Pub Date : 2022-11-27DOI: 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.
{"title":"The Kohn–Laplacian and Cauchy–Szegö projection on model domains","authors":"D. Chang, Ji Li, Jingzhi Tie, Qingyan Wu","doi":"10.4310/amsa.2023.v8.n1.a4","DOIUrl":"https://doi.org/10.4310/amsa.2023.v8.n1.a4","url":null,"abstract":"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.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47148458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/amsa.2022.v7.n2.a5
Y. Shehu, J. Yao
{"title":"Weak convergence of two-step inertial iteration for countable family of quasi-nonexpansive mappings","authors":"Y. Shehu, J. Yao","doi":"10.4310/amsa.2022.v7.n2.a5","DOIUrl":"https://doi.org/10.4310/amsa.2022.v7.n2.a5","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 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.
{"title":"Local discontinuous Galerkin methods for the carpet cloak model","authors":"Xinyue Yu, Jichun Li, Chi-Wang Shu","doi":"10.4310/amsa.2022.v7.n1.a4","DOIUrl":"https://doi.org/10.4310/amsa.2022.v7.n1.a4","url":null,"abstract":". 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.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/amsa.2022.v7.n1.a1
Xing-Long Lyu
{"title":"A structure-preserving algorithm for the linear lossless dissipative Hamiltonian eigenvalue problem","authors":"Xing-Long Lyu","doi":"10.4310/amsa.2022.v7.n1.a1","DOIUrl":"https://doi.org/10.4310/amsa.2022.v7.n1.a1","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/amsa.2022.v7.n2.a1
Leehwa Yeh
{"title":"Wigner rotation and its $SO(3)$ model: an active-frame approach","authors":"Leehwa Yeh","doi":"10.4310/amsa.2022.v7.n2.a1","DOIUrl":"https://doi.org/10.4310/amsa.2022.v7.n2.a1","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.4310/amsa.2022.v7.n2.a2
Changli Liu, J. Xue, Ren-Cang Li
{"title":"On nonlinear matrix equations from the first standard form","authors":"Changli Liu, J. Xue, Ren-Cang Li","doi":"10.4310/amsa.2022.v7.n2.a2","DOIUrl":"https://doi.org/10.4310/amsa.2022.v7.n2.a2","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-05DOI: 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.
{"title":"On the non-blow up of energy critical nonlinear massless scalar fields in ‘$3+1$’ dimensional globally hyperbolic spacetimes: light cone estimates","authors":"P. Mondal","doi":"10.4310/amsa.2021.v6.n2.a5","DOIUrl":"https://doi.org/10.4310/amsa.2021.v6.n2.a5","url":null,"abstract":"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.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48266897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/amsa.2021.v6.n2.a2
Kai Liu, Chang-Hong Wu
{"title":"Lyapunov functionals for some distributed delay models in epidemiology","authors":"Kai Liu, Chang-Hong Wu","doi":"10.4310/amsa.2021.v6.n2.a2","DOIUrl":"https://doi.org/10.4310/amsa.2021.v6.n2.a2","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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