This paper introduces a relation between resultant and the Jacobian determinant
by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:  ,            and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.

In this paper we investigate the automatic recognition of emotion in text. We propose a new method for emotion recognition based on the PPM (PPM is short for Prediction by Partial Matching) character-based text compression scheme in order to recognize Ekman’s six basic emotions (Anger, Disgust, Fear, Happiness, Sadness, Surprise). Experimental results with three datasets show that the new method is very effective when compared with traditional word-based text classification methods. We have also found that our method works best if the sizes of text in all classes used for training are similar, and that performance significantly improves with increased data.

In Automatic Speech Recognition (ASR) the non-linear data projection provided by a one hidden layer Multilayer Perceptron (MLP), trained to recognize phonemes, and has previous experiments to provide feature enhancement substantially increased ASR performance, especially in noise. Previous attempts to apply an analogous approach to speaker identification have not succeeded in improving performance, except by combining MLP processed features with other features. We present test results for the TIMIT database which show that the advantage of MLP preprocessing for open set speaker identification increases with the number of speakers used to train the MLP and that improved identification is obtained as this number increases beyond sixty.

In this paper, a subspace identification method for bilinear systems is used . Wherein a " three-block " and " four-block " subspace algorithms are used. In this algorithms the input signal to the system does not have to be white . Simulation of these algorithms shows that the " four-block " gives fast convergence and the dimensions of the matrices involved are significantly smaller so that the computational complexity is lower as a comparison with " three-block " algorithm .

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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 This paper adapted the neural network for the estimating of the direction of arrival (DOA). It uses an unsupervised adaptive neural network with GHA algorithm to extract the principal components that in turn, are used by Capon method to estimate the DOA, where by the PCA neural network we take signal subspace only and use it in Capon (i.e. we will ignore the noise subspace, and take the signal subspace only).