Portugaliae Mathematica最新文献

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Automorphisms of tropical Hassett spaces 热带哈塞特空间的自同构
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2021-02-24 DOI: 10.4171/pm/2075
S. Freedman, J. Hlavinka, S. Kannan
{"title":"Automorphisms of tropical Hassett spaces","authors":"S. Freedman, J. Hlavinka, S. Kannan","doi":"10.4171/pm/2075","DOIUrl":"https://doi.org/10.4171/pm/2075","url":null,"abstract":"Given an integer $g geq 0$ and a weight vector $w in mathbb{Q}^n cap (0, 1]^n$ satisfying $2g - 2 + sum w_i>0$, let $Delta_{g, w}$ denote the moduli space of $n$-marked, $w$-stable tropical curves of genus $g$ and volume one. We calculate the automorphism group $mathrm{Aut}(Delta_{g, w})$ for $g geq 1$ and arbitrary $w$, and we calculate the group $mathrm{Aut}(Delta_{0, w})$ when $w$ is heavy/light. In both of these cases, we show that $mathrm{Aut}(Delta_{g, w}) cong mathrm{Aut}(K_w)$, where $K_w$ is the abstract simplicial complex on ${1, ldots, n}$ whose faces are subsets with $w$-weight at most $1$. We show that these groups are precisely the finite direct products of symmetric groups. The space $Delta_{g, w}$ may also be identified with the dual complex of the divisor of singular curves in the algebraic Hassett space $overline{mathcal{M}}_{g, w}$. Following the work of Massarenti and Mella on the biregular automorphism group $mathrm{Aut}(overline{mathcal{M}}_{g, w})$, we show that $mathrm{Aut}(Delta_{g, w})$ is naturally identified with the subgroup of automorphisms which preserve the divisor of singular curves.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46755860","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
The Talbot effect as the fundamental solution to the free Schrödinger equation 塔尔博特效应是自由Schrödinger方程的基本解
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2021-02-23 DOI: 10.4171/PM/2068
Daniel Eceizabarrena
{"title":"The Talbot effect as the fundamental solution to the free Schrödinger equation","authors":"Daniel Eceizabarrena","doi":"10.4171/PM/2068","DOIUrl":"https://doi.org/10.4171/PM/2068","url":null,"abstract":"The Talbot effect is usually modeled using the Helmholtz equation, but its main experimental features are captured by the solution to the free Schr\"odinger equation with the Dirac comb as initial datum. This simplified description is a consequence of the paraxial approximation in geometric optics. However, it is a heuristic approximation that is not mathematically well justified, so K. I. Oskolkov raised the problem of\"mathematizing\"it. We show that it holds exactly in the sense of distributions.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46485188","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 a class of nonlocal obstacle type problems related to the distributional Riesz fractional derivative 一类与分布Riesz分数阶导数有关的非局部障碍型问题
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2021-01-18 DOI: 10.4171/PM/2100
Catharine Lo, J. Rodrigues
{"title":"On a class of nonlocal obstacle type problems related to the distributional Riesz fractional derivative","authors":"Catharine Lo, J. Rodrigues","doi":"10.4171/PM/2100","DOIUrl":"https://doi.org/10.4171/PM/2100","url":null,"abstract":"In this work, we consider the nonlocal obstacle problem with a given obstacle $psi$ in a bounded Lipschitz domain $Omega$ in $mathbb{R}^{d}$, such that $mathbb{K}_psi^s={vin H^s_0(Omega):vgeqpsi text{ a.e. in }Omega}neqemptyset$, given by [uinmathbb{K}_psi^s:langlemathcal{L}_au,v-uranglegeqlangle F,v-uranglequadforall vinmathbb{K}^s_psi,] for $Fin H^{-s}(Omega)$, the dual space of $H^s_0(Omega)$, $0<s<1$. The nonlocal operator $mathcal{L}_a:H^s_0(Omega)to H^{-s}(Omega)$ is defined with a measurable, bounded, strictly positive singular kernel $a(x,y)$, possibly not symmetric, by [langlemathcal{L}_au,vrangle=P.V.int_{mathbb{R}^d}int_{mathbb{R}^d}v(x)(u(x)-u(y))a(x,y)dydx=mathcal{E}_a(u,v),] with $mathcal{E}_a$ being a Dirichlet form. Also, the fractional operator $tilde{mathcal{L}}_A=-D^scdot AD^s$ defined with the distributional Riesz $s$-fractional derivative and a bounded matrix $A(x)$ gives a well defined integral singular kernel. The corresponding $s$-fractional obstacle problem converges as $snearrow1$ to the obstacle problem in $H^1_0(Omega)$ with the operator $-Dcdot AD$ given with the gradient $D$. We mainly consider problems involving the bilinear form $mathcal{E}_a$ with one or two obstacles, and the N-membranes problem, deriving a weak maximum principle, comparison properties, approximation by bounded penalization, and the Lewy-Stampacchia inequalities. This provides regularity of the solutions, including a global estimate in $L^infty(Omega)$, local H\"older regularity when $a$ is symmetric, and local regularity in $W^{2s,p}_{loc}(Omega)$ and $C^1(Omega)$ for fractional $s$-Laplacian obstacle-type problems. These novel results are complemented with the extension of the Lewy-Stampacchia inequalities to the order dual of $H^s_0(Omega)$ and some remarks on the associated $s$-capacity for general $mathcal{L}_a$.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47723559","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: 3
Weak König’s lemma in herbrandized classical second-order arithmetic 广义经典二阶算法中的弱König引理
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-12-22 DOI: 10.4171/pm/2056
Fernando Ferreira
{"title":"Weak König’s lemma in herbrandized classical second-order arithmetic","authors":"Fernando Ferreira","doi":"10.4171/pm/2056","DOIUrl":"https://doi.org/10.4171/pm/2056","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49020880","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
Strongly Mackey topologies and Radon vector measures 强Mackey拓扑和Radon向量测度
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-12-22 DOI: 10.4171/pm/2052
M. Nowak
{"title":"Strongly Mackey topologies and Radon vector measures","authors":"M. Nowak","doi":"10.4171/pm/2052","DOIUrl":"https://doi.org/10.4171/pm/2052","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41395914","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
On the discriminant locus of a rank $n-1$ vector bundle on $mathbb P^{n-1}$ 在$mathbb P^{n-1}$上秩$n-1$向量束的判别轨迹
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-12-22 DOI: 10.4171/pm/2053
Hirotachi Abo
{"title":"On the discriminant locus of a rank $n-1$ vector bundle on $mathbb P^{n-1}$","authors":"Hirotachi Abo","doi":"10.4171/pm/2053","DOIUrl":"https://doi.org/10.4171/pm/2053","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42989518","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
Endowing evolution algebras with properties of discrete structures 赋予演化代数离散结构的性质
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-12-22 DOI: 10.4171/pm/2058
R. González-López, J. Núñez
{"title":"Endowing evolution algebras with properties of discrete structures","authors":"R. González-López, J. Núñez","doi":"10.4171/pm/2058","DOIUrl":"https://doi.org/10.4171/pm/2058","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41961669","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
State dependent nonconvex sweeping processes in smooth Banach spaces 光滑Banach空间中的状态相关非凸扫频过程
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-10-14 DOI: 10.4171/pm/2049
Dj. Bounekhel, M. Bounkhel, M. Bachar
{"title":"State dependent nonconvex sweeping processes in smooth Banach spaces","authors":"Dj. Bounekhel, M. Bounkhel, M. Bachar","doi":"10.4171/pm/2049","DOIUrl":"https://doi.org/10.4171/pm/2049","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"77 1","pages":"197-218"},"PeriodicalIF":0.8,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48138663","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
Overdetermined constraints and rigid synchrony patterns for network equilibria 网络平衡的超定约束和刚性同步模式
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-10-14 DOI: 10.4171/pm/2048
I. Stewart
{"title":"Overdetermined constraints and rigid synchrony patterns for network equilibria","authors":"I. Stewart","doi":"10.4171/pm/2048","DOIUrl":"https://doi.org/10.4171/pm/2048","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42536421","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
Convergence of a full discrete finite element method for the Korteweg–de Vries equation Korteweg–de Vries方程的全离散有限元方法的收敛性
IF 0.8 4区 数学
Portugaliae Mathematica Pub Date : 2020-09-09 DOI: 10.4171/pm/2043
Pengzhan Huang
{"title":"Convergence of a full discrete finite element method for the Korteweg–de Vries equation","authors":"Pengzhan Huang","doi":"10.4171/pm/2043","DOIUrl":"https://doi.org/10.4171/pm/2043","url":null,"abstract":"","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":"77 1","pages":"31-43"},"PeriodicalIF":0.8,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47359789","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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