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Large Deviations for the LS Estimator in Nonlinear Regression Model under Sub-linear Expectations 亚线性期望下非线性回归模型LS估计量的大偏差
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-026-0015-3
Yi Wu, Xue-jun Wang, Li-xin Zhang
{"title":"Large Deviations for the LS Estimator in Nonlinear Regression Model under Sub-linear Expectations","authors":"Yi Wu,&nbsp;Xue-jun Wang,&nbsp;Li-xin Zhang","doi":"10.1007/s10255-026-0015-3","DOIUrl":"10.1007/s10255-026-0015-3","url":null,"abstract":"<div><p>In this paper, we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations. The large deviation results for the estimator are established under some general conditions. As applications, the results on weak consistency and strong consistency are obtained under the meaning of capacity. A simulation study is also presented to verify the validity of the theoretical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"474 - 488"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579592","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
A Note on the Liouville Type Theorem for the Steady-state Magnetohydrodynamic Equations 关于稳态磁流体动力学方程的Liouville型定理的注记
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-026-0022-4
Hui-ying Fan, Meng Wang
{"title":"A Note on the Liouville Type Theorem for the Steady-state Magnetohydrodynamic Equations","authors":"Hui-ying Fan,&nbsp;Meng Wang","doi":"10.1007/s10255-026-0022-4","DOIUrl":"10.1007/s10255-026-0022-4","url":null,"abstract":"<div><p>In this paper, we are concentrated on demonstrating the Liouville type theorem for the stationary incompressible Magnetohydrodynamic equations in the whole space, the half-space, or a periodic slab, and presenting the solution must vanish under the condition that for some 0 ≤ <i>δ</i> ≤ 1 &lt; <i>L</i> and <span>(q = {{6({3 - delta})} over {6 - delta}},mathop {lim ,inf}limits_{R to infty} {1 over R}Vert{({{bf{u}},{bf{h}}})}Vert_{R &lt; vert x vert &lt; LR}^{3 - delta} = 0)</span>. We also deduce sufficient conditions by allowing shrinking ratio <i>L</i> = 1 + <i>R</i><sup>−<i>α</i></sup>. When in slab with zero boundary condition, stronger decay rate is needed. We do not assume the global bound of the velocity field u and the magnetic field h and investigate the Liouville type theorems by the conditions lim inf rather than lim.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"450 - 461"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-026-0022-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Patterns of Emergent Nonlinear Waves in an Initial Discontinuity Problem of the Bad Jaulent-Miodek Equation Bad Jaulent-Miodek方程初始不连续问题中涌现非线性波的模式
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-024-1142-3
Ya-qing Liu, Bo-ling Guo, Deng-shan Wang
{"title":"Patterns of Emergent Nonlinear Waves in an Initial Discontinuity Problem of the Bad Jaulent-Miodek Equation","authors":"Ya-qing Liu,&nbsp;Bo-ling Guo,&nbsp;Deng-shan Wang","doi":"10.1007/s10255-024-1142-3","DOIUrl":"10.1007/s10255-024-1142-3","url":null,"abstract":"<div><p>By means of the Whitham modulation theory, this paper studies the discontinuous initial value problem of the bad Jaulent-Miodek (JM) equation, which is compared with the good JM equation. The linear stability of the good and bad JM equations is analyzed to show the difference between the two equations. Also the physical significance of the JM equations is discussed by considering the reduction of the Euler’s equation. Then the zero-, one-, two-phase periodic solutions and the corresponding Whitham equations in the framework of the bad JM equation are derived by finite-gap integration approach. The degeneration of the one-phase periodic solution along with the genus-one Whitham equation are analyzed by taking the two sides limits of the modulus <i>m</i> of the Jacobi elliptic functions. The basic rarefaction wave patterns and dispersive shock wave patterns are proposed analytically and graphically, and then the complete classification of solutions and the all possible waveforms evolving from discontinuous initial values in the bad JM equation are established. In the results, various patterns of emergent nonlinear waves that appear to be new and are being detected for the first time</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"582 - 607"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579598","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
On the Some Nonlinear Boundary Value Problems of Type Vibration in Sobolev Spaces with Variable Exponents 变指数Sobolev空间型振动的非线性边值问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-026-0089-y
Fouzia Bouzeghaya, Boubakeur Merouani
{"title":"On the Some Nonlinear Boundary Value Problems of Type Vibration in Sobolev Spaces with Variable Exponents","authors":"Fouzia Bouzeghaya,&nbsp;Boubakeur Merouani","doi":"10.1007/s10255-026-0089-y","DOIUrl":"10.1007/s10255-026-0089-y","url":null,"abstract":"<div><p>In this work, we investigate a class of nonlinear boundary value problems within the framework of Sobolev spaces with variable exponents. After establishing precise formulations of these problems, we reformulate them as nonlinear hyperbolic-type equations. For each of the six problems considered, we establish both existence and uniqueness results. Furthermore, we address the associated stationary problems and prove the existence of solutions by applying a suitable variant of Brouwer’s fixed-point theorem.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"353 - 370"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579595","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
Equilibrium Joining Strategies of Retrial Queueing Systems with Two-phase Service and Priority-purchasing 具有两阶段服务和优先级购买的重审排队系统的均衡加入策略
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-024-1064-0
Fan Xu, Rui-ling Tian, Qi Shao
{"title":"Equilibrium Joining Strategies of Retrial Queueing Systems with Two-phase Service and Priority-purchasing","authors":"Fan Xu,&nbsp;Rui-ling Tian,&nbsp;Qi Shao","doi":"10.1007/s10255-024-1064-0","DOIUrl":"10.1007/s10255-024-1064-0","url":null,"abstract":"<div><p>This paper considers the customer’s equilibrium joining-balking behavior in a retrial queue with two-phase service and priority-purchasing. If the arriving customer finds the server busy, the customer can make three choices (joining the orbit, purchasing the priority or balking) based on different levels of the system information. We consider two cases: the partially observable case and the fully unobservable case. The customer’s equilibrium strategy for the partially observable case and the fully unobservable case are derived. Then, an algorithm is developed to solve the optimal fee that maximizes the service provider’s profit. Finally, the influence of system parameters on performance measures, equilibrium joining strategies and the service provider’s profits is illustrated by numerical examples.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"489 - 511"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579593","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
Existence of Multiple Normalized Solutions for Schrödinger-Choquard Equation with Mixed Nonlinearities 混合非线性Schrödinger-Choquard方程多个归一化解的存在性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-024-1086-7
Li-qin Tang, Li Wang, Jun Wang
{"title":"Existence of Multiple Normalized Solutions for Schrödinger-Choquard Equation with Mixed Nonlinearities","authors":"Li-qin Tang,&nbsp;Li Wang,&nbsp;Jun Wang","doi":"10.1007/s10255-024-1086-7","DOIUrl":"10.1007/s10255-024-1086-7","url":null,"abstract":"<div><p>This paper considers the existence of multiple normalized solutions of the following Schrödinger-Choquard equation </p><div><div><span>$$begin{cases}- Delta u = lambda u + k(varepsilon x),(I_{alpha} * |u|^{q}),|u|^{q-2}u + mu (I_{alpha} * |u|^{p}),|u|^{p-2}u, quad x in mathbb{R}^N, displaystyle int_{mathbb{R}^N} |u|^2 , dx = c^2, qquadqquadqquadqquadqquadqquadqquadqquadqquadqquad x in mathbb{R}^N.end{cases}$$</span></div></div><p> where <i>c, ε, μ</i> &gt; 0, <i>N</i> ≥ 3, <i>α</i>, ∈ (0; <i>N</i>), <span>({{N + alpha} over N} &lt; q &lt; 1 + {{alpha + 2} over N} &lt; p le {{N + alpha } over {N - 2}})</span>, λ ∈ ℝ is a Lagrange multiplier which is unknown, <i>I</i><sub><i>α</i></sub> is the Riesz potential, <i>k</i>:ℝ<sup><i>N</i></sup> → [0; ∞) is a continuous and positive function. When <i>ε</i> is small enough, we prove that the numbers of normalized solutions are at least the numbers of global maximum points of <i>k</i> by Ekeland’s variational principle and truncated skill.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"531 - 551"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579594","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
Local and Parallel Finite Element Algorithms Based on Two-grid Discretizations for the Unsteady MHD Equations with Low Electromagnetic Reynolds Number 低电磁雷诺数非定常MHD方程的两网格离散化局部和并行有限元算法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-04-01 DOI: 10.1007/s10255-024-1085-8
Shi-lin Mi, Guang-zhi Du, Yao Rong, Li-yun Zuo
{"title":"Local and Parallel Finite Element Algorithms Based on Two-grid Discretizations for the Unsteady MHD Equations with Low Electromagnetic Reynolds Number","authors":"Shi-lin Mi,&nbsp;Guang-zhi Du,&nbsp;Yao Rong,&nbsp;Li-yun Zuo","doi":"10.1007/s10255-024-1085-8","DOIUrl":"10.1007/s10255-024-1085-8","url":null,"abstract":"<div><p>This paper mainly presents and studies some local and parallel finite element methods for the unsteady magnetohydrodynamic equations with low electromagnetic Reynolds number. Firstly, both the semi discrete and fully discrete local algorithms are provided and investigated, and the theoretical tool crucial to the analysis of the fully discrete local algorithm is obtained. Subsequently, we generalize the fully discrete local algorithm to the fully discrete parallel algorithm. At the end, some numerical experiments are provided to validate the effectiveness and efficiency of our algorithms.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"512 - 530"},"PeriodicalIF":0.9,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579597","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
Fast Algorithm for Toeplitz Matrix Recovery via a Hybrid Thresholding Operator 基于混合阈值算子的Toeplitz矩阵快速恢复算法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-03-10 DOI: 10.1007/s10255-026-0024-2
Chuanlong Wang, Jie Guo
{"title":"Fast Algorithm for Toeplitz Matrix Recovery via a Hybrid Thresholding Operator","authors":"Chuanlong Wang,&nbsp;Jie Guo","doi":"10.1007/s10255-026-0024-2","DOIUrl":"10.1007/s10255-026-0024-2","url":null,"abstract":"<div><p>In this paper, an efficient algorithm is proposed for Toeplitz matrix recovery via hybrid thresholding operator. The algorithm is based on the mean-value augmented Lagrangian multiplier algorithm and the singular values are processed by hybrid singular value threshold operator. The new algorithm ensures that the matrix generated by the iteration has a Toeplitz structure, which reduces the calculation time and obtains a more accurate Toeplitz matrix. The convergence of the new algorithm is discussed under certain assumptions. Numerical experiments show that the new algorithm achieves lower CPU time than the mean-value augmented Lagrangian multiplier algorithm, smooth augmented Lagrangian multiplier algorithm, and augmented Lagrangian multiplier algorithm.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"436 - 449"},"PeriodicalIF":0.9,"publicationDate":"2026-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579397","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
Stationary Distribution of a Stochastic Hybrid Model with Fear: a Markov Semigroup Theory 具有恐惧的随机混合模型的平稳分布：一个马尔可夫半群理论
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-01-29 DOI: 10.1007/s10255-026-0008-2
Hao-kun Qi, Bing Liu, Shi Li
{"title":"Stationary Distribution of a Stochastic Hybrid Model with Fear: a Markov Semigroup Theory","authors":"Hao-kun Qi,&nbsp;Bing Liu,&nbsp;Shi Li","doi":"10.1007/s10255-026-0008-2","DOIUrl":"10.1007/s10255-026-0008-2","url":null,"abstract":"<div><p>In this paper, we investigate the stationary distribution of a novel stochastic hybrid predator-prey model with fear effect and Beddington-DeAngelis functional response. Based on Markov semigroup theory, the existence of asymptotically stable stationary distribution of stochastic hybrid system is established, which can converge in <i>L</i><sup>1</sup> to an invariant density under appropriate conditions. Moreover, we derive sufficient conditions for extinction and persistence of prey and predator populations in the stochastic hybrid model.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"337 - 352"},"PeriodicalIF":0.9,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579549","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
The Sequential Search Algorithm to Solve Airplane Refueling Problem 求解飞机加油问题的顺序搜索算法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2026-01-29 DOI: 10.1007/s10255-026-0020-6
Jin-chuan Cui, Xiao-ya Li
{"title":"The Sequential Search Algorithm to Solve Airplane Refueling Problem","authors":"Jin-chuan Cui,&nbsp;Xiao-ya Li","doi":"10.1007/s10255-026-0020-6","DOIUrl":"10.1007/s10255-026-0020-6","url":null,"abstract":"<div><p>Airplane refueling problem is a nonlinear unconstrained optimization problem with <i>n</i>! feasible solutions. Given a fleet of <i>n</i> airplanes with mid-air refueling technique, the question is to find the best refueling policy to make the last remaining airplane travel the farthest. At first, we proposed the definition of sequential feasible solution. We proved that if an airplane refueling instance has feasible solutions, it must have sequential feasible solutions; and the optimal feasible solution must be the optimal sequential feasible solution. We proposed the <i>sequential search algorithm</i> which aims to seek out all of the sequential feasible solutions and to search for the maximal sequential feasible solution by bubble sorting all of the sequential feasible solutions. We observed that the number of the sequential feasible solutions will change to grow at a polynomial rate when <i>n</i> is greater than an inflection point <i>N</i>. Moreover, we built an efficient computability scheme, according to which we could forecast within a polynomial time the computational complexity of the sequential search algorithm that runs on any given airplane refueling instance.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"42 2","pages":"552 - 568"},"PeriodicalIF":0.9,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579550","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
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