Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a functionf that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives off at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear combination for 5th degree polynomials linear space and same approach develops to introduce 5th degree fuzzy piecewise Hermite interpolation polynomials.At first, construction method along with an example has presented for 5 th degree fuzzy Hermite interpolation. Because of the introduced method applies for interpolation of first order Generalized Hukuhara differentiable functions so during an example cubic fuzzy Hermite interpolation polynomial compares with fuzzy Hermite polynomial and we explain the superiority of the presented piecewise method next in the end we provide 5th degree fuzzy piecewise Hermite interpolation polynomial. Using such interpolant shows that the smoothness condition improves for interpolation polynomial core when successive degree of fuzzy piecewise Hermite interpolation polynomial comes up from three to five.

This paper presents the extension of the Lagrange Interpolating Polynomial (LIP) scheme for solving differential equations by using the finite volume method called the Very high-order Spatial Lagrange Interpolating Polynomial (VS-LIP) scheme. The advantage of the VS-LIP scheme is its convenience for extending the order of accuracy. The correctness of the VS-LIP scheme solutions is assessed by comparing the solutions with analytical, benchmark, published, and experimental solutions of five verification problems involving one- and two-dimensional heat transfer and fluid flow. The assessment is carried out to the sixth and twelfth orders of spatial accuracy. The assessment results indicated that the VS-LIP scheme delivers the correct solutions.

This paper focuses on the problem of accurate Fault Characteristic Frequency (FCF) estimation of rolling bearing. Teager-Kaiser Energy Operator (TKEO) demodulation has been applied widely to rolling bearing fault detection. FCF can be extracted from vibration signals, which is pre-treatment by TEKO demodulation method. However, because of strong noise background of fault vibration signal, it is difficult to extract FCF with high precision. In this paper, the improved algorithm of rolling bearing fault diagnosis is analyzed. Based on the envelope analysis by TKEO demodulation, it combines zero padding technique and the Improved Iterative Windowed Interpolation DFT (IIWIpDFT) algorithm to correct demodulated signal. Experimental result shows that the proposed algorithm decreases Root Mean Square Error (RMSE) of FCF(inner race) form about 2Hz~5. 5Hz to about 0. 5Hz for short data length, the same treatment also decreases RMSE form about 1. 1Hz~3Hz to about 0. 4~0. 5Hz for longer data length in most cases. Meanwhile, the RMSE of FCF (outer race) improved 2. 3 to 84. 5% as compared to the application of traditional TEKO demodulation alone.

In this paper we investigate the relation between universal Interpolating sequence and the approximate point spectrum of the adjoint multiplication operator acting on the Hilbert spaces of formal power series.

This study proposes the model for Interpolating time series to use them to forecast effectively for future. This model is established based on the improved fuzzy clustering analysis problem, which is implemented by the Matlab procedure. The proposed model is illustrated by a data set and tested for many other datasets, especially for 3003 series in M3-Competition data. Comparing to the existing models, the proposed model always gives the best result. We also apply the proposed model in forecasting the salt peak for a coastal province of Vietnam. Examples and applications show the potential of the studied problem.

Calling tradition is among clearest areas which can be found in modern dramatic literary and artistic texts. The ancient hero is quite well known and since long has found his place in literature and art of different nations especially in legends, epics, folk tales, oral literature and dramatic texts such that it was in a battle with other elements and defeated them. Abou Khalil Alqabbani, the first Syrian playwright and among leaders of play writing in Arab and eastern world generally wrote many plays and borrowed some of their subjects from ancient narrations including "Antar ibn Shaddad". Although there were other dramatic texts in Arabic literature about this hero, importance of Alqabani's play is latent in this fact that this is the first work of this kind in the Arab world and is investigated in descriptive- analytical method based on hero's characteristic in original story as a literary text and modern play as a dramatic art .The results of his study shows that although Alqabbani does not emphasize the story of Antar as a historical event, he calls story of the hero to describe situation in which he lives and social condition of his own society because his society needs to remind a brave hero with good ethic and chivalric features whom Antar represents.

Over the last decade or so, wavelets have had a growing impact on signal processing theory and practice, both because of their unifying role and their successes in applications. Filter banks, which lie at the heart of wavelet-based algorithms, have become standard signal processing operators, used routinely in applications ranging from compression to modems. The contributions of wavelets have often been in the subtle interplay between discrete-time and continuous-time signal processing. The purpose of this article is to look at recent wavelet advances from a signal processing perspective. In particular, approximation results are reviewed, and the implication on compression algorithms is discussed. New constructions and open problems are also addressed. Finding a good basis to solve aproblem dates at least back to Fourier and his investigation of the heat equation. The series proposed by Fourier has several distinguishing features: The series is able to represent any finite energy function on an interval. The basis functions are eigenfunctions of linear shift invariant systems or, in other words, Fourier series diagonalize linear, shift invariant operators.