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

This article studies a comprehensive methods of edge detection and algorithms in digital images which is reflected a basic process in the field of image processing and analysis. The purpose of edge detection technique is discovering the borders that distinct diverse areas of an image, which donates to refining the understanding of the image contents and extracting structural information. The article starts by clarifying the idea of an edge and its importance in image analysis and studying the most noticeable edge detection methods utilized in this field, (e.g. Sobel, Prewitt, and Canny filters), besides other schemes based on distinguishing unexpected modifications in light intensity and color gradation. The research as well discuss

This study aims at investigating the partial Islamic rules of preparing and distributing cartoons in order to issue an overall Islamic rul. To reach an end, descriptive and analytical approaches are adopted to clarify the nature of cartoons and other related concepts. The researcher, as well, with reference to verses of the Holy Quran, tradition (Hadith) and Islamic jurists, adopts a deductive approach to issue Islamic rules related to the industry of cartoons and it's distribution
The study consists of three sections. The first Section addresses the following issues: Definition animation; and related wordy. The second Section: Origin of Cartoon's history and it's negative and positive effects. The third Section: Islamic rules related

Onchocerciasis is an infection with cutaneous, ocular and systemic manifestations caused by the filarial nematode Onchocerca volvulus, which is transmitted by the bite of various species of the anthropophilic blood-sucking Simulium vectors (black flies). Onchocerciasis is endemic to the savannahs and rainforests of subequatorial Africa and in some countries of the Arabian Peninsula, notably Yemen and Oman, and in Central America, and the Amazon basin of South America. Onchocercomas, which can be defined as subcutaneous fibrous nodules containing adult worms, are among the variable clinical manifestations of this infestation; they are either superficial or deep and usually located over bony prominences. In this paper we report a case of an o

Objectives: Although the Frankfort Horizontal (FH) and sella-nasion were routinely used as craniofacial reference planes, the inter-individual orientations were changeable when related to true horizontal (HOR). Natural head position (NHP) is a reproducible, standardized position, with the head in an upright posture and eyes focused on a point in the distance at eye level so that the visual axis is horizontal. The natural head position has importance in anthropological as well as in orthodontic fields, as this position has a relatively fixed relationship to the true horizontal and vertical planes. However, NHP is clinically not simple and it takes long time to be recorded, in addition to a deficiency in the tools utilized in the NHP and l

     In this review paper, several research studies were surveyed to assist future researchers to identify available techniques in the field of infectious disease modeling across complex networks. Infectious disease modelling is becoming increasingly important because of the microbes and viruses that threaten people’s lives and societies in all respects. It has long been a focus of research in many domains, including mathematical biology, physics, computer science, engineering, economics, and the social sciences, to properly represent and analyze spreading processes. This survey first presents a brief overview of previous literature and some graphs and equations to clarify the modeling in complex networks, the detection of soc

This paper is intended to focus on the existing relation between 'logic' and 'meaning', and how 'meaning' is looked at through logical perspective. Besides, this paper adopts simple logical symbols to represent some aspects of meaning.

    Since meaning is still regarded as a thorny area that needs further study to determine its nature and borderline, this paper proposes to resort to logic and logical rules. This paper points out how logical rules are used and how they clarify some oblique sentences. The paper also sheds light on how meaningful sentences are logically symbolized and how logic can define the borderline of meaning in an adequate manner. This paper hypothesizes that logic, l

     In this review paper, several research studies were surveyed to assist future researchers to identify available techniques in the field of infectious disease modeling across complex networks. Infectious disease modelling is becoming increasingly important because of the microbes and viruses that threaten people’s lives and societies in all respects. It has long been a focus of research in many domains, including mathematical biology, physics, computer science, engineering, economics, and the social sciences, to properly represent and analyze spreading processes. This survey first presents a brief overview of previous literature and some graphs and equations to clarify the modeling in complex networks, the detection of soc