In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of...In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation (SDDPE) is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.展开更多
The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and envi...The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.展开更多
The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linea...The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.展开更多
Bilingual children' s word awareness can reflect the impact of bilingualism on language cognition from the aspect of psycholinguistics. The current studies on bilingual children's word awareness both at home and abr...Bilingual children' s word awareness can reflect the impact of bilingualism on language cognition from the aspect of psycholinguistics. The current studies on bilingual children's word awareness both at home and abroad show that there exist quite opposite points of views: bilingual disadvantage and bilingual advantage. The interpretation mechanisms of interference effect, word frequency, and mutual exclusivity constraint are used to support the bilingual disadvantage; while the interpretation mechanisms of bilingual advantage include sound coding, short-term memory, and inhibitory control. In effect, there is no negative impact of bilingualism on children's word awareness, and the so-called negative effects only exist on the theoretical aspect of research. The development of children's word awareness is influenced by many factors including age of acquisition, learning environment, and bilingual proficiency, etc.展开更多
文摘In this paper, a deterministic delay differential pantograph equation (DDPE) with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation (SDDPE) is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.
基金Under the auspices of the National Natural Science Foundation of China (No. 40576012, No. 40676016, No. 10471039), the State Key Program for Basic Research of China (No. 2003CB415101-03, No. 2004CB418304), the Key Project of the Chinese Academy of Sciences (No. KZCX3-SW-221), E-Institutes of Shanghai Municipal Education Commission (No. N.E03004)
文摘The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment, but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-eogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value. It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.
基金Under the auspices of National Natural Science Foundation of China(No.40876010)Main Direction Program of Knowledge Innovation Programs of the Chinese Academy of Sciences(No.KZCX2-YW-Q03-08)+3 种基金R & D Special Fund for Public Welfare Industry(meteorology)(No.GYHY200806010)LASG State Key Laboratory Special FundFoundation of Shanghai Municipal Education Commission(No.E03004)Natural Science Foundation of Zhejiang Province(No.Y6090164)
文摘The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.
基金Acknowledgements: This study was supported by National Social Science Foundation (grant number 14BYY060), a China Postdoctoral Science Foundation (grant number 2012M520057), and a Startup Fund for Advanced Talents of Nanjing Forestry University (grant number GXL022).
文摘Bilingual children' s word awareness can reflect the impact of bilingualism on language cognition from the aspect of psycholinguistics. The current studies on bilingual children's word awareness both at home and abroad show that there exist quite opposite points of views: bilingual disadvantage and bilingual advantage. The interpretation mechanisms of interference effect, word frequency, and mutual exclusivity constraint are used to support the bilingual disadvantage; while the interpretation mechanisms of bilingual advantage include sound coding, short-term memory, and inhibitory control. In effect, there is no negative impact of bilingualism on children's word awareness, and the so-called negative effects only exist on the theoretical aspect of research. The development of children's word awareness is influenced by many factors including age of acquisition, learning environment, and bilingual proficiency, etc.