Acta Mathematicae Applicatae Sinica, English Series最新文献_第4页

Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Its Applications to Hardy-Littlewood Inequalities 与球准巴纳赫函数空间相关的各向异性哈代空间的傅立叶变换及其在哈代-利特尔伍德不等式中的应用

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1124-5

Chao-an Li, Xian-jie Yan, Da-chun Yang

{"title":"Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and Its Applications to Hardy-Littlewood Inequalities","authors":"Chao-an Li, Xian-jie Yan, Da-chun Yang","doi":"10.1007/s10255-024-1124-5","DOIUrl":"https://doi.org/10.1007/s10255-024-1124-5","url":null,"abstract":"Let A be a general expansive matrix and X be a ball quasi-Banach function space on ℝn, whose certain power (namely its convexification) supports a Fefferman-Stein vector-valued maximal inequality and the associate space of whose other power supports the boundedness of the powered Hardy-Littlewood maximal operator. Let H\u0000AX\u0000(ℝn) be the anisotropic Hardy space associated with A and X. The authors first prove that the Fourier transform of f ∈ H\u0000AX\u0000(ℝn) coincides with a continuous function F on ℝn in the sense of tempered distributions. Moreover, the authors obtain a pointwise inequality that the function F is less than the product of the anisotropic Hardy space norm of f and a step function with respect to the transpose matrix of the expansive matrix A. Applying this, the authors further induce a higher order convergence for the function F at the origin and give a variant of the Hardy-Littlewood inequality in H\u0000AX\u0000(ℝn). All these results have a wide range of applications. Particularly, the authors apply these results, respectively, to classical (variable and mixed-norm) Lebesgue spaces, Lorentz spaces, Orlicz spaces, Orlicz-slice spaces, and local generalized Herz spaces and, even on the last four function spaces, the obtained results are completely new.","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192395","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

Two-grid Method of Expanded Mixed Finite Element Approximations for Parabolic Integro-differential Optimal Control Problems 抛物线积分微分优化控制问题的双网格扩展混合有限元逼近法

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1099-2

Yan-ping Chen, Jian-wei Zhou, Tian-liang Hou

{"title":"Two-grid Method of Expanded Mixed Finite Element Approximations for Parabolic Integro-differential Optimal Control Problems","authors":"Yan-ping Chen, Jian-wei Zhou, Tian-liang Hou","doi":"10.1007/s10255-024-1099-2","DOIUrl":"https://doi.org/10.1007/s10255-024-1099-2","url":null,"abstract":"This paper aims to construct a two-grid scheme of fully discretized expanded mixed finite element methods for optimal control problems governed by parabolic integro-differential equations and discuss a priori error estimates. The state variables and co-state variables are discretized by the lowest order Raviart-Thomas mixed finite element, and the control variable is approximated by piecewise constant functions. The time derivative is discretized by the backward Euler method. Firstly, we define some new mixed elliptic projections and prove the corresponding error estimates which play an important role in subsequent convergence analysis. Secondly, we derive a priori error estimates for all variables. Thirdly, we present a two-grid scheme and analyze its convergence. In the two-grid scheme, the solution of the parabolic optimal control problem on a fine grid is reduced to the solution of the parabolic optimal control problem on a much coarser grid and the solution of a decoupled linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy. At last, a numerical example is presented to verify the theoretical results.","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192339","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

Uniform Large Deviations for Stochastic Generalized Burgers-Huxley Equation Driven by Multiplicative Noise 乘法噪声驱动的随机广义伯格斯-赫胥黎方程的均匀大偏差

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1129-0

Hui Guo, Xi-liang Li, Jin Ma

引用次数: 0

The P5-saturation Game 五常饱和游戏

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1125-4

Zhen He, Mei Lu

{"title":"The P5-saturation Game","authors":"Zhen He, Mei Lu","doi":"10.1007/s10255-024-1125-4","DOIUrl":"https://doi.org/10.1007/s10255-024-1125-4","url":null,"abstract":"Let F, G and H be three graphs with G ⊆ H. We call G an F-saturated graph relative to H, if there is no copy of F in G but there is a copy of F in G + e for any e ∈ E(H) E(G). The F-saturation game on host graph H consists of two players, named Max and Min, who alternately add edges of H to G such that each chosen edge avoids creating a copy of F in G, and the players continue to choose edges until G becomes F-saturated relative to H. Max wishes to maximize the length of the game, while Min wishes to minimize the process. Let satg(F, H) (resp. sat′g(F, H)) denote the number of edges chosen when Max (resp. when Min) starts the game and both players play optimally. In this article, we show that satg(P5, Kn) = sat′g(P5, Kn) = n + 2 for n ≥ 15, and satg(P5, Km,n), sat′g(P5, Km,n) lie in (left{ {m + n - leftlfloor {{{m - 2} over 4}} rightrfloor ,,m + n - leftlceil {{{m - 3} over 4}} rightrceil } right}) if (n ge {5 over 2}m) and m ≥ 4, respectively.","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192428","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

Asymptotic Property of Parabolic Equations Involving Pseudo-relativistic Schrödinger Operators 涉及伪相对论薛定谔算子的抛物方程的渐近特性

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1097-4

Chen Qiao, Su-fang Tang

引用次数: 0

Itô-Taylor Expansion Method of European Spread Option Pricing for Multivariate Diffusions with Jumps 带有跳跃的多变量扩散的欧式利差期权定价的伊托-泰勒扩展法

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1094-7

Ge Wang, Yu-xuan Lu, Qing Zhou, Wei-lin Xiao

引用次数: 0

Privacy-Preserving Frank-Wolfe on Shuffle Model 洗牌模型上的隐私保护弗兰克-沃尔夫

IF 0.9 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1095-6

Ling-jie Zhang, Shi-song Wu, Hai Zhang

{"title":"Privacy-Preserving Frank-Wolfe on Shuffle Model","authors":"Ling-jie Zhang, Shi-song Wu, Hai Zhang","doi":"10.1007/s10255-024-1095-6","DOIUrl":"10.1007/s10255-024-1095-6","url":null,"abstract":"<div>In this paper, we design the differentially private variants of the classical Frank-Wolfe algorithm with shuffle model in the optimization of machine learning. Under weak assumptions and the generalized linear loss (GLL) structure, we propose a noisy Frank-Wolfe with shuffle model algorithm (NoisyFWS) and a noisy variance-reduced Frank-Wolfe with the shuffle model algorithm (NoisyVRFWS) by adding calibrated laplace noise under shuffling scheme in the ℓp(p ∈ [1, 2])-case, and study their privacy as well as utility guarantees for the Hölder smoothness GLL. In particular, the privacy guarantees are mainly achieved by using advanced composition and privacy amplification by shuffling. The utility bounds of the NoisyFWS and NoisyVRFWS are analyzed and obtained the optimal excess population risks ({cal O}({n^{ - {{1 + alpha } over {4alpha }}}} + {{log (d)sqrt {log ({1 mathord{left/ {vphantom {1 delta }} right.} delta })} } over {nepsilon,}})) and ({cal O}({n^{ - {{1 + alpha } over {4alpha }}}} + {{log (d)sqrt {log ({1 mathord{left/ {vphantom {1 delta }} right.} delta })} } over {{n^2epsilon},}})) with gradient complexity ({cal O}({n^{ - {{{{(1 + alpha )}^2}} over {4{alpha ^2}}}}})) for (alpha in left[ {{1 mathord{left/ {vphantom {1 {sqrt 3 ,,1}}} right.} {sqrt 3 ,,1}}} right]). It turns out that the risk rates under shuffling scheme are a nearly-dimension independent rate, which is consistent with the previous work in some cases. In addition, there is a vital tradeoff between (α, L)-Hölder smoothness GLL and the gradient complexity. The linear gradient complexity ({cal O}(n)) is showed by the parameter α = 1.</div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141192397","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

Meromorphic Solutions to Higher Order Nonlinear Delay Differential Equations 高阶非线性延迟微分方程的同构解

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-01 DOI: 10.1007/s10255-024-1098-3

Ye-zhou Li, Ming-yue Wu, He-qing Sun

引用次数: 0

Information Heterogeneity: Implications for Liquidity and Price Efficiency 信息异质性：对流动性和价格效率的影响

IF 0.8 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-05-11 DOI: 10.1007/s10255-024-1092-9

Zhi-hua Li, Hong Liu, Qing-shan Yang

引用次数: 0

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate 具有检疫和标准发病率的流行病模型的均匀持续性新分析方法

IF 0.9 4区数学

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-05-02 DOI: 10.1007/s10255-023-1078-y

Song-bai Guo, Yu-ling Xue, Xi-liang Li, Zuo-huan Zheng

引用次数: 0