of Genocchi numbers modulo 45.
我们建立了以720为模的高阶欧拉多项式的同余式。我们将这一结果应用于构造欧拉正割数e4 n (cid:3) 5 ð mod 60 Þ的Stern同余的类似物;e4n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ到Euler正切数和Genocchi数。我们证明了欧拉正切数满足下列同余式e4n þ 1 (cid:3) 16 ð mod 720 Þ和e4n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ。建立了以45为模的Genocchi数的12周期性质。
{"title":"Euler tangent numbers modulo 720 and Genocchi numbers modulo 45","authors":"A. Dzhumadil'daev, Medet Jumadildayev","doi":"10.3792/pjaa.98.012","DOIUrl":"https://doi.org/10.3792/pjaa.98.012","url":null,"abstract":": We establish congruences for higher order Euler polynomials modulo 720. We apply this result for constructing analogues of Stern congruences for Euler secant numbers E 4 n (cid:3) 5 ð mod 60 Þ ; E 4 n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ to Euler tangent numbers and Genocchi numbers. We prove that Euler tangent numbers satisfy the following congruences E 4 n þ 1 (cid:3) 16 ð mod 720 Þ , and E 4 n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ . We establish 12-periodic property of Genocchi numbers modulo 45.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87974751","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 [8] the first author classified automorphism groups of smooth plane curves of degree not less than four into five types. If the curve has a unique outer Galois point, then the quotient group of its automorphism group by the Galois group at the point, which is called the reduced automorphism group, is a finite subgroup of one-dimensional projective linear group. This article is a sequel of [10] and [9]. In this article, we shall determine the defining equation of the curve when the reduced automorphism group is an icosahedral group and give a description of the full automorphism group.
{"title":"Smooth plane curves with outer Galois points whose reduced automorphism group is $A_{5}$","authors":"Takeshi Harui, Kei Miura, A. Ohbuchi","doi":"10.3792/pjaa.98.013","DOIUrl":"https://doi.org/10.3792/pjaa.98.013","url":null,"abstract":": In [8] the first author classified automorphism groups of smooth plane curves of degree not less than four into five types. If the curve has a unique outer Galois point, then the quotient group of its automorphism group by the Galois group at the point, which is called the reduced automorphism group, is a finite subgroup of one-dimensional projective linear group. This article is a sequel of [10] and [9]. In this article, we shall determine the defining equation of the curve when the reduced automorphism group is an icosahedral group and give a description of the full automorphism group.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72673710","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":"Perverse sheaves on $mathbf{C}^{2}$ without vanishing cycles at the origin along a general plane curve with singularities","authors":"Dérille Kouemo Djoukoue, Philibert Nang","doi":"10.3792/pjaa.98.011","DOIUrl":"https://doi.org/10.3792/pjaa.98.011","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77618325","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 verify that the $p$-integrable Teichm"uller space $T_p$ admits the canonical complex Banach manifold structure for any $p geq 1$. Moreover, we characterize a quasisymmetric homeomorphism corresponding to an element of $T_p$ in terms of the $p$-Besov space for any $p>1$.
{"title":"The $p$-integrable Teichmüller space for $p geqslant 1$","authors":"Huaying Wei, Katsuhiko Matsuzaki","doi":"10.3792/pjaa.99.008","DOIUrl":"https://doi.org/10.3792/pjaa.99.008","url":null,"abstract":"We verify that the $p$-integrable Teichm\"uller space $T_p$ admits the canonical complex Banach manifold structure for any $p geq 1$. Moreover, we characterize a quasisymmetric homeomorphism corresponding to an element of $T_p$ in terms of the $p$-Besov space for any $p>1$.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88250112","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":"The transcendence of zeros of natural basis elements for the space of the weakly holomorphic modular forms for $Gamma_{0}^{+}(3)$","authors":"Soyoung Choi","doi":"10.3792/pjaa.98.009","DOIUrl":"https://doi.org/10.3792/pjaa.98.009","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85609887","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":"Lehmer’s conjecture via model theory","authors":"H. Göral","doi":"10.3792/pjaa.98.010","DOIUrl":"https://doi.org/10.3792/pjaa.98.010","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72613737","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 show that the description of Deligne--Beilinson cohomology is improved by using log Hodge theory. We consider the log relative version of it, and also present a fundamental conjecture in log Hodge theory.
{"title":"Deligne–Beilinson cohomology and log Hodge theory","authors":"Kazuya Kato, Chikara Nakayama, S. Usui","doi":"10.3792/pjaa.99.006","DOIUrl":"https://doi.org/10.3792/pjaa.99.006","url":null,"abstract":"We show that the description of Deligne--Beilinson cohomology is improved by using log Hodge theory. We consider the log relative version of it, and also present a fundamental conjecture in log Hodge theory.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76192226","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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