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The Kohn–Laplacian and Cauchy–Szegö projection on model domains 模型域上的Kohn–Laplacian和Cauchy–Szegö投影
IF 0.6 Pub Date : 2022-11-27 DOI: 10.4310/amsa.2023.v8.n1.a4
D. Chang, Ji Li, Jingzhi Tie, Qingyan Wu
We study the Kohn-Laplacian and its fundamental solution on some model domains in $mathbb C^{n+1}$, and further discuss the explicit kernel of the Cauchy-Szeg"o projections on these model domains using the real analysis method. We further show that these Cauchy-Szeg"o kernels are Calder'on-Zygmund kernels under the suitable quasi-metric.
我们研究了$mathbb C^{n+1}$中某些模型域上的Kohn-Laplacian及其基本解,并用实分析方法进一步讨论了这些模型域上Cauchy-Szeg ' o投影的显式核。我们进一步证明了这些Cauchy-Szeg o核在合适的准度量下是Calder on-Zygmund核。
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引用次数: 2
Weak convergence of two-step inertial iteration for countable family of quasi-nonexpansive mappings 拟非扩张映射可数族两步惯性迭代的弱收敛性
IF 0.6 Pub Date : 2022-01-01 DOI: 10.4310/amsa.2022.v7.n2.a5
Y. Shehu, J. Yao
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引用次数: 0
Index search method for solving nonnegative matrix factorization 求解非负矩阵分解的索引搜索方法
IF 0.6 Pub Date : 2022-01-01 DOI: 10.4310/amsa.2022.v7.n2.a6
Yi-Shin Cheng, Ching-Sung Liu
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引用次数: 0
Local discontinuous Galerkin methods for the carpet cloak model 地毯斗篷模型的局部不连续伽辽金方法
IF 0.6 Pub Date : 2022-01-01 DOI: 10.4310/amsa.2022.v7.n1.a4
Xinyue Yu, Jichun Li, Chi-Wang Shu
. The DG methods have been shown to have good performance in numerical simulations of the carpet cloak model in [32]. However, the stability analysis and the error estimate are left to be done. In this paper, we introduce the leap-frog DG methods to solve the carpet cloak model. We prove the stability of the semi-discrete scheme, the sub-optimal error estimate for unstructured meshes, and the optimal error estimate for tensor-product meshes. Then, the fully discrete scheme is stated and the stability is proved. Finally, the numerical accuracy tests on rectangular and triangular meshes are given respectively, and the results of numerical simulations of the wave propagation in the carpet cloak model using the DG scheme are presented.
。DG方法在b[32]中地毯斗篷模型的数值模拟中显示出良好的性能。但是,系统的稳定性分析和误差估计还有待进一步研究。本文介绍了一种求解地毯斗篷模型的跨越式DG方法。证明了半离散格式的稳定性、非结构化网格的次优误差估计和张量积网格的最优误差估计。然后,给出了全离散格式,并证明了其稳定性。最后,分别对矩形网格和三角形网格进行了数值精度测试,并给出了采用DG格式对地毯斗篷模型中的波传播进行数值模拟的结果。
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引用次数: 0
A structure-preserving algorithm for the linear lossless dissipative Hamiltonian eigenvalue problem 线性无损耗散哈密顿特征值问题的结构保持算法
IF 0.6 Pub Date : 2022-01-01 DOI: 10.4310/amsa.2022.v7.n1.a1
Xing-Long Lyu
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引用次数: 0
Wigner rotation and its $SO(3)$ model: an active-frame approach Wigner旋转及其$SO(3)$模型:一种主动帧方法
IF 0.6 Pub Date : 2022-01-01 DOI: 10.4310/amsa.2022.v7.n2.a1
Leehwa Yeh
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引用次数: 1
On nonlinear matrix equations from the first standard form 关于非线性矩阵方程的第一种标准形式
IF 0.6 Pub Date : 2022-01-01 DOI: 10.4310/amsa.2022.v7.n2.a2
Changli Liu, J. Xue, Ren-Cang Li
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引用次数: 1
On the non-blow up of energy critical nonlinear massless scalar fields in ‘$3+1$’ dimensional globally hyperbolic spacetimes: light cone estimates “$3+1$”维全局双曲时空中能量临界非线性无质量标量场的非爆炸:光锥估计
IF 0.6 Pub Date : 2021-07-05 DOI: 10.4310/amsa.2021.v6.n2.a5
P. Mondal
Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a parametrix for the wave equation in a globally hyperbolic curved spacetime, we derive an apriori pointwise bound for the solution of the nonlinear wave equation in terms of the initial energy, from which the global existence follows in a straightforward way. This is accomplished by two steps. First, based on Moncrief’s light cone formulation we derive an expression for the scalar field in terms of integrals over the past light cone from an arbitrary spacetime point to an ‘initial’, Cauchy hypersurface and additional integrals over the intersection of this cone with the initial hypersurface. Secondly, we obtain apriori estimates for the energy associated with three quasi-local approximate time-like conformal Killing and one approximate Killing vector fields. Utilizing these naturally defined energies associated with the physical stress-energy tensor together with the integral equation, we show that the spacetime L∞ norm of the scalar field remains bounded in terms of the initial data and continues to be so as long as the spacetime remains singularity/Cauchy-horizon free.
本文证明了具有临界非线性的半线性波动方程解的全局存在性定理。在全局双曲曲面时空中,我们为波动方程建立了一个参数,导出了非线性波动方程解的初始能量先验逐点界,由此可以直接得出全局存在性。这需要两个步骤来完成。首先,基于Moncrief的光锥公式,我们导出了标量场的表达式,表示为从任意时空点到“初始”柯西超曲面的过去光锥的积分,以及该锥与初始超曲面相交处的附加积分。其次,我们得到了与三个拟局部近似类时间共形Killing和一个近似Killing矢量场相关的能量的先验估计。利用这些与物理应力-能量张量相关的自然定义的能量以及积分方程,我们证明了标量场的时空L∞范数在初始数据方面保持有界,并且只要时空保持奇异性/柯西视界自由,就一直保持有界。
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引用次数: 4
A structure-preserving method for solving the complex $mathsf{T}$-Hamiltonian eigenvalue problem 求解复$mathsf{T}$-哈密顿特征值问题的结构保持方法
IF 0.6 Pub Date : 2021-01-01 DOI: 10.4310/amsa.2021.v6.n2.a4
Heng Tian, Xing-Long Lyu, Tie-xiang Li
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引用次数: 0
Lyapunov functionals for some distributed delay models in epidemiology 流行病学中一些分布延迟模型的Lyapunov泛函
IF 0.6 Pub Date : 2021-01-01 DOI: 10.4310/amsa.2021.v6.n2.a2
Kai Liu, Chang-Hong Wu
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引用次数: 0
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