Annales Polonici Mathematici最新文献

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On the Pontryagin Maximum Principle under differential constraints of higher order 高阶微分约束下的庞特里亚金极大原理
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-10-13 DOI: 10.4064/ap220814-15-3
F. Cardin, C. Giannotti, A. Spiro
{"title":"On the Pontryagin Maximum Principle under differential constraints of higher order","authors":"F. Cardin, C. Giannotti, A. Spiro","doi":"10.4064/ap220814-15-3","DOIUrl":"https://doi.org/10.4064/ap220814-15-3","url":null,"abstract":"Exploiting our previous results on higher order controlled Lagrangians in [Nonlinear Anal. {bf 207} (2021), 112263], we derive here an analogue of the classical first order Pontryagin Maximum Principle (PMP) for cost minimising problems subjected to higher order differential constraints $frac{d^k x^j}{dt^k} = f^jbig(t, x(t), frac{d x}{dt}(t), ldots, frac{d^{k-1} x}{dt^{k-1}}(t), u(t)big)$, $t in [0,T]$, where $u(t)$ is a control curve in a compact set $K subset mathbb R^m$. This result and its proof can be considered as a detailed illustration of one of the claims of that previous paper, namely that the results of that paper, originally established in a smooth differential geometric framework, yield directly properties holding under much weaker and more common assumptions. In addition, for further clarifying our motivations, in the last section we display a couple of quick indications on how the two-step approach of this paper (i.e., a preliminary easy-to-get differential geometric discussion followed by a refining analysis to weaken the regularity assumptions) might be fruitfully exploited also in the context of control problems governed by partial differential equations or in studies on the dynamics of controlled mechanical systems.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48418599","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}
引用次数: 0
Regular projections and regular covers ino-minimal structures 规则的投影和规则的覆盖最小的结构
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-10-12 DOI: 10.4064/ap211206-3-1
M'hammed Oudrane
{"title":"Regular projections and regular covers in\u0000o-minimal structures","authors":"M'hammed Oudrane","doi":"10.4064/ap211206-3-1","DOIUrl":"https://doi.org/10.4064/ap211206-3-1","url":null,"abstract":"In this paper we prove that for any definable subset $Xsubset mathbb{R}^{n}$ in a polynomially bounded o-minimal structure, with $dim(X)<n$, there is a finite set of regular projections (in the sense of Mostowski ). We give also a weak version of this theorem in any o-minimal structure, and we give a counter example in o-minimal structures that are not polynomially bounded. As an application we show that in any o-minimal structure there exist a regular cover in the sense of Parusi'nski.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48892901","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}
引用次数: 0
Dynamics of low-degree rational inner skew-products on $mathbb{T}^2$ $mathbb{T}^2上的低次有理内斜积的动力学$
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-09-08 DOI: 10.4064/ap211108-28-2
A. Sola, R. Tully-Doyle
{"title":"Dynamics of low-degree rational inner skew-products on $mathbb{T}^2$","authors":"A. Sola, R. Tully-Doyle","doi":"10.4064/ap211108-28-2","DOIUrl":"https://doi.org/10.4064/ap211108-28-2","url":null,"abstract":"We examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis on simple maps of the form Φ(z1, z2) = (φ(z1, z2), z2). If φ has degree 1 in the first variable, the dynamics on each horizontal fiber can be described in terms of Möbius transformations but the global dynamics on the 2-torus exhibit some complexity, encoded in terms of certain T-symmetric polynomials. We describe the dynamical behavior of such mappings Φ and give criteria for different configurations of fixed point curves and rotation belts in terms of zeros of a related one-variable polynomial.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49617796","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}
引用次数: 2
On the composition operators on Besov and Triebel–Lizorkin spaces with power weights Besov和triiebel - lizorkin空间上幂权的复合算子
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-08-02 DOI: 10.4064/ap220314-23-9
D. Drihem
{"title":"On the composition operators on Besov and Triebel–Lizorkin spaces with power weights","authors":"D. Drihem","doi":"10.4064/ap220314-23-9","DOIUrl":"https://doi.org/10.4064/ap220314-23-9","url":null,"abstract":". Let G : R → R be a continuous function. Under some assumptions on G , s, α, p and q we prove that { : f ∈ p,q implies G is a linear function. Here A sp,q ( R n , | · | α ) stands for either the Besov space B s p,q ( R n , | · | α ) or the Triebel-Lizorkin space F s p,q ( R n , | · | α ). These spaces unify and generalize many classical function spaces such as Sobolev spaces of power weights. One of the main difficulties to study this problem is that the norm of the A s p,q ( R n , |·| α ) spaces with α 6 = 0 is not translation invariant, so some new techniques must be developed.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44480292","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}
引用次数: 0
Hardy’s inequalities, Hilbert inequalities and fractional integrals on function spaces of $q$-integral $p$-variation $q$-积分$p$-变分函数空间上的Hardy不等式、Hilbert不等式和分数积分
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-04-30 DOI: 10.4064/AP200224-11-1
K. Ho
{"title":"Hardy’s inequalities, Hilbert inequalities and fractional integrals on function spaces of $q$-integral $p$-variation","authors":"K. Ho","doi":"10.4064/AP200224-11-1","DOIUrl":"https://doi.org/10.4064/AP200224-11-1","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45683154","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}
引用次数: 2
Finite time blow-up for the heat flow of$H$-surface with constant mean curvature 具有常平均曲率的$H$-表面热流的有限时间爆破
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-04-04 DOI: 10.4064/ap210403-26-7
Haixia Li
{"title":"Finite time blow-up for the heat flow of\u0000$H$-surface with constant mean curvature","authors":"Haixia Li","doi":"10.4064/ap210403-26-7","DOIUrl":"https://doi.org/10.4064/ap210403-26-7","url":null,"abstract":"Abstract In this paper, the authors consider an initial boundary value problem for the heat flow of equation of surfaces with constant mean curvatures, which was investigated in [On the heat flow of equation of surfaces of constant mean curvatures, Manuscripta Mathematica, 2011, 134: 259-271] by Huang et al., where global well-posedness and finite time blow-up of regular solutions were obtained. Their results are complemented in this paper in the sense that some new conditions on the initial data are provided for the solutions to develop finite time singularity.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47042204","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}
引用次数: 0
Rooftop envelopes and residual plurisubharmonic functions 屋顶围护结构与残余多次谐波函数
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-03-26 DOI: 10.4064/ap210624-12-11
A. Rashkovskii
{"title":"Rooftop envelopes and residual plurisubharmonic functions","authors":"A. Rashkovskii","doi":"10.4064/ap210624-12-11","DOIUrl":"https://doi.org/10.4064/ap210624-12-11","url":null,"abstract":"Given a negative plurisubharmonic function φ in a bounded pseudoconvex domain of C, we introduce and study its residual function gφ determined by the asymptotic behavior of φ near its singularity points, both inside the domain and on its boundary. For certain choices of φ, the function gφ coincides with different versions of pluricomplex Green functions. The considerations are motivated by a problem on when two given plurisubharmonic functions can be connected by a plurisubharmonic geodesic. Mathematic Subject Classification: 32U05, 32U15, 32U35, 32W20","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"23 5","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41302357","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}
引用次数: 5
The Łojasiewicz exponent in non-degenerate deformations of surface singularities 曲面奇点非简并变形中的Łojasiewicz指数
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-03-15 DOI: 10.4064/ap210209-1-6
S. Brzostowski, Tadeusz Krasi'nski, Grzegorz Oleksik
{"title":"The Łojasiewicz exponent in non-degenerate deformations of surface singularities","authors":"S. Brzostowski, Tadeusz Krasi'nski, Grzegorz Oleksik","doi":"10.4064/ap210209-1-6","DOIUrl":"https://doi.org/10.4064/ap210209-1-6","url":null,"abstract":"We prove the constancy of the Lojasiewicz exponent in non-degenerate μ-constant deformations of surface singularities. This is a positive answer to a question posed by B. Teissier.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42099747","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}
引用次数: 1
Remarks on the regularity criteria for the axisymmetric MHD system 轴对称MHD系统的正则性准则
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-01-01 DOI: 10.4064/ap200221-15-9
Zujin Zhang, Yali Zhang
{"title":"Remarks on the regularity criteria for the axisymmetric MHD system","authors":"Zujin Zhang, Yali Zhang","doi":"10.4064/ap200221-15-9","DOIUrl":"https://doi.org/10.4064/ap200221-15-9","url":null,"abstract":"We show several weighted regularity criteria for the axisymmetric solutions to the three-dimensional magnetohydrodynamic equations, involving u, u; u, b, ∂ru , ∂rb ; u, b, ∂zu, ∂zb; u, b, ∂ru, ∂rb; or ω, where u, u, u are the angular, swirl and axial components of the velocity respectively and ω denotes the swirl component of the vorticity.","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70581093","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}
引用次数: 0
Characterization of hypercyclic weightedcomposition operators on the space of holomorphic functions 全纯函数空间上的超循环加权复合算子的表征
IF 0.5 4区 数学
Annales Polonici Mathematici Pub Date : 2021-01-01 DOI: 10.4064/ap210215-8-9
M. Golinski, A. Przestacki
{"title":"Characterization of hypercyclic weighted\u0000composition operators on the space of holomorphic functions","authors":"M. Golinski, A. Przestacki","doi":"10.4064/ap210215-8-9","DOIUrl":"https://doi.org/10.4064/ap210215-8-9","url":null,"abstract":"","PeriodicalId":55513,"journal":{"name":"Annales Polonici Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70582771","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}
引用次数: 1
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