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

     Various document types play an influential role in a lot of our lives activities today; hence preserving their integrity is an important matter. Such documents have various forms, including texts, videos, sounds, and images.  The latter types' authentication will be our concern here in this paper. Images can be handled spatially by doing the proper modification directly on their pixel values or spectrally through conducting some adjustments to some of the addressed coefficients. Due to spectral (frequency) domain flexibility in handling data, the domain coefficients are utilized for the watermark embedding purpose. The integer wavelet transform (IWT), which is a wavelet transform based on the lifting scheme,

    Glaucoma is one of the most dangerous eye diseases. It occurs as a result of an imbalance in the drainage and flow of the retinal fluid. Consequently, intraocular pressure is generated, which is a significant risk factor for glaucoma. Intraocular pressure causes progressive damage to the optic nerve head, thus leading to vision loss in the advanced stages. Glaucoma does not give any signs of disease in the early stages, so it is called "the Silent Thief of Sight". Therefore, early diagnosis and treatment of retinal eye disease is extremely important to prevent vision loss. Many articles aim to analyze fundus retinal images and diagnose glaucoma. This review can be used as a guideline to help diagnose glaucoma. It presents 63 artic

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

It is known that images differ from texts in many aspects, such as high repetition and correlation, local structure, capacitance characteristics and frequency. As a result, traditional encryption methods can not be applied to images. In this paper we present a method for designing a simple and efficient messy system using a difference in the output sequence. To meet the requirements of image encryption, we create a new coding system for linear and nonlinear structures based on the generation of a new key based on chaotic maps.

The design uses a kind of chaotic maps including the Chebyshev 1D map, depending on the parameters, for a good random appearance. The output is a test in several measurements, including the complexity of th

     Feature selection, a method of dimensionality reduction, is nothing but collecting a range of appropriate feature subsets from the total number of features. In this paper, a point by point explanation review about the feature selection in this segment preferred affairs and its appraisal techniques are discussed. I will initiate my conversation with a straightforward approach so that we consider taking care of features and preferred issues depending upon meta-heuristic strategy. These techniques help in obtaining the best highlight subsets. Thereafter, this paper discusses some system models that drive naturally from the environment are discussed and calculations are performed so that we can take care of the prefe

A fault is an error that has effects on system behaviour. A software metric is a value that represents the degree to which software processes work properly and where faults are more probable to occur. In this research, we study the effects of removing redundancy and log transformation based on threshold values for identifying faults-prone classes of software. The study also contains a comparison of the metric values of an original dataset with those after removing redundancy and log transformation. E-learning and system dataset were taken as case studies. The fault ratio ranged from 1%-31% and 0%-10% for the original dataset and 1%-10% and 0%-4% after removing redundancy and log transformation, respectively. These results impacted direct

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.

      Recently, digital communication has become a critical necessity and so the Internet has become the most used medium and most efficient for digital communication. At the same time, data transmitted through the Internet are becoming more vulnerable. Therefore, the issue of maintaining secrecy of data is very important, especially if the data is personal or confidential. Steganography has provided a reliable method for solving such problems. Steganography is an effective technique in secret communication in digital worlds where data sharing and transfer is increasing through the Internet, emails and other ways. The main challenges of steganography methods are the undetectability and the imperceptibility of con

Hand gestures are currently considered one of the most accurate ways to communicate in many applications, such as sign language, controlling robots, the virtual world, smart homes, and the field of video games. Several techniques are used to detect and classify hand gestures, for instance using gloves that contain several sensors or depending on computer vision. In this work, computer vision is utilized instead of using gloves to control the robot's movement. That is because gloves need complicated electrical connections that limit user mobility, sensors may be costly to replace, and gloves can spread skin illnesses between users. Based on computer vision, the MediaPipe (MP) method is used. This method is a modern method that is discover