In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0...In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0≤j≤n-3)a1(ε)u(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer corrections.Under some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved.展开更多
Active semi-supervised fuzzy clustering integrates fuzzy clustering techniques with limited labeled data,guided by active learning,to enhance classification accuracy,particularly in complex and ambiguous datasets.Alth...Active semi-supervised fuzzy clustering integrates fuzzy clustering techniques with limited labeled data,guided by active learning,to enhance classification accuracy,particularly in complex and ambiguous datasets.Although several active semi-supervised fuzzy clustering methods have been developed previously,they typically face significant limitations,including high computational complexity,sensitivity to initial cluster centroids,and difficulties in accurately managing boundary clusters where data points often overlap among multiple clusters.This study introduces a novel Active Semi-Supervised Fuzzy Clustering algorithm specifically designed to identify,analyze,and correct misclassified boundary elements.By strategically utilizing labeled data through active learning,our method improves the robustness and precision of cluster boundary assignments.Extensive experimental evaluations conducted on three types of datasets—including benchmark UCI datasets,synthetic data with controlled boundary overlap,and satellite imagery—demonstrate that our proposed approach achieves superior performance in terms of clustering accuracy and robustness compared to existing active semi-supervised fuzzy clustering methods.The results confirm the effectiveness and practicality of our method in handling real-world scenarios where precise cluster boundaries are critical.展开更多
We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains.The discretization...We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains.The discretization is defined on a body-fitted triangular mesh,i.e.the boundary nodes of the mesh lie on the curved physical boundary.However,the boundary edges of the triangular mesh,which are straight,may not coincide with the curved physical boundary.A boundary value correction technique is then designed to transform the Neumann boundary condition from the physical boundary to the boundary of the triangular mesh.One advantage of the boundary value correction method is that it avoids using curved mesh elements and thus reduces the complexity of implementation.We prove that the proposed method reaches optimal convergence for arbitrary order discretizations.Supporting numerical results are presented.展开更多
In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales￣[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver...In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales￣[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver-Stodes equations.展开更多
Hypersonic high-enthalpy wind tunnels have been a challenge to ground tests in aerospace research area for decades and its test flow uniformity is one of the most important parameters for evaluating wind tunnel perfor...Hypersonic high-enthalpy wind tunnels have been a challenge to ground tests in aerospace research area for decades and its test flow uniformity is one of the most important parameters for evaluating wind tunnel performances.Regarding to the performance requirement,theories and methods for designing hypersonic flow nozzles at high enthalpy conditions are quite difficult,but very interesting topics,especially when air molecule dissociations take place in wind tunnel test gas reservoirs.In this paper,fundamental theories and important methods for nozzle designs are briefly reviewed with the emphasis on two-dimensional axisymmetric nozzles for hypersonic high-enthalpy wind tunnels,including the Method of Characteristics(MOC),the graphic design method,the Sivells method,the theory for boundary correction,and the CFD-based design optimization methods.These theories and methods had been proposed based on several physical issues,respectively,which play important roles in nozzle flow expansion processes.These issues cover the expansion wave generation and reflection,the boundary layer development,the real gas effect of hypersonic high-enthalpy flows.Difficulties arising from applications of these methods in hypersonic high-enthalpy nozzle design are discussed in detail and the state of the art of the nozzle design technologies that have reached for decades is summarized with some brief comments.Finally,the prospect for the hypersonic nozzle design methods,and its numerical and experimental verifications are provided with from authors’viewpoint for readers’reference.展开更多
The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying b...The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying boundary evaluations. Experimental tests prove that range errors caused by the fluctuation of the number of photon counts in the laser echo pulse leads to the range drift of the time point spread function. The function relationship between the range error and the photon counting ratio is determined by using numerical fitting.Range errors due to a different echo energy is calibrated so that the corrected range root mean square error is improved to 1 cm.展开更多
文摘In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0≤j≤n-3)a1(ε)u(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer corrections.Under some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved.
文摘Active semi-supervised fuzzy clustering integrates fuzzy clustering techniques with limited labeled data,guided by active learning,to enhance classification accuracy,particularly in complex and ambiguous datasets.Although several active semi-supervised fuzzy clustering methods have been developed previously,they typically face significant limitations,including high computational complexity,sensitivity to initial cluster centroids,and difficulties in accurately managing boundary clusters where data points often overlap among multiple clusters.This study introduces a novel Active Semi-Supervised Fuzzy Clustering algorithm specifically designed to identify,analyze,and correct misclassified boundary elements.By strategically utilizing labeled data through active learning,our method improves the robustness and precision of cluster boundary assignments.Extensive experimental evaluations conducted on three types of datasets—including benchmark UCI datasets,synthetic data with controlled boundary overlap,and satellite imagery—demonstrate that our proposed approach achieves superior performance in terms of clustering accuracy and robustness compared to existing active semi-supervised fuzzy clustering methods.The results confirm the effectiveness and practicality of our method in handling real-world scenarios where precise cluster boundaries are critical.
基金supported by the National Natural Science Foundation of China under Grant No.12171244.
文摘We propose a boundary value correction method for the Brezzi-Douglas-Marini mixed finite element discretization of the Darcy flow with non-homogeneous Neumann boundary condition on 2D curved domains.The discretization is defined on a body-fitted triangular mesh,i.e.the boundary nodes of the mesh lie on the curved physical boundary.However,the boundary edges of the triangular mesh,which are straight,may not coincide with the curved physical boundary.A boundary value correction technique is then designed to transform the Neumann boundary condition from the physical boundary to the boundary of the triangular mesh.One advantage of the boundary value correction method is that it avoids using curved mesh elements and thus reduces the complexity of implementation.We prove that the proposed method reaches optimal convergence for arbitrary order discretizations.Supporting numerical results are presented.
文摘In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales￣[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver-Stodes equations.
基金co-supported by the National Natural Science Foundation of China(Nos.11672357,11727901).
文摘Hypersonic high-enthalpy wind tunnels have been a challenge to ground tests in aerospace research area for decades and its test flow uniformity is one of the most important parameters for evaluating wind tunnel performances.Regarding to the performance requirement,theories and methods for designing hypersonic flow nozzles at high enthalpy conditions are quite difficult,but very interesting topics,especially when air molecule dissociations take place in wind tunnel test gas reservoirs.In this paper,fundamental theories and important methods for nozzle designs are briefly reviewed with the emphasis on two-dimensional axisymmetric nozzles for hypersonic high-enthalpy wind tunnels,including the Method of Characteristics(MOC),the graphic design method,the Sivells method,the theory for boundary correction,and the CFD-based design optimization methods.These theories and methods had been proposed based on several physical issues,respectively,which play important roles in nozzle flow expansion processes.These issues cover the expansion wave generation and reflection,the boundary layer development,the real gas effect of hypersonic high-enthalpy flows.Difficulties arising from applications of these methods in hypersonic high-enthalpy nozzle design are discussed in detail and the state of the art of the nozzle design technologies that have reached for decades is summarized with some brief comments.Finally,the prospect for the hypersonic nozzle design methods,and its numerical and experimental verifications are provided with from authors’viewpoint for readers’reference.
基金supported by the National Natural Science Foundation of China(Nos.61101196 and 61271332)the Natural Science Research Foundation of Jiangsu Province(No.168JB510015)
文摘The Cramer–Rao lower bound on range error is modeled for pseudo-random ranging systems using Geiger-mode avalanche photodiodes. The theoretical results are shown to agree with the Monte Carlo simulation, satisfying boundary evaluations. Experimental tests prove that range errors caused by the fluctuation of the number of photon counts in the laser echo pulse leads to the range drift of the time point spread function. The function relationship between the range error and the photon counting ratio is determined by using numerical fitting.Range errors due to a different echo energy is calibrated so that the corrected range root mean square error is improved to 1 cm.
