Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,the...Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.展开更多
In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth...In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth regenerating(MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage regenerating(LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group(4, 2) or(5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. Theoretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.展开更多
Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,the...Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.展开更多
基金Sponsored by the Foundation of Pre-973 Program of China under grant2006CB708304the National NSFC under grant 10771195the NSF of Zhejiang Province under grant Y607128
文摘Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.
基金supported in part by the National Natural Science Foundation of China (61640006, 61572188)the Natural Science Foundation of Shaanxi Province, China (2015JM6307, 2016JQ6011)the project of science and technology of Xi’an City (2017088CG/RC051(CADX002))
文摘In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth regenerating(MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage regenerating(LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group(4, 2) or(5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. Theoretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.
基金Sponsored by the Foundation of Pre-973 Program of China under grant2006CB708304+2 种基金 the National NSFC under grant 10771195 the NSF of Zhejiang Province under grant Y607128
文摘Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.
