In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results fo...In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.展开更多
Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along th...Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.展开更多
In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_...In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_(n,σ)(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that d_(n,H)(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that d_(n,σ)(f)≤‖σ‖/(n+1)V(f)and d_(n,H)(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.展开更多
To get simpler operation in modified fuzzy adaptive learning control network （FALCON） in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership functi...To get simpler operation in modified fuzzy adaptive learning control network （FALCON） in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership function. For making the modified FALCON learning more efficient and stable, a simulated annealing （SA） learning coefficient is introduced into learning algorithm. At first, the basic concepts and main advantages of FALCON were briefly reviewed. Subsequently, the topological structure and nodes operation were illustrated; the gradient-descent learning algorithm with SA learning coefficient was derived; and the distinctions between the archetype and the modification were analyzed. Eventually, the significance and worthiness of the modified FALCON were validated by its application to probability prediction of anode effect in aluminium electrolysis cells.展开更多
Reynolds-averaged Navier-Stokes(RANS)turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow,which causes the unphysical motion of the interface in sloshing simulation.In ...Reynolds-averaged Navier-Stokes(RANS)turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow,which causes the unphysical motion of the interface in sloshing simulation.In order to avoid the unphysical motion of the interface,a novel eddy-viscosity eliminator based on sigmoid functions is designed to reduce the excessive turbulence level,and the eddy-viscosity eliminator based on polynomials is extracted from the cavitation simulations.Surface elevations by combining the eddy-viscosity eliminators and classical two-equation closure models are compared with the experiments,the ones by using the adaptive asymptotic model(AAM)and the ones by using the modified two-equation closure models.The root-mean-squared error(RMSE)is introduced to quantify the accuracies of surface elevations and the forces.The relation between the turbulence level in the transition layer and RMSEs of surface elevations is studied.Besides,the parametric analysis of the eddy-viscosity eliminators is carried out.The studies suggest that(1)the excessive turbulence level in the transition layer around the interface has a significant influence on the accuracies of surface elevations and the forces;(2)the eddy-viscosity eliminators can effectively reduce the excessive turbulence level in the transition layer to avoid the unphysical motion of the interface;(3)the k-ωSST model combined with the eddy-viscosity eliminators is appropriate for predicting surface elevations and forces in RANS simulations of sloshing flow.展开更多
Objective: To evaluate left ventricular regional and global systolic function by measuring left ventricular longitudinal strain (LS) in hypertensive patients with sigmoid-shaped interventricular septum (SIS) by two-di...Objective: To evaluate left ventricular regional and global systolic function by measuring left ventricular longitudinal strain (LS) in hypertensive patients with sigmoid-shaped interventricular septum (SIS) by two-dimensional speckle tracking (2D-STE);in order to explore whether the sigmoid-shaped interventricular septum affects the left ventricular systolic function in patients with hypertension. Methods: Routine echocardiographic parameters were measured in 30 hypertensive patients with SIS (SIS group) and 30 hypertensive patients without SIS (non-SIS group). The left ventricular segments and global LS were measured by 2D-STE, and the two sets of parameters were compared. Results: The value of the thickness of the basal segment of the interventricular septum (IVSBT), the thickness of the middle segment of the interventricular septum (IVSMT) and the ratio of the basal segment of the ventricular septum to the middle segment of the interventricular septum (IVSBT/IVSMT) in SIS group was higher than that in non-SIS group. However, the value of left ventricular outflow tract diameter (LVOTD) in SIS group was lower than that in non-SIS group. There was a significant difference between the two groups (all P Conclusion: SIS affects left ventricular regional systolic function of patients with hypertension. 2D-STE can early evaluate left ventricular longitudinal systolic function in hypertensive patients with SIS.展开更多
针对船舶超大空间火灾对人员疏散能力的影响难以量化问题,本文基于元胞自动机理论,构建了一种行人个体自主分析火灾环境下温度和能见度影响的疏散模型(cellular automata model considering visibility and temperature, CAVT)。CAVT模...针对船舶超大空间火灾对人员疏散能力的影响难以量化问题,本文基于元胞自动机理论,构建了一种行人个体自主分析火灾环境下温度和能见度影响的疏散模型(cellular automata model considering visibility and temperature, CAVT)。CAVT模型采用Sigmoid函数和历史实验数据建立温度、能见度与人员运动能力的映射关系,基于FDS数值模拟结果建立火灾环境场对人员个体运动能力影响的时空耦合关系,使用熵值法计算温度场和能见度场在火灾环境场中的权重。以某客船超大空间为例开展研究分析,结果表明:火灾环境下人员疏散时间受火源功率影响较大,火源位置影响较小,出口宽度大于3 m,不影响疏散效率。与Pathfinder软件相比,CAVT模型可更准确模拟人员因高温和低能见度导致的运动能力的动态下降反馈。展开更多
基金supported, in part, by the GNAMPA and the GNFM of the Italian INdAM
文摘In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L^p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives （whenever these exist）, are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.
基金supported by the National Natural Science Foundation of China(Nos.11672071,11302046,and 11672072)the Fundamental Research Funds for the Central Universities(No.N150504003)
文摘Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material （S-FGM） plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D＇Alembert＇s principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.
文摘In this paper we study the degree of approximation by superpositions of a sigmoidal function.We mainly consider the univariate case.If f is a continuous function,we prove that for any bounded sigmoidal function σ,d_(n,σ)(f)≤‖σ‖ω(f,1/(n+1)).For the Heaviside function H(x),we prove that d_(n,H)(f)≤ω(f,1/(2(n+1))). If f is a continuous funnction of bounded variation,we prove that d_(n,σ)(f)≤‖σ‖/(n+1)V(f)and d_(n,H)(f)≤ 1/(2(n+1))V(f).For he Heaviside function,the coefficient 1 and the approximation orders are the best possible.We compare these results with the classical Jackson and Bernstein theorems,and make some conjec- tures for further study.
文摘To get simpler operation in modified fuzzy adaptive learning control network （FALCON） in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership function. For making the modified FALCON learning more efficient and stable, a simulated annealing （SA） learning coefficient is introduced into learning algorithm. At first, the basic concepts and main advantages of FALCON were briefly reviewed. Subsequently, the topological structure and nodes operation were illustrated; the gradient-descent learning algorithm with SA learning coefficient was derived; and the distinctions between the archetype and the modification were analyzed. Eventually, the significance and worthiness of the modified FALCON were validated by its application to probability prediction of anode effect in aluminium electrolysis cells.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.11802176,11802301)。
文摘Reynolds-averaged Navier-Stokes(RANS)turbulence modeling can lead to the excessive turbulence level around the interface in two-phase flow,which causes the unphysical motion of the interface in sloshing simulation.In order to avoid the unphysical motion of the interface,a novel eddy-viscosity eliminator based on sigmoid functions is designed to reduce the excessive turbulence level,and the eddy-viscosity eliminator based on polynomials is extracted from the cavitation simulations.Surface elevations by combining the eddy-viscosity eliminators and classical two-equation closure models are compared with the experiments,the ones by using the adaptive asymptotic model(AAM)and the ones by using the modified two-equation closure models.The root-mean-squared error(RMSE)is introduced to quantify the accuracies of surface elevations and the forces.The relation between the turbulence level in the transition layer and RMSEs of surface elevations is studied.Besides,the parametric analysis of the eddy-viscosity eliminators is carried out.The studies suggest that(1)the excessive turbulence level in the transition layer around the interface has a significant influence on the accuracies of surface elevations and the forces;(2)the eddy-viscosity eliminators can effectively reduce the excessive turbulence level in the transition layer to avoid the unphysical motion of the interface;(3)the k-ωSST model combined with the eddy-viscosity eliminators is appropriate for predicting surface elevations and forces in RANS simulations of sloshing flow.
文摘Objective: To evaluate left ventricular regional and global systolic function by measuring left ventricular longitudinal strain (LS) in hypertensive patients with sigmoid-shaped interventricular septum (SIS) by two-dimensional speckle tracking (2D-STE);in order to explore whether the sigmoid-shaped interventricular septum affects the left ventricular systolic function in patients with hypertension. Methods: Routine echocardiographic parameters were measured in 30 hypertensive patients with SIS (SIS group) and 30 hypertensive patients without SIS (non-SIS group). The left ventricular segments and global LS were measured by 2D-STE, and the two sets of parameters were compared. Results: The value of the thickness of the basal segment of the interventricular septum (IVSBT), the thickness of the middle segment of the interventricular septum (IVSMT) and the ratio of the basal segment of the ventricular septum to the middle segment of the interventricular septum (IVSBT/IVSMT) in SIS group was higher than that in non-SIS group. However, the value of left ventricular outflow tract diameter (LVOTD) in SIS group was lower than that in non-SIS group. There was a significant difference between the two groups (all P Conclusion: SIS affects left ventricular regional systolic function of patients with hypertension. 2D-STE can early evaluate left ventricular longitudinal systolic function in hypertensive patients with SIS.
文摘针对船舶超大空间火灾对人员疏散能力的影响难以量化问题,本文基于元胞自动机理论,构建了一种行人个体自主分析火灾环境下温度和能见度影响的疏散模型(cellular automata model considering visibility and temperature, CAVT)。CAVT模型采用Sigmoid函数和历史实验数据建立温度、能见度与人员运动能力的映射关系,基于FDS数值模拟结果建立火灾环境场对人员个体运动能力影响的时空耦合关系,使用熵值法计算温度场和能见度场在火灾环境场中的权重。以某客船超大空间为例开展研究分析,结果表明:火灾环境下人员疏散时间受火源功率影响较大,火源位置影响较小,出口宽度大于3 m,不影响疏散效率。与Pathfinder软件相比,CAVT模型可更准确模拟人员因高温和低能见度导致的运动能力的动态下降反馈。
