Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

• The problem of infertility considers one of the chronic problem a which faced the
  individual & families equally . This problem causes a negative effects in psychological ,
  social and development fields. The infertility contributes in weakening the human
  development, when the human development has become as a centre point which centered
  about individual preparing , rehabilitation, training and knowledge toreach to the required
  excellence.
  We think that , the infertility destroys the socially development; therefore the socially and
  scientific institutions are working hard to find successful solution to resolve the problem
  infertility through sophisticated and scientific methods. This problem

The purpose of this paper is to solve the stochastic demand for the unbalanced transport problem using heuristic algorithms to obtain the optimum solution, by minimizing the costs of transporting the gasoline product for the Oil Products Distribution Company of the Iraqi Ministry of Oil. The most important conclusions that were reached are the results prove the possibility of solving the random transportation problem when the demand is uncertain by the stochastic programming model. The most obvious finding to emerge from this work is that the genetic algorithm was able to address the problems of unbalanced transport, And the possibility of applying the model approved by the oil products distribution company in the Iraqi Ministry of Oil to m

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

Abstract

Due to the momentum of winning in the streets of the city of Baghdad as a result of the large number of checkpoints so felt researcher to conduct a field visit to find out the main reasons that led to this congestion and to find practical solutions to mitigate wastage winning the arrival time citizen to where you want the least possible time.

This research aims to overcome the difficulties experienced by citizens to reach their places of work and reduce waste at the time of service and waiting time as well as reduce the cost of waiting.

Has emerged study a set of conclusions, including the use of model queue (G / G / C) and the mome

This study investigates the challenges encountered by first-grade intermediate students in learning the Arabic language. It aims to identify specific obstacles that hinder language acquisition and proficiency among this demographic. Through qualitative and quantitative methods, including surveys and interviews with students, teachers, and parents, the research highlights key issues such as limited vocabulary, difficulties in grammar, lack of engagement with the material, and inadequate teaching resources. The findings reveal a complex interplay between cognitive, social, and educational factors that contribute to these challenges. The study underscores the need for targeted interventions, such as enhanced pedagogical strategies and improved

Background: Patients with decompensated cirrhosis are often given therapeutic and prophylactic drugs. Polypharmacy raises both the likelihood of prescription errors and the complications associated with drugs. Clinical pharmacists are excellent at recognizing, addressing, and preventing clinically significant drug-related problems.

Objectives: Identification types of pharmacist interventions to address drug-related problems in patients with decompensated cirrhosis and assess the acceptance/implementation of these recommendations. And identify patient factors associated with accepting pharmacist recommend

A simple analytical method was used in the present work for the simultaneous quantification of Ciprofloxacin and Isoniazid in pharmaceutical preparations. UV-Visible spectrophotometry has been applied to quantify these compounds in pure and mixture solutions using the first-order derivative method. The method depends on the first derivative spectrophotometry using zero-cross, peak to baseline, peak to peak and peak area measurements. Good linearity was shown in the concentration range of 2 to 24 µg∙mL-1 for Ciprofloxacin and 2 to 22 µg∙mL-1 for Isoniazid in the mixture, and the correlation coefficients were 0.9990 and 0.9989 respectively using peak area mode. The limits of detection (LOD) and limits of quantification (LOQ) were