How to deal with the imprecise information retrieval has become more and more important in the present information society. An efficient and effective method of information retrieval based on multi tuple rough set is...How to deal with the imprecise information retrieval has become more and more important in the present information society. An efficient and effective method of information retrieval based on multi tuple rough set is discussed in this paper. The new approach is considered as a generalization of the original rough set model for flexible information retrieval. The imprecise query results can be obtained by multi tuple approximations.展开更多
For a compact operator tuple A, if its projective spectrum P(A*) is smooth, then there exists a natural Hermitian holomorphic line bundle EAover P(A*) which is a unitary invariant for A. This paper shows that under so...For a compact operator tuple A, if its projective spectrum P(A*) is smooth, then there exists a natural Hermitian holomorphic line bundle EAover P(A*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, EAis a complete unitary invariant, i.e., EAcan determine the compact operator tuple up to unitary equivalence.展开更多
This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tupleT n is (-1) n time wrapping number of φ n around the origin. As one of the applications ...This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tupleT n is (-1) n time wrapping number of φ n around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincaré domain. As another application, it is shown thatC*(Ω)?C*(Bn) for every Poincare domain Ω inC n (n≠2). It is also noticed thatC*(Ω)?C*(B 2) if and only if the Poincaré conjecture is true for ?Ω.展开更多
In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singul...In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and(ⅱ) each nonzero Zeigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.展开更多
A new approach of relation extraction is described in this paper. It adopts a bootstrap- ping model with a novel iteration strategy, which generates more precise examples of specific relation. Compared with previous m...A new approach of relation extraction is described in this paper. It adopts a bootstrap- ping model with a novel iteration strategy, which generates more precise examples of specific relation. Compared with previous methods, the proposed method has three main advantages: first, it needs less manual intervention; second, more abundant and reasonable information are introduced to represent a relation pattern; third, it reduces the risk of circular dependency occurrence in bootstrapping. Scalable evaluation methodology and metrics are developed for our task with comparable techniques over TianWang 100G corpus. The experimental results show that it can get 90% precision and have excellent expansibility.展开更多
How to select appropriate wolds in a translation is a significant problem in current studies of machine translation, because it directly decides the translation quality. This paper uses an unsupervised corpus-based st...How to select appropriate wolds in a translation is a significant problem in current studies of machine translation, because it directly decides the translation quality. This paper uses an unsupervised corpus-based statisticalmethod to select target word. Based on the concurrence probabilities, all ambiguous words in a sentence are disambiguated at the same time. Because a corpus of limited size cannot cover all the collocation of words, we use an effectivesmoothing method to increase the coverage of the corpus. In ceder to solve the problem in our English-Chinese MT system, we have applied the algorithm to disambiguate senses of verbs, nouns and adjectitves in target language, and theresult shows that the approach is very promising.展开更多
In this paper, an interval-gap-based 1NF temporal tuple calculus language and the corresponding temporal relation algebra are established on the basis of considering the trouble of stack operations in both S. Gadia’s...In this paper, an interval-gap-based 1NF temporal tuple calculus language and the corresponding temporal relation algebra are established on the basis of considering the trouble of stack operations in both S. Gadia’s TCAL and temporal tuple calculus due to their NINF.展开更多
A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary...A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.展开更多
In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure f...In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.展开更多
文摘How to deal with the imprecise information retrieval has become more and more important in the present information society. An efficient and effective method of information retrieval based on multi tuple rough set is discussed in this paper. The new approach is considered as a generalization of the original rough set model for flexible information retrieval. The imprecise query results can be obtained by multi tuple approximations.
基金supported by National Natural Science Foundation of China(Grant No.11671078)。
文摘For a compact operator tuple A, if its projective spectrum P(A*) is smooth, then there exists a natural Hermitian holomorphic line bundle EAover P(A*) which is a unitary invariant for A. This paper shows that under some additional spectral conditions, EAis a complete unitary invariant, i.e., EAcan determine the compact operator tuple up to unitary equivalence.
文摘This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tupleT n is (-1) n time wrapping number of φ n around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincaré domain. As another application, it is shown thatC*(Ω)?C*(Bn) for every Poincare domain Ω inC n (n≠2). It is also noticed thatC*(Ω)?C*(B 2) if and only if the Poincaré conjecture is true for ?Ω.
基金supported by National Natural Science Foundation of China(Grant No.11771328)Young Elite Scientists Sponsorship Program by Tianjin and the Natural Science Foundation of Zhejiang Province of China(Grant No.LD19A010002)。
文摘In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which have found many applications in diverse areas. The main results are:(ⅰ)each(Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and(ⅱ) each nonzero Zeigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.
基金Supported by the National Natural Science Foundation of China (No.60503072, No.60575042 and No.60435020).
文摘A new approach of relation extraction is described in this paper. It adopts a bootstrap- ping model with a novel iteration strategy, which generates more precise examples of specific relation. Compared with previous methods, the proposed method has three main advantages: first, it needs less manual intervention; second, more abundant and reasonable information are introduced to represent a relation pattern; third, it reduces the risk of circular dependency occurrence in bootstrapping. Scalable evaluation methodology and metrics are developed for our task with comparable techniques over TianWang 100G corpus. The experimental results show that it can get 90% precision and have excellent expansibility.
文摘How to select appropriate wolds in a translation is a significant problem in current studies of machine translation, because it directly decides the translation quality. This paper uses an unsupervised corpus-based statisticalmethod to select target word. Based on the concurrence probabilities, all ambiguous words in a sentence are disambiguated at the same time. Because a corpus of limited size cannot cover all the collocation of words, we use an effectivesmoothing method to increase the coverage of the corpus. In ceder to solve the problem in our English-Chinese MT system, we have applied the algorithm to disambiguate senses of verbs, nouns and adjectitves in target language, and theresult shows that the approach is very promising.
基金Supported by both the High Technology Research Development Programme of Chinathe National Natural Science Foundation of China
文摘In this paper, an interval-gap-based 1NF temporal tuple calculus language and the corresponding temporal relation algebra are established on the basis of considering the trouble of stack operations in both S. Gadia’s TCAL and temporal tuple calculus due to their NINF.
文摘A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.
文摘In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.
