Development of new triangular elements for free surface flows

New finite elements have been developed to simulate steady and unsteady two-dimensional free surface flows. The depth-averaged velocity components with the free surface elevation have been used as independent variables in the model. The differences between the various elements presented lie in the choice of velocity approximation. The Newton–Raphson method has been used to solve the non-linear system of equations. Emphasis is put on bench-mark examples to assess the accuracy and efficiency of the elements. A simple stable new element tested herein shows promising advantages for industrial finite element codes.     

On the discounted penalty function in the renewal risk model with general interclaim times

The defective renewal equation satisfied by the Gerber-Shiu discounted penalty function in the renewal risk model with arbitrary interclaim times is analyzed. The ladder height distribution is shown to be a mixture of residual lifetime claim severity distributions, which results in an invariance property satisfied by a large class of claim amount models. The class of exponential claim size distributions is considered, and the Laplace transform of the (discounted) defective density of the surplus immediately prior to ruin is obtained. The mixed Erlang claim size class is also examined. The simplified defective renewal equation which results when the penalty function only involves the deficit is used to obtain moments of the discounted deficit.     

Estimation of covariance matrices in fixed and mixed effects linear models

The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein–Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linear models.     

Bubble—函数稳定化混合有限元分析

本文针对混合结构抽象问题，基于「９」的非标准稳定化有限元方法的一般框架研究了ｂｕｂｂｌｅ－函数稳定化方法，该逼近代格式使得Ｂａｂｕｓｋａ－Ｂｒｅｚｚｉ条件是不必要的。     

表面活性剂在水溶液中聚集状态的1H NMR研究

表面活性剂在水溶液中的自扩散系数,¹H化学位移和自旋晶格弛豫的NMR测量表明,上述参数随表面活性剂浓度而变化,并在某一浓度开始有转折点.这一转折点恰好对应着各自的临界胶团浓度.表面活性剂分子的不同基团的质子化学位移随其浓度变化幅度的不同提供胶团形成的分子水平描述.     

A mixed integer programming model for advanced planning and scheduling (APS)

This paper presents a mixed integer programming (MIP) model which succeeds in a system integration of the production planning and shop floor scheduling problems. The proposed advanced planning and scheduling (APS) model explicitly considers capacity constraints, operation sequences, lead times and due dates in a multi-order environment. The objective of the model is to seek the minimum cost of both production idle time and tardiness or earliness penalty of an order. The output of the model is operation schedules with order starting time and finish time. Numerical result shows that the suggested APS model can favorably produce optimal schedules.     

Fixed points for mixed monotone multivalued operators in Banach spaces with applications

In this paper, the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed. We present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition. We also give some applications to differential inclusions with discontinuous right hand side in Banach spaces and to Hammerstein integral inclusions on RN.     

Transport properties of polymer–aluminophosphate nano-composites prepared by simple mixing

Nano-composite polymer–aluminophosphate membranes do not have molecular sieving properties as previously claimed. The layered microporous aluminophosphate [Al₃P₄O₁₆]⁺·3[NH₃CH₂CH₃]⁻ was swollen with a surfactant and incorporated into cellulose acetate, Matrimid 5218©, UDEL P-3500©, PDMS, and a PDMS–6FDA–6FpDA co-polymer using simple mixing in organic solvents. It was anticipated that the addition of layered, microporous aluminophosphate to the polymer matrices would enhance the selectivity of large gas species compared to small gases through a molecular sieving effect. However, the selectivity was not improved using this technique due to insufficient exfoliation of the aluminophosphate and low dispersion of the particles into the respective polymer matrices.     

A continuous approach for the concave cost supply problem via DC programming and DCA

The paper addresses an important but difficult class of concave cost supply management problems which consist in minimizing a separable increasing concave objective function subject to linear and disjunctive constraints. We first recast these problems into mixed zero-one nondifferentiable concave minimization over linear constraints problems and then apply exact penalty techniques to state equivalent nondifferentiable polyhedral DC (Difference of Convex functions) programs. A new deterministic approach based on DC programming and DCA (DC Algorithms) is investigated to solve the latter ones. Finally numerical simulations are reported which show the efficiency, the robustness and the globality of our approach.     

Well-Posedness for Mixed Quasivariational-Like Inequalities

In this paper, we introduce concepts of well-posedness, and well-posedness in the generalized sense, for mixed quasivariational-like inequalities where the underlying map is multivalued. We give necessary and sufficient conditions for the various kinds of well-posedness to occur. Our results generalize and strengthen previously found results for variational and quasivariational inequalities. Part of this research was done while the second and the third authors were visiting the Department of Applied Mathematics, National Sun-Yat-Sen University. The authors wish to thank the Department for its hospitality.