Acta Mathematica Sinica-English Series最新文献

{"title":"Simple Harish–Chandra Modules over the Super Affine-Virasoro Algebra","authors":"Yan He,&nbsp;Dong Liu,&nbsp;Yan Wang","doi":"10.1007/s10114-026-4566-2","DOIUrl":"10.1007/s10114-026-4566-2","url":null,"abstract":"<div><p>The super affine-Virasoro algebra <span>(widehat{cal{L}} = cal{W} ltimes (frak{g} otimes cal{A}) oplus mathbb{C}C)</span> can be regarded as a super version of the affine-Virasoro algebra, where <span>(cal{A})</span> is the tensor product of the Laurent polynomial algebra and the Grassmann algebra, <span>(cal{W})</span> is the Lie superalgebra of superderivations of <span>(cal{A})</span>, and <span>(frak{g})</span> is a finite-dimensional perfect Lie superalgebra. In this paper, we classify all simple Harish-Chandra modules over the super affine-Virasoro algebra.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2295 - 2307"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007381","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}

{"title":"Frobenius Functors and Relative Homological Dimensions of Complexes","authors":"Yiming Lei,&nbsp;Li Liang","doi":"10.1007/s10114-026-4482-5","DOIUrl":"10.1007/s10114-026-4482-5","url":null,"abstract":"<div><p>We define and study a notion of projectively coresolved Gorenstein flat dimension (PGF-dimension for short) for complexes of modules over associative rings. An upper bound for the PGF-dimension of complexes is given via the PGF-dimension of each component. Then we prove that each faithful Frobenius functor preserves the PGF-dimension of complexes.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2267 - 2280"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007382","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}

{"title":"On Global Solutions of a Cauchy Problem in Terms of Measure of Weak Noncompactness of Banach Spaces","authors":"Lixin Cheng,&nbsp;Chulei Liu,&nbsp;Wen Zhang","doi":"10.1007/s10114-026-4521-2","DOIUrl":"10.1007/s10114-026-4521-2","url":null,"abstract":"<div><p>In this paper, as an application of Tychonoff’s fixed point theorem, we show that the Cauchy initial problem <i>dx</i>/<i>dt</i> = <i>f</i>(<i>t, x</i>), <i>x</i>(<i>a</i>) = <i>x</i>₀ in a Banach space <i>X</i> has a global solution <i>x</i> ∈ <i>C</i>¹(<i>I, X</i>) in terms of measure of weak noncompactness, where <i>I</i> = [<i>a, b</i>] ⊂ ℝ⁺ or, [<i>a</i>, ∞) and the differentiability of <i>x</i> is about the norm of <i>X</i>. Precisely, we show that for every Banach space <i>X</i>, the problem mentioned above always has a global solution <i>x</i> ∈ <i>C</i>¹ (<i>I, X</i>) in assuming that (1) with a bounded range, <i>f</i>: <i>I</i> × <i>X</i> → <i>X</i> is uniformly continuous and weak-to-weak continuous on each bounded subset of <i>I</i> × <i>X</i>; (2) there exist a measure of weak noncompactness <i>μ</i> on <i>X</i> and a constant <i>γ</i> &gt; 0 such that <i>μ</i>(<i>f</i>(<i>t, S</i>)) ≤ <i>γμ</i>(<i>S</i>) for all <i>t</i> ∈ <i>I</i> and all nonempty bounded subsets <i>S</i> ⊂ <i>X</i>. This is an extension of relative results about local solvability of above problem with the measure of noncompactness condition or the assumption of weak compactness.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2201 - 2212"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007290","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}

{"title":"The Penrose Inequality for Metrics with Singular Sets","authors":"Huaiyu Zhang","doi":"10.1007/s10114-026-4671-2","DOIUrl":"10.1007/s10114-026-4671-2","url":null,"abstract":"<div><p>We study the Penrose inequality and its rigidity for metrics with singular sets. It is known that if the singular set is a hypersurface satisfying some additional conditions on its mean curvature, the metric is smooth away from the hypersurface and it is Lipschitz across the singular set, then the Penrose inequality still holds. And there are counter-examples which show that the additional conditions on the mean curvature are indispensable. As a complement, this paper studies the case of singular set of lower dimensions. We prove that the Penrose inequality still holds if the singular set is of dimensions not greater than <i>n</i> − 2, without any additional conditions.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2394 - 2412"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007305","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}

{"title":"On Some Stein–Weiss Type Inequality and Its Reversed Form on ℝn−m × ℝn","authors":"Xiang Li,&nbsp;Zifei Shen,&nbsp;Minbo Yang","doi":"10.1007/s10114-026-4585-z","DOIUrl":"10.1007/s10114-026-4585-z","url":null,"abstract":"<div><p>We prove a new Stein–Weiss type inequality of the form</p><div><div><span>$$int_{mathbb{R}^{n-m}} int_{mathbb{R}^n} frac{f(y)g(x)}{|x|^{beta}|x-y|^{mu}|y|^{alpha}}dx dy leq C(n,p,m,mu,alpha,beta)|f|_{L^p(mathbb{R}^{n-m})} |g|_{L^{q^{prime}}(mathbb{R}^n)},$$</span></div></div><p>for any positive functions <i>f</i> ∈ <i>L</i>^<i>p</i>(ℝ^{<i>n</i>−<i>m</i>}), <span>(g in L^{q^{prime}}(mathbb{R}^n))</span>, and <i>p, q</i>′ ∈ (1, ∞), <i>α, β, μ</i> such that <span>(frac{n-m}{n}frac{1}{p}+frac{1}{q^{prime}} + frac{alpha+beta+mu}{n} = frac{2n-m}{n})</span>. As a result, we prove the existence of optimizers for such inequality and introduce a family of Stein–Weiss inequalities with partial weight in ℝ^<i>m</i>. Furthermore, we consider the reverse version of the above inequality. Our approach relied on the Hardy inequality on the ℝ^{<i>n</i>−<i>m</i>} × ℝ^<i>n</i> and rearrangement argument, which allows us to study whether the best constant in this inequality is attained. We also prove asymptotic estimates and the necessary conditions of existence for the corresponding Euler–Lagrange equation.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2308 - 2334"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007384","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}

{"title":"Streets–Tian Conjecture on Lie Algebras with Codimension 2 Abelian Ideals","authors":"Kexiang Cao,&nbsp;Fangyang Zheng","doi":"10.1007/s10114-026-4527-9","DOIUrl":"10.1007/s10114-026-4527-9","url":null,"abstract":"<div><p>A Hermitian-symplectic metric is a Hermitian metric whose Kähler form is given by the (1, 1)-part of a closed 2-form. Streets–Tian Conjecture states that a compact complex manifold admitting a Hermitian-symplectic metric must be Kählerian (i.e., admitting a Kähler metric). The conjecture is known to be true in dimension 2 but is open in dimensions 3 or higher in general, except in a number of special situations, such as twistor spaces (Verbitsky), Fujiki <span>(cal{C})</span> spaces (Chiose) and Vaisman manifolds (Angella–Otiman). For Lie-complex manifolds (namely, compact quotients <i>G</i>/Γ of Lie groups by discrete subgroups with left-invariant complex structures), the conjecture has also been confirmed in a number of special cases, including when <i>G</i> is nilpotent (Enrietti–Fino–Vezzoni), when <i>G</i> is completely solvable (Fino–Kasuya), or when <i>J</i> is abelian (Fino–Kasuya–Vezzoni), or <i>G</i> is almost abelian (Fino–Kasuya–Vezzoni, Fino–Paradiso). In this article, we conduct a detailed case analysis and confirm Streets–Tian Conjecture for <i>G</i> whose Lie algebra contains an abelian ideal of codimension 2. Such Lie algebras are always solvable of step at most 3, but are not 2-step solvable and not completely solvable in general. Our approach is explicit in nature by describing both the Hermitian-symplectic metrics on such Lie algebras and the pathways of deforming them into Kähler ones, in hope of advancing our understanding of the subtlety and intricacy of this interesting conjecture in non-Kähler geometry.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2252 - 2266"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007303","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}

{"title":"Local Well-posedness of 2D Two-Phase Compressible MHD Boundary Layer Equations Without Resistivity","authors":"Junpei Gao,&nbsp;Lizhi Ruan","doi":"10.1007/s10114-026-4659-y","DOIUrl":"10.1007/s10114-026-4659-y","url":null,"abstract":"<div><p>In this paper, we study the well-posedness of boundary layer problems for the two-phase compressible magnetohydrodynamics (MHD) equations without resistivity, which are derived from the compressible two-phase model with magnetic field. Based on the structure of the equations, we introduce a positive symmetric matrix <span>(cal{L})</span> to obtain a good symmetric structure. Under the non-degeneracy condition on the tangential magnetic field, the local-in-time existence and uniqueness of two-phase compressible MHD boundary layer equations are established in Sobolev spaces.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2359 - 2393"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007304","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}

{"title":"Collapsibility of k-edge Connected Graphs and (s, t)-supereulerian Problem","authors":"Lan Lei,&nbsp;Xiaoli Wang,&nbsp;Yang Wu,&nbsp;Xiaomin Li","doi":"10.1007/s10114-026-5221-7","DOIUrl":"10.1007/s10114-026-5221-7","url":null,"abstract":"<div><p>Let <i>s</i> ≥ 0 and <i>t</i> ≥ 0 be integers, a graph <i>G</i> is (<i>s, t</i>)-<b>supereulerian</b> if for any pair of disjoint edge subsets <i>X</i> and <i>Y</i> with ∣<i>Y</i>∣ ≤ <i>s</i> and ∣<i>X</i>∣ ≤ <i>t, G</i> has a spanning eulerian subgraph <i>H</i> with <i>Y</i> ⊆ <i>E</i>(<i>H</i>) and <i>E</i>(<i>H</i>) ∩ <i>X</i> = ∅. In this paper, we study the collapsibility and (<i>s, t</i>)-supereulerian properties of <i>k</i>-edge-connected graphs, thereby not only extending existing results on collapsible graphs but also further revealing the structural characteristics of (<i>s, t</i>)-supereulerian graphs. Let <i>K</i><span>\u0000 ^<i>c</i>₂\u0000 \u0000 </span> denote the edgeless graph on two vertices and (<i>G</i> − <i>X</i>)_<i>Y</i> be the graph obtained by deleting edges in <i>X</i> and subdividing edges in <i>Y</i>. We prove the following results. Let <i>k, s</i> and <i>t</i> be given nonnegative integers and <i>G</i> be a graph with <i>κ′</i>(<i>G</i>) = <i>k</i> ≥ 4. For any disjoint sets <i>X,Y</i> ⊆ <i>E</i>(<i>G</i>) with ∣<i>X</i>∣ + ∣<i>Y</i>∣ ≤ <i>k</i>, each of the following holds.\u0000</p><ol>\u0000 <li>\u0000 <span>(i)</span>\u0000 \u0000 <p>If ∣<i>Y</i>∣ ≤ <i>s</i> and ∣<i>X</i>∣ ≤ <i>t</i>, then <i>G</i> is (<i>s, t</i>)-supereulerian if and only if (<i>G</i> − <i>X</i>)_<i>Y</i> can not be contracted to {<i>K</i><span>\u0000 ^<i>c</i>₂\u0000 \u0000 </span>, <i>K</i>₂} ∪ {<i>K</i>_2,<i>p</i> ∣ <i>p</i> is odd and <i>p</i> ≤ <i>s</i>}.</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(ii)</span>\u0000 \u0000 <p>If ∣<i>Y</i>∣ ≤ <i>s</i>, then either (<i>G</i> − <i>X</i>)_<i>Y</i> is collapsible or (<i>G</i> − <i>X</i>)_<i>Y</i> can be contracted to a member in {<i>K</i><span>\u0000 ^<i>c</i>₂\u0000 \u0000 </span>, <i>K</i>₂} ∪ {<i>K</i>_2,<i>p</i>∣<i>p</i> ≤ <i>s</i>}.</p>\u0000 \u0000 </li>\u0000 </ol></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2413 - 2424"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007306","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}

{"title":"Global Solutions to a Chemotaxis-Growth System with Signal-Dependent Diffusion and Generalized Logistic Source","authors":"Songzhi Li,&nbsp;Changchun Liu","doi":"10.1007/s10114-026-4597-8","DOIUrl":"10.1007/s10114-026-4597-8","url":null,"abstract":"<div><p>This paper deals with the following signal-dependent chemotaxis-growth system</p><div><div><span>$$begin{cases}u_t = Delta(v^{alpha} u) + a u - b u^{sigma}, &amp; x in Omega, t &gt; 0, v_t = Delta v - v + u, &amp; x in Omega, t &gt; 0,end{cases}$$</span></div></div><p>under homogeneous Neumann boundary condition in a smooth bounded domain Ω ⊂ ℝ^<i>n</i> (<i>n</i> ≥ 1) with constants <i>a, b, α</i> &gt; 0 and <i>σ</i> &gt; 1. It is shown that there exists a global classical solution (<i>u, v</i>) for all <i>α</i> &gt; 0 and <i>σ</i> &gt; 1 when <i>n</i> ∈ {1, 2}. On the other hand, in the case <i>n</i> ≥ 3, the global existence of classical solutions is proved for all <span>(sigma &gt; 1 + frac{n}{2})</span>. Additionally, the global existence of weak solutions in the sense of Definition 1.4 is established provided <span>(sigma &gt; frac{n}{2-2alpha(n-2)})</span> and <span>(0 &lt; alpha leq frac{2}{n+2})</span>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2213 - 2240"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007355","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}

{"title":"Existence and Stability of Exponential Attractor for Suspension Bridge Equation with Rotational Inertia, Nonlocal Energy Damping and Time Delay","authors":"Lulu Wang,&nbsp;Qiaozhen Ma","doi":"10.1007/s10114-026-4609-8","DOIUrl":"10.1007/s10114-026-4609-8","url":null,"abstract":"<div><p>Suspension bridges play an important role in our daily life, which are a type of bridges that use cables or chains suspended from vertical towers to support the bridge deck. This paper is devoted to investigating the stability and long-time dynamical behavior of the solutions for suspension bridge equation with rotational inertia, nonlocal energy damping and time delay in a rectangular domain Ω = (0, <i>π</i>) × (−<i>l, l</i>). Because of the existence of the rotational inertia and nonlocal energy damping, the method of maximal monotone operators to prove well-posedness is no longer suitable, so we establish the well-posedness of the solutions by means of the Galerkin approximation methods. After that, the existence of bounded absorbing set is obtained. Finally, the asymptotic smoothness of the semigroup is verified, and then the existence of global and generalized exponential attractors with finite fractal dimension is proved. Comparing with Sun–Yang [Attractors and their continuity for an extensible beam equation with rotational inertia and nonlocal energy damping. <i>J. Math. Anal. Appl.</i>, <b>512</b>, 126148, (2022)], the free boundary conditions in this paper bring us some difficulties, which we overcome.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 9","pages":"2335 - 2358"},"PeriodicalIF":0.9,"publicationDate":"2026-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149007383","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}