This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control qua

    This study was based on the determination of aphid species that infested Chrysanthemum sp. (Asterales, Asteraceae) in the middle of Iraq; five aphid species belong to subfamily Aphidinae were recorded: Aphis fabae Scopoli, 1763, Aphis gossypii Glover, 1877,  Coloradoa rufomaculata (Wilson, 1908), Macrosiphoniella sanborni (Gillette, 1908) and Myzus persicae (Sulzer, 1776). A. gossypii was the most dominant species throughout the study period while M. persicae  is the lesser species.

    A summary of  the main taxonomic characters is presented here and a pictorial key which was designed to separate aphi

The quality of groundwater should be improved by keeping safe water sources from contaminants in protective way by doing regular measuring and checkup before it supplied for usage. Private Wells do not receive the same services that wells supplying the public do. Well owners are responsible for protecting their drinking water. This work was carried out in Badra city, Iraq from December 2017 to May 2018, six wells water were investigated to determine the general characteristics of wells as well as studying the effect of environmental factors on the quality of water. The average of six wells were eleven parameters that is out of permissible limits were EC, Sal., Alk., TH, TDS, Na, Ca, Cl, SO₄, Fe, Zn (4402-5183 /cm, 2.76-3.9 ppt

The traveling salesman problem (TSP) is a well-known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. In this paper we exploit the TSP to evaluate the minimum total cost (distance or time) for Iraqi cities. So two main methods are investigated to solve this problem; these methods are; Dynamic Programming (DP) and Branch and Bound Technique (BABT). For the BABT, more than one lower and upper bounds are be derived to gain the best one. The results of BABT are completely identical to DP, with less time for number of cities (n), 5 ≤ n ≤ 25. These results proof the efficiency of BABT compared with so