Key Engineering Materials Vols. 439-440

Abstract: In this paper, the notion of orthogonal vector-valued wavelets is introduced. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is presented by using paraunitary vector filter bank theory, time-frequency analysis method and matrix theory. A new method for constructing a class of orthog- -onal finitectly supported vector-valued wavelets is presented.

Abstract: Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure (GMS) of is also introduced. The construction of a GMS of Paley-Wiener subspaces of is investigated. The pyramid decomposition scheme is derived based on a GMS. As a major new constribution the sufficient condition for the existence of multiple pseudoframes for subspaces is derived based on such a GMS.

Abstract: Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function.

Abstract: In the work, the concept of orthogonal vector-valued trivariate wavelet packets, which is a generalization of uniwavelet packets, is introduced. A new method for constructing them is developed, and their characteristics is discussed by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established.

Abstract: The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

Abstract: The distribution of observation errors is determined according to their magnitudes by using the distribution collocation test method or figure method taking into account the result, sample total, the interval density etc. It is therefore difficult to get the specific type of error distribution of observations by conventional methods. In analyzing the actual situation of the observation error distribution using their statistical properties, this paper proposes the use of unsymmetrical distribution to express the true distribution of the observation errors. The P-norm distribution is a generalized form of a group of error distributions, and from the statistical properties of random errors we can arrive at an unsymmetrical P-norm distribution according to the practical situation of the occurrence of random errors. The common P-norm distribution is the specific case of this distribution. This paper deduces the density function equation of the unsymmetrical P-norm distribution, obtained the statistical properties of the distribution function and the evaluation of precision index. By choosing appropriate value for p, we can get closer to the distribution function of the true error distribution.

Abstract: Wavelet analysis is a popular subject in science research. The notion of univariate orthog- onal wavelet packets is generalized. The definition of biorthogonal nonseparable two-dimensional wavelet packets is presented and a procedure for constructing them is proposed. The biorthogonality property of bivariate wavelet packets is investigated. Two biorthogonality formulas regarding these wavelet packets are established.

Abstract: Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing biorthogonal matrix–valued trivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three biorthogonality formulas concerning these wavelet packets are provided. Finally, new Riesz bases of space is obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.

Abstract: Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this paper, the notion of biorthogonal two-direction compactly supported wavelet packets with poly-scale is developed. A new method for designing two-direction biorthogonal wavelet packets is proposed and their properties is investigated by algebra theory, means of time-frequency analysis methodand, operator theory. The direct decomposition relationship is provided. Finally, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are derived.

Abstract: In this paper, a kind of grid task scheduling optimization algorithm based on cloud model is proposed with the characteristics of cloud model. With the target being the cloud droplets of the cloud model, this algorithm gets three characteristic values of cloud through the reverse cloud: expectations, entropy and excess entropy, and then obtains cloud droplets using the forward cloud algorithm by adjusting the values of entropy and excess entropy. After several iterations, it achieves the optimal solution of task scheduling. Theoretical analysis and results of simulation experiments show that this scheduling algorithm effectively achieves load balancing of resources and avoids such problems as the local optimal solution of genetic algorithms and premature convergence caused by too much selection pressure with higher accuracy and faster convergence.