The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a usef...The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.展开更多
The tobacco Ralstonia Solanacearum were both cultured on nutrient agar plates and inoculated in seedling stage of tobacco, then treated with K1 and K2, two anti-bacterial agents, at a serial con-centrations to study t...The tobacco Ralstonia Solanacearum were both cultured on nutrient agar plates and inoculated in seedling stage of tobacco, then treated with K1 and K2, two anti-bacterial agents, at a serial con-centrations to study their inhibitory efficiency. The result indicated that K1 can inhibit R. Solanacearum growth entirely, at the concentration range from 1/50 to 1/5000. K2 can reach the same result at the concentration range from 1/50 to 1/50000. Compared with the control plates, K1, at the concentration 1/50000, had no significant differences, and the average number of colony per plate was 112-115. The immature tobacco shown wilt as soon as inoculated with R. Solanacearum, and recovered gradually after using K1, K2. The densities of microbial suspension, handled by K1, K2 within 10 hs, were both significantly lower than the controlled ones. The optical microscopy also shown that handled microbial body differed from the controlled, whose body was regular short, rod shape as opposed to the handled ones with irregular rod shape and damaged body. All the results indicated that K1 and K2 both had inhibitory effects on tobacco R. Solanacearum, and K2 was more efficient than K1.展开更多
We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.
In this paper, we prove a local HSlder estimate of （K1, K2）-quasiconformal mappings be- tween n-dimensional hypersurfaces of Rn＋l under an assumption of bounded mean curvature of the original hypersurface M. With s...In this paper, we prove a local HSlder estimate of （K1, K2）-quasiconformal mappings be- tween n-dimensional hypersurfaces of Rn＋l under an assumption of bounded mean curvature of the original hypersurface M. With some new ingredients of the isoperimetric inequality and the co-area formula on manifolds, we extend Simon＇s work of quasiconformal mappings on surfaces of R3 to the setting of n-dimensional hypersurfaces of Rn＋1.展开更多
基金Research supported by NSFC (10471149)Special Fund of Mathematics Research of Natural Science Foundation of Hebei Province (07M003)Doctoral Foundation of Hebei Province Ministry of Education (B2004103).
文摘The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.
文摘The tobacco Ralstonia Solanacearum were both cultured on nutrient agar plates and inoculated in seedling stage of tobacco, then treated with K1 and K2, two anti-bacterial agents, at a serial con-centrations to study their inhibitory efficiency. The result indicated that K1 can inhibit R. Solanacearum growth entirely, at the concentration range from 1/50 to 1/5000. K2 can reach the same result at the concentration range from 1/50 to 1/50000. Compared with the control plates, K1, at the concentration 1/50000, had no significant differences, and the average number of colony per plate was 112-115. The immature tobacco shown wilt as soon as inoculated with R. Solanacearum, and recovered gradually after using K1, K2. The densities of microbial suspension, handled by K1, K2 within 10 hs, were both significantly lower than the controlled ones. The optical microscopy also shown that handled microbial body differed from the controlled, whose body was regular short, rod shape as opposed to the handled ones with irregular rod shape and damaged body. All the results indicated that K1 and K2 both had inhibitory effects on tobacco R. Solanacearum, and K2 was more efficient than K1.
基金Special Fund of Mathematical Study of Natural Science Foundation of Hebei Province(07M003)Doctoral Foundation of Hebei Province(B2004103)Foundation of the Department of Education of Hunan Province(06C516)
文摘We obtain a new inequality for weakly （K1,K2）-quasiregular mappings by using the McShane extension method. This inequality can be used to derive the self-improving regularity of （K1, K2）-Quasiregular Mappings.
基金Supported by National Natural Science Foundation of China(Grant No.11371050)
文摘In this paper, we prove a local HSlder estimate of （K1, K2）-quasiconformal mappings be- tween n-dimensional hypersurfaces of Rn＋l under an assumption of bounded mean curvature of the original hypersurface M. With some new ingredients of the isoperimetric inequality and the co-area formula on manifolds, we extend Simon＇s work of quasiconformal mappings on surfaces of R3 to the setting of n-dimensional hypersurfaces of Rn＋1.
