A chaotic system with adjustable number of coexisting attractors was proposed with Silnikov theorem. Firstly, a chaotic system with simple structure is constructed based on a classical chaotic system. Dynamic properties of the system are investigated and chaotic characteristics of the system in the sense of horseshoe are verified. Then, multi-zero piecewise function is introduced into the system to expand balance point of the system with adding invariant set of the system. A chaotic system with adjustable number of coexisting attractors is established. Due to complexity of coexisting attractors, the system has potential application in secure communication.

For a Fibonacci chain constructed recursively with S_m+1={S_m|S_m-1}, in a tight-binding model of single electron, we investigate numerically density of electronic states and electronic energy band structure with negative eigenvalue theory and three diagonally symmetric matrixes. Trifurcating structure of energy band of the system is demonstrated. With renormalization-group method and scattering theory, we study localization length and transmission coefficients of electronic states in a chain. At particular eigen-energies, extend states with localization lengths greater than size of the system are found and transmission coefficient is equal nearly to 1. At most eigen-energies, corresponding electronic states are localized states due to short localization length. In addition, relations between transmission coefficients and parameters of Fibonacci chain are qualitatively investigated.

The motion of a neutral particle with magnetic moment,μ antiparallel to the field of an Ioffe trap is studied are obtained. With interaction between the magnetic moment of the particle and the magnetic field, classical motion equations of neutral particles in an Ioffe trap are abtained. With limited conditions we derive concise form of the motion equations using a perturbative method. They are Mathieu equations. With proper parameters the Mathieu equations are solved with traditional WKBJ method. As an attempt, we study periodic solutions, i.e., Floquet solutions of the Mathieu equation. It is necessary that parameters (λ and q) in the Mathieu equation satisfy special relations. With appropriate Ioffe trap parameters and initial condition of the particle, we present several periodic solutions.

The densities of electronic states (DOS) of quasi-one-dimensional disordered systems with three parallel chains are computed with thirty thousand sites based on the negative eigenvalue theory. Compared with one-dimensional and quasi-one-dimensional disordered systems under conditions as diagonal disordered system and non-diagonal disordered system, the electronic structure, the localization of electrons, the distribution of the system energy and the dimensional effects are discussed. The results show that the diagonal disorder causes increasing of the number of localized electrons, and the non-diagonal disorder leads to changing of the distribution of the system energy. Comparing the electronic structure of one-dimensional system and quasi-one-dimensional system with three chains, we find that the peak number of the DOS increase, and the bandgap energy of zero DOS decreases.The dimensional effect of system under the same condition is shown.

An improved algorithm based on finite element method to calculate the sensitivity distribution of capacitance sensor is presented. By fast generating of global siffness matrix and fast calculating capacitance values, the calculation speed of sensitivity distribution is raised.

The electronic structure of quasi-one-dimensional disordered system is studied by the computation of the density of electronic states with the help of the negative eigenvalue theory. The localization of electronic states and the distribution zone of the system energy are discussed to the parameters of system size and the disordered degree of diagonal and non-diagonal elements. The electronic localized states are increased with the enhancing of the diagonal disordered degree and the distribution zone of the system energy is widened with the enhancing of the non-diagonal disordered degree.

At the base of nonsteady heat transfer theory, using modern count-physical method, the applicable mathematical models and physical models are set up and the reasonable boundafy conditions was given. It was indicated by the numerical calculation on the computer VAX11/785 that the temperature inside room could reach 14℃ at the area of Zhengzhou without heating.

A new method for solving directly a hermitian five diagonal matrix is applied in this paper. The electronic eigenvectors are obtained in one-dimensional Anderson disordered model with second-neighbour interaction and 500 to 10000 site points. The result shows the change of eigenvectors in this model from the extended state to the localized state with the increasing of site point and the change speed is affected by the degree of the system disorder.

A method for solving directly the eigenvectors of a Hermitian five diagonal matrix is developed. It does not use a block tridiagonal matrix to solve. The results of calculation demonstrate that this method with high accuracy and low storage is very suitable to the disordered sys tem. It can be used to calculate high order matrix in order to meet the needs of disordered system.