Pub Date : 2018-08-01DOI: 10.1007/S13373-017-0104-Y
F. Marcellán, Yamilet Quintana, José M. Rodríguez
{"title":"Weighted Sobolev spaces: Markov-type inequalities and duality","authors":"F. Marcellán, Yamilet Quintana, José M. Rodríguez","doi":"10.1007/S13373-017-0104-Y","DOIUrl":"https://doi.org/10.1007/S13373-017-0104-Y","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86647577","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}
Pub Date : 2018-07-20DOI: 10.1142/S1664360719500115
N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš
We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-Delta _p,W^{1,p}_0(Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$lambda >0$$λ>0.
{"title":"Positive solutions for nonlinear parametric singular Dirichlet problems","authors":"N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš","doi":"10.1142/S1664360719500115","DOIUrl":"https://doi.org/10.1142/S1664360719500115","url":null,"abstract":"We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-Delta _p,W^{1,p}_0(Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$lambda >0$$λ>0.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82427083","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}
Pub Date : 2018-07-05DOI: 10.1142/S1664360719500206
Nikola Advzaga
A Diophantine [Formula: see text]-tuple is a set of [Formula: see text] distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in the rings of integers of imaginary quadratic fields. By using a gap principle proven by Diophantine approximations, we show that [Formula: see text]. Our proof is relatively simple compared to the proofs of similar results in positive integers.
{"title":"On the size of Diophantine m-tuples in imaginary quadratic number rings","authors":"Nikola Advzaga","doi":"10.1142/S1664360719500206","DOIUrl":"https://doi.org/10.1142/S1664360719500206","url":null,"abstract":"A Diophantine [Formula: see text]-tuple is a set of [Formula: see text] distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem in the rings of integers of imaginary quadratic fields. By using a gap principle proven by Diophantine approximations, we show that [Formula: see text]. Our proof is relatively simple compared to the proofs of similar results in positive integers.","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86214081","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}
Pub Date : 2018-05-18DOI: 10.1007/S13373-018-0125-1
Sheng-Sen Lu, Miaochao Chen, Qilin Liu
{"title":"A nonlinear inverse problem of the Korteweg-de Vries equation","authors":"Sheng-Sen Lu, Miaochao Chen, Qilin Liu","doi":"10.1007/S13373-018-0125-1","DOIUrl":"https://doi.org/10.1007/S13373-018-0125-1","url":null,"abstract":"","PeriodicalId":9348,"journal":{"name":"Bulletin of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2018-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79238217","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}
Pub Date : 2018-05-10DOI: 10.1142/s1664360720500058
A. Garreta, A. Miasnikov, D. Ovchinnikov
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].
{"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":null,"pages":null},"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}
Pub Date : 2018-04-01DOI: 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":null,"pages":null},"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}
Pub Date : 2018-04-01DOI: 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":null,"pages":null},"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}
Pub Date : 2018-02-22DOI: 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":null,"pages":null},"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}
Pub Date : 2018-02-22DOI: 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":null,"pages":null},"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}
Pub Date : 2018-02-07DOI: 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":null,"pages":null},"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}
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