The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion...The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.展开更多
In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case,...In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.展开更多
This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral ave...This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral averaging technique,new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation.Our results generalize and improve some known theorems.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 11101247 and 11201209)Shandong Provincial Natural Science Foundation of China (Grant No.ZR2011AQ020)+3 种基金a project of Shandong Province Higher Educational Science and Technology Program (GrantNo. J11LE08)supported by National Natural Science Foundation of China (GrantNo. 11101317)supported by National Basic Research Program of China (Grant No.2005CB321701)the Reward Fund of CAS for National Prize
文摘The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.
基金This research is supported by Youth Science Foundation of Beijing Normal University.
文摘In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.
基金Supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2010AM031 and ZR2011AL001the Development Program in Science and Technology of Shandong Province of China under Grant No. 2010GWZ20401
文摘This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral averaging technique,new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation.Our results generalize and improve some known theorems.
