Background: This study assessed the clinical usefulness of the solid phantom, which may compensate for the disadvantages of the water phantom, by comparing the radiological doses between the two depending on their depths. Materials and Methods: The experimental equipment used was a linear accelerator for medical use, water phantom, solid phantom, Farmer type ion chamber and electrometer. The di...

Minimum concave Cost Network Flow Problems (MCNFPs) arise naturally in many practical applications such as communication, transportation, distribution, and manufacturing, due to economic considerations. In addition, it has been shown that every MCNFP with general nonlinear cost functions can be transformed into a concave MCNFP on an expanded network. It must also be noted, that multiple source ...

The primary purpose of this paper is to identify recent major accomplishments and prophesy (suggest) future trends in the solution, modeling, and human engineering aspects of network and network-related problems. In particular, the suggested future trends consist of an integrated sequence of modeling, theoretical and computational developments which may allow mathematical programming to attain ...

We present a new algebraic algorithmic scheme to solve convex integer maximization problems of the following form, where c is a convex function on R and w1x, . . . , wdx are linear forms on R, max {c(w1x, . . . , wdx) : Ax = b, x ∈ N} . This method works for arbitrary input data A, b, d, w1, . . . , wd, c. Moreover, for fixed d and several important classes of programs in variable dimension, we...

We consider the following transportation problem with both random and fuzzy factors. There exist m supply points and n demand points. For each route between supply point and demand point, unit transportation cost is a random variable according to a normal distribution and existence possibility denoting the preference choosing this route is attached. The probability that the total transportation...