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In the area of response-adaptive design based on randomized urn models, Professor Bai's research has been focused on providing a mathematically rigorous of generalized Friedman's urn model. In a series of papers, matrix recursions and martingale theory were introduced to study randomized urn models. Based on these techniques, some fundamental questions were answered.

The demand for materials of superior properties is increasing day by day. Due to this materials scientist are developing new materials to meet the demand of growing need of materials. The material scientist for the development of metal matrix composite has been given much attention, which are continuously replacing traditional materials. There are several fabrication techniques for the production of MMC. Among the fabrication processes of MMCs of recent development, powder metallurgy is one of the most widely used fabrication techniques. Powder Metallurgy (P/M) offers designers and users a versatile and efficient method of producing components. The process is versatile because it can be used for simple and complex shapes, and a full range of chemical, physical and mechanical properties is possible to obtain. P/M is efficient because it produces moderate to high-volume net or near-net shapes, with very little raw material loss. In general, the process has very good potential to improve performance through uniform properties, fine grain structures, and chemical homogeneity. During the process, the matrix material powders and the reinforcement particles are blended to produce a homogeneous distribution and fed into a mould of desired shape, hot press to a desired level of compaction and final consolidation by extrusion, forging, rolling or some other hot working method. The powder metallurgy attracted attention of the parts manufacturer during the last decades based on progress in materials, process and equipment. The conventional powder metallurgy process consists of three main-steps: powder mixing, compacting (sintering) and extrusion. To carry out the processing of MMC through powder metallurgy, development of powder metallurgy set up is essential. Powder metallurgy set up consists of several main parts such as die, mould, in which the powder is contained, punches, which are used to apply compacting pressure and heater for hot compaction as well as hot extrusion of MMCs. The main aim of the article is to discuss model design, process planning and fabrication of powder metallurgy set up as well as heating system for hot compacting /extrusion (direct and indirect).

We show that for n × n nonsingular matrices A₁, A₂, …, A_k (k ≥ 2) over a commutative principal ideal domain R with relatively coprime determinants there exist invertible n × n matrices U, V₁, …, V_k over R such that UA_iV_i = S_Ai are the Smith normal forms of the matrices A_i.

In this paper, we present a matrix-based representation of rough approximations in multi-source hybrid information systems (MHIS). Besides, an incremental method for updating rough approximations is proposed in MHIS under the variation of features, objects and feature values simultaneously. An example is illustrated to show its effectiveness.

In this paper, we first propose a general composite ordered rough set model, which can deal with various types of attributes with a preference order. Then, we present a matrix method for computing approximations in composite ordered decision systems. Finally, we introduce an incremental method for updating approximations in composite ordered decision systems under the variation of attributes.

In this paper, a super-hyper network model based on Khatri-Rao Product on the correlation matrix of a series of hypergraphs is proposed. Both marginal and joint node degree, node hyperdegree, hyperedge degree and their corresponding polynomials are introduced to describe this super-hyper network model. It is shown that it is fractal since its correlation matrix is a fractal matrix. The fractal parameter is then provided. It is also validated that it is small-world for its diameter won't exceed twice the summation of the diameter of primitive hypergraphs. By a novel product of either marginal or joint node degree polynomial, node hyperdegree polynomial and hyperedge degree polynomial, the corresponding marginal and joint node degree, node hyperdegree and hyperedge degree are obtained.

The objects of investigation are the most widespread Nature Systems on the Land - River Basins, their geodynamics and geoinformatics. For the purpose we worked out the Virtual Nature Systems (VNS) as computer doubles of River Basins and of their components in view to research their dynamics and evolution under continual influence of external factors, in analogy with the Actual Nature Systems (ANS).