Using a fixed point theorem of Krasnosel＇skii type, this article proves the exis- tence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in two variables.
The generic Newton polygon of L-functions associated with the exponential sums of poly- nomials of degree 3 in two variables is studied by Dwork＇s analytic methods. Wan＇s conjecture is shown to be true for this case.
By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential...By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.展开更多
A linear system arising from a polynomial problem in the approximation theory is studied, and the necessary and sufficient conditions for existence and uniqueness of its solutions are presented. Together with a class ...A linear system arising from a polynomial problem in the approximation theory is studied, and the necessary and sufficient conditions for existence and uniqueness of its solutions are presented. Together with a class of determinant identities, the resulting theory is used to determine the unique solution to the polynomial problem. Some homogeneous polynomial identities as well as results on the structure of related polynomial ideals are just by-products.展开更多
基金the support given by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under Project 101.01-2012.12
文摘Using a fixed point theorem of Krasnosel＇skii type, this article proves the exis- tence of asymptotically stable solutions for a Volterra-Hammerstein integral equation in two variables.
基金Supported by National Natural Science Foundation of China (Grant No. 10671015)
文摘The generic Newton polygon of L-functions associated with the exponential sums of poly- nomials of degree 3 in two variables is studied by Dwork＇s analytic methods. Wan＇s conjecture is shown to be true for this case.
文摘By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.
文摘A linear system arising from a polynomial problem in the approximation theory is studied, and the necessary and sufficient conditions for existence and uniqueness of its solutions are presented. Together with a class of determinant identities, the resulting theory is used to determine the unique solution to the polynomial problem. Some homogeneous polynomial identities as well as results on the structure of related polynomial ideals are just by-products.
