Mathematische Nachrichten最新文献

{"title":"Two Properties of Higher-Order Nash Blow-Up Local Algebras","authors":"Shuanghe Fan,&nbsp;Stephen S.-T. Yau,&nbsp;Huaiqing Zuo","doi":"10.1002/mana.70205","DOIUrl":"https://doi.org/10.1002/mana.70205","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the higher-order Nash blow-up local algebras associated with isolated hypersurface singularities, particularly focusing on the nonexistence of negative weighted derivations. Building on our earlier conjecture, which was proved by Badilla-Céspedes, Castorena, Duarte, and Núñez-Betancourt, we propose a new conjecture that generalizes our previous one. Inspired by the result of Badilla-Céspedes et al., we further demonstrate that the results in this paper validate our new conjecture partially. Besides, from the perspective of minors, we elucidate the structure of higher-order Nash blow-up algebras, which constitutes another main result of this paper. These findings contribute to the broader understanding of singularities and extend the applicability of higher-order Nash blow-up local algebras.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2525-2541"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871923","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 Impact of Robin Boundary Condition on a Chemotaxis–Consumption–Growth Model","authors":"Piotr Knosalla","doi":"10.1002/mana.70198","DOIUrl":"https://doi.org/10.1002/mana.70198","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate a parabolic–elliptic chemotaxis–consumption–growth system with a Robin boundary condition imposed on the signal. First, we analyze the steady-state problem, then we show that the solutions of the system are global and uniformly bounded in time in any space dimension. Next, under smallness assumption on the boundary data, we show that the solutions converge to non-constant steady states as time tends to infinity.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2422-2435"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872042","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 of Infinitely Many New Solutions to Singularly Perturbed Fractional Schrödinger Equations","authors":"Shengbing Deng,&nbsp;Peng Liao","doi":"10.1002/mana.70196","DOIUrl":"https://doi.org/10.1002/mana.70196","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper establishes a new dichotomy phenomenon concerning concentrating solutions for the following perturbed fractional Schrödinger equation:\u0000\u0000 &lt;/p&gt;&lt;div&gt;&lt;span&gt;&lt;span&gt;&lt;!--FIGURE--&gt;&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;V&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mtext&gt;in&lt;/mtext&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$begin{equation*} varepsilon ^{2s}(-Delta)^{s} u+ V(x)u=|u|^{p-2}u, nobreakspace text{in}nobreakspace mathbb {R}^N, end{equation*}$$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;&lt;/div&gt;where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2384-2404"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871825","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 Boundedness Induced by Asymptotically Non-Degenerate Motility in a Fully Parabolic Chemotaxis Model with Local Sensing","authors":"Jie Jiang,&nbsp;Philippe Laurençot","doi":"10.1002/mana.70197","DOIUrl":"https://doi.org/10.1002/mana.70197","url":null,"abstract":"<div>\u0000 \u0000 <p>A fully parabolic chemotaxis model of Keller–Segel type with local sensing is considered. The system features a signal-dependent asymptotically non-degenerate motility function, which accounts for a repulsion-dominated chemotaxis. Global boundedness of classical solutions is proved for an initial Neumann boundary value problem of the system in any space dimension. In addition, stabilization toward the homogeneous steady state is shown, provided that the motility is monotone non-decreasing. The key steps of the proof consist of the introduction of several auxiliary functions and a refined comparison argument, along with uniform-in-time estimates for a functional involving nonlinear coupling between the unknowns and auxiliary functions.</p>\u0000 </div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2405-2421"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871966","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":"Rigidity Results for Submanifolds in Warped Product Manifolds","authors":"Fábio R. dos Santos,&nbsp;Matheus N. Soares","doi":"10.1002/mana.70204","DOIUrl":"https://doi.org/10.1002/mana.70204","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate closed submanifolds immersed in a suitable warped product space and obtain an integral estimate relating the warping function, the second fundamental form, and the eigenvalues of the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2513-2524"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871925","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":"Spectral Bounds and Heat Kernel Upper Estimates for Dirichlet Forms","authors":"Aobo Chen,&nbsp;Zhenyu Yu","doi":"10.1002/mana.70207","DOIUrl":"https://doi.org/10.1002/mana.70207","url":null,"abstract":"<div>\u0000 \u0000 <p>We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part, where the scale function may vary with position. We further show that this Harnack-type inequality is preserved under quasi-symmetric changes of metric on uniformly perfect metric spaces. This generalizes the work of Mariano and Wang [<i>Stochastic Process. Appl</i>. <b>189</b> (2025): 104707].</p>\u0000 </div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2566-2589"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872164","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":"Spectral Expansion for the One-Dimensional Dirac Operator With a Complex-Valued Periodic Potential","authors":"O. A. Veliev","doi":"10.1002/mana.70209","DOIUrl":"https://doi.org/10.1002/mana.70209","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we construct the spectral expansion for the one-dimensional non–self-adjoint Dirac operator <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mi>Q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$L(Q)$</annotation>\u0000 </semantics></math> with a complex-valued periodic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>×</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$2times 2$</annotation>\u0000 </semantics></math> matrix potential <span></span><math>\u0000 <semantics>\u0000 <mi>Q</mi>\u0000 <annotation>$Q$</annotation>\u0000 </semantics></math> in the space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mi>∞</mi>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L_{2}^{2}(-infty,infty)$</annotation>\u0000 </semantics></math>. To this end, we study in detail asymptotic formulas for the Bloch eigenvalues and Bloch functions that are uniform with respect to the complex quasimomentum, as well as the essential spectral singularities of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mo>(</mo>\u0000 <mi>Q</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$L(Q)$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2624-2643"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871924","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":"Cactus Varieties of Sufficiently Ample Embeddings of Projective Schemes Have Determinantal Equations","authors":"Weronika Buczyńska,&nbsp;Jarosław Buczyński,&nbsp;Łucja Farnik","doi":"10.1002/mana.70182","DOIUrl":"https://doi.org/10.1002/mana.70182","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;For a fixed projective scheme &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, a property &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;annotation&gt;$P$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of line bundles is satisfied by sufficiently ample line bundles if there exists a line bundle &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$L_0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; such that &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$P(L_0+L)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; holds for any ample line bundle &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;annotation&gt;$L$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. As an example, sufficiently ample line bundles are very ample. Moreover, for a normal variety &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the embedding corresponding to a sufficiently ample line bundle is projectively normal. The grandfather of such properties and a basic ingredient used to study this concept is Fujita's vanishing theorem, which is a strengthening of Serre's vanishing theorem to sufficiently ample line bundles. The &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;th cactus variety of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is an analog of the secant variety, and it is defined using linear spans of finite schemes of degree &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this paper, we show that cactus varieties of sufficiently ample embeddings of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are set-theoretically defined by minors of matrices with linear entries. The topic is closely related to a conjecture of Eisenbud–Koh–Stillman, which was proved by Ginensky in the case &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;seman","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2332-2358"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871927","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":"Visibility and Intersection Density for Boolean Models in Hyperbolic Space","authors":"Tillmann Bühler,&nbsp;Daniel Hug,&nbsp;Christoph Thäle","doi":"10.1002/mana.70206","DOIUrl":"https://doi.org/10.1002/mana.70206","url":null,"abstract":"<p>For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally considered in the analysis of Boolean models in Euclidean space. In particular, we determine a necessary and sufficient condition for the finiteness of the mean visible volume of a Boolean model in terms of the intensity and the mean surface area of the typical grain.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2542-2565"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871972","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}

{"title":"On Milnor Classes of Constructible Functions","authors":"Mauri Pereira da Silva","doi":"10.1002/mana.70210","DOIUrl":"https://doi.org/10.1002/mana.70210","url":null,"abstract":"<div>\u0000 \u0000 <p>The goal of this work is to generalize the intersection product formulas for the Fulton–Johnson, Schwartz–MacPherson, and Milnor classes, originally obtained in the work of Callejas-Bedregal, Morgado, and Seade, to a broader framework of characteristic classes. More precisely, we extend these formulas to the classes introduced by Schürmann, which are characteristic classes relative to constructible functions.</p>\u0000 </div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2644-2651"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872143","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}