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Lp-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon 有限或无限时间水平线上多维斜反射 BSDE 的 Lp 解与最优切换问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1136-1
Xue-jun Shi, Qun Feng, Long Jiang
{"title":"Lp-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon","authors":"Xue-jun Shi,&nbsp;Qun Feng,&nbsp;Long Jiang","doi":"10.1007/s10255-024-1136-1","DOIUrl":"10.1007/s10255-024-1136-1","url":null,"abstract":"<div><p>In this paper, we study mulit-dimensional oblique reflected backward stochastic differential equations (RBSDEs) in a more general framework over finite or infinite time horizon, corresponding to the pricing problem for a type of real option. We prove that the equation can be solved uniquely in <i>L</i><sup><i>p</i></sup>(1 &lt; <i>p</i> ≤ 2)-space, when the generators are uniformly continuous but each component taking values independently. Furthermore, if the generator of this equation fulfills the infinite time version of Lipschitzian continuity, we can also conclude that the solution to the oblique RBSDE exists and is unique, despite the fact that the values of some generator components may affect one another.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1127 - 1146"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587789","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
Uniformity of Asymmetric Augmented Designs 不对称增强设计的均匀性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1135-2
Zhi-qing Wang, Xiang-yu Fang, Zu-jun Ou
{"title":"Uniformity of Asymmetric Augmented Designs","authors":"Zhi-qing Wang,&nbsp;Xiang-yu Fang,&nbsp;Zu-jun Ou","doi":"10.1007/s10255-024-1135-2","DOIUrl":"10.1007/s10255-024-1135-2","url":null,"abstract":"<div><p>Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering. When some additional resources or information become available after the initial design of experiment is carried out, some additional runs and/or factors may be added in the follow-up stage. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two-, three- and four-level is investigated. The uniformity of augmented designs is discussed under the wrap-around <i>L</i><sub>2</sub>-discrepancy. Some lower bounds of wrap-around <i>L</i><sub>2</sub>-discrepancy for the augmented designs are obtained, which can be used to assess uniformity of augmented design. Numerical results show that augmented designs have high efficiency, which have low discrepancy and close to the proposed lower bounds.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1025 - 1044"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587904","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 Chromatic Number of (P5, HVN)-free Graphs 无 (P5, HVN) 图形的色度数
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1029-3
Yian Xu
{"title":"The Chromatic Number of (P5, HVN)-free Graphs","authors":"Yian Xu","doi":"10.1007/s10255-024-1029-3","DOIUrl":"10.1007/s10255-024-1029-3","url":null,"abstract":"<div><p>Let <i>G</i> be a graph. We use <i>χ</i>(<i>G</i>) and <i>ω</i>(<i>G</i>) to denote the chromatic number and clique number of <i>G</i> respectively. A <i>P</i><sub>5</sub> is a path on 5 vertices, and an HVN is a <i>K</i><sub>4</sub> together with one more vertex which is adjacent to exactly two vertices of <i>K</i><sub>4</sub>. Combining with some known result, in this paper we show that if <i>G</i> is (<i>P</i><sub>5</sub>, <i>HVN</i>)-free, then <i>χ</i>(<i>G</i>) ≤ max{min{16, <i>ω</i>(<i>G</i>) + 3}, <i>ω</i>(<i>G</i>) + 1}. This upper bound is almost sharp.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1098 - 1110"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587782","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 Thickness of Some Complete Bipartite and Tripartite Graphs 一些完整二方图和三方图的厚度
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1128-1
Si-wei Hu, Yi-chao Chen
{"title":"The Thickness of Some Complete Bipartite and Tripartite Graphs","authors":"Si-wei Hu,&nbsp;Yi-chao Chen","doi":"10.1007/s10255-024-1128-1","DOIUrl":"10.1007/s10255-024-1128-1","url":null,"abstract":"<div><p>In this paper, we obtain the thickness for some complete <i>k</i>–partite graphs for <i>k</i> = 2, 3. We first compute the thickness of <i>K</i><sub><i>n,n</i>+8</sub> by giving a planar decomposition of <i>K</i><sub>4<i>k</i>−1,4<i>k</i>+7</sub> for <i>k</i> ≥ 3. Then, two planar decompositions for <i>K</i><sub>1,<i>g,g</i>(<i>g</i>−1)</sub> when <i>g</i> is even and for <span>(K_{1,g,{1over{2}}(g-1)^{2}})</span> when <i>g</i> is odd are obtained. Using a recursive construction, we also obtain the thickness for some complete tripartite graphs. The results here support the long-standing conjecture that the thickness of <i>K</i><sub><i>m,n</i></sub> is <span>(lceil {mnover{2(m+n-2)}}rceil)</span> for any positive integers <i>m, n</i>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1001 - 1014"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587903","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
Conflict-free Incidence Coloring of Outer-1-planar Graphs 外-1-平面图的无冲突入射着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1033-7
Meng-ke Qi, Xin Zhang
{"title":"Conflict-free Incidence Coloring of Outer-1-planar Graphs","authors":"Meng-ke Qi,&nbsp;Xin Zhang","doi":"10.1007/s10255-024-1033-7","DOIUrl":"10.1007/s10255-024-1033-7","url":null,"abstract":"<div><p>An incidence of a graph <i>G</i> is a vertex-edge pair (<i>v, e</i>) such that <i>v</i> is incidence with <i>e</i>. A conflict-free incidence coloring of a graph is a coloring of the incidences in such a way that two incidences (<i>u, e</i>) and (<i>v, f</i>) get distinct colors if and only if they conflict each other, i.e., (i) <i>u = v</i>, (ii) <i>uv</i> is <i>e</i> or <i>f</i>, or (iii) there is a vertex <i>w</i> such that <i>uw</i> = <i>e</i> and <i>vw</i> = <i>f</i>. The minimum number of colors used among all conflict-free incidence colorings of a graph is the conflict-free incidence chromatic number. A graph is outer-1-planar if it can be drawn in the plane so that vertices are on the outer-boundary and each edge is crossed at most once. In this paper, we show that the conflict-free incidence chromatic number of an outer-1-planar graph with maximum degree Δ is either 2Δ or 2Δ + 1 unless the graph is a cycle on three vertices, and moreover, all outer-1-planar graphs with conflict-free incidence chromatic number 2Δ or 2Δ + 1 are completely characterized. An efficient algorithm for constructing an optimal conflict-free incidence coloring of a connected outer-1-planar graph is given.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"929 - 942"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587781","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 Ananthakrishna Model Under Non-synchronous Perturbation 非同步扰动下的阿南塔克里什纳模型
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1077-8
Yi-wen Tao, Sue Ann Campbell, Jing-li Ren
{"title":"The Ananthakrishna Model Under Non-synchronous Perturbation","authors":"Yi-wen Tao,&nbsp;Sue Ann Campbell,&nbsp;Jing-li Ren","doi":"10.1007/s10255-024-1077-8","DOIUrl":"10.1007/s10255-024-1077-8","url":null,"abstract":"<div><p>The Ananthakrishna model, seeking to explain the Portevin-Le Chatelier effect, is studied with or without non-synchronous perturbations. For the unperturbed model, Bogdanov-Takens bifurcation and zero-Hopf bifurcation are detected. For the perturbed model, rich dynamical behaviors are given by researching the Poincaré map, including solutions of different periods, quasi-periodic solutions, chaotic solutions, and bistability. Moreover, an augmented temperature-dependent perturbation amplitude induces a transition from non-serrated to serrated flow on the stress-time curve. Notably, on the stress-strain curve, the phenomenon of repeated yielding diminishes with an increase in the value of a temperature-dependent parameter, while it persists with an increase in the value of a temperature-independent parameter. Sensitivity analysis sheds light on the factors exerting the most significant influence on dislocation density.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1078 - 1097"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587788","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
Backward Doubly Stochastic Differential Equations with Stochastic Non-Lipschitz Coefficients 具有随机非 Lipschitz 系数的后向双随机微分方程
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1137-0
Si-yan Xu, Yi-dong Zhang
{"title":"Backward Doubly Stochastic Differential Equations with Stochastic Non-Lipschitz Coefficients","authors":"Si-yan Xu,&nbsp;Yi-dong Zhang","doi":"10.1007/s10255-024-1137-0","DOIUrl":"10.1007/s10255-024-1137-0","url":null,"abstract":"<div><p>In this paper, we prove an existence and uniqueness theorem for backward doubly stochastic differential equations under a new kind of stochastic non-Lipschitz condition which involves stochastic and time-dependent condition. As an application, we use the result to obtain the existence of stochastic viscosity solution for some nonlinear stochastic partial differential equations under stochastic non-Lipschitz conditions.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"908 - 928"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587901","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
Lp Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators 具有一个连续障碍和准线性增长发生器的反射 BSDE 的 Lp 解法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1133-4
Sheng-jun Fan
{"title":"Lp Solution of Reflected BSDEs with One Continuous Barrier and Quasi-linear Growth Generators","authors":"Sheng-jun Fan","doi":"10.1007/s10255-024-1133-4","DOIUrl":"10.1007/s10255-024-1133-4","url":null,"abstract":"<div><p>This paper is devoted to solving a reflected backward stochastic differential equation (BSDE in short) with one continuous barrier and a quasi-linear growth generator <i>g</i>, which has a linear growth in (<i>y</i>, <i>z</i>), except the upper direction in case of <i>y</i> &lt; 0, and is more general than the usual linear growth generator. By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal <i>L</i><sup><i>p</i></sup> (<i>p</i> &gt; 1) solutions for the reflected BSDEs. We also prove that the minimal <i>L</i><sup><i>p</i></sup> solution can be approximated by a sequence of <i>L</i><sup><i>p</i></sup> solutions of certain reflected BSDEs with Lipschitz generators.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"943 - 953"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587906","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 Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation 不可压缩非牛顿流体的流体-粒子系统和弗拉索夫方程的全局弱解法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1080-0
Pei-yu Zhang, Li Fang, Zhen-hua Guo
{"title":"Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation","authors":"Pei-yu Zhang,&nbsp;Li Fang,&nbsp;Zhen-hua Guo","doi":"10.1007/s10255-024-1080-0","DOIUrl":"10.1007/s10255-024-1080-0","url":null,"abstract":"<div><p>The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation. The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for <span>(pgeqslant {11over 5})</span>. The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function. The advantage of the new formulation is to control the external force term <span>(G=-int_mathbb{{R}^{d}}(mathbf{u}-mathbf{v})fdmathbf{v} (d=2,3))</span>. The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques. We further prove the uniqueness of weak solutions to the considered system.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"954 - 978"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587902","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 Initial Layer and the Limit Behavior for Chemotaxis System with the Effect of Fluid in Fourier Space 论傅立叶空间中具有流体效应的趋化系统的初始层和极限行为
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1134-3
Jian-xiang Wan, Hai-ping Zhong
{"title":"On the Initial Layer and the Limit Behavior for Chemotaxis System with the Effect of Fluid in Fourier Space","authors":"Jian-xiang Wan,&nbsp;Hai-ping Zhong","doi":"10.1007/s10255-024-1134-3","DOIUrl":"10.1007/s10255-024-1134-3","url":null,"abstract":"<div><p>The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid </p><div><div><span>$$left{ {matrix{ {u_t^varepsilon + {u^varepsilon } cdot nabla {u^varepsilon } - Delta {u^varepsilon } + nabla {{rm{P}}^varepsilon } = {n^varepsilon }nabla {c^varepsilon },} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {nabla cdot {u^varepsilon } = 0,} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {n_t^varepsilon + {u^varepsilon } cdot nabla {n^varepsilon } - Delta {n^varepsilon } = - nabla cdot left( {{n^varepsilon }nabla {c^varepsilon }} right),} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {{1 over varepsilon }c_t^varepsilon - Delta {c^varepsilon } = {n^varepsilon },} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d} times left( {0,infty } right),} hfill cr {left( {{u^varepsilon },{n^varepsilon },{c^varepsilon }} right){|_{t = 0}} = left( {{u_0},{n_0},{c_0}} right),} hfill &amp; {{rm{in}}} hfill &amp; {{mathbb{R}^d},} hfill cr } } right.$$</span></div></div><p> where <i>d</i> ≥ 2. It is known that for each <i>ϵ</i> &gt; 0 and all sufficiently small initial data (<i>u</i><sub>0</sub>, <i>n</i><sub>0</sub>, <i>c</i><sub>0</sub>) belongs to certain Fourier space, the problem possesses a unique global solution (<i>u</i><sup><i>ϵ</i></sup>, <i>n</i><sup><i>ϵ</i></sup>, <i>c</i><sup><i>ϵ</i></sup>) in Fourier space. The present work asserts that these solutions stabilize to (<i>u</i><sup>∞</sup>, <i>n</i><sup>∞</sup>, <i>c</i><sup>∞</sup>) as <i>ϵ</i><sup>−1</sup> → 0. Moreover, we show that <i>c</i><sup><i>ϵ</i></sup>(<i>t</i>) has the initial layer as <i>ϵ</i><sup>−1</sup> → 0. As one expects its limit behavior maybe give a new viewlook to understand the system.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1015 - 1024"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-024-1134-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587905","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
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