{"title":"A Kind of Integral Representation on Complex Manifold","authors":"Teqing Chen null, Zhiwei Li","doi":"10.4208/jms.v55n1.22.08","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.08","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"s-Sequence-Covering Mappings on Metric Spaces","authors":"Xiangeng Zhou null, Li Liu","doi":"10.4208/jms.v55n1.22.04","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.04","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Repdigits Base $b$ as Difference of Two Fibonacci Numbers","authors":"Z. Şiar, F. Null, R. Keskin","doi":"10.4208/jms.v55n1.22.07","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.07","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we present a third-order weighted essentially non-oscillatory (WENO) method for generalized Rosenau-KdV-RLW equation. The third order finite difference WENO reconstruction and central finite differences are applied to discrete advection terms and other terms, respectively, in spatial discretization. In order to achieve the third order accuracy both in space and time, four stage third-order L-stable SSP Implicit-Explicit RungeKutta method (Third-order SSP EXRK method and third-order DIRK method) is applied to temporal discretization. The high order accuracy and essentially non-oscillatory property of finite difference WENO reconstruction are shown for solitary wave and shock wave for Rosenau-KdV and Rosenau-KdV-RLW equations. The efficiency, reliability and excellent SSP property of the numerical scheme are demonstrated by several numerical experiments with large CFL number.
{"title":"SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation","authors":"Muyassar Ahmat null, J. Qiu","doi":"10.4208/jms.v55n1.22.01","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.01","url":null,"abstract":"In this article, we present a third-order weighted essentially non-oscillatory (WENO) method for generalized Rosenau-KdV-RLW equation. The third order finite difference WENO reconstruction and central finite differences are applied to discrete advection terms and other terms, respectively, in spatial discretization. In order to achieve the third order accuracy both in space and time, four stage third-order L-stable SSP Implicit-Explicit RungeKutta method (Third-order SSP EXRK method and third-order DIRK method) is applied to temporal discretization. The high order accuracy and essentially non-oscillatory property of finite difference WENO reconstruction are shown for solitary wave and shock wave for Rosenau-KdV and Rosenau-KdV-RLW equations. The efficiency, reliability and excellent SSP property of the numerical scheme are demonstrated by several numerical experiments with large CFL number.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gradient Bounds for Almost Complex Special Lagrangian Equation with Supercritical Phase","authors":"Jiao-Ling Zhang","doi":"10.4208/jms.v55n1.22.06","DOIUrl":"https://doi.org/10.4208/jms.v55n1.22.06","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is positive in the bulk and at the boundaries of the domain of interest. The resulting model consists of two equations, a heat-like equation and a mass-conservation equation that describes how the atom density changes in time and space. The model is simple, yet it can properly capture the variation in the free energy landscape as the temperature is changed. We describe to construct a temperature-atomdensity phase diagram using this energy landscape, and we give a simple demonstration of solidification using the model.
{"title":"A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux","authors":"Cheng Wang null, S. Wise","doi":"10.4208/jms.v55n4.22.01","DOIUrl":"https://doi.org/10.4208/jms.v55n4.22.01","url":null,"abstract":"In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is positive in the bulk and at the boundaries of the domain of interest. The resulting model consists of two equations, a heat-like equation and a mass-conservation equation that describes how the atom density changes in time and space. The model is simple, yet it can properly capture the variation in the free energy landscape as the temperature is changed. We describe to construct a temperature-atomdensity phase diagram using this energy landscape, and we give a simple demonstration of solidification using the model.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41323826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Note on Gaussian BV Function and Its Heat Semigroup Characterization","authors":"Xiaona Liu, Xiang-sheng Xie, Yu Liu","doi":"10.4208/jms.v54n3.21.02","DOIUrl":"https://doi.org/10.4208/jms.v54n3.21.02","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43502625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the smoothness of weak solutions to a class of complex Hessian equations on closed Kähler manifolds, by use of the smoothing property of the corresponding gradient flow. AMS subject classifications: 32W20, 35K55, 53C44.
{"title":"Regularity of Weak Solutions to a Class of Complex Hessian Equations on Kähler Manifolds","authors":"Weimin Wang","doi":"10.4208/JMS.V54N2.21.04","DOIUrl":"https://doi.org/10.4208/JMS.V54N2.21.04","url":null,"abstract":"We prove the smoothness of weak solutions to a class of complex Hessian equations on closed Kähler manifolds, by use of the smoothing property of the corresponding gradient flow. AMS subject classifications: 32W20, 35K55, 53C44.","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46526169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent","authors":"global AdilAbbassi","doi":"10.4208/jms.v54n4.21.01","DOIUrl":"https://doi.org/10.4208/jms.v54n4.21.01","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44686508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the $h$-almost Yamabe Soliton","authors":"global FanqiZeng","doi":"10.4208/jms.v54n4.21.03","DOIUrl":"https://doi.org/10.4208/jms.v54n4.21.03","url":null,"abstract":"","PeriodicalId":43526,"journal":{"name":"Journal of Mathematical Study","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47435186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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