In this paper, a modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of nonlinear PDEs. By the method, rich families of exact solutions of nonlinear PDEs have been obtained, including soliton-like solutions, trigonometric function solutions and rational solutions. The method can be applied to solve massive nonlinear PDEs (group), as well as helps us find new exact solutions. Furthermore, with the aid of computer symbolic systems (Mathematica or Maple), the method can be conveniently operated. Some illustrative equations are investigated by this method and some figures of partial solutions are provided for direct-viewing analysis.

A local shape preserving interpolation scheme for 2D data is discussed by using piecewise rational quadratic function. To preserve the shape of the data in the view of curves, constraints are made on free parameters in the description of rational quadratic function.

Using two numerical methods, we will obtain numerical positive solutions of the equation u λ=∆− is a superlinear function of u . We study the behavior of the branches of numerical positive solutions for varying

Using a numerical method based on sub-super solution, we will obtain positive solution to the coupled-system of boundary value problems of the form ,( ), vuxf

The basic concepts of Pawlak rough function model are improved. The concepts of double approximation operators that are scale upper (lower) approximation and real line upper (lower) approximation are defined and their properties and antithesis characteristics are analyzed. Scale bijection theorem as well as relative propositions and conclusions are proposed furthermore. Based on the indiscernibility relation, the new real line-scale rough function model is established by generalizing the double approximation operators into two-dimensional space. That deepens and generalizes rough function model based on rough set theory, and makes the scheme of rough function theory more distinct and completed. The transformation of real function analysis from real line to scale is achieved therefore, which provides necessary theoretical foundation and technical support for further discussion of properties and practical application of rough function model.

In software development, it is difficult to evaluate the impact brought by the requirement changes because of the complexities and dependencies among the changed and unchanged requirements. In this paper, the relations of these dependencies are analyzed and established. The scope of the impact caused by requirement changes is identified by a back-tracing algorithm, and impact was quantified. An algorithm developed to quantitatively evaluate the effect of requirement changes is presented. Lastly, the feasibility of this evaluation algorithm is shown through a case-study.

Bloom filters are used for resource routing and distance-weighted Bloom filters (dwBFs) are used as a concise representation of routing information for scattered resources in overlay networks. Today's DHT-based P2P lookups are always influenced by unnecessarily long routers in the underlay network. The reason is that the false positives appearing in DHT lookup can lead to incorrect direction. To apply dwBFs to scattered resources in overlay network can form a routing correcting mechanism. It can reduce the possibilities of incorrect direction under cases of false positives. To use dwBFs also can resolve another problem with DHT, its ineffectiveness in replica-handle. This paper describes a routing algorithm based on dwBFs and shows the results of simulation experiment.

The boundary element method (BEM) is sufficient for calculating Transmission Loss in the acoustics silencer systems. BEM will be implemented by either the conventional four-pole transfer matrix method or the recently developed three-point method, but there are some short for each method. The three- point method is easier to use, and faster than four-pole methods. It does not produce the 4-pole parameters, the section being evaluated cannot be inter-linked with other sections. In order to perform such an evaluation, in this study, an improved method based on the four-pole parameters for use in the BEM is presented. The major advantage of the improved method is that it not only provides a very fast method for computing the TL, but it also produces the four-pole parameters.

Sequential graph partitioning algorithms have been developed to fulfill the requirements of emerging multi-phase problems in circuit delay models. In this paper we propose a heuristic algorithm for k- partition, which minimizes the circuit delay and cut size. Experimental results with MCNC benchmark circuits have shown that the delay in the circuit can be reduced by marginally in comparison with the other algorithms [2,3,11].

This paper presents the unconventional boundary-value problems and it’s superposition solution for the physical geometric nonlinear plane beam system .firstly, this paper takes AK type microswitchs as example and builds the model of the installment process and working process. Secondly, this paper builds a general mathematic model and points out the superposition solution for the unconventional boundary value problems. Lastly, it presents the computing example for the static process of the AK type microswitchs .

The Preconditioned Conjugate Gradient (PCG) method has proven to be extremely powerful for solving symmetric positive definite linear systems. This method can also be applied to nonsymmetric linear systems when combined with the NR/NE techniques. It has been shown in [1] that the CGNR algorithm, which is a nonsymmetric variant of the Conjugate Gradient (CG) method, is error-reducing with respect to the Euclidean norm. However, in practice the simple CGNR algorithm is seldom used because of the squared condition number of the iteration matrix. Preconditioning is frequently needed to overcome this difficulty. In the present paper we give a much richer result concerning the error-reducing property of the CG procedure. Assume that the preconditioner M is also symmetric positive definite. It is shown that the PCG method is error-reducing with respect to the M-norm.