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Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions 一类相互作用的分支量值扩散的田中公式和局部时间
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-08 DOI: 10.1007/s10114-023-2308-2
Donald A. Dawson, Jean Vaillancourt, Hao Wang
{"title":"Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions","authors":"Donald A. Dawson, Jean Vaillancourt, Hao Wang","doi":"10.1007/s10114-023-2308-2","DOIUrl":"https://doi.org/10.1007/s10114-023-2308-2","url":null,"abstract":"<p>We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ<sup><i>d</i></sup> with <i>d</i> ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝ<sup><i>d</i></sup>, their local times exist when <i>d</i> ≤ 3. A Tanaka formula of the local time is also derived.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Proper Holomorphic Mappings between Equidimensional Hartogs Domains over Hermitian Symmetric Manifolds 论赫米对称漫域上等维哈托格域之间的适当全态映射
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-08 DOI: 10.1007/s10114-023-2054-5
En Chao Bi
{"title":"On the Proper Holomorphic Mappings between Equidimensional Hartogs Domains over Hermitian Symmetric Manifolds","authors":"En Chao Bi","doi":"10.1007/s10114-023-2054-5","DOIUrl":"https://doi.org/10.1007/s10114-023-2054-5","url":null,"abstract":"<p>In this paper, we study a family of Hartogs domains fibred over Hermitian symmetric manifolds being a unit ball in ℂ<sup><i>m</i></sup>. The aim of the present study is to establish the rigidity results about proper holomorphic mappings between two equidimensional Hartogs domains over Hermitian symmetric manifolds. In particular, we can fully determine its biholomorphic equivalence and automorphism group.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Homoclinic Solutions for a Class of Perturbed Fractional Hamiltonian Systems with Subquadratic Conditions 具有亚二次方条件的一类受扰动分式哈密顿系统的同次解法
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-08 DOI: 10.1007/s10114-023-2322-4
Ying Luo, Fei Guo, Yan Liu
{"title":"Homoclinic Solutions for a Class of Perturbed Fractional Hamiltonian Systems with Subquadratic Conditions","authors":"Ying Luo, Fei Guo, Yan Liu","doi":"10.1007/s10114-023-2322-4","DOIUrl":"https://doi.org/10.1007/s10114-023-2322-4","url":null,"abstract":"<p>In this paper, we consider the following perturbed fractional Hamiltonian systems </p><span>$$left{ {matrix{{_tD_infty ^alpha {(_{ - infty }}D_t^alpha u(t)) + L(t)u(t) = {nabla _u}W(t,u(t)) + {nabla _u}G(t,u(t)),} hfill &amp; {t in mathbb{R},} hfill cr {u in {H^alpha }(mathbb{R},{mathbb{R}^N}),} hfill &amp; {} hfill cr } } right.$$</span><p> where <span>(alpha in (1/2,1],,,L in C(mathbb{R},{mathbb{R}^{N times N}}))</span> is symmetric and not necessarily required to be positive definite, <span>(W in {C^1}(mathbb{R}times {mathbb{R}^N},mathbb{R}))</span> is locally subquadratic and locally even near the origin, and perturbed term <span>(G in {C^1}(mathbb{R} times {mathbb{R}^N},mathbb{R}))</span> maybe has no parity in <i>u</i>. Utilizing the perturbed method improved by the authors, a sequence of nontrivial homoclinic solutions is obtained, which generalizes previous results.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138574922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Boundary Regularity for k-Hessian Equations k-Hessian 方程的边界正则性
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-07 DOI: 10.1007/s10114-023-0066-9
You Li, Meng Ni Li, Yan Nan Liu
{"title":"Boundary Regularity for k-Hessian Equations","authors":"You Li,&nbsp;Meng Ni Li,&nbsp;Yan Nan Liu","doi":"10.1007/s10114-023-0066-9","DOIUrl":"10.1007/s10114-023-0066-9","url":null,"abstract":"<div><p>In this paper we focus on the boundary regularity for a class of <i>k</i>-Hessian equations which can be degenerate and (or) singular on the boundary of the domain. Motivated by the case of Monge–Ampère equations, we first construct sub-solutions, then apply the characteristic of the global Hölder continuity for convex functions, and finally use the maximum principle to obtain the boundary Hölder continuity for the solutions of the <i>k</i>-Hessian equations. However, finding such sub-solutions is very difficult due to the complexity of the <i>k</i>-Hessian operator. In particular, we employ the symmetric mean to overcome the difficulties.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
New Identities for Moore–Penrose Inverses of Some Operator Products and Their Reverse-order Laws 某些算子乘积的摩尔-彭罗斯倒数及其反阶定律的新同式
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-12-07 DOI: 10.1007/s10114-023-1645-5
Mehdi Mohammadzadeh Karizaki, Javad Farokhi-Ostad
{"title":"New Identities for Moore–Penrose Inverses of Some Operator Products and Their Reverse-order Laws","authors":"Mehdi Mohammadzadeh Karizaki,&nbsp;Javad Farokhi-Ostad","doi":"10.1007/s10114-023-1645-5","DOIUrl":"10.1007/s10114-023-1645-5","url":null,"abstract":"<div><p>We establish new identities for Moore–Penrose inverses of some operator products, and prove their associated reverse-order laws. Moreover, our results concerning the Moore–Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville’s inclusions are made into equalities.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Single Peak Solutions for a Schrödinger Equation with Variable Exponent 变指数Schrödinger方程的单峰解
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2616-6
Zhong Yuan Liu, Peng Luo, Hua Fei Xie
{"title":"Single Peak Solutions for a Schrödinger Equation with Variable Exponent","authors":"Zhong Yuan Liu,&nbsp;Peng Luo,&nbsp;Hua Fei Xie","doi":"10.1007/s10114-023-2616-6","DOIUrl":"10.1007/s10114-023-2616-6","url":null,"abstract":"<div><p>We study the following Schrödinger equation with variable exponent </p><div><div><span>$$ - Delta u + u = {u^{p + epsilon a(x)}},,,,u &gt; 0,,{rm{in}},,{mathbb{R}^N},$$</span></div></div><p> where <span>(epsilon &gt; 0,,,1 &lt; p &lt; {{N + 2} over {N - 2}},,,a(x) in {C^1}({mathbb{R}^N}) cap {L^infty }({mathbb{R}^N}),,,N ge 3)</span> Under certain assumptions on a vector field related to <i>a</i>(<i>x</i>), we use the Lyapunov–Schmidt reduction to show the existence of single peak solutions to the above problem. We also obtain local uniqueness and exact multiplicity results for this problem by the Pohozaev type identity.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Group LASSO for Change-points in Functional Time Series 函数时间序列中变化点的群LASSO
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-1665-1
Chang Xiong Chi, Rong Mao Zhang
{"title":"Group LASSO for Change-points in Functional Time Series","authors":"Chang Xiong Chi,&nbsp;Rong Mao Zhang","doi":"10.1007/s10114-023-1665-1","DOIUrl":"10.1007/s10114-023-1665-1","url":null,"abstract":"<div><p>Multiple change-points estimation for functional time series is studied in this paper. The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions. Group least absolute shrinkage and selection operator (LASSO) is then applied to estimate the number and the locations of possible change points. However, the group LASSO (GLASSO) always overestimate the true points. To circumvent this problem, a further Information Criterion (IC) is applied to eliminate the redundant estimated points. It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently. Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Fully Nonlinear Equations of Krylov Type on Riemannian Manifolds with Totally Geodesic Boundary 具有完全测地线边界的riemann流形上的Krylov型全非线性方程
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-1620-1
Li Chen, Yan He
{"title":"Fully Nonlinear Equations of Krylov Type on Riemannian Manifolds with Totally Geodesic Boundary","authors":"Li Chen, Yan He","doi":"10.1007/s10114-023-1620-1","DOIUrl":"https://doi.org/10.1007/s10114-023-1620-1","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136228638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Derivatives of Intersection Local Time for Two Independent Symmetric α-stable Processes 两个独立对称α-稳定过程的交点局部时间导数
3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-2516-9
Huan Zhou, Guang Jun Shen, Qian Yu
{"title":"Derivatives of Intersection Local Time for Two Independent Symmetric α-stable Processes","authors":"Huan Zhou, Guang Jun Shen, Qian Yu","doi":"10.1007/s10114-023-2516-9","DOIUrl":"https://doi.org/10.1007/s10114-023-2516-9","url":null,"abstract":"","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136229533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Every Graph Embedded on the Surface with Euler Characteristic Number ε = −1 is Acyclically 11-choosable 每一个嵌入在欧拉特征数ε =−1的曲面上的图都是非循环可选的
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI: 10.1007/s10114-023-1518-y
Lin Sun, Guang Long Yu, Xin Li
{"title":"Every Graph Embedded on the Surface with Euler Characteristic Number ε = −1 is Acyclically 11-choosable","authors":"Lin Sun,&nbsp;Guang Long Yu,&nbsp;Xin Li","doi":"10.1007/s10114-023-1518-y","DOIUrl":"10.1007/s10114-023-1518-y","url":null,"abstract":"<div><p>A proper vertex coloring of a graph <i>G</i> is acyclic if there is no bicolored cycles in <i>G</i>. A graph <i>G</i> is <i>acyclically k-choosable</i> if for any list assignment <i>L</i> = {<i>L</i>(<i>v</i>): <i>v</i> ∈ <i>V</i>(<i>G</i>)} with ∣<i>L</i>(<i>v</i>)∣ ≥ <i>k</i> for each vertex <i>v</i> ∈ <i>V</i>(<i>G</i>), there exists an acyclic proper vertex coloring <i>ϕ</i> of <i>G</i> such that <i>ϕ</i>(<i>v</i>) ∈ <i>L</i>(<i>v</i>) for each vertex <i>v</i> ∈ <i>V</i>(<i>G</i>). In this paper, we prove that every graph <i>G</i> embedded on the surface with Euler characteristic number <i>ε</i> = −1 is acyclically 11-choosable.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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