A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided differenc...A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.展开更多
Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given ...Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem.展开更多
Chrysophanol （1,8-dihydroxy-3-methylanthraquinone） is a free anthraquinone compound and a secondary metabolite of medicinal plant rhubarb. Chrysophanol has been reported to have both protective and curative activity...Chrysophanol （1,8-dihydroxy-3-methylanthraquinone） is a free anthraquinone compound and a secondary metabolite of medicinal plant rhubarb. Chrysophanol has been reported to have both protective and curative activity against Sphaerotheca fuliginea （Schlechtend.：Fr.） Pollacci, the causal agent of cucumber powdery mildew. In this paper the ultrastructure of powdery mildew on cucumber leaves was studied using electron microscopy after the leaves were treated with chrysophanol. Results showed that preventive treatments with chrysophanol affected fungal development, including spore germination, appressorial formation, and penetration. In the curative treatment, chrysophanol affected fungal survival, resulting in broken cell wall of germ tubes, swelling and collapse of hyphal tips, hyphal malformation, delayed and reduced sporulation. The morphological changes induced by chrysophanol at the ultrastructural level were reflected by haustorium deformation, vacuolization, abortion, and necrosis. Host cell walls infected or adjacent to haustoria were thickened. All these morphological changes of S. fuliginea further confirmed the fungicidal activity of chrysophanol on powdery mildew of cucumber.展开更多
基金Supported by the National Natural Science Foundation of China (10871178)the Natural Science Foundation of Zhejiang Province of China (Y606154)Foundation of the Education Department of Zhejiang Province of China (20071362)
文摘A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.
基金Supported by the National Natural Science Foundation of China (10871178)the Natural Science Foundation(Y606154)the Foundation of the Eduction Department of Zhejiang Province of China (Y200804008)
文摘Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem.
基金supported by the Special Fund for Agroscientific Research in the Public Interest, Ministry of Agriculture of China (200903004)
文摘Chrysophanol （1,8-dihydroxy-3-methylanthraquinone） is a free anthraquinone compound and a secondary metabolite of medicinal plant rhubarb. Chrysophanol has been reported to have both protective and curative activity against Sphaerotheca fuliginea （Schlechtend.：Fr.） Pollacci, the causal agent of cucumber powdery mildew. In this paper the ultrastructure of powdery mildew on cucumber leaves was studied using electron microscopy after the leaves were treated with chrysophanol. Results showed that preventive treatments with chrysophanol affected fungal development, including spore germination, appressorial formation, and penetration. In the curative treatment, chrysophanol affected fungal survival, resulting in broken cell wall of germ tubes, swelling and collapse of hyphal tips, hyphal malformation, delayed and reduced sporulation. The morphological changes induced by chrysophanol at the ultrastructural level were reflected by haustorium deformation, vacuolization, abortion, and necrosis. Host cell walls infected or adjacent to haustoria were thickened. All these morphological changes of S. fuliginea further confirmed the fungicidal activity of chrysophanol on powdery mildew of cucumber.
