In this paper,path-connectivity of the set of some special wavelets in L^(2)(R),which is the topological geometric property of wavelets,is introduced.In particular,the main progress of wavelet connectivity in the past...In this paper,path-connectivity of the set of some special wavelets in L^(2)(R),which is the topological geometric property of wavelets,is introduced.In particular,the main progress of wavelet connectivity in the past twenty years is reviewed and some unsolved problems are listed.The corresponding results of high dimension case and other cases are also briefly explained.展开更多
We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural ...We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact Rs, while for the nonconvex problem we show that it is path connected, Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.展开更多
基金the National Natural Science Foundation of China(Grant No.61471410).
文摘In this paper,path-connectivity of the set of some special wavelets in L^(2)(R),which is the topological geometric property of wavelets,is introduced.In particular,the main progress of wavelet connectivity in the past twenty years is reviewed and some unsolved problems are listed.The corresponding results of high dimension case and other cases are also briefly explained.
文摘We contimle the work initiated in [1] （Second order nonlinear evolution inclusions I： Existence and relaxation results. Acta Mathematics Science, English Series, 21（5）, 977-996 （2005）） and study the structural properties of the solution set of second order evolution inclusions which are defined in the analytic framework of the evolution triple. For the convex problem we show that the solution set is compact Rs, while for the nonconvex problem we show that it is path connected, Also we show that the solution set is closed only if the multivalued nonlinearity is convex valued. Finally we illustrate the results by considering a nonlinear hyperbolic problem with discontinuities.
