This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

A Multiple System Biometric System Based on ECG Data

In recent years, with the rapid development of the current classification system in digital content identification, automatic classification of images has become the most challenging task in the field of computer vision. As can be seen, vision is quite challenging for a system to automatically understand and analyze images, as compared to the vision of humans. Some research papers have been done to address the issue in the low-level current classification system, but the output was restricted only to basic image features. However, similarly, the approaches fail to accurately classify images. For the results expected in this field, such as computer vision, this study proposes a deep learning approach that utilizes a deep learning algorithm.

Fractal image compression depends on representing an image using affine transformations. The main concern for researches in the discipline of fractal image compression (FIC) algorithm is to decrease encoding time needed to compress image data. The basic technique is that each portion of the image is similar to other portions of the same image. In this process, there are many models that were developed. The presence of fractals was initially noticed and handled using Iterated Function System (IFS); that is used for encoding images. In this paper, a review of fractal image compression is discussed with its variants along with other techniques. A summarized review of contributions is achieved to determine the fulfillment of fractal ima

In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

Abstract: Residual ridge resorption is chronic, progressive, irreversible and cumulative condition associated with teeth loss. Management of a residual ridge with severe resorption to fulfill the patient’s esthetic and functional requirements is quite difficult for the practitioner and also in the construction of an acceptable appliance. As the height of the edentulous ridge reduces the mandibular denture will be improperly function. Severe resorption of the mandibular alveolar ridge may cause instability and discomfort of the convention acrylic resin denture. Dealing with this condition requires clinical skills and knowledge. Treating the severely resorbed mandibular ridge is a challenging effort for prosthodontics. This research present