This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

The present work was conducted in the fields of Al-Sewarah and Kurkok stations which belong to the State Board of Agricultural Researches, Ministry of Agriculture, Iraq during the growing season of 2018. The goal of the study was to test the effects of the application of cyanobacteria  (Anabaena circinalis and Nostoc commune) alone or in combination with reducing the dose of chemical fertilizers (CFs), which consisted of diammonium phosphate (DAP) and urea (46% nitrogen), on growth, yield and yield components of wheat cv. IPA99. Application of 50%  and 100% of CFs without cyanobacteria as well as control (without cyanobacteria and CFs) were also included in this study for comparison.

The resul

     This paper is concerned with a Holling-II stage-structured predator-prey system in which predators are divided into an immature and mature predators. The aim is to explore the impact of the prey's fear caused by the dread of mature predators in a prey-predator model including intraspecific competitions and prey shelters. The theoretical study includes the local and global stability analysis for the three equilibrium points of the system and shows the prey's fear may lead to improving the stability at the positive equilibrium point. A numerical analysis is given to ensure the accuracy of the theoretical outcomes and to testify the conditions of stability of the system near the non-trivial equilibrium points.

The study included examination of three types of different origin and orange juice at the rate of recurring per sample, the results showed that the highest rates of acid (pH) in the A and juice were (4). And salts of calcium is 120 ppm in juice C and 86 ppm of magnesium in the juice B, for heavy metals the highest rate of lead .18 recorded ppm in juice B, 1.32 ppm of copper in juice A, 5 ppm of iron in the juice B, 1.3 ppm of zinc in the juice B, 0.05 ppm of aluminum in each of the sappy B and A, 0.02 ppm of cobalt in the juice B, 0.3 ppm of nickel in the juice B, 170.6 ppm sodium in C juice, but for the acids, organic that the highest rates were 3.2 part Millions of acid in the juice owner a, 260 ppm of the acid in the juice the ascorbi

In dental and medical applications, poly-methyl methacrylate (PMMA) has been widely accepted due to the excellent biocompatibility and easy fabrication. Yet, some of the physical and mechanical characteristics of this compound are considered inferior. Seven groups of PMMA nano-composite samples were reported to be fabricated at laboratory temperature . These samples could be used in manufacturing the complete or partial maxillary denture base. The aim of this research is to prepare nano-composite materials which consist of PMMA as a matrix material and two different types of powder (prepared nanoparticles of SnO₂ and natural egg shell powder (ESP)) as strengthening materials. The selected additives were used in many cases as p

The demand on energy sources throughout the world have led to an increase in the production processes of crude oil which is considered to be the main source of energy, without considering the impact on the environment. The objective of this study is to evaluate the environmental impact of drilling processes and crude oil spillage on soil in the Rumaila oil field, Basra, Southern Iraq. An investigation was undertaken to determine the content of Polycyclic Aromatic Hydrocarbons (PAHs) and heavy metals in the soil. Ten soil samples were collected near oil wells and analyzed. The results showed a high concentration of PAHsin the soil, particularly (Acenaphthene, Fluorene, Anthracene, Fluoranthene and Pyrene) due to crude oil spillage. The he

Albumin is the most abundant protein in blood plasma, serves as a circulating depot for endogenous and exogenous (e.g. drugs) compounds due to its ligand binding properties, this work aim to get information about the binding of Amoxicillin (antibiotics) with albumin, and the influence of the solvent polarity and ionic strength on it by using UV -vis spectrophotometric measurements in phosphate buffer of pH7.4 and three different temperature (290, 300, 310) K. The UV absorption shows a change and a shift in the absorbency and a shift in albumin and amoxicillin peaks, the two changes are indicative of complex formation. The stoichiometry of the interaction were calculated by the method of continuous variations which was1:1at pH 7.4.The equ

Mishrif Formation regards one of the most important reservoirs in Iraq. Well logging represents one of the most important tool in the formation evaluation. According to the Petrophysical properties that have been gotten from well logging, Mishrif Formation in terms of reservoirs units, consist of several reservoirs units. Major reservoirs units divided into three reservoir units,MA,MB&MC. Each of these major units divided into minor reservoirs units (MB11,MB12,MC2&MC3).MB major reservoir units represent the best reservoir unit. These reservoirs units separated by cap rocks(mainly tight limestone)(CR1,CR2,CR3,CR4,CR5,CR6,and CR7).CPI were demonstrated for all wells.Hydrocarbon saturation vs.