发布求助
文献互助 智能选刊 最新文献

Applied Mathematics Letters最新文献

筛选
英文 中文
Ground state solution of Schrödinger–Bopp–Podolsky system in the mass subcritical case 质量亚临界情况下Schrödinger-Bopp-Podolsky系统的基态解
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-07 DOI: 10.1016/j.aml.2026.109870
Yiqiu Du, Yu Su
{"title":"Ground state solution of Schrödinger–Bopp–Podolsky system in the mass subcritical case","authors":"Yiqiu Du,&nbsp;Yu Su","doi":"10.1016/j.aml.2026.109870","DOIUrl":"10.1016/j.aml.2026.109870","url":null,"abstract":"<div><div>The Schrödinger–Bopp–Podolsky system arises in the second order gauge theory for the electromagnetic theory. When the exponent of power nonlinearity involved in the system is <span><math><mrow><mi>p</mi><mo>∈</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mfrac><mrow><mn>10</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mrow></math></span> (this is a special mass subcritical case), it presents a new phenomenon due to the “conflict” between the Laplacian and Bopp–Podolsky term. In this case, Ramos–Siciliano [Zeitschrift für angewandte Mathematik und Physik, 74 (2023)] proved that there exists a constant <span><math><mrow><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>&gt;</mo><mn>0</mn></mrow></math></span> such that for any <span><math><mrow><mi>c</mi><mo>&gt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, the system has a ground state solution. However, they just showed the existence of the constant <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. It is important for us to understand the constant <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. Hence, we estimate the constant <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> by the best constant of the Gagliardo–Nirenberg–Coulomb inequality. Moreover, we show the existence of ground state solution.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109870"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Existence and parameter estimation for nonlinear boundary value problems involving fractional Laplacian 涉及分数阶拉普拉斯的非线性边值问题的存在性及参数估计
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-09 DOI: 10.1016/j.aml.2026.109871
Ziqing Yuan
{"title":"Existence and parameter estimation for nonlinear boundary value problems involving fractional Laplacian","authors":"Ziqing Yuan","doi":"10.1016/j.aml.2026.109871","DOIUrl":"10.1016/j.aml.2026.109871","url":null,"abstract":"<div><div>Nonlinear boundary value problems involving the fractional Laplacian operator are studied to establish precise conditions for the existence of solutions. By combining the method of sub- and super-solutions with fractional comparison principles, we prove the existence of nonnegative solutions and derive sharp estimates for the critical parameters. These results provide a theoretical foundation for analyzing threshold phenomena in applications such as disease transmission dynamics, where nonlocal interactions play a crucial role.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109871"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 priori estimates on the weak flocking of the Cucker–Smale–Fokker–Planck equation cucker - small - fokker - planck方程弱群集的先验估计
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2025-12-30 DOI: 10.1016/j.aml.2025.109861
Seung-Yeal Ha , Jaemoon Lee , Qinghua Xiao , Fanqin Zeng
{"title":"A priori estimates on the weak flocking of the Cucker–Smale–Fokker–Planck equation","authors":"Seung-Yeal Ha ,&nbsp;Jaemoon Lee ,&nbsp;Qinghua Xiao ,&nbsp;Fanqin Zeng","doi":"10.1016/j.aml.2025.109861","DOIUrl":"10.1016/j.aml.2025.109861","url":null,"abstract":"<div><div>We study the weak flocking of the Cucker–Smale–Fokker–Planck (in short, CS–FP) equation with a degenerate diffusion coefficient. When the communication weight function has a positive lower bound, weak flocking occurs asymptotically. In contrast, when the communication weight function tend to zero, it is not known whether weak flocking occurs or not. In this paper, we revisit this delicate situation in which the communication weight function tends to zero at infinity and the noise amplitude also decays to zero sufficiently fast. To bypass the difficulty, we use the method of effective domain by identifying a time-varying region in which the total mass outside of it decays to zero sufficiently fast. Moreover, we show that if the communication weight function and the noise amplitude both have a suitable polynomial decay, then weak flocking occurs.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109861"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 fast explicit hybrid numerical method for image inpainting using the viscous Cahn–Hilliard model 一种基于粘性Cahn-Hilliard模型的快速显式混合数值方法
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-12 DOI: 10.1016/j.aml.2026.109874
Chenyu Zhang , Junying Cao , Shuying Zhai
{"title":"A fast explicit hybrid numerical method for image inpainting using the viscous Cahn–Hilliard model","authors":"Chenyu Zhang ,&nbsp;Junying Cao ,&nbsp;Shuying Zhai","doi":"10.1016/j.aml.2026.109874","DOIUrl":"10.1016/j.aml.2026.109874","url":null,"abstract":"<div><div>We present a fast and effective method for image inpainting based on a modified viscous Cahn–Hilliard equation. By employing the second-order operator time-splitting method, the original problem is discretized into two subproblems based on the distinct properties of each part of the model, where the linear subproblem is handled by a Crank–Nicolson (CN) finite difference scheme, and the nonlinear subproblem is treated explicitly with the second-order strong stability preserving Runge–Kutta (SSP-RK) method. Theoretical analysis indicates that the stability of the algorithm depends on the viscosity coefficient <span><math><mi>α</mi></math></span>, and it is progressively strengthened as <span><math><mi>α</mi></math></span> increases. Numerical experiments are presented to verify the robustness and accuracy of the proposed method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109874"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Non-homogeneous discrete Dirichlet problem with singular ϕ-Laplacian 具有奇异φ -拉普拉斯算子的非齐次离散Dirichlet问题
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2025-12-27 DOI: 10.1016/j.aml.2025.109859
Andreea Gruie, Călin Şerban
{"title":"Non-homogeneous discrete Dirichlet problem with singular ϕ-Laplacian","authors":"Andreea Gruie,&nbsp;Călin Şerban","doi":"10.1016/j.aml.2025.109859","DOIUrl":"10.1016/j.aml.2025.109859","url":null,"abstract":"<div><div>We prove that, for any continuous <span><math><mrow><mi>f</mi><mo>:</mo><mi>Z</mi><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>×</mo><msup><mrow><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></mrow><mrow><mi>T</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>, the non-homogeneous discrete Dirichlet problem <span><math><mrow><mi>Δ</mi><mrow><mo>[</mo><mi>ϕ</mi><mrow><mo>(</mo><mi>Δ</mi><mi>u</mi><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow><mo>]</mo></mrow><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mo>…</mo><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mrow><mo>(</mo><mi>n</mi><mo>∈</mo><mi>Z</mi><mrow><mo>[</mo><mn>1</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>;</mo><mspace></mspace><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mi>A</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>T</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mi>B</mi><mo>,</mo></mrow></math></span> where <span><math><mrow><mi>ϕ</mi><mo>:</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> is a potential homeomorphism, is solvable iff <span><math><mrow><mrow><mo>|</mo><mi>A</mi><mo>−</mo><mi>B</mi><mo>|</mo></mrow><mo>&lt;</mo><mrow><mo>(</mo><mi>T</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>a</mi></mrow></math></span>. Our approach relies on the Legendre–Fenchel transform and Brouwer’s fixed point theorem.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109859"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145845079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 solutions to 3D MHD equations with fractional dissipation 具有分数耗散的三维MHD方程的全局解
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-12 DOI: 10.1016/j.aml.2026.109873
Xiaoping Zhai
{"title":"Global solutions to 3D MHD equations with fractional dissipation","authors":"Xiaoping Zhai","doi":"10.1016/j.aml.2026.109873","DOIUrl":"10.1016/j.aml.2026.109873","url":null,"abstract":"<div><div>The construction of global solutions for the compressible magnetohydrodynamic equations without magnetic diffusion in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> remains a challenging open problem. In an effort to address this issue, we study the Cauchy problem for the compressible magnetohydrodynamic equations with fractional dissipation <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup></math></span> on the magnetic field. We show that for any <span><math><mrow><mn>0</mn><mo>≤</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the system admits a unique global solution in Besov spaces under the assumption of small initial data. Moreover, we develop a Lyapunov-type energy argument that yields time-decay estimates of the solutions without imposing additional smallness assumptions on the low-frequency part of the initial data.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109873"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Invariant measure and numerical simulations for a stochastic predator–prey model — An example of verifying two-dimensional boundary measure integration 随机捕食者-猎物模型的不变测度和数值模拟——验证二维边界测度积分的一个例子
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-12 DOI: 10.1016/j.aml.2026.109872
Cong Lin, Xiaoling Zou, Jingliang Lv
{"title":"Invariant measure and numerical simulations for a stochastic predator–prey model — An example of verifying two-dimensional boundary measure integration","authors":"Cong Lin,&nbsp;Xiaoling Zou,&nbsp;Jingliang Lv","doi":"10.1016/j.aml.2026.109872","DOIUrl":"10.1016/j.aml.2026.109872","url":null,"abstract":"<div><div>With the continuous development of the theory of stochastic biological population models, the study of the persistence of predator–prey models has become a very meaningful topic. This paper proves the sufficient conditions for the existence of a unique ergodic invariant measure for a three-dimensional stochastic predator–prey model with Markov switching, and subsequently proposes an approximate numerical method to verify the conditions of the two-dimensional boundary measure integration, thereby providing strong numerical support for the survival analysis of the model.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109872"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145956604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Strong convergence of a fully discrete finite element approximation of non-Lipschitz SPDEs with multiplicative noise 具有乘性噪声的非lipschitz SPDEs的全离散有限元逼近的强收敛性
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-02 DOI: 10.1016/j.aml.2025.109868
Ruisheng Qi
{"title":"Strong convergence of a fully discrete finite element approximation of non-Lipschitz SPDEs with multiplicative noise","authors":"Ruisheng Qi","doi":"10.1016/j.aml.2025.109868","DOIUrl":"10.1016/j.aml.2025.109868","url":null,"abstract":"<div><div>In this paper, we consider strong convergence of a novel fully discrete finite element approximation of stochastic PDEs with non-globally Lipschitz coefficients and multiplicative noise in space dimension <span><math><mrow><mi>d</mi><mo>≤</mo><mn>3</mn></mrow></math></span>. The discretization in space is the standard finite element method and the discretization in time is a tamed drift semi-implicit scheme. This scheme makes the nonlinearity be solved explicitly while being unconditionally stable. Under regularity assumptions, we establish the optimal strong convergence rates in both space and time for the considered scheme.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109868"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Small perturbations of convective singular eigenvalue problems 对流奇异特征值问题的小扰动
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2025-12-30 DOI: 10.1016/j.aml.2025.109860
Ahmed Alsaedi , Nikolaos S. Papageorgiou , Vicenţiu D. Rădulescu
{"title":"Small perturbations of convective singular eigenvalue problems","authors":"Ahmed Alsaedi ,&nbsp;Nikolaos S. Papageorgiou ,&nbsp;Vicenţiu D. Rădulescu","doi":"10.1016/j.aml.2025.109860","DOIUrl":"10.1016/j.aml.2025.109860","url":null,"abstract":"<div><div>We consider a nonlinear Dirichlet problem with gradient dependence. The features of this paper are twofold: (i) the problem is driven by a general nonlinear nonhomogeneous differential operator with Uhlenbeck–Lieberman structure; (ii) the reaction blows-up at the origin and it is gradient dependent. Using a topological approach based on fixed point theory, we show that for all small values of <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> there are “eigenvalues” of the problem with smooth corresponding eigenfunctions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109860"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Multivalued random dynamics of colored noise driven BBM equations on 3D unbounded channels with cubic polynomial vector fields 带三次多项式向量场的三维无界通道上彩色噪声驱动BBM方程的多值随机动力学
IF 2.8 2区 数学
Applied Mathematics Letters Pub Date : 2026-05-01 Epub Date: 2026-01-02 DOI: 10.1016/j.aml.2025.109869
Ruiyi Xu, Linsong Chen, Liguang Zhou, Xuping Zhang
{"title":"Multivalued random dynamics of colored noise driven BBM equations on 3D unbounded channels with cubic polynomial vector fields","authors":"Ruiyi Xu,&nbsp;Linsong Chen,&nbsp;Liguang Zhou,&nbsp;Xuping Zhang","doi":"10.1016/j.aml.2025.109869","DOIUrl":"10.1016/j.aml.2025.109869","url":null,"abstract":"<div><div>We study the long-term multivalued random dynamical behavior for a non-autonomous Benjamin–Bona–Mahony equation on a 3D unbounded channel with a <em>non-Lipschitz diffusion coefficient</em> and a <em>cubic polynomial growth vector field</em>. Our main results are the existence of multivalued non-autonomous random dynamical systems and strongly compact random attractors in <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>. Such results for <em>quadratic polynomial vector fields</em> have been proved by Chen, Wang, Wang and Zhang (Math. Ann, 386 (2023) 343–373) and Chen, Wang and Zhang (SIAM J. Math. Anal. 56 (2024) 254–274) by the spectral decomposition method. In this paper, we prove that such results are also valid for a weak integrability condition on the time-dependent external forcing and the polynomial vector fields of <em>cubic</em> growth which involving a <em>critical</em> Sobolev embedding. The famous energy balance equation method developed by Ball (Discrete Contin. Dyn. Syst., 10 (2004) 31–52) is used to deal with the non-compact embedding problems and the non-applicability of the spectral decomposition method for cubic polynomial vector fields.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"176 ","pages":"Article 109869"},"PeriodicalIF":2.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信
小红书