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Frontiers of Mathematics in China最新文献

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Gradient Estimates for a Class of Elliptic and Parabolic Equations on Riemannian Manifolds 黎曼流形上一类椭圆型和抛物型方程的梯度估计
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0420-0
Jie Wang
{"title":"Gradient Estimates for a Class of Elliptic and Parabolic Equations on Riemannian Manifolds","authors":"Jie Wang","doi":"10.1007/s11464-021-0420-0","DOIUrl":"https://doi.org/10.1007/s11464-021-0420-0","url":null,"abstract":"Let (N, g) be a complete noncompact Riemannian manifold with Ricci curvature bounded from below. In this paper, we study the gradient estimates of positive solutions to a class of nonlinear elliptic equations $$Delta u(x) + a(x)u(x)log u(x) + b(x)u(x) = 0$$ on N where a(x) is C2-smooth while b(x) is C1 and its parabolic counterparts $$left({Delta - {partial over {partial t}}} right)u(x,t) + a(x,t)u(x,t)log u(x,t) + b(x,t)u(x,t) = 0$$ on N × [0, ∞) where a(x, t) and b(x, t) are C2 with respect to x ∊ N while are C1 with respect to the time t. In contrast with lots of similar results, here we do not assume the coefficients of equations are constant, so our results can be viewed as extensions to several classical estimates.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894811","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
Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem 矩阵加权Kolmogorov-Riesz紧性定理
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0103-x
Shenyu Liu, Dongyong Yang, Ciqiang Zhuo
{"title":"Matrix Weighted Kolmogorov–Riesz’s Compactness Theorem","authors":"Shenyu Liu, Dongyong Yang, Ciqiang Zhuo","doi":"10.1007/s11464-021-0103-x","DOIUrl":"https://doi.org/10.1007/s11464-021-0103-x","url":null,"abstract":"In this paper, several versions of the Kolmogorov–Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight W is in the known Ap class, a characterization of totally bounded subsets in Lp(W) with p ∈ (1, ∞) is established.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894819","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: 1
Some Bounds on the Spectral Radius of Uniform Hypergraphs 一致超图谱半径的若干界
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0025-7
Xiaona Fang, Yufei Huang, Lihua You
{"title":"Some Bounds on the Spectral Radius of Uniform Hypergraphs","authors":"Xiaona Fang, Yufei Huang, Lihua You","doi":"10.1007/s11464-021-0025-7","DOIUrl":"https://doi.org/10.1007/s11464-021-0025-7","url":null,"abstract":"Let ℋ be a uniform hypergraph. In this paper, we obtain several bounds for the spectral radius of ℋ in terms of the parameters such as q-average-degrees, diameter, and characterize the corresponding extremal hypergraphs. Moreover, we discuss the change for the spectral radius of a uniform hypergraph after deleting a vertex, and give a comparison of our results with some known ones.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995425","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
Multiple Solutions for a Kirchhoff-type Problem with Vanishing Nonlocal Term and Fractional p-Laplacian 一类非局部项消失的分数阶p-拉普拉斯kirchhoff型问题的多重解
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0019-5
Zhenhai Liu, Dumitru Motreanu, Shengda Zeng
{"title":"Multiple Solutions for a Kirchhoff-type Problem with Vanishing Nonlocal Term and Fractional p-Laplacian","authors":"Zhenhai Liu, Dumitru Motreanu, Shengda Zeng","doi":"10.1007/s11464-021-0019-5","DOIUrl":"https://doi.org/10.1007/s11464-021-0019-5","url":null,"abstract":"The goal of the paper is to investigate a Kirchhoff-type elliptic problem driven by a generalized nonlocal fractional p-Laplacian whose nonlocal term vanishes at finitely many points. Multiple nontrivial solutions are obtained by applying a variational method combined with truncation techniques.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995420","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
Combined Effects of Concave and Convex Nonlinearities for Kirchhoff Type Equations with Steep Potential Well and 1 < p < 2 < q < 4 具有陡势井和1 &lt的Kirchhoff型方程的凹凸非线性联合效应p & lt;2 & lt;问& lt;4
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0071-1
Jianhua Chen, Xianjiu Huang, Bitao Cheng
{"title":"Combined Effects of Concave and Convex Nonlinearities for Kirchhoff Type Equations with Steep Potential Well and 1 &lt; p &lt; 2 &lt; q &lt; 4","authors":"Jianhua Chen, Xianjiu Huang, Bitao Cheng","doi":"10.1007/s11464-021-0071-1","DOIUrl":"https://doi.org/10.1007/s11464-021-0071-1","url":null,"abstract":"In this paper, we study a class of Kirchhoff type equations with concave and convex nonlinearities and steep potential well. Firstly, we obtain a positive energy solution $$u_{b,lambda}^ + $$ by a truncated functional. Furthermore, the concentration behavior of $$u_{b,lambda}^ + $$ is also explored on the set V−1 (0) as λ → ∞. Secondly, we also give the existence of a negative solution $$u_{b,lambda}^ - $$ via Ekeland variational principle. Finally, we show a nonexistence result of the nontrivial solutions.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135587805","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
Response Solutions for KdV Equations with Liouvillean Frequency 具有liouville频率的KdV方程的响应解
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0099-2
Ningning Chang, Jiansheng Geng, Yingnan Sun
{"title":"Response Solutions for KdV Equations with Liouvillean Frequency","authors":"Ningning Chang, Jiansheng Geng, Yingnan Sun","doi":"10.1007/s11464-021-0099-2","DOIUrl":"https://doi.org/10.1007/s11464-021-0099-2","url":null,"abstract":"In this paper, we prove an infinite dimensional KAM (Kolmogorov–Arnold–Moser) theorem, which can be used to the KdV equations $${u_t} + {partial _{xxx}}u - varepsilon {partial _x}f(omega t,x,u) = 0,$$ where $$omega = xi bar omega ,,,bar omega = (1,alpha)$$ is Liouvillean forced frequency and f is real analytic. We obtain a C∞ smooth response solution under zero mean-value periodic boundary conditions. The proof is based on a modified infinite dimensional KAM theory.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995418","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
Hochschild (Co)homologies of DG K-algebras and Their Koszul Duals DG - k -代数的Hochschild (Co)同调及其Koszul对偶
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-020-0213-x
Yang Han, Xin Liu, Kai Wang
{"title":"Hochschild (Co)homologies of DG K-algebras and Their Koszul Duals","authors":"Yang Han, Xin Liu, Kai Wang","doi":"10.1007/s11464-020-0213-x","DOIUrl":"https://doi.org/10.1007/s11464-020-0213-x","url":null,"abstract":"We compare the Hochschild (co)homologies of a complete typical DG K-algebra and its Koszul dual. We show that the Koszul dual of a finite dimensional complete typical symmetric DG K-algebra is a Calabi–Yau DG K-algebra whose Hochschild cohomology is a Batalin–Vilkovisky algebra. Furthermore, we prove that the Hochschild cohomologies of a finite dimensional complete typical symmetric DG K-algebra and its Koszul dual are isomorphic as Batalin–Vilkovisky algebras.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995424","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
Some Comparisons of Dirichlet, Neumann and Buckling Eigenvalues on Riemannian Manifolds 黎曼流形上Dirichlet、Neumann和屈曲特征值的一些比较
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0078-7
Guangyue Huang, Bingqing Ma
{"title":"Some Comparisons of Dirichlet, Neumann and Buckling Eigenvalues on Riemannian Manifolds","authors":"Guangyue Huang, Bingqing Ma","doi":"10.1007/s11464-021-0078-7","DOIUrl":"https://doi.org/10.1007/s11464-021-0078-7","url":null,"abstract":"In this paper, we study some comparisons of Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds. By introducing a new parameter, we provide some new relationships, which improve corresponding results of Ilias and Shouman in [Calc. Var. Partial Differential Equations, 2020, 59: Paper No. 127, 15 pp.] in some sense.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995419","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
Joint Distributions Concerning Last Exit Time for Diffusion Processes 扩散过程最后退出时间的联合分布
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0094-7
Ye Chen, Yingqiu Li
{"title":"Joint Distributions Concerning Last Exit Time for Diffusion Processes","authors":"Ye Chen, Yingqiu Li","doi":"10.1007/s11464-021-0094-7","DOIUrl":"https://doi.org/10.1007/s11464-021-0094-7","url":null,"abstract":"Adopting a Poisson approach in Li and Zhou [Statist. Probab. Lett., 2014, 94: 48–55], for one-dimensional diffusion processes, we consider some joint distributions, including the last exit time from a semi-infinite interval, the value of the process at the last exit time and the associated occupation time. Our results are expressed in term of solutions to the differential equations associated with the diffusion generator.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995422","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
Recursion Formulas on Hall Numbers for Weighted Projective Lines 加权投影线霍尔数的递推公式
3区 数学
Frontiers of Mathematics in China Pub Date : 2023-09-01 DOI: 10.1007/s11464-021-0123-6
Xiaofeng Zhang
{"title":"Recursion Formulas on Hall Numbers for Weighted Projective Lines","authors":"Xiaofeng Zhang","doi":"10.1007/s11464-021-0123-6","DOIUrl":"https://doi.org/10.1007/s11464-021-0123-6","url":null,"abstract":"We study the property of Hall numbers for the category of coherent sheaves over a weighted projective line. Several recursion formulas on Hall numbers are obtained, whose proofs rely on Green’s formula. Similar formulas for tame quivers and cyclic quivers are discussed.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995421","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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