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Incidence Coloring of Outer-1-planar Graphs 外-1-平面图的入射着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1126-3
Meng-ke Qi, Xin Zhang
{"title":"Incidence Coloring of Outer-1-planar Graphs","authors":"Meng-ke Qi,&nbsp;Xin Zhang","doi":"10.1007/s10255-024-1126-3","DOIUrl":"10.1007/s10255-024-1126-3","url":null,"abstract":"<div><p>A graph is outer-1-planar if it can be drawn in the plane so that all vertices lie on the outer-face and each edge crosses at most one another edge. It is known that every outer-1-planar graph is a planar partial 3-tree. In this paper, we conjecture that every planar graph <i>G</i> has a proper incidence (Δ(<i>G</i>) + 2)-coloring and confirm it for outer-1-planar graphs with maximum degree at least 8 or with girth at least 4. Specifically, we prove that every outer-1-planar graph <i>G</i> has an incidence (Δ(<i>G</i>) + 3, 2)-coloring, and every outer-1-planar graph <i>G</i> with maximum degree at least 8 or with girth at least 4 has an incidence (Δ(<i>G</i>) + 2, 2)-coloring.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"840 - 848"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256357","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
Barrier Option Pricing in Regime Switching Models with Rebates 有回扣的制度转换模型中的障碍期权定价
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1053-3
Yue-xu Zhao, Jia-yong Bao
{"title":"Barrier Option Pricing in Regime Switching Models with Rebates","authors":"Yue-xu Zhao,&nbsp;Jia-yong Bao","doi":"10.1007/s10255-024-1053-3","DOIUrl":"10.1007/s10255-024-1053-3","url":null,"abstract":"<div><p>This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific rebates. The integral formulas of the rebates are derived via matrix Wiener-Hopf factorizations and Fourier transform techniques, also, the integral representations of the option prices are constructed. Moreover, the first-passage time density functions in two-state regime model are derived. As applications, several numerical algorithms and numerical examples are presented.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"849 - 861"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256262","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
Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem: without Solitons 具有衰减初值问题的反向时空非局部广达方程的长时渐近线：无孤子
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1121-8
Wei-qi Peng, Yong Chen
{"title":"Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem: without Solitons","authors":"Wei-qi Peng,&nbsp;Yong Chen","doi":"10.1007/s10255-024-1121-8","DOIUrl":"10.1007/s10255-024-1121-8","url":null,"abstract":"<div><p>In this work, we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector. Start from the Lax pair, we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation. Furthermore, using the approach of Deift-Zhou nonlinear steepest descent, the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived. For the reverse space-time nonlocal Hirota equation, since the symmetries of its scattering matrix are different with the local Hirota equation, the <i>ϑ</i>(<i>λ</i><sub><i>i</i></sub>) (<i>i</i> = 0, 1) would like to be imaginary, which results in the <span>(delta _{{{rm{lambda}}_i}}^0)</span> contains an increasing <span>(t{{pm ,Imvartheta ({{rm{lambda}}_i})} over 2})</span>, and then the asymptotic behavior for nonlocal Hirota equation becomes differently.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"708 - 727"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256245","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
Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem 一类准线性椭圆问题的无限多解
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1091-x
Xiao-yao Jia, Zhen-luo Lou
{"title":"Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem","authors":"Xiao-yao Jia,&nbsp;Zhen-luo Lou","doi":"10.1007/s10255-024-1091-x","DOIUrl":"10.1007/s10255-024-1091-x","url":null,"abstract":"<div><p>In this paper, we study the following quasi-linear elliptic equation</p><div><div><span>$$left{{matrix{{- ,{rm{div(}}phi {rm{(}}left| {nabla u} right|{rm{)}}nabla u{rm{) = lambda}}psi {rm{(}}left| u right|{rm{)}}u + ,varphi {rm{(}}left| u right|{rm{)}}u,,,,,{rm{in}},,,Omega,,,,} cr {u = 0,,,,,,,,{rm{on}},,partial Omega {rm{,}},,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,} cr}} right.$$</span></div></div><p>where Ω ⊂ ℝ<sup><i>N</i></sup> is a bounded domain, λ &gt; 0 is a parameter. The function <i>ψ</i>(∣<i>t</i>∣)<i>t</i> is the subcritical term, and <i>ϕ</i>(∣<i>t</i>∣)<i>t</i> is the critical Orlicz-Sobolev growth term with respect to <i>φ</i>. Under appropriate conditions on <i>φ</i>, <i>ψ</i> and <i>ϕ</i>, we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation, for <i>λ</i> ∈ (0, <i>λ</i><sub>0</sub>), where <i>λ</i><sub>0</sub> &gt; 0 is a fixed constant.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"728 - 743"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256449","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
Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator 具有多项式换向器的六度均匀等时中心系统的全局相位特征
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1081-z
Li-na Guo, Ai-yong Chen, Shuai-feng Zhao
{"title":"Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator","authors":"Li-na Guo,&nbsp;Ai-yong Chen,&nbsp;Shuai-feng Zhao","doi":"10.1007/s10255-024-1081-z","DOIUrl":"10.1007/s10255-024-1081-z","url":null,"abstract":"<div><p>This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator. Such systems have the form <span>(dot x = - y + xf(x,,y),,,dot y = x + yf(x,,y))</span>, where <i>f</i>(<i>x, y</i>) = <i>a</i><sub>1</sub><i>x</i> + <i>a</i><sub>2</sub><i>xy</i> + <i>a</i><sub>3</sub><i>xy</i><sup>2</sup> + <i>a</i><sub>4</sub><i>xy</i><sup>3</sup> + <i>a</i><sub>5</sub><i>xy</i><sup>4</sup> = <i>xσ</i>(<i>y</i>), and any zero of 1 + <i>a</i><sub>1</sub><i>y</i> + <i>a</i><sub>2</sub><i>y</i><sup>2</sup> + <i>a</i><sub>3</sub><i>y</i><sup>3</sup> + <i>a</i><sub>4</sub><i>y</i><sup>4</sup> + <i>a</i><sub>5</sub><i>y</i><sup>5</sup>, <span>(y = bar y)</span> is an invariant straight line. At last, all global phase portraits are drawn on the Poincaré disk.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"577 - 599"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-024-1081-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256036","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
Derivation of Expanded Isospectral-Nonisospectral Integrable Hierarchies via the Column-vector Loop Algebra 通过柱向量环代数推导扩展等谱-非等谱可积分层次结构
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1047-1
Hai-feng Wang, Yu-feng Zhang
{"title":"Derivation of Expanded Isospectral-Nonisospectral Integrable Hierarchies via the Column-vector Loop Algebra","authors":"Hai-feng Wang,&nbsp;Yu-feng Zhang","doi":"10.1007/s10255-024-1047-1","DOIUrl":"10.1007/s10255-024-1047-1","url":null,"abstract":"<div><p>A scheme for generating nonisospectral integrable hierarchies is introduced. Based on the method, we deduce a nonisospectral hierarchy of soliton equations by considering a linear spectral problem. It follows that the corresponding expanded isospectral and nonisospectral integrable hierarchies are deduced based on a 6 dimensional complex linear space <span>(widetilde{mathbb{C}}^{6})</span>. By reducing these integrable hierarchies, we obtain the expanded isospectral and nonisospectral derivative nonlinear Schrödinger equation. By using the trace identity, the bi-Hamiltonian structure of these two hierarchies are also obtained. Moreover, some symmetries and conserved quantities of the resulting hierarchy are discussed.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"778 - 800"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256096","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 Degree Condition for Graphs Having All (a, b)-parity Factors 具有所有 (a, b) 奇偶因子的图的度条件
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1090-y
Hao-dong Liu, Hong-liang Lu
{"title":"A Degree Condition for Graphs Having All (a, b)-parity Factors","authors":"Hao-dong Liu,&nbsp;Hong-liang Lu","doi":"10.1007/s10255-024-1090-y","DOIUrl":"10.1007/s10255-024-1090-y","url":null,"abstract":"<div><p>Let <i>a</i> and <i>b</i> be positive integers such that <i>a</i> ≤ <i>b</i> and <i>a</i> ≡ <i>b</i> (mod 2). We say that <i>G</i> has all (<i>a, b</i>)-parity factors if <i>G</i> has an <i>h</i>-factor for every function <i>h</i>: <i>V</i>(<i>G</i>) → {<i>a, a</i> + 2, ⋯, <i>b</i> − 2, <i>b</i>} with <i>b</i>∣<i>V</i>(<i>G</i>)∣ even and <i>h</i>(<i>v</i>) ≡ <i>b</i> (mod 2) for all <i>v</i> ∈ <i>V</i>(<i>G</i>). In this paper, we prove that every graph <i>G</i> with <i>n</i> ≥ 2(<i>b</i> + 1)(<i>a</i> + <i>b</i>) vertices has all (<i>a, b</i>)-parity factors if <i>δ</i>(<i>G</i>) ≥ (<i>b</i><sup>2</sup> − <i>b</i>)/<i>a</i>, and for any two nonadjacent vertices <span>(u,,v, in ,V,(G),,max {{d_G}(u),,{d_G}(v)} , ge {{bn} over {a + b}})</span>. Moreover, we show that this result is best possible in some sense.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"656 - 664"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256211","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 Strong Approximation for a Simple Reentrant Line in Light Traffic Under First-buffer First-served Service Discipline 论 "先缓冲先服务 "纪律下轻度交通中简单重入线的强近似值
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1093-8
Kai-ming Yang, Yong-jiang Guo
{"title":"On the Strong Approximation for a Simple Reentrant Line in Light Traffic Under First-buffer First-served Service Discipline","authors":"Kai-ming Yang,&nbsp;Yong-jiang Guo","doi":"10.1007/s10255-024-1093-8","DOIUrl":"10.1007/s10255-024-1093-8","url":null,"abstract":"<div><p>For a 2-station and 3-class reentrant line under first-buffer first-served (FBFS) service discipline in light traffic, we firstly construct the strong approximations for performance measures including the queue length, workload, busy time and idle time processes. Based on the obtained strong approximations, we use a strong approximation method to find all the law of the iterated logarithms (LILs) for the above four performance measures, which are expressed as some functions of system parameters: means and variances of interarrival and service times, and characterize the fluctuations around their fluid approximations.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"823 - 839"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256633","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
Optimal Timing of Business Conversion for Solvency Improvement 改善偿付能力的最佳业务转型时机
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1048-0
Peng Li, Ming Zhou
{"title":"Optimal Timing of Business Conversion for Solvency Improvement","authors":"Peng Li,&nbsp;Ming Zhou","doi":"10.1007/s10255-024-1048-0","DOIUrl":"10.1007/s10255-024-1048-0","url":null,"abstract":"<div><p>In this paper, we study the optimal timing to convert the risk of business for an insurance company in order to improve its solvency. The cash flow of company evolves according to a jump-diffusion process. Business conversion option offers the company an opportunity to transfer the jump risk business out. In exchange for this option, the company needs to pay both fixed and proportional transaction costs. The proportional cost can also be seen as the profit loading of the jump risk business. We formulated this problem as an optimal stopping problem. By solving this stopping problem, we find that the optimal timing of business conversion mainly depends on the profit loading of the jump risk business. A larger profit loading would make the conversion option valueless. The fixed cost, however, only delays the optimal timing of business conversion. In the end, numerical results are provided to illustrate the impacts of transaction costs and environmental parameters to the optimal strategies.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"744 - 757"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256103","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
Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations 次线性期望下加权和的强极限定理
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1127-2
Feng-xiang Feng, Ding-cheng Wang, Qun-ying Wu, Hai-wu Huang
{"title":"Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations","authors":"Feng-xiang Feng,&nbsp;Ding-cheng Wang,&nbsp;Qun-ying Wu,&nbsp;Hai-wu Huang","doi":"10.1007/s10255-024-1127-2","DOIUrl":"10.1007/s10255-024-1127-2","url":null,"abstract":"<div><p>In this article, we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations. Our results of strong limit theorems are more general than some related results previously obtained by Thrum (1987), Li et al. (1995) and Wu (2010) in classical probability space.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 3","pages":"862 - 874"},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256192","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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