A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
与均匀阵列相比,稀疏阵列可以使天线阵列成本降低,减少数据处理,同时带来更大的阵列孔径提高信号解析能力,在信号处理中有着广泛的应用。但是由于其排布的不规则性,计算量较大,二维面阵合成协方差矩阵存在空洞,对角度估计的准确性造成...与均匀阵列相比,稀疏阵列可以使天线阵列成本降低,减少数据处理,同时带来更大的阵列孔径提高信号解析能力,在信号处理中有着广泛的应用。但是由于其排布的不规则性,计算量较大,二维面阵合成协方差矩阵存在空洞,对角度估计的准确性造成负面影响,增强了系统对噪声的敏感度。为了克服这些问题,本文提出了一种新的角度估计方法,采用截断核范数以降低噪声的影响,并通过ℓ_(p)范数优化提升信号的稀疏表示,利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)算法构造子问题恢复出完整的阵列信号。随后采用子阵划分技术和基于最小二乘的传播算子模型(Propagator Method,PM)对恢复的信号处理,精确估计信号源的方位和俯仰角。仿真结果表明,所提出的角度估计算法在角度精度和时间复杂度方面具有优越性。展开更多
Non-interlayer liquid phase diffusion welding (China Patent) and laser welding methods for aluminum matrix composite are mainly described in this paper. In the non-interlayer liquid phase diffusion welding, the key pr...Non-interlayer liquid phase diffusion welding (China Patent) and laser welding methods for aluminum matrix composite are mainly described in this paper. In the non-interlayer liquid phase diffusion welding, the key processing parameters affecting the strength of joint is welding temperature. When temperature rises beyond solidus temperature, the bonded line vanishes. The strength of joint reaches the maximum and becomes constant when welding temperature is close to liquid phase temperature. Oxide film in the interface is no longer detected by SEM in the welded joint. With this kind of technique, particle reinforced aluminum matrix composite Al2 O3p/6061Al is welded successfully, and the joint strength is about 80% of the strength of composite (as-casted). In the laser welding, results indicate that because of the huge specific surface area of the reinforcement, the interfacial reaction between the matrix and the reinforcement is restrained intensively at certain laser power and pulsed laser beam. The laser pulse frequency directly affects the reinforcement segregation and the reinforcement distribution in the weld, so that the weldability of the composite could be improved by increasing the laser pulse frequency. The maximum strength of the weld can reach 70% of the strength of the parent.展开更多
Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M m...Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.展开更多
Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive...Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.展开更多
A new type of iron-based matrix formula as a potential substitute for traditional WC-based matrix formula for hot pressed diamond bit was investigated.Iron,phosphor-iron,663-Cu,nickel,cobalt and certain additives were...A new type of iron-based matrix formula as a potential substitute for traditional WC-based matrix formula for hot pressed diamond bit was investigated.Iron,phosphor-iron,663-Cu,nickel,cobalt and certain additives were selected as the studied formula constituents.Among matrix performances,the hardness and wear resistance were chosen as experimental indexes in this paper.Constrained uniform design method was used for the formula design of iron-based matrix.Two forms of regression models of matrix hardness and wear resistance were obtained by regression analysis using MATLAB.Moreover,the optimization of matrix formulae and matrix performances were also achieved through constrained nonlinear programming.It was found that matrix hardness,significantly affected by the factor of Ni-Co-additives and Fe,increased with the increment of Ni-Co-additives,Fe and P-Fe,but reduced with the increase of 663-Cu.On the other hand,matrix wear resistance is mainly affected by Fe;the effect of the interaction between Fe and P-Fe is also relatively obvious. The increment of 663-Cu powder may result in a slight improvement in matrix wear resistance.In addition,the results of nonlinear programming revealed that the predictive optimum value of hardness was 139.5 HRB and the optimum wear resistance was 0.056 g,whereas they could not reach the optimum value at the same time.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
Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review...Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review, modify and combine various techniques of numerical linear algebra and rational algebraic computations (with no error) to achieve our main goal of decreasing the bit-precision for computing detA or its sign and enable us to obtain the solution with few arithmetic operations. In particular, we improved the precision bits of the p-adic lifting algorithm (H = 2h for a natural number h), which may exceed the computer precision β (see Section 5.2), to at most bits (see Section 6). The computational cost of the p-adic lifting can be performed in O(hn4). We reduced this cost to O(n3) by employing the faster p-adic lifting technique (see Section 5.3).展开更多
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
文摘与均匀阵列相比,稀疏阵列可以使天线阵列成本降低,减少数据处理,同时带来更大的阵列孔径提高信号解析能力,在信号处理中有着广泛的应用。但是由于其排布的不规则性,计算量较大,二维面阵合成协方差矩阵存在空洞,对角度估计的准确性造成负面影响,增强了系统对噪声的敏感度。为了克服这些问题,本文提出了一种新的角度估计方法,采用截断核范数以降低噪声的影响,并通过ℓ_(p)范数优化提升信号的稀疏表示,利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)算法构造子问题恢复出完整的阵列信号。随后采用子阵划分技术和基于最小二乘的传播算子模型(Propagator Method,PM)对恢复的信号处理,精确估计信号源的方位和俯仰角。仿真结果表明,所提出的角度估计算法在角度精度和时间复杂度方面具有优越性。
基金supported by the National Natural Science Foundation of China(No.50171025)open project of foundation of National Key Laboratory of Metal Matrix Composite,Shanghai Jiaotong University
文摘Non-interlayer liquid phase diffusion welding (China Patent) and laser welding methods for aluminum matrix composite are mainly described in this paper. In the non-interlayer liquid phase diffusion welding, the key processing parameters affecting the strength of joint is welding temperature. When temperature rises beyond solidus temperature, the bonded line vanishes. The strength of joint reaches the maximum and becomes constant when welding temperature is close to liquid phase temperature. Oxide film in the interface is no longer detected by SEM in the welded joint. With this kind of technique, particle reinforced aluminum matrix composite Al2 O3p/6061Al is welded successfully, and the joint strength is about 80% of the strength of composite (as-casted). In the laser welding, results indicate that because of the huge specific surface area of the reinforcement, the interfacial reaction between the matrix and the reinforcement is restrained intensively at certain laser power and pulsed laser beam. The laser pulse frequency directly affects the reinforcement segregation and the reinforcement distribution in the weld, so that the weldability of the composite could be improved by increasing the laser pulse frequency. The maximum strength of the weld can reach 70% of the strength of the parent.
文摘Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.
基金Supported by the Education Department Foundation of Hebei Province（QN2015218） Supported by the Natural Science Foundation of Hebei Province（A2015403050）
文摘Let P ∈ C^(n×n) be a Hermitian and {k + 1}-potent matrix, i.e., P^(k+1)= P = P~*,where(·)*~stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive(anti-reflexive) if PXP = X(P XP =-X). The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.
文摘A new type of iron-based matrix formula as a potential substitute for traditional WC-based matrix formula for hot pressed diamond bit was investigated.Iron,phosphor-iron,663-Cu,nickel,cobalt and certain additives were selected as the studied formula constituents.Among matrix performances,the hardness and wear resistance were chosen as experimental indexes in this paper.Constrained uniform design method was used for the formula design of iron-based matrix.Two forms of regression models of matrix hardness and wear resistance were obtained by regression analysis using MATLAB.Moreover,the optimization of matrix formulae and matrix performances were also achieved through constrained nonlinear programming.It was found that matrix hardness,significantly affected by the factor of Ni-Co-additives and Fe,increased with the increment of Ni-Co-additives,Fe and P-Fe,but reduced with the increase of 663-Cu.On the other hand,matrix wear resistance is mainly affected by Fe;the effect of the interaction between Fe and P-Fe is also relatively obvious. The increment of 663-Cu powder may result in a slight improvement in matrix wear resistance.In addition,the results of nonlinear programming revealed that the predictive optimum value of hardness was 139.5 HRB and the optimum wear resistance was 0.056 g,whereas they could not reach the optimum value at the same time.
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.
文摘Computing the sign of the determinant or the value of the determinant of an n × n matrix A is a classical well-know problem and it is a challenge for both numerical and algebraic methods. In this paper, we review, modify and combine various techniques of numerical linear algebra and rational algebraic computations (with no error) to achieve our main goal of decreasing the bit-precision for computing detA or its sign and enable us to obtain the solution with few arithmetic operations. In particular, we improved the precision bits of the p-adic lifting algorithm (H = 2h for a natural number h), which may exceed the computer precision β (see Section 5.2), to at most bits (see Section 6). The computational cost of the p-adic lifting can be performed in O(hn4). We reduced this cost to O(n3) by employing the faster p-adic lifting technique (see Section 5.3).
