Annulus fibrosus （AF） tissue engineering has recently received increasing attention as a treatment for intervertebral disc 0VD） degeneration; however, such engineering remains challenging because of the remarkable ...Annulus fibrosus （AF） tissue engineering has recently received increasing attention as a treatment for intervertebral disc 0VD） degeneration; however, such engineering remains challenging because of the remarkable complexity of AF tissue. In order to engineer a functional AF replacement, the fabrication of cell-scaffold constructs that mimic the cellular, biochemical and structural features of native AF tissue is critical. In this study, we fabricated aligned fibroua polyurethane scaffolds using an electrospinning technique and used them for culturing AF-derived-stem/progenitor cells （AFSCs）. Random fibrous scaffolds, also prepared via electrospinningy were used as a control. We compared the morphology, proliferation, gene expression and matrix production of AFSCs on aligned scaffolds and random scaffolds. There was no apparent difference in the attachment or proliferation of cells cultured on aligned scaffolds and random scaffolds. However, compared to cells on random scaffolds, the AFSCs on aligned scaffolds were more elongated and better aligned, and they exhibited higher gene expression and matrix production of coUagen-I and aggrecan. The gene expression and protein production of coUagen-II did not appear to differ between the two groups. Together, these findings indicate that aligned fibrous scaffolds may provide a favourable microenvironment for the differentiation of AFSCs into cells similar to outer AF cells, which predominantly produce collagen-I matrix.展开更多
In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obta...In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.展开更多
We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free ferm...We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.展开更多
A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained....A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.展开更多
In terms of reflection transformation of a matrix product state (MPS),the parity of the MPS is defined.Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e> and the odd-par...In terms of reflection transformation of a matrix product state (MPS),the parity of the MPS is defined.Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e> and the odd-parity state|Ψ_o>.It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations;insteadthe even-parity state |Ψ_e> and the odd-parity state |Ψ_o> constructed from them have the same long-range correlationsfor the parity non-conserved block operators.Moreover,the entanglement between a block of n contiguous spins and therest of the spin chain for the states |Ψ_e> and |Ψ_o> is larger than that for the reflective MPS pair except for n = 1,and thedifference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1.These characteristicsindicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode,andthat the parity conserved MPSs contain more correlation,coherence,and entanglement than the parity non-conservedones.展开更多
The application of work strategies taking into account, from the initial stages, all the factors involved in the product design process is considered essential by the researches to generate higher quality products, as...The application of work strategies taking into account, from the initial stages, all the factors involved in the product design process is considered essential by the researches to generate higher quality products, assess users’ needs and anticipate design problems. This paper presents two approaches of design project development, denominated respectively: projects with imposed specifications and projects with derived specifications and proposes the use of the matrix that integrates specifications and design factors (SFM). This design support tool complements others already used in the development of product concepts by higher education students, increasing the capacity of synthesis and structuring of information in order to facilitate decision-making into the design process. Its elaboration implies understanding of objectives, identifying of factors and establishing of specifications. At the same time, it aims to foster the reflection process and an integrated information analysis. The application of SFM and its contribution to different project approaches are shown in this paper.展开更多
Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple ...Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.展开更多
In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard ...In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.展开更多
In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple grap...In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.展开更多
基金supported by the National Natural Science Foundation of China (81171479, 51303120, 81471790)the China Postdoctoral Science Foundation (2012M521121)+2 种基金the Natural Science Foundation of Jiangsu Province (BK20130335)the Jiangsu Provincial Special Program of Medical Science (BL2012004)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Annulus fibrosus （AF） tissue engineering has recently received increasing attention as a treatment for intervertebral disc 0VD） degeneration; however, such engineering remains challenging because of the remarkable complexity of AF tissue. In order to engineer a functional AF replacement, the fabrication of cell-scaffold constructs that mimic the cellular, biochemical and structural features of native AF tissue is critical. In this study, we fabricated aligned fibroua polyurethane scaffolds using an electrospinning technique and used them for culturing AF-derived-stem/progenitor cells （AFSCs）. Random fibrous scaffolds, also prepared via electrospinningy were used as a control. We compared the morphology, proliferation, gene expression and matrix production of AFSCs on aligned scaffolds and random scaffolds. There was no apparent difference in the attachment or proliferation of cells cultured on aligned scaffolds and random scaffolds. However, compared to cells on random scaffolds, the AFSCs on aligned scaffolds were more elongated and better aligned, and they exhibited higher gene expression and matrix production of coUagen-I and aggrecan. The gene expression and protein production of coUagen-II did not appear to differ between the two groups. Together, these findings indicate that aligned fibrous scaffolds may provide a favourable microenvironment for the differentiation of AFSCs into cells similar to outer AF cells, which predominantly produce collagen-I matrix.
文摘In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)the National Natural Science Foundation of China(Grant Nos.11774398 and T2121001)。
文摘We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.
文摘A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.
基金Supported by the Scientific Research Foundation of CUIT under Grant No.KYTZ201024the National Natural Science Foundation of China under Grant Nos.10775100,10974137 the Fund of Theoretical Nuclear Center of HIRFL of China
文摘In terms of reflection transformation of a matrix product state (MPS),the parity of the MPS is defined.Based on the reflective parity non-conserved MPS pair we construct the even-parity state |Ψ_e> and the odd-parity state|Ψ_o>.It is interesting to find that the parity non-conserved reflective MPS pair have no long-range correlations;insteadthe even-parity state |Ψ_e> and the odd-parity state |Ψ_o> constructed from them have the same long-range correlationsfor the parity non-conserved block operators.Moreover,the entanglement between a block of n contiguous spins and therest of the spin chain for the states |Ψ_e> and |Ψ_o> is larger than that for the reflective MPS pair except for n = 1,and thedifference of them approaches 1 monotonically and asymptotically from 0 as n increases from 1.These characteristicsindicate that MPS parity as a conserved physical quantity represents a kind of coherent collective quantum mode,andthat the parity conserved MPSs contain more correlation,coherence,and entanglement than the parity non-conservedones.
文摘The application of work strategies taking into account, from the initial stages, all the factors involved in the product design process is considered essential by the researches to generate higher quality products, assess users’ needs and anticipate design problems. This paper presents two approaches of design project development, denominated respectively: projects with imposed specifications and projects with derived specifications and proposes the use of the matrix that integrates specifications and design factors (SFM). This design support tool complements others already used in the development of product concepts by higher education students, increasing the capacity of synthesis and structuring of information in order to facilitate decision-making into the design process. Its elaboration implies understanding of objectives, identifying of factors and establishing of specifications. At the same time, it aims to foster the reflection process and an integrated information analysis. The application of SFM and its contribution to different project approaches are shown in this paper.
基金The NSF (10571114) of Chinathe Natural Science Basic Research Plan (2005A1) of Shaanxi Province of China
文摘Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.
文摘In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.
文摘In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.
