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A simple theoretical model was developed to predict equilibrium between precipitate and matrix in a multicomponent microalloyed steel. The solute concentration in the matrix, the composition and the volume fraction of the precipitated second phases, and the reduction in critical precipitation temperature of AlN induced by carbonitride were quantified by the proposed thermodynamic model. The results predicted by the developed model and those by other approaches are in a good agreement. The main advantages of this model over the existing models are that the process of formulation derivation is simple and the model can be easily solved by a personal program.

A kinetic model based on the classical nucleation and growth theory has been proposed to predict the precipitation behavior of complex precipitate. The method for calculating absolute solution temperature, which is an important guidance for determining solution treatment temperature, is also proposed based on thermodynamic model. In the model, nucleation of the second phase is assumed to be controlled by the effective diffusion, which involves the bulk diffusion and dislocation pipe diffusion, and growth is controlled by the bulk diffusion of forming elements. The interfacial energy of complex precipitate is calculated by the linear interpolation method, and the effects of alloying elements on precipitation behavior are manifested using weighted means of their diffusivities and concentration. The predictions were compared with the experimental measurements, and a good agreement was obtained.

An asymmetric synthesis of 14-methyl-1-octadecene, the sex pheromone of the peach leafminer moth has been achieved. The target molecule was synthesized in six linear steps and in 30.3% overall yield from commercially available hexanoyl chloride, (S)-4-benzyloxazolidin-2-one and 1,9-nonanediol. The hexanoyl chloride was connected with (S)-4-benzyloxazolidin-2-one, and with the induction of the chiral oxazolidinone auxiliary, after chiral methylation, LAH reduction and then tosylation gave the chiral key intermediate 5 in high stereoselectivity. 1,9-Nonanediol, was selectively brominated, THP protected and subjected to Li2CuCl4-mediated C-C coupling to afford a C12 intermediate. The target molecule, (S)-14-methyl-1-octadecene, was obtained after the two parts were subjected to a second Li2CuCl4-mediated C-C coupling. Our synthetic approach represents the first time a substrate-control asymmetric synthesis of (S)-14-methyl-1-octadecene has been reported.

The essence of the rough set theory (RST) is to deal with the inconsistent problems by two definable subsets which are called the lower and upper approximations respectively. Asymmetric Similarity relation based Rough Sets (ASRS) model is one kind of extensions of the classical rough set model in incomplete information systems. In this paper, we propose a new matrix view of ASRS model and give the matrix representation of the lower and upper approximations of a concept under ASRS model. According to this matrix view, a new method is obtained for calculation of the lower and upper approximations under ASRS model. An example is given to illustrate processes of calculating the approximations of a concept based on the matrix point of view.

To investigate the complex dynamics and chaos control in airlines' price competition, the dynamic price competition model of airlines with duopoly is established by using the theory of bifurcation of dynamical systems, and the existence and stability of equilibrium points of this model are discussed. The complex dynamics of this model in different market parameters are shown though numerical simulation. The simulation results show that the speed of price adjustment has an obvious impact on the stability of model. Compared with the equilibrium average profits, all airlines' average profits are decreased obviously when chaos is occurred. The dynamic price competition model of airlines can return to stable state from chaotic state by delayed feedback chaos control method while suitable controlling factor is chosen. The analysis and results in this paper are interesting in mathematics and economics.

A simple and efficient synthesis of 1,2-diarylethanols has been developed. The procedure involved the reaction between a variety of toluene derivatives and aryl aldehydes under conventional heating and ultrasound irradiation. This procedure possesses several advantages such as operational simplicity, high yield, safety and environment benignancy. Ultrasound was proved to be very helpful to the reaction, markedly improving the yield and the reaction rate.

Previous work on sequential pattern discovery was mainly focused on studying scalable algorithms while less on its theoretical foundations. Based on Galois closed operator, identifier set, sequential set in sequential database together with their binary relation constituted a context. The relation between fixed point and closed sequential pattern was established. To mine all frequent closed sequential patterns is equal to build fixed point lattice and mine all points on it that satisfy support constraint, which serves as theoretical foundations of sequential patterns and makes it possible to use the existing fixed point and lattice theories to support more effective sequential pattern mining tasks.

Data mining is the efficient discovery of previously unknown patterns in large databases. How to use the existing knowledge to update knowledge is one of the important research areas in data mining. Since knowledge found by rough set is an apparent quantitative description and can be understood, of which data mining is in pursuit. Presently, several approaches based on classical rough set which aims at complete information system have been proposed for the mining task of updating knowledge. However, many information systems are incomplete in practical application. So it is important to develop approaches for updating knowledge in incomplete information systems in order to support more effective data mining. In this paper, based on an extension of the classical rough set theory for dealing with incomplete information systems, we have proposed a method for incremental updating approximations of a concept in incomplete information systems which may realize adding and deleting some attributes simultaneously at a time, that is very important to effectively handle dynamic attribute generalization and enhance the efficiency of data mining.

The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, the definition of fuzzy entropy is firstly introduced. Then some important fuzzy entropy formulae are given and some properties among them are discussed. Finally, a class of new fuzzy entropy formulae is presented. They will provide more choice for engineers to analyze and design a fuzzy system.

Association rule mining is one of the most important research areas in data mining. Yet there exist two big problems in process of acquiring rule by traditional mining algorithms, i.e., the quantity and the quality of rule. Presently there are many methods focus on resolving these two problems. Although these methods can reduce the amount of rules derived to some extent, but the total number is too big as ever. We first propose the notations of upper closed itemset and generalized association rule base, and obtain a generalized association rule base of a database, which not only contains the whole information of all association rules, but also has conform structure that is convenient for practical applications. Also, we propose a mining algorithm of generalized association rule base. From our propositions and example, the algorithm is shown valid and can efficiently solve the problem of quantity of rule.

Association rule mining is an important research area in data mining, which has a broad application background. There exist two short-comings in the classical association rule mining problem, namely every itemset is treated equivalently and use a uniform minimum support and minimum conference as weighting standard. Through introducing the function of the degree of interest on itemsets, /spl phi/, a direct generation of the problem of association rule mining, called /spl phi/-association rule mining, was introduced in Li (2001). It can solve the two short-comings at the same time. Based on an FP-tree, a universal algorithm for mining a T-frequent closed itemset was proposed in Li et al. (2001). Because this algorithm is based on general definition of /spl phi/, it will not perform well for all /spl phi/. In this paper, aiming at a kind of specific /spl phi/, namely, the degree of interest of every item is given, we present an improved algorithm. The experimental and performance studies show that our algorithm is more efficient than previous algorithm.

In this paper, we took filter of lattice implication algebra as the measure of reliability for premises and inference rule and applied it to uncertainty reasoning. Firstly, we analyzed the properties of filter and pointed out that it can be regarded as a semantical model of hypothetical syllogism. Secondly, we discussed the closeness of inference rule with respect to value of reliability and shown some inference rules which closed with respect to filter. Then we studied the feature of reliability changing dynamically in a running reasoning through the paradox of bald man. Finally, we presented an uncertainty reasoning method based on filter.

Uncertainty reasoning is one of the important issues of many research fields such as artificial intelligence, knowledge-based system, data mining, etc. In the framework of lattice-valued propositional logic LP(X), the present work focus on how to deal with uncertainty reasoning with incomparable information by taking filter of lattice implication algebra as the measure of reliability of antecedents and conclusions. Firstly, we investigated the unsuitability of inference rules of classical logics in uncertainty reasoning and discussed the relation between inference rule and truth-values. Secondly, by taking filter as a measure of reliability, we studied the dynamic and hierarchical characteristics of uncertainty reasoning governed by the underlying lattice-valued propositional logic LP(X). Finally, we illustrate our uncertainty reasoning method through a simple example.