In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and dedu...In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases.展开更多
A foremost issue of our time is our response to risks,especially those arising from scientific uncertainty,such as genetically modified organisms(GMOs).In this context,we need to achieve and maintain environmental jus...A foremost issue of our time is our response to risks,especially those arising from scientific uncertainty,such as genetically modified organisms(GMOs).In this context,we need to achieve and maintain environmental justice.This should be based on the corresponding scientific research;essentially,however,it is a kind of social construct.We must maintain a free market mechanism for the development,application,and dissemination of modern technology,including genetically modified biotech and its products.At the same time,the necessary government intervention and legal regulation of the relevant science and technology should be put in place to ensure public safety and the interests of socially disadvantaged groups.展开更多
In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asympto...In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.展开更多
In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4...In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4） （2016） 989-1020] to the problem of prostate cancer immunotherapy. We extend this method in two directions： first, we apply the method to a system of nonlinear ordinary differential equation, and second, we propose a new technique for finding the base functions in the considered algorithm.展开更多
基金Supported by the PCSIRT of Education of China(IRT0621)Supported by the Innovation Program of Shanghai Municipal Education Committee of China(08ZZ24)Supported by the Henan Innovation Project for University Prominent Research Talents of China(2007KYCX0021)
文摘In this paper,we prove the Srivastava-Pint'er's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods.We also provide some analoges of these addition theorems and deduce the corresponding special cases.
文摘A foremost issue of our time is our response to risks,especially those arising from scientific uncertainty,such as genetically modified organisms(GMOs).In this context,we need to achieve and maintain environmental justice.This should be based on the corresponding scientific research;essentially,however,it is a kind of social construct.We must maintain a free market mechanism for the development,application,and dissemination of modern technology,including genetically modified biotech and its products.At the same time,the necessary government intervention and legal regulation of the relevant science and technology should be put in place to ensure public safety and the interests of socially disadvantaged groups.
文摘In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.
文摘In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4） （2016） 989-1020] to the problem of prostate cancer immunotherapy. We extend this method in two directions： first, we apply the method to a system of nonlinear ordinary differential equation, and second, we propose a new technique for finding the base functions in the considered algorithm.
