In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

Analysis the economic and financial phenomena and other requires to build the appropriate model, which represents the causal relations between factors. The operation building of the model depends on Imaging conditions and factors surrounding an in mathematical formula and the Researchers target to build that formula appropriately. Classical linear regression models are an important statistical tool, but used in a limited way, where is assumed that the relationship between the variables illustrations and response variables identifiable. To expand the representation of relationships between variables that represent the phenomenon under discussion we used Varying Coefficient Models

In this paper, an efficient method for compressing color image is presented. It allows progressive transmission and zooming of the image without need to extra storage. The proposed method is going to be accomplished using cubic Bezier surface (CBI) representation on wide area of images in order to prune the image component that shows large scale variation. Then, the produced cubic Bezier surface is subtracted from the image signal to get the residue component. Then, bi-orthogonal wavelet transform is applied to decompose the residue component. Both scalar quantization and quad tree coding steps are applied on the produced wavelet sub bands. Finally, adaptive shift coding is applied to handle the remaining statistical redundancy and attain e

Reconstruction an object from its Fourier magnitude has taken a great deal in the literature and there is still no obvious solution for the failure of this algorithm. In this paper, the frequent failure of the phase retrieval is discussed in details and it has been shown that when the object is cento-symmetric, the object support is vital element to ensure uniqueness while for asymmetric object; the asymmetric support of the object is not enough to ensure uniqueness but the reconstruction appear to include most of the information of the original object. This is also true for the reconstruction of a complex function.

In this work, watershed transform method was implemented to detect and extract tumors and abnormalities in MRI brain skull stripped images. An adaptive technique has been proposed to improve the performance of this method.Watershed transform algorithm based on clustering techniques: K-Means and FCM were implemented to reduce the oversegmentation problem. The K-Means and FCM clustered images were utilized as input images to the watershed algorithm as well as of the original image. The relative surface area of the extracted tumor region was calculated for each application. The results showed that watershed trnsform algorithm succeedeed to detect and extract the brain tumor regions very well according to the consult of a specialist doctor a

One of the challenging and active research topics in the recent years is Facial Expression. This paper presents the method to extract the features from the facial expressions from still images. Feature extraction is very important for classification and recognition process. This paper involve three stages which contain capture the images, pre-processing and feature extractions. This method is very efficient in feature extraction by applying haar wavelet and Karhunen-Loève Transform (KL-T). The database used in this research is from Cohen-Kanade which used six expressions of anger, sadness fear, happiness, disgust and surprise. Features that have been extracted from the image of facial expressions were used as inputs to the neural networ

     Image content verification is to confirm the validity of the images, i.e. . To test if the image has experienced any alteration since it was made. Computerized watermarking has turned into a promising procedure for image content verification in light of its exceptional execution and capacity of altering identification.

     In this study, a new scheme for image verification reliant on two dimensional chaotic maps and Discrete Wavelet Transform (DWT) is introduced. Arnold transforms is first applied to Host image (H) for scrambling as a pretreatment stage, then the scrambled host image is partitioned into sub-blocks of size 2×2 in which a 2D DWT is utilized on  ea

     In today's world, digital image storage and transmission play an essential role,where images are mainly involved in data transfer. Digital images usually take large storage space and bandwidth for transmission, so image compression is important in data communication. This paper discusses a unique and novel lossy image compression approach. Exactly 50% of image pixels are encoded, and other 50% pixels are excluded. The method uses a block approach. Pixels of the block are transformed with a novel transform. Pixel nibbles are mapped as a single bit in a transform table generating more zeros, which helps achieve compression. Later, inverse transform is applied in reconstruction, and a single bit value from the table is rem

Electrocardiogram (ECG) is an important physiological signal for cardiac disease diagnosis. With the increasing use of modern electrocardiogram monitoring devices that generate vast amount of data requiring huge storage capacity. In order to decrease storage costs or make ECG signals suitable and ready for transmission through common communication channels, the ECG data
volume must be reduced. So an effective data compression method is required. This paper presents an efficient technique for the compression of ECG signals. In this technique, different transforms have been used to compress the ECG signals. At first, a 1-D ECG data was segmented and aligned to a 2-D data array, then 2-D mixed transform was implemented to compress the