Pub Date : 2023-11-04DOI: 10.1007/s00605-023-01917-z
Nuno Costa Dias, Cristina Jorge, João Nuno Prata
Abstract We prove that there exists essentially one minimal differential algebra of distributions $$mathcal A$$ A , satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l’impossibilité de la multiplication des distributions, 1954], and such that $$mathcal C_p^{infty } subseteq mathcal Asubseteq mathcal D' $$ Cp∞⊆A⊆D′ (where $$mathcal C_p^{infty }$$ Cp∞ is the set of piecewise smooth functions and $$mathcal D'$$ D′ is the set of Schwartz distributions over $$mathbb R$$ R ). This algebra is endowed with a multiplicative product of distributions, which is a generalization of the product defined in [N.C.Dias, J.N.Prata, A multiplicative product of distributions and a class of ordinary differential equations with distributional coefficients, 2009]. If the algebra is not minimal, but satisfies the previous conditions, is closed under anti-differentiation and the dual product by smooth functions, and the distributional product is continuous at zero then it is necessarily an extension of $$mathcal A$$ A .
摘要证明了存在一个极小的分布微分代数 $$mathcal A$$ A，满足Schwartz不可能结果中的所有性质[L]。Schwartz, Sur l ' impossible it de la multiplication des distribution(1954)，等等 $$mathcal C_p^{infty } subseteq mathcal Asubseteq mathcal D' $$ C p∞(其中 $$mathcal C_p^{infty }$$ C p∞是分段光滑函数和的集合 $$mathcal D'$$ D '是Schwartz分布的集合 $$mathbb R$$ R)。这个代数被赋予了分布的乘法积，它是在[N.C.]中定义的乘积的推广Dias, J.N.Prata，一类具有分布系数的常微分方程的乘积[j]。如果代数不是极小的，但满足上述条件，在反微分和光滑函数的对偶积下是封闭的，并且分布积在零处连续，那么它必然是一个扩展 $$mathcal A$$ 选A。
{"title":"An existence and uniqueness result about algebras of Schwartz distributions","authors":"Nuno Costa Dias, Cristina Jorge, João Nuno Prata","doi":"10.1007/s00605-023-01917-z","DOIUrl":"https://doi.org/10.1007/s00605-023-01917-z","url":null,"abstract":"Abstract We prove that there exists essentially one minimal differential algebra of distributions $$mathcal A$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> , satisfying all the properties stated in the Schwartz impossibility result [L. Schwartz, Sur l’impossibilité de la multiplication des distributions, 1954], and such that $$mathcal C_p^{infty } subseteq mathcal Asubseteq mathcal D' $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>p</mml:mi> <mml:mi>∞</mml:mi> </mml:msubsup> <mml:mo>⊆</mml:mo> <mml:mi>A</mml:mi> <mml:mo>⊆</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> (where $$mathcal C_p^{infty }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>p</mml:mi> <mml:mi>∞</mml:mi> </mml:msubsup> </mml:math> is the set of piecewise smooth functions and $$mathcal D'$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:math> is the set of Schwartz distributions over $$mathbb R$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>R</mml:mi> </mml:math> ). This algebra is endowed with a multiplicative product of distributions, which is a generalization of the product defined in [N.C.Dias, J.N.Prata, A multiplicative product of distributions and a class of ordinary differential equations with distributional coefficients, 2009]. If the algebra is not minimal, but satisfies the previous conditions, is closed under anti-differentiation and the dual product by smooth functions, and the distributional product is continuous at zero then it is necessarily an extension of $$mathcal A$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>A</mml:mi> </mml:math> .","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135774120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1007/s00605-023-01918-y
Raja Milad, Keith F. Taylor
{"title":"A two plus one dimensional continuous wavelet transform","authors":"Raja Milad, Keith F. Taylor","doi":"10.1007/s00605-023-01918-y","DOIUrl":"https://doi.org/10.1007/s00605-023-01918-y","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"129 S201","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1007/s00605-023-01916-0
Christian Müller, Helmut Pottmann
Abstract The geometry of webs has been investigated over more than a century driven by still open problems. In our paper we contribute to extending the knowledge on webs from the perspective of the geometry of webs on surfaces in three dimensional space. Our study of AGAG-webs is motivated by architectural applications of gridshell structures where four families of manufactured curves on a curved surface are realizations of asymptotic lines and geodesic lines. We describe all discrete AGAG-webs in isotropic space and propose a method to construct them. Furthermore, we prove that some sub-nets of an AGAG-web are timelike minimal surfaces in Minkowski space and can be embedded into a one-parameter family of discrete isotropic Voss nets.
{"title":"The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space","authors":"Christian Müller, Helmut Pottmann","doi":"10.1007/s00605-023-01916-0","DOIUrl":"https://doi.org/10.1007/s00605-023-01916-0","url":null,"abstract":"Abstract The geometry of webs has been investigated over more than a century driven by still open problems. In our paper we contribute to extending the knowledge on webs from the perspective of the geometry of webs on surfaces in three dimensional space. Our study of AGAG-webs is motivated by architectural applications of gridshell structures where four families of manufactured curves on a curved surface are realizations of asymptotic lines and geodesic lines. We describe all discrete AGAG-webs in isotropic space and propose a method to construct them. Furthermore, we prove that some sub-nets of an AGAG-web are timelike minimal surfaces in Minkowski space and can be embedded into a one-parameter family of discrete isotropic Voss nets.","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"20 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135818196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-02DOI: 10.1007/s00605-023-01912-4
Nadia Taghipour, Shamila Bayati, Farhad Rahmati
In this paper, we investigate when symbolic and ordinary powers of the parity binomial edge ideal of a graph fail to be equal. It turns out that if $${mathcal {I}}_{G}$$ is the parity binomial edge ideal of a graph G, then in each of the following cases the symbolic power $${mathcal {I}}_{G}^{(t)}$$ and the ordinary power $${mathcal {I}}_{G}^t$$ are not equal for some t: (i) the clique number of G is greater than 3; (ii) G has a net; or (iii) G has a PT as an induced subgraph.
{"title":"Comparison of symbolic and ordinary powers of parity binomial edge ideals","authors":"Nadia Taghipour, Shamila Bayati, Farhad Rahmati","doi":"10.1007/s00605-023-01912-4","DOIUrl":"https://doi.org/10.1007/s00605-023-01912-4","url":null,"abstract":"In this paper, we investigate when symbolic and ordinary powers of the parity binomial edge ideal of a graph fail to be equal. It turns out that if $${mathcal {I}}_{G}$$ is the parity binomial edge ideal of a graph G, then in each of the following cases the symbolic power $${mathcal {I}}_{G}^{(t)}$$ and the ordinary power $${mathcal {I}}_{G}^t$$ are not equal for some t: (i) the clique number of G is greater than 3; (ii) G has a net; or (iii) G has a PT as an induced subgraph.","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"75 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1007/s00605-023-01911-5
T. A. Medina-Tejeda
{"title":"Extendibility and boundedness of invariants on singularities of wavefronts","authors":"T. A. Medina-Tejeda","doi":"10.1007/s00605-023-01911-5","DOIUrl":"https://doi.org/10.1007/s00605-023-01911-5","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135271415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1007/s00605-023-01910-6
Petr Hasil, Michal Pospíšil, Jiřina Šišoláková, Michal Veselý
Abstract Applying an averaging technique for the adapted Prüfer angle, we obtain an oscillation criterion for linear second order differential equations whose coefficients consist of products of powers of natural logarithm and general (bounded or unbounded) continuous functions. The presented criterion is illustrated by new corollaries and examples. The novelty is caused by the used averaging technique over unbounded intervals.
{"title":"Oscillation criterion for linear equations with coefficients containing powers of natural logarithm","authors":"Petr Hasil, Michal Pospíšil, Jiřina Šišoláková, Michal Veselý","doi":"10.1007/s00605-023-01910-6","DOIUrl":"https://doi.org/10.1007/s00605-023-01910-6","url":null,"abstract":"Abstract Applying an averaging technique for the adapted Prüfer angle, we obtain an oscillation criterion for linear second order differential equations whose coefficients consist of products of powers of natural logarithm and general (bounded or unbounded) continuous functions. The presented criterion is illustrated by new corollaries and examples. The novelty is caused by the used averaging technique over unbounded intervals.","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-05DOI: 10.1007/s00605-023-01901-7
Yeansu Kim, Ivan Matić
{"title":"Discrete series of odd general spin groups","authors":"Yeansu Kim, Ivan Matić","doi":"10.1007/s00605-023-01901-7","DOIUrl":"https://doi.org/10.1007/s00605-023-01901-7","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134973811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-04DOI: 10.1007/s00605-023-01897-0
B. A. F. Wehrfritz
Abstract We prove in particular that if G is a soluble group with no non-trivial locally finite normal subgroups, then G is p-potent for every prime p for which G has no Prüfer p-sections. (A group G is p-potent if for every power n of p and for any element x of G of infinite order or of finite order divisible by n there is a normal subgroup N of G of finite index such that the order of x modulo N is n. A Prüfer p-group is an infinite locally cyclic p-group.) This extends to soluble groups in general, and gives a more direct proof of, recent results of Azarov on polycyclic groups and soluble minimax groups.
{"title":"Potency in soluble groups","authors":"B. A. F. Wehrfritz","doi":"10.1007/s00605-023-01897-0","DOIUrl":"https://doi.org/10.1007/s00605-023-01897-0","url":null,"abstract":"Abstract We prove in particular that if G is a soluble group with no non-trivial locally finite normal subgroups, then G is p-potent for every prime p for which G has no Prüfer p-sections. (A group G is p-potent if for every power n of p and for any element x of G of infinite order or of finite order divisible by n there is a normal subgroup N of G of finite index such that the order of x modulo N is n. A Prüfer p-group is an infinite locally cyclic p-group.) This extends to soluble groups in general, and gives a more direct proof of, recent results of Azarov on polycyclic groups and soluble minimax groups.","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 10.1007/s00605-023-01909-z
Mitra Amiri, Ali Rejali
{"title":"$$C^{*}$$-algebra structure on vector valued-Banach algebras","authors":"Mitra Amiri, Ali Rejali","doi":"10.1007/s00605-023-01909-z","DOIUrl":"https://doi.org/10.1007/s00605-023-01909-z","url":null,"abstract":"","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：