{"title":"Simple Hurwitz groups and eta invariant","authors":"Takayuki Morifuji","doi":"10.2969/jmsj/88218821","DOIUrl":"https://doi.org/10.2969/jmsj/88218821","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43566659","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 consider the summability of formal solutions with singularities (such as logarithmic singularities, functional power singularities, etc.) of nonlinear partial differential equations in the complex domain. The main result is as follows: when a formal solution with singularities is given, under appropriate assumptions related to the formal solution, the equation has a true solution that admits the given formal solution as an asymptotic expansion. The proof is done by constructing a new formal solution that is equivalent to the given formal solution in the asymptotic sense and is multisummable in a suitable direction. The assumptions are stated in terms of the Newton polygon associated with the given formal solution.
{"title":"Asymptotic existence theorem for formal solutions with singularities of nonlinear partial differential equations via multisummability","authors":"H. Tahara","doi":"10.2969/jmsj/88248824","DOIUrl":"https://doi.org/10.2969/jmsj/88248824","url":null,"abstract":"In this paper, we consider the summability of formal solutions with singularities (such as logarithmic singularities, functional power singularities, etc.) of nonlinear partial differential equations in the complex domain. The main result is as follows: when a formal solution with singularities is given, under appropriate assumptions related to the formal solution, the equation has a true solution that admits the given formal solution as an asymptotic expansion. The proof is done by constructing a new formal solution that is equivalent to the given formal solution in the asymptotic sense and is multisummable in a suitable direction. The assumptions are stated in terms of the Newton polygon associated with the given formal solution.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47942395","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 introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C + associated with the ax + b (affine) group, depending on an admissible Hardy function ψ . We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω ⊂ C + . As a special case one recovers the DPP related to the weighted Bergman kernel. When ψ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.
{"title":"The affine ensemble: determinantal point processes associated with the $ax + b$ group","authors":"L. D. Abreu, P. Balázs, Smiljana Jakvsi'c","doi":"10.2969/jmsj/88018801","DOIUrl":"https://doi.org/10.2969/jmsj/88018801","url":null,"abstract":". We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C + associated with the ax + b (affine) group, depending on an admissible Hardy function ψ . We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω ⊂ C + . As a special case one recovers the DPP related to the weighted Bergman kernel. When ψ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44314132","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":"On polynomial images of a closed ball","authors":"J. Fernando, Carlos Ueno","doi":"10.2969/jmsj/88468846","DOIUrl":"https://doi.org/10.2969/jmsj/88468846","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41869120","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 deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.
{"title":"On braids and links up to link-homotopy","authors":"Emmanuel Graff","doi":"10.2969/jmsj/90449044","DOIUrl":"https://doi.org/10.2969/jmsj/90449044","url":null,"abstract":"This paper deals with links and braids up to link-homotopy, studied from the viewpoint of Habiro's clasper calculus. More precisely, we use clasper homotopy calculus in two main directions. First, we define and compute a faithful linear representation of the homotopy braid group, by using claspers as geometric commutators. Second, we give a geometric proof of Levine's classification of 4-component links up to link-homotopy, and go further with the classification of 5-component links in the algebraically split case.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41856746","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 study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary.
{"title":"Liouville's formulae and Hadamard variation with respect to general domain perturbations","authors":"Takashi Suzuki, T. Tsuchiya","doi":"10.2969/jmsj/88958895","DOIUrl":"https://doi.org/10.2969/jmsj/88958895","url":null,"abstract":"We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42515682","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":"Robustness of exponential attractors for infinite dimensional dynamical systems with small delay and application to 2D nonlocal diffusion delay lattice systems","authors":"Lin Yang, Yejuan Wang, P. Kloeden","doi":"10.2969/jmsj/88438843","DOIUrl":"https://doi.org/10.2969/jmsj/88438843","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42121880","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}
Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906), we construct infinite families of symplectic 4-dimensional manifolds, obtained as total spaces of Lefschetz pencils constructed by explicit monodromy factorizations. Then, generalizing work of the author (arXiv:2108.04868), we show that each of these manifolds is diffeomorphic to a complex surface that is a fiber sum formed from two standard examples of hyperelliptic Lefschetz fibrations. Consequently, we see that these hyperelliptic Lefschetz fibrations, as well as all fiber sums of them, admit an infinite family of explicitly described Lefschetz pencils, which we observe are different from families formed by the degree doubling procedure.
{"title":"Branched covers and pencils on hyperelliptic Lefschetz fibrations","authors":"Terry Fuller","doi":"10.2969/jmsj/90089008","DOIUrl":"https://doi.org/10.2969/jmsj/90089008","url":null,"abstract":"Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906), we construct infinite families of symplectic 4-dimensional manifolds, obtained as total spaces of Lefschetz pencils constructed by explicit monodromy factorizations. Then, generalizing work of the author (arXiv:2108.04868), we show that each of these manifolds is diffeomorphic to a complex surface that is a fiber sum formed from two standard examples of hyperelliptic Lefschetz fibrations. Consequently, we see that these hyperelliptic Lefschetz fibrations, as well as all fiber sums of them, admit an infinite family of explicitly described Lefschetz pencils, which we observe are different from families formed by the degree doubling procedure.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48163694","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 p be an odd prime number and 2e+1 be the highest power of 2 dividing p − 1. For 0 ≤ n ≤ e, let kn be the real cyclic field of conductor p and degree 2n. For a certain imaginary quadratic field L0, we put Ln = L0kn. For 0 ≤ n ≤ e − 1, let Fn be the imaginary quadratic subextension of the imaginary (2, 2)-extension Ln+1/kn with Fn ̸= Ln. We study the Galois module structure of the 2-part of the ideal class group of the imaginary cyclic field Fn. This generalizes a classical result of Rédei and Reichardt for the case n = 0.
{"title":"On the class groups of certain imaginary cyclic fields of 2-power degree","authors":"H. Ichimura, Hiroki Sumida-Takahashi","doi":"10.2969/jmsj/86438643","DOIUrl":"https://doi.org/10.2969/jmsj/86438643","url":null,"abstract":"Let p be an odd prime number and 2e+1 be the highest power of 2 dividing p − 1. For 0 ≤ n ≤ e, let kn be the real cyclic field of conductor p and degree 2n. For a certain imaginary quadratic field L0, we put Ln = L0kn. For 0 ≤ n ≤ e − 1, let Fn be the imaginary quadratic subextension of the imaginary (2, 2)-extension Ln+1/kn with Fn ̸= Ln. We study the Galois module structure of the 2-part of the ideal class group of the imaginary cyclic field Fn. This generalizes a classical result of Rédei and Reichardt for the case n = 0.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69573974","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 prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan-Wilkerson showing that if X is a rational CW-complex of finite type such that dimH∗(X,Z) < ∞ or dimπ∗(X) < ∞, then the group of self-homotopy equivalences of X is isomorphic to a linear algebraic group defined over Q.
{"title":"The group of self-homotopy equivalences of a rational space cannot be a free abelian group","authors":"M. Benkhalifa","doi":"10.2969/jmsj/87158715","DOIUrl":"https://doi.org/10.2969/jmsj/87158715","url":null,"abstract":"In this paper, we prove that a free abelian group cannot occur as the group of self-homotopy equivalences of a rational CW-complex of finite type. Thus, we generalize a result due to Sullivan-Wilkerson showing that if X is a rational CW-complex of finite type such that dimH∗(X,Z) < ∞ or dimπ∗(X) < ∞, then the group of self-homotopy equivalences of X is isomorphic to a linear algebraic group defined over Q.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45081143","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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