Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey...Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey? weak multiplier sequentially continuous problem of infinite matrix algebras (λ,μ).展开更多
In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz ...In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.展开更多
Circuits with switched current are described by an admittance matrix and seeking current transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit a...Circuits with switched current are described by an admittance matrix and seeking current transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit analysis in addition to algebraic methods, it is clearly possible in theory to carry out an analysis of the whole switched circuit in two-phase switching exclusively by the graph method as well. For this purpose it is possible to plot a Mason graph of a circuit, use transformation graphs to reduce Mason graphs for all the four phases of switching, and then plot a summary graph from the transformed graphs obtained this way. First the author draws nodes and possible branches, obtained by transformation graphs for transfers of EE （even-even） and OO （odd-odd） phases. In the next step, branches obtained by transformation graphs for EO and OE phase are drawn between these nodes, while their resulting transfer is 1 multiplied by z^1/2. This summary graph is extended by two branches from input node and to output node, the extended graph can then be interpreted by the Mason＇s relation to provide transparent current transfers. Therefore it is not necessary to compose a sum admittance matrix and to express this consequently in numbers, and so it is possible to reach the final result in a graphical way.展开更多
Associative multiplications of cubic matrices are provided.The N3-dimensional3-Lie algebras are realized by cubic matrices,and structures of the 3-Lie algebras are studied.
We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diago...We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).展开更多
Boolean functions used in a cryptographic system should have high algebraic immunity to resist algebraic attacks. This paper presents a matrix method for constructing balanced Boolean functions achieving maximum algeb...Boolean functions used in a cryptographic system should have high algebraic immunity to resist algebraic attacks. This paper presents a matrix method for constructing balanced Boolean functions achieving maximum algebraic immunity.展开更多
Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational...Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.展开更多
文摘Let λ and μ are sequence spaces and have both the signed_weak gliding hump property, (λ,μ) be the algebra of the infinite matrix operators which transform λ into μ, in this paper, we study the strong? Mackey? weak multiplier sequentially continuous problem of infinite matrix algebras (λ,μ).
文摘In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.
文摘Circuits with switched current are described by an admittance matrix and seeking current transfers then means calculating the ratio of algebraic supplements of this matrix. As there are also graph methods of circuit analysis in addition to algebraic methods, it is clearly possible in theory to carry out an analysis of the whole switched circuit in two-phase switching exclusively by the graph method as well. For this purpose it is possible to plot a Mason graph of a circuit, use transformation graphs to reduce Mason graphs for all the four phases of switching, and then plot a summary graph from the transformed graphs obtained this way. First the author draws nodes and possible branches, obtained by transformation graphs for transfers of EE （even-even） and OO （odd-odd） phases. In the next step, branches obtained by transformation graphs for EO and OE phase are drawn between these nodes, while their resulting transfer is 1 multiplied by z^1/2. This summary graph is extended by two branches from input node and to output node, the extended graph can then be interpreted by the Mason＇s relation to provide transparent current transfers. Therefore it is not necessary to compose a sum admittance matrix and to express this consequently in numbers, and so it is possible to reach the final result in a graphical way.
基金supported by the National Natural Science Foundation of China(No.11371245)the Natural Science Foundation of Hebei Province(No.A2010000194)
文摘Associative multiplications of cubic matrices are provided.The N3-dimensional3-Lie algebras are realized by cubic matrices,and structures of the 3-Lie algebras are studied.
基金supported by National Natural Science Foundation of China(Grant No.11371290)
文摘We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)^+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012).
基金supported by the National Natural Science Foundation of China under Grant Nos.61070172 and 10990011the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No. XDA06010702the State Key Laboratory of Information Security,Chinese Academy of Sciences
文摘Boolean functions used in a cryptographic system should have high algebraic immunity to resist algebraic attacks. This paper presents a matrix method for constructing balanced Boolean functions achieving maximum algebraic immunity.
基金the Engineering and Physical Sciences Research Council National Quantum Technology Hub in Networked Quantum Information Technology(EP/M013243/1)Japan Student Services Organization(JASSO)Student Exchange Support Program(Graduate Scholarship for Degree Seeking Students)+1 种基金the National Natural Science Foundation of China(U1730449)the European Quantum Technology Flagship project AQTION。
文摘Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.
