In this paper, we present a new class of hybrid methods for the numerical solution of first order ordinary differential equations (ODEs). The accuracy and stability properties of the new methods are investigated. In the final section, we apply new hybrid methods to solve two stiff chemical problems such as Robertson problem.

‎‎‎Given a fuzzy normed space, we will introduce the notion of fuzzy near best APPROXIMATION as a generalization of the notion of fuzzy best APPROXIMATION. Some basic properties are characterized and also many examples for illustration are presented. Also, the hereditary properties of the fuzzy near best APPROXIMATION on direct sum and tensor product of linear spaces are discussed.

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.

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In this paper, the detector of a moving target in MIMO radar with widely separated antenna in the presence of the a-STABLE clutter is proposed. Due to the complexity of the unknown parameter estimation in the presence of the target, the Rao test is applied. The a-STABLE model is a general model that can be applied to different environments with appropriate selection of parameters. The problem with this model is inexistence of a closed form for the probability density function of the distribution. Fortunately, there are models that approximate the distribution by a closed form expression. In the present paper, mixing of Gaussian and Cauchy model is used for expressing clutter. Finally, the performance of the proposed detector is compared with the optimal Gaussian and MiniMax detector by a graph of the probability of detection versus signal-to-clutter ratio. The simulation results, show that the performance of the proposed detector is better than the optimal Gaussian and MiniMax detector.

In this paper, we study wavelet APPROXIMATION of the Chebyshev polyno-mials of the first, second, third, and fourth kinds. We estimate the wavelet APPROXIMATION of a function f having bounded first derivatives.