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The Spectrum Estimates for Random Graphs with Given Expected Degrees 给定期望度随机图的谱估计
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-5245-z
Dan Hu, Hajo Broersma, Xueliang Li, Shenggui Zhang
{"title":"The Spectrum Estimates for Random Graphs with Given Expected Degrees","authors":"Dan Hu,&nbsp;Hajo Broersma,&nbsp;Xueliang Li,&nbsp;Shenggui Zhang","doi":"10.1007/s10114-026-5245-z","DOIUrl":"10.1007/s10114-026-5245-z","url":null,"abstract":"<div><p>We consider the random graph model <i>G</i>(<b>w</b>) for a given expected degree sequence <b>w</b> = (<i>w</i><sub>1</sub>, <i>w</i><sub>2</sub>,…, <i>w</i><sub><i>n</i></sub>), where the probability <i>p</i><sub><i>ij</i></sub> of an edge between vertices <i>v</i><sub><i>i</i></sub> and <i>v</i><sub><i>j</i></sub> is defined as <i>w</i><sub><i>i</i></sub><i>w</i><sub><i>j</i></sub><i>ρ</i> with <span>(rho = frac{1}{sumnolimits_{i=1}^{n} w_i})</span>. In this paper, we apply a matrix concentration inequality to derive an upper bound on the largest eigenvalue of the adjacency matrix of the random graph with given expected degrees. We further analyze the expectation of the largest eigenvalue of the adjacency matrix and establish its concentration properties. Additionally, by utilizing an extension of the matrix Chernoff inequality that incorporates an intrinsic dimension parameter, we investigate the expectation and tail behavior of the largest eigenvalue of the Laplacian matrix for the random graph model <i>G</i>(<b>w</b>).</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2125 - 2138"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878116","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
Singular Extinction Profiles of Solutions to Fast Diffusion Equation with Caffarelli–Kohn–Nirenberg Weights 具有Caffarelli-Kohn-Nirenberg权值的快速扩散方程解的奇异消光曲线
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-5007-y
Tao Zhang
{"title":"Singular Extinction Profiles of Solutions to Fast Diffusion Equation with Caffarelli–Kohn–Nirenberg Weights","authors":"Tao Zhang","doi":"10.1007/s10114-026-5007-y","DOIUrl":"10.1007/s10114-026-5007-y","url":null,"abstract":"<div><p>In this paper, we study the extinction profiles of solutions to weighted fast diffusion equation <span>(u_t = vert xvert^{gamma} nabla cdot (vert xvert^{-beta} nabla u^{m}))</span>, with 0 &lt; <i>m</i> &lt; 1, posed in ℝ<sup><i>N</i></sup> × [0, ∞). The range of parameters for weights ∣<i>x</i>∣<sup><i>γ</i></sup> and ∣<i>x</i>∣<sup>−<i>β</i></sup> satisfies <i>γ</i> &lt; <i>N</i> and <span>(gamma - 2 &lt; beta leq frac{gamma(N-2)}{N})</span>, which is optimal for the validity of a class of Caffarelli–Kohn–Nirenberg inequalities. When the initial data belongs to the Marcinkiewicz space and <i>m</i> be in the very fast diffusion range, we obtain the extinction profiles of solutions to the weighted fast diffusion equation.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2085 - 2100"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878119","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
Stability of Composite Wave for Inflow Problem for Compressible Navier–Stokes/Allen–Cahn System 可压缩Navier-Stokes / Allen-Cahn系统入流问题复合波的稳定性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-08-15 DOI: 10.1007/s10114-026-5520-z
Ting Luo
{"title":"Stability of Composite Wave for Inflow Problem for Compressible Navier–Stokes/Allen–Cahn System","authors":"Ting Luo","doi":"10.1007/s10114-026-5520-z","DOIUrl":"10.1007/s10114-026-5520-z","url":null,"abstract":"<div><p>In this paper, we investigate the large-time behavior of solutions to an initial-boundary value problem for the compressible non-isentropic Navier–Stokes/Allen–Cahn system in a half line ℝ<sub>+</sub>:= (0,+∞). We focus our attention on the inflow problem and give a rigorous proof of the asymptotic stability of the composite wave which is composed of the boundary layer solution, the contact wave and the rarefaction wave under some smallness conditions. Meanwhile, we obtain the global existence of solutions based on the basic energy method by taking into account the complexity of composite wave.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 8","pages":"2168 - 2200"},"PeriodicalIF":0.9,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878123","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
Analytical Smoothing Effect of Solution for the MHD-Boussinesq Equations MHD-Boussinesq方程解的解析平滑效应
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4624-9
Feng Cheng, Xiuhui Wang
{"title":"Analytical Smoothing Effect of Solution for the MHD-Boussinesq Equations","authors":"Feng Cheng,&nbsp;Xiuhui Wang","doi":"10.1007/s10114-026-4624-9","DOIUrl":"10.1007/s10114-026-4624-9","url":null,"abstract":"<div><p>In this paper we study the analytical smoothing effect of Cauchy problem for the incompressible MHD-Boussinesq equations. Precisely, we used the Fourier Gevrey space method to show that the Sobolev <i>H</i><sup>1</sup>-solution to the incompressible MHD-Boussinesq equations in periodic domain is analytical for both spatial variable and time variable.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1848 - 1868"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613218","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 Metric Mean Dimensions of Divergence Points 散度点的度量平均维数
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-5407-z
Tian Zhan, Yong Ji, Yunping Wang
{"title":"On the Metric Mean Dimensions of Divergence Points","authors":"Tian Zhan,&nbsp;Yong Ji,&nbsp;Yunping Wang","doi":"10.1007/s10114-026-5407-z","DOIUrl":"10.1007/s10114-026-5407-z","url":null,"abstract":"<div><p>For the topological dynamical system with infinite entropy and the specification property, in the context of continuous and affine deformations of empirical measures, the set of divergence points is either empty, or its Bowen and packing metric mean dimensions equal those of the full phase space. We also establish the variational principles of Bowen and packing metric mean dimension for the sup set.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1937 - 1956"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613224","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
Normalized Solutions for Nonhomogeneous Chern–Simons–Schrödinger Equations with Critical Exponential Growth 临界指数增长的非齐次Chern-Simons-Schrödinger方程的归一化解
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4581-3
Chenlu Wei, Sitong Chen, Xin’ao Zhou
{"title":"Normalized Solutions for Nonhomogeneous Chern–Simons–Schrödinger Equations with Critical Exponential Growth","authors":"Chenlu Wei,&nbsp;Sitong Chen,&nbsp;Xin’ao Zhou","doi":"10.1007/s10114-026-4581-3","DOIUrl":"10.1007/s10114-026-4581-3","url":null,"abstract":"<div><p>This paper investigates the existence of normalized solutions for the following Chern–Simons–Schrödinger equation</p><div><div><span>$$begin{cases}-Delta u + lambda u + left(dfrac{h^2(|x|)}{|x|^2} + int_{|x|}^{infty} dfrac{h(s)}{s} u^2(s) , ds right) u = (e^{u^2} - 1)u + g(x), &amp; x in mathbb{R}^2, u in H_r^1(mathbb{R}^2), quad int_{mathbb{R}^2} u^2 , dx = c,end{cases}$$</span></div></div><p>where <i>c</i> &gt; 0, <i>λ</i> ∈ ℝ acts as a Lagrange multiplier and <i>g</i> ∈ <i>C</i>(∝<sup>2</sup>, [0, +∞)) satisfies suitable assumptions. In addition to the loss of compactness caused by the nonlinearity with critical exponential growth, the intricate interactions among it, the nonlocal term, and the nonhomogeneous term significantly affect the geometric structure of the constrained functional, thereby making this research particularly challenging. By specifying explicit conditions on <i>c</i>, we subtly establish a structure of local minima of the constrained functional. Based on the structure, we employ new analytical techniques to prove the existence of two solutions: one being a local minimizer and one of mountain-pass type. Our results are entirely new, even for the Schrödinger equation that is when nonlocal terms are absent. We believe our methods may be adapted and modified to deal with more constrained problems with nonhomogeneous perturbation.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1821 - 1847"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613310","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
Yamabe-Harmonic Flow on Locally Conformally Flat Manifolds 局部共形平面流形上的yamabe -调和流
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-3129-x
Zihao Wang
{"title":"Yamabe-Harmonic Flow on Locally Conformally Flat Manifolds","authors":"Zihao Wang","doi":"10.1007/s10114-026-3129-x","DOIUrl":"10.1007/s10114-026-3129-x","url":null,"abstract":"<div><p>In this paper we introduce a new geometric flow consisting of the Yamabe flow coupled with harmonic heat flow of a function on a closed manifold <i>M</i>, or shortly Yamabe-harmonic flow. It is define by</p><div><div><span>$$begin{cases}dfrac{partial}{partial t}g = -(R - phi)g, phi = (n - 1)Delta_g phi.end{cases}$$</span></div></div><p>To begin with we establish the short-time extsience via conformal transformation for any smooth initial data. Furthermore we derive interior-in-time derivative estimates for the Riemannian curvature and Lapse function and obtain the global existence of Yamabe-harmonic flow. Moreover, compact gradient Yamabe-harmonic solitons are proved to be manifolds with R = <i>ϕ</i> = Constant. Eventually we obtain the classification of singularities by blow-up rate of AC curvature, which is analogous to that of Ricci-harmonic flow and Ricci-connection flow. The relationship between singularity models and solitons shall appear in forthcoming work.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1768 - 1784"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613222","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
An Lp Estimate for a Class of Flag Trilinear Pseudo-differential Operators 一类标志型三线性伪微分算子的Lp估计
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4607-x
Jing Qiao, Lu Zhang
{"title":"An Lp Estimate for a Class of Flag Trilinear Pseudo-differential Operators","authors":"Jing Qiao,&nbsp;Lu Zhang","doi":"10.1007/s10114-026-4607-x","DOIUrl":"10.1007/s10114-026-4607-x","url":null,"abstract":"<div><p>In this work, we prove an <span>(L^{p_1} times L^{p_2} times L^{p_3} rightarrow L^p)</span> estimate for a trilinear pseudo-differential operators with flag-type symbols taking the form of <i>a</i>(<i>x, ξ</i><sub>1</sub>, <i>ξ</i><sub>2</sub>, <i>ξ</i><sub>3</sub>)<i>b</i>(<i>x, ξ</i><sub>1</sub>, <i>ξ</i><sub>2</sub> + <i>ξ</i><sub>3</sub>). The study of such operators is motivated by investigations on the corresponding flag Fourier multipliers studied by Muscalu [<i>Rev. Mat. Iberoam.</i>, <b>23</b>, 705–742 (2007); <i>Contemp. Math.</i>, <b>505</b>, 131–151 (2010)], Germain, Masmoudi, Shatah [<i>J. Math. Pures Appl.</i>, <b>97</b>, 505–543 (2012); <i>Ann. of Math.</i>, <b>175</b>, 691–754 (2012)] and Miyachi, Tomita [<i>Math. Z.</i>, <b>282</b>, 577–613 (2016)].</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1881 - 1898"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613223","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 Trace Range of Products of Three Projections 关于三投影积的迹域
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-5379-z
Linzhe Huang, Wenming Wu, Yifeng Ye
{"title":"On Trace Range of Products of Three Projections","authors":"Linzhe Huang,&nbsp;Wenming Wu,&nbsp;Yifeng Ye","doi":"10.1007/s10114-026-5379-z","DOIUrl":"10.1007/s10114-026-5379-z","url":null,"abstract":"<div><p>The trace range of products of three projections in a finite factor (ℳ, <i>τ</i>), with their trace equal to <i>λ</i> is studied in this article. When <span>(lambdaleqfrac{1}{2})</span>, the corresponding boundary curve of the trace range is shown to be a degenerate elliptic curve. For <i>n</i> ≥ 3, when ℳ is of type I<sub><i>n</i></sub> and <span>(lambda=frac{n-1}{n})</span>, it is shown that the corresponding boundary curve of the trace range is an algebraic curve in the complex plane.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1921 - 1936"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613221","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
Manin’s Question and Hopf Algebras via the Boson-fermionic Quantum Weyl Algebra 基于玻色子-费米子量子Weyl代数的Manin问题和Hopf代数
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2026-07-15 DOI: 10.1007/s10114-026-4574-2
Ge Feng, Naihong Hu, Xiaoting Zhang, Rushu Zhuang
{"title":"Manin’s Question and Hopf Algebras via the Boson-fermionic Quantum Weyl Algebra","authors":"Ge Feng,&nbsp;Naihong Hu,&nbsp;Xiaoting Zhang,&nbsp;Rushu Zhuang","doi":"10.1007/s10114-026-4574-2","DOIUrl":"10.1007/s10114-026-4574-2","url":null,"abstract":"<div><p>The aim of this article is to introduce a boson-fermionic quantum Weyl algebra <span>({cal{W}}_q(2(m mid n)))</span> of type <i>A</i>(<i>m</i>∣<i>n</i>), which is the quantum differential operators (QDO) algebra (also denoted by Diff<sub><i>q</i></sub>(Ω<sub><i>q</i></sub>)) defined on Ω<sub><i>q</i></sub>(<i>m</i>∣<i>n</i>), the quantum Grassmann super-algebra Ω<sub><i>q</i></sub>(<i>m</i>∣<i>n</i>) we defined. Here we develop a constructive approach of Radford–Majid bosonization theory to yield some pointed Hopf algebras via QDO. This addresses a basic problem due to Manin, namely, any QDO approach might help to yield new Hopf algebras (see §2.2. Basic problem, p. 1010 of Manin’s paper in 1992). Remarkably, <span>({cal{W}}_q(2(m mid n)))</span> itself is not a Hopf algebra, however, it contains some interesting pointed Hopf algebras as its subquotient objects, like the bosonization <span>({frak{A}}_{q}(2(m mid n)))</span> of the quantum Manin (<i>m</i>∣<i>n</i>)-superspace <i>A</i><span>\u0000 <sup><i>m</i>∣<i>n</i></sup><sub><i>q</i></sub>\u0000 \u0000 </span>, the bosonization <span>({frak{G}}_{q}(2(m mid n)))</span> of Ω<sub><i>q</i></sub>(<i>m</i>∣<i>n</i>), the multi-rank Taft algebras of 2(<i>m</i>∣<i>n</i>)-type, the homomorphic image of pointed Hopf algebra <span>({cal{U}}_{q}({frak{g}}{frak{l}}(m mid n)))</span> over Ω<sub><i>q</i></sub>(<i>m</i>∣<i>n</i>) or Ω<span>\u0000 <sup>!</sup><sub><i>q</i></sub>\u0000 \u0000 </span>(<i>m</i>∣<i>n</i>) (the quantum dual Grassmann superalgebra), etc.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"42 7","pages":"1785 - 1820"},"PeriodicalIF":0.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613244","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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