Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum represent...Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.展开更多
This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a rep...This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. The stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched systems can be constructed a stable tensor-product representation of finite dimension. It is shown that the tensor-product representation provides a high level framework for describing the dynamic behavior. The interpretation of expressions within the tensor-product representation framework leads to enhanced conceptual and physical understanding of switched linear systems dynamic behavior.展开更多
An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditio...An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.展开更多
Horizon control,maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient,is a key technique in longwall mining automation.To identify the coal seam gradient,a geological model o...Horizon control,maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient,is a key technique in longwall mining automation.To identify the coal seam gradient,a geological model of the coal seam was constructed using in-seam seismic surveying technology.By synthesizing the control resolution of the range arm and the geometric characteristics of the coal seam,a gradient identification method based on piecewise linear representation(PLR)is proposed.To achieve the maximum exploitation rate within the shearer's capacity,the control resolution of the range arm is selected as the threshold parameter of PLR.The control resolution significantly influenced the number of line segments and the fitting error.With the decrease of the control resolution from 0.01 to 0.02 m,the number of line segments decreased from 65 to 15,which was beneficial to horizon control.However,the average fitting error increased from 0.055 to 0.14 m,which would induce a decrease in the exploitation rate.To avoid significant deviation between the cutting range and the coal seam,the control resolution of the range arm must be lower than 0.02 m.In a field test,the automated horizon control of the longwall face was realized by coal seam gradient identification.展开更多
The performances of repaired image depend on the local information in the repaired area and the consistency between the repair directions with structural content.Image repair algorithm with texture information perform...The performances of repaired image depend on the local information in the repaired area and the consistency between the repair directions with structural content.Image repair algorithm with texture information performs well in repairing seriously damaged images,but it has bad performances when the images have the abundant structure information.The dual optimization image repair algorithm based on the linear structure and the optimal texture is proposed.The algorithm uses the double-constraint sparse model to reconstruct the missed information in large area in order to improve the clarity of repaired images.After adopting the preference of Criminisi priority,the image repair algorithm of self-similarity characteristics is proposed to improve the fault and fuzzy distortion phenomena in the repaired image.The results show that the proposed algorithm has more clarity in the image texture and structure and better effectiveness,and the peak signal-to-noise ratio of the repaired images by proposed algorithm is superior to that by other algorithms.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
This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, s...This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.展开更多
An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at...An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.展开更多
In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satis...In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility,and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal;they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.展开更多
The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of se...The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of sequence families, it is shown that the terms of a linear recurring sequence over Z/(pe) may be represented by the roots of its characteristic polynomial and the representation is uniquely determined by the sequence.展开更多
为解决因排查效率低、数据更新不及时等因素导致低压配电网户变关系连接形式与实际不符的问题,提出一种基于角度分段线性近似(anglepiecewiselinearrepresentation,APLR)和改进密度峰值聚类(improved clustering by fast search find of...为解决因排查效率低、数据更新不及时等因素导致低压配电网户变关系连接形式与实际不符的问题,提出一种基于角度分段线性近似(anglepiecewiselinearrepresentation,APLR)和改进密度峰值聚类(improved clustering by fast search find of density peaks,ICFSFDP)相结合的户变关系识别方法。首先,根据电压曲线中相邻线段的角度变化量提取曲线的转折点,利用APLR对曲线进行自适应降维重构;随后,使用ICFSFDP算法对降维数据组展开聚类分析,在决策图中由拟合函数与坐标轴围成面积的最小值得到最优类簇数目,进而得到聚类和非聚类中心用户;最后,使用动态时间弯曲(dynamic time warping,DTW)距离计算聚类和非聚类中心用户之间的距离相似度,进而得到户变关系。将所提方法应用于模拟和真实数据中,均可证实所提方法的有效性。算例分析结果表明:该方法能够对时间间隔不同、不等维的序列进行分析,且不需要人为设定聚类算法的参数,户变关系识别准确率高。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11347026,11147009,and 11244005)the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2013AM012 and ZR2012AM004)the Scientific Research Project of Liaocheng,China
文摘Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.
文摘This paper presents the method for the construction of tensor-product representation for multivariate switched linear systems, based on a suitable tensor-product representation of vectors and matrices. We obtain a representation theorem for multivariate switched linear systems. The stability properties of the tensor-product representation are investigated in depth, achieving the important result that any stable switched systems can be constructed a stable tensor-product representation of finite dimension. It is shown that the tensor-product representation provides a high level framework for describing the dynamic behavior. The interpretation of expressions within the tensor-product representation framework leads to enhanced conceptual and physical understanding of switched linear systems dynamic behavior.
基金Supported by the Excellent Young Teachers Program of the Ministry of Education, P. R. China (No. 2001-1739 and No. 2003-145)
文摘An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.
基金supported in part by the Funds of the National Natural Science Foundation of China(Nos.51874279 and U1610251)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘Horizon control,maintaining the alignment of the shearer's exploitation gradient with the coal seam gradient,is a key technique in longwall mining automation.To identify the coal seam gradient,a geological model of the coal seam was constructed using in-seam seismic surveying technology.By synthesizing the control resolution of the range arm and the geometric characteristics of the coal seam,a gradient identification method based on piecewise linear representation(PLR)is proposed.To achieve the maximum exploitation rate within the shearer's capacity,the control resolution of the range arm is selected as the threshold parameter of PLR.The control resolution significantly influenced the number of line segments and the fitting error.With the decrease of the control resolution from 0.01 to 0.02 m,the number of line segments decreased from 65 to 15,which was beneficial to horizon control.However,the average fitting error increased from 0.055 to 0.14 m,which would induce a decrease in the exploitation rate.To avoid significant deviation between the cutting range and the coal seam,the control resolution of the range arm must be lower than 0.02 m.In a field test,the automated horizon control of the longwall face was realized by coal seam gradient identification.
基金Project(12GJ6055)supported by the Natural Science Foundation of Hunan Province,ChinaProject(2010FJ4107)supported by Hunan Provincial Science and Technology Department,China
文摘The performances of repaired image depend on the local information in the repaired area and the consistency between the repair directions with structural content.Image repair algorithm with texture information performs well in repairing seriously damaged images,but it has bad performances when the images have the abundant structure information.The dual optimization image repair algorithm based on the linear structure and the optimal texture is proposed.The algorithm uses the double-constraint sparse model to reconstruct the missed information in large area in order to improve the clarity of repaired images.After adopting the preference of Criminisi priority,the image repair algorithm of self-similarity characteristics is proposed to improve the fault and fuzzy distortion phenomena in the repaired image.The results show that the proposed algorithm has more clarity in the image texture and structure and better effectiveness,and the peak signal-to-noise ratio of the repaired images by proposed algorithm is superior to that by other algorithms.
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.
文摘This paper aims to present, in a unified manner, algebraic techniques for linear equations which are valid on both the algebras of quaternions and split quaternions. This paper, introduces a concept of v-quaternion, studies the problem of v-quaternionic linear equations by means of a complex representation and a real representation of v-quaternion matrices, and gives two algebraic methods for solving v-quaternionic linear equations. This paper also gives a unification of algebraic techniques for quaternionic and split quaternionic linear equations in quaternionic and split quaternionic mechanics.
基金Sponsored by 863 Project (Grant No.2002AA517020) Developing Fund of Shanghai Science Committee (Grant No.011607033).
文摘An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.
基金Supported by the Natural Science Foundation of China(11171221)
文摘In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility,and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal;they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.
基金Project supported by the State Key Laboratory of Information Security,Graduate School of Academia Sinica.
文摘The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of sequence families, it is shown that the terms of a linear recurring sequence over Z/(pe) may be represented by the roots of its characteristic polynomial and the representation is uniquely determined by the sequence.
文摘为解决因排查效率低、数据更新不及时等因素导致低压配电网户变关系连接形式与实际不符的问题,提出一种基于角度分段线性近似(anglepiecewiselinearrepresentation,APLR)和改进密度峰值聚类(improved clustering by fast search find of density peaks,ICFSFDP)相结合的户变关系识别方法。首先,根据电压曲线中相邻线段的角度变化量提取曲线的转折点,利用APLR对曲线进行自适应降维重构;随后,使用ICFSFDP算法对降维数据组展开聚类分析,在决策图中由拟合函数与坐标轴围成面积的最小值得到最优类簇数目,进而得到聚类和非聚类中心用户;最后,使用动态时间弯曲(dynamic time warping,DTW)距离计算聚类和非聚类中心用户之间的距离相似度,进而得到户变关系。将所提方法应用于模拟和真实数据中,均可证实所提方法的有效性。算例分析结果表明:该方法能够对时间间隔不同、不等维的序列进行分析,且不需要人为设定聚类算法的参数,户变关系识别准确率高。
