Darboux Transformation for Tzitzeica Equation

We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,

Multi-objective Evolutionary Algorithms for MILP and MINLP in Process Synthesis

Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitness assignment strategy of non-dominated sorting genetic algorithm (NSGA). The fitness assignment strategy is improved and a new self-adjustment scheme of is proposed. This algorithm is proved to be very efficient both computationally and in terms of the quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one. Finally, SNSGA is introduced to solve multi-objective mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP) problems in process synthesis.

The Effective Clustering Partition Algorithm Based on the Genetic Evolution

To the problem that it is hard to determine the clustering number and the abnormal points by using the clustering validity function, an effective clustering partition model based on the genetic algorithm is built in this paper. The solution to the problem is formed by the combination of the clustering partition and the encoding samples, and the fitness function is defined by the distances among and within clusters. The clustering number and the samples in each cluster are determined and the abnormal points are distinguished by implementing the triple random crossover operator and the mutation. Based on the known sample data, the results of the novel method and the clustering validity function are compared. Numerical experiments are given and the results show that the novel method is more effective.

Multi-objective optimization for draft scheduling of hot strip mill

A multi-objective optimization model for draft scheduling of hot strip mill was presented, rolling power minimizing, rolling force ratio distribution and good strip shape as the objective functions. A multi-objective differential evolution algorithm based on decomposition （MODE/D）. The two-objective and three-objective optimization experiments were performed respectively to demonstrate the optimal solutions of trade-off. The simulation results show that MODE/D can obtain a good Pareto-optimal front, which suggests a series of alternative solutions to draft scheduling. The extreme Pareto solutions are found feasible and the centres of the Pareto fronts give a good compromise. The conflict exists between each two ones of three objectives. The final optimal solution is selected from the Pareto-optimal front by the importance of objectives, and it can achieve a better performance in all objective dimensions than the empirical solutions. Finally, the practical application cases confirm the feasibility of the multi-objective approach, and the optimal solutions can gain a better rolling stability than the empirical solutions, and strip flatness decreases from （0± 63） IU to （0±45） IU in industrial production.

A brief review on the strategy for selection of orthology prediction methods in phylogenomic studies

With the development and decreasing cost of sequencing techniques, it is possible for scientists to conduct deeper research in phylogenomics. During the procedure of phylogenomic analysis, the mostimportant and vitalest step is orthology prediction, for that the prerequisite to phylogenetic reconstruction is that the genes being compared are orthologous. Here we briefly review the related concept of orthology anddifferent methods for orthology prediction. We also provide recommendations to give some advice for better selection of orthology prediction methods.

Divisia Decomposition Method and Its Application to Changes of Net Oil Import Intensity

The existing oil import dependence index cannot exactly measure the economic cost or scales, and it is difficult to describe the economical aspect of oil security. To measure the foreign dependence of one country's economy and reflect its oil economic security, this paper defines the net oil import intensity as the ratio of net oil import cost to GDP. By using Divisia Index Decomposition, the change of net oil import intensity in five industrialized countries and five newly industrialized countries during 1971—2010 is decomposed into five factors: oil price, oil intensity, oil self-sufficiency, domestic price level and exchange rate. The result shows that the dominating factors are oil price and oil intensity; moreover, the newly industrialized countries have higher net oil import intensity than industrialized countries.

A Class of Strongly Nonlinear Singular Perturbed Boundary Value Problems

In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.

Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation Using an Extended sinh-Gordon Equation Expansion Method

The sinh-Gordon equation expansion method is further extended by generMizing the sinh-Gordon equation and constructing new ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Konopelchenko-Dubrovsky equation is investigated and abundant exact travelling wave solutions are explicitly obtained including solitary wave solutions, trigonometric function solutions and Jacobi elliptic doubly periodic function solutions, some of which are new exact solutions that we have never seen before within our knowledge. The method can be applied to other nonlinear evolution equations in mathematical physics.

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to （2＋1）-Dimensional Stochastic Dispersive Long Wave System

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the （2＋ 1）-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

β-Cyclodextrin Promoted Oxidation of Cinnamaldehyde to Natural Benzaldehyde in Water

A facile and efficient procedure has been developed systematically for the oxidative cleavage of cinna-maldehyde to benzaldehyde by sodium hypochlorite with water as the only solvent in the presence of β-cyclodextrin （abbreviated as β-CD）. Different factors influencing cinnamaldehyde oxidation e.g. reaction temperature, the amount of catalyst and oxidant, have been investigated. The yield of benzaldehyde reaches 76% under the optimum conditions （333 K, 4 h, molar ratio of cinnamaldehyde to β-CD is 1：1）. Furthermore, a feasible reaction mecha-nism including the formation of benzaldehyde and the two main byproducts （phenylacetaldehyde and epoxide of cinnamaldehyde） has been proposed.

Research on a randomized real-valued negative selection algorithm

A real-valued negative selection algorithm with good mathematical foundation is presented to solve some of the drawbacks of previous approach. Specifically, it can produce a good estimate of the optimal number of detectors needed to cover the non-self space, and the maximization of the non-self coverage is done through an optimization algorithm with proven convergence properties. Experiments are performed to validate the assumptions made while designing the algorithm and to evaluate its performance.

Multi-Objective Genetic Algorithm to Design Manufacturing Process Line Including Feasible and Infeasible Solutions in Neighborhood

This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ordinarily assigned to each center. Here, infeasible solutions are easily generated by precedence relationship of work elements in process design. The number of infeasible solutions generated is ordinarily larger than that of feasible solutions generated in the process. Therefore, feasible and infeasible solutions are located in any neighborhood in solution space. It is difficult to seek high quality Pareto solutions in this problem by using conventional multi-objective evolutional algorithms. We consider that the problem includes difficulty to seek high quality solutions by the following characteristics： （1） Since infeasible solutions are resemble to good feasible solutions, many infeasible solutions which have good values of objective functions are easily sought in the search process, （2） Infeasible solutions are useful to select new variable conditions generating good feasible solutions in search process. In this study, a multi-objective genetic algorithm including local search is proposed using these characteristics. Maximum value of average operation times and maximum value of dispersion of operation time in all work centers are used as objective functions to promote productivity. The optimal weighted coefficient is introduced to control the ratio of feasible solutions to all solutions selected in crossover and selection process in the algorithm. This paper shows the effectiveness of the proposed algorithm on simple model.

Degradation of p-nitrotoluene by O_3/H_2O_2 process and oxidation mechanism

The degradation of p-nitrotoluene by O3/H2O2 process in a bubble contact column was investigated. Effects of the molar ratio of hydrogen peroxide to ozone,pH value and t-butanol on the oxidation process were discussed. It was found that the proper H2O2/O3 molar ratio for the degradation of p-nitrotoluene was around 0.6, different pH values and the presence of t-butanol highly influenced the removal efficiency of p-nitrotoluene. 5-methyl-2-nitrophenol, 2-methyl-5-nitrophenol, (4-nitrophenyl) methanol, 5-(hydroxymethyl)-2-nitro phenol, acetic acid, 2-methylpropane diacid and 2-(hydroxylmethyl)propane diacid were identified as degradation intermediates and products through GC-MS. Radical reaction mechanism and degradation pathway were proposed based on the results of experiments. It is deduced that the benzene ring of p-nitrotoluene can be only destroyed by hydroxyl radicals through a polyhydroxy intermediate pathway. Then unstable polyhydroxy intermediates can be oxidized to different acids with low molecular weight rapidly.

Periodic Solutions of Evolution Variational Inequalities—a Method of Guiding Functions

This paper focuses on a part of the presentation given by the third author at the Shanghai Forum on Industrial and Applied Mathematics(Shanghai 2006).It is related to the existence of a periodic solution of evolution variational inequalities.The approach is based on the method of guiding functions.