Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
Time series bioaccumulation of rare earth elements （REEs） in field-grown wheat with and without a dressing of extraneous REE fertilizer at different growth stages and fractionation of REEs during their transport in ...Time series bioaccumulation of rare earth elements （REEs） in field-grown wheat with and without a dressing of extraneous REE fertilizer at different growth stages and fractionation of REEs during their transport in a soil-wheat system were determined. Time-dependent accumulation of extraneous REEs was found in different parts of wheat. An upward transport of extraneous REEs from roots to shoots under a soil dressing and a downward transport from leaves to roots with a foliar dressing were also observed. Moreover, fractionation of REEs occurred in the soil-wheat system. Compared to the host soil a positive Eu anomaly in the stems and grains as well as heavy REE enrichment in the grains were found. The ability of the different wheat organs to fractionate Eu from the REE series was ranked in the order of sterns 〉 grains 〉 leaves 〉 roots.展开更多
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
基金The project supported by Scientific Research Fund of Heilongjiang Province of China under Grant No. 11511008The author would like to thank referees for their valuable suggestions.
文摘Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.
基金Project supported by the National Natural Science Foundation of China (Nos. 40232022 and 40571146).
文摘Time series bioaccumulation of rare earth elements （REEs） in field-grown wheat with and without a dressing of extraneous REE fertilizer at different growth stages and fractionation of REEs during their transport in a soil-wheat system were determined. Time-dependent accumulation of extraneous REEs was found in different parts of wheat. An upward transport of extraneous REEs from roots to shoots under a soil dressing and a downward transport from leaves to roots with a foliar dressing were also observed. Moreover, fractionation of REEs occurred in the soil-wheat system. Compared to the host soil a positive Eu anomaly in the stems and grains as well as heavy REE enrichment in the grains were found. The ability of the different wheat organs to fractionate Eu from the REE series was ranked in the order of sterns 〉 grains 〉 leaves 〉 roots.
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.
