CSpaceCommunity: 数学所
http://ir.amss.ac.cn:80/handle/2S8OKBNM/5
Thu, 29 Feb 2024 12:25:58 GMT2024-02-29T12:25:58ZExistence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61527
Title: Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations
Authors: Luo, Haijun; Zhang, Zhitao
Description: We study the existence and orbital stability of normalized solutions of the biharmonic equation with the mixed dispersion and a general nonlinear term
gamma Delta(2)u - beta Delta u + lambda u = f(u), x is an element of R-N
with a priori prescribed L-2-norm constraint S-a := {u is an element of H-2(R-N) : integral R-N |u|(2)dx = ao, where a > 0, gamma > 0, beta. R and the nonlinear term f satisfies the suitable L-2-subcritical assumptions. When beta >= 0, we prove that there exists a threshold value a(0) >= 0 such that the equation above has a ground state solution which is orbitally stable if a > a0 and has no ground state solution if a < a(0). However, for beta < 0, this case is more involved. Under an additional assumption on f, we get the similar results on the existence and orbital stability of ground state. Finally, we consider a specific nonlinearity f (u) = |u|(p-2)u + mu|u|(q-2)u, 2 < q < p < 2 + 8/N, mu < 0 under the case beta < 0, which does not satisfy the additional assumption. And we use the example to show that the energy in the case beta < 0 exhibits a more complicated nature than that of the case beta = 0.Tue, 07 Feb 2023 00:56:54 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615272023-02-07T00:56:54ZSome results on free boundary problems of incompressible ideal magnetohydrodynamics equations
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61524
Title: Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations
Authors: Hao, Chengchun; Luo, Tao
Description: We survey some recent results related to free boundary problems of incompressible ideal magnetohydrodynamics equations, and present the main ideas in the proofs of the ill-posedness in 2D when the Taylor sign condition is violated given [1], and the well-posedness of a linearized problem given in [2] in general n-dimensions (n. 2) when the Taylor sign condition is satisfied and the free boundaries are closed.Tue, 07 Feb 2023 00:56:53 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/615242023-02-07T00:56:53ZClustering using matrix product states
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61497
Title: Clustering using matrix product states
Authors: Shi, Xiao; Shang, Yun; Guo, Chu
Description: The matrix product state has been demonstrated to be able to explore the most relevant portion of the exponentially large quantum Hilbert space and find accurate solutions for one-dimensional interacting quantum many-body systems. Inspired by this success, here we propose a clustering algorithm based on the matrix product state, which first maps the classical data into quantum states represented as matrix product states, and then minimizes the loss function using a variational matrix product states algorithm in the enlarged space. We demonstrate this algorithm by applying it to several commonly used machine learning data sets, showing that this algorithm could reach higher learning precision and that it is less likely to be trapped in local minima compared to the standard K-means algorithm. We also show that this algorithm can achieve state-of-the-art learning precision on popular computer vision data sets when used in combination with better initialization schemes.Tue, 07 Feb 2023 00:56:49 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/614972023-02-07T00:56:49ZGlobal Existence of Strong and Weak Solutions to 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61343
Title: Global Existence of Strong and Weak Solutions to 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum
Authors: Fan, Xinyu; Li, Jiaxu; Li, Jing
Description: The barotropic compressible Navier-Stokes system subject to the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain is considered. For initial density allowed to vanish, the global existence of strong and weak solutions is established when the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. It should be mentioned that this result is obtained without any restrictions on the size of initial value. To get over the difficulties brought by boundary, on the one hand, Riemann mapping theorem and the pull-back Green's function method are applied to get a pointwise representation of the effective viscous flux. On the other hand, since the orthogonality is preserved under conformal mapping due to its preservation on the angle, the slip boundary conditions are used to reduce the integral representation to the desired commutator form whose singularities can be cancelled out by using the estimates on the spatial gradient of the velocity.Tue, 07 Feb 2023 00:56:25 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/613432023-02-07T00:56:25ZNetworked Knowledge and Complex Networks: An Engineering View
http://ir.amss.ac.cn:80/handle/2S8OKBNM/61115
Title: Networked Knowledge and Complex Networks: An Engineering View
Authors: Lu, Jinhu; Wen, Guanghui; Lu, Ruqian; Wang, Yong; Zhang, Songmao
Description: Along with the development of information technologies such as mobile Internet, information acquisition technology, cloud computing and big data technology, the traditional knowledge engineering and knowledge-based software engineering have undergone fundamental changes where the network plays an increasingly important role. Within this context, it is required to develop new methodologies as well as technical tools for network-based knowledge representation, knowledge services and knowledge engineering. Obviously, the term "network" has different meanings in different scenarios. Meanwhile, some breakthroughs in several bottleneck problems of complex networks promote the developments of the new methodologies and technical tools for network-based knowledge representation, knowledge services and knowledge engineering. This paper first reviews some recent advances on complex networks, and then, in conjunction with knowledge graph, proposes a framework of networked knowledge which models knowledge and its relationships with the perspective of complex networks. For the unique advantages of deep learning in acquiring and processing knowledge, this paper reviews its development and emphasizes the role that it played in the development of knowledge engineering. Finally, some challenges and further trends are discussed.Tue, 07 Feb 2023 00:55:50 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/611152023-02-07T00:55:50ZAnnotating regulatory elements by heterogeneous network embedding
http://ir.amss.ac.cn:80/handle/2S8OKBNM/60394
Title: Annotating regulatory elements by heterogeneous network embedding
Authors: Lu, Yurun; Feng, Zhanying; Zhang, Songmao; Wang, Yong
Description: Motivation: Regulatory elements (REs), such as enhancers and promoters, are known as regulatory sequences functional in a heterogeneous regulatory network to control gene expression by recruiting transcription regulators and carrying genetic variants in a context specific way. Annotating those REs relies on costly and labor-intensive next-generation sequencing and RNA-guided editing technologies in many cellular contexts.
Results: We propose a systematic Gene Ontology Annotation method for Regulatory Elements (RE-GOA) by leveraging the powerful word embedding in natural language processing. We first assemble a heterogeneous network by integrating context specific regulations, protein-protein interactions and gene ontology (GO) terms. Then we perform network embedding and associate regulatory elements with GO terms by assessing their similarity in a low dimensional vector space. With three applications, we show that RE-GOA outperforms existing methods in annotating TFs' binding sites from ChIP-seq data, in functional enrichment analysis of differentially accessible peaks from ATAC-seq data, and in revealing genetic correlation among phenotypes from their GWAS summary statistics data.Tue, 21 Jun 2022 07:53:12 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/603942022-06-21T07:53:12ZON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES
http://ir.amss.ac.cn:80/handle/2S8OKBNM/60182
Title: ON THE HOMOTOPY OF CLOSED MANIFOLDS AND FINITE CW-COMPLEXES
Authors: Su, Yang; Wu, Xiaolei
Description: We study the finite generation of homotopy groups of closed manifolds and finite CW-complexes by relating it to the cohomology of their fundamental groups. Our main theorems are as follows: when X is a finite CW-complex of dimension n and pi(1)(X) is virtually a Poincare duality group of dimension >= n - 1, then pi(i)(X) is not finitely generated for some i unless X is homotopy equivalent to the Eilenberg-MacLane space K(pi(1)(X), 1); when M is an n-dimensional closed manifold and pi(1)(M) is virtually a Poincare duality group of dimension >= n - 1, then for some i <= [n/2], pi(i)(M) is not finitely generated, unless M itself is an aspherical manifold. These generalize theorems of M. Damian [Trans. Amer. Math. Soc. 361 (2009), pp. 1791-1809] from polycyclic groups to any virtually Poincare duality groups.Fri, 29 Apr 2022 00:46:20 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/601822022-04-29T00:46:20Z同余数问题和Goldfeld猜想
http://ir.amss.ac.cn:80/handle/2S8OKBNM/58376
Title: 同余数问题和Goldfeld猜想
Authors: 田野
Description: 本文介绍同余数问题的最新进展,特别地,同余椭圆曲线Goldfeld猜想的进展.Mon, 26 Apr 2021 00:57:38 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/583762021-04-26T00:57:38ZGlobal Well-Posedness and Exponential Stability of 3D Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum in Unbounded Domains
http://ir.amss.ac.cn:80/handle/2S8OKBNM/57953
Title: Global Well-Posedness and Exponential Stability of 3D Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum in Unbounded Domains
Authors: He, Cheng; Li, Jing; Lu, Boqiang
Description: We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional (3D) nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. After establishing some key a priori exponential decay-in-time rates of the strong solutions, we obtain both the global existence and exponential stability of strong solutions in the whole three-dimensional space, provided that the initial velocity is suitably small in some homogeneous Sobolev space which may be optimal compared with the case of homogeneous Navier-Stokes equations. Note that this result is proved without any smallness conditions on the initial density which contains vacuum and even has compact support.Mon, 26 Apr 2021 00:56:24 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/579532021-04-26T00:56:24ZOn uniqueness of static asymptotically anti-de Sitter black hole
http://ir.amss.ac.cn:80/handle/2S8OKBNM/52124
Title: On uniqueness of static asymptotically anti-de Sitter black hole
Authors: He,Xiaokai; Cao,Zhoujian; Fang,Xiongjun; Jing,Jiliang; Wu,Xiaoning
Description: AbstractIn this paper, the asymptotically anti-de Sitter spacetime with a hypersurface orthogonal Killing vector field is discussed near the conformal boundary by using Newman–Penrose formalism. We first investigate the multipole structure of a static, asymptotically anti-de Sitter spacetime. We note that, different to asymptotically flat case in which the multipoles are contained in Ψ0k, the multipoles of a static, asymptotically anti-de Sitter spacetime are all contained in Ψ20. We then show that the Schwarzschild anti-de Sitter spacetime is the only asymptotically anti-de Sitter, vacuum, static, axisymmetric, type-D analytic solution of vacuum Einstein equation with a negative cosmological constant in a Bondi coordinate neighborhood of the conformal boundary if the spherical harmonic expansion of Ψ20 is finite.Thu, 14 Jan 2021 00:16:58 GMThttp://ir.amss.ac.cn:80/handle/2S8OKBNM/521242021-01-14T00:16:58Z