{"title":"Proof of a Gromov conjecture on the infinitesimal invertibility of the metric-inducing operators","authors":"R. De Leo","doi":"10.4310/ajm.2019.v23.n6.a2","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n6.a2","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391866","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":"Isometries of extrinsic symmetric spaces","authors":"J. Eschenburg, P. Quast, M. Tanaka","doi":"10.4310/AJM.2019.V23.N3.A4","DOIUrl":"https://doi.org/10.4310/AJM.2019.V23.N3.A4","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391229","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}
Yuejiao Wang, Yingqiu Li, Quansheng Liu, Zaiming Liu
{"title":"Quenched weighted moments of a supercritical branching process in a random environment","authors":"Yuejiao Wang, Yingqiu Li, Quansheng Liu, Zaiming Liu","doi":"10.4310/ajm.2019.v23.n6.a5","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n6.a5","url":null,"abstract":"We consider a supercritical branching process $(Z_n)$ in an independent and identically distributed random environment $xi =(xi_n)$. Let $W$ be the limit of the natural martingale $W_n = Z_n / E_xi Z_n (n geq 0)$, where $E_xi $ denotes the conditional expectation given the environment $xi$. We find a necessary and sufficient condition for the existence of quenched weighted moments of $W$ of the form $E_{xi} W^{alpha} l(W)$, where $alpha > 1$ and $l$ is a positive function slowly varying at $infty$. The same conclusion is also proved for the maximum of the martingale $W^* = sup_{ngeq 1} W_n $ instead of the limit variable $W$. In the proof we first show an extended version of Doob's inequality about weighted moments for nonnegative submartingales, which is of independent interest.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391879","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":"The $mathit{Quot}$ functor of a quasi-coherent sheaf","authors":"Gennaro di Brino","doi":"10.4310/ajm.2019.v23.n1.a1","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n1.a1","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70390840","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":"High order linear extended state observer and error analysis of active disturbance rejection control","authors":"Ji Shi, Xiuqiong Chen, S. Yau","doi":"10.4310/ajm.2019.v23.n4.a5","DOIUrl":"https://doi.org/10.4310/ajm.2019.v23.n4.a5","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391405","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":"Convergence of discrete conformal geometry and computation of uniformization maps","authors":"D. Gu, F. Luo, Tianqi Wu","doi":"10.4310/AJM.2019.V23.N1.A2","DOIUrl":"https://doi.org/10.4310/AJM.2019.V23.N1.A2","url":null,"abstract":"The classical uniformization theorem of Poincaré and Koebe states that any simply connected surface with a Riemannian metric is conformally diffeomorphic to the Riemann sphere, or the complex plane or the unit disk. Using the work by Gu-Luo-Sun-Wu [9] on discrete conformal geometry for polyhedral surfaces, we show that the uniformization maps for simply connected Riemann surfaces are computable.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391080","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":"Normal bundles on the exceptional sets of simple small resolutions","authors":"Rong Du, X. Fang","doi":"10.4310/ajm.2021.v25.n2.a7","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n2.a7","url":null,"abstract":"We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $mathbb{Z}$ and the normal bundle of it has some good filtration. In particular, for the exceptional set is a projective space with the split normal bundle, we generalized Nakayama and Ando's results to higher dimension. Moreover, we also generalize Laufer's results of rationality and embedding dimension to higher dimension.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48210628","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":"Automorphism groups of Inoue and Kodaira surfaces","authors":"Yuri Prokhorov, C. Shramov","doi":"10.4310/ajm.2020.v24.n2.a8","DOIUrl":"https://doi.org/10.4310/ajm.2020.v24.n2.a8","url":null,"abstract":"We prove that automorphism groups of Inoue and primary Kodaira surfaces are Jordan.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2018-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43176230","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}