Portugaliae Mathematica最新文献_第7页

Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip Möbius带上Dirichlet本征函数的Courant sharp性质

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2020-05-03 DOI: 10.4171/PM/2059

Pierre B'erard, B. Helffer, R. Kiwan

引用次数: 7

On Gaussian curvatures and singularities of Gauss maps of cuspidal edges 关于高斯曲率和高斯倒钩边映射的奇异性

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2020-03-24 DOI: 10.4171/pm/2065

Keisuke Teramoto

引用次数: 2

Varieties of regular semigroups with uniquely defined inversion 具有唯一定义反转的正则半群的变异

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2020-02-13 DOI: 10.4171/pm/2033

J. Araújo, M. Kinyon, Yves Robert

引用次数: 4

Joint differential invariants of binary and ternary forms 二元和三元形式的联合微分不变量

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2020-02-13 DOI: 10.4171/pm/2032

G. Polat, P. Olver

引用次数: 4

Universal compactified Jacobians 泛紧Jacobian

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2020-02-13 DOI: 10.4171/pm/2028

Margarida Melo

引用次数: 4

Compensated compactness and corrector stress tensor for the Einstein equations in $mathbb T^2$ symmetry 对称性为$mathbb T^2$的爱因斯坦方程的补偿紧性和修正应力张量

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2019-12-30 DOI: 10.4171/pm/2057

B. Floch, P. LeFloch

{"title":"Compensated compactness and corrector stress tensor for the Einstein equations in $mathbb T^2$ symmetry","authors":"B. Floch, P. LeFloch","doi":"10.4171/pm/2057","DOIUrl":"https://doi.org/10.4171/pm/2057","url":null,"abstract":"We consider the Einstein equations in T2 symmetry, either for vacuum spacetimes or coupled to the Euler equations for a compressible fluid, and we introduce the notion of T2 areal flows on T3 with finite total energy. By uncovering a hidden structure of the Einstein equations, we establish a compensated compactness framework and solve the global evolution problem for vacuum spacetimes as well as for self-gravitating compressible fluids. We study the stability and instability of such flows and prove that, when the initial data are well-prepared, any family of T2 areal flows is sequentially compact in a natural topology. In order to handle general initial data we propose a relaxed notion of T2 areal flows endowed with a corrector stress tensor (as we call it) which is a bounded measure generated by geometric oscillations and concentrations propagating at the speed of light. This generalizes a result for vacuum spacetimes in: Le Floch B. and LeFloch P.G., Arch. Rational Mech. Anal. 233 (2019), 45-86. In addition, we determine the global geometry of the corresponding future Cauchy developments and we prove that the area of the T2 orbits generically approaches infinity in the future-expanding regime. In the future-contracting regime, the volume of the T3 spacelike slices approaches zero and, for generic initial data, the area of the orbits of symmetry approaches zero in Gowdy symmetric matter spacetimes and in T2 vacuum spacetimes.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49626271","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: 8

$C^1$-generic sectional Axiom A flows have only trivial symmetries $C^1$-一般截面公理A流只有平凡对称性

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2019-09-30 DOI: 10.4171/pm/2025

Wescley Bonomo, P. Varandas

引用次数: 2

Metastability of the proximal point algorithm with multi-parameters 多参数近点算法的亚稳态

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2019-06-21 DOI: 10.4171/pm/2054

Bruno Miguel Antunes Dinis, P. Pinto

引用次数: 7

A noninequality for the fractional gradient 分数阶梯度的一个非不等式

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2019-06-13 DOI: 10.4171/pm/2031

Daniel Spector

引用次数: 17

Three-dimensional registration and shape reconstruction from depth data without matching: A PDE approach 无匹配深度数据的三维配准和形状重建：一种PDE方法

IF 0.8 4区数学

Portugaliae Mathematica Pub Date : 2019-06-06 DOI: 10.4171/pm/2020

D. A. Gomes, J. Costeira, João Saúde

{"title":"Three-dimensional registration and shape reconstruction from depth data without matching: A PDE approach","authors":"D. A. Gomes, J. Costeira, João Saúde","doi":"10.4171/pm/2020","DOIUrl":"https://doi.org/10.4171/pm/2020","url":null,"abstract":"The widespread availability of depth sensors like the Kinect camera makes it easy to gather three-dimensional (3D) data. However, accurately and efficiently merging large datasets collected from different views is still a core problem in computer vision. This question is particularly challenging if the relative positions of the views are not known, if there are few or no overlapping points, or if there are multiple objects. Here, we develop a method to reconstruct the 3D shapes of objects from depth data taken from different views whose relative positions are not known. Our method does not assume that common points in the views exist nor that the number of objects is known a priori. To reconstruct the shapes, we use partial differential equations (PDE) to compute upper and lower bounds for distance functions, which are solutions of the Eikonal equation constrained by the depth data. To combine various views, we minimize a function that measures the compatibility of relative positions. As we illustrate in several examples, we can reconstruct complex objects, even in the case where multiple views do not overlap, and, therefore, do not have points in common. We present several simulations to illustrate our method including multiple objects, non-convex objects, and complex shapes. Moreover, we present an application of our PDE approach to object classification from depth data. D. Gomes was partially supported by baseline and start-up funds, from King Abdullah University of Science and Technology (KAUST). J. Saúde was partially supported by by the Portuguese Foundation for Science and Technology through the Carnegie Mellon Portugal Program under the Grant SFRH/BD/52162/2013.","PeriodicalId":51269,"journal":{"name":"Portugaliae Mathematica","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/pm/2020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45998202","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