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Approximation by Convolution Translation Networks on Conic Domains 圆锥域上的卷积平移网络逼近
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-4019-8
Bao Huai Sheng, Dao Hong Xiang
{"title":"Approximation by Convolution Translation Networks on Conic Domains","authors":"Bao Huai Sheng,&nbsp;Dao Hong Xiang","doi":"10.1007/s10114-024-4019-8","DOIUrl":"10.1007/s10114-024-4019-8","url":null,"abstract":"<div><p>We give investigations on the approximation order of translation networks produced by the convolution translation operators defined on a Jacobi cone and the surface cone. We deal with the convolution translation from the view of Fourier analysis, express the translation operator with orthogonal basis and provide a sufficient condition to ensure the density for the translation networks. Based on these facts, we construct with the near best approximation operator and the Gauss integral formula two kinds of translation network operators and show their approximation orders in the best polynomial approximation.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"3127 - 3150"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Symmetric Brake Orbits with Minimal Period of First-order Anisotropic Hamiltonian Systems 一阶各向异性哈密顿系统最小周期对称制动轨道
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-15 DOI: 10.1007/s10114-024-2441-6
Xiao Fei Zhang, Fan Jing Wang
{"title":"Symmetric Brake Orbits with Minimal Period of First-order Anisotropic Hamiltonian Systems","authors":"Xiao Fei Zhang,&nbsp;Fan Jing Wang","doi":"10.1007/s10114-024-2441-6","DOIUrl":"10.1007/s10114-024-2441-6","url":null,"abstract":"<div><p>Via the homology link theorem and the <i>L</i><sub>0</sub>-index theory, symmetric brake orbits with minimal period are ensured for first-order Hamiltonian systems under anisotropic growth assumptions, which are variant forms of sub-quadratic growth conditions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 12","pages":"3079 - 3092"},"PeriodicalIF":0.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142870385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
L2 Schrödinger Maximal Estimates Associated with Finite Type Phases in ℝ2 与ℝ2 中有限类型相位相关的 L2 薛定谔最大估计值
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3401-x
Zhuo Ran Li, Jun Yan Zhao, Teng Fei Zhao
{"title":"L2 Schrödinger Maximal Estimates Associated with Finite Type Phases in ℝ2","authors":"Zhuo Ran Li,&nbsp;Jun Yan Zhao,&nbsp;Teng Fei Zhao","doi":"10.1007/s10114-024-3401-x","DOIUrl":"10.1007/s10114-024-3401-x","url":null,"abstract":"<div><p>In this paper, we establish Schrödinger maximal estimates associated with the finite type phase </p><div><div><span>$$phi(xi_{1},xi_{2}):=xi_{1}^{m}+xi_{2}^{m},$$</span></div></div><p> where <i>m</i> ≥ 4 is an even number. Following [12], we prove an <i>L</i><sup>2</sup> fractal restriction estimate associated with the surface </p><div><div><span>$${(xi_{1},xi_{2},phi(xi_{1},xi_{2})) : (xi_{1},xi_{2})in[0,1]^{2}}$$</span></div></div><p> as the main result, which also gives results on the average Fourier decay of fractal measures associated with these surfaces. The key ingredients of the proof include the rescaling technique from [16], Bourgain–Demeter’s <i>ℓ</i><sup>2</sup> decoupling inequality, the reduction of dimension arguments from [17] and induction on scales. We notice that our Theorem 1.1 has some similarities with the results in [8]. However, their results do not cover ours. Their arguments depend on the positive definiteness of the Hessian matrix of the phase function, while our phase functions are degenerate.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2809 - 2839"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Degenerate KAM Theorem for Partial Differential Equations with Unbounded Perturbations 无界扰动偏微分方程的退化 KAM 定理
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3159-1
Mei Na Gao, Jian Jun Liu
{"title":"A Degenerate KAM Theorem for Partial Differential Equations with Unbounded Perturbations","authors":"Mei Na Gao,&nbsp;Jian Jun Liu","doi":"10.1007/s10114-024-3159-1","DOIUrl":"10.1007/s10114-024-3159-1","url":null,"abstract":"<div><p>In this paper, an infinite dimensional KAM theorem with unbounded perturbations and double normal frequencies is established under qualitative non-degenerate conditions. This is an extension of the degenerate KAM theorem with bounded perturbations by Bambusi, Berti, Magistrelli, and us. As applications, for derivative nonlinear Schrödinger equation with periodic boundary conditions, quasi-periodic solutions around constant solutions are obtained.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2719 - 2734"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Adaptive Distributed Inference for Multi-source Massive Heterogeneous Data 多源海量异构数据的自适应分布式推理
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2524-4
Xin Yang, Qi Jing Yan, Mi Xia Wu
{"title":"Adaptive Distributed Inference for Multi-source Massive Heterogeneous Data","authors":"Xin Yang,&nbsp;Qi Jing Yan,&nbsp;Mi Xia Wu","doi":"10.1007/s10114-024-2524-4","DOIUrl":"10.1007/s10114-024-2524-4","url":null,"abstract":"<div><p>In this paper, we consider the distributed inference for heterogeneous linear models with massive datasets. Noting that heterogeneity may exist not only in the expectations of the subpopulations, but also in their variances, we propose the heteroscedasticity-adaptive distributed aggregation (HADA) estimation, which is shown to be communication-efficient and asymptotically optimal, regardless of homoscedasticity or heteroscedasticity. Furthermore, a distributed test for parameter heterogeneity across subpopulations is constructed based on the HADA estimator. The finite-sample performance of the proposed methods is evaluated using simulation studies and the NYC flight data.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2751 - 2770"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Variable Degeneracy of Planar Graphs without Chorded 6-Cycles 无弦 6 循环平面图的可变退化性
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2245-8
Hui Hui Fang, Dan Jun Huang, Tao Wang, Wei Fan Wang
{"title":"Variable Degeneracy of Planar Graphs without Chorded 6-Cycles","authors":"Hui Hui Fang,&nbsp;Dan Jun Huang,&nbsp;Tao Wang,&nbsp;Wei Fan Wang","doi":"10.1007/s10114-024-2245-8","DOIUrl":"10.1007/s10114-024-2245-8","url":null,"abstract":"<div><p>A cover of a graph <i>G</i> is a graph <i>H</i> with vertex set <i>V</i> (<i>H</i>) = ∪<sub><i>v</i>∈<i>V</i>(<i>G</i>)</sub> <i>L</i><sub><i>v</i></sub>, where <i>L</i><sub><i>v</i></sub> = {<i>v</i>} × [<i>s</i>], and the edge set <i>M</i> = ∪<sub><i>uv</i>∈<i>E</i>(<i>G</i>)</sub> <i>M</i><sub><i>uv</i></sub>, where <i>M</i><sub><i>uv</i></sub> is a matching between <i>L</i><sub><i>u</i></sub> and <i>L</i><sub><i>v</i></sub>. A vertex set <i>T</i> ⊆ <i>V</i> (<i>H</i>) is a transversal of <i>H</i> if ∣<i>T</i> ∩ <i>L</i><sub><i>v</i></sub>∣ = 1 for each <i>v</i> ∈ <i>V</i>(<i>G</i>). Let <i>f</i> be a nonnegative integer valued function on the vertex-set of <i>H</i>. If for any nonempty subgraph Γ of <i>H</i>[<i>T</i>], there exists a vertex <i>x</i> ∈ <i>V</i> (<i>H</i>) such that <i>d</i>(<i>x</i>) &lt; <i>f</i>(<i>x</i>), then <i>T</i> is called a strictly <i>f</i>-degenerate transversal. In this paper, we give a sufficient condition for the existence of strictly <i>f</i>-degenerate transversal for planar graphs without chorded 6-cycles. As a consequence, every planar graph without subgraphs isomorphic to the configurations is DP-4-colorable.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2735 - 2750"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the Centralizers of Rescaling Separating Differentiable Vector Fields 论重缩分微分矢量场的中心点
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3170-6
Bo Han, Xiao Wen
{"title":"On the Centralizers of Rescaling Separating Differentiable Vector Fields","authors":"Bo Han,&nbsp;Xiao Wen","doi":"10.1007/s10114-024-3170-6","DOIUrl":"10.1007/s10114-024-3170-6","url":null,"abstract":"<div><p>In this paper, we introduce a new concept of expansiveness, similar to the separating property. Specifically, we consider a compact Riemannian manifold <i>M</i> without boundary and a <i>C</i><sup>1</sup> vector field <i>X</i> on <i>M</i>, which generates a flow <i>φ</i><sub><i>t</i></sub> on <i>M</i>. We say that <i>X is rescaling separating</i> on a compact invariant set Λ of <i>X</i> if there is a constant <i>δ</i> &gt; 0 such that, for any <i>x</i>, <i>y</i> ∈ Λ, if <i>d</i>(<i>φ</i><sub><i>t</i></sub>(<i>x</i>), <i>φ</i><sub><i>t</i></sub>(<i>y</i>)) ≤ <i>δ</i>∥<i>X</i> (<i>φ</i><sub><i>t</i></sub>(<i>x</i>))∥ for all <i>t</i> ∈ ℝ, then <i>y</i> ∈ Orb(<i>x</i>). We prove that if <i>X</i> is rescaling separating on Λ and every singularity of <i>X</i> in Λ is hyperbolic, then any <i>C</i><sup>1</sup> vector field <i>Y</i>, whose flow commutes with <i>φ</i><sub><i>t</i></sub> on Λ, must be collinear to <i>X</i> on Λ. As applications of this result, we show that the centralizer of a rescaling separating <i>C</i><sup>1</sup> vector field without nonhyperbolic singularity is quasi-trivial. We also proved that there is an open and dense set <span>({cal U} subset {{cal X}^{1}}(M))</span> such that for any star vector field <span>(X in {cal U})</span>, the centralizer of <i>X</i> is collinear to <i>X</i> on the chain recurrent set of <i>X</i>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2671 - 2683"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
The Scattered Range Problem of Elementary Operators on ({cal B}({cal H})) 初等算子在({cal B}({cal H}))上的散射范围问题
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-3346-0
Peng Cao, Cun Wang
{"title":"The Scattered Range Problem of Elementary Operators on ({cal B}({cal H}))","authors":"Peng Cao,&nbsp;Cun Wang","doi":"10.1007/s10114-024-3346-0","DOIUrl":"10.1007/s10114-024-3346-0","url":null,"abstract":"<div><p>A scattered operator is a bounded linear operator with at most countable spectrum. In this paper, we prove that for any elementary operator on <span>({cal B}({cal H}))</span>, not only for finite length but also for infinite length, if the range of the elementary operator is contained in scattered operators, then the corresponding sum of multipliers is a compact operator. We also prove that for some special classes of elementary operators, such as the elementary operators of length 2, higher order inner derivations and generalized inner derivation, if the range of the elementary operator is contained in the set of scattered operators, then the range is contained in the set of power compact operators. At the same time, the multipliers of the corresponding elementary operators are characterized.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2684 - 2692"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Weak ∞-Functor in Morse Theory 莫尔斯理论中的弱∞矢量
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2523-5
Shan Zhong Sun, Chen Xi Wang
{"title":"A Weak ∞-Functor in Morse Theory","authors":"Shan Zhong Sun,&nbsp;Chen Xi Wang","doi":"10.1007/s10114-024-2523-5","DOIUrl":"10.1007/s10114-024-2523-5","url":null,"abstract":"<div><p>In the spirit of Morse homology initiated by Witten and Floer, we construct two ∞-categories <span>({cal A})</span> and <span>({cal B})</span>. The weak one <span>({cal A})</span> comes out of the Morse–Smale pairs and their higher homotopies, and the strict one <span>({cal B})</span> concerns the chain complexes of the Morse functions. Based on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters, we build up a weak ∞-functor <span>({cal F}:{cal A} rightarrow {cal B})</span>. Higher algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2571 - 2614"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Characterizations of Weighted Besov Spaces with Variable Exponents 具有可变指数的加权贝索夫空间的特征
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-11-15 DOI: 10.1007/s10114-024-2623-2
Sheng Rong Wang, Peng Fei Guo, Jing Shi Xu
{"title":"Characterizations of Weighted Besov Spaces with Variable Exponents","authors":"Sheng Rong Wang,&nbsp;Peng Fei Guo,&nbsp;Jing Shi Xu","doi":"10.1007/s10114-024-2623-2","DOIUrl":"10.1007/s10114-024-2623-2","url":null,"abstract":"<div><p>In this paper, we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal functions. Then we obtain decomposition characterizations of these spaces by atom, molecule and wavelet. As an application, we obtain the boundedness of the pseudo-differential operators on these spaces.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 11","pages":"2855 - 2878"},"PeriodicalIF":0.8,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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