The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of t...The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, co...Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.展开更多
Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used parti...Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression （PLSR） models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM＋ data. The established models were optimized according to the variable importance for projection （VIP） criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test （p〈0.05）. The simplified models without insignificant variables （VIP 〈1） performed as well as the full model but with less computation time. The relative root mean square error （RMSE%） was 29% for canopy closure density, and 58% for above ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above ground biomass.展开更多
The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features becau...The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.展开更多
A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercriti...A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.展开更多
Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of s...Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.展开更多
Rapid and sensitive recognition of herbal pieces according to different concocted processing is crucial to quality control and pharmaceutical effect. Near-infrared （NIR） and mid-infrared （MIR） technology combined ...Rapid and sensitive recognition of herbal pieces according to different concocted processing is crucial to quality control and pharmaceutical effect. Near-infrared （NIR） and mid-infrared （MIR） technology combined with supervised pattern recognition based on partial least-squares discriminant analysis （PLSDA） was attempted to classify and recognize six different concocted processing pieces of 600 Areca catechu L. samples and the influence of fingerprint information preprocessing methods on recognition performance was also investigated in this work. Recognition rates of 99.24%, 100% and 99.49% for original fingerprint, multiple scatter correct （MSC） fingerprint and second derivative （2nd derivative） fingerprint of NIR spectra were achieved by PLSDA models, respectively. Meanwhile, a perfect recognition rate of 100% was obtained for the above three fingerprint models of MIR spectra. In conclusion, PLSDA can rapidly and effectively extract otherness of fingerprint information from NIR and MIR spectra to identify different concocted herbal pieces ofA. catechu.展开更多
With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion a...With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.展开更多
Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity, etc. The...Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity, etc. The present paper deals with a general introduction and classification of partial differential equations and the numerical methods available in the literature for the solution of partial differential equations.展开更多
In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically ind...In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares （PLS） regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.展开更多
For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows....For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.展开更多
In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the...In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the classical wave equation in two space dimensions.Combining with the Crank-Nicolson method in temporal direction,efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed,respectively.The corresponding stability and convergence analysis of the numerical methods are discussed.Numerical results are provided to verify the theoretical analysis.展开更多
BACKGROUND Gastric ulcer perforation is a critical condition that can lead to significant morbidity and mortality if not promptly addressed.It is often the result of chronic peptic ulcer disease,which is characterized...BACKGROUND Gastric ulcer perforation is a critical condition that can lead to significant morbidity and mortality if not promptly addressed.It is often the result of chronic peptic ulcer disease,which is characterized by a breach in the gastric wall due to ulceration.Surgical intervention is essential for managing this life-threatening complication.However,the optimal surgical technique remains debatable among clinicians.Various methods have been employed,including simple closure,omental patch repair,and partial gastrectomy,each with distinct advantages and disadvantages.Understanding the comparative efficacy and postoperative outcomes of these techniques is crucial for improving patient care and surgical decision-making.This study addresses the need for a comprehensive analysis in this area.AIM To compare the efficacy and postoperative complications of different surgical methods for the treatment of gastric ulcer perforation.METHODS A retrospective analysis was conducted on 120 patients who underwent surgery for gastric ulcer perforation between September 2020 and June 2023.The patients were divided into three groups based on the surgical method:Simple closure,omental patch repair,and partial gastrectomy.The primary outcomes were the operative success rate and incidence of postoperative complications.Secondary outcomes included the length of hospital stay,recovery time,and long-term quality of life.RESULTS The operative success rates for simple closure,omental patch repair,and partial gastrectomy were 92.5%,95%,and 97.5%,respectively.Postoperative complications occurred in 20%,15%,and 17.5%of patients in each group,respectively.The partial gastrectomy group showed a significantly longer operative time(P<0.001)but the lowest rate of ulcer recurrence(2.5%,P<0.05).The omental patch repair group demonstrated the shortest hospital stay(mean 7.2 days,P<0.05)and fastest recovery time.CONCLUSION While all three surgical methods showed high success rates,omental patch repair demonstrated the best overall outcomes,with a balance of high efficacy,low complication rates,and shorter recovery time.However,the choice of the surgical method should be tailored to individual patient factors and the surgeon’s expertise.展开更多
The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are est...The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.展开更多
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi...A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.展开更多
In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training ...In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.展开更多
A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary ...A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.展开更多
The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by tradit...The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.展开更多
In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the line...In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.展开更多
文摘The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金Supported by "863" Program of P. R. China(2002AA2Z4291)
文摘Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting.
基金supported by the 948 Program of the State Forestry Administration (2009-4-43)the National Natura Science Foundation of China (No.30870420)
文摘Boreal forests play an important role in global environment systems. Understanding boreal forest ecosystem structure and function requires accurate monitoring and estimating of forest canopy and biomass. We used partial least square regression （PLSR） models to relate forest parameters, i.e. canopy closure density and above ground tree biomass, to Landsat ETM＋ data. The established models were optimized according to the variable importance for projection （VIP） criterion and the bootstrap method, and their performance was compared using several statistical indices. All variables selected by the VIP criterion passed the bootstrap test （p〈0.05）. The simplified models without insignificant variables （VIP 〈1） performed as well as the full model but with less computation time. The relative root mean square error （RMSE%） was 29% for canopy closure density, and 58% for above ground tree biomass. We conclude that PLSR can be an effective method for estimating canopy closure density and above ground biomass.
基金This project is supported by Research Foundation for Doctoral Program of Higher Education, China (No.98033532)
文摘The main purpose of reverse engineering is to convert discrete data pointsinto piecewise smooth, continuous surface models. Before carrying out model reconstruction it issignificant to extract geometric features because the quality of modeling greatly depends on therepresentation of features. Some fitting techniques of natural quadric surfaces with least-squaresmethod are described. And these techniques can be directly used to extract quadric surfaces featuresduring the process of segmentation for point cloud.
基金the National Science Council ot Taiwan,China for funding this research(Project no.:NSC 94-2218-E-035-011)
文摘A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.
基金the National Science Council of Taiwan for funding this research (NSC 96-2221-E-019-061).
文摘Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
基金supported by the National Natural Science Foundation of China(Nos.21205145,21276006,21036009)the Open Funds of State Key Laboratory of Chemo/Biosensing and Chemometrics of Hunan University(No.201111)+1 种基金the Special Fund for Basic Scientific Research of Central Colleges,South-Central University for Nationalities(Nos.CZZ10005 and CZQ11012)the 'Five-twelfth' National Science and Technology Support Program (No.2012BAI27B00)
文摘Rapid and sensitive recognition of herbal pieces according to different concocted processing is crucial to quality control and pharmaceutical effect. Near-infrared （NIR） and mid-infrared （MIR） technology combined with supervised pattern recognition based on partial least-squares discriminant analysis （PLSDA） was attempted to classify and recognize six different concocted processing pieces of 600 Areca catechu L. samples and the influence of fingerprint information preprocessing methods on recognition performance was also investigated in this work. Recognition rates of 99.24%, 100% and 99.49% for original fingerprint, multiple scatter correct （MSC） fingerprint and second derivative （2nd derivative） fingerprint of NIR spectra were achieved by PLSDA models, respectively. Meanwhile, a perfect recognition rate of 100% was obtained for the above three fingerprint models of MIR spectra. In conclusion, PLSDA can rapidly and effectively extract otherness of fingerprint information from NIR and MIR spectra to identify different concocted herbal pieces ofA. catechu.
基金partially supported by the National Natural Science Foundation of China (No.41230318)
文摘With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least squares migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, various techniques to optimize these data-fitting seismic inversion problems have been implemented to cater for the industrial need for much improved efficiency. In this study, we propose a general stochastic conjugate gradient method for these data-fitting related inverse problems. We first prescribe the basic theory of our method and then give synthetic examples. Our numerical experiments illustrate the potential of this method for large-size seismic inversion application.
文摘Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity, etc. The present paper deals with a general introduction and classification of partial differential equations and the numerical methods available in the literature for the solution of partial differential equations.
基金National Natural Science Foundation of China No.40301038
文摘In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares （PLS） regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.
基金supported by the National Natural Science Foundation of China(Nos.11702329,12102247)the Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems,China(No.VATLAB-2021-01)。
文摘For the second-order finite volume method,implicit schemes and reconstruction methods are two main algorithms which influence the robustness and efficiency of the numerical simulations of compressible turbulent flows.In this paper,a compact least-squares reconstruction method is proposed to calculate the gradients for the distribution of flow field variables approximation.The compactness of the new reconstruction method is reflected in the gradient calculation process.The geometries of the face-neighboring elements are no longer utilized,and the weighted average values at the centroid of the interfaces are used to calculate the gradients instead of the values at the centroid of the face-neighboring elements.Meanwhile,an exact Jacobian solving strategy is developed for implicit temporal discretization.The accurate processing of Jacobian matrix can extensively improve the invertibility of the Jacobian matrix and avoid introducing extra numerical errors.In addition,a modified Venkatakrishnan limiter is applied to deal with the shock which may appear in transonic flows and the applicability of the mentioned methods is enhanced further.The combination of the proposed methods makes the numerical simulations of turbulent flow converge rapidly and steadily with an adaptive increasing CFL number.The numerical results of several benchmarks indicate that the proposed methods perform well in terms of robustness,efficiency and accuracy,and have good application potential in turbulent flow simulations of complex configurations.
基金supported by the Guangxi Natural Science Foundation[grant numbers 2018GXNSFBA281020,2018GXNSFAA138121]the Doctoral Starting up Foundation of Guilin University of Technology[grant number GLUTQD2016044].
文摘In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the classical wave equation in two space dimensions.Combining with the Crank-Nicolson method in temporal direction,efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed,respectively.The corresponding stability and convergence analysis of the numerical methods are discussed.Numerical results are provided to verify the theoretical analysis.
文摘BACKGROUND Gastric ulcer perforation is a critical condition that can lead to significant morbidity and mortality if not promptly addressed.It is often the result of chronic peptic ulcer disease,which is characterized by a breach in the gastric wall due to ulceration.Surgical intervention is essential for managing this life-threatening complication.However,the optimal surgical technique remains debatable among clinicians.Various methods have been employed,including simple closure,omental patch repair,and partial gastrectomy,each with distinct advantages and disadvantages.Understanding the comparative efficacy and postoperative outcomes of these techniques is crucial for improving patient care and surgical decision-making.This study addresses the need for a comprehensive analysis in this area.AIM To compare the efficacy and postoperative complications of different surgical methods for the treatment of gastric ulcer perforation.METHODS A retrospective analysis was conducted on 120 patients who underwent surgery for gastric ulcer perforation between September 2020 and June 2023.The patients were divided into three groups based on the surgical method:Simple closure,omental patch repair,and partial gastrectomy.The primary outcomes were the operative success rate and incidence of postoperative complications.Secondary outcomes included the length of hospital stay,recovery time,and long-term quality of life.RESULTS The operative success rates for simple closure,omental patch repair,and partial gastrectomy were 92.5%,95%,and 97.5%,respectively.Postoperative complications occurred in 20%,15%,and 17.5%of patients in each group,respectively.The partial gastrectomy group showed a significantly longer operative time(P<0.001)but the lowest rate of ulcer recurrence(2.5%,P<0.05).The omental patch repair group demonstrated the shortest hospital stay(mean 7.2 days,P<0.05)and fastest recovery time.CONCLUSION While all three surgical methods showed high success rates,omental patch repair demonstrated the best overall outcomes,with a balance of high efficacy,low complication rates,and shorter recovery time.However,the choice of the surgical method should be tailored to individual patient factors and the surgeon’s expertise.
基金the Science Foundation of the Science and Technology Commission of Shanghai Municipality(No.075105118)the Shanghai Leading Academic Discipline Project(No.T0401)the Fund for E-institute of Shanghai Universities(No.E03004)
文摘The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.
文摘A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.
基金This study was funded by the National Natural Science Foundation of China(Nos.11972077 and 12272039).
文摘In this paper,we present a novel initial costates solver for initializing time-optimal trajectory problems in relative motion with continuous low thrust.The proposed solver consists of two primary components:training a Multilayer Perceptron(MLP)for generating reference sequence and Time of Flight(TOF)to the target,and deriving a system of linear algebraic equations for obtaining the initial costates.To overcome the challenge of generating training samples for the MLP,the backward generation method is proposed to obtain five different training databases.The training database and sample form are determined by analyzing the input and output correlation using the Pearson correlation coefficient.The best-performing MLP is obtained by analyzing the training results with various hyper-parameter combinations.A reference sequence starting from the initial states is obtained by integrating forward with the near-optimal control vector from the output of MLP.Finally,a system of linear algebraic equations for estimating the initial costates is derived using the reference sequence and the necessary conditions for optimality.Simulation results demonstrate that the proposed initial costates solver improves the convergence ratio and reduce the function calls of the shooting function.Furthermore,Monte-Carlo simulation illustrates that the initial costates solver is applicable to different initial velocities,demonstrating excellent generalization ability.
文摘A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal H-t and L-2-error estimates are derived under the standard regularity assumption on the finite element partition ( the LBB-condition is not required). Far the evolutionary equation, optimal L-2 estimates are derived under the conventional Raviart-Thomas spaces.
文摘The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.
文摘In this paper, a least-squares finite element method for the upper-convected Maxell (UCM) fluid is proposed. We first linearize the constitutive and momentum equations and then apply a least-squares method to the linearized version of the viscoelastic UCM model. The L2 least-squares functional involves the residuals of each equation multiplied by proper weights. The corresponding homogeneous functional is equivalent to a natural norm. The error estimates of the finite element solution are analyzed when the conforming piecewise polynomial elements are used for the unknowns.
