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On decomposition of collocation matrices for the Cauchy–Bernstein basis and applications Cauchy-Bernstein基下配置矩阵的分解及其应用
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-24 DOI: 10.1016/j.aml.2024.109391
Zhao Yang , Tao Chen , Sanyang Liu
{"title":"On decomposition of collocation matrices for the Cauchy–Bernstein basis and applications","authors":"Zhao Yang ,&nbsp;Tao Chen ,&nbsp;Sanyang Liu","doi":"10.1016/j.aml.2024.109391","DOIUrl":"10.1016/j.aml.2024.109391","url":null,"abstract":"<div><div>In this paper, we show that collocation matrices of the Cauchy–Bernstein basis can be decomposed as products of a Cauchy–Vandermonde matrix and a block diagonal matrix. A useful application of this result is that the explicit expression of the determinant for the collocation matrices is presented. Consequently, an algorithm is provided to accurately compute the determinants. Numerical experiments confirm the high accuracy of the algorithm.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109391"},"PeriodicalIF":2.9,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142756235","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
SAV unconditional stable estimate of parallel decoupled stabilized finite element algorithm for the fully mixed Stokes–Darcy problems 针对完全混合斯托克斯-达西问题的并行解耦稳定有限元算法的 SAV 无条件稳定估计
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-23 DOI: 10.1016/j.aml.2024.109393
Chunchi Liu , Yizhong Sun , Jiaping Yu
{"title":"SAV unconditional stable estimate of parallel decoupled stabilized finite element algorithm for the fully mixed Stokes–Darcy problems","authors":"Chunchi Liu ,&nbsp;Yizhong Sun ,&nbsp;Jiaping Yu","doi":"10.1016/j.aml.2024.109393","DOIUrl":"10.1016/j.aml.2024.109393","url":null,"abstract":"<div><div>This paper investigates a fully parallel decoupled approach of the discrete stabilized finite element method for the time-dependent Stokes–Darcy problem. By introducing an auxiliary function, we rigorously demonstrate that the parallel algorithm is unconditionally stable.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109393"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723173","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
Multiple solutions of the Ambrosetti–Rabinowitz problem 安布罗塞蒂-拉宾诺维茨问题的多种解决方案
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-23 DOI: 10.1016/j.aml.2024.109390
Ziliang Yang , Jiabao Su , Mingzheng Sun
{"title":"Multiple solutions of the Ambrosetti–Rabinowitz problem","authors":"Ziliang Yang ,&nbsp;Jiabao Su ,&nbsp;Mingzheng Sun","doi":"10.1016/j.aml.2024.109390","DOIUrl":"10.1016/j.aml.2024.109390","url":null,"abstract":"<div><div>In this paper, we consider the following elliptic problem <span><math><mrow><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mspace></mspace></mtd><mtd><mtext>on</mtext><mspace></mspace><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></mrow></math></span> where the nonlinearity <span><math><mi>f</mi></math></span> satisfies the Ambrosetti–Rabinowitz condition. Using an additional growth condition of <span><math><mi>f</mi></math></span> at a bounded region, we can obtain five nontrivial solutions of <span><math><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></math></span> by applying homological linking arguments and Morse theory.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109390"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723172","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
Qualitative analysis and analytical solution for higher dimensional gas-filled hyper-spherical bubbles in an ideal fluid 理想流体中高维气体填充超球形气泡的定性分析和解析解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-23 DOI: 10.1016/j.aml.2024.109392
Yupeng Qin , Zhen Wang , Li Zou
{"title":"Qualitative analysis and analytical solution for higher dimensional gas-filled hyper-spherical bubbles in an ideal fluid","authors":"Yupeng Qin ,&nbsp;Zhen Wang ,&nbsp;Li Zou","doi":"10.1016/j.aml.2024.109392","DOIUrl":"10.1016/j.aml.2024.109392","url":null,"abstract":"<div><div>The present work concerns with the higher dimensional Rayleigh–Plesset equation for describing the nonlinear dynamics of gas-filled hyper-spherical bubbles in an ideal fluid. A strict qualitative analysis is made by means of the bifurcation theory of dynamic system, indicating that the bubble oscillation type is periodic. An analytical approach based on elliptic function is suggested to construct parametric analytical solution with arbitrary space dimension <span><math><mi>N</mi></math></span>, polytropic exponent <span><math><mi>κ</mi></math></span> and surface tension <span><math><mi>σ</mi></math></span> to the normalized higher dimensional Rayleigh–Plesset equation. The new obtained analytical solution extends the known ones for arbitrary (or some special cases of) <span><math><mi>N</mi></math></span> and <span><math><mi>κ</mi></math></span> without considering the effect of surface tension. In addition, we also discuss the dynamic characteristics for the oscillating hyper-spherical bubbles.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109392"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723212","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
Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems 分数薛定谔-泊松系统的无限多负能量解
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-22 DOI: 10.1016/j.aml.2024.109389
Anbiao Zeng, Guangze Gu
{"title":"Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems","authors":"Anbiao Zeng,&nbsp;Guangze Gu","doi":"10.1016/j.aml.2024.109389","DOIUrl":"10.1016/j.aml.2024.109389","url":null,"abstract":"<div><div>We consider the following fractional Schrödinger–Poisson system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mi>ϕ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>ϕ</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is a fixed constant, <span><math><mi>f</mi></math></span> is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109389"},"PeriodicalIF":2.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723211","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 double-parameter shifted convolution quadrature formula and its application to fractional mobile/immobile transport equations 双参数移位卷积正交公式及其在分数移动/不移动传输方程中的应用
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-21 DOI: 10.1016/j.aml.2024.109388
Zhihao Sheng , Yang Liu , Yonghai Li
{"title":"A double-parameter shifted convolution quadrature formula and its application to fractional mobile/immobile transport equations","authors":"Zhihao Sheng ,&nbsp;Yang Liu ,&nbsp;Yonghai Li","doi":"10.1016/j.aml.2024.109388","DOIUrl":"10.1016/j.aml.2024.109388","url":null,"abstract":"<div><div>In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter <span><math><mi>θ</mi></math></span> and a new variable parameter <span><math><mi>δ</mi></math></span>. We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109388"},"PeriodicalIF":2.9,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696438","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 new observation on the positive solutions for Kirchhoff equations in the exterior of a ball 对球外部基尔霍夫方程正解的新观察
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-19 DOI: 10.1016/j.aml.2024.109380
Shubin Yu
{"title":"A new observation on the positive solutions for Kirchhoff equations in the exterior of a ball","authors":"Shubin Yu","doi":"10.1016/j.aml.2024.109380","DOIUrl":"10.1016/j.aml.2024.109380","url":null,"abstract":"<div><div>We consider the existence of positive solutions for following Kirchhoff equation <span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mtext>on</mtext><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span> where <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>Ω</mi><mo>=</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>:</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>&gt;</mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span> is the exterior of the unit ball in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> and <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. It is well-known that if <span><math><mrow><mn>4</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span>, by standard minimization method on the Nehari manifold, one can obtain a positive radial solution. In present paper, we prove the existence of positive radial solutions for <span><math><mrow><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>4</mn></mrow></math></span>. This is the first contribution to the Kirchhoff equation in exterior domains provided that <span><math><mrow><mn>2</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>4</mn><mo>.</mo></mrow></math></span></div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109380"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696452","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
Optical soliton noninteraction transmission in optical communication systems 光通信系统中的光孤子非交互传输
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-19 DOI: 10.1016/j.aml.2024.109383
Xin Zhang , Xiaofeng Li , Guoli Ma
{"title":"Optical soliton noninteraction transmission in optical communication systems","authors":"Xin Zhang ,&nbsp;Xiaofeng Li ,&nbsp;Guoli Ma","doi":"10.1016/j.aml.2024.109383","DOIUrl":"10.1016/j.aml.2024.109383","url":null,"abstract":"<div><div>The building of the national communication infrastructure and growing demand for data traffic both depend heavily on the advancement of optical soliton communication technology. In particular, by studying the interaction of optical solitons, some methods of controlling optical solitons can be explored to design more stable and efficient optical communication systems. In this paper, the interactions between optical solitons are studied based on the theory of generalized Schrödinger–Hirota equation. By studying the amplitude ratio, spacing and phase difference of the optical solitons, the interactions between the optical solitons occurring in the optical fiber transmission process are attenuated. The noninteraction transmission of optical solitons are realized with small spacing between them. The conclusions of this paper are not only of great significance for the in-depth understanding of the nature of optical soliton interactions, but also of great practical value for promoting the application of optical solitons in optical communications and other fields.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109383"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696450","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
Simultaneous uniqueness identification of the fractional order and diffusion coefficient in a time-fractional diffusion equation 时间分数扩散方程中分数阶和扩散系数的同时唯一性识别
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-19 DOI: 10.1016/j.aml.2024.109386
Xiaohua Jing , Junxiong Jia , Xueli Song
{"title":"Simultaneous uniqueness identification of the fractional order and diffusion coefficient in a time-fractional diffusion equation","authors":"Xiaohua Jing ,&nbsp;Junxiong Jia ,&nbsp;Xueli Song","doi":"10.1016/j.aml.2024.109386","DOIUrl":"10.1016/j.aml.2024.109386","url":null,"abstract":"<div><div>This article is concerned with the uniqueness of simultaneously determining the fractional order of the derivative in time, diffusion coefficient, and Robin coefficient, in one-dimensional time-fractional diffusion equations with derivative order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and non-zero boundary conditions. The measurement data, which is the solution to the initial–boundary value problem, is observed at a single boundary point over a finite time interval. Based on the expansion of eigenfunctions for the solution to the forward problem and the asymptotic properties of the Mittag-Leffler function, the uniqueness of the fractional order is established. Subsequently, the uniqueness of the eigenvalues and the absolute value of the eigenfunction evaluated at <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span> for the associated operator are demonstrated. Then, the uniqueness of identifying the diffusion coefficient and the Robin coefficient is proven via an inverse boundary spectral analysis for the eigenvalue problem of the spatial differential operator. The results show that the uniqueness of three parameters can be simultaneously determined using limited boundary observations at a single spatial endpoint over a finite time interval, without imposing any constraints on the eigenfunctions of the spatial differential operator.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109386"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696359","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
Rotational symmetries of 3D point clouds using the covariance matrix and higher-order tensors 利用协方差矩阵和高阶张量计算三维点云的旋转对称性
IF 2.9 2区 数学
Applied Mathematics Letters Pub Date : 2024-11-19 DOI: 10.1016/j.aml.2024.109381
Juan Gerardo Alcázar , Michal Bizzarri , Miroslav Lávička , Jan Vršek
{"title":"Rotational symmetries of 3D point clouds using the covariance matrix and higher-order tensors","authors":"Juan Gerardo Alcázar ,&nbsp;Michal Bizzarri ,&nbsp;Miroslav Lávička ,&nbsp;Jan Vršek","doi":"10.1016/j.aml.2024.109381","DOIUrl":"10.1016/j.aml.2024.109381","url":null,"abstract":"<div><div>We prove that, under generic conditions, the covariance matrix of a 3D point cloud with rotational symmetry has a simple eigenvalue, whose associated eigenvector provides the direction of the axis of rotation, and a double eigenvalue. The direction of the axis of rotation can also be computed from higher order tensors related to the point cloud, which is useful in pathological cases. This leads to a very simple algorithm for detecting rotational symmetry and computing the axis of rotation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109381"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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