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Operator Equations Inducing Some Generalizations of Slant Hankel Operators 诱导斜向汉克尔算子某些广义化的算子方程
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-3084-3
Gopal Datt, Bhawna Bansal Gupta
{"title":"Operator Equations Inducing Some Generalizations of Slant Hankel Operators","authors":"Gopal Datt, Bhawna Bansal Gupta","doi":"10.1007/s10114-024-3084-3","DOIUrl":"https://doi.org/10.1007/s10114-024-3084-3","url":null,"abstract":"<p>An extension of slant Hankel operator, namely, the <i>k</i>-th-order λ-slant Hankel operator on the Lebesgue space <span>(L^{2}(mathbb{T}^{n}))</span>, where <span>(mathbb{T})</span> is the unit circle and <i>n</i> ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially <i>k</i>-th-order λ-slant Hankel operators on <span>(L^{2}(mathbb{T}^{n}))</span>.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613347","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
Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity 用松弛惯性法求解多输出集的分裂单调变分包容问题（无共卷性和立普茨连续性
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2594-3
Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo
{"title":"Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity","authors":"Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo","doi":"10.1007/s10114-024-2594-3","DOIUrl":"https://doi.org/10.1007/s10114-024-2594-3","url":null,"abstract":"<p>In this paper, we study the concept of split monotone variational inclusion problem with multiple output sets. We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces. Our proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued operators. Moreover, some parameters are relaxed to accommodate a larger range of values for the step sizes. Under some mild conditions on the control parameters and without prior knowledge of the operator norms, we obtain strong convergence result for the proposed method. Finally, we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed method. Several of the existing results in the literature could be viewed as special cases of our result in this paper.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613351","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
Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System 可压缩纳维-斯托克斯/阿伦-卡恩耦合系统的全局球对称解
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-3399-0
Chang Ming Song, Jian Lin Zhang, Yuan Yuan Wang
{"title":"Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System","authors":"Chang Ming Song, Jian Lin Zhang, Yuan Yuan Wang","doi":"10.1007/s10114-024-3399-0","DOIUrl":"https://doi.org/10.1007/s10114-024-3399-0","url":null,"abstract":"<p>In this paper, we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids. We prove the existence and uniqueness of global classical solution, weak solution and strong solution under the assumption of spherically symmetry condition for initial data <i>ρ</i><sub>0</sub> without vacuum state.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613348","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
The Complete Classification of Graphs whose Second Largest Eigenvalue of the Eccentricity Matrix is Less Than 1 偏心矩阵第二最大特征值小于 1 的图的完整分类
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2413-x
Jian Feng Wang, Xing Yu Lei, Shu Chao Li, Zoran Stanić
{"title":"The Complete Classification of Graphs whose Second Largest Eigenvalue of the Eccentricity Matrix is Less Than 1","authors":"Jian Feng Wang, Xing Yu Lei, Shu Chao Li, Zoran Stanić","doi":"10.1007/s10114-024-2413-x","DOIUrl":"https://doi.org/10.1007/s10114-024-2413-x","url":null,"abstract":"<p>The eccentricity matrix of a graph is obtained from the distance matrix by keeping the entries that are largest in their row or column, and replacing the remaining entries by zero. This matrix can be interpreted as an opposite to the adjacency matrix, which is on the contrary obtained from the distance matrix by keeping only the entries equal to 1. In the paper, we determine graphs having the second largest eigenvalue of eccentricity matrix less than 1.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613375","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
A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L 2 a (ℝ+;ma(x)dx) L 2 a (ℝ+;ma(x)dx) 中涉及索引惠特克变换的一对伪微分算子
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-3162-6
Jeetendrasingh Maan, Akhilesh Prasad
{"title":"A Pair of Pseudo-differential Operators Involving Index Whittaker Transform in L 2 a (ℝ+;ma(x)dx)","authors":"Jeetendrasingh Maan, Akhilesh Prasad","doi":"10.1007/s10114-024-3162-6","DOIUrl":"https://doi.org/10.1007/s10114-024-3162-6","url":null,"abstract":"<p>Pseudo-differential operators (PDO) <span>(Q(x,{{cal L}_{a,x}}))</span> and <span>({cal Q}(x,{{cal L}_{a,x}}))</span> involving the index Whittaker transform are defined. Estimates for these operators in Hilbert space <i>L</i><span>\u0000<sup><i>a</i></sup><sub>2</sub>\u0000</span>(ℝ<sub>+</sub>;<i>m</i><sub><i>a</i></sub>(<i>x</i>)<i>dx</i>) are obtained. A symbol class Ω is introduced. Later product and commutators for the PDO are investigated and their boundedness results are discussed.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613349","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
Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform 与韦恩斯坦变换相关的同符号类伪微分算子
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2405-x
Santosh Kumar Upadhyay, Mohd Sartaj
{"title":"Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform","authors":"Santosh Kumar Upadhyay, Mohd Sartaj","doi":"10.1007/s10114-024-2405-x","DOIUrl":"https://doi.org/10.1007/s10114-024-2405-x","url":null,"abstract":"<p>In this paper, pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced. The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on <i>ℌ</i><span>\u0000<sup><i>r</i></sup><sub><i>α</i>,2</sub>\u0000</span> are proven with the help of the Weinstein transform technique.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613342","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
P-symmetric Subharmonic Solutions for Nonlinear Hamiltonian Systems 非线性哈密顿系统的 P 对称次谐波解
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2752-7
Duan Zhi Zhang, Zhi Hao Zhao
{"title":"P-symmetric Subharmonic Solutions for Nonlinear Hamiltonian Systems","authors":"Duan Zhi Zhang, Zhi Hao Zhao","doi":"10.1007/s10114-024-2752-7","DOIUrl":"https://doi.org/10.1007/s10114-024-2752-7","url":null,"abstract":"<p>In this paper, we prove that for each positive <i>k</i> ≡ 1 mod <i>m</i> there exists a <i>P</i>-symmetric <i>kmτ</i>-periodic solution <i>x</i><sub><i>k</i></sub> for asymptotically linear <i>mτ</i>-periodic Hamiltonian systems, which are nonautonomous and endowed with a <i>P</i>-symmetry. If the <i>P</i>-symmetric Hamiltonian function is semi-positive, one can prove, under a new iteration inequality of the Maslov-type <i>P</i>-index, that <span>({x_{{k_1}}})</span> and <span>({x_{{k_2}}})</span> are geometrically distinct for <i>k</i><sub>1</sub>/<i>k</i><sub>2</sub> ≥ (2<i>n</i> + 1)<i>m</i> + 1; and <span>({x_{{k_1}}})</span>, <span>({x_{{k_2}}})</span> are geometrically distinct for <i>k</i><sub>1</sub>/<i>k</i><sub>2</sub> ≥ <i>m</i> + 1 provided <span>({x_{{k_1}}})</span> is non-degenerate.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613350","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
Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball 单位球上一类非解析单项式引起的托普利兹算子的还原子空间
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-04-15 DOI: 10.1007/s10114-024-2709-x
Yan Yue Shi, Bo Zhang, Xu Tang, Yu Feng Lu
{"title":"Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball","authors":"Yan Yue Shi, Bo Zhang, Xu Tang, Yu Feng Lu","doi":"10.1007/s10114-024-2709-x","DOIUrl":"https://doi.org/10.1007/s10114-024-2709-x","url":null,"abstract":"<p>In this paper, we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball <span>({mathbb{B}_2})</span>. It is proved that each minimal reducing subspace <i>M</i> is finite dimensional, and if dim <i>M</i> ≥ 3, then <i>M</i> is induced by a monomial. Furthermore, the structure of commutant algebra <span>(nu ({T_{overline w {N_z}N}}): = {{ M_{{w^N}}^ * {M_{{z^N}}},M_{{z^N}}^ * {M_{{w^N}}}} ^prime })</span> is determined by <i>N</i> and the two dimensional minimal reducing subspaces of <span>({T_{overline w {N_z}N}})</span>. We also give some interesting examples.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613346","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
Special Unipotent Representations of Simple Linear Lie Groups of Type A A 型简单线性李群的特殊单能代表
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-03-15 DOI: 10.1007/s10114-024-3206-y
Dan Barbasch, Jia Jun Ma, Bin Yong Sun, Chen Bo Zhu
{"title":"Special Unipotent Representations of Simple Linear Lie Groups of Type A","authors":"Dan Barbasch, Jia Jun Ma, Bin Yong Sun, Chen Bo Zhu","doi":"10.1007/s10114-024-3206-y","DOIUrl":"https://doi.org/10.1007/s10114-024-3206-y","url":null,"abstract":"<p>Let <i>G</i> be a special linear group over the real, the complex or the quaternion, or a special unitary group. In this note, we determine all special unipotent representations of <i>G</i> in the sense of Arthur and Barbasch–Vogan, and show in particular that all of them are unitarizable.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140037354","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 Stability Discrimination of Limit Cycles for Piecewise Smooth Systems 论片断平滑系统极限循环的稳定性判别
IF 0.7 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-03-15 DOI: 10.1007/s10114-024-2266-3
Mao An Han, Xia Yu Zhou
{"title":"On Stability Discrimination of Limit Cycles for Piecewise Smooth Systems","authors":"Mao An Han, Xia Yu Zhou","doi":"10.1007/s10114-024-2266-3","DOIUrl":"https://doi.org/10.1007/s10114-024-2266-3","url":null,"abstract":"<p>This paper is concerned with the problem of stability discrimination of limit cycles for piecewise smooth systems. We first establish the Poincaré map near a periodic orbit, and deduce the first order derivative of the map for general piecewise smooth systems on the plane. Then, we obtain a sufficient condition for determining the stability of limit cycles for these systems.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151210","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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