The paper discusses the detail solution procedure of fuzzy linear systems and fully fuzzy linear system. Each case has been solved by using the concept of Strong and Weak solution with some numerical examples. We have also developed some theorems regarding the existence of the solution.

This paper presents, Daubechies wavelet based full approximation scheme (DWFAS) for the numerical solution of Burgers’ equation, which is nonlinear partial differential equation (PDE) arising in fluid dynamics using Daubechies wavelet intergrid operartors. The numerical solutions obtained are compared with existing numerical methods and exact solution. Some of the test problems are presented to demonstrate that DWFAS has fast convergence in low computational time and is very effective, convenient and quite accurate to systems of PDEs.

In this paper, the complete synchronization of 4D Chua systems is investigated via linear controllers. Especially, the synchronization can be realized using only one or two linear controllers. By analyzing simulation results, it is known that when realizing the synchronization, the choice of linear controller has greater flexibility and the controlled variables can also be randomly selected.

In this paper wavelet preconditioned method is used for the solution of Electrohydrodynamic flow problem. A finite difference method is used for the solution of Electrohydrodynamic flow equation. The method comprise the nonlinear Newton iteration on the outer loop and a linear iteration on the inside loop where wavelet based preconditioned GMRES (Generalized Minimum Residual) method is used. In the scheme the Jacobian vector product is approximated accurately with much ease (without forming Jacobian explicitly and requiring no extra storage). It overcomes the limitations of conventional schemes for the numerical solution of Electrohydrodynamic flow problem, for computing fluid velocity, covering wide range of Hartmann electric number (Ha) parameter with constant of practical interest. To confirm and validate the solutions obtained, by the present method, are compared with those obtained by GMRES method.

Locality sensitive discriminant analysis is a typical and very effective graph-based dimensionality reduction method which has been successfully applied in pattern recognition problems. LSDA aims to find a projection which maximizes the margin between data points from different classes at each local area. As a result, it can discover the local geometrical structure of the data samples. However, just as linear discriminant analysis, it has the small sample size (SSS) problem. To overcome this limitation, we propose a novel exponential locality sensitive discriminant analysis algorithm in this paper. The proposed algorithm can make nearby objects with the same labels in the input space also nearby in the new representation; while nearby objects with different labels in the input space should be far apart. In addition, it can also deal with the SSS problem. The experiments on gene expression data sets verify the effectiveness of the proposed algorithm.

In this paper, we consider the series of Padovan numbers. Thereby, we introduce universal coding scheme based on Padovan numbers. This universal coding are used in source coding as well as in cryptography.

A method for solving the descriptor continuous-time linear system is focused. For easily, it is converted to two standard continuous-time linear systems by the definition of a derivative and propositional state feedback. Then partial eigenvalue assignment is used for obtaining the derivative and propositional state feedbacks and solving the standard systems. In partial eigenvalue assignment, just a part of the open loop spectrums of two standard linear systems are reassigned, while leaving the rest of the spectrum invariant and for reassigning, similarity transformation is used. Using partial eigenvalue assignment is easier than using eigenvalue assignment. Because by partial eigenvalue assignment, size of matrices and state and input vectors are decreased and stability is kept, too. It is worthy to mention that eigenvalues of closed-loop matrix of original system, i.e., descriptor and second converted system are inverse of each other. Also concluding remarks and an algorithm are proposed to the descriptions be obvious. At the end, convergence of state and input vectors in the descriptor system to balance point (zero) are showed by figures in a numerical example.

Krill herd optimization is a novel bionic swarm intelligence optimization method, but currently it is mostly used only in the field of engineering optimization. Since node’s energy is limited and establishing effective routing is difficult in wireless sensor networks, in this paper, we try to apply krill herd optimization in anycast routing algorithm for wireless sensor networks. The krill are moved to the high fitness area (anycast paths with better energy consumption condition) through induced motion, foraging movement and random diffusion behaviors. Moreover, crossover and mutation operators in genetic reproduction mechanisms are adopted for improving the ability of accelerating optimization speed and breaking away from the local optimum. In comparison with ant colony optimization, simulation experiments results show that the performances of the proposed algorithm are better in terms of convergence speed, optimization results and scalability.