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学者姓名：苏延辉
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Abstract ：
In this paper, we prove some analogues of Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice Z(n). This partially answers a question posed by Chung and Oden (Pac J Math 192(2):257-273, 2000).
Keyword ：
Dirichlet Laplacians on graphs Dirichlet Laplacians on graphs Eigenvalues Eigenvalues Universal inequalities for eigenvalues Universal inequalities for eigenvalues
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| GB/T 7714 | Hua, Bobo , Lin, Yong , Su, Yanhui . Payne-Polya-Weinberger, Hile-Protter and Yang's Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices [J]. | JOURNAL OF GEOMETRIC ANALYSIS , 2023 , 33 (7) . |
| MLA | Hua, Bobo 等. "Payne-Polya-Weinberger, Hile-Protter and Yang's Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices" . | JOURNAL OF GEOMETRIC ANALYSIS 33 . 7 (2023) . |
| APA | Hua, Bobo , Lin, Yong , Su, Yanhui . Payne-Polya-Weinberger, Hile-Protter and Yang's Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices . | JOURNAL OF GEOMETRIC ANALYSIS , 2023 , 33 (7) . |
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We prove that the total curvature of any planar graph with non negative combinatorial curvature is an integral multiple of 112. As a corollary, this answers a question proposed by T. Re ' ti.
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| GB/T 7714 | Hua, Bobo , Su, Yanhui . TOTAL CURVATURE OF PLANAR GRAPHS WITH NONNEGATIVE COMBINATORIAL CURVATURE [J]. | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY , 2022 . |
| MLA | Hua, Bobo 等. "TOTAL CURVATURE OF PLANAR GRAPHS WITH NONNEGATIVE COMBINATORIAL CURVATURE" . | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2022) . |
| APA | Hua, Bobo , Su, Yanhui . TOTAL CURVATURE OF PLANAR GRAPHS WITH NONNEGATIVE COMBINATORIAL CURVATURE . | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY , 2022 . |
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In this article, we consider the numerical solution for the time fractional differential equations (TFDEs). We propose a parallel in time method, combined with a spectral collocation scheme and the finite difference scheme for the TFDEs. The parallel in time method follows the same sprit as the domain decomposition that consists in breaking the domain of computation into subdomains and solving iteratively the sub-problems over each subdomain in a parallel way. Concretely, the iterative scheme falls in the category of the predictor-corrector scheme, where the predictor is solved by finite difference method in a sequential way, while the corrector is solved by computing the difference between spectral collocation and finite difference method in a parallel way. The solution of the iterative method converges to the solution of the spectral method with high accuracy. Some numerical tests are performed to confirm the efficiency of the method in three areas: (i) convergence behaviors with respect to the discretization parameters are tested; (ii) the overall CPU time in parallel machine is compared with that for solving the original problem by spectral method in a single processor; (iii) for the fixed precision, while the parallel elements grow larger, the iteration number of the parallel method always keep constant, which plays the key role in the efficiency of the time parallel method. © The Author(s) 2021.
Keyword ：
Convergence of numerical methods Convergence of numerical methods Domain decomposition methods Domain decomposition methods Efficiency Efficiency Finite difference method Finite difference method Iterative methods Iterative methods Spectroscopy Spectroscopy
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| GB/T 7714 | Li, Xianjuan , Su, Yanhui . A parallel in time/spectral collocation combined with finite difference method for the time fractional differential equations [J]. | Journal of Algorithms and Computational Technology , 2021 , 15 . |
| MLA | Li, Xianjuan 等. "A parallel in time/spectral collocation combined with finite difference method for the time fractional differential equations" . | Journal of Algorithms and Computational Technology 15 (2021) . |
| APA | Li, Xianjuan , Su, Yanhui . A parallel in time/spectral collocation combined with finite difference method for the time fractional differential equations . | Journal of Algorithms and Computational Technology , 2021 , 15 . |
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Woess [30] introduced a curvature notion on the set of edges of a planar graph, called Psi-curvature in our paper, which is stable under the planar duality. We study geometric and combinatorial properties for the class of infinite planar graphs with non-negative Psi-curvature. By using the discharging method, we prove that for such an infinite graph the number of vertices (resp. faces) of degree k, except k = 3, 4 or 6, is finite. As a main result, we prove that for an infinite planar graph with non-negative Psi-curvature the sum of the number of vertices of degree at least 8 and the number of faces of degree at least 8 is at most one. (C) 2021 Elsevier Inc. All rights reserved.
Keyword ：
4-regular 4-regular Combinatorial curvature Combinatorial curvature Planar graph Planar graph Psi-curvature Psi-curvature
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| GB/T 7714 | Akama, Yohji , Hua, Bobo , Su, Yanhui et al. A curvature notion for planar graphs stable under planar duality [J]. | ADVANCES IN MATHEMATICS , 2021 , 385 . |
| MLA | Akama, Yohji et al. "A curvature notion for planar graphs stable under planar duality" . | ADVANCES IN MATHEMATICS 385 (2021) . |
| APA | Akama, Yohji , Hua, Bobo , Su, Yanhui , Wang, Lili . A curvature notion for planar graphs stable under planar duality . | ADVANCES IN MATHEMATICS , 2021 , 385 . |
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The dying ReLU refers to the problem when ReLU neurons become inactive and only output 0 for any input. There are many empirical and heuristic explanations of why ReLU neurons die. However, little is known about its theoretical analysis. In this paper, we rigorously prove that a deep ReLU network will eventually die in probability as the depth goes to infinite. Several methods have been proposed to alleviate the dying ReLU. Perhaps, one of the simplest treatments is to modify the initialization procedure. One common way of initializing weights and biases uses symmetric probability distributions, which suffers from the dying ReLU. We thus propose a new initialization procedure, namely, a randomized asymmetric initialization. We show that the new initialization can effectively prevent the dying ReLU. All parameters required for the new initialization are theoretically designed. Numerical examples are provided to demonstrate the effectiveness of the new initialization procedure.
Keyword ：
Dying ReLU Dying ReLU Neural network Neural network Randomized asym-metric initialization Randomized asym-metric initialization Vanishing/Exploding gradient Vanishing/Exploding gradient
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| GB/T 7714 | Lu, Lu , Shin, Yeonjong , Su, Yanhui et al. Dying ReLU and Initialization: Theory and Numerical Examples [J]. | COMMUNICATIONS IN COMPUTATIONAL PHYSICS , 2020 , 28 (5) : 1671-1706 . |
| MLA | Lu, Lu et al. "Dying ReLU and Initialization: Theory and Numerical Examples" . | COMMUNICATIONS IN COMPUTATIONAL PHYSICS 28 . 5 (2020) : 1671-1706 . |
| APA | Lu, Lu , Shin, Yeonjong , Su, Yanhui , Karniadakis, George Em . Dying ReLU and Initialization: Theory and Numerical Examples . | COMMUNICATIONS IN COMPUTATIONAL PHYSICS , 2020 , 28 (5) , 1671-1706 . |
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In this paper, we give the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature. Based on this, we show that the automorphism group of a planar-possibly infinite-graph with nonnegative combinatorial curvature and positive total curvature is a finite group, and give an upper bound estimate for the order of the group. (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
Automorphism group Automorphism group Combinatorial curvature Combinatorial curvature Planar graph Planar graph Total curvature Total curvature
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| GB/T 7714 | Hua, Bobo , Su, Yanhui . The set of vertices with positive curvature in a planar graph with nonnegative curvature [J]. | ADVANCES IN MATHEMATICS , 2019 , 343 : 789-820 . |
| MLA | Hua, Bobo et al. "The set of vertices with positive curvature in a planar graph with nonnegative curvature" . | ADVANCES IN MATHEMATICS 343 (2019) : 789-820 . |
| APA | Hua, Bobo , Su, Yanhui . The set of vertices with positive curvature in a planar graph with nonnegative curvature . | ADVANCES IN MATHEMATICS , 2019 , 343 , 789-820 . |
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We prove that the total curvature of a planar graph with nonnegative combinatorial curvature is at least 1/12 if it is positive. Moreover, we classify the metric structures of ambient polygonal surfaces for planar graphs attaining this bound.
Keyword ：
combinatorial curvature combinatorial curvature planar graphs planar graphs total curvature total curvature
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| GB/T 7714 | Hua, Bobo , Su, Yanhui . The first gap for total curvatures of planar graphs with nonnegative curvature [J]. | JOURNAL OF GRAPH THEORY , 2019 , 93 (3) : 395-439 . |
| MLA | Hua, Bobo et al. "The first gap for total curvatures of planar graphs with nonnegative curvature" . | JOURNAL OF GRAPH THEORY 93 . 3 (2019) : 395-439 . |
| APA | Hua, Bobo , Su, Yanhui . The first gap for total curvatures of planar graphs with nonnegative curvature . | JOURNAL OF GRAPH THEORY , 2019 , 93 (3) , 395-439 . |
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Abstract ：
研究正组合曲率带边有限图的分类,证明除正多边形外,带边有限图只有71种互不同构的类型,并给出全部分类.另外,得到正组合曲率有限图的最大顶点数为28.
Keyword ：
分类问题 分类问题 有限图 有限图 组合曲率 组合曲率
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| GB/T 7714 | 苏延辉 . 正组合曲率带边有限图的分类 [J]. | 福州大学学报（自然科学版） , 2018 , 46 (6) : 759-763 . |
| MLA | 苏延辉 . "正组合曲率带边有限图的分类" . | 福州大学学报（自然科学版） 46 . 6 (2018) : 759-763 . |
| APA | 苏延辉 . 正组合曲率带边有限图的分类 . | 福州大学学报（自然科学版） , 2018 , 46 (6) , 759-763 . |
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The Ladyzenskaja-Babuska-Brezzi (LBB) condition is a necessary condition for the well-posedness of discrete saddle point problems stemming from discretizing the Stokes equations. In this paper, we prove the LBB condition and provide the (optimal) lower bound for this condition for the triangular spectral method proposed by L. Chen, J. Shen, and C. Xu in [3]. Then this lower bound is used to derive an error estimate for the pressure. Some numerical examples are provided to confirm the theoretical estimates.
Keyword ：
Inf-Sup Condition Inf-Sup Condition Stokes Equations Stokes Equations Triangular Spectral Method Triangular Spectral Method
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| GB/T 7714 | Su, Yanhui , Chen, Lizhen , Li, Xianjuan et al. On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations [J]. | COMPUTATIONAL METHODS IN APPLIED MATHEMATICS , 2016 , 16 (3) : 507-522 . |
| MLA | Su, Yanhui et al. "On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations" . | COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 16 . 3 (2016) : 507-522 . |
| APA | Su, Yanhui , Chen, Lizhen , Li, Xianjuan , Xu, Chuanju . On the Inf-Sup Constant of a Triangular Spectral Method for the Stokes Equations . | COMPUTATIONAL METHODS IN APPLIED MATHEMATICS , 2016 , 16 (3) , 507-522 . |
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We provide a parallel spectral element method for the fractional Lorenz system numerically. The detailed construction and implementation of the method are presented. Thanks to the spectral accuracy of the presented method, the storage requirement due to the "global time dependence" can be considerably relaxed. Also, the parareal method combining spectral element method reduces the computing time greatly. Finally, we have tested the chaotic behaviors of fractional Lorenz system. Our numerical results are in excellent agreement with the results from other numerical methods.
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| GB/T 7714 | Su, Yanhui . A Parallel Spectral Element Method for Fractional Lorenz System [J]. | DISCRETE DYNAMICS IN NATURE AND SOCIETY , 2015 . |
| MLA | Su, Yanhui . "A Parallel Spectral Element Method for Fractional Lorenz System" . | DISCRETE DYNAMICS IN NATURE AND SOCIETY (2015) . |
| APA | Su, Yanhui . A Parallel Spectral Element Method for Fractional Lorenz System . | DISCRETE DYNAMICS IN NATURE AND SOCIETY , 2015 . |
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