This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we o...This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we obtain an L^(P)-result(p>2),including the existence and uniqueness of the p-th power integrable solution,a p-th power estimate,and a related continuous dependence property of the solution on the coefficients,for coupled linear FBSDEs in the monotonicity framework over large time intervals.In order to get rid of the stubborn constraint commonly existing in the literature,i.e.,the Lipschitz constant of σ with respect to z is very small,we introduce a linear transformation to overcome the difficulty on small intervals,and then"splice"the L^(P)-results obtained on many small intervals to yield the desired one on a large interval.展开更多
In this short note,we give a proof of our partial C^0-estimate for Kähler-Einstein metrics.Our proof uses a compactness theorem of Cheeger-Colding-Tian and L^2-estimate for∂^--operator.
In this work, we will prove the existence of bounded solutions m W0' (f) N L (fl) for nonlinear elliptic equations - div(a(x,u, Vu)) +g(x,u,Vu) + H(x, Vu) = f, where a, g and H are Carath6odory function...In this work, we will prove the existence of bounded solutions m W0' (f) N L (fl) for nonlinear elliptic equations - div(a(x,u, Vu)) +g(x,u,Vu) + H(x, Vu) = f, where a, g and H are Carath6odory functions which satisfy some conditions, and the rizht hand side f belongs to W-l'q (Ω).展开更多
We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation law with degenerate viscosity in several dimensions on the half-line space, where the ...We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L2-energy method and L1-estimate.展开更多
We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimat...We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.展开更多
The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l...The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).展开更多
We study conditions of Hormander's L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander's L^(2)-estimate under...We study conditions of Hormander's L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander's L^(2)-estimate under some regularity assumptions on an n-dimensional domain.This result is a partial generalization of the one-dimensional result obtained by Berndtsson(1998).We also define new positivity notions for vector bundles with singular Hermitian metrics by using these conditions.We investigate these positivity notions and compare them with classical positivity notions.展开更多
Support vector machine (SVM) technique has recently become a research focus in intrusion detection field for its better generalization performance when given less priori knowledge than other soft-computing techniques....Support vector machine (SVM) technique has recently become a research focus in intrusion detection field for its better generalization performance when given less priori knowledge than other soft-computing techniques. But the randomicity of parameter selection in its implement often prevents it achieving expected performance. By utilizing genetic algorithm (GA) to optimize the parameters in data preprocessing and the training model of SVM simultaneously, a hybrid optimization algorithm is proposed in the paper to address this problem. The experimental results demonstrate that it’s an effective method and can improve the performance of SVM-based intrusion detection system further.展开更多
When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot ...When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.展开更多
The authors will use a method in metric geometry to show an L^(P)-estimate for gradient of the weak solutions to elliptic equations with discontinuous coefficients,even the BMO semi-norms of the coefficients are not s...The authors will use a method in metric geometry to show an L^(P)-estimate for gradient of the weak solutions to elliptic equations with discontinuous coefficients,even the BMO semi-norms of the coefficients are not small.They also extend them to the weak solutions to parabolic equations.展开更多
We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R+ = (0, ∞),with the Dirichlet boundary condition u(0, t) = 0. S. Kawashima and Y. Tanaka [Kyushu...We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R+ = (0, ∞),with the Dirichlet boundary condition u(0, t) = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58(2004), 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u+. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution (u, q) is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.展开更多
The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)...The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)-estimate was used by Jeffres-MazzeoRubinstein in their proof of the existence of K¨ahler-Einstein metrics with conic singularities.展开更多
In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We ...In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We consider a fully discrete second order backward difference formula based on a finite element method to approximate the temperature and electric potential,and establish optimal L^(2) error estimates for the fully discrete finite element solution without any restriction on the time-step size.The discrete solution is bounded in infinite norm.Finally,several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11871310,12271304 and 11971262)the Natural Science Foundation of Shandong Province(Grant No.ZR2020MA014)。
文摘This paper is concerned with coupled linear forward-backward stochastic differential equations(FBSDEs,for short).When the homogeneous coefficients are deterministic(the non-homogeneous coefficients can be random),we obtain an L^(P)-result(p>2),including the existence and uniqueness of the p-th power integrable solution,a p-th power estimate,and a related continuous dependence property of the solution on the coefficients,for coupled linear FBSDEs in the monotonicity framework over large time intervals.In order to get rid of the stubborn constraint commonly existing in the literature,i.e.,the Lipschitz constant of σ with respect to z is very small,we introduce a linear transformation to overcome the difficulty on small intervals,and then"splice"the L^(P)-results obtained on many small intervals to yield the desired one on a large interval.
文摘In this short note,we give a proof of our partial C^0-estimate for Kähler-Einstein metrics.Our proof uses a compactness theorem of Cheeger-Colding-Tian and L^2-estimate for∂^--operator.
文摘In this work, we will prove the existence of bounded solutions m W0' (f) N L (fl) for nonlinear elliptic equations - div(a(x,u, Vu)) +g(x,u,Vu) + H(x, Vu) = f, where a, g and H are Carath6odory functions which satisfy some conditions, and the rizht hand side f belongs to W-l'q (Ω).
基金supported by the NSF of China (10625105,10431060)the Program for New Centary Excellent Talents in University (NCEF-04-0745)
文摘We investigate the decay rates of the planar viscous rarefaction wave of the initial-boundary value problem to scalar conservation law with degenerate viscosity in several dimensions on the half-line space, where the corresponding one-dimensional problem admits the rarefaction wave as an asymptotic state. The analysis is based on the standard L2-energy method and L1-estimate.
基金supported by Le Centre de recherche en géométrie et topologie Fellowship during the visit to Institut des sciences mathématiques of Universitédu QuébecàMontréal。
文摘We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.
基金supported by the National Science Foundation of China under Grant Nos.61573342,61473126the Key Research Program of Frontier Sciences,Chinese Academy of Sciences,under Grant No.QYZDJ-SSWSYS011 the Fundamental Research Funds for the Central Universities
文摘The authors establish weighted L^2-estimates of solutions for the damped wave equations with variable coefficients utt-div A(x)▽u + au_t = 0 in IR^nunder the assumption a(x) ≥ a_0[1 + ρ(x)]^(-l),where a_0 > 0, l < 1, ρ(x) is the distance function of the metric g = A^(-1)(x) on IR^n. The authors show that these weighted L^2-estimates are closely related to the geometrical properties of the metric g = A^(-1)(x).
基金supported by the Program for Leading Graduate Schools,the Ministry of Education,Culture,Sports,Science and Technology,Japan,and Japan Society for the Promotion of Science,Grants-in-Aid for Scientific Research(Grant No.18J22119)。
文摘We study conditions of Hormander's L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander's L^(2)-estimate under some regularity assumptions on an n-dimensional domain.This result is a partial generalization of the one-dimensional result obtained by Berndtsson(1998).We also define new positivity notions for vector bundles with singular Hermitian metrics by using these conditions.We investigate these positivity notions and compare them with classical positivity notions.
基金This work was supported by the Research Grant of SEC E-Institute :Shanghai High Institution Grid and the Science Foundation ofShanghai Municipal Commission of Science and Technology No.00JC14052
文摘Support vector machine (SVM) technique has recently become a research focus in intrusion detection field for its better generalization performance when given less priori knowledge than other soft-computing techniques. But the randomicity of parameter selection in its implement often prevents it achieving expected performance. By utilizing genetic algorithm (GA) to optimize the parameters in data preprocessing and the training model of SVM simultaneously, a hybrid optimization algorithm is proposed in the paper to address this problem. The experimental results demonstrate that it’s an effective method and can improve the performance of SVM-based intrusion detection system further.
基金supported by the National Natural Science Foundation of China under Grant Nos.12271294,12171225 and 12071248.
文摘When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.
基金supported by the National Key R&D Program of China(No.2021YFA1003001).
文摘The authors will use a method in metric geometry to show an L^(P)-estimate for gradient of the weak solutions to elliptic equations with discontinuous coefficients,even the BMO semi-norms of the coefficients are not small.They also extend them to the weak solutions to parabolic equations.
基金The research was supported by the National Natural Science Foundation of China #10625105 and #10431060, the Program for New Century Excellent Talents in University #NCET-04-0745. Acknowledgement Authors would like to thank the anonymous referee for his/her helpful suggestions and comments.
文摘We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R+ = (0, ∞),with the Dirichlet boundary condition u(0, t) = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58(2004), 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u+. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution (u, q) is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.
文摘The author applies the arguments in his PKU Master degree thesis in 1988 to derive a third derivative estimate, and consequently, a C^(2,α)-estimate, for complex MongeAmpere equations in the conic case. This C^(2,α)-estimate was used by Jeffres-MazzeoRubinstein in their proof of the existence of K¨ahler-Einstein metrics with conic singularities.
基金supported by National Natural Science Foundation of China(Grant Nos.11871451,12071485 and 12071035)supported by the University of Chinese Academy of Sciencessupported by Beijing Natural Science Foundation(Grant Nos.1202012 and Z190003)。
文摘We give characterizations of(quasi-)plurisubharmonic functions in terms of L^(p)-estimates of■and Lp-extensions of holomorphic functions.
文摘In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We consider a fully discrete second order backward difference formula based on a finite element method to approximate the temperature and electric potential,and establish optimal L^(2) error estimates for the fully discrete finite element solution without any restriction on the time-step size.The discrete solution is bounded in infinite norm.Finally,several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.