In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.
{"title":"HARNACK ESTIMATES FOR NONLINEAR BACKWARD HEAT EQUATIONS WITH POTENTIALS ALONG THE RICCI-BOURGUIGNON FLOW","authors":"Jian-hong Wang","doi":"10.4134/JKMS.J190049","DOIUrl":"https://doi.org/10.4134/JKMS.J190049","url":null,"abstract":"In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"313-329"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511363","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 gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Fur- thermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Fi- nally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.
{"title":"GRADIENT ALMOST RICCI SOLITONS WITH VANISHING CONDITIONS ON WEYL TENSOR AND BACH TENSOR","authors":"J. Co., Seungsu Hwang","doi":"10.4134/JKMS.J190201","DOIUrl":"https://doi.org/10.4134/JKMS.J190201","url":null,"abstract":". In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Fur- thermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Fi- nally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"539-552"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511576","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":"STATIC AND RELATED CRITICAL SPACES WITH HARMONIC CURVATURE AND THREE RICCI EIGENVALUES","authors":"Jong Su Kim","doi":"10.4134/JKMS.J190685","DOIUrl":"https://doi.org/10.4134/JKMS.J190685","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"1435-1449"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70513362","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 the existence of infinitely many large energy solutions for the supercubic fractional Schr¨odinger-Poisson sys- tems. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-know Ambrosetti-Rabinowitz type condi- tion. We obtain three different existence results in this setting by using the Fountain Theorem, all these results extend some results for semelinear Schr¨odinger-Poisson systems to the nonlocal fractional setting.
{"title":"THE FRACTIONAL SCHRÖDINGER-POISSON SYSTEMS WITH INFINITELY MANY SOLUTIONS","authors":"T. Jin, Zhipeng Yang","doi":"10.4134/JKMS.J190156","DOIUrl":"https://doi.org/10.4134/JKMS.J190156","url":null,"abstract":". In this paper, we study the existence of infinitely many large energy solutions for the supercubic fractional Schr¨odinger-Poisson sys- tems. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-know Ambrosetti-Rabinowitz type condi- tion. We obtain three different existence results in this setting by using the Fountain Theorem, all these results extend some results for semelinear Schr¨odinger-Poisson systems to the nonlocal fractional setting.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"489-506"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511539","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}
Motivated by the traffic flow model with Arrhenius lookahead relaxation dynamics introduced in [25], this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, comparing to other well-known macroscopic traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects
{"title":"TRAFFIC FLOW MODELS WITH NONLOCAL LOOKING AHEAD-BEHIND DYNAMICS","authors":"Yongki Lee","doi":"10.4134/JKMS.J190488","DOIUrl":"https://doi.org/10.4134/JKMS.J190488","url":null,"abstract":"Motivated by the traffic flow model with Arrhenius lookahead relaxation dynamics introduced in [25], this paper proposes a traffic flow model with look ahead relaxation-behind intensification by inserting look behind intensification dynamics to the flux. Finite time shock formation conditions in the proposed model with various types of interaction potentials are identified. Several numerical experiments are performed in order to demonstrate the performance of the modified model. It is observed that, comparing to other well-known macroscopic traffic flow models, the model equipped with look ahead relaxation-behind intensification has both enhanced dispersive and smoothing effects","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"987-1004"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511789","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":"CYCLOTOMIC QUIVER HECKE ALGEBRAS CORRESPONDING TO MINUSCULE REPRESENTATIONS","authors":"Park Euiyong","doi":"10.4134/JKMS.J190647","DOIUrl":"https://doi.org/10.4134/JKMS.J190647","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"1373-1388"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70512527","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}
This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer s ≥ 2 and 0 ≤ a < 1, we give an algorithm for finding a simple form of fs,a(n) such that
{"title":"ASYMPTOTIC BEHAVIOR OF THE INVERSE OF TAILS OF HURWITZ ZETA FUNCTION","authors":"Ho-Hyeong Lee, Jong-Do Park","doi":"10.4134/JKMS.J190789","DOIUrl":"https://doi.org/10.4134/JKMS.J190789","url":null,"abstract":"This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer s ≥ 2 and 0 ≤ a < 1, we give an algorithm for finding a simple form of fs,a(n) such that","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"1535-1549"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70513501","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 the present paper, we give some characterization of the L 2 maximal estimate for the operator P ta,γ f (cid:0) Γ( x,t ) (cid:1) along curve with complex time, which is defined by where t,γ > 0 and a ≥ 2 , curve Γ is a function such that Γ : R × [0 , 1] → R , and satisfies H¨older’s condition of order σ and bilipschitz conditions. The authors extend the results of the Schr¨odinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schr¨odinger operators along the curves.
． 本文给出了算子P ta，γ f (cid:0) Γ(x,t) (cid:1)沿复时间曲线的l2极大估计的一些刻画，该曲线定义为t，γ > 0和a≥2，曲线Γ是满足Γ: R x[0,1]→R的函数，满足H¨older的阶σ条件和bilipschitz条件。作者将Bailey[1]和Cho, Lee和Vargas[3]的复时Schr¨odinger型的结果推广到沿曲线的Schr¨odinger算子。
{"title":"ESTIMATES FOR SCHRÖDINGER MAXIMAL OPERATORSALONG CURVE WITH COMPLEX TIME","authors":"Yao-ming Niu, Ying Xue","doi":"10.4134/JKMS.J180558","DOIUrl":"https://doi.org/10.4134/JKMS.J180558","url":null,"abstract":". In the present paper, we give some characterization of the L 2 maximal estimate for the operator P ta,γ f (cid:0) Γ( x,t ) (cid:1) along curve with complex time, which is defined by where t,γ > 0 and a ≥ 2 , curve Γ is a function such that Γ : R × [0 , 1] → R , and satisfies H¨older’s condition of order σ and bilipschitz conditions. The authors extend the results of the Schr¨odinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schr¨odinger operators along the curves.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"89-111"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70510316","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":"EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRODINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN R-N","authors":"Jae‐Myoung Kim, Yun-Ho Kim, Jongrak Lee","doi":"10.4134/JKMS.J180785","DOIUrl":"https://doi.org/10.4134/JKMS.J180785","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"56 1","pages":"1529-1560"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70510878","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":"CONSTRUCTION OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMS: O + (2n, 2 r ) CASE","authors":"Dae San Kim","doi":"10.4134/JKMS.J190225","DOIUrl":"https://doi.org/10.4134/JKMS.J190225","url":null,"abstract":"","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"585-602"},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70511150","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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