The corrosion of coal mine equipment immersed in coal slurry is addressed. The corrosion of low carbon steel samples immersed in coal slurries of different concentrations （80, 130, and 180g/L） prepared from coals of...The corrosion of coal mine equipment immersed in coal slurry is addressed. The corrosion of low carbon steel samples immersed in coal slurries of different concentrations （80, 130, and 180g/L） prepared from coals of different rank （long-flame coal, meager lean coal, and anthracite） and different granularity （0.25-0.5 ram, 0.074-0.25 mm, and less than 0.074 mm particle size） was studied by the electrochemical method of polarization curve measurement, controlled potential sweeping, and continuous scanning. The results show that the corrosion rate in an anthracite slurry, where the coal has high coalification, is far greater than corrosion in a long-flame or a meager lean coal slurry. Furthermore the corrosion current, polarization current, and corrosion rate of low carbon steel become larger, and the polarizability becomes smaller, as the coal particle size decreases. The same trend is seen as the concentration of the coal slurry increases.展开更多
In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a cla...In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.展开更多
Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We first...Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We firstly establish the uniqueness for this inverse problem, which provides the theoretical basis for the reconstruction scheme. Then based on the contrast source inversion(CSI) method, we propose an algorithm determining the refraction index and the artificial wave sources alternately by a dynamic iterative scheme. The algorithm defines the iterates by solving a series of minimization problems with uniformly convex penalty terms, which are allowed to be non-smooth to include L1 and total variation like functionals, ensuring the reconstruction quality when the unknown refraction index has the special features such as sparsity and discontinuity. By choosing the regularizing parameter automatically, the algorithm is terminated in terms of discrepancy principle. The convergence property of the iterative sequence is rigorously proven. Numerical implementations demonstrate the validity of the proposed algorithm.展开更多
We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is c...We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.展开更多
基金subsidized by the National Natural Science Foundation of China for Innovative Research Group (No.50921002)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘The corrosion of coal mine equipment immersed in coal slurry is addressed. The corrosion of low carbon steel samples immersed in coal slurries of different concentrations （80, 130, and 180g/L） prepared from coals of different rank （long-flame coal, meager lean coal, and anthracite） and different granularity （0.25-0.5 ram, 0.074-0.25 mm, and less than 0.074 mm particle size） was studied by the electrochemical method of polarization curve measurement, controlled potential sweeping, and continuous scanning. The results show that the corrosion rate in an anthracite slurry, where the coal has high coalification, is far greater than corrosion in a long-flame or a meager lean coal slurry. Furthermore the corrosion current, polarization current, and corrosion rate of low carbon steel become larger, and the polarizability becomes smaller, as the coal particle size decreases. The same trend is seen as the concentration of the coal slurry increases.
文摘In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.
基金supported by National Natural Science Foundation of China(Grant Nos.11421110002,11531005 and 11501102)National Science Foundation of Jiangsu Province(Grant No.BK20150594)
文摘Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We firstly establish the uniqueness for this inverse problem, which provides the theoretical basis for the reconstruction scheme. Then based on the contrast source inversion(CSI) method, we propose an algorithm determining the refraction index and the artificial wave sources alternately by a dynamic iterative scheme. The algorithm defines the iterates by solving a series of minimization problems with uniformly convex penalty terms, which are allowed to be non-smooth to include L1 and total variation like functionals, ensuring the reconstruction quality when the unknown refraction index has the special features such as sparsity and discontinuity. By choosing the regularizing parameter automatically, the algorithm is terminated in terms of discrepancy principle. The convergence property of the iterative sequence is rigorously proven. Numerical implementations demonstrate the validity of the proposed algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.1136103011271049 and 11271049)+5 种基金the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry(Grant Nos.CUHK400412HKBU502814211911and 12302714)Hong Kong Research Grants Council(Grant No.Ao E/M-05/12)FRGs of Hong Kong Baptist University
文摘We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.
