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Inhomogeneous Oscillator Representations of P(n) P(n)的非齐次振子表示
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3419-8
Ling Chen
{"title":"Inhomogeneous Oscillator Representations of P(n)","authors":"Ling Chen","doi":"10.1007/s10114-025-3419-8","DOIUrl":"10.1007/s10114-025-3419-8","url":null,"abstract":"<div><p>We study inhomogeneous oscillator representations of the strange Lie superalgebras <i>P</i>(<i>n</i>) on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions. We obtain the composition series for these representations. The obtained irreducible modules are infinite dimensional. Some of them are not of highest-weight type and even not weight modules.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1717 - 1752"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100706","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
Hypercyclicity and Supercyclicity for Upper Triangular Operator Matrices 上三角算子矩阵的超环性和超环性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI: 10.1007/s10114-025-3332-1
Gaohuizi Feng, Pengtong Li
{"title":"Hypercyclicity and Supercyclicity for Upper Triangular Operator Matrices","authors":"Gaohuizi Feng,&nbsp;Pengtong Li","doi":"10.1007/s10114-025-3332-1","DOIUrl":"10.1007/s10114-025-3332-1","url":null,"abstract":"<div><p>An operator <i>T</i> on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector <span>(y in cal{H})</span> such that the orbit Orb(<i>T, y</i>) = {<i>y, Ty, T</i><sup>2</sup><i>y, T</i><sup>3</sup><i>y</i>, …} is dense in <span>(cal{H})</span>. Hypercyclic property and supercyclic proeprty are liable to fail for 2 × 2 upper triangular operator matrices. In this paper, we aim to explore and characterize the hypercyclicity and the supercyclicity for 2 × 2 upper triangular operator matrices. We obtain a spectral characterization of the norm-closure of the class of all hypercyclic (supercyclic) operators for 2 × 2 upper triangular operator matrices.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 7","pages":"1775 - 1788"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145100689","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
Translating Solitons in ℝ3 of Linear Weingarten Type 线性Weingarten型的l_3中的平移孤子
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3330-3
Yu Fu, Rafael López, Yanru Luo, Dan Yang
{"title":"Translating Solitons in ℝ3 of Linear Weingarten Type","authors":"Yu Fu,&nbsp;Rafael López,&nbsp;Yanru Luo,&nbsp;Dan Yang","doi":"10.1007/s10114-025-3330-3","DOIUrl":"10.1007/s10114-025-3330-3","url":null,"abstract":"<div><p>In this paper, we consider λ-translating solitons in ℝ<sup>3</sup>. These surfaces are critical points of the weighted area when the density is a coordinate function. If λ = 0, these surfaces evolve by translations along the mean curvature flow. We give a full classification of λ-translating solitons that satisfy a linear Weingarten relation between their curvatures. These surfaces are planes, circular cylinders, grim reapers and certain types of cylindrical surfaces. We also prove that planes and circular cylinders are the only λ-translating soliton with constant squared norm of the second fundamental form.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1617 - 1634"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143414","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
Sum Formulas for Various Kinds of Cyclotomic Multiple Zeta Values 各种分眼倍数Zeta值的求和公式
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-2533-y
Jiangtao Li
{"title":"Sum Formulas for Various Kinds of Cyclotomic Multiple Zeta Values","authors":"Jiangtao Li","doi":"10.1007/s10114-025-2533-y","DOIUrl":"10.1007/s10114-025-2533-y","url":null,"abstract":"<div><p>Cyclotomic multiple zeta values are generalizations of multiple zeta values. In this paper, we establish sum formulas for various kinds of cyclotomic multiple zeta values. As an interesting application, we show that the ℚ-algebra generated by Riemann zeta values are contained in the ℚ-algebra generated by unit cyclotomic multiple zeta values of level <i>N</i> for any <i>N</i> ≥ 2.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1703 - 1716"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143772","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 Lattice Completion of Quantum Logic 量子逻辑的点阵补全
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3398-9
Meixing Zhao, Jinchuan Hou, Kan He, Feng Zhang
{"title":"The Lattice Completion of Quantum Logic","authors":"Meixing Zhao,&nbsp;Jinchuan Hou,&nbsp;Kan He,&nbsp;Feng Zhang","doi":"10.1007/s10114-025-3398-9","DOIUrl":"10.1007/s10114-025-3398-9","url":null,"abstract":"<div><p>The main purpose of this article is to study the lattice structure of quantum logics by using the theory of partially order sets. The goal is achieved by constructing a natural embedding map from the quantum logic posets into the complete lattices. The embedding map needs to be dense (in the order sense) and such complete lattices are so-called extended logics which preserve all essential features of the quantum logic. We obtain that the extended logic is unique up to a lattice isomorphism.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1664 - 1676"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143410","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 Analysis of Block Joint Sparse Recovery Using Block Signal Space Matching Pursuit 基于块信号空间匹配追踪的块联合稀疏恢复分析
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3171-0
Haifeng Li, Hao Ying, Jinming Wen
{"title":"The Analysis of Block Joint Sparse Recovery Using Block Signal Space Matching Pursuit","authors":"Haifeng Li,&nbsp;Hao Ying,&nbsp;Jinming Wen","doi":"10.1007/s10114-025-3171-0","DOIUrl":"10.1007/s10114-025-3171-0","url":null,"abstract":"<div><p>In many practical applications, we need to recover block sparse signals. In this paper, we encounter the system model where joint sparse signals exhibit block structure. To reconstruct this category of signals, we propose a new algorithm called block signal subspace matching pursuit (BSSMP) for the block joint sparse recovery problem in compressed sensing, which simultaneously reconstructs the support of block jointly sparse signals from a common sensing matrix. To begin with, we consider the case where block joint sparse matrix <b>X</b> has full column rank and any <i>r</i> nonzero row-blocks are linearly independent. Based on these assumptions, our theoretical analysis indicates that the BSSMP algorithm could reconstruct the support of <b>X</b> through at most <span>(k - r + leftlceil {{r over L}} rightrceil)</span> iterations if sensing matrix <b>A</b> satisfies the block restricted isometry property of order <i>L</i>(<i>K</i> − <i>r</i>) + <i>r</i> + 1 with <span>({delta _{{B_{L( {K - r}) + r + 1}}}}&lt; max {{{{sqrt r} over {sqrt {K + {r over 4}} + sqrt {{r over 4}} }},{{sqrt L} over {sqrt {Kd} + sqrt L}}}})</span>. This condition improves the existing result.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1635 - 1652"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10114-025-3171-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Inference Analysis of Relationships Between Best Linear Minimum Bias Predictors Under Two Transformed General Linear Models 两种变换后的一般线性模型下最佳线性最小偏差预测量关系的推理分析
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3574-y
Yongge Tian, Bo Jiang
{"title":"Inference Analysis of Relationships Between Best Linear Minimum Bias Predictors Under Two Transformed General Linear Models","authors":"Yongge Tian,&nbsp;Bo Jiang","doi":"10.1007/s10114-025-3574-y","DOIUrl":"10.1007/s10114-025-3574-y","url":null,"abstract":"<div><p>Regression models are often transformed into certain alternative forms in statistical inference theory. In this paper, we assume that a general linear model (GLM) is transformed into two different forms, and our aim is to study some comparison problems under the two transformed general linear models (TGLMs). We first construct a general vector composed of all unknown parameters under the two different TGLMs, derive exact expressions of best linear minimum bias predictors (BLMBPs) by solving a constrained quadratic matrix-valued function optimization problem in the Löwner partial ordering, and describe a variety of mathematical and statistical properties and performances of the BLMBPs. We then approach some algebraic characterization problems concerning relationships between the BLMBPs under two different TGLMs. As applications, two specific cases are presented to illustrate the main contributions in the study.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1591 - 1616"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143409","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
Infinitely Many Bubbling Solutions and Non-Degeneracy Results to Fractional Prescribed Curvature Problems 分数阶规定曲率问题的无穷多冒泡解和非退化结果
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3086-9
Lixiu Duan, Qing Guo
{"title":"Infinitely Many Bubbling Solutions and Non-Degeneracy Results to Fractional Prescribed Curvature Problems","authors":"Lixiu Duan,&nbsp;Qing Guo","doi":"10.1007/s10114-025-3086-9","DOIUrl":"10.1007/s10114-025-3086-9","url":null,"abstract":"<div><p>We consider the following fractional prescribed curvature problem </p><div><div><span>$$(-Delta)^{s}u=K(y)u^{2_{s}^{*}-1}, quad u&gt;0,,y in {mathbb R}^{N},$$</span></div><div>\u0000 ((0.1))\u0000 </div></div><p> where <span>(s in (0,, {1 over 2}))</span> for <i>N</i> = 3, <i>s</i> ∈ (0, 1) for <i>N</i> ≥ 4 and <span>(2_{s}^{*}={2N over N-2s})</span> is the fractional critical Sobolev exponent, <i>K</i>(<i>y</i>) has a local maximum point in <i>r</i> ∈ (<i>r</i><sub>0</sub> − <i>δ</i>, <i>r</i><sub>0</sub> + <i>δ</i>). First, for any sufficient large <i>k</i>, we construct a 2<i>k</i> bubbling solution to (0.1) of some new type, which concentrates on an upper and lower surfaces of an oblate cylinder through the Lyapunov–Schmidt reduction method. Furthermore, a non-degeneracy result of the multi-bubbling solutions is proved by use of various Pohozaev identities, which is new in the study of the fractional problems.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1531 - 1564"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143417","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 Note on Characteristic Endpoints Question for Decreasing Iterative Roots on Characteristic Interval 关于特征区间上递减迭代根的特征端点问题的一个注记
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3154-1
Siyi Zhao, Liu Liu
{"title":"A Note on Characteristic Endpoints Question for Decreasing Iterative Roots on Characteristic Interval","authors":"Siyi Zhao,&nbsp;Liu Liu","doi":"10.1007/s10114-025-3154-1","DOIUrl":"10.1007/s10114-025-3154-1","url":null,"abstract":"<div><p>For a piecewise monotone function <i>F</i> of height 1, an open question was raised: Does <i>F</i> have an iterative root <i>f</i> of order <i>n</i> ≤ <i>N</i>(<i>F</i>) + 1 if the ‘characteristic endpoints condition’ is not satisfied? This question was answered partly in the case that <i>F</i> is strictly increasing on its characteristic interval <i>K</i>(<i>F</i>) but <i>f</i> is strictly decreasing on <i>K</i>(<i>F</i>). In this paper we discuss the question for <i>F</i> increasing on <i>K</i>(<i>F</i>) in some remaining cases, giving the necessary and sufficient conditions for the existence of continuous iterative roots <i>f</i> decreasing on <i>K</i>(<i>F</i>) of order <i>n</i> = <i>N</i>(<i>F</i>) &gt; 2 with <i>H</i>(<i>f</i>) = <i>n</i> − 1.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1653 - 1663"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143419","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
Complete Convergence and Complete Moment Convergence for Maximum of Weighted Sums of ρ−-mixing Random Variables and Its Application ρ−混合随机变量加权和最大值的完全收敛性和完全矩收敛性及其应用
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3031-y
Jinyu Zhou, Jigao Yan
{"title":"Complete Convergence and Complete Moment Convergence for Maximum of Weighted Sums of ρ−-mixing Random Variables and Its Application","authors":"Jinyu Zhou,&nbsp;Jigao Yan","doi":"10.1007/s10114-025-3031-y","DOIUrl":"10.1007/s10114-025-3031-y","url":null,"abstract":"<div><p>In this paper, complete convergence and complete moment convergence for maximal weighted sums of <i>ρ</i><sup>−</sup>-mixing random variables are investigated, and some sufficient conditions for the convergence are provided. The relationships among the weights of the partial sums, boundary function and weight function are in a sense revealed. Additionally, a Marcinkiewicz–Zygmund type strong law of large numbers for maximal weighted sums of <i>ρ</i><sup>−</sup>-mixing random variables is established. The results obtained extend the corresponding ones for random variables with independence structure and some dependence structures. As an application, the strong consistency for the tail-value-at-risk (TVaR) estimator in the financial and actuarial fields is established.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1677 - 1702"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143412","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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