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

DBN Rashid, IMPAT: International Journal of Research in Humanities, Arts, and Literature, 2016 - Cited by 5

• 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

An advertisement is a form of communication intended to promote the sale of a product or service, influence public opinion, gain political support, or to elicit some other response. It consists of various type, including style, target audience, geographic scope, medium, or purpose. An advertisement should catch a person's attention and quickly create a memorable impression. The main aim of the present paper is to investigate the phonological problems of translating English international TV advertisements into Arabic. It deals with the most common and popular TV advertisements. The importance of such advertisements lies not in its information content rather than in the achievement of the desired impact on the receivers. When translating such

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.

Background: Imaging techniques play a very important role in the specialty of endodontic. The ultrasonographic technique is non-expensive procedure, safe, and reproducible. The aim of the study was to determine the sensitivity, specificity, and accuracy of ultrasound and color Doppler ultrasonography in evaluation of periapical lesions (cyst, granuloma, mixed lesion “cyst within graulomas mass”, and abscess. Subject, Material and method: The sample consists of prospective study for 64 Iraqi participants who attended Karbalaa Specialized Center for Dentistry (males & females). Those patients were diagnosed clinically and radiographically as having periapical lesions of dental origin. They were examined by real time ultrasound and color

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time [Formula: see text]. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integ

This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-