This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of C<sup>m</sup>） and th...This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of C<sup>m</sup>） and the generalized in A<sub>T,S</sub> For the special case when b ∈AT and dim（T）=dim（AT）, this splitting iterative methverse A<sub>T,S</sub> hod converges to A<sub>T,S</sub>b （the unique solution of the general restricted system Ax=bx ∈T）.展开更多
In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are...In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.展开更多
This paper addresses the observer design problem for a class of nonlinear descriptor systems whose nonlinear terms are slope-restricted. The full-order observer is formulated as a nonlinear descriptor system. A linear...This paper addresses the observer design problem for a class of nonlinear descriptor systems whose nonlinear terms are slope-restricted. The full-order observer is formulated as a nonlinear descriptor system. A linear matrix inequality （LMI） condition is derived to construct the full-order observer. The existence and uniqueness of the solution to the obtained observer system are guaranteed. Furthermore, under the same LMI condition and a common assumption, a reduced-order observer is designed. Finally, the design methods are reduced to a strict LMI problem and illustrated by a numerical example.展开更多
We present a quantum game with the restricted strategic space and its realization with linear optical system, which can be played by two players who are separated remotely. This game can also be realized on any other ...We present a quantum game with the restricted strategic space and its realization with linear optical system, which can be played by two players who are separated remotely. This game can also be realized on any other quantum computers. We find that the constraint brings some interesting properties that are useful for making game models.展开更多
The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the...The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.展开更多
Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triax...Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.展开更多
In this paper, we give the representation of the best linear unbiased predictor（BLUP）of the new observations under Mrf. Through the representation, we give necessary and sufficient conditions that the estimators, OL...In this paper, we give the representation of the best linear unbiased predictor（BLUP）of the new observations under Mrf. Through the representation, we give necessary and sufficient conditions that the estimators, OLSEs（ordinary least squares estimators） and BLUEs（best linear unbiased estimators）, under Mf and Mrf, and the predictor, BLUP, under Mf continue to be the BLUP under Mrf, respectively.展开更多
For the growth curve model with respect to inequality restriction： Y = XBZ ＋ε,ε（0, σ2V I）, trNB ≥0, this paper gives some necessary and sufficient conditions for the linear estimator of KBL to be admissible in...For the growth curve model with respect to inequality restriction： Y = XBZ ＋ε,ε（0, σ2V I）, trNB ≥0, this paper gives some necessary and sufficient conditions for the linear estimator of KBL to be admissible in the class of homogeneous linear estimators LH and nonhomogeneous linear estimators LI, respectively, under the quadratic loss function tr（d（Y） - KBL）＇（d（Y） - KBL）.展开更多
The existence and stability of stationary solutions of the restricted three body problem under the effect of the dissipative force, Stokes drag, are investigated. It is observed that there exist two non collinear stat...The existence and stability of stationary solutions of the restricted three body problem under the effect of the dissipative force, Stokes drag, are investigated. It is observed that there exist two non collinear stationary solutions. Further, it is also found that these stationary solutions are unstable for all values of the parameters.展开更多
In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearit...In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.展开更多
In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). T...In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>展开更多
针对雷达、微波辐射计及无线通信系统中大阵元最小冗余线性阵列(minimum redundancy linear array,MRLA)的获取难题——计算机长时间运算仅得有限解、易遗漏适配应用的最优阵列,通过分析L上元素最少的受限差基、最大连续基线长为L的MRL...针对雷达、微波辐射计及无线通信系统中大阵元最小冗余线性阵列(minimum redundancy linear array,MRLA)的获取难题——计算机长时间运算仅得有限解、易遗漏适配应用的最优阵列,通过分析L上元素最少的受限差基、最大连续基线长为L的MRLA、长度是L的完美稀疏尺的刻度值、L条边的极小优美图顶点标号各自定义的条件,经循环论证,证明四者数学等价;证明得到:线性阵列成对存在;线性阵列的冗余度≥1,阵元数超过4时冗余度>1;若MRLA最大连续基线长度为L且阵元数为n,则最大连续基线长度为L+1的MRLA阵元数不超过n+1.基于大规模MRLA数据分析,提出假设:冗余度≤1.5的线性阵列可视为MRLA.研究还发现了两类新型线性阵列解析公式,能高效筛选出无穷多的MRLA配置模式(即均为完美稀疏尺的刻度数值),并可根据实际需求灵活设定线性阵列冗余度的筛选阈值,为MRLA的应用和完美稀疏尺的设计提供了理论支撑.展开更多
In order to solve linear interaction programming, the vertex-searching method is proposed in this paper. First, the existence of equilibrium is analyzed for the model of linear interaction programming. Then the conclu...In order to solve linear interaction programming, the vertex-searching method is proposed in this paper. First, the existence of equilibrium is analyzed for the model of linear interaction programming. Then the conclusion is obtained in which the equi- librium is in the boundary of the restriction region of linear interaction programming. Also, a searching equilibrium solution is deduced from the conclusion.展开更多
Taking the nonlinear nature of runoff system into account,and combining auto-regression method and multi-regression method,a Nonlinear Mixed Regression Model (NMR) was established to analyze the impact of temperature ...Taking the nonlinear nature of runoff system into account,and combining auto-regression method and multi-regression method,a Nonlinear Mixed Regression Model (NMR) was established to analyze the impact of temperature and precipitation changes on annual river runoff process. The model was calibrated and verified by using BP neural network with observed meteorological and runoff data from Daiying Hydrological Station in the Chaohe River of Hebei Province in 1956–2000. Compared with auto-regression model,linear multi-regression model and linear mixed regression model,NMR can improve forecasting precision remarkably. Therefore,the simulation of climate change scenarios was carried out by NMR. The results show that the nonlinear mixed regression model can simulate annual river runoff well.展开更多
In this paper, we give a class of fuation and use to dicuss general admissibility according to general optimality ceriteria defined uader restricted growth curve model. General admissible characterization are obtained...In this paper, we give a class of fuation and use to dicuss general admissibility according to general optimality ceriteria defined uader restricted growth curve model. General admissible characterization are obtained. Moreover, these conditions are then utilize to characterize infulueace that restrictions involved in growth curve model have on the class of admissible linear展开更多
From the recent thirty years, scientists will never stop exploring the outer space. To assist the development of travelling into the universe, I devote myself into providing theoretical support and future indications ...From the recent thirty years, scientists will never stop exploring the outer space. To assist the development of travelling into the universe, I devote myself into providing theoretical support and future indications for designing the optimal orbit for satellite to travel in a Three-Body System. This paper offers the optimal orbit for satellite to change path in the earth-moon system. Also, it provides the path for the satellite to use the least fuel to go to the L4 and L5 Lagrange points. These inspiring results are obtained through several steps: to solve the problems caused by the non-linear character of Three-Body System, I use Koopman eigenfunction to change the system into a linear one. Data-driven method is adopted to find the most suitable Koopman eigenfunction to apply control. The traditional LQR operator for linear system is used to design the optimal orbit for the satellite.展开更多
基金This project is supported by Science and Technology Foundation of Shanghai Higher Eduction,Doctoral Program Foundation of Higher Education in China.National Nature Science Foundation of China and Youth Science Foundation of Universities in Shanghai.
文摘This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T （where, b ∈AT, and T is an arbitrary but fixed subspace of C<sup>m</sup>） and the generalized in A<sub>T,S</sub> For the special case when b ∈AT and dim（T）=dim（AT）, this splitting iterative methverse A<sub>T,S</sub> hod converges to A<sub>T,S</sub>b （the unique solution of the general restricted system Ax=bx ∈T）.
文摘In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.
基金supported by National Basic Research Program of China (973 Program) (No. 2009CB320601)National Natural Science Foundation of China (No. 60904009)Fundamental Research Funds for the Central Universities (No. 100406010, No. 090408001)
文摘This paper addresses the observer design problem for a class of nonlinear descriptor systems whose nonlinear terms are slope-restricted. The full-order observer is formulated as a nonlinear descriptor system. A linear matrix inequality （LMI） condition is derived to construct the full-order observer. The existence and uniqueness of the solution to the obtained observer system are guaranteed. Furthermore, under the same LMI condition and a common assumption, a reduced-order observer is designed. Finally, the design methods are reduced to a strict LMI problem and illustrated by a numerical example.
文摘We present a quantum game with the restricted strategic space and its realization with linear optical system, which can be played by two players who are separated remotely. This game can also be realized on any other quantum computers. We find that the constraint brings some interesting properties that are useful for making game models.
文摘The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.
文摘Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.
基金Supported by the Talent Program of Anhui Science and Technology University(Grant No.XXYJ201703)
文摘In this paper, we give the representation of the best linear unbiased predictor（BLUP）of the new observations under Mrf. Through the representation, we give necessary and sufficient conditions that the estimators, OLSEs（ordinary least squares estimators） and BLUEs（best linear unbiased estimators）, under Mf and Mrf, and the predictor, BLUP, under Mf continue to be the BLUP under Mrf, respectively.
文摘For the growth curve model with respect to inequality restriction： Y = XBZ ＋ε,ε（0, σ2V I）, trNB ≥0, this paper gives some necessary and sufficient conditions for the linear estimator of KBL to be admissible in the class of homogeneous linear estimators LH and nonhomogeneous linear estimators LI, respectively, under the quadratic loss function tr（d（Y） - KBL）＇（d（Y） - KBL）.
文摘The existence and stability of stationary solutions of the restricted three body problem under the effect of the dissipative force, Stokes drag, are investigated. It is observed that there exist two non collinear stationary solutions. Further, it is also found that these stationary solutions are unstable for all values of the parameters.
文摘In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.
文摘In this paper, we use Port-Hamiltonian framework to stabilize the Lagrange <span style="font-family:Verdana;">points in the Sun-Earth three-dimensional Circular Restricted Three-Body Problem (CRTBP). Through rewriting the CRTBP into Port-Hamiltonian framework, we are allowed to design the feedback controller through ener</span><span style="font-family:Verdana;">gy-shaping and dissipation injection. The closed-loop Hamiltonian is </span><span style="font-family:Verdana;">a candidate of the Lyapunov function to establish nonlinear stability of the designed equilibrium, which enlarges the application region of feedback controller compared with that based on linearized dynamics. Results show that th</span><span style="font-family:Verdana;">e Port-Hamiltonian</span><span style="font-family:Verdana;"> a</span><span style="font-family:Verdana;">pproach allows us to successfully stabilize the Lagrange points, where the Linear Quadratic Regulator (LQR) may fail. The feedback </span><span style="font-family:Verdana;">system based on Port-Hamiltonian approach is also robust against whit</span><span style="font-family:Verdana;">e noise in the inputs.</span>
文摘针对雷达、微波辐射计及无线通信系统中大阵元最小冗余线性阵列(minimum redundancy linear array,MRLA)的获取难题——计算机长时间运算仅得有限解、易遗漏适配应用的最优阵列,通过分析L上元素最少的受限差基、最大连续基线长为L的MRLA、长度是L的完美稀疏尺的刻度值、L条边的极小优美图顶点标号各自定义的条件,经循环论证,证明四者数学等价;证明得到:线性阵列成对存在;线性阵列的冗余度≥1,阵元数超过4时冗余度>1;若MRLA最大连续基线长度为L且阵元数为n,则最大连续基线长度为L+1的MRLA阵元数不超过n+1.基于大规模MRLA数据分析,提出假设:冗余度≤1.5的线性阵列可视为MRLA.研究还发现了两类新型线性阵列解析公式,能高效筛选出无穷多的MRLA配置模式(即均为完美稀疏尺的刻度数值),并可根据实际需求灵活设定线性阵列冗余度的筛选阈值,为MRLA的应用和完美稀疏尺的设计提供了理论支撑.
基金Supported by the National Soft Science Research Project of China (2006GXSZD085)
文摘In order to solve linear interaction programming, the vertex-searching method is proposed in this paper. First, the existence of equilibrium is analyzed for the model of linear interaction programming. Then the conclusion is obtained in which the equi- librium is in the boundary of the restriction region of linear interaction programming. Also, a searching equilibrium solution is deduced from the conclusion.
基金Under the auspices of National Natural Science Foundation of China (No. 50809004)
文摘Taking the nonlinear nature of runoff system into account,and combining auto-regression method and multi-regression method,a Nonlinear Mixed Regression Model (NMR) was established to analyze the impact of temperature and precipitation changes on annual river runoff process. The model was calibrated and verified by using BP neural network with observed meteorological and runoff data from Daiying Hydrological Station in the Chaohe River of Hebei Province in 1956–2000. Compared with auto-regression model,linear multi-regression model and linear mixed regression model,NMR can improve forecasting precision remarkably. Therefore,the simulation of climate change scenarios was carried out by NMR. The results show that the nonlinear mixed regression model can simulate annual river runoff well.
文摘In this paper, we give a class of fuation and use to dicuss general admissibility according to general optimality ceriteria defined uader restricted growth curve model. General admissible characterization are obtained. Moreover, these conditions are then utilize to characterize infulueace that restrictions involved in growth curve model have on the class of admissible linear
文摘From the recent thirty years, scientists will never stop exploring the outer space. To assist the development of travelling into the universe, I devote myself into providing theoretical support and future indications for designing the optimal orbit for satellite to travel in a Three-Body System. This paper offers the optimal orbit for satellite to change path in the earth-moon system. Also, it provides the path for the satellite to use the least fuel to go to the L4 and L5 Lagrange points. These inspiring results are obtained through several steps: to solve the problems caused by the non-linear character of Three-Body System, I use Koopman eigenfunction to change the system into a linear one. Data-driven method is adopted to find the most suitable Koopman eigenfunction to apply control. The traditional LQR operator for linear system is used to design the optimal orbit for the satellite.
