The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation l...The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.展开更多
In this paper, an algorithm for computing near-centers of a nearly round body inany dimension is shown. The algorithm generalizes a recent result [2]. It is quite simpleand needs only d "parallel" probe step...In this paper, an algorithm for computing near-centers of a nearly round body inany dimension is shown. The algorithm generalizes a recent result [2]. It is quite simpleand needs only d "parallel" probe steps including d(d + 1) probes in d-dimension.展开更多
Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of ze...Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation. After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model.展开更多
文摘The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.
文摘In this paper, an algorithm for computing near-centers of a nearly round body inany dimension is shown. The algorithm generalizes a recent result [2]. It is quite simpleand needs only d "parallel" probe steps including d(d + 1) probes in d-dimension.
文摘Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation. After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model.
