It is observed in practice that the numerical accuracy of the two unconventional plate elements, i. e., the nine parameter quasi-conforming and generalized conforming elements, is better than that of the usual Zienkie...It is observed in practice that the numerical accuracy of the two unconventional plate elements, i. e., the nine parameter quasi-conforming and generalized conforming elements, is better than that of the usual Zienkiewicz in compatible cubic element and of a new element proposed recently by Specht, although all these elements have the same asymptotical rate of convergence O(h) in the energy norm. In the paper a careful error analysis for the quasi-conforming and generalized conforming elements is given. It is shown that the consistency error due to nonconformity of the two unconventional elements is of order O(h^2), one order high than that of other conventional nonconforming elements with nine parameters.展开更多
An increase in crop intensity could improve crop yield but may also lead to a series of environmental problems, such as depletion of ground water and increased soil salinity. The generation of high resolution(30 m) cr...An increase in crop intensity could improve crop yield but may also lead to a series of environmental problems, such as depletion of ground water and increased soil salinity. The generation of high resolution(30 m) crop intensity maps is an important method used to monitor these changes, but this is challenging because the temporal resolution of the 30-m image time series is low due to the long satellite revisit period and high cloud coverage. The recently launched Sentinel-2 satellite could provide optical images at 10–60 m resolution and thus improve the temporal resolution of the 30-m image time series. This study used harmonized Landsat Sentinel-2(HLS) data to identify crop intensity. The sixth polynomial function was used to fit the normalized difference vegetation index(NDVI) and enhanced vegetation index(EVI) curves. Then, 15-day NDVI and EVI time series were then generated from the fitted curves and used to generate the extent of croplands. Lastly, the first derivative of the fitted VI curves were used to calculate the VI peaks;spurious peaks were removed using artificially defined thresholds and crop intensity was generated by counting the number of remaining VI peaks. The proposed methods were tested in four study regions, with results showing that 15-day time series generated from the fitted curves could accurately identify cropland extent. Overall accuracy of cropland identification was higher than 95%. In addition, both the harmonized NDVI and EVI time series identified crop intensity accurately as the overall accuracies, producer’s accuracies and user’s accuracies of non-cropland, single crop cycle and double crop cycle were higher than 85%. NDVI outperformed EVI as identifying double crop cycle fields more accurately.展开更多
In some recent work concerning the number of limit cycles of the planar polynomial differential system, by using the different methods and examples, N. G. Lloyd et al., D. M. Wang, and LIU Yi-rong have successively sh...In some recent work concerning the number of limit cycles of the planar polynomial differential system, by using the different methods and examples, N. G. Lloyd et al., D. M. Wang, and LIU Yi-rong have successively shown that there exist at least six limit cycles bifurcated from the origin in the planar cubic differential system （E<sub>3</sub>）. Namely, the value of cyclicity of multiple Hopf bifurcation （in the sense of Bautin） satisfies M（3）≥6.展开更多
Our general mechanization method of polynomial equations-solving is applied to the chemical equilibrium problem. A concrete case is analyzed and discussed in details.
Polynomial factorization is indispensable in many fields and we are looking forward to having an efficient algorithm. The methods of Kronecker-Hermann and Van der Waerden-Tr?ger are too complicated to be put into prac...Polynomial factorization is indispensable in many fields and we are looking forward to having an efficient algorithm. The methods of Kronecker-Hermann and Van der Waerden-Tr?ger are too complicated to be put into practice in concrete cases. In recent years, there are many works about polynomial factorization, for example, [4 and 5], but the methods are not very efficient yet. In this paper,展开更多
The viscosily splitting method for the Navier-Stokes equations on two dimensional multi-connected domains is considered. The equation is split into an Euler equation and a non-stationary Stekes equation within each ti...The viscosily splitting method for the Navier-Stokes equations on two dimensional multi-connected domains is considered. The equation is split into an Euler equation and a non-stationary Stekes equation within each time step. The author proves the convergence theorem as he has done for the problem on simply connected domains, and the rate of convergence is improved from loss than 1/4 to 1.展开更多
Given a system of polynomials PS: h<sub>1</sub>（y<sub>1</sub>,…, y<sub>n</sub>）,…,h<sub>s</sub>（y<sub>1</sub>,…y<sub>n</sub>）, by Ritt-Wu ...Given a system of polynomials PS: h<sub>1</sub>（y<sub>1</sub>,…, y<sub>n</sub>）,…,h<sub>s</sub>（y<sub>1</sub>,…y<sub>n</sub>）, by Ritt-Wu wellordering principle and changing notations for the variables appropriately, we can obtain an ascending chain AS:展开更多
Using the modern information technology,this paper analyzes the 20 years of experimental observation data of wheat ear differentiation research team led by Professor Cui Jinmei.It reveals that in the appropriate sowin...Using the modern information technology,this paper analyzes the 20 years of experimental observation data of wheat ear differentiation research team led by Professor Cui Jinmei.It reveals that in the appropriate sowing period,there is a quartic polynomial regression relationship between the sowing period and spike primordium period,namely between duration of vegetative growth stage and the average daily temperature.It is of great significance to determining the suitable sowing period of wheat.展开更多
In this report, we give answers to the three questions proposed by A. J. Schwenk and obtain the following results: (1) There exist integral trees with diameter greater than 4. An infinite set of integral trees with di...In this report, we give answers to the three questions proposed by A. J. Schwenk and obtain the following results: (1) There exist integral trees with diameter greater than 4. An infinite set of integral trees with diameter 6 is found. (2) There exist integral trees of diameter 4 other than those specified by Schwenk and, a new infinite set of integral trees with diameter 4 is also discovered.展开更多
In this paper,we have suggested several interpolating formulae which are convinient for vector com- puters to perform vector calculation.Analysis shows that for a simple advective problem,the semi-Lagrangian schemes c...In this paper,we have suggested several interpolating formulae which are convinient for vector com- puters to perform vector calculation.Analysis shows that for a simple advective problem,the semi-Lagrangian schemes constructed with these formulae are linearly unconditionally stable.Moreover,we have discussed the nonlinear computational chaos in the semi-Lagrangian schemes.It is found that for a simple nonlinear advective problem,we can introduce physically unreal and direct interaction of three or more waves.Nu- merical tests indicate that this phenomenon has certain influence on the simulated results of two-dimensional Benard convection.展开更多
Mordoukhay-Boltovskoy （Doklady Akad. Nauk S. S. S. R., 52（1946）, 483—486, and Math. Reviews, 8（1948）, 317g）attempted to prove the following result: Let a<sub>1</sub>,…, a, be algebraic numbers and ...Mordoukhay-Boltovskoy （Doklady Akad. Nauk S. S. S. R., 52（1946）, 483—486, and Math. Reviews, 8（1948）, 317g）attempted to prove the following result: Let a<sub>1</sub>,…, a, be algebraic numbers and let P∈Z[x<sub>1</sub>,…, x<sub>5</sub>, y] be a non-zero polynomial. If η is展开更多
Considering the polynomial f<sub>n</sub>（z）=a<sub>0</sub>z<sup>n</sup>+a<sub>1</sub>z<sup>n-1</sup>+...+a<sub>n-1</sub>z+a<sub>n</sub&...Considering the polynomial f<sub>n</sub>（z）=a<sub>0</sub>z<sup>n</sup>+a<sub>1</sub>z<sup>n-1</sup>+...+a<sub>n-1</sub>z+a<sub>n</sub>, （1） let P=（P<sub>0</sub>, P<sub>1</sub>,...,P<sub>n</sub>）, q=（q<sub>0</sub>, q<sub>1</sub>,...,q<sub>n</sub>）, a=（a<sub>0</sub>, a<sub>1</sub>,...,a<sub>n</sub>）, where p<sub>i</sub>, q<sub>i</sub>, a<sub>i</sub> are real numbers, satisfying the展开更多
Polynomial Chaos Expansion(PCE)has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis.However,traditional PCE suffers from two major drawbacks.First,the ortho...Polynomial Chaos Expansion(PCE)has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis.However,traditional PCE suffers from two major drawbacks.First,the orthogonality of polynomial basis functions holds only for independent input variables,limiting the model’s ability to propagate uncertainty in dependent variables.Second,PCE encounters the"curse of dimensionality"due to the high computational cost of training the model with numerous polynomial coefficients.In practical manufacturing,compressor blades are subject to machining precision limitations,leading to deviations from their ideal geometric shapes.These deviations require a large number of geometric parameters to describe,and exhibit significant correlations.To efficiently quantify the impact of high-dimensional dependent geometric deviations on the aerodynamic performance of compressor blades,this paper firstly introduces a novel approach called Data-driven Sparse PCE(DSPCE).The proposed method addresses the aforementioned challenges by employing a decorrelation algorithm to directly create multivariate basis functions,accommodating both independent and dependent random variables.Furthermore,the method utilizes an iterative Diffeomorphic Modulation under Observable Response Preserving Homotopy regression algorithm to solve the unknown coefficients,achieving model sparsity while maintaining fitting accuracy.Then,the study investigates the simultaneous effects of seven dependent geometric deviations on the aerodynamics of a high subsonic compressor cascade by using the DSPCE method proposed and sensitivity analysis of covariance.The joint distribution of the dependent geometric deviations is determined using Quantile-Quantile plots and normal copula functions based on finite measurement data.The results demonstrate that the correlations between geometric deviations significantly impact the variance of aerodynamic performance and the flow field.Therefore,it is crucial to consider these correlations f展开更多
A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the...A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.展开更多
文摘It is observed in practice that the numerical accuracy of the two unconventional plate elements, i. e., the nine parameter quasi-conforming and generalized conforming elements, is better than that of the usual Zienkiewicz in compatible cubic element and of a new element proposed recently by Specht, although all these elements have the same asymptotical rate of convergence O(h) in the energy norm. In the paper a careful error analysis for the quasi-conforming and generalized conforming elements is given. It is shown that the consistency error due to nonconformity of the two unconventional elements is of order O(h^2), one order high than that of other conventional nonconforming elements with nine parameters.
基金supported by the China Postdoctoral Science Foundation (2017M620075 and BX201700286)the National Natural Science Foundation of China (NSFC-61661136006)
文摘An increase in crop intensity could improve crop yield but may also lead to a series of environmental problems, such as depletion of ground water and increased soil salinity. The generation of high resolution(30 m) crop intensity maps is an important method used to monitor these changes, but this is challenging because the temporal resolution of the 30-m image time series is low due to the long satellite revisit period and high cloud coverage. The recently launched Sentinel-2 satellite could provide optical images at 10–60 m resolution and thus improve the temporal resolution of the 30-m image time series. This study used harmonized Landsat Sentinel-2(HLS) data to identify crop intensity. The sixth polynomial function was used to fit the normalized difference vegetation index(NDVI) and enhanced vegetation index(EVI) curves. Then, 15-day NDVI and EVI time series were then generated from the fitted curves and used to generate the extent of croplands. Lastly, the first derivative of the fitted VI curves were used to calculate the VI peaks;spurious peaks were removed using artificially defined thresholds and crop intensity was generated by counting the number of remaining VI peaks. The proposed methods were tested in four study regions, with results showing that 15-day time series generated from the fitted curves could accurately identify cropland extent. Overall accuracy of cropland identification was higher than 95%. In addition, both the harmonized NDVI and EVI time series identified crop intensity accurately as the overall accuracies, producer’s accuracies and user’s accuracies of non-cropland, single crop cycle and double crop cycle were higher than 85%. NDVI outperformed EVI as identifying double crop cycle fields more accurately.
基金Project supported by the National Natural Science Foundation of China.
文摘In some recent work concerning the number of limit cycles of the planar polynomial differential system, by using the different methods and examples, N. G. Lloyd et al., D. M. Wang, and LIU Yi-rong have successively shown that there exist at least six limit cycles bifurcated from the origin in the planar cubic differential system （E<sub>3</sub>）. Namely, the value of cyclicity of multiple Hopf bifurcation （in the sense of Bautin） satisfies M（3）≥6.
文摘Our general mechanization method of polynomial equations-solving is applied to the chemical equilibrium problem. A concrete case is analyzed and discussed in details.
文摘Polynomial factorization is indispensable in many fields and we are looking forward to having an efficient algorithm. The methods of Kronecker-Hermann and Van der Waerden-Tr?ger are too complicated to be put into practice in concrete cases. In recent years, there are many works about polynomial factorization, for example, [4 and 5], but the methods are not very efficient yet. In this paper,
基金This Work was Supported by the Science Foundation of Academia Sicina under Grant (84)-103.
文摘The viscosily splitting method for the Navier-Stokes equations on two dimensional multi-connected domains is considered. The equation is split into an Euler equation and a non-stationary Stekes equation within each time step. The author proves the convergence theorem as he has done for the problem on simply connected domains, and the rate of convergence is improved from loss than 1/4 to 1.
基金Project supported by the National Natural Science Foundation of China.
文摘Given a system of polynomials PS: h<sub>1</sub>（y<sub>1</sub>,…, y<sub>n</sub>）,…,h<sub>s</sub>（y<sub>1</sub>,…y<sub>n</sub>）, by Ritt-Wu wellordering principle and changing notations for the variables appropriately, we can obtain an ascending chain AS:
基金Supported by National"12th Five-year Plan"Technology Support Program(2014BAD10B06)Major Research Project in Henan Province(30600341)
文摘Using the modern information technology,this paper analyzes the 20 years of experimental observation data of wheat ear differentiation research team led by Professor Cui Jinmei.It reveals that in the appropriate sowing period,there is a quartic polynomial regression relationship between the sowing period and spike primordium period,namely between duration of vegetative growth stage and the average daily temperature.It is of great significance to determining the suitable sowing period of wheat.
文摘In this report, we give answers to the three questions proposed by A. J. Schwenk and obtain the following results: (1) There exist integral trees with diameter greater than 4. An infinite set of integral trees with diameter 6 is found. (2) There exist integral trees of diameter 4 other than those specified by Schwenk and, a new infinite set of integral trees with diameter 4 is also discovered.
基金Supported by National Natural Science Foundation of China.
文摘In this paper,we have suggested several interpolating formulae which are convinient for vector com- puters to perform vector calculation.Analysis shows that for a simple advective problem,the semi-Lagrangian schemes constructed with these formulae are linearly unconditionally stable.Moreover,we have discussed the nonlinear computational chaos in the semi-Lagrangian schemes.It is found that for a simple nonlinear advective problem,we can introduce physically unreal and direct interaction of three or more waves.Nu- merical tests indicate that this phenomenon has certain influence on the simulated results of two-dimensional Benard convection.
文摘Mordoukhay-Boltovskoy （Doklady Akad. Nauk S. S. S. R., 52（1946）, 483—486, and Math. Reviews, 8（1948）, 317g）attempted to prove the following result: Let a<sub>1</sub>,…, a, be algebraic numbers and let P∈Z[x<sub>1</sub>,…, x<sub>5</sub>, y] be a non-zero polynomial. If η is
文摘Considering the polynomial f<sub>n</sub>（z）=a<sub>0</sub>z<sup>n</sup>+a<sub>1</sub>z<sup>n-1</sup>+...+a<sub>n-1</sub>z+a<sub>n</sub>, （1） let P=（P<sub>0</sub>, P<sub>1</sub>,...,P<sub>n</sub>）, q=（q<sub>0</sub>, q<sub>1</sub>,...,q<sub>n</sub>）, a=（a<sub>0</sub>, a<sub>1</sub>,...,a<sub>n</sub>）, where p<sub>i</sub>, q<sub>i</sub>, a<sub>i</sub> are real numbers, satisfying the
基金the National Science and Technology Major Project of China(No.J2019-I-0011)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX2023057)for supporting the research work.
文摘Polynomial Chaos Expansion(PCE)has gained significant popularity among engineers across various engineering disciplines for uncertainty analysis.However,traditional PCE suffers from two major drawbacks.First,the orthogonality of polynomial basis functions holds only for independent input variables,limiting the model’s ability to propagate uncertainty in dependent variables.Second,PCE encounters the"curse of dimensionality"due to the high computational cost of training the model with numerous polynomial coefficients.In practical manufacturing,compressor blades are subject to machining precision limitations,leading to deviations from their ideal geometric shapes.These deviations require a large number of geometric parameters to describe,and exhibit significant correlations.To efficiently quantify the impact of high-dimensional dependent geometric deviations on the aerodynamic performance of compressor blades,this paper firstly introduces a novel approach called Data-driven Sparse PCE(DSPCE).The proposed method addresses the aforementioned challenges by employing a decorrelation algorithm to directly create multivariate basis functions,accommodating both independent and dependent random variables.Furthermore,the method utilizes an iterative Diffeomorphic Modulation under Observable Response Preserving Homotopy regression algorithm to solve the unknown coefficients,achieving model sparsity while maintaining fitting accuracy.Then,the study investigates the simultaneous effects of seven dependent geometric deviations on the aerodynamics of a high subsonic compressor cascade by using the DSPCE method proposed and sensitivity analysis of covariance.The joint distribution of the dependent geometric deviations is determined using Quantile-Quantile plots and normal copula functions based on finite measurement data.The results demonstrate that the correlations between geometric deviations significantly impact the variance of aerodynamic performance and the flow field.Therefore,it is crucial to consider these correlations f
基金Project supported by the National Basic Research Program(973 Program)of China(No.2015CB057400)the National Natural Science Foundation of China(No.11602070)+1 种基金the China Postdoctoral Science Foundation(No.2016M590277)the Heilongjiang Postdoctoral Financial Assistance(No.LBH-Z16067)
文摘A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.
