We show that with small modifications in diverse expressions for the shifted Legendre polynomials, we can obtain the corresponding relations for Daubechies polynomials.

In the production process of strip tandem cold rolling mills, flatness control system is important for improving quality. The efficiency actuators a pivotal factor affecting accuracy. At present, data-driven methods to intelligently identify have become research hotspot. this paper, wavelet transform longitudinal denoising method, combined with genetic algorithm (GA-WT), proposed handle big noi...

Due to increasing applications of extended surfaces as passive methods of cooling, study of thermal behaviors and development of mathematical solutions to nonlinear thermal models of extended surfaces have been the subjects of research in cooling technology over the years. In the thermal analysis of fin, various methods have been applied to solve the nonlinear thermal models. This paper focuses...

A mesh refinement method is described for solving a continuous-time optimal control problem using collocation at Legendre–Gauss–Radau points. The method allows for changes in both the number of mesh intervals and the degree of the approximating polynomial within a mesh interval. First, a relative error estimate is derived based on the difference between the Lagrange polynomial approximation of ...

A mesh refinement method is described for solving a continuous-time optimal control problem using collocation at Legendre-Gauss-Radau points. The method allows for changes in both the number of mesh intervals and the degree of the approximating polynomial within a mesh interval. First, a relative error estimate is derived based on the difference between the Lagrange polynomial approximation of ...

Many quantitative traits are measured repeatedly during the life of an organism. Such traits are called dynamic traits. The pattern of the changes of a dynamic trait is called the growth trajectory. Studying the growth trajectory may enhance our understanding of the genetic architecture of the growth trajectory. Recently, we developed an interval-mapping procedure to map QTL for dynamic traits ...

The efficiency of defect detection for filters and wavelets is a fundamental problem in image processing. It has recently been shown that natural symmetries such as rotational invariance is of primary importance to solve this problem [1, 2]. We herewith investigate the detection of tunable singularities in natural textures from the Brodatz database and in parts of mammographies. We compare seve...