Based on the output-voltage error function, a novel time discrete modulation technique is proposed for matrix converters （MCs） and time-discrete difference equations of a MC circuit are derived. Switch states of MC ...Based on the output-voltage error function, a novel time discrete modulation technique is proposed for matrix converters （MCs） and time-discrete difference equations of a MC circuit are derived. Switch states of MC are obtained when the output voltage error function is minimized, thus the optimum combination of switch states is derived for the closed-loop control of MC. Meanwhile, advantages of the least calculation workload, the simple process, and the convenient for implementation are brought while switch states are described as space vectors in the α-β coordination system. Simulation and experimental results demonstrate the validity of the time-discrete modulation technique and the feasibility of the control approach.展开更多
Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot...Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.展开更多
Background Excessive deposition of extraceUular matrix(ECM)in the kidney is the hallmark of diabetic nephropathy.Increased matrix synthesis has been well documented but the effects of diabetes on degradative pathways,...Background Excessive deposition of extraceUular matrix(ECM)in the kidney is the hallmark of diabetic nephropathy.Increased matrix synthesis has been well documented but the effects of diabetes on degradative pathways,particularly in the in vivo setting.The renal protective effect of these pathways on matrix accumulation has not been fully elucidated.The present study was understaken to investigate the activity of matrix metalloproteinase-2(MMP-2),the expression of MMP-2 and tissue inhibitor of metalloproteinase-2(TIMP-2)in kidney tissues of diabetic rats,and to explore the degradative pathway of typeⅣcollagen(Ⅳ-C)and the renal protective effects of ACE inhibition-benazepril.展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro...In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.展开更多
A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put...A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put forward a method for data classification. Namely, firstly, we use discernibility matrix and discernibility function to delete superfluous attributes in formation system and get a necessary attribute set. Secondly, we delete superfluous attribute values and get decision rules. Finally, we classify data by means of decision rules. The experiments show that data classification using this method is simpler in the structure, and can improve the efficiency of classification.展开更多
Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value j...Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.展开更多
A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative recons...A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction（IR） method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo（MC） simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization（OSEM） algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast,and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.展开更多
A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure ass...A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.展开更多
Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the di...Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.展开更多
We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quant...We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.展开更多
For the reduction of bovine serum proteins from wastewater,a novel mixed matrix membrane was prepared by functionalizing the substrate material polyaryletherketone(PAEK),followed by carboxyl groups(C-SPAEKS),and then ...For the reduction of bovine serum proteins from wastewater,a novel mixed matrix membrane was prepared by functionalizing the substrate material polyaryletherketone(PAEK),followed by carboxyl groups(C-SPAEKS),and then adding amino-functionalized UiO-66-NH_(2)(Am-UiO-66-NH_(2)).Aminofunctionalization of UiO-66 was accomplished by melamine,followed by an amidation reaction to immobilize Am-UiO-66-NH_(2),which was immobilized on the surface of the membrane as well as in the pore channels,which enhanced the hydrophilicity of the membrane surface while increasing the negative potential of the membrane surface.This nanoparticle-loaded ultrafiltration membrane has good permeation performance,with a pure water flux of up to 482.3 L·m^(-2)·h^(-1) for C-SPAEKS/AmUiO-66-NH_(2) and a retention rate of up to 98.7%for bovine serum albumin(BSA)-contaminated solutions.Meanwhile,after several hydrophilic modifications,the flux recovery of BSA contaminants by this series of membranes increased from 56.2%to 80.55%of pure membranes.The results of ultra-filtration flux time tests performed at room temperature showed that the series of ultrafiltration membranes remained relatively stable over a test time of 300 min.Thus,the newly developed mixed matrix membrane showed potential for high efficiency and stability in wastewater treatment containing bovine serum proteins.展开更多
Matrix within cells,the cytoskeleton,and that which surrounds cells,the extracellular matrix（ECM）,are connected to one another through a number of receptors including those in primary cilia,serving as an important c...Matrix within cells,the cytoskeleton,and that which surrounds cells,the extracellular matrix（ECM）,are connected to one another through a number of receptors including those in primary cilia,serving as an important chemical and physical signaling system：Mechanical forces generated through the matrix play a critical role in determining the form and function of tissues（Hughes et al.,2018）.展开更多
In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix ...In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.展开更多
In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a th...In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.展开更多
In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessar...In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.展开更多
The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positi...The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positive integers p and q are greater than one, an integral representation of pHq 2 is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the p and q-Horn’s matrix function.展开更多
By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded s...By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.展开更多
The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain syst...The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.展开更多
The main aim of this paper is to define and study of a new matrix functions, say, the pl(m,n)-Kummer matrix function of two complex variables. The radius of regularity, recurrence relation and several new results on t...The main aim of this paper is to define and study of a new matrix functions, say, the pl(m,n)-Kummer matrix function of two complex variables. The radius of regularity, recurrence relation and several new results on this function are established when the positive integers p is greater than one. Finally, we obtain a higher order partial differential equation satisfied by the pl(m,n)-Kummer matrix function and some special properties.展开更多
文摘Based on the output-voltage error function, a novel time discrete modulation technique is proposed for matrix converters （MCs） and time-discrete difference equations of a MC circuit are derived. Switch states of MC are obtained when the output voltage error function is minimized, thus the optimum combination of switch states is derived for the closed-loop control of MC. Meanwhile, advantages of the least calculation workload, the simple process, and the convenient for implementation are brought while switch states are described as space vectors in the α-β coordination system. Simulation and experimental results demonstrate the validity of the time-discrete modulation technique and the feasibility of the control approach.
基金National Natural Science Foundation of China Under Grant No.50378063
文摘Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.
基金This study was supported by a grant from the Natural Science Foundation of Shandong Province(No.Y2002C35).
文摘Background Excessive deposition of extraceUular matrix(ECM)in the kidney is the hallmark of diabetic nephropathy.Increased matrix synthesis has been well documented but the effects of diabetes on degradative pathways,particularly in the in vivo setting.The renal protective effect of these pathways on matrix accumulation has not been fully elucidated.The present study was understaken to investigate the activity of matrix metalloproteinase-2(MMP-2),the expression of MMP-2 and tissue inhibitor of metalloproteinase-2(TIMP-2)in kidney tissues of diabetic rats,and to explore the degradative pathway of typeⅣcollagen(Ⅳ-C)and the renal protective effects of ACE inhibition-benazepril.
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
文摘In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.
基金Supported by the National Natural Science Foun-dation of China(60474022)
文摘A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put forward a method for data classification. Namely, firstly, we use discernibility matrix and discernibility function to delete superfluous attributes in formation system and get a necessary attribute set. Secondly, we delete superfluous attribute values and get decision rules. Finally, we classify data by means of decision rules. The experiments show that data classification using this method is simpler in the structure, and can improve the efficiency of classification.
文摘Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.Y4811H805C and 81101175)
文摘A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction（IR） method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo（MC） simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization（OSEM） algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast,and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.
文摘A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.
基金supported by the National Natural Science Foundation of China(No.51877013),(ZJ),(http://www.nsfc.gov.cn/)the Natural Science Foundation of Jiangsu Province(No.BK20181463),(ZJ),(http://kxjst.jiangsu.gov.cn/)sponsored by Qing Lan Project of Jiangsu Province(no specific grant number),(ZJ),(http://jyt.jiangsu.gov.cn/).
文摘Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.
文摘We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.
基金financial support of this work by Natural Science Foundation of China(22075031,51673030,51603017 and 51803011)Jilin Provincial Science&Technology Department(20220201105GX)Chang Bai Mountain Scholars Program of Jilin Province.
文摘For the reduction of bovine serum proteins from wastewater,a novel mixed matrix membrane was prepared by functionalizing the substrate material polyaryletherketone(PAEK),followed by carboxyl groups(C-SPAEKS),and then adding amino-functionalized UiO-66-NH_(2)(Am-UiO-66-NH_(2)).Aminofunctionalization of UiO-66 was accomplished by melamine,followed by an amidation reaction to immobilize Am-UiO-66-NH_(2),which was immobilized on the surface of the membrane as well as in the pore channels,which enhanced the hydrophilicity of the membrane surface while increasing the negative potential of the membrane surface.This nanoparticle-loaded ultrafiltration membrane has good permeation performance,with a pure water flux of up to 482.3 L·m^(-2)·h^(-1) for C-SPAEKS/AmUiO-66-NH_(2) and a retention rate of up to 98.7%for bovine serum albumin(BSA)-contaminated solutions.Meanwhile,after several hydrophilic modifications,the flux recovery of BSA contaminants by this series of membranes increased from 56.2%to 80.55%of pure membranes.The results of ultra-filtration flux time tests performed at room temperature showed that the series of ultrafiltration membranes remained relatively stable over a test time of 300 min.Thus,the newly developed mixed matrix membrane showed potential for high efficiency and stability in wastewater treatment containing bovine serum proteins.
文摘Matrix within cells,the cytoskeleton,and that which surrounds cells,the extracellular matrix（ECM）,are connected to one another through a number of receptors including those in primary cilia,serving as an important chemical and physical signaling system：Mechanical forces generated through the matrix play a critical role in determining the form and function of tissues（Hughes et al.,2018）.
文摘In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.
文摘In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.
基金Project supported by the National Natural Science Foundation of China(Nos.51135003 and U1234208)the Major State Basic Research Development Program of China(973 Program)(No.2014CB046303)
文摘In a structural system reliability analysis that lacks probabilistic information, calculating the numerical characteristics of the state functions, especially the first four moments of the state functions, is necessary. Based on that, the structural system reliability is analyzed with a fourth-order moment method. The reliability sensitivity is required to conduct the differential operation of the numerical characteristic functions. A reliability sensitivity analysis formula is then derived in combination with the relation of the differential operation. Based on the matrix theory and Kronecker algebra, this paper systematically derives a matrix expression of the first four moments of the state functions, and establishes the matrix relation between the first four moments of the state functions and those of the basic random variables. On this basis, a differential operation formula of the first four moments of the state functions is further derived against the first four moments of the basic random variables. The vector relation between the state functions and the multidimensional basic random variables is described by means of the matrix operation to extend the operation method. Finally, a concise and intuitive formula is obtained to explore the inherent essential relation between the numerical characteristics of the state functions and those of the basic random variables, leading to a universal equation for the two kinds of numerical characteristics.
文摘The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positive integers p and q are greater than one, an integral representation of pHq 2 is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the p and q-Horn’s matrix function.
基金supported by Portuguese funds through the CIDMA Center for Research and Development in Mathematics and Applicationsthe Portuguese Foundation for Science and Technology(FCT–Fundao para a Ciência e a Tecnologia)within project UID/MAT/04106/2013the recipient of a Postdoctoral Foundation from FCT under Grant No. SFRH/BPD/74581/2010
文摘By the characterization of the matrix Hilbert transform in the Hermitian Clifford analysis, we introduce the matrix Szeg5 projection operator for the Hardy space of Hermitean monogenic functions defined on a bounded sub-domain of even dimensional Euclidean space, establish the Kerzman-Stein formula which closely connects the matrix Szego projection operator with the Hardy projection operator onto the Hardy space, and get the matrix Szego projection operator in terms of the Hardy projection operator and its adjoint. Furthermore, we construct the explicit matrix Szego kernel function for the Hardy space on the sphere as an example, and get the solution to a boundary value problem for matrix functions.
基金supported by the National Natural Science Foundation of China (6090405161021002)
文摘The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.
文摘The main aim of this paper is to define and study of a new matrix functions, say, the pl(m,n)-Kummer matrix function of two complex variables. The radius of regularity, recurrence relation and several new results on this function are established when the positive integers p is greater than one. Finally, we obtain a higher order partial differential equation satisfied by the pl(m,n)-Kummer matrix function and some special properties.
