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 tuple T n is ( -1)n time wrapping number of n around the origin. As one of the applications of...This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tuple T n is ( -1)n time wrapping number of n around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincare domain. As another application, it is shown that C* (Ω) ≌ C* ( Bn) for every Poincare domain Ω in Cn( n≠2). It is also noticed that C* (Ω) ≌ C* ( B2) 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
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
Structures using constructors are of ordinary use in functional programming to represent data structures of unbound size. Lack of associativity of constructors, however, hinders program analyses or efficient execution...Structures using constructors are of ordinary use in functional programming to represent data structures of unbound size. Lack of associativity of constructors, however, hinders program analyses or efficient executions. This paper describes ideas of abstraction toward constructors, and similarly abstraction from constructing functions, which we call functional constructors. We demonstrate our ideas making program analyses easier and enable transformation to efficient execution.展开更多
Multi-target tracking is facing the difficulties of modeling uncertain motion and observation noise.Traditional tracking algorithms are limited by specific models and priors that may mismatch a real-world scenario.In ...Multi-target tracking is facing the difficulties of modeling uncertain motion and observation noise.Traditional tracking algorithms are limited by specific models and priors that may mismatch a real-world scenario.In this paper,considering the model-free purpose,we present an online Multi-Target Intelligent Tracking(MTIT)algorithm based on a Deep Long-Short Term Memory(DLSTM)network for complex tracking requirements,named the MTIT-DLSTM algorithm.Firstly,to distinguish trajectories and concatenate the tracking task in a time sequence,we define a target tuple set that is the labeled Random Finite Set(RFS).Then,prediction and update blocks based on the DLSTM network are constructed to predict and estimate the state of targets,respectively.Further,the prediction block can learn the movement trend from the historical state sequence,while the update block can capture the noise characteristic from the historical measurement sequence.Finally,a data association scheme based on Hungarian algorithm and the heuristic track management strategy are employed to assign measurements to targets and adapt births and deaths.Experimental results manifest that,compared with the existing tracking algorithms,our proposed MTIT-DLSTM algorithm can improve effectively the accuracy and robustness in estimating the state of targets appearing at random positions,and be applied to linear and nonlinear multi-target tracking scenarios.展开更多
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 tuple T n is ( -1)n time wrapping number of n around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincare domain. As another application, it is shown that C* (Ω) ≌ C* ( Bn) for every Poincare domain Ω in Cn( n≠2). It is also noticed that C* (Ω) ≌ C* ( B2) 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.
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.
基金Supported by Research Fellowships of Japan Society for the Promotion of Science for Young Scientists(11-0 6 2 82 )
文摘Structures using constructors are of ordinary use in functional programming to represent data structures of unbound size. Lack of associativity of constructors, however, hinders program analyses or efficient executions. This paper describes ideas of abstraction toward constructors, and similarly abstraction from constructing functions, which we call functional constructors. We demonstrate our ideas making program analyses easier and enable transformation to efficient execution.
基金supported by the National Natural Science Foundation of China(No.62276204)Open Foundation of Science and Technology on Electronic Information Control Laboratory,Natural Science Basic Research Program of Shanxi,China(Nos.2022JM-340 and 2023-JC-QN-0710)China Postdoctoral Science Foundation(Nos.2020T130494 and 2018M633470).
文摘Multi-target tracking is facing the difficulties of modeling uncertain motion and observation noise.Traditional tracking algorithms are limited by specific models and priors that may mismatch a real-world scenario.In this paper,considering the model-free purpose,we present an online Multi-Target Intelligent Tracking(MTIT)algorithm based on a Deep Long-Short Term Memory(DLSTM)network for complex tracking requirements,named the MTIT-DLSTM algorithm.Firstly,to distinguish trajectories and concatenate the tracking task in a time sequence,we define a target tuple set that is the labeled Random Finite Set(RFS).Then,prediction and update blocks based on the DLSTM network are constructed to predict and estimate the state of targets,respectively.Further,the prediction block can learn the movement trend from the historical state sequence,while the update block can capture the noise characteristic from the historical measurement sequence.Finally,a data association scheme based on Hungarian algorithm and the heuristic track management strategy are employed to assign measurements to targets and adapt births and deaths.Experimental results manifest that,compared with the existing tracking algorithms,our proposed MTIT-DLSTM algorithm can improve effectively the accuracy and robustness in estimating the state of targets appearing at random positions,and be applied to linear and nonlinear multi-target tracking scenarios.
