Applied Mechanics and Materials Vols. 543-547

Abstract: In this paper we describe an algorithm which is based on Differential Evolution Algorithm using self-adaption and opposition-Based Mechanisms (SAODE). The mutation control parameter f_i is self-adapted according to the deviation of search parameters in each generation. Opposition-based optimization is included in the initialization, and in the evolutionary process itself. In order to demonstrate the behavior of our algorithm we applied it in 4 benchmark functions with a combination of self-adaptive and opposition-based optimization. According to the obtained results, SAODE surpasses DE on 3 functions among 4 test functions about the convergence speeds.

Abstract: Autoregressive process is better than other stochastic processes, which models flexibility, and simulates some other stochastic processes by setting the parameters of model. This paper firstly describes in detail the basic definition of autoregressive process and its stationary conditions, and then studies estimation autoregressive process parameters with residuals briefly in order to research Hubors М-estimation for autoregressive process with symmetric stable residuals. Secondly, prove autoregressive processes with residuals, which are-stable random variables, are also stationary processes, and use Markov's inequality and related theories to discuss Hubors М-estimation for autoregressive process with symmetric stable residuals. Finally, prove the consistency and asymptotic normality of this estimate further.

Abstract: Mathematical statistics is a branch of mathematics has extensive application of interval estimation and hypothesis testing, which are two important problems of statistical inference. As two important statistical inference methods, interval estimation and hypothesis testing problem is more and more widely used in the field of economic management, finance and insurance, scientific research, engineering technology, the science of decision functions are recognized by more and more people. Can go further to establish mutual influence and communication between the interval estimation and hypothesis testing, can use the theory to explain the problem of interval estimation of parameter hypothesis test, this is an important problem to improve the statistical inference theory. Therefore, the basis on the internal relations between the interval estimation and hypothesis test for deep research, explain the problem of hypothesis testing and interval estimation from the point of view, discusses the difference and connection between the two.

Abstract: For the problem of various non-Gaussian signals and noises have distinct spiky and impulsive characteristics in practice, which cannot be solved by Gaussian distribution, we focus on the Alpha stable distribution. This paper firstly sets forth the representation of standard parameterization, and gives some properties in this parameterization. Secondly, define a representation of the parameterization for the purpose of being suitable for numerical calculation and modeling, clears the meaning of each parameter, finds relations between parameters in these representations. Finally, analyze and prove the properties equally apply in this parameterization.

Abstract: In view of the problem that present most clustering algorithms are given priority to save energy but ignoring fault tolerance, this paper puts forward a new kind of hexagonal fault-tolerant clustering algorithm (HFTC). By increasing the middle management node, which controls nodes rate of false positives and managements topology within the cluster, this algorithm completes nondestructive substitution between nodes. At the same time, the introduction of backup nodes, it also improves the networks fault tolerance. The simulation experiments show that HFTC can guarantee a high fault tolerance in networks, make the network to send more packets, and prolong the network life effectively.

Abstract: One of the core issues about multi-resolution modeling needed to solve were the aggregation and disaggregation of models. In this paper, the location, velocity, state and the degree of damage of models were discussed by a new method basic on AHP under the background which armored equipment motion models. In the end, the practical applicability and validity of this method were given in detail.

Abstract: The paper constructs the planar dynamic systems with truncated Fourier series. We propose a method to generate planar tiling images of the iterative mapping with truncated Fourier series. It constructed the planar tessellations of planar dynamic systems with cyclic windows. The iterative mapping is constructed. Then we generate cyclic windows of the dynamic plane with these mappings. Filled-in Julia sets are created by generating the coordinates of any cyclic windows. The images in different windows are continuous. We can choose any cyclic windows as the basic computing region and stretch it into a square, which is transferred to the plane to compose the new form chaos attractor and filled-in Julia sets images in the Euclidian plane. Experimental results show the effectiveness of the proposed approach.

Abstract: In the visualization of nonlinear dynamic systems with computer, we construct the planar symmetry dynamic systems with truncated trigonometric series by Clifford A.Reiters method of constructing crystallographic groups. To analyze the characteristics of the iteration mapping with truncated trigonometric series. It used the operation of matrix product as tool. To construct dynamic systems of the nonlinear function with truncated trigonometric series. We construct two planar dynamic systems with truncated trigonometric series. Monte Carlo method is used to search the parameter vectors in the parameter space. The Lyapunov exponent is used to judge the characteristics of dynamical systems. We construct chaotic graphics in the cyclic windows. We present a method to construct symmetry dynamical systems which can be used to generate square plane tiling. A great of chaotic attractors in the fundamental regions can be continuously tiled without gaps in the plane. Furthermore, we can provide a plenty of material with a novel and unique structure for the decorative patterns of the buildings.

Abstract: The paper applies the matrix calculation in source entropy calculation and propose the algorithm implementation, which can decrease the calculation cost and increase the accuracy significantly significantly.

Abstract: Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial an analysis way and elementary method to create new series.