This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s function...This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s functions, a method of finite elements, a boundary elements method, a method of Kupradze, a T-matrix method and a method of a geometrical theory of a diffraction.展开更多
In this paper, bifurcations of limit cycles at three fine focuses for a class of Z2-equivariant non-analytic cubic planar differential systems axe studied. By a transformation, we first transform non- analytic systems...In this paper, bifurcations of limit cycles at three fine focuses for a class of Z2-equivariant non-analytic cubic planar differential systems axe studied. By a transformation, we first transform non- analytic systems into analytic systems. Then sufficient and necessary conditions for critical points of the systems being centers are obtained. The fact that there exist 12 small amplitude limit cycles created from the critical points is also proved. Henceforth we give a lower bound of cyclicity of Z2-equivaxiant non-analytic cubic differential systems.展开更多
文摘This review analyzes following numerical methods of a solution of problems of a sound diffraction on ideal and elastic scatterers of a non-analytical form: a method of integral equations, a method of Green’s functions, a method of finite elements, a boundary elements method, a method of Kupradze, a T-matrix method and a method of a geometrical theory of a diffraction.
基金Supported by National Nature Science Foundation of China (Grant Nos. 11071222, 11101126)
文摘In this paper, bifurcations of limit cycles at three fine focuses for a class of Z2-equivariant non-analytic cubic planar differential systems axe studied. By a transformation, we first transform non- analytic systems into analytic systems. Then sufficient and necessary conditions for critical points of the systems being centers are obtained. The fact that there exist 12 small amplitude limit cycles created from the critical points is also proved. Henceforth we give a lower bound of cyclicity of Z2-equivaxiant non-analytic cubic differential systems.
