We give an algorithm for computing the Teichm"uller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichm"uller polynomial.
{"title":"TEICHMÜLLER POLYNOMIALS OF FIBERED ALTERNATING LINKS","authors":"Robert Billet, L. Liechti","doi":"10.18910/73628","DOIUrl":"https://doi.org/10.18910/73628","url":null,"abstract":"We give an algorithm for computing the Teichm\"uller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichm\"uller polynomial.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67913586","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 describe the homotopy type of the homotopy fixed point sets of S 3 -actions on rational spheres and complex projective spaces, and provide some properties of S 1 -actions on a general rational complex.
{"title":"The homotopy fixed point sets of spheres actions on rational complexes","authors":"Yanlong Hao, X. Liu, Qianwen Sun","doi":"10.18910/58892","DOIUrl":"https://doi.org/10.18910/58892","url":null,"abstract":": In this paper, we describe the homotopy type of the homotopy fixed point sets of S 3 -actions on rational spheres and complex projective spaces, and provide some properties of S 1 -actions on a general rational complex.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67876438","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":"Ill-posedness issue for the drift diffusion system in the homogeneous Besov spaces","authors":"T. Iwabuchi, T. Ogawa","doi":"10.18910/58903","DOIUrl":"https://doi.org/10.18910/58903","url":null,"abstract":"","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67877532","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":"Conjugacy class and discreteness in $mathit{SL}(2, mathbb{C})$","authors":"Shihai Yang, Tie-hong Zhao","doi":"10.18910/58891","DOIUrl":"https://doi.org/10.18910/58891","url":null,"abstract":"","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67876233","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}
Abstract For the ring ofp-adic integers,p being a fixed prime, any sequence which plays a similar role to Weyl’s irrational rotation has not been pro posed yet. We will see that a modifiedp-adic van der Corput sequence provides us with a reasonable c ounterpart of Weyl’s irrational rotation in the ring. We will pr esent a similar random Weyl sampling on the ring to the one proposed by Sugita and Tak anobu. In the process of establishing the counterpart, a sampling method bas ed on a function with naturally extended domain to the field of p-adic numbers in terms of the additive characters will be mentioned.
摘要对于p为固定素数的p进整数环，目前还没有提出任何类似Weyl不合理旋转的序列。我们将看到，修改后的p-adic van der Corput序列为我们提供了Weyl在环中的不合理旋转的合理c对应。我们将在环上提出一个类似于杉田和德anobu提出的随机Weyl抽样。在建立对应物的过程中，将提到一种基于自然扩展到p进数域的加性特征函数的采样方法。
{"title":"A pairwise independent random sampling method in the ring of $p$-adic integers","authors":"H. Kaneko, H. Matsumoto","doi":"10.18910/58869","DOIUrl":"https://doi.org/10.18910/58869","url":null,"abstract":"Abstract For the ring ofp-adic integers,p being a fixed prime, any sequence which plays a similar role to Weyl’s irrational rotation has not been pro posed yet. We will see that a modifiedp-adic van der Corput sequence provides us with a reasonable c ounterpart of Weyl’s irrational rotation in the ring. We will pr esent a similar random Weyl sampling on the ring to the one proposed by Sugita and Tak anobu. In the process of establishing the counterpart, a sampling method bas ed on a function with naturally extended domain to the field of p-adic numbers in terms of the additive characters will be mentioned.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67875053","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}
Abstract We investigate the large-time behavior of the radially symm etric solution for Burgers equation on the exterior of a small ball in multi-dim ensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to 0 or negative, the asymptotic stability is the same as that for the vis cou conservation law. In the present paper, it is proved that if the boundary data is po sitive, the asymptotic state is a superposition of the stationary wave and the raref action wave, which is a new wave phenomenon. The proof is given using a standard L2 energy method and the characteristic curve method.
{"title":"BEHAVIOR OF SOLUTIONS FOR RADIALLY SYMMETRIC SOLUTIONS FOR BURGERS EQUATION WITH A BOUNDARY CORRESPONDING TO THE RAREFACTION WAVE","authors":"Itsuko Hashimoto","doi":"10.18910/58900","DOIUrl":"https://doi.org/10.18910/58900","url":null,"abstract":"Abstract We investigate the large-time behavior of the radially symm etric solution for Burgers equation on the exterior of a small ball in multi-dim ensional space, where the boundary data and the data at the far field are prescribed. In a previous paper [1], we showed that, for the case in which the boundary data is equal to 0 or negative, the asymptotic stability is the same as that for the vis cou conservation law. In the present paper, it is proved that if the boundary data is po sitive, the asymptotic state is a superposition of the stationary wave and the raref action wave, which is a new wave phenomenon. The proof is given using a standard L2 energy method and the characteristic curve method.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67877340","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":"A NOTE ON THE EXPONENTIAL DECAY FOR THE NONLINEAR SCHRÖDINGER EQUATION","authors":"F. Natali","doi":"10.18910/58893","DOIUrl":"https://doi.org/10.18910/58893","url":null,"abstract":"","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67876559","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 compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g = 3 into SL(2, C), and also of the moduli space of twisted representations. The case of genus g = 1, 2 has already been done in [12]. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.
{"title":"E-polynomials of $mathrm{SL}(2, mathbb{C})$-character varieties of complex curves of genus $3$","authors":"Javier Martínez, V. Muñoz","doi":"10.18910/58905","DOIUrl":"https://doi.org/10.18910/58905","url":null,"abstract":"We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g = 3 into SL(2, C), and also of the moduli space of twisted representations. The case of genus g = 1, 2 has already been done in [12]. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67877056","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}
Abstract In this paper, we are concerned with the solvability of the in itial boundary value problem of a system which describes double-diffusive conve ction phenomena in some porous medium under general domains, especially unbounded domains. In previous works where the boundedness of the space domain is imposed, s ome global solvability results have been already derived. However, when we cons ider our problem in general domains, some compactness theorems are not availab le. Hence it becomes difficult to follow the same strategies as before. Neverthel ess, we can assure the global existence of a unique solution via the contraction me thod. Moreover, it is revealed that the global solvability holds for higher space di mension and larger class of the initial data than those assumed in previous works.
{"title":"Global solvability for double-diffusive convection system based on Brinkman--Forchheimer equation in general domains","authors":"M. Otani, S. Uchida","doi":"10.18910/58870","DOIUrl":"https://doi.org/10.18910/58870","url":null,"abstract":"Abstract In this paper, we are concerned with the solvability of the in itial boundary value problem of a system which describes double-diffusive conve ction phenomena in some porous medium under general domains, especially unbounded domains. In previous works where the boundedness of the space domain is imposed, s ome global solvability results have been already derived. However, when we cons ider our problem in general domains, some compactness theorems are not availab le. Hence it becomes difficult to follow the same strategies as before. Neverthel ess, we can assure the global existence of a unique solution via the contraction me thod. Moreover, it is revealed that the global solvability holds for higher space di mension and larger class of the initial data than those assumed in previous works.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67875086","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 concept of a moduleM being almostN-injective, whereN is some module, was introduced by Baba (1989). For a given module M , the class of modules N, for which M is almostN-injective, is not closed under direct sums. Baba gave a nece ssary and sufficient condition under which a uniform, finite le ngth moduleU is almost V-injective, whereV is a finite direct sum of uniform, finite length modules, in ter ms of extending properties of simple submodules of V . Let M be a uniform module and V be a finite direct sum of indecomposable modules. Some condit i s under whichM is almostV-injective are determined, thereby Baba’s result is genera liz d. A module M that is almostM-injective is called an almost self-injective module. Comm utative indecomposable rings and von Neumann regular rings that are almost self-injective are studied. It is proved that any minimal right ideal of a von Neumann regular, almost right self-injective ring, is injective. This result i s used to give an example of a von Neumann regular ring that is not almost right self-injec tive.
{"title":"Almost relative injective modules","authors":"Surjeet Singh","doi":"10.18910/58910","DOIUrl":"https://doi.org/10.18910/58910","url":null,"abstract":"The concept of a moduleM being almostN-injective, whereN is some module, was introduced by Baba (1989). For a given module M , the class of modules N, for which M is almostN-injective, is not closed under direct sums. Baba gave a nece ssary and sufficient condition under which a uniform, finite le ngth moduleU is almost V-injective, whereV is a finite direct sum of uniform, finite length modules, in ter ms of extending properties of simple submodules of V . Let M be a uniform module and V be a finite direct sum of indecomposable modules. Some condit i s under whichM is almostV-injective are determined, thereby Baba’s result is genera liz d. A module M that is almostM-injective is called an almost self-injective module. Comm utative indecomposable rings and von Neumann regular rings that are almost self-injective are studied. It is proved that any minimal right ideal of a von Neumann regular, almost right self-injective ring, is injective. This result i s used to give an example of a von Neumann regular ring that is not almost right self-injec tive.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67877382","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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