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A nonlinear inverse problem of the Korteweg-de Vries equation Korteweg-de Vries方程的非线性反问题
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-05-18 DOI: 10.1007/S13373-018-0125-1
Sheng-Sen Lu, Miaochao Chen, Qilin Liu
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引用次数: 2
Diophantine problems in solvable groups 可解群中的丢番图问题
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-05-10 DOI: 10.1142/s1664360720500058
A. Garreta, A. Miasnikov, D. Ovchinnikov
{"title":"Diophantine problems in solvable groups","authors":"A. Garreta, A. Miasnikov, D. Ovchinnikov","doi":"10.1142/s1664360720500058","DOIUrl":"https://doi.org/10.1142/s1664360720500058","url":null,"abstract":"We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc.), which satisfy some natural “non-commutativity” conditions. For each group [Formula: see text] in one of these classes, we prove that there exists a ring of algebraic integers [Formula: see text] that is interpretable in [Formula: see text] by finite systems of equations ([Formula: see text]-interpretable), and hence that the Diophantine problem in [Formula: see text] is polynomial time reducible to the Diophantine problem in [Formula: see text]. One of the major open conjectures in number theory states that the Diophantine problem in any such [Formula: see text] is undecidable. If true this would imply that the Diophantine problem in any such [Formula: see text] is also undecidable. Furthermore, we show that for many particular groups [Formula: see text] as above, the ring [Formula: see text] is isomorphic to the ring of integers [Formula: see text], so the Diophantine problem in [Formula: see text] is, indeed, undecidable. This holds, in particular, for free nilpotent or free solvable non-abelian groups, as well as for non-abelian generalized Heisenberg groups and uni-triangular groups [Formula: see text]. Then, we apply these results to non-solvable groups that contain non-virtually abelian maximal finitely generated nilpotent subgroups. For instance, we show that the Diophantine problem is undecidable in the groups [Formula: see text].","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2018-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91236763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Belavin–Drinfeld solutions of the Yang–Baxter equation: Galois cohomology considerations Yang-Baxter方程的Belavin-Drinfeld解:伽罗瓦上同调的考虑
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-04-01 DOI: 10.1007/S13373-016-0094-1
A. Pianzola, A. Stolin
{"title":"Belavin–Drinfeld solutions of the Yang–Baxter equation: Galois cohomology considerations","authors":"A. Pianzola, A. Stolin","doi":"10.1007/S13373-016-0094-1","DOIUrl":"https://doi.org/10.1007/S13373-016-0094-1","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"29 1","pages":"1-14"},"PeriodicalIF":1.2,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90824966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
An improved regularity criterion for the Navier–Stokes equations in terms of one directional derivative of the velocity field 用速度场的一个方向导数改进了Navier-Stokes方程的正则性判据
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-04-01 DOI: 10.1007/S13373-016-0098-X
Zujin Zhang
{"title":"An improved regularity criterion for the Navier–Stokes equations in terms of one directional derivative of the velocity field","authors":"Zujin Zhang","doi":"10.1007/S13373-016-0098-X","DOIUrl":"https://doi.org/10.1007/S13373-016-0098-X","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"73 1","pages":"33-47"},"PeriodicalIF":1.2,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83958420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
Correction to: The Weyl product on quasi-Banach modulation spaces 修正:拟巴拿赫调制空间上的Weyl积
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-02-22 DOI: 10.1007/S13373-018-0122-4
Yuan-yuan Chen, J. Toft, P. Wahlberg
{"title":"Correction to: The Weyl product on quasi-Banach modulation spaces","authors":"Yuan-yuan Chen, J. Toft, P. Wahlberg","doi":"10.1007/S13373-018-0122-4","DOIUrl":"https://doi.org/10.1007/S13373-018-0122-4","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"44 1","pages":"1-2"},"PeriodicalIF":1.2,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82488526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tosio Kato’s work on non-relativistic quantum mechanics: part 2 加藤俊雄在非相对论量子力学方面的工作:第二部分
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-02-22 DOI: 10.1007/S13373-018-0121-5
B. Simon
{"title":"Tosio Kato’s work on non-relativistic quantum mechanics: part 2","authors":"B. Simon","doi":"10.1007/S13373-018-0121-5","DOIUrl":"https://doi.org/10.1007/S13373-018-0121-5","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"149 1","pages":"1-99"},"PeriodicalIF":1.2,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86583908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
How to glue derived categories 如何粘合派生类别
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-02-07 DOI: 10.1007/S13373-018-0119-Z
D. Kaledin
{"title":"How to glue derived categories","authors":"D. Kaledin","doi":"10.1007/S13373-018-0119-Z","DOIUrl":"https://doi.org/10.1007/S13373-018-0119-Z","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"22 1","pages":"477-602"},"PeriodicalIF":1.2,"publicationDate":"2018-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72677432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Amenability of coarse spaces and K -algebras. 粗糙空间与K -代数的可调和性。
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2018-01-01 Epub Date: 2017-11-09 DOI: 10.1007/s13373-017-0109-6
Pere Ara, Kang Li, Fernando Lledó, Jianchao Wu
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Amenability of coarse spaces and <ns0:math><ns0:mi>K</ns0:mi></ns0:math> -algebras.","authors":"Pere Ara,&nbsp;Kang Li,&nbsp;Fernando Lledó,&nbsp;Jianchao Wu","doi":"10.1007/s13373-017-0109-6","DOIUrl":"https://doi.org/10.1007/s13373-017-0109-6","url":null,"abstract":"<p><p>In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. We apply our general analysis to two important classes of algebras: the unital Leavitt path algebras and the translation algebras on locally finite extended metric spaces. In particular, we show that the amenability of a metric space is equivalent to the algebraic amenability of the corresponding translation algebra.</p>","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"8 2","pages":"257-306"},"PeriodicalIF":1.2,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s13373-017-0109-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37162254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Decomposition of ordinary differential equations 常微分方程的分解
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2017-12-01 DOI: 10.1007/S13373-017-0110-0
F. Schwarz
{"title":"Decomposition of ordinary differential equations","authors":"F. Schwarz","doi":"10.1007/S13373-017-0110-0","DOIUrl":"https://doi.org/10.1007/S13373-017-0110-0","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"67 1","pages":"575-613"},"PeriodicalIF":1.2,"publicationDate":"2017-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88615524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Words of Engel type are concise in residually finite groups 恩格尔型的词在剩余有限群中是简洁的
IF 1.2 2区 数学
Bulletin of Mathematical Sciences Pub Date : 2017-11-13 DOI: 10.1007/s13373-018-0130-4
E. Detomi, M. Morigi, P. Shumyatsky
{"title":"Words of Engel type are concise in residually finite groups","authors":"E. Detomi, M. Morigi, P. Shumyatsky","doi":"10.1007/s13373-018-0130-4","DOIUrl":"https://doi.org/10.1007/s13373-018-0130-4","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":"53 1","pages":"1-19"},"PeriodicalIF":1.2,"publicationDate":"2017-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77202189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
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