In this paper,the dynamics of the higher-order soliton solutions for the coupled mixed derivative nonlinear Schrodinger equation¨are investigated via generalized Darboux transformation.Given a pair of linearly in...In this paper,the dynamics of the higher-order soliton solutions for the coupled mixed derivative nonlinear Schrodinger equation¨are investigated via generalized Darboux transformation.Given a pair of linearly independent solutions of the Lax pair,the oneto three-soliton solutions are obtained via algebraic iteration.Furthermore,two and three solitons are respectively displayed via numerical simulation.Moreover,the dynamics of solitons are illustrated with corresponding evolution plots,such as elastic collisions,inelastic collisions,and bound states.It is found that there are some novel phenomena of interactions among solitons,which may provide a theoretical basis for studying optical solitons in experiments.展开更多
Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asympt...Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.展开更多
The Editor welcomes submissions for possible publication in the Letters to the Editor section that consist of commentary on an article published in the Journal or other relevant issues. Letters commenting on an artic...The Editor welcomes submissions for possible publication in the Letters to the Editor section that consist of commentary on an article published in the Journal or other relevant issues. Letters commenting on an article published in the Journal will be considered if they are received within 6 weeks of the time the article was published. Authors of the article being commented on will be given an展开更多
The study on options for catalytic cracking of VGO derived from the Kazakhstan-Russian mixed crude was carried out in a small-scale riser FCC unit. The influence of several catalysts and the LCC-A additive for increas...The study on options for catalytic cracking of VGO derived from the Kazakhstan-Russian mixed crude was carried out in a small-scale riser FCC unit. The influence of several catalysts and the LCC-A additive for increasing propylene yield on the distribution and quality of FCC products was analyzed. This article sets forth the possible issues arising from processing the Kazakhstan-Russian mixed crude in FCC unit and the response measures to be adopted.展开更多
In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \...In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11602232)Shanxi Natural Science Foundation(Grant No.201901D111179)the Fund for Shanxi(Grant 1331KIRT).
文摘In this paper,the dynamics of the higher-order soliton solutions for the coupled mixed derivative nonlinear Schrodinger equation¨are investigated via generalized Darboux transformation.Given a pair of linearly independent solutions of the Lax pair,the oneto three-soliton solutions are obtained via algebraic iteration.Furthermore,two and three solitons are respectively displayed via numerical simulation.Moreover,the dynamics of solitons are illustrated with corresponding evolution plots,such as elastic collisions,inelastic collisions,and bound states.It is found that there are some novel phenomena of interactions among solitons,which may provide a theoretical basis for studying optical solitons in experiments.
基金supported by the Natural Science Foundation of China (Grant No.10671019)Research Fund for the Doctoral Program of Higher Education (Grant No.20050027007)
文摘Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.
文摘The Editor welcomes submissions for possible publication in the Letters to the Editor section that consist of commentary on an article published in the Journal or other relevant issues. Letters commenting on an article published in the Journal will be considered if they are received within 6 weeks of the time the article was published. Authors of the article being commented on will be given an
文摘The study on options for catalytic cracking of VGO derived from the Kazakhstan-Russian mixed crude was carried out in a small-scale riser FCC unit. The influence of several catalysts and the LCC-A additive for increasing propylene yield on the distribution and quality of FCC products was analyzed. This article sets forth the possible issues arising from processing the Kazakhstan-Russian mixed crude in FCC unit and the response measures to be adopted.
基金supported by the National Natural Science Foundation of China (Grant No. 10671019)the Research Fund for the Doctoral Program of Higher Education (Grant No. 20050027007)
文摘In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW p,α r ( $ \mathbb{T}^d $ ), 1 < p < ∞, in the norm of L q ( $ \mathbb{T}^d $ ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem.
