Ideal submanifolds have been studied from various aspects since Chen invented $delta$-invariants in early 1990s (see [12] for a survey). In centroaffine differential geometry, Chen's invariants denoted by $delta^{sharp}$ are used to determine an optimal bound for the squared norm of the Tchebychev vector field of a hypersurface. We point out that a hypersurface attaining this bound is said to be an ideal centroaffine hypersurface. In this paper, we deal with $delta^{sharp}(2,2)$-ideal centroaffine hypersurfaces in $mathbb{R}^{5}$ and in particularly, we focus on $4$-dimensional $delta^{sharp}(2,2)$-ideal centroaffine hypersurfaces of type $1$.
{"title":"$delta^{sharp}(2,2)$-Ideal Centroaffine Hypersurfaces of Dimension 4","authors":"Handan Yıldırım, Luc Vrancken","doi":"10.11650/tjm/230706","DOIUrl":"https://doi.org/10.11650/tjm/230706","url":null,"abstract":"Ideal submanifolds have been studied from various aspects since Chen invented $delta$-invariants in early 1990s (see [12] for a survey). In centroaffine differential geometry, Chen's invariants denoted by $delta^{sharp}$ are used to determine an optimal bound for the squared norm of the Tchebychev vector field of a hypersurface. We point out that a hypersurface attaining this bound is said to be an ideal centroaffine hypersurface. In this paper, we deal with $delta^{sharp}(2,2)$-ideal centroaffine hypersurfaces in $mathbb{R}^{5}$ and in particularly, we focus on $4$-dimensional $delta^{sharp}(2,2)$-ideal centroaffine hypersurfaces of type $1$.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135262144","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, a modified alternately linear implicit (MALI) iteration method is derived for solving the non-symmetric coupled algebraic Riccati equation (NCARE). In the MALI iteration algorithm, the coefficient matrices of the linear matrix equations are fixed at each iteration step. In addition, the MALI iteration method utilizes a weighted average of the estimates in both the last step and current step to update the estimates in the next iteration step. Further, we give the convergence theory of the modified algorithm. Last, numerical examples demonstrate the effectiveness and feasibility of the derived algorithm.
{"title":"A Modified Iterative Method for Solving the Non-symmetric Coupled Algebraic Riccati Equation","authors":"Li Wang, Yibo Wang","doi":"10.11650/tjm/231101","DOIUrl":"https://doi.org/10.11650/tjm/231101","url":null,"abstract":"In this paper, a modified alternately linear implicit (MALI) iteration method is derived for solving the non-symmetric coupled algebraic Riccati equation (NCARE). In the MALI iteration algorithm, the coefficient matrices of the linear matrix equations are fixed at each iteration step. In addition, the MALI iteration method utilizes a weighted average of the estimates in both the last step and current step to update the estimates in the next iteration step. Further, we give the convergence theory of the modified algorithm. Last, numerical examples demonstrate the effectiveness and feasibility of the derived algorithm.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135660055","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":"Blow-up Phenomena for a Reaction-diffusion Equation with Nonlocal Gradient Terms","authors":"Su-Cheol Yi, Z. Fang","doi":"10.11650/tjm/230401","DOIUrl":"https://doi.org/10.11650/tjm/230401","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48729901","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 give Schwarz lemma at the boundary for holomorphic mappings between $p$-unit ball $B_{p}^{n} subset mathbb{C}^{n}$ and $B_{p}^{N} subset mathbb{C}^{N}$, where $p geq 2$. When $p = 2$, this result reduces to that of Liu, Chen and Pan [21] between the Euclidean unit balls, and our method is new. By generalizing pluriharmonic Schwarz lemma of Chen and Gauthier [5] from $p = 2$ to $p geq 2$, we obtain the boundary Schwarz lemma for pluriharmonic mappings between $p$-unit balls.
{"title":"Schwarz Lemma at the Boundary for Holomorphic and Pluriharmonic Mappings Between $p$-unit Balls","authors":"Jianfei Wang","doi":"10.11650/tjm/230902","DOIUrl":"https://doi.org/10.11650/tjm/230902","url":null,"abstract":"We give Schwarz lemma at the boundary for holomorphic mappings between $p$-unit ball $B_{p}^{n} subset mathbb{C}^{n}$ and $B_{p}^{N} subset mathbb{C}^{N}$, where $p geq 2$. When $p = 2$, this result reduces to that of Liu, Chen and Pan [21] between the Euclidean unit balls, and our method is new. By generalizing pluriharmonic Schwarz lemma of Chen and Gauthier [5] from $p = 2$ to $p geq 2$, we obtain the boundary Schwarz lemma for pluriharmonic mappings between $p$-unit balls.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"317 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135446552","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 study a class of asymptotically periodic fractional $p$-Laplacian equations. Under the suitable conditions, the existence of ground state solutions are obtained via the variational method.
{"title":"Existence of Solutions for Asymptotically Periodic Fractional $p$-Laplacian Equations","authors":"Shuwen He","doi":"10.11650/tjm/231102","DOIUrl":"https://doi.org/10.11650/tjm/231102","url":null,"abstract":"In this paper we study a class of asymptotically periodic fractional $p$-Laplacian equations. Under the suitable conditions, the existence of ground state solutions are obtained via the variational method.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135705338","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 first introduce the pseudo-entropy of free semigroup actions and show that it is equal to the topological entropy of free semigroup actions defined by Bufetov [9]. Second, for free semigroup actions, the concepts of chain recurrence and chain recurrence time, chain mixing and chain mixing time are introduced, and upper bounds for these recurrence times are calculated. Furthermore, the lower box dimension and the chain mixing time provide a lower bound on topological entropy of free semigroup actions. Third, the structure of chain transitive systems of free semigroup actions is discussed. Our analysis generalizes the results obtained by Misiurewicz [21], Richeson and Wiseman [23], and Bufetov [9] etc.
{"title":"Chain Recurrence Rates and Topological Entropy of Free Semigroup Actions","authors":"Yanjie Tang, Xiaojiang Ye, Dongkui Ma","doi":"10.11650/tjm/230903","DOIUrl":"https://doi.org/10.11650/tjm/230903","url":null,"abstract":"In this paper, we first introduce the pseudo-entropy of free semigroup actions and show that it is equal to the topological entropy of free semigroup actions defined by Bufetov [9]. Second, for free semigroup actions, the concepts of chain recurrence and chain recurrence time, chain mixing and chain mixing time are introduced, and upper bounds for these recurrence times are calculated. Furthermore, the lower box dimension and the chain mixing time provide a lower bound on topological entropy of free semigroup actions. Third, the structure of chain transitive systems of free semigroup actions is discussed. Our analysis generalizes the results obtained by Misiurewicz [21], Richeson and Wiseman [23], and Bufetov [9] etc.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135650554","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, utilizing Bregman projections which are different from the sunny generalized nonexpansive retractions and generalized metric projection in Banach spaces, we introduce some new parallel extragradient methods for finding the solution of the multiple-sets split equilibrium problem and the solution of the multiple-sets split variational inequality problem in $p$-uniformly convex and uniformly smooth Banach spaces. Moreover, we introduce a $Delta$-Lipschitz-type condition on the equilibrium bifunctions to prove strongly convergent of the generated iterates in parallel extragradient methods. To illustrate the usability of our results and also to show the efficiency of the proposed methods, we present some comparative examples with several existing schemes in the literature in finite and infinite dimensional spaces.
{"title":"Bregman Projections and Parallel Extragradient Methods for Solving Multiple-sets Split Problems","authors":"Fridoun Moradlou, Zeynab Jouymandi, Fahimeh Akhavan Ghassabzade","doi":"10.11650/tjm/230904","DOIUrl":"https://doi.org/10.11650/tjm/230904","url":null,"abstract":"In this paper, utilizing Bregman projections which are different from the sunny generalized nonexpansive retractions and generalized metric projection in Banach spaces, we introduce some new parallel extragradient methods for finding the solution of the multiple-sets split equilibrium problem and the solution of the multiple-sets split variational inequality problem in $p$-uniformly convex and uniformly smooth Banach spaces. Moreover, we introduce a $Delta$-Lipschitz-type condition on the equilibrium bifunctions to prove strongly convergent of the generated iterates in parallel extragradient methods. To illustrate the usability of our results and also to show the efficiency of the proposed methods, we present some comparative examples with several existing schemes in the literature in finite and infinite dimensional spaces.","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135652644","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 Depth-dependent Stability Estimate in an Iterative Method for Solving a Cauchy Problem for the Laplace Equation","authors":"Akari Ishida","doi":"10.11650/tjm/230102","DOIUrl":"https://doi.org/10.11650/tjm/230102","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41703583","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":"Computing $h$-functions of Some Planar Simply Connected Two-dimensional Regions","authors":"Arunmaran Mahenthiram","doi":"10.11650/tjm/230704","DOIUrl":"https://doi.org/10.11650/tjm/230704","url":null,"abstract":"","PeriodicalId":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49527085","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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