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Non degenerating Dehn fillings on genus two Heegaard splittings of knots' complements

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Science China mathematics 2018年第6期61卷 1099-1108页

作者： Jiming Ma Ruifeng Qiu Yanqing Zou School of Mathematical Sciences Fudan University department of mathematics Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal University department of mathematics Dalian Minzu University

It is Thurston's result that for a hyperbolic knot K in S^3, almost all Dehn fillings on its complement result in hyperbolic 3-manifolds except some exceptional cases. So almost all produced 3-manifolds have the same geometry. It is known that its complement in S^3, denoted by E(K), admits a Heegaard splitting. Then it is expected that there is a similar result on Heegaard distance for Dehn fillings. In this paper, Dehn fillings on genus two Heegaard splittings are studied. More precisely, we prove that if the distance of a given genus two Heegaard splitting of E(K) is at least 3, then for any two degenerating slopes on ?E(K), there is a universal bound of their distance in the curve complex of ?E(K).

关键词： Heegaard distance Dehn filling hyperbolic knot curve complex

Tensor Tomography: Progress and Challenges

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Chinese Annals of mathematics,Series B 2014年第3期35卷 399-428页

作者： Gabriel P. PATERNAIN Mikko SALO Gunther UHLMANN department of pure mathematics and Mathematical Statistics University of Cambridge department of mathematics and Statistics University of Jyvskyl department of mathematics University of Washington and University of HelsinkiBox 354350 Seattle Washington 98195-4350 USA

The authors survey recent progress in the problem of recovering a tensor field from its integrals along geodesics. Several open problems are also proposed.

关键词： Inverse problem Integral geometry Tensor tomography

EXISTENCE TO FRACTIONAL CRITICAL EQUATION WITH HARDY-LITTLEWOOD-SOBOLEV NONLINEARITIES

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Acta Mathematica Scientia 2021年第4期41卷 1321-1332页

作者： Nemat NYAMORADI Abdolrahman RAZANI department of mathematics Razi UniversityKermanshahIran department of pure mathematics Faculty of ScienceImam Khomeini International University34149-16818QazvinIran

In this paper,we consider the following new Kirchhoff-type equations involving the fractional p-Laplacian and Hardy-Littlewood-Sobolev critical nonlinearity:(A+B∫∫_(R^(2N))|u(x)-u(y)|^(p)/|x-y|^(N+ps)dxdy)^(p-1)(-△)_(p)^(s)u+λV(x)|u|^(p-2)u=(∫_(R^(N))|U|^(P_(μ,S)^(*))/|x-y|^(μ)dy)|u|^(P_(μ,S)^(*))^(-2)u,x∈R^(N),where(-△)_(p)^(s)is the fractional p-Laplacian with 0ps,a,b>0,λ>0 is a parameter,V:R^(N)→R^(+)is a potential function,θ∈[1,2_(μ,s)^(*))and P_(μ,S)^(*)=pN-pμ/2/N-ps is the critical exponent in the sense of Hardy-Littlewood-Sobolev *** get the existence of infinitely many solutions for the above problem by using the concentration compactness principle and Krasnoselskii’s genus *** the best of our knowledge,our result is new even in Choquard-Kirchhoff-type equations involving the p-Laplacian case.

关键词： Hardy-Littlewood-Sobolev inequality concentration-compactness principle variational method Fractional p-Laplacian operators multiple solutions

Cohomogeneity One de Sitter Space S1 n

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Acta Mathematica Sinica,English Series 2010年第10期26卷 1915-1926页

作者： P.AHMADI S.M.B.KASHANI H.ABEDI department of pure mathematics Faculty of Mathematical SciencesTarbiat Modares University Group of mathematics School of Sciences Bu-Ali Sina University

In this paper we study the cohomogeneity one de Sitter space S1 n. We consider the actions in both proper and non-proper cases. In the first case we characterize the acting groups and orbits and we prove that the orbit space is homeomorphic to R. In the latter case we determine the groups and consequently the orbits in some different cases and prove that the orbit space is not Hausdorff.

关键词： Cohomogeneity one Lorentzian space de Sitter space

Stable recovery of signals from frame coefficients with erasures at unknown locations

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Science China mathematics 2018年第1期61卷 151-172页

作者： Deguang Han Fusheng Lv Wenchang Sun department of mathematics University of Central Florida School of Mathematical Sciences and the Key Laboratory of pure mathematics and Combinatorics Ministry of Education Nankai University

In an earlier work, we proposed a frame-based kernel analysis approach to the problem of recovering erasures from unknown locations. The new approach led to the stability question on recovering a signal from noisy partial frame coefficients with erasures occurring at unknown locations. In this continuing work, we settle this problem by obtaining a complete characterization of frames that provide stable reconstructions. We show that an encoding frame provides a stable signal recovery from noisy partial frame coefficients at unknown locations if and only if it is totally robust with respect to erasures. We present several characterizations for either totally robust frames or almost robust frames. Based on these characterizations several explicit construction algorithms for totally robust and almost robust frames are proposed. As a consequence of the construction methods, we obtain that the probability for a randomly generated frame to be totally robust with respect to a fixed number of erasures is one.

关键词： frames erasures signal recovery almost robust frames totally robust frames

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE

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Acta Mathematica Scientia 2023年第5期43卷 2204-2214页

作者： Ali ABKAR department of pure mathematics Faculty of ScienceImam Khomeini International UniversityQazvin 34149Iran

We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the u... 详细信息

关键词： mean approximation dilatation non-radial weight angular weight weighted Bergman space weighted Besov space

Braids with Trivial Simple Centralizer

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Algebra Colloquium 2015年第4期22卷 561-566页

作者： U. Ali F. Azam I. Javaid A. Haider Center for Advanced Studies in pure and Applied mathematics Bahauddin Zakariya university Multan Pakistan department of mathematics Jazan University Jazan Saudi Arabia

In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnect... 详细信息

关键词： simple braid simple centralizer commuting graph

VARIATIONAL IMAGE FUSION WITH FIRST AND SECOND-ORDER GRADIENT INFORMATION

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Journal of Computational mathematics 2016年第2期34卷 200-222页

作者： Fang Li Tieyong Zeng department of mathematics East China Normal University and Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai China department of mathematics Hong Kong Baptist University Kowloon Tong Hong Kong

Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method based on the first and second-order gradient information. Firstly, we select the target first-order and second-order gradient information from the source images by a new and simple salience criterion. Then we build our model by requiring that the first-order and second-order gradient information of the fused image match with the target gradient information, and meanwhile the fused image is close to the source images. Theoretically, we can prove that our variational model has a unique minimizer. In the numerical implementation, we take use of the split Bregman method to get an efficient algorithm. Moreover, four-direction difference scheme is proposed to discrete gradient operator, which can dramatically enhance the fusion quality. A number of experiments and comparisons with some popular existing methods demonstrate that the proposed model is promising in various image fusion applications.

关键词： Image fusion Feature selection Bounded variation Second bounded variation,Split Bregman

Existence of positive solutions to some nonlinear equations on locally finite graphs

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Science China mathematics 2017年第7期60卷 1311-1324页

作者： GRIGOR''YAN Alexander LIN Yong YANG YunYan department of mathematics University of BielefeldBielefeld 33501Germany School of Mathematical Sciences and Laboratory of pure mathematics and Combinatorics Nankai UniversityTianjin 300071China department of mathematics Renmin University of ChinaBeijing 100872China

Let G =(V,E) be a locally finite graph,whose measure μ(x) has positive lower bound,and A be the usual graph *** the mountain-pass theorem due to Ambrosetti and Rabinowitz(1973),we establish existence results for some nonlinear equations,namely △u+hu=f(x,u),x∈*** particular,we prove that if h and f satisfy certain assumptions,then the above-mentioned equation has strictly positive ***,we consider existence of positive solutions of the perturbed equation △u+hu=f(x,u)+∈*** problems have been extensively studied on the Euclidean space as well as on Riemannian manifolds.

关键词： variational method mountain-pass theorem semi-linear equation on graphs