针对光学显微镜景深扩展中的多聚焦图像融合问题,提出了一种基于方向特性的新轮廓波域多聚焦图像融合算法。该算法首先对图像进行新轮廓波变换(New Contourlet Transform with Sharp Frequency Localization,NCT-SFL),分解得到不同尺度...针对光学显微镜景深扩展中的多聚焦图像融合问题,提出了一种基于方向特性的新轮廓波域多聚焦图像融合算法。该算法首先对图像进行新轮廓波变换(New Contourlet Transform with Sharp Frequency Localization,NCT-SFL),分解得到不同尺度、不同方向的高低频系数,低频系数融合使用算术平均法,高频系数融合分为两步:先采用改进拉普拉斯能量和(Sum Modified Laplacian,SML)提取特征值;然后定义新的与方向分解一一对应的椭圆方向窗,在确定的椭圆窗参数下,对提取的特征值进行累加并以此为依据对高频系数进行融合,最后通过反新轮廓波变换得到融合图像。在实验部分用定义的新的客观评价指标互结构信息(Mutual Structural Information,MSI)对融合算法进行了评价,结果表明:对多聚焦图像本文所提方法比新轮廓波域方形窗算法MSI提高了2.94%,比Contourlet域方形窗与椭圆窗算法MSI分别提高了10.44%和8.56%。说明本文方法能提取源图像中更多的清晰信息到融合图像,是一种有效的景深扩展手段。展开更多
The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary ...The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.展开更多
A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficien...A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficient KdV equation under an external forcing isderived for large amplitude equatorial Rossby wave in a shear How. And then various periodic-likestructures for these equatorial Rossby waves are obtained with the help of Jacobi ellipticfunctions. It is shown that the external forcing plays an important role in various periodic-likestructures.展开更多
We study a generalized nonlinear Schrodinger equation, and obtain some exact solutions, including domain wall arrays （periodic solutions in terms of elliptic functions）, fronts, bright and dark solitons. In certain ...We study a generalized nonlinear Schrodinger equation, and obtain some exact solutions, including domain wall arrays （periodic solutions in terms of elliptic functions）, fronts, bright and dark solitons. In certain parameter domains, fundamental bright and dark solitons show directionality and hence are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. Moreover, the chirping reversal phenomena of bright and dark solitons are found.展开更多
By using function one direction S-rough sets （function one direction singular rough sets）, the concept of one direction rough law is proposed, where one direction rough law is the law pair { w（x）-, w（x） - } comp...By using function one direction S-rough sets （function one direction singular rough sets）, the concept of one direction rough law is proposed, where one direction rough law is the law pair { w（x）-, w（x） - } composed by w（x）- and w（x）-, ffthe attribute set {a_ , a-} of function one direction S-rough sets changes, then one direction rough law { w（x）_, w（x）- } will change, too. By employing ellipse curves, the concept of one direction rough law security is presented, the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security, which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves, is a new applied research direction of function S-rough sets.展开更多
In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N...In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.展开更多
We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet...We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.展开更多
This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, un...This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, under some local conditions on K(y), this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2),there exists solutions whose functional energy is in the order of ε^(-(N-2-m)/((N-2)~2)).展开更多
文摘The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.
文摘A simple shallow-water model with influence of external forcing on a β-planeis applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By theperturbation method, the extended variable-coefficient KdV equation under an external forcing isderived for large amplitude equatorial Rossby wave in a shear How. And then various periodic-likestructures for these equatorial Rossby waves are obtained with the help of Jacobi ellipticfunctions. It is shown that the external forcing plays an important role in various periodic-likestructures.
基金Supported by the National Natural Science Foundation of China under Grant No.11005092the Program for Innovative Research Team of Young Teachers in Zhejiang A & F University under Grant No.2009RC01the Scientific Research and Developed Fund of Zhejiang A & F University under Grant Nos.2351000928,2009FK42
文摘We study a generalized nonlinear Schrodinger equation, and obtain some exact solutions, including domain wall arrays （periodic solutions in terms of elliptic functions）, fronts, bright and dark solitons. In certain parameter domains, fundamental bright and dark solitons show directionality and hence are chiral, and the propagation direction is determined by the sign of the self-steepening parameter. Moreover, the chirping reversal phenomena of bright and dark solitons are found.
基金Natural Science Foundation of Fujian Province of China( No.2009J01293)Open Project of Brain-like Key Laboratory Research of Fujian Province of China (No. BLISSOS20101015)
文摘By using function one direction S-rough sets （function one direction singular rough sets）, the concept of one direction rough law is proposed, where one direction rough law is the law pair { w（x）-, w（x） - } composed by w（x）- and w（x）-, ffthe attribute set {a_ , a-} of function one direction S-rough sets changes, then one direction rough law { w（x）_, w（x）- } will change, too. By employing ellipse curves, the concept of one direction rough law security is presented, the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security, which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves, is a new applied research direction of function S-rough sets.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901112, 11001255)Beijing Natural Science Foundation (Grant No. 1102013)China Postdoctoral Science Foundation (Grant No. 20090460548)
文摘In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.
基金supported by National Natural Science Foundation of China (Grant No. 11471141)the Basic Research of the Science and Technology Development Program of Jilin Province (Grant No. 20150101058JC)
文摘We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.
基金Tian Yuan Special Funds of National Natural Science Foundation of China (Grant No. 11426088)
文摘This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, under some local conditions on K(y), this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2),there exists solutions whose functional energy is in the order of ε^(-(N-2-m)/((N-2)~2)).
