{"title":"Boundary Effects on Eigen-problems of Discrete Laplacian in Lattices","authors":"Yueh-Cheng Kuo, Shih-Feng Shieh","doi":"10.11650/tjm/220202","DOIUrl":"https://doi.org/10.11650/tjm/220202","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47696454","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}
. Let S be a Burniat surface with K 2 S = 6 and ϕ be the bicanonical map of S . In this paper we show optimal lower bounds of log canonical thresholds of members of pluricanonical sublinear systems of S via Klein group G induced by ϕ . Indeed, for a positive even integer m , the log canonical threshold of members of an invariant (resp. anti-invariant) part of | mK S | is greater than or equal to 1 / (2 m ) (resp. 1 / (2 m − 2)). For a positive odd integer m , the log canonical threshold of members of an invariant (resp. anti-invariant) part of | mK S | is greater than or equal to 1 / (2 m − 5) (resp. 1 / (2 m )). The inequalities are all optimal.
． 设S为一个Burniat曲面，其中K 2 S = 6， φ为S的双标准映射。本文通过Klein群G，给出了由φ诱导的S的多正则次线性系统的对数正则阈值的最优下界。实际上，对于正偶数m，一个不变量(正则表达式)的成员的对数正则阈值。逆不变)部分| mK S |大于或等于1 / (2 m)(相对于。1 / (2 m−2))。对于正奇数m，不变量(正则表达式)的成员的对数正则阈值。逆不变)部分| mK S |大于等于1 / (2 m−5)(p < 0.05)。1 / (2m))。不等式都是最优的。
{"title":"Log Canonical Thresholds on Burniat Surfaces with $K^2 = 6$ via Pluricanonical Divisors","authors":"In-kyun Kim, Y. Shin","doi":"10.11650/tjm/220605","DOIUrl":"https://doi.org/10.11650/tjm/220605","url":null,"abstract":". Let S be a Burniat surface with K 2 S = 6 and ϕ be the bicanonical map of S . In this paper we show optimal lower bounds of log canonical thresholds of members of pluricanonical sublinear systems of S via Klein group G induced by ϕ . Indeed, for a positive even integer m , the log canonical threshold of members of an invariant (resp. anti-invariant) part of | mK S | is greater than or equal to 1 / (2 m ) (resp. 1 / (2 m − 2)). For a positive odd integer m , the log canonical threshold of members of an invariant (resp. anti-invariant) part of | mK S | is greater than or equal to 1 / (2 m − 5) (resp. 1 / (2 m )). The inequalities are all optimal.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46944013","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":"Oscillation and Nonoscillation for Two-dimensional Nonlinear Systems of Ordinary Differential Equations","authors":"Manabu Naito","doi":"10.11650/tjm/221001","DOIUrl":"https://doi.org/10.11650/tjm/221001","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48838520","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 consider the p -Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we prove global existence, infinite time blow up and asymptotic behavior of solutions in two cases E (0) < d and E (0) = d . Furthermore, the infinite time blow up of solutions for the problem with E (0) > 0 ( ω = 0) is studied.
{"title":"Global Well-posedness of Solutions for the $p$-Laplacian Hyperbolic Type Equation with Weak and Strong Damping Terms and Logarithmic Nonlinearity","authors":"N. Boumaza, Billel Gheraibia, Gongwei Liu","doi":"10.11650/tjm/220702","DOIUrl":"https://doi.org/10.11650/tjm/220702","url":null,"abstract":". In this paper, we consider the p -Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we prove global existence, infinite time blow up and asymptotic behavior of solutions in two cases E (0) < d and E (0) = d . Furthermore, the infinite time blow up of solutions for the problem with E (0) > 0 ( ω = 0) is studied.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49149420","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 are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann’s non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function qε, rather than super exponential function.
{"title":"Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings","authors":"Peng-Ruei Huang","doi":"10.11650/tjm/220201","DOIUrl":"https://doi.org/10.11650/tjm/220201","url":null,"abstract":"In this paper we are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann’s non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function qε, rather than super exponential function.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44510884","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}
. The Eakin–Nagata theorem examines the condition that the Noetherian property passes through each other between subrings and extension rings in 1968. Later, a noncommutative version of Eakin–Nagata theorem was also proved. Lam called this version Eakin–Nagata–Eisenbud theorem. In addition, Anderson and Dumitrescu introduced the S -Noetherian concept which is an extended notion of the Noetherian property on commutative rings in 2002. In this paper, we consider the S -variant of Eakin–Nagata–Eisenbud theorem for general rings by using S -Noetherian modules. We also show that every right S -Noetherian domain is right Ore, which is embedded into a division ring. For a right S -Noetherian ring, we obtain sufficient conditions for its right ring of fractions to be right S -Noetherian or right Noetherian. As applications, the S -variant of Eakin–Nagata–Eisenbud theorem is applied to the composite polynomial, composite power series and composite skew polynomial rings.
{"title":"Eakin–Nagata–Eisenbud Theorem for Right $S$-Noetherian Rings","authors":"Gangyong Lee, Jongwook Baeck, J. Lim","doi":"10.11650/tjm/221101","DOIUrl":"https://doi.org/10.11650/tjm/221101","url":null,"abstract":". The Eakin–Nagata theorem examines the condition that the Noetherian property passes through each other between subrings and extension rings in 1968. Later, a noncommutative version of Eakin–Nagata theorem was also proved. Lam called this version Eakin–Nagata–Eisenbud theorem. In addition, Anderson and Dumitrescu introduced the S -Noetherian concept which is an extended notion of the Noetherian property on commutative rings in 2002. In this paper, we consider the S -variant of Eakin–Nagata–Eisenbud theorem for general rings by using S -Noetherian modules. We also show that every right S -Noetherian domain is right Ore, which is embedded into a division ring. For a right S -Noetherian ring, we obtain sufficient conditions for its right ring of fractions to be right S -Noetherian or right Noetherian. As applications, the S -variant of Eakin–Nagata–Eisenbud theorem is applied to the composite polynomial, composite power series and composite skew polynomial rings.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43357873","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 Mixed Joint Discrete Universality for a Class of Zeta-functions: One More Case","authors":"R. Kačinskaitė, Kohji Matsumoto, Łukasz Pańkowski","doi":"10.11650/tjm/220804","DOIUrl":"https://doi.org/10.11650/tjm/220804","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49001266","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}
Mahdi Rezaei Bahrmand, H. Khaloozadeh, P. R. Ardabili
{"title":"A Minimum Principle for Stochastic Optimal Control Problem with Interval Cost Function","authors":"Mahdi Rezaei Bahrmand, H. Khaloozadeh, P. R. Ardabili","doi":"10.11650/tjm/221102","DOIUrl":"https://doi.org/10.11650/tjm/221102","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44367910","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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