In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values o...In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.展开更多
The average stretching direction,local rotation angular,and stretching ratio parameters of molecular trains were used to express the rheology deformation.Based on this micro geometrical deformation,the macro deformati...The average stretching direction,local rotation angular,and stretching ratio parameters of molecular trains were used to express the rheology deformation.Based on this micro geometrical deformation,the macro deformation of medium was expressed.Then,using intrinsic elasticity concept,the stress-strain relation was obtained.In this theoretic formulation,the response functions of extension ratio and rotation angular were used to express the rheology feature of medium.For medium composed by incompressible molecular trains,the local rotation angular divides rheology deformation into three kinds:viscoelastic deformation or elasticity enhancement,viscoplastic deformation or elasticity degenerate and constant elasticity range.These results explain the experimental features of rheology deformation well.展开更多
A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected...A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.展开更多
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard ...Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root.展开更多
面向云环境中精确密文检索需求,设计了一种多属性、双索引(Multi-Rationality for Dual-Indexing,MRDI)检索方案。检索时对查询关键词进行语义扩展,并利用语义相似度过滤扩展结果来获得扩展查询集,以便更好地理解用户查询意图。从建索...面向云环境中精确密文检索需求,设计了一种多属性、双索引(Multi-Rationality for Dual-Indexing,MRDI)检索方案。检索时对查询关键词进行语义扩展,并利用语义相似度过滤扩展结果来获得扩展查询集,以便更好地理解用户查询意图。从建索和检索两方面改进传统密文检索方案,高效检索出包含对应关键词的文件目录信息,同时提高了查准率。实验结果表明,该方案具有高效性和可行性。展开更多
文摘In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.
文摘The average stretching direction,local rotation angular,and stretching ratio parameters of molecular trains were used to express the rheology deformation.Based on this micro geometrical deformation,the macro deformation of medium was expressed.Then,using intrinsic elasticity concept,the stress-strain relation was obtained.In this theoretic formulation,the response functions of extension ratio and rotation angular were used to express the rheology feature of medium.For medium composed by incompressible molecular trains,the local rotation angular divides rheology deformation into three kinds:viscoelastic deformation or elasticity enhancement,viscoplastic deformation or elasticity degenerate and constant elasticity range.These results explain the experimental features of rheology deformation well.
基金supported by National Researcher Program of National Research Foundation of Korea(Grant No.2010-0020413)
文摘A fundamental result in the theory of minimal rational curves on projective manifolds is Cartan- Fubini extension theorem proved by Hwang and Mok, which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents （VMRT）, under a mild geometric assumption on the second fundamental forms of VMRT＇s. Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Pano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends VMRT＇s onto linear sections of VMRT＇s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT＇s. In the current paper, we give a generalization of Hong and Mok＇s result, under the same condition on second fundamental forms, assuming only that the holomorphic immersions send VMRT＇s to VMRT＇s. Our argument is different from Hong and Mok＇s and is based on the study of natural foliations on the total family of VMRT＇s. This gives a substantially simpler proof than Hong and Mok＇s argument.
基金supported by the National Researcher Program 2010-0020413 of NRFGA17-19437S of Czech Science Foundation(GACR)+3 种基金partially supported by the Simons-Foundation grant 346300the Polish Government MNi SW 2015-2019 matching fundsupported by BK21 PLUS SNU Mathematical Sciences DivisionIBS-R003-Y1
文摘Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root.
文摘面向云环境中精确密文检索需求,设计了一种多属性、双索引(Multi-Rationality for Dual-Indexing,MRDI)检索方案。检索时对查询关键词进行语义扩展,并利用语义相似度过滤扩展结果来获得扩展查询集,以便更好地理解用户查询意图。从建索和检索两方面改进传统密文检索方案,高效检索出包含对应关键词的文件目录信息,同时提高了查准率。实验结果表明,该方案具有高效性和可行性。
