We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The co...We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.展开更多
The numerical investigation on extrudate swell through capillary die forviscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted byemploying the finite element method with the calcu...The numerical investigation on extrudate swell through capillary die forviscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted byemploying the finite element method with the calculation of viscoelastic extra stress in theconventional finite element. The method of avoiding singularity was also adopted by integrating thestrain history of the Gauss points for each element near the wall and the free surface. Theconvergence solutions at high Weissenberg number can be obtained by using the appropriate methods toreduce errors and improve the speed of convergence of the calculation, which include adding arelaxation factor of velocity in iteration process, or enlarging the reference viscosity, orreducing the elapsed time. The highest Weissenberg number obtained here is up to 3. 8, while thesolution at the Weissenberg number of 3. 75 was given in the previous work with similar extrudateswell ratio and the exit pressure drop by using differential Maxwell model with Elastic-ViscousStress Split (EVSS) combined with Streamline Upwind Petrov-Galerkin (SUPG) scheme. The calculationsindicated that the method of dealing with integral consti- tutive equation introduced in this paperis suitable in simulating viscoelastic flow characterized by integral constitutive equation at highe-lastic level.展开更多
The high-purity distillation column system is strongly nonlinear and coupled,which makes it difficult to control.Active disturbance rejection control(ADRC)has been widely used in distillation systems,but it has limita...The high-purity distillation column system is strongly nonlinear and coupled,which makes it difficult to control.Active disturbance rejection control(ADRC)has been widely used in distillation systems,but it has limitations in controlling distillation systems with large time delays since ADRC employs ESO and feedback control law to estimate the total disturbance of the system without considering the large time delays.This paper designs a proportion integral-type active disturbance rejection generalized predictive control(PI-ADRGPC)algorithm to control the distillation column system with large time delay.It replaces the PD controller in ADRC with a proportion integral-type generalized predictive control(PI-GPC),thereby improving the performance of control systems with large time delays.Since the proposed controller has many parameters and is difficult to tune,this paper proposes to use the grey wolf optimization(GWO)to tune these parameters,whose structure can also be used by other intelligent optimization algorithms.The performance of GWO tuned PI-ADRGPC is compared with the control performance of GWO tuned ADRC method,multi-verse optimizer(MVO)tuned PI-ADRGPC and MVO tuned ADRC.The simulation results show that the proposed strategy can track reference well and has a good disturbance rejection performance.展开更多
We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result...We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.展开更多
A family of integral-type goodness-of-fit tests is investigated. This family includes some existing tests, such as the Cramer-von Mises test and Anderson-Darling test, etc. The asymptotic distributions of the tests in...A family of integral-type goodness-of-fit tests is investigated. This family includes some existing tests, such as the Cramer-von Mises test and Anderson-Darling test, etc. The asymptotic distributions of the tests in the family under the null and local alternative hypotheses are established. The almost sure convergence under a fixed underlying distribution is obtained. Furthermore, simulations are conducted to compare the powers of the tests in the family. Simulation results show that for different alternatives, the more powerful tests are different, and the parameter ）, has great influence on the tests in small sample cases.展开更多
We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes.Meanwhile,main results are applied to more general integral-type downward functio...We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes.Meanwhile,main results are applied to more general integral-type downward functionals.展开更多
This paper investigates the coordinated attitude control problem for flexible spacecraft formation with the consideration of actuator configuration misalignment.First,an integral-type sliding mode adaptive control law...This paper investigates the coordinated attitude control problem for flexible spacecraft formation with the consideration of actuator configuration misalignment.First,an integral-type sliding mode adaptive control law is designed to compensate the effects of flexible mode,environmental disturbance and actuator installation deviation.The basic idea of the Integral-type Sliding Mode Control(ISMC)is to design a proper sliding manifold so that the sliding mode starts from the initial time instant,and thus the robustness of the system can be guaranteed from the beginning of the process and the reaching phase is eliminated.Then,considering the nominal system of spacecraft formation based on directed topology,an attitude cooperative control strategy is developed for the nominal system with or without communication delay.The proposed control law can guarantee that for each spacecraft in the spacecraft formation,the desired attitude objective can be achieved and the attitude synchronization can be maintained with other spacecraft in the formation.Finally,simulation results are given to show the effectiveness of the proposed control algorithm.展开更多
In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in Lp（1≤ p 〈＋∞）has been obtained.
基金Acknowledgements The authors would like to thank Professor Yong-Hua Mao for useful discussion. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11571372, 11501576, 11771452） and the Excellent Young Scientific Research Fund of Hunan Provincial Education Department （Grant No. 15B252）.
文摘We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.
文摘The numerical investigation on extrudate swell through capillary die forviscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted byemploying the finite element method with the calculation of viscoelastic extra stress in theconventional finite element. The method of avoiding singularity was also adopted by integrating thestrain history of the Gauss points for each element near the wall and the free surface. Theconvergence solutions at high Weissenberg number can be obtained by using the appropriate methods toreduce errors and improve the speed of convergence of the calculation, which include adding arelaxation factor of velocity in iteration process, or enlarging the reference viscosity, orreducing the elapsed time. The highest Weissenberg number obtained here is up to 3. 8, while thesolution at the Weissenberg number of 3. 75 was given in the previous work with similar extrudateswell ratio and the exit pressure drop by using differential Maxwell model with Elastic-ViscousStress Split (EVSS) combined with Streamline Upwind Petrov-Galerkin (SUPG) scheme. The calculationsindicated that the method of dealing with integral consti- tutive equation introduced in this paperis suitable in simulating viscoelastic flow characterized by integral constitutive equation at highe-lastic level.
基金funded by the National Natural Science Foundation of China(61973175,62073177 and 61973172)South African National Research Foundation(132797)+2 种基金South African National Research Foundation Incentive(114911)Eskom Tertiary Education Support Programme Grant of South AfricaTianjin Research Innovation Project for Postgraduate Students(2021YJSB018,2020YJSB003)。
文摘The high-purity distillation column system is strongly nonlinear and coupled,which makes it difficult to control.Active disturbance rejection control(ADRC)has been widely used in distillation systems,but it has limitations in controlling distillation systems with large time delays since ADRC employs ESO and feedback control law to estimate the total disturbance of the system without considering the large time delays.This paper designs a proportion integral-type active disturbance rejection generalized predictive control(PI-ADRGPC)algorithm to control the distillation column system with large time delay.It replaces the PD controller in ADRC with a proportion integral-type generalized predictive control(PI-GPC),thereby improving the performance of control systems with large time delays.Since the proposed controller has many parameters and is difficult to tune,this paper proposes to use the grey wolf optimization(GWO)to tune these parameters,whose structure can also be used by other intelligent optimization algorithms.The performance of GWO tuned PI-ADRGPC is compared with the control performance of GWO tuned ADRC method,multi-verse optimizer(MVO)tuned PI-ADRGPC and MVO tuned ADRC.The simulation results show that the proposed strategy can track reference well and has a good disturbance rejection performance.
文摘We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10661003, 10371126the Guangxi Science Foundation under Grant No. 0832102the Doctor Foundation of Guangxi Normal University
文摘A family of integral-type goodness-of-fit tests is investigated. This family includes some existing tests, such as the Cramer-von Mises test and Anderson-Darling test, etc. The asymptotic distributions of the tests in the family under the null and local alternative hypotheses are established. The almost sure convergence under a fixed underlying distribution is obtained. Furthermore, simulations are conducted to compare the powers of the tests in the family. Simulation results show that for different alternatives, the more powerful tests are different, and the parameter ）, has great influence on the tests in small sample cases.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11571043,11771047,11871008).
文摘We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes.Meanwhile,main results are applied to more general integral-type downward functionals.
基金supported by the National Natural Science Foundation of China(Nos.61833009,61690212 and 51875119)the National Key Research and Development Project(No.2016YFB0501203)。
文摘This paper investigates the coordinated attitude control problem for flexible spacecraft formation with the consideration of actuator configuration misalignment.First,an integral-type sliding mode adaptive control law is designed to compensate the effects of flexible mode,environmental disturbance and actuator installation deviation.The basic idea of the Integral-type Sliding Mode Control(ISMC)is to design a proper sliding manifold so that the sliding mode starts from the initial time instant,and thus the robustness of the system can be guaranteed from the beginning of the process and the reaching phase is eliminated.Then,considering the nominal system of spacecraft formation based on directed topology,an attitude cooperative control strategy is developed for the nominal system with or without communication delay.The proposed control law can guarantee that for each spacecraft in the spacecraft formation,the desired attitude objective can be achieved and the attitude synchronization can be maintained with other spacecraft in the formation.Finally,simulation results are given to show the effectiveness of the proposed control algorithm.
基金Supported by the NNSF of China(10371080)Supported by the Educational Committee Foundation of Beijing(01KJ-101)
文摘In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in Lp（1≤ p 〈＋∞）has been obtained.
