The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient b_i is random variable

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.

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

The digital revolution had greatly affected the methods through which we communicate, starting from the basic concepts of the internet technology and the web content in addition to the important issues that concern the culture of the digital media, the internet governance and the variation in the digital age in general and the graphic and internal design in particular.
This research addresses an important topic that goes along with the scientific development in the field of the digital design, especially in the internal and graphic designs. This study consists of two sections: the first includes the problem of the study and the need for it. Starting from the problem of the research, there is no clear perception of the formal characte

In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t

   Let M is a Г-ring. In this paper the concept of orthogonal symmetric higher bi-derivations on semiprime Г-ring is presented and studied and the relations of two symmetric higher bi-derivations on Г-ring are introduced.

Optical Mark Recognition (OMR) is an important technology for applications that require speedy, high-accuracy processing of a huge volume of hand-filled forms. The aim of this technology is to reduce manual work, human effort, high accuracy in assessment, and minimize time for evaluation answer sheets. This paper proposed OMR by using Modify Bidirectional Associative Memory (MBAM), MBAM has two phases (learning and analysis phases), it will learn on the answer sheets that contain the correct answers by giving its own code that represents the number of correct answers, then detection marks from answer sheets by using analysis phase. This proposal will be able to detect no selection or select more than one choice, in addition, using M

Optical Mark Recognition (OMR) is an important technology for applications that require speedy, high-accuracy processing of a huge volume of hand-filled forms. The aim of this technology is to reduce manual work, human effort, high accuracy in assessment, and minimize time for evaluation answer sheets. This paper proposed OMR by using Modify Bidirectional Associative Memory (MBAM), MBAM has two phases (learning and analysis phases), it will learn on the answer sheets that contain the correct answers by giving its own code that represents the number of correct answers, then detection marks from answer sheets by using analysis phase. This proposal will be able to detect no selection or select more than one choice, in addition, using M