An improved decision tree method for web information retrieval with self-mapping attributes is proposed.The self-mapping tree has a value of self-mapping attribute in its internal node,and information based on dissimi...An improved decision tree method for web information retrieval with self-mapping attributes is proposed.The self-mapping tree has a value of self-mapping attribute in its internal node,and information based on dissimilarity between a pair of mapping sequences.This method selects self-mapping which exists between data by exhaustive search based on relation and attribute information.Experimental results confirm that the improved method constructs comprehensive and accurate decision tree.Moreover,an example shows that the self-mapping decision tree is promising for data mining and knowledge discovery.展开更多
We prove that over an algebraically closed field of arbitrary characteristic,a bounded-degree group of birational self-maps of an irreducible projective variety can be simultaneously regularized.In other words,there e...We prove that over an algebraically closed field of arbitrary characteristic,a bounded-degree group of birational self-maps of an irreducible projective variety can be simultaneously regularized.In other words,there exists another projective variety that is birational to the original one such that every element of the boundeddegree group turns into an automorphism after the birational transformation.Over the field of complex numbers,this result was stated in an article by Cantat(2014)and the proof originates from a work of Huckleberry and Zaitsev(1996).The original proof,however,is not purely algebraic.By adapting their methods,we provide a purely algebraic proof of this statement in arbitrary characteristic.Moreover,we discuss a corollary of this result that is useful in arithmetic dynamics.展开更多
Let I = [0,1], 0 < a < b < 1. Let Φab ≡ {F ∈ C0(I): both F|[0,a] and F|[b, 1] are strictly increasing, and F|[a, b] is constant }. In this paper we discuss necessary and sufficient conditions for F ∈Φab ...Let I = [0,1], 0 < a < b < 1. Let Φab ≡ {F ∈ C0(I): both F|[0,a] and F|[b, 1] are strictly increasing, and F|[a, b] is constant }. In this paper we discuss necessary and sufficient conditions for F ∈Φab to have monotone iterative roots.展开更多
In this paper, Schwarz-Pick estimates for high order FrSchet derivatives of holo- morphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Sc：hwarz-Pick est...In this paper, Schwarz-Pick estimates for high order FrSchet derivatives of holo- morphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Sc：hwarz-Pick estimates of higher-order partial derivatives for bounded holomorphic functions on classical domains.展开更多
Denote by z(p)(resp.Zp)the p localization(resp.p completion)of z.Then we have the canonical inclusion Z(p)→zp.Let S2n-1(p)be the p-local(2n-1)-sphere and let B2n(p)be a connected p-local space satisfying S2n-l(p)≌Ω...Denote by z(p)(resp.Zp)the p localization(resp.p completion)of z.Then we have the canonical inclusion Z(p)→zp.Let S2n-1(p)be the p-local(2n-1)-sphere and let B2n(p)be a connected p-local space satisfying S2n-l(p)≌ΩB2n(p),then H*B2n(p),Z(p))=Z(p)[U]with|u|=2n.Define the degree of a self-map f of B2n(p)to be k E Z(p)such that f*(u)=ku.Using the theory of integer-valued polynomials we show that there exists a self-map of B2n(p)of degree k if and only if k is an n-th power in Zp.展开更多
Let I be the interval [0,1].We denote by (I) the space of all continuous mapsfrom I into itself with the C^0 topology,i.e.the topology induced by the metric ρ(f,g) =sup{|f(x)-g(x)||x∈I}. Let f∈(I).A subset C of I i...Let I be the interval [0,1].We denote by (I) the space of all continuous mapsfrom I into itself with the C^0 topology,i.e.the topology induced by the metric ρ(f,g) =sup{|f(x)-g(x)||x∈I}. Let f∈(I).A subset C of I is said to be Li-Yorke chaotic in respect to f if forany two points x,y∈C with x≠y,展开更多
1. Let （X, d） be a compact metric space, and denote by C0（X, X） the set of all continuous self-mappings of X with C0-topology. Let f∈C0 （X, X） and ε>0. If x,y∈X, an ε-chain from x to y is a finite sequenc...1. Let （X, d） be a compact metric space, and denote by C0（X, X） the set of all continuous self-mappings of X with C0-topology. Let f∈C0 （X, X） and ε>0. If x,y∈X, an ε-chain from x to y is a finite sequence of points {x0,…, xn} of X with x=x0, y=xn and d(f(xi-1), xi)<ε for i=1, …, n. Let CRε（x） denote the set of y∈X such that there is an ε-chain from x to y. We say x can展开更多
If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.
Let M be a 2-dimensional closed manifold, orientable or non-orientable. The construction of every compact locally connected subspace X of M without cut-points is analyzed. It is proved that every orientation-preservin...Let M be a 2-dimensional closed manifold, orientable or non-orientable. The construction of every compact locally connected subspace X of M without cut-points is analyzed. It is proved that every orientation-preserving (or reversing, or relatively preserving) point-wise periodic continuous self-map of X can be extended to a periodic self-homeomorphism of M (or of a 2-dimensional compact submanifold of M). In addition, every orientation-preserving (or reversing, or relatively preserving) pointwise periodic continuous self-map f of any path-connected subspace of M is proved to be a periodic self-homeomorphism, the number of the shorter-periodic points of f is shown to be finite, and generalization of Weaver’s conclusion is given.展开更多
文摘An improved decision tree method for web information retrieval with self-mapping attributes is proposed.The self-mapping tree has a value of self-mapping attribute in its internal node,and information based on dissimilarity between a pair of mapping sequences.This method selects self-mapping which exists between data by exhaustive search based on relation and attribute information.Experimental results confirm that the improved method constructs comprehensive and accurate decision tree.Moreover,an example shows that the self-mapping decision tree is promising for data mining and knowledge discovery.
基金supported by National Natural Science Foundation of China(Grant No.12271007)。
文摘We prove that over an algebraically closed field of arbitrary characteristic,a bounded-degree group of birational self-maps of an irreducible projective variety can be simultaneously regularized.In other words,there exists another projective variety that is birational to the original one such that every element of the boundeddegree group turns into an automorphism after the birational transformation.Over the field of complex numbers,this result was stated in an article by Cantat(2014)and the proof originates from a work of Huckleberry and Zaitsev(1996).The original proof,however,is not purely algebraic.By adapting their methods,we provide a purely algebraic proof of this statement in arbitrary characteristic.Moreover,we discuss a corollary of this result that is useful in arithmetic dynamics.
基金Supported by the National Natural Science Foundation of China !(19961001)
文摘Let I = [0,1], 0 < a < b < 1. Let Φab ≡ {F ∈ C0(I): both F|[0,a] and F|[b, 1] are strictly increasing, and F|[a, b] is constant }. In this paper we discuss necessary and sufficient conditions for F ∈Φab to have monotone iterative roots.
基金supported by the National Natural Science Foundation of China (Nos. 11171255, 11101373)the Doctoral Program Foundation of the Ministry of Education of China (No. 20090072110053)+1 种基金the Zhejiang Provincial Natural Science Foundation of China (No. Y6100007)the Zhejiang Innovation Project (No. T200905)
文摘In this paper, Schwarz-Pick estimates for high order FrSchet derivatives of holo- morphic self-mappings on classical domains are presented. Moreover, the obtained result can deduce the early work on Sc：hwarz-Pick estimates of higher-order partial derivatives for bounded holomorphic functions on classical domains.
文摘Denote by z(p)(resp.Zp)the p localization(resp.p completion)of z.Then we have the canonical inclusion Z(p)→zp.Let S2n-1(p)be the p-local(2n-1)-sphere and let B2n(p)be a connected p-local space satisfying S2n-l(p)≌ΩB2n(p),then H*B2n(p),Z(p))=Z(p)[U]with|u|=2n.Define the degree of a self-map f of B2n(p)to be k E Z(p)such that f*(u)=ku.Using the theory of integer-valued polynomials we show that there exists a self-map of B2n(p)of degree k if and only if k is an n-th power in Zp.
基金Project supported by the Youth Science Foundation of Anhui University.
文摘Let I be the interval [0,1].We denote by (I) the space of all continuous mapsfrom I into itself with the C^0 topology,i.e.the topology induced by the metric ρ(f,g) =sup{|f(x)-g(x)||x∈I}. Let f∈(I).A subset C of I is said to be Li-Yorke chaotic in respect to f if forany two points x,y∈C with x≠y,
基金Project supported in part by the Foundation of Zhongshan University Advanced Research Centre.
文摘1. Let （X, d） be a compact metric space, and denote by C0（X, X） the set of all continuous self-mappings of X with C0-topology. Let f∈C0 （X, X） and ε>0. If x,y∈X, an ε-chain from x to y is a finite sequence of points {x0,…, xn} of X with x=x0, y=xn and d(f(xi-1), xi)<ε for i=1, …, n. Let CRε（x） denote the set of y∈X such that there is an ε-chain from x to y. We say x can
基金supported by KAKENHI,Grant-in-Aid for Scientific Research(C)(Grant No.18K03304)
文摘If G is a compact connected Lie group and T is a maximal torus, we give a wedge decomposition of ΣG/T by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of G/T.
文摘Let M be a 2-dimensional closed manifold, orientable or non-orientable. The construction of every compact locally connected subspace X of M without cut-points is analyzed. It is proved that every orientation-preserving (or reversing, or relatively preserving) point-wise periodic continuous self-map of X can be extended to a periodic self-homeomorphism of M (or of a 2-dimensional compact submanifold of M). In addition, every orientation-preserving (or reversing, or relatively preserving) pointwise periodic continuous self-map f of any path-connected subspace of M is proved to be a periodic self-homeomorphism, the number of the shorter-periodic points of f is shown to be finite, and generalization of Weaver’s conclusion is given.
