Decoupled schemes for unsteady MHD equations. I. time discretization

In this article, a time discretization decoupled scheme for two‐dimensional magnetohydrodynamics equations is proposed. The almost unconditional stability and convergence of this scheme are provided. The optimal error estimates for velocity and magnet are provided, and the optimal error estimate for pressure are deduced as well. Finite element spatial discretization and numerical implementation are considered in our article (Zhang and He, Comput Math Appl 69 (2015), 1390–1406). © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 956–973, 2017     

A note on functional a posteriori estimates for elliptic optimal control problems

In this work, new results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed, and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two‐sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 403–424, 2017     

一个二元叠加码M_q(t,k,d)生成的二元等重码

研究了二元叠加码Mq(t,k,d)也是一个二元等重码,给出了它成为最佳等重码的条件,研究了它的检错性.     

粘性解框架下的完全耦合正倒向随机系统最优控制问题的验证定理

研究了完全耦合正倒向随机控制系统的最优控制问题.得到了粘性解框架下的,控制变量同时出现在正倒向随机系统的漂移项和扩散项中的最优控制问题的验证定理.还讨论了验证定理在构造随机最优反馈控制中的应用.     

Adsorbing behavior of polycarboxylate superplasticizer in the presence of the ester group in side chain

The effect of the ester group in side chain on adsorbing behavior and dispersion of polycarboxylate superplasticizer (PC) was studied by comparing the performance of two types of PC. The fluidity of cement paste was tested to discuss the dispersing ability and dispersing retention ability of PC. The total organic carbon analyzer was used to measure the adsorption amount, and the adsorption layer was obtained by x-ray photoelectron spectroscopy. Fourier-transform infrared spectroscopy, nuclear magnetic resonance, and pH value were used to verify the stability of the ester group, and the electrokinetic properties of cement particle were confirmed using the zeta potential measurement. The results show that the ester group in side chain reduces the initial dispersing ability while it increases the dispersing retention ability. The dispersing retention ability depends on the increase of adsorption amount and adsorption layer in 5–60 minutes, and the greater increase leads to the better dispersing retention ability. The ester group can be decomposed to release carboxyl group to enhance the adsorbing ability of PC under the condition of cement hydration, which is the main reason for the greater increase of adsorption amount and adsorption layer and the improvement in dispersing retention ability. It suggests that grafting the ester group is a good way to enhance the dispersing retention ability.     

Effect of water on the retention on diol and amide columns in hydrophilic interaction liquid chromatography

The amount of water adsorbed on polar columns plays important role in hydrophilic interaction liquid chromatography. It may strongly differ for the individual types of polar columns used in this separation mode. We measured adsorption isotherms of water on an amide and three diol‐bonded stationary phases that differ in the chemistry of the bonded ligands and properties of the silica gel support. We studied the effects of the adsorbed water on the retention of aromatic carboxylic acids, flavonoids, benzoic acid derivatives, nucleic bases, and nucleosides in aqueous‐acetonitrile mobile phases over the full composition range. The graphs of the retention factors versus the volume fraction of water in mobile phase show “U‐profile” characteristic of a dual hydrophilic interaction–reversed phase retention mechanism. The minimum on the graph that marks the changing retention mechanism depends on the amount of adsorbed water. The linear solvation energy relationship model suggests that the retention in the hydrophilic interaction liquid chromatography mode is controlled mainly by proton–donor interactions in the stationary phase, depending on the column type. Finally, the accuracy of hydrophilic interaction liquid chromatography gradient prediction improves for columns that show a high water adsorption.     

Finite Difference Method for an Optimal Control Problem for a Nonlinear Time-dependent Schrödinger Equation

The finite difference method is applied to an optimal control problem for a system governed by a nonlinear Schrödinger equation with a complex coe?cient. The optimal control problem is discretized by the finite difference method, the error estimate for the finite difference scheme is established and the convergence of difference approximations of the optimal control according to the functional is proved.     

A modified pseudospectral method for solving trajectory optimization problems with singular arc

This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.