Pub Date : 2022-11-11DOI: 10.1142/s0219199722500778
Grzegorz Bajor, A. Cichocka, L. van Wyk, M. Ziembowski
{"title":"Maximal commutative subalgebras of leavitt path algebras","authors":"Grzegorz Bajor, A. Cichocka, L. van Wyk, M. Ziembowski","doi":"10.1142/s0219199722500778","DOIUrl":"https://doi.org/10.1142/s0219199722500778","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45910425","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 : 2022-11-09DOI: 10.1142/s0219199723500177
M. Ballesteros, Gerardo Franco C'ordova, I. Naumkin, H. Schulz-Baldes
This paper proves new results on spectral and scattering theory for matrix-valued Schr"odinger operators on the discrete line with non-compactly supported perturbations whose first moments are assumed to exist. In particular, a Levinson theorem is proved, in which a relation between scattering data and spectral properties (bound and half bound states) of the corresponding Hamiltonians is derived. The proof is based on stationary scattering theory with prominent use of Jost solutions at complex energies that are controlled by Volterra-type integral equations.
{"title":"Levinson theorem for discrete Schrodinger operators on the line with matrix potentials having a first moment","authors":"M. Ballesteros, Gerardo Franco C'ordova, I. Naumkin, H. Schulz-Baldes","doi":"10.1142/s0219199723500177","DOIUrl":"https://doi.org/10.1142/s0219199723500177","url":null,"abstract":"This paper proves new results on spectral and scattering theory for matrix-valued Schr\"odinger operators on the discrete line with non-compactly supported perturbations whose first moments are assumed to exist. In particular, a Levinson theorem is proved, in which a relation between scattering data and spectral properties (bound and half bound states) of the corresponding Hamiltonians is derived. The proof is based on stationary scattering theory with prominent use of Jost solutions at complex energies that are controlled by Volterra-type integral equations.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47626727","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 : 2022-10-06DOI: 10.1142/s0219199722500717
Krzysztof Piszczek
{"title":"Derivations of Kothe Echelon Algebras of Order Zero and Infinity","authors":"Krzysztof Piszczek","doi":"10.1142/s0219199722500717","DOIUrl":"https://doi.org/10.1142/s0219199722500717","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48677415","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 : 2022-10-01DOI: 10.1142/s0219199723500207
Jo'e Brendel, F. Schlenk
The complex projective plane CP^2 contains certain Lagrangian CW-complexes called pinwheels, which have interesting rigidity properties related to solutions of the Markov equation. We compute the Gromov width of the complement of pinwheels and show that it is strictly smaller than the Gromov width of CP^2, meaning that pinwheels are Lagrangian barriers in the sense of Biran. The accumulation points of the set of these Gromov widths are in a simple bijection with the Lagrange spectrum below 3.
{"title":"Pinwheels as Lagrangian barriers","authors":"Jo'e Brendel, F. Schlenk","doi":"10.1142/s0219199723500207","DOIUrl":"https://doi.org/10.1142/s0219199723500207","url":null,"abstract":"The complex projective plane CP^2 contains certain Lagrangian CW-complexes called pinwheels, which have interesting rigidity properties related to solutions of the Markov equation. We compute the Gromov width of the complement of pinwheels and show that it is strictly smaller than the Gromov width of CP^2, meaning that pinwheels are Lagrangian barriers in the sense of Biran. The accumulation points of the set of these Gromov widths are in a simple bijection with the Lagrange spectrum below 3.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41573385","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 : 2022-09-29DOI: 10.1142/s0219199722500377
Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros
In this paper, we prove a new Friedrich-type inequality. As an application, we derive some existence and non-existence results to the quasilinear elliptic problem with Robin boundary condition where is an exterior domain such that .
{"title":"On a Hardy–Sobolev-type inequality and applications","authors":"Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros","doi":"10.1142/s0219199722500377","DOIUrl":"https://doi.org/10.1142/s0219199722500377","url":null,"abstract":"<p>In this paper, we prove a new Friedrich-type inequality. As an application, we derive some existence and non-existence results to the quasilinear elliptic problem with Robin boundary condition <disp-formula-group><span><math altimg=\"eq-00001.gif\" display=\"block\" overflow=\"scroll\"><mrow><mfenced close=\"\" open=\"{\" separators=\"\"><mrow><mtable columnlines=\"none\" equalcolumns=\"false\" equalrows=\"false\"><mtr><mtd columnalign=\"left\"><mo stretchy=\"false\">−</mo><mstyle><mtext>div</mtext></mstyle><mo stretchy=\"false\">(</mo><mo>|</mo><mo>∇</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>N</mi><mo stretchy=\"false\">−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">+</mo><mi>h</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo stretchy=\"false\">−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>=</mo><mi>λ</mi><mi>k</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo stretchy=\"false\">−</mo><mn>2</mn></mrow></msup><mi>u</mi><mspace width=\"1em\"></mspace></mtd><mtd columnalign=\"left\"><mstyle><mtext>in </mtext></mstyle><mi mathvariant=\"normal\">Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd columnalign=\"left\"><mo>|</mo><mo>∇</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>N</mi><mo stretchy=\"false\">−</mo><mn>2</mn></mrow></msup><mo stretchy=\"false\">(</mo><mo>∇</mo><mi>u</mi><mo stretchy=\"false\">⋅</mo><mi>ν</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">+</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>N</mi><mo stretchy=\"false\">−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn><mspace width=\"1em\"></mspace></mtd><mtd columnalign=\"left\"><mstyle><mtext>on </mtext></mstyle><mi>∂</mi><mi mathvariant=\"normal\">Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></mrow></math></span><span></span></disp-formula-group> where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Ω</mi><mo>⊂</mo><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span><span></span> is an exterior domain such that <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mn>0</mn><mo>∉</mo><mover accent=\"false\"><mrow><mi mathvariant=\"normal\">Ω</mi></mrow><mo accent=\"true\">¯</mo></mover></math></span><span></span>.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"23 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512912","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 : 2022-09-09DOI: 10.1142/s0219199722500626
M. Winkler
{"title":"Arbitrarily fast grow-up rates in quasilinear Keller-Segel systems","authors":"M. Winkler","doi":"10.1142/s0219199722500626","DOIUrl":"https://doi.org/10.1142/s0219199722500626","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46782105","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 : 2022-08-29DOI: 10.1142/S0219199723500062
Florian Besau, Steven Hoehner
A new intrinsic volume metric is introduced for the class of convex bodies in $mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes with a restricted number of vertices under this metric. This result improves the best known estimate, and shows that dropping the restriction that the polytope is contained in the ball or vice versa improves the estimate by at least a factor of dimension. The same phenomenon has already been observed in the special cases of volume, surface area and mean width approximation of the ball.
{"title":"An intrinsic volume metric for the class of convex bodies in ℝn","authors":"Florian Besau, Steven Hoehner","doi":"10.1142/S0219199723500062","DOIUrl":"https://doi.org/10.1142/S0219199723500062","url":null,"abstract":"A new intrinsic volume metric is introduced for the class of convex bodies in $mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes with a restricted number of vertices under this metric. This result improves the best known estimate, and shows that dropping the restriction that the polytope is contained in the ball or vice versa improves the estimate by at least a factor of dimension. The same phenomenon has already been observed in the special cases of volume, surface area and mean width approximation of the ball.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47565165","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 : 2022-08-23DOI: 10.1142/S021919972250081X
Carl Johan Peter Johansson, Riccardo Tione
In this paper we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in Section 7 of [Kirchheim, M"uller, v{S}ver'ak, 2003] and many of its properties have already been shown in [Lorent, Peng, 2019]-[Lorent, Peng, 2020]. In particular, in [Lorent, Peng 2020] it is shown that the differential inclusion does not contain any $T_4$ configurations. Here we continue that study by showing that the differential inclusion does not contain $T_5$ configurations.
{"title":"T5 Configurations and Hyperbolic Systems","authors":"Carl Johan Peter Johansson, Riccardo Tione","doi":"10.1142/S021919972250081X","DOIUrl":"https://doi.org/10.1142/S021919972250081X","url":null,"abstract":"In this paper we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in Section 7 of [Kirchheim, M\"uller, v{S}ver'ak, 2003] and many of its properties have already been shown in [Lorent, Peng, 2019]-[Lorent, Peng, 2020]. In particular, in [Lorent, Peng 2020] it is shown that the differential inclusion does not contain any $T_4$ configurations. Here we continue that study by showing that the differential inclusion does not contain $T_5$ configurations.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45533187","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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