AIM:To evaluate alterations in conjunctival vascular density(CVD)and macular capillary density(MCD)in female patients with type 2 diabetes mellitus(T2DM)and gestational diabetes mellitus(GDM)using optical coherence to...AIM:To evaluate alterations in conjunctival vascular density(CVD)and macular capillary density(MCD)in female patients with type 2 diabetes mellitus(T2DM)and gestational diabetes mellitus(GDM)using optical coherence tomography angiography(OCTA).METHODS:A total of 60 female participants were recruited,comprising 20 patients with T2DM,20 patients with GDM,and 20 healthy age-matched controls(HCs).OCTA was used to assess superficial and deep retinal and conjunctival capillary plexuses.Subsequently,changes in MCD were analyzed using a circular segmentation method(C1-C6),a hemispheric quadrant segmentation method[superior right(SR),superior left(SL),inferior left(IL),and inferior right(IR)],and the early treatment diabetic retinopathy study(ETDRS)segmentation method(S,I,R,L).RESULTS:OCTA unequivocally demonstrated that the variations in CVD among HCs,T2DM,and GDM groups were statistically significant(P<0.001).In the superficial retinal capillary plexus(sRCP),significant differences were observed in the densities of total microvascular(TMI),microvasculature(MIR),and macrovascular(MAR)between patients with T2DM and HCs(P<0.05).Furthermore,the GDM group exhibited a more substantial reduction in MIR density compared to the T2DM group(P<0.01).In the deep retinal capillary plexus(dRCP),significant differences in the densities of TMI and MIR were identified between the T2DM group and HCs(P<0.05),with a notable difference in TMI density also observed between the GDM and T2DM groups(P<0.01).In the receiver operating characteristic(ROC)curve analysis,the area under the ROC curve(AUC)for TMI in sRCP between the T2DM group and HCs was 0.975,with a 95%confidence interval(CI)of 0.941–1.The AUC for MIR was highest in dRCP,with an AUC value of 0.914 and a 95%CI ranging from 0.847 to 0.981.In comparing the GDM and T2DM groups,the AUC for I region was maximized in sRCP,achieving a value of 0.978 with a 95%CI of 0.953–1.Additionally,the AUC for R region was maximized in dRCP,reaching a value of 0.99 with a 95%CI of 0.975 to 1.CONCLUSION:The sRCP and dRCP densities show higher diagnostic sensitivity for T2DM and GDM.OCTA holds potential as a significant instrument for the early diagnosis and differentiation of T2DM and GDM.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
To investigate the thermal stability of ceramic-matrix composites,three kinds of C/C−ZrC−SiC composites with different Zr/Si molar ratios were synthesized by reactive melt infiltration.Employing region labeling method...To investigate the thermal stability of ceramic-matrix composites,three kinds of C/C−ZrC−SiC composites with different Zr/Si molar ratios were synthesized by reactive melt infiltration.Employing region labeling method,the high-temperature thermal stability of the composites was systematically studied by changing the temperature and holding time of thermal treatment.Results show that the mass loss rate of low Si composites has a growth trend with increasing temperature,and a crystal transformation from β-SiC toα-SiC occurs in the composites.In the calibrated area,SiC phase experiences Ostwald ripening and volume change with location migration,while ZrC phase experiences a re-sintering process with diffusion.Moreover,it is found that increasing temperature has a more obvious effect on the thermal stability than extending holding time,which is mainly attributed to the faster diffusion rate of atoms.展开更多
A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical res...A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.展开更多
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum...A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.展开更多
Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The adva...Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.展开更多
The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we ...The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.展开更多
In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of comput...In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.展开更多
A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided proje...A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.展开更多
Regional agriculture is the basis of regional sustainable development, so sustainable regional agricultural development is essential to the sustainable development of the whole society and becomes the focus of global ...Regional agriculture is the basis of regional sustainable development, so sustainable regional agricultural development is essential to the sustainable development of the whole society and becomes the focus of global research. The classification of regional agricultural structure is the basic work of regional agriculture study. This paper constructs index system （27 indices） of regional agricultural structure types with the three big indices： natural resources, developmental level of the agro-economy, and agro-ecological conditions. This paper also endows weight to every sub-classification index by means of AHP and obtains the comprehensive evaluation value of the three types of indices with arithmetic average weight approach. The regional agricultural structure can be classified into eight types in accordance with this evaluation results. The empirical study of China shows that the 31 provinces （municipalities and autonomous regions） are of different agriculture structural types. Finally, countermeasures of sustainsable agricultural development are put forward for the different agriculture structure features.展开更多
consists of forecasting for the total reserves of regional mineral resources and evaluation,compreIn general,based on evaluated objects and factors involved,evaluation of mineral resources hensive evaluation of region...consists of forecasting for the total reserves of regional mineral resources and evaluation,compreIn general,based on evaluated objects and factors involved,evaluation of mineral resources hensive evaluation of regional mineral resources, and economic and technical evaluation of deposits. Here a region can be a country, a province, or a mining area, while a deposit is mainly related to a single type of mineral, although it can contain more than one types of minerals. In the past, to assess mineral resources was primarily to evaluate and forecast the total reserves of regional mineral resources. With the advancement of science, technology, and economy, the evaluation of mineral resources has developed from forecasting the reserves of them to comprehensively evaluating them on the basis of numerous factors.展开更多
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with...In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.展开更多
In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required...In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.展开更多
Massive multiple-input multiple-output(MIMO)emerges as one of the most promising technologies for 5G mobile communication systems.Compared to the conventional MIMO channel models,channel researches and measurements sh...Massive multiple-input multiple-output(MIMO)emerges as one of the most promising technologies for 5G mobile communication systems.Compared to the conventional MIMO channel models,channel researches and measurements show that significant nonstationary properties rise in massive MIMO channels.Therefore,an accurate channel model is indispensable for the sake of massive MIMO system design and performance evaluation.This article presents an overview of methods of modeling non-stationary properties on both the array and time axes,which are mainly divided into two major categories:birth-death(BD)process and cluster visibility region(VR)method.The main concepts and theories are described,together with useful implementation guidelines.In conclusion,a comparison between these two methods is made.展开更多
A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstra...A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.展开更多
It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving uncon- strained optimization problems. The proposed...It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving uncon- strained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.展开更多
We discovered three large HⅡ regions： G148.8＋2.3, G149.5＋0.0 and G169.9＋2.0 in the Sino-German A6 cm polarization survey of the Galactic plane. They have been identified based on the flat spectral indexes and the...We discovered three large HⅡ regions： G148.8＋2.3, G149.5＋0.0 and G169.9＋2.0 in the Sino-German A6 cm polarization survey of the Galactic plane. They have been identified based on the flat spectral indexes and the strong infrared emission properties.展开更多
This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programmin...This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.展开更多
In this study, the flow stability of the flat-bottomed hopper was investigated via GPU-based discrete element method(DEM) simulation. With the material height inside the hopper reducing, the fluctuation of the flow ra...In this study, the flow stability of the flat-bottomed hopper was investigated via GPU-based discrete element method(DEM) simulation. With the material height inside the hopper reducing, the fluctuation of the flow rate indicates an unstable discharge. The flow regions of the unstable discharge were compared with that of the stable discharge, a key transformation zone, where the voidage showed the largest difference between unstable and stable discharge, was revealed. To identify the relevance of the key transformation zone and the hopper flow stability, the voidage variation of the key transformation zone with material height reducing was studied.A sharp increase in the voidage in the key transformation zone was considered to be the standard for judging the unstable hopper flow, and the ‘Top–Bottom effect' of the hopper was defined, which indicated the hopper flow was unstable when the hopper only had the top area and the bottom area, because the voidage of particles in the top area and the bottom area were both variables.展开更多
基金Supported by National Natural Science Foundation of China(No.82160195,No.82460203)The Science and Technology Innovation Program of Changde City(No.2023YD25).
文摘AIM:To evaluate alterations in conjunctival vascular density(CVD)and macular capillary density(MCD)in female patients with type 2 diabetes mellitus(T2DM)and gestational diabetes mellitus(GDM)using optical coherence tomography angiography(OCTA).METHODS:A total of 60 female participants were recruited,comprising 20 patients with T2DM,20 patients with GDM,and 20 healthy age-matched controls(HCs).OCTA was used to assess superficial and deep retinal and conjunctival capillary plexuses.Subsequently,changes in MCD were analyzed using a circular segmentation method(C1-C6),a hemispheric quadrant segmentation method[superior right(SR),superior left(SL),inferior left(IL),and inferior right(IR)],and the early treatment diabetic retinopathy study(ETDRS)segmentation method(S,I,R,L).RESULTS:OCTA unequivocally demonstrated that the variations in CVD among HCs,T2DM,and GDM groups were statistically significant(P<0.001).In the superficial retinal capillary plexus(sRCP),significant differences were observed in the densities of total microvascular(TMI),microvasculature(MIR),and macrovascular(MAR)between patients with T2DM and HCs(P<0.05).Furthermore,the GDM group exhibited a more substantial reduction in MIR density compared to the T2DM group(P<0.01).In the deep retinal capillary plexus(dRCP),significant differences in the densities of TMI and MIR were identified between the T2DM group and HCs(P<0.05),with a notable difference in TMI density also observed between the GDM and T2DM groups(P<0.01).In the receiver operating characteristic(ROC)curve analysis,the area under the ROC curve(AUC)for TMI in sRCP between the T2DM group and HCs was 0.975,with a 95%confidence interval(CI)of 0.941–1.The AUC for MIR was highest in dRCP,with an AUC value of 0.914 and a 95%CI ranging from 0.847 to 0.981.In comparing the GDM and T2DM groups,the AUC for I region was maximized in sRCP,achieving a value of 0.978 with a 95%CI of 0.953–1.Additionally,the AUC for R region was maximized in dRCP,reaching a value of 0.99 with a 95%CI of 0.975 to 1.CONCLUSION:The sRCP and dRCP densities show higher diagnostic sensitivity for T2DM and GDM.OCTA holds potential as a significant instrument for the early diagnosis and differentiation of T2DM and GDM.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
基金supported by the National Natural Science Foundation of China(No.U19A2099)the CAS Key Laboratory of Carbon Materials,China(No.KLCMKFJJ2005)the Fund of Aerospace Research Institute of Material and Processing Technology,China(No.6142906200108).
文摘To investigate the thermal stability of ceramic-matrix composites,three kinds of C/C−ZrC−SiC composites with different Zr/Si molar ratios were synthesized by reactive melt infiltration.Employing region labeling method,the high-temperature thermal stability of the composites was systematically studied by changing the temperature and holding time of thermal treatment.Results show that the mass loss rate of low Si composites has a growth trend with increasing temperature,and a crystal transformation from β-SiC toα-SiC occurs in the composites.In the calibrated area,SiC phase experiences Ostwald ripening and volume change with location migration,while ZrC phase experiences a re-sintering process with diffusion.Moreover,it is found that increasing temperature has a more obvious effect on the thermal stability than extending holding time,which is mainly attributed to the faster diffusion rate of atoms.
基金Supported by SF of Guangxi University(X061041)Supported by NSF of China(10761001)
文摘A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.
基金Supported by the National Natural Science Foundation of P.R.China(1 9971 0 0 2 ) and the Subject ofBeijing Educational Committ
文摘A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
文摘Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.
文摘The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.
基金Supported by the National Natural Science Foundation of China (10871130)the Research Fund for the Doctoral Program of Higher Education of China (20093127110005)the Scientific Computing Key Laboratory of Shanghai Universities
文摘In this paper, a projected gradient trust region algorithm for solving nonlinear equality systems with convex constraints is considered. The global convergence results are developed in a very general setting of computing trial directions by this method combining with the line search technique. Close to the solution set this method is locally Q-superlinearly convergent under an error bound assumption which is much weaker than the standard nonsingularity condition.
文摘A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global convergence.The algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.
基金supported by the Natural Sci-ence Foundation of Jiangsu Province (Grant No. BK2005040)the MOHURD Program of China (Grant No. 06-R5-10).
文摘Regional agriculture is the basis of regional sustainable development, so sustainable regional agricultural development is essential to the sustainable development of the whole society and becomes the focus of global research. The classification of regional agricultural structure is the basic work of regional agriculture study. This paper constructs index system （27 indices） of regional agricultural structure types with the three big indices： natural resources, developmental level of the agro-economy, and agro-ecological conditions. This paper also endows weight to every sub-classification index by means of AHP and obtains the comprehensive evaluation value of the three types of indices with arithmetic average weight approach. The regional agricultural structure can be classified into eight types in accordance with this evaluation results. The empirical study of China shows that the 31 provinces （municipalities and autonomous regions） are of different agriculture structural types. Finally, countermeasures of sustainsable agricultural development are put forward for the different agriculture structure features.
文摘consists of forecasting for the total reserves of regional mineral resources and evaluation,compreIn general,based on evaluated objects and factors involved,evaluation of mineral resources hensive evaluation of regional mineral resources, and economic and technical evaluation of deposits. Here a region can be a country, a province, or a mining area, while a deposit is mainly related to a single type of mineral, although it can contain more than one types of minerals. In the past, to assess mineral resources was primarily to evaluate and forecast the total reserves of regional mineral resources. With the advancement of science, technology, and economy, the evaluation of mineral resources has developed from forecasting the reserves of them to comprehensively evaluating them on the basis of numerous factors.
文摘In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
基金Supported by the Natural Science Foundation of Hainan Province(80552)
文摘In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.
基金supported in part by the National Natural Science of Foundation for Creative Research Groups of China under Grant No.61421061Huawei Innovation Research Program.
文摘Massive multiple-input multiple-output(MIMO)emerges as one of the most promising technologies for 5G mobile communication systems.Compared to the conventional MIMO channel models,channel researches and measurements show that significant nonstationary properties rise in massive MIMO channels.Therefore,an accurate channel model is indispensable for the sake of massive MIMO system design and performance evaluation.This article presents an overview of methods of modeling non-stationary properties on both the array and time axes,which are mainly divided into two major categories:birth-death(BD)process and cluster visibility region(VR)method.The main concepts and theories are described,together with useful implementation guidelines.In conclusion,a comparison between these two methods is made.
文摘A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.
基金Supported by the National Natural Science Foundation of China(11661009)the Guangxi Science Fund for Distinguished Young Scholars(2015GXNSFGA139001)+1 种基金the Guangxi Natural Science Key Fund(2017GXNSFDA198046)the Basic Ability Promotion Project of Guangxi Young and Middle-Aged Teachers(2017KY0019)
文摘It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving uncon- strained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.
基金the National Natural Science Foundation of China
文摘We discovered three large HⅡ regions： G148.8＋2.3, G149.5＋0.0 and G169.9＋2.0 in the Sino-German A6 cm polarization survey of the Galactic plane. They have been identified based on the flat spectral indexes and the strong infrared emission properties.
基金the National Natural Science Foundation of China ( 1 0 4 71 0 94) ,the ScienceFoundation of Shanghai Technical Sciences Committee ( 0 2 ZA1 40 70 ) and the Science Foundation ofShanghai Education Committee( 0 2 DK0 6)
文摘This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.
基金Supported by the State Key Development Program for Basic Research of China(2015CB251402)the National Natural Science Foundation of China(21325628,91334108)the Mole-8.5 Supercomputing System developed by Institute of Process Engineering,Chinese Academy of Sciences
文摘In this study, the flow stability of the flat-bottomed hopper was investigated via GPU-based discrete element method(DEM) simulation. With the material height inside the hopper reducing, the fluctuation of the flow rate indicates an unstable discharge. The flow regions of the unstable discharge were compared with that of the stable discharge, a key transformation zone, where the voidage showed the largest difference between unstable and stable discharge, was revealed. To identify the relevance of the key transformation zone and the hopper flow stability, the voidage variation of the key transformation zone with material height reducing was studied.A sharp increase in the voidage in the key transformation zone was considered to be the standard for judging the unstable hopper flow, and the ‘Top–Bottom effect' of the hopper was defined, which indicated the hopper flow was unstable when the hopper only had the top area and the bottom area, because the voidage of particles in the top area and the bottom area were both variables.
