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New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications 复合瑞利分布的新概化：基于渐进式ii型滤波方案的不同估计方法及其应用
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-03-28 DOI: 10.21136/AM.2025.0078-24
Omid Shojaee, Reza Azimi
{"title":"New generalization of compound Rayleigh distribution: Different estimation methods based on progressive type-II censoring schemes and applications","authors":"Omid Shojaee,&nbsp;Reza Azimi","doi":"10.21136/AM.2025.0078-24","DOIUrl":"10.21136/AM.2025.0078-24","url":null,"abstract":"<div><p>Fitting a suitable distribution to the data from a real experiment is a crucial topic in statistics. However, many of the existing distributions cannot account for the effect of environmental conditions on the components under test. Moreover, the components are usually heterogeneous, meaning that they do not share the same distribution. In this article, we aim to obtain a new generalization of the Compound Rayleigh distribution by using mixture models and incorporating the environmental conditions on the components. The new distribution is expected to be a flexible distribution that encompasses some other distributions as special cases. We will also examine the properties and aging criteria of the new distribution. Over the past decades, various methods to estimate the unknown parameters of a statistical distribution have been proposed from the availability of type-II censored data. Thus, we estimate the parameters of the proposed distribution in the presence of type-II censored data using a Monte Carlo simulation study and real data analysis with maximum likelihood, maximum product of spacings, and Bayesian methods. Finally, different methods are compared by calculating the mean square error (MSE) of the resulting estimators.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 2","pages":"231 - 256"},"PeriodicalIF":0.7,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169926","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 well-posedness of solutions to 2D magnetic Prandtl model in the Prandtl-Hartmann regime 二维磁性Prandtl模型在Prandtl- hartmann区域解的局部适定性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-03-26 DOI: 10.21136/AM.2025.0062-24
Yuming Qin, Xiuqing Wang, Junchen Liu
{"title":"Local well-posedness of solutions to 2D magnetic Prandtl model in the Prandtl-Hartmann regime","authors":"Yuming Qin,&nbsp;Xiuqing Wang,&nbsp;Junchen Liu","doi":"10.21136/AM.2025.0062-24","DOIUrl":"10.21136/AM.2025.0062-24","url":null,"abstract":"<div><p>We consider the 2D magnetic Prandtl equation in the Prandtl-Hartmann regime in a periodic domain and prove the local existence and uniqueness of solutions by energy methods in a polynomial weighted Sobolev space. On the one hand, we have noted that the <i>x</i>-derivative of the pressure <i>P</i> plays a key role in all known results on the existence and uniqueness of solutions to the Prandtl-Hartmann regime equations, in which the case of favorable <i>P</i> (<i>∂</i><sub><i>x</i></sub><i>P</i> &lt; 0) or the case of <i>∂</i><sub><i>x</i></sub><i>P</i> = 0 (led by constant outer flow <i>U</i> = constant) was only considered. While in this paper, we have no restriction on the sign of <i>∂</i><sub><i>x</i></sub><i>P</i>, which has generalized all previous results and definitely gives rise to a difficulty in mathematical treatments. To overcome this difficulty, we shall use the skill of cancellation mechanism which is valid under the monotonicity assumption. One the other hand, we consider the general outer flow <i>U</i> ≠ constant, leading to the boundary data at <i>y</i> = 0 being much more complicated. To deal with these boundary data, some more delicate estimates and mathematical induction method will be used. Therefore, our result also provides an extension of earlier studies by addressing the challenges arising from general outer flow.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 2","pages":"169 - 202"},"PeriodicalIF":0.7,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170287","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
Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems 非线性全耦合准静态热孔弹性问题的对称内罚不连续Galerkin方法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2025-02-19 DOI: 10.21136/AM.2025.0197-24
Fan Chen, Ming Cui, Chenguang Zhou
{"title":"Symmetric interior penalty discontinuous Galerkin method for nonlinear fully coupled quasi-static thermo-poroelasticity problems","authors":"Fan Chen,&nbsp;Ming Cui,&nbsp;Chenguang Zhou","doi":"10.21136/AM.2025.0197-24","DOIUrl":"10.21136/AM.2025.0197-24","url":null,"abstract":"<div><p>We propose a symmetric interior penalty discontinuous Galerkin (DG) method for nonlinear fully coupled quasi-static thermo-poroelasticity problems. Firstly, a fully implicit nonlinear discrete scheme is constructed by adopting the DG method for the spatial approximation and the backward Euler method for the temporal discretization. Subsequently, the existence and uniqueness of the solution of the numerical scheme is proved, and then we derive the a priori error estimate for the three variables, i.e., the displacement, the pressure and the temperature. Lastly, we carry out numerical experiments to confirm the theoretical findings of our suggested approach.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"97 - 123"},"PeriodicalIF":0.6,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594615","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-step Ulm-Chebyshev-like method for inverse singular value problems with multiple singular values 多奇异值反奇异值问题的两步ulm - chebyshevlike方法
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2025-02-18 DOI: 10.21136/AM.2025.0237-24
Wei Ma, Yuqing Zhu, Yawei Dang
{"title":"Two-step Ulm-Chebyshev-like method for inverse singular value problems with multiple singular values","authors":"Wei Ma,&nbsp;Yuqing Zhu,&nbsp;Yawei Dang","doi":"10.21136/AM.2025.0237-24","DOIUrl":"10.21136/AM.2025.0237-24","url":null,"abstract":"<div><p>We study the convergence of two-step Ulm-Chebyshev-like method for solving the inverse singular value problems. We focus on the case when the given singular values are positive and multiple. This work extends the result of W. Ma (2022). We show that the new method is cubically convergent. Moreover, numerical experiments are given in the last section, which show that the proposed method is practical and efficient.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"65 - 95"},"PeriodicalIF":0.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594503","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 Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point 周期振荡悬点自由阻尼摆平衡的Lyapunov稳定性/不稳定性
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2025-02-03 DOI: 10.21136/AM.2025.0206-24
Jiří Šremr
{"title":"On Lyapunov stability/instability of equilibria of free damped pendulum with periodically oscillating suspension point","authors":"Jiří Šremr","doi":"10.21136/AM.2025.0206-24","DOIUrl":"10.21136/AM.2025.0206-24","url":null,"abstract":"<div><p>We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green’s functions of the periodic boundary value problems for linearized equations. Furthermore, we show that if both lower and upper equilibria are stable, then the pendulum considered may possess a periodic motion that corresponds to the “quasistatic solution” of Bogolyubov as well as to the “quasistatic balance” of Kapitza.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"11 - 45"},"PeriodicalIF":0.6,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594577","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 multipoint constraints in FETI methods FETI方法中的多点约束
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2025-01-26 DOI: 10.21136/AM.2025.0114-24
Pavla Hrušková, Zdeněk Dostál, Oldřich Vlach, Petr Vodstrčil
{"title":"On multipoint constraints in FETI methods","authors":"Pavla Hrušková,&nbsp;Zdeněk Dostál,&nbsp;Oldřich Vlach,&nbsp;Petr Vodstrčil","doi":"10.21136/AM.2025.0114-24","DOIUrl":"10.21136/AM.2025.0114-24","url":null,"abstract":"<div><p>FETI (finite element tearing and interconnecting) based domain decomposition methods are well-established massively parallel methods for solving huge linear systems arising from discretizing partial differential equations. The first steps of FETI decompose the domain into nonoverlapping subdomains, discretize the subdomains using matching grids, and interconnect the adjacent variables by multipoint constraints. However, the multipoint constraints enforcing identification of the corners’ variables do not have a unique representation and their proper choice and modification can improve the performance of FETI. Here, we briefly review the main options, including orthogonal, fully redundant, or localized constraints, and use the basic linear algebra and spectral graph theory to examine the quantitative effect of their choice on the effective control of the feasibility error and rate of convergence of FETI.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"47 - 64"},"PeriodicalIF":0.6,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2025.0114-24.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594758","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
A note on the shift theorem for the Laplacian in polygonal domains 关于多边形域拉普拉斯变换定理的注解
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2024-12-11 DOI: 10.21136/AM.2024.0049-24
Jens Markus Melenk, Claudio Rojik
{"title":"A note on the shift theorem for the Laplacian in polygonal domains","authors":"Jens Markus Melenk,&nbsp;Claudio Rojik","doi":"10.21136/AM.2024.0049-24","DOIUrl":"10.21136/AM.2024.0049-24","url":null,"abstract":"<div><p>We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 5","pages":"653 - 693"},"PeriodicalIF":0.7,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.21136/AM.2024.0049-24.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121608","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
Theoretical analysis for ℓ1-ℓ2 minimization with partial support information 具有部分支持信息的1- 2最小化的理论分析
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-11-26 DOI: 10.21136/AM.2024.0068-24
Haifeng Li, Leiyan Guo
{"title":"Theoretical analysis for ℓ1-ℓ2 minimization with partial support information","authors":"Haifeng Li,&nbsp;Leiyan Guo","doi":"10.21136/AM.2024.0068-24","DOIUrl":"10.21136/AM.2024.0068-24","url":null,"abstract":"<div><p>We investigate the recovery of <i>k</i>-sparse signals using the <i>ℓ</i><sub>1</sub>-<i>ℓ</i><sub>2</sub> minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume <i>k</i>-sparse signals <b>x</b> with the prior support <i>T</i> which is composed of <i>g</i> true indices and <i>b</i> wrong indices, i.e., ∣<i>T</i>∣ = <i>g+b</i> ⩽ <i>k</i>. First, we derive a new condition based on RIP of order 2<i>α</i> (<i>α = k − g</i>) to guarantee signal recovery via <i>ℓ</i><sub>1</sub>-<i>ℓ</i><sub>2</sub> minimization with partial support information. Second, we also derive the high order RIP with <i>tα</i> for some <i>t</i> ⩾ 3 to guarantee signal recovery via <i>ℓ</i><sub>1</sub>-<i>ℓ</i><sub>2</sub> minimization with partial support information.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"125 - 148"},"PeriodicalIF":0.6,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594759","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
Conforming simplicial partitions of product-decomposed polytopes 积分解多面体的一致性简单划分
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-11-17 DOI: 10.21136/AM.2024.0163-24
Sergey Korotov, Jon Eivind Vatne
{"title":"Conforming simplicial partitions of product-decomposed polytopes","authors":"Sergey Korotov,&nbsp;Jon Eivind Vatne","doi":"10.21136/AM.2024.0163-24","DOIUrl":"10.21136/AM.2024.0163-24","url":null,"abstract":"<div><p>We propose some approaches for the generation of conforming simplicial partitions with various regularity properties for polytopic domains that are products or a union of products, thus generalizing our earlier results. The techniques presented can be used for finite element simulations of higher-dimensional problems.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 1","pages":"1 - 10"},"PeriodicalIF":0.6,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594820","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 self-scaling memoryless BFGS based conjugate gradient method using multi-step secant condition for unconstrained minimization 基于共轭梯度法的无记忆自缩放 BFGS，利用多步秒条件实现无约束最小化
IF 0.6 4区 数学
Applications of Mathematics Pub Date : 2024-11-15 DOI: 10.21136/AM.2024.0204-23
Yongjin Kim, Yunchol Jong, Yong Kim
{"title":"A self-scaling memoryless BFGS based conjugate gradient method using multi-step secant condition for unconstrained minimization","authors":"Yongjin Kim,&nbsp;Yunchol Jong,&nbsp;Yong Kim","doi":"10.21136/AM.2024.0204-23","DOIUrl":"10.21136/AM.2024.0204-23","url":null,"abstract":"<div><p>Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. Based on the self-scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (SSML-BFGS) method, new conjugate gradient algorithms CG-DESCENT and CGOPT have been proposed by W. Hager, H. Zhang (2005) and Y. Dai, C. Kou (2013), respectively. It is noted that the two conjugate gradient methods perform more efficiently than the SSML-BFGS method. Therefore, C. Kou, Y. Dai (2015) proposed some suitable modifications of the SSML-BFGS method such that the sufficient descent condition holds. For the sake of improvement of modified SSML-BFGS method, in this paper, we present an efficient SSML-BFGS-type three-term conjugate gradient method for solving unconstrained minimization using Ford-Moghrabi secant equation instead of the usual secant equations. The method is shown to be globally convergent under certain assumptions. Numerical results compared with methods using the usual secant equations are reported.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"847 - 866"},"PeriodicalIF":0.6,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845068","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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