In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free bo...In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.展开更多
For complex planar objects, which are composed of simple spatial objects, the existent models of topological relations may not be able to describe some topological attributes of complex objects well. Taking the topolo...For complex planar objects, which are composed of simple spatial objects, the existent models of topological relations may not be able to describe some topological attributes of complex objects well. Taking the topological content between complex objects into account, this paper presents a model of basic topological relations between line/planar objects, and then in which the basic topological relations and the concept of the overlapping area are leveraged to describe the topological relations of simple planar objects. The definition of traversing of the hole’s boundary and planar with a hole is used to describe the topological relations between complex planar objects. Finally, the five basic topological relationship description modes of complex planar objects are summarized to realize description of the details of topological relations between partitions of complex planar objects.展开更多
Constant weight code is an important error-correcting control code in communications. Basic structure of constant weight codes for some arriving at Johnson bound, A（n, 2u, w）, is presented. Some correlative property...Constant weight code is an important error-correcting control code in communications. Basic structure of constant weight codes for some arriving at Johnson bound, A（n, 2u, w）, is presented. Some correlative propertys of the codes, the solution of arriving at Johnson bound, and the results on the couple constant code and some constant weight codes are discussed. The conclusion is verified through four examples.展开更多
基金supported by NSFC Grant No.11171153supported by NSFC Grant No.11322106supported by the Fundamental Research Funds for the Central Universities No.2015ZCQ-LY-01 and No.BLX2015-27
文摘In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.
基金The National Naturadl Science Foundation of China(41871305)The National Key Research and Development Program of China(2017YFC0602204).
文摘For complex planar objects, which are composed of simple spatial objects, the existent models of topological relations may not be able to describe some topological attributes of complex objects well. Taking the topological content between complex objects into account, this paper presents a model of basic topological relations between line/planar objects, and then in which the basic topological relations and the concept of the overlapping area are leveraged to describe the topological relations of simple planar objects. The definition of traversing of the hole’s boundary and planar with a hole is used to describe the topological relations between complex planar objects. Finally, the five basic topological relationship description modes of complex planar objects are summarized to realize description of the details of topological relations between partitions of complex planar objects.
文摘Constant weight code is an important error-correcting control code in communications. Basic structure of constant weight codes for some arriving at Johnson bound, A（n, 2u, w）, is presented. Some correlative propertys of the codes, the solution of arriving at Johnson bound, and the results on the couple constant code and some constant weight codes are discussed. The conclusion is verified through four examples.
