Digital image is widely used in computer applications. This paper introduces a proposed method of image zooming based upon inverse slantlet transform and image scaling. Slantlet transform (SLT) is based on the principle of designing different filters for different scales.

      First we apply SLT on color image, the idea of transform color image into slant, where large coefficients are mainly the   signal and smaller one represent the noise. By suitably modifying these coefficients , using scaling up image by  box and Bartlett filters so that the image scales up to 2X2 and then inverse slantlet transform from modifying coefficients using to the reconstructed image .

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In this paper, an algorithm for reconstruction of a completely lost blocks using Modified
Hybrid Transform. The algorithms examined in this paper do not require a DC estimation
method or interpolation. The reconstruction achieved using matrix manipulation based on
Modified Hybrid transform. Also adopted in this paper smart matrix (Detection Matrix) to detect
the missing blocks for the purpose of rebuilding it. We further asses the performance of the
Modified Hybrid Transform in lost block reconstruction application. Also this paper discusses
the effect of using multiwavelet and 3D Radon in lost block reconstruction.

In this paper we present a method to analyze five types with fifteen wavelet families for eighteen different EMG signals. A comparison study is also given to show performance of various families after modifying the results with back propagation Neural Network. This is actually will help the researchers with the first step of EMG analysis. Huge sets of results (more than 100 sets) are proposed and then classified to be discussed and reach the final.

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

   Let  be a commutative ring with identity, and  be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept.  also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.

The integer simulation and development finite impulse response (FIR) filters taking into account the possibilities of their realization on digital integer platforms are considered. The problem statement and solution of multifunctional synthesis of digital FIR filters such a problem on the basis of the numerical methods of integer nonlinear mathematical programming are given. As an several examples, the problem solution of synthesis FIR-filters with short coefficient word length  has been given. The analysis of their characteristics is resulted. The paper discusses issues of modeling and synthesis of digital FIR filters with provision for the possibilities of their implementation on digital platforms with integer computation arithme

This paper included derivative method for the even r power sums of even integer numbers formula to approach high even (r+2) power sums of even integer numbers formula so on we can approach from derivative odd r power sums of even integer numbers formula to high odd (r+2) power sums of even integer numbers formula this derivative excellence have ability to used by computer programming language or any application like Microsoft Office Excel. Also this research discovered the relationship between r power sums of even integer numbers formula and both formulas for same power sums of odd integer numbers formula and for r power sums of all integer numbers formula in another way.