For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimat...For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala （1981） are strengthened and consequences in Puntanen and Nurhonen （1992）, and Puntanen （1996） are extended.展开更多
In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of ...In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of the result in [3].展开更多
In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-...In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.展开更多
New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a...New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.展开更多
We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as ...We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.展开更多
The paper discusses the regression analysis of current status data,which is common in various fields such as tumorigenic research and demographic studies.Analyzing this type of data poses a significant challenge and h...The paper discusses the regression analysis of current status data,which is common in various fields such as tumorigenic research and demographic studies.Analyzing this type of data poses a significant challenge and has recently gained considerable interest.Furthermore,the authors consider an even more difficult scenario where,apart from censoring,one also faces left-truncation and informative censoring,meaning that there is a potential correlation between the examination time and the failure time of interest.The authors propose a sieve maximum likelihood estimation(MLE)method and in the proposed method for inference,a copula-based procedure is applied to depict the informative censoring.Additionally,the authors utilise the splines to estimate the unknown nonparametric functions in the model,and the asymptotic properties of the proposed estimator are established.The simulation results indicate that the developed approach is effective in practice,and it has been successfully applied to a set of real data.展开更多
In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optim...In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.展开更多
The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a lin...The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.展开更多
In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws...In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.展开更多
In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called du...In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called dual couple in this work, is valuable for any other dual couple, so that from the known translation operator exp(a∂<sub>x</sub>) one may obtain the explicit form and properties of a category of linear and linear canonical transformations in 2N-phase spaces. Moreover, other forms of LCTs are also obtained in this work as so as the transforms by them of functions by integrations as so as by derivations. In this way, different kinds of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are found again.展开更多
In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous aut...In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function,and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas.Currently,the BDF is only defined for continuous signals.However,for both simulation and experimental purposes,the signals must be discrete.This necessitates the development of a BDF analysis workflow for discrete signals.In this work,we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts.Our results permit more accurate simulations using BDFs,which will be useful in applying them to problems such as partial coherence.展开更多
A novel robust diagnostic system based on a linear fractional transform(LFT)representation combined with a static redundancy approach is proposed to design a residual generator for fault detection and localization in ...A novel robust diagnostic system based on a linear fractional transform(LFT)representation combined with a static redundancy approach is proposed to design a residual generator for fault detection and localization in a wind system using the doubly fed induction generator(DFIG).As a result,faults in DFIG-based grid-connected wind systems can be grouped into three classes of faults,namely,model uncertainty-related faults(FLMU),set point disturbance-related faults(FLDS)and parameter uncertainty-related faults(FLPU).Based on the parity-space residual generations,an artificial neural network(ANN)structure has been combined with the classification to enable the assessment of hidden,indistinguishable or small amplitude faults.The training validation with two data sizes of 1278*4 and 1278*1 respectively at the inputs and outputs of the proposed ANN,presents better performance for a mean squared error value(MSE=3.0532e 9),and a good correlation between outputs and targets for a regression value(R=1).It emerges that the proposed robust and complete diagnostic system for the optimal and sustainable integration of wind turbines into the grid,offers very great advan-tages,particularly with regard to the precise and rapid detection of faults,and the assessment of hidden faults and/or ambiguous fault states in the wind system based on DFIG.In addition,the proposed approach allows the use of a reduced number of data,sensors and actuators required.Consequently,the system maintenance difficulties,complexity and cost of the diagnostic system are reduced.展开更多
With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear tra...With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.展开更多
Any linear transform matrix can be used to easily calculate a consistent form, and a plurality of conversion can be easily connected together by matrix multiplication. When performing file transfers, you can encrypt f...Any linear transform matrix can be used to easily calculate a consistent form, and a plurality of conversion can be easily connected together by matrix multiplication. When performing file transfers, you can encrypt files matrix transformation. Article presents a matrix-based electronic document encryption and decryption algorithm, which relies on a special class of matrices combinatorial problems, the method to improve the security of electronic document system is feasible and effective, and finally give the source code and programming software.展开更多
A multi-gap and multi-channel gas switch with convexo-convex discal planet electrodes was designed and investigated. Eight gaps are formed in series by a trigger electrode, six intermediate electrodes and two high vol...A multi-gap and multi-channel gas switch with convexo-convex discal planet electrodes was designed and investigated. Eight gaps are formed in series by a trigger electrode, six intermediate electrodes and two high voltage electrodes with a uniform gap length of 5 ram. The self breakdown and triggered breakdown performance of the switch are reported. Both the delay time and jitter decrease with the increase in the trigger voltage, switching coefficient and the decrease in the trigger isolating resistor. The delay time of the switch is about 40 ns, and the jitter is less than 2 ns when charged with 4-85 kV and triggered by a voltage pule of -75 kV. The inductance of the switch is about 30 nH.展开更多
Output-pulse shaping capability of a linear transformer driver （LTD） module under different conditions is studied, by conducting the whole circuit model simulation by using the PSPICE code. Results indicate that a h...Output-pulse shaping capability of a linear transformer driver （LTD） module under different conditions is studied, by conducting the whole circuit model simulation by using the PSPICE code. Results indicate that a higher impedance profile of the internal transmission line would lead to a wider adjustment range for the output current rise time and a narrower adjustment range for the current peak. The number of cavities in series has a positive effect on the output- pulse shaping capability of LTD. Such an improvement in the output-pulse shaping capability can primarily be ascribed to the increment in the axial electric length of LTD. For a triggering time interval longer than the time taken by a pulse to propagate through the length of one cavity, the output parameters of LTD could be improved significantly. The present insulating capability of gas switches and other elements in the LTD cavities may only tolerate a slightly longer deviation in the triggering time interval. It is feasible for the LTD module to reduce the output current rise time, though it is not useful to improve the peak power effectively.展开更多
A whole circuit model of a linear transformer drivers （LTD） module composed of 60 cavities in series was developed in the software PSPICE to study the influence of switching jitter on the operational performances of...A whole circuit model of a linear transformer drivers （LTD） module composed of 60 cavities in series was developed in the software PSPICE to study the influence of switching jitter on the operational performances of LTDs. In the model, each brick in each cavity is capable of operating with jitter in its switch. Additionally, the manner of triggering cables entering into cavities was considered. The performances of the LTD module operating with three typical cavity-triggering sequences were simulated and the simulation results indicate that switching jitter affects slightly the peak and starting time of the output current pulse. However, the enhancement in switching jitter would significantly lengthen the rise time of the output current pulse. Without considering other factors, a jitter lower than 10 ns may be necessary for the switches in the LTD module to provide output current parameters with an acceptable deviation.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
基金The project was supported by the Mathematical Tian Yuan Youth Foundation of China (10226024)Postdoctoral Science Foundation of Chinathe Science Foundation for Yong Teachers of Northeast Normal University.
文摘For a singular linear model A = （y, Xβ, σ2 V） and its transformed model MF = （Fy, FXβ, σ 2FVF＇）, where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala （1981） are strengthened and consequences in Puntanen and Nurhonen （1992）, and Puntanen （1996） are extended.
基金Supported by the NSF of Educational Department of Henan Province(200510482001)
文摘In this paper, we introduce a practical method for obtaining the structure of thegroup of units for the ring of linear transformations of a vector space over an arbitrary field,and we give a further generalization of the result in [3].
文摘In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.
文摘New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.
文摘We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.
基金supported by the National Natural Science Foundation of China under Grant Nos.12171328,12001093,12231011,and 12071176the National Key Research and Development Program of China under Grant No.2020YFA0714102Beijing Natural Science Foundation under Grant No.Z210003。
文摘The paper discusses the regression analysis of current status data,which is common in various fields such as tumorigenic research and demographic studies.Analyzing this type of data poses a significant challenge and has recently gained considerable interest.Furthermore,the authors consider an even more difficult scenario where,apart from censoring,one also faces left-truncation and informative censoring,meaning that there is a potential correlation between the examination time and the failure time of interest.The authors propose a sieve maximum likelihood estimation(MLE)method and in the proposed method for inference,a copula-based procedure is applied to depict the informative censoring.Additionally,the authors utilise the splines to estimate the unknown nonparametric functions in the model,and the asymptotic properties of the proposed estimator are established.The simulation results indicate that the developed approach is effective in practice,and it has been successfully applied to a set of real data.
基金the National Natural Science Foundation of China(No.11471062).
文摘In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.
文摘The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.
基金supported by National Natural Science Foundation of China (No. 60934007, No. 61074060)China Postdoctoral Science Foundation (No. 20090460627)+1 种基金Shanghai Postdoctoral Scientific Program (No. 10R21414600)China Postdoctoral Science Foundation Special Support (No. 201003272)
文摘In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control （MPC） approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.
文摘In order to obtain with simplicity the known and new properties of linear canonical transformations (LCTs), we show that any relation between a couple of operators (A,B) having commutator identical to unity, called dual couple in this work, is valuable for any other dual couple, so that from the known translation operator exp(a∂<sub>x</sub>) one may obtain the explicit form and properties of a category of linear and linear canonical transformations in 2N-phase spaces. Moreover, other forms of LCTs are also obtained in this work as so as the transforms by them of functions by integrations as so as by derivations. In this way, different kinds of LCTs such as Fast Fourier, Fourier, Laplace, Xin Ma and Rhodes, Baker-Campbell-Haussdorf, Bargman transforms are found again.
基金supported by National Natural Science Foundation of China(61374065,61374002,61503225,61573215)the Research Fund for the Taishan Scholar Project of Shandong Province of Chinathe Natural Science Foundation of Shandong Province(ZR2015FQ003)
基金the support of the University College Dublin through a John Sheridan Scholarship.Min Wan thanks 4TU.RECENTRE program(Award No.OA102070)the National Growth Fund programme PhotonDelta in The Netherlands.
文摘In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function,and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas.Currently,the BDF is only defined for continuous signals.However,for both simulation and experimental purposes,the signals must be discrete.This necessitates the development of a BDF analysis workflow for discrete signals.In this work,we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts.Our results permit more accurate simulations using BDFs,which will be useful in applying them to problems such as partial coherence.
文摘A novel robust diagnostic system based on a linear fractional transform(LFT)representation combined with a static redundancy approach is proposed to design a residual generator for fault detection and localization in a wind system using the doubly fed induction generator(DFIG).As a result,faults in DFIG-based grid-connected wind systems can be grouped into three classes of faults,namely,model uncertainty-related faults(FLMU),set point disturbance-related faults(FLDS)and parameter uncertainty-related faults(FLPU).Based on the parity-space residual generations,an artificial neural network(ANN)structure has been combined with the classification to enable the assessment of hidden,indistinguishable or small amplitude faults.The training validation with two data sizes of 1278*4 and 1278*1 respectively at the inputs and outputs of the proposed ANN,presents better performance for a mean squared error value(MSE=3.0532e 9),and a good correlation between outputs and targets for a regression value(R=1).It emerges that the proposed robust and complete diagnostic system for the optimal and sustainable integration of wind turbines into the grid,offers very great advan-tages,particularly with regard to the precise and rapid detection of faults,and the assessment of hidden faults and/or ambiguous fault states in the wind system based on DFIG.In addition,the proposed approach allows the use of a reduced number of data,sensors and actuators required.Consequently,the system maintenance difficulties,complexity and cost of the diagnostic system are reduced.
文摘With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.
文摘Any linear transform matrix can be used to easily calculate a consistent form, and a plurality of conversion can be easily connected together by matrix multiplication. When performing file transfers, you can encrypt files matrix transformation. Article presents a matrix-based electronic document encryption and decryption algorithm, which relies on a special class of matrices combinatorial problems, the method to improve the security of electronic document system is feasible and effective, and finally give the source code and programming software.
基金supported by National Natural Science Foundation of China(Nos.50477019,50637010)the State Key Laboratory of Electrical Insulation and Power Equipment of China(EIPE.09207)
文摘A multi-gap and multi-channel gas switch with convexo-convex discal planet electrodes was designed and investigated. Eight gaps are formed in series by a trigger electrode, six intermediate electrodes and two high voltage electrodes with a uniform gap length of 5 ram. The self breakdown and triggered breakdown performance of the switch are reported. Both the delay time and jitter decrease with the increase in the trigger voltage, switching coefficient and the decrease in the trigger isolating resistor. The delay time of the switch is about 40 ns, and the jitter is less than 2 ns when charged with 4-85 kV and triggered by a voltage pule of -75 kV. The inductance of the switch is about 30 nH.
基金supported by National Natural Science Foundation of China (Nos. 50637010, 51077111)the State Key Laboratory of Electrical Insulation and Power Equipment of Xi'an Jiaotong University of China (EIPE 09207)
文摘Output-pulse shaping capability of a linear transformer driver （LTD） module under different conditions is studied, by conducting the whole circuit model simulation by using the PSPICE code. Results indicate that a higher impedance profile of the internal transmission line would lead to a wider adjustment range for the output current rise time and a narrower adjustment range for the current peak. The number of cavities in series has a positive effect on the output- pulse shaping capability of LTD. Such an improvement in the output-pulse shaping capability can primarily be ascribed to the increment in the axial electric length of LTD. For a triggering time interval longer than the time taken by a pulse to propagate through the length of one cavity, the output parameters of LTD could be improved significantly. The present insulating capability of gas switches and other elements in the LTD cavities may only tolerate a slightly longer deviation in the triggering time interval. It is feasible for the LTD module to reduce the output current rise time, though it is not useful to improve the peak power effectively.
基金supported partly by National Natural Science Foundation of China(Nos.50637010,51077111)partly by the State Key Laboratory of Electrical Insulation and Power Equipment of Xi'an Jiaotong University of China(EIPE09207)
文摘A whole circuit model of a linear transformer drivers （LTD） module composed of 60 cavities in series was developed in the software PSPICE to study the influence of switching jitter on the operational performances of LTDs. In the model, each brick in each cavity is capable of operating with jitter in its switch. Additionally, the manner of triggering cables entering into cavities was considered. The performances of the LTD module operating with three typical cavity-triggering sequences were simulated and the simulation results indicate that switching jitter affects slightly the peak and starting time of the output current pulse. However, the enhancement in switching jitter would significantly lengthen the rise time of the output current pulse. Without considering other factors, a jitter lower than 10 ns may be necessary for the switches in the LTD module to provide output current parameters with an acceptable deviation.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
