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 expansion in water projects implementations in Turkey and Syria becomes of great concern to the workers in the field of water resources management in Iraq. Such expansion with the absence of bi-lateral agreement between the three riparian countries of Tigris and Euphrates Rivers; Turkey, Syria and Iraq, is expected to lead to a substantially reduction of water inflow to the territories of Iraq. Accordingly, this study consists of two parts: first part is aiming to study the changes of the water inflow to the territory of Iraq, at Turkey and Syria borders, from 1953 to 2009; the results indicated that the annual mean inflow in Tigris River was decreased from 677 m³/sec to 526 m³/sec, after operating Turkey reserv

In this study, the volatile compounds found in lemon trees infested and uninfested with Planococcus citri (Risso) (Hemiptera: Pseudococcidae) were investigated. In addition, the interest of the predator Cryptolaemus montrouzieri (Coleoptera: Coccinellidae) and the parasitoid Leptomastix dactylopii (Hymenoptera: Encyrtidae) in lemon trees infested and uninfested with P. citri and some volatile compounds was investigated. According to the results obtained, most of the volatile compounds obtained from mealybug-infested lemon trees showed changes compared to healthy lemon trees. Since volatile compounds play an important role in attracting pests and natural enemies, linalyl acetate was selected as the compound showing the highest amount of chan

Improving in assembling technology has provided machines of higher evaluation with better resistances and managed behavior. This machinery led to remarkably higher dynamic forces and therefore higher stresses. In this paper, a dynamic investigation of rectangular machine diesel and gas engines foundation at the top surface of one-layer dry sand with various states (i.e., loose, medium and dense) was carried out. The dynamic investigation is performed numerically by utilizing limited component programming, PLAXIS 3D. The soil is accepted as flexible totally plastic material submits to Mohr-Coulomb yield basis. A harmonic load is applied at the foundation with amplitude of 10 kPa at a frequency of (10, 15 and 20) HZ and se

In the image processing’s field and computer vision it’s important to represent the image by its information. Image information comes from the image’s features that extracted from it using feature detection/extraction techniques and features description. Features in computer vision define informative data. For human eye its perfect to extract information from raw image, but computer cannot recognize image information. This is why various feature extraction techniques have been presented and progressed rapidly. This paper presents a general overview of the feature extraction categories for image.

Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how chemotherapy and anxiety work together to affect the speed at which cancer cells multiply and the immune system’s response model is necessary to come up with ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological scare and chemotherapy on the interaction of cancer and immunity. The proposed model is accurately described. The focus of the model’s dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish three equilibrium positions. The stability analysis reveals that all equilibrium points consi