We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix repr...We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quan- tum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature.展开更多
Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generali...Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].展开更多
NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can repres...NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design.展开更多
In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be in...In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be infinite dimensional Banach spaces over complex field A. Denote by Y} the set of all bounded linear operators from X to Y. If X=Y, we write instead of B(X, F). For T^B(X"), let -D(T), ker T, R(T} denote the domain, kerner and the range of T respectively. For a subset MdX, M denotes the closure of M. Let H be a Hilbert space and MdH, then ML denotes the annihilator of If.展开更多
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the g...This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.展开更多
This paper is focused on automated reasoning based on classical propositional logic and lattice valued propositional logic LP(X) . A new method of automated reasoning is given, and the soundness and completeness...This paper is focused on automated reasoning based on classical propositional logic and lattice valued propositional logic LP(X) . A new method of automated reasoning is given, and the soundness and completeness theorems of this method are proved.展开更多
A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a ...A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given.展开更多
Let H_F be the generalized quaternion division algebra over a field F with charF≠2. In this paper, the ad joint matrix of any n×n matrix over H_F[λ] is defined and its properties is discussed. By using the adjo...Let H_F be the generalized quaternion division algebra over a field F with charF≠2. In this paper, the ad joint matrix of any n×n matrix over H_F[λ] is defined and its properties is discussed. By using the adjoint matrix and the method of representation matrix, this paper obtains several necessary and sufficieut conditions for the existence of a solution or a unique solution to the matrix equation sum from n=i to k A^iXB_i=E over H_F, and gives some explicit formulas of solutions.展开更多
This paper mainly investigates some properties of Cheng projection,which was proposed recently by Prof.Cheng to reduce the dimension of vector.As a linear transformation from the original vector space to the target ve...This paper mainly investigates some properties of Cheng projection,which was proposed recently by Prof.Cheng to reduce the dimension of vector.As a linear transformation from the original vector space to the target vector space,the matrix representation of Cheng projection is given.Then,the structure matrix of Cheng projection,called the Cheng projection matrix,is obtained.Algebraic properties of Cheng projection are derived via its projection matrix.Furthermore,the product and norm of Cheng projection matrices are concerned.展开更多
For any element a in a generalized 2^n-dimensional Clifford algebra Lln (F) over an arbitrary field F of characteristic not equal to two, it is shown that there exits a universal invertible matrix Pn over Lln(F) s...For any element a in a generalized 2^n-dimensional Clifford algebra Lln (F) over an arbitrary field F of characteristic not equal to two, it is shown that there exits a universal invertible matrix Pn over Lln(F) such that Pn^-1DnPn= φ(α)∈F^2n×2n, where φ(a) is a matrix representation of α over and Dα is a diagonal matrix consisting of a or its conjugate.展开更多
By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.
Knowledge graph representation has been a long standing goal of artificial intelligence. In this paper,we consider a method for knowledge graph embedding of hyper-relational data, which are commonly found in knowledge...Knowledge graph representation has been a long standing goal of artificial intelligence. In this paper,we consider a method for knowledge graph embedding of hyper-relational data, which are commonly found in knowledge graphs. Previous models such as Trans(E, H, R) and CTrans R are either insufficient for embedding hyper-relational data or focus on projecting an entity into multiple embeddings, which might not be effective for generalization nor accurately reflect real knowledge. To overcome these issues, we propose the novel model Trans HR, which transforms the hyper-relations in a pair of entities into an individual vector, serving as a translation between them. We experimentally evaluate our model on two typical tasks—link prediction and triple classification.The results demonstrate that Trans HR significantly outperforms Trans(E, H, R) and CTrans R, especially for hyperrelational data.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11347026)the Natural Science Foundation of Shandong Province+1 种基金China(Grant Nos.ZR2013AM012 and ZR2012AM004)the Research Fund for the Doctoral Program and Scientific Research Project of Liaocheng University,Shandong Province,China
文摘We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quan- tum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature.
基金National Natural science Foundation of China(10171082)the Cultivation Fund of the Key Scientific Technical Innovation Project,Ministry of Education of ChinaTRAPOYT
文摘Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either (S,≤) satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].
文摘NURBS curve is one of the most commonly used tools in CAD systems and geometric modeling for its various specialties, which means that its shape is locally adjustable as well as its continuity order, and it can represent a conic curve precisely. But how to do degree reduction of NURBS curves in a fast and efficient way still remains a puzzling problem. By applying the theory of the best uniform approximation of Chebyshev polynomials and the explicit matrix representation of NURBS curves, this paper gives the necessary and sufficient condition for degree reducible NURBS curves in an explicit form. And a new way of doing degree reduction of NURBS curves is also presented, including the multi-degree reduction of a NURBS curve on each knot span and the multi-degree reduction of a whole NURBS curve. This method is easy to carry out, and only involves simple calculations. It provides a new way of doing degree reduction of NURBS curves, which can be widely used in computer graphics and industrial design.
文摘In this paper we introduce the concepts of "O-state" and "I--state" for nilpotent operators and give a fine matrix representation for each nilpotent operator according to its state.Let X’, Y be infinite dimensional Banach spaces over complex field A. Denote by Y} the set of all bounded linear operators from X to Y. If X=Y, we write instead of B(X, F). For T^B(X"), let -D(T), ker T, R(T} denote the domain, kerner and the range of T respectively. For a subset MdX, M denotes the closure of M. Let H be a Hilbert space and MdH, then ML denotes the annihilator of If.
基金This research is supported by the Natural Science Foundation of the Educational Committee of Jiang Su Province.
文摘This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.
基金theNationalNaturalScienceFoundationofChina (No .60 0 740 1 4)
文摘This paper is focused on automated reasoning based on classical propositional logic and lattice valued propositional logic LP(X) . A new method of automated reasoning is given, and the soundness and completeness theorems of this method are proved.
基金Sponsored by the Ministry of Education Foundation of China(5220308)
文摘A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed. Then an algorithm of 3D object recognition using the linear Lie algebra models is presented. It is a convenient recognition method for the objects which are symmetric about some axis. By using the presented algorithm, the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained. At last some recognition results of practicalities are given.
基金the National Natural Science Foundation of China and Hunan
文摘Let H_F be the generalized quaternion division algebra over a field F with charF≠2. In this paper, the ad joint matrix of any n×n matrix over H_F[λ] is defined and its properties is discussed. By using the adjoint matrix and the method of representation matrix, this paper obtains several necessary and sufficieut conditions for the existence of a solution or a unique solution to the matrix equation sum from n=i to k A^iXB_i=E over H_F, and gives some explicit formulas of solutions.
基金supported by the National Natural Science Foundation of China under Grant Nos.61773371,61877036the Natural Science Fund of Shandong Province under Grant No.ZR2019MF002。
文摘This paper mainly investigates some properties of Cheng projection,which was proposed recently by Prof.Cheng to reduce the dimension of vector.As a linear transformation from the original vector space to the target vector space,the matrix representation of Cheng projection is given.Then,the structure matrix of Cheng projection,called the Cheng projection matrix,is obtained.Algebraic properties of Cheng projection are derived via its projection matrix.Furthermore,the product and norm of Cheng projection matrices are concerned.
文摘For any element a in a generalized 2^n-dimensional Clifford algebra Lln (F) over an arbitrary field F of characteristic not equal to two, it is shown that there exits a universal invertible matrix Pn over Lln(F) such that Pn^-1DnPn= φ(α)∈F^2n×2n, where φ(a) is a matrix representation of α over and Dα is a diagonal matrix consisting of a or its conjugate.
基金Supported by National Natural Science Foundation of China(Grant No.10971020)
文摘By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.
基金partially supported by the National Natural Science Foundation of China(Nos.61302077,61520106007,61421061,and 61602048)
文摘Knowledge graph representation has been a long standing goal of artificial intelligence. In this paper,we consider a method for knowledge graph embedding of hyper-relational data, which are commonly found in knowledge graphs. Previous models such as Trans(E, H, R) and CTrans R are either insufficient for embedding hyper-relational data or focus on projecting an entity into multiple embeddings, which might not be effective for generalization nor accurately reflect real knowledge. To overcome these issues, we propose the novel model Trans HR, which transforms the hyper-relations in a pair of entities into an individual vector, serving as a translation between them. We experimentally evaluate our model on two typical tasks—link prediction and triple classification.The results demonstrate that Trans HR significantly outperforms Trans(E, H, R) and CTrans R, especially for hyperrelational data.