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Mathematical Model, Numerical Simulation and Convergence Analysis of a Semiconductor Device Problem with Heat and Magnetic Influences 受热和磁场影响的半导体器件问题的数学模型、数值模拟和收敛性分析
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1088-5
Chang-feng Li, Yi-rang Yuan, Huai-ling Song
{"title":"Mathematical Model, Numerical Simulation and Convergence Analysis of a Semiconductor Device Problem with Heat and Magnetic Influences","authors":"Chang-feng Li,&nbsp;Yi-rang Yuan,&nbsp;Huai-ling Song","doi":"10.1007/s10255-024-1088-5","DOIUrl":"10.1007/s10255-024-1088-5","url":null,"abstract":"<div><p>In this paper, the authors discuss a three-dimensional problem of the semiconductor device type involved its mathematical description, numerical simulation and theoretical analysis. Two important factors, heat and magnetic influences are involved. The mathematical model is formulated by four nonlinear partial differential equations (PDEs), determining four major physical variables. The influences of magnetic fields are supposed to be weak, and the strength is parallel to the <i>z</i>-axis. The elliptic equation is treated by a block-centered method, and the law of conservation is preserved. The computational accuracy is improved one order. Other equations are convection-dominated, thus are approximated by upwind block-centered differences. Upwind difference can eliminate numerical dispersion and nonphysical oscillation. The diffusion is approximated by the block-centered difference, while the convection term is treated by upwind approximation. Furthermore, the unknowns and adjoint functions are computed at the same time. These characters play important roles in numerical computations of conductor device problems. Using the theories of priori analysis such as energy estimates, the principle of duality and mathematical inductions, an optimal estimates result is obtained. Then a composite numerical method is shown for solving this problem.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 2","pages":"302 - 319"},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313976","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
Rainbow Pancyclicity in a Collection of Graphs Under the Dirac-type Condition 狄拉克型条件下图形集合的彩虹泛函性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI: 10.1007/s10255-024-1076-9
Lu-yi Li, Ping Li, Xue-liang Li
{"title":"Rainbow Pancyclicity in a Collection of Graphs Under the Dirac-type Condition","authors":"Lu-yi Li,&nbsp;Ping Li,&nbsp;Xue-liang Li","doi":"10.1007/s10255-024-1076-9","DOIUrl":"10.1007/s10255-024-1076-9","url":null,"abstract":"<div><p>Let <b>G</b> = {<i>G</i><sub><i>i</i></sub>: <i>i</i> ∈ [<i>n</i>]} be a collection of not necessarily distinct <i>n</i>-vertex graphs with the same vertex set <i>V</i>, where <b>G</b> can be seen as an edge-colored (multi)graph and each <i>G</i><sub><i>i</i></sub> is the set of edges with color <i>i</i>. A graph <i>F</i> on <i>V</i> is called <i>rainbow</i> if any two edges of <i>F</i> come from different <i>G</i><sub><i>i</i></sub>s’. We say that <b>G</b> is <i>rainbow pancyclic</i> if there is a rainbow cycle <i>C</i><sub>ℓ</sub> of length <i>ℓ</i> in <b>G</b> for each integer <i>ℓ</i> ∈ [3, <i>n</i>]. In 2020, Joos and Kim proved a rainbow version of Dirac’s theorem: If <span>(delta ({G_i}) ge {n over 2})</span> for each <i>i</i> ∈ [<i>n</i>], then there is a rainbow Hamiltonian cycle in <b>G</b>. In this paper, under the same condition, we show that <b>G</b> is rainbow pancyclic except that <i>n</i> is even and <b>G</b> consists of <i>n</i> copies of <span>({K_{{n over 2},{n over 2}}})</span>. This result supports the famous meta-conjecture posed by Bondy.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 2","pages":"269 - 274"},"PeriodicalIF":0.9,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140313838","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
Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups 马尔可夫-费勒半群的最终连续性与 E 特性之间的关系
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-023-1072-5
Yong Liu, Zi-yu Liu
{"title":"Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups","authors":"Yong Liu,&nbsp;Zi-yu Liu","doi":"10.1007/s10255-023-1072-5","DOIUrl":"10.1007/s10255-023-1072-5","url":null,"abstract":"<div><p>We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior, then the e-property is satis ed on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"1 - 16"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092398","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 Positive Solutions to a Fractional-Kirchhoff System 分数基尔霍夫系统正解的存在性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1111-x
Peng-fei Li, Jun-hui Xie, Dan Mu
{"title":"Existence of Positive Solutions to a Fractional-Kirchhoff System","authors":"Peng-fei Li,&nbsp;Jun-hui Xie,&nbsp;Dan Mu","doi":"10.1007/s10255-024-1111-x","DOIUrl":"10.1007/s10255-024-1111-x","url":null,"abstract":"<div><p>Let Ω be a bounded smooth domain in ℝ<sup><i>N</i></sup> (<i>N</i> ≥ 3). Assuming that 0 &lt; <i>s</i> &lt; 1, <span>(1 &lt; p,q le {{N + 2s} over {N - 2s}})</span> with <span>((p,q) ne ({{N + 2s} over {N - 2s}},{{N + 2s} over {N - 2s}}))</span>, and <i>a, b</i> &gt; 0 are constants, we consider the existence results for positive solutions of a class of fractional elliptic system below,</p><div><div><span>$$left{{matrix{{(a + b[u]_s^2){{(- Delta)}^s}u = {v^p} + {h_1}(x,u,v,nabla u,nabla v),} hfill &amp; {x in Omega,} hfill cr {{{(- Delta)}^s}v = {u^q} + {h_2}(x,u,v,nabla u,nabla v),} hfill &amp; {x in Omega,} hfill cr {u,v &gt; 0,} hfill &amp; {x in Omega,} hfill cr {u = v = 0,} hfill &amp; {x in {mathbb{R}^N}backslash Omega.} hfill cr}}right.$$</span></div></div><p>Under some assumptions of <i>h</i><sub><i>i</i></sub>(<i>x, u, v</i>, ∇<i>u</i>, ∇<i>v</i>)(<i>i</i> = 1, 2), we get a priori bounds of the positive solutions to the problem (1.1) by the blow-up methods and rescaling argument. Based on these estimates and degree theory, we establish the existence of positive solutions to problem (1.1).</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"225 - 240"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092400","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
Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model 扩散性 SIS 流行病模型中的自发感染和域的周期性演变
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1107-6
Qiang Wen, Guo-qiang Ren, Bin Liu
{"title":"Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model","authors":"Qiang Wen,&nbsp;Guo-qiang Ren,&nbsp;Bin Liu","doi":"10.1007/s10255-024-1107-6","DOIUrl":"10.1007/s10255-024-1107-6","url":null,"abstract":"<div><p>In this paper, we consider a susceptible-infective-susceptible (SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique, the uniform boundedness of solution is established. In addition, the spatial-temporal risk index <span>({{cal R}_0}(rho))</span> depending on the domain evolution rate <i>ρ</i>(<i>t</i>) as well as its analytical properties are discussed. The monotonicity of <span>({{cal R}_0}(rho))</span> with respect to the diffusion coefficients of the infected <i>d</i><sub><i>I</i></sub>, the spontaneous infection rate <i>η</i>(<i>ρ</i>(<i>t</i>)<i>y</i>) and interval length <i>L</i> is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"164 - 191"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092147","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 Pathwise Uniqueness of Solutions of One-dimensional Reflected Stochastic Differential Equations with Jumps 论有跳跃的一维反射随机微分方程解的路径唯一性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1105-8
Hua Zhang
{"title":"On the Pathwise Uniqueness of Solutions of One-dimensional Reflected Stochastic Differential Equations with Jumps","authors":"Hua Zhang","doi":"10.1007/s10255-024-1105-8","DOIUrl":"10.1007/s10255-024-1105-8","url":null,"abstract":"<div><p>In this paper, we are concerned with the problem of the pathwise uniqueness of one-dimensional reflected stochastic differential equations with jumps under the assumption of non-Lipschitz continuous coefficients whose proof are based on the technique of local time.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"149 - 163"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092407","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
Double Moving Extremes Ranked Set Sampling Design 双移动极值排序集合抽样设计
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1104-9
Meng Chen, Wang-xue Chen, Rui Yang
{"title":"Double Moving Extremes Ranked Set Sampling Design","authors":"Meng Chen,&nbsp;Wang-xue Chen,&nbsp;Rui Yang","doi":"10.1007/s10255-024-1104-9","DOIUrl":"10.1007/s10255-024-1104-9","url":null,"abstract":"<div><p>The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more e cient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more e cient than SRS for usual asymmetric distribution (exponential) for small sample sizes.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"75 - 90"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092092","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
Nonlinear Extrapolation Estimates of π π的非线性外推法估计值
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1115-6
Wen-qing Xu, Sha-sha Wang, Da-chuan Xu
{"title":"Nonlinear Extrapolation Estimates of π","authors":"Wen-qing Xu,&nbsp;Sha-sha Wang,&nbsp;Da-chuan Xu","doi":"10.1007/s10255-024-1115-6","DOIUrl":"10.1007/s10255-024-1115-6","url":null,"abstract":"<div><p>The classical Archimedean approximation of <i>π</i> uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in ℝ<sup>2</sup> and it is well-known that by using linear combinations of these basic estimates, modern extrapolation techniques can greatly speed up the approximation process. Similarly, when <i>n</i> vertices are randomly selected on the circle, the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to <i>π</i> almost surely as <i>n</i> → ∞, and by further applying extrapolation processes, faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random polygons. In this paper, we further develop nonlinear extrapolation methods for approximating <i>π</i> through certain nonlinear functions of the semiperimeter and area of such polygons. We focus on two types of extrapolation estimates of the forms <span>({{cal X}_n} = {cal S}_n^alpha {cal A}_n^beta )</span> and <span>({{cal Y}_n}(p) = {(alpha {cal S}_n^p + beta {cal A}_n^p)^{1/p}})</span> where <i>α</i> + <i>β</i> = 1, <i>p</i> ≠ 0, and <span>({{cal S}_n})</span> and <span>({{cal A}_n})</span> respectively represents the semiperimeter and area of a random <i>n</i>-gon inscribed in the unit circle in ℝ<sup>2</sup>, and <span>({{cal X}_n})</span> may be viewed as the limit of <span>({{cal Y}_n}(p))</span> when <i>p</i> → 0. By deriving probabilistic asymptotic expansions with carefully controlled error estimates for <span>({{cal X}_n})</span> and <span>({{cal Y}_n}(p))</span>, we show that the choice <i>α</i> = 4/3, <i>β</i>= −1/3 minimizes the approximation error in both cases, and their distributions are also asymptotically normal.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"91 - 108"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092099","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
Acyclic Edge Coloring of 1-planar Graphs without 4-cycles 无 4 循环的 1 平面图的无循环边着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1101-z
Wei-fan Wang, Yi-qiao Wang, Wan-shun Yang
{"title":"Acyclic Edge Coloring of 1-planar Graphs without 4-cycles","authors":"Wei-fan Wang,&nbsp;Yi-qiao Wang,&nbsp;Wan-shun Yang","doi":"10.1007/s10255-024-1101-z","DOIUrl":"10.1007/s10255-024-1101-z","url":null,"abstract":"<div><p>An acyclic edge coloring of a graph <i>G</i> is a proper edge coloring such that there are no bichromatic cycles in <i>G</i>. The acyclic chromatic index <span>(cal{X}_{alpha}^{prime}(G))</span> of <i>G</i> is the smallest <i>k</i> such that <i>G</i> has an acyclic edge coloring using <i>k</i> colors. It was conjectured that every simple graph <i>G</i> with maximum degree Δ has <span>(cal{X}_{alpha}^{prime}(G)leDelta+2)</span>. A 1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge. In this paper, we show that every 1-planar graph <i>G</i> without 4-cycles has <span>(cal{X}_{alpha}^{prime}(G)leDelta+22)</span>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 1","pages":"35 - 44"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092405","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
Clustering for Bivariate Functional Data 二元函数数据聚类
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-01-03 DOI: 10.1007/s10255-024-1116-5
Shi-yun Cao, Yan-qiu Zhou, Yan-ling Wan, Tao Zhang
{"title":"Clustering for Bivariate Functional Data","authors":"Shi-yun Cao,&nbsp;Yan-qiu Zhou,&nbsp;Yan-ling Wan,&nbsp;Tao Zhang","doi":"10.1007/s10255-024-1116-5","DOIUrl":"10.1007/s10255-024-1116-5","url":null,"abstract":"<div><p>In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The <i>k</i>-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, <i>k</i>-centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"613 - 629"},"PeriodicalIF":0.9,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139092088","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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