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

A quadruped (four-legged) robot locomotion has the potential ability for using in different applications such as walking over soft and rough terrains and to grantee the mobility and flexibility. In general, quadruped robots have three main periodic gaits:  creeping gait, running gait and galloping gait. The main problem of the quadruped robot during walking is the needing to be statically stable for slow gaits such as creeping gait. The statically stable walking as a condition depends on the stability margins that calculated particularly for this gait. In this paper, the creeping gait sequence analysis of each leg step during the swing and fixed phases has been carried out. The calculation of the minimum stability margins depends up

Bioaccumulation of heavy metals in the terrestrial invertebrates in Al-Jadriyia district Baghdad- Iraq were investigated. Forth terrestrial invertebrates snails, slug, isopods, and diplopods , were selected for this study. The results showed that all invertebrate groups have the ability in accumulate considerable amounts of heavy metals. Higher levels of zinc and copper were observed in the isopods specimens, it's about ( 60.50±0.58 ) and ( 96.00±0.58 ) ppm respectively , while higher levels of lead were observed in the diplopods specimens ,it's about ( 23.00±1.15 ) ppm ,but the higher levels of both iron and cadmium were observed in snail specimens , it's about ( 590.00±1.15 ) and ( 9.50±1.15 ) ppm respectively .but the

Globally, the COVID-19 pandemic’s development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease’s indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system’s solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used

There are many studies dealt with handoff management in mobile communication systems and some of these studies presented handoff schemes to manage this important process in cellular network. All previous schemes used relative signal strength (RSS) measurements. In this work, a new proposed handoff scheme had been presented depending not only on the RSS measurements but also used the threshold distance and neighboring BSS power margins in order to improve the handoff management process. We submitted here a threshold RSS as a condition to make a handoff when a mobile station moves from one cell to another this at first, then we submitted also a specified margin between the current received signal and the ongoing BS's received signal must be s

The concept of Assemblage appeared obviously in Postdramatic works, where a character or a text may stand as an assemblage of potentialities in the sense that it signifies unidentified subjectivity. Assemblages are constituted essentially of heterogeneous elements yet fused without specific demarcations. In order to enjoy the desired productivity at a "smooth pace," the regularities of political and societal institutionalization are disseminated. To achieve this dissemination, Deleuze-Guattari suggest an unsatiated platform of a "Body without Organs' (BwO), where desire escapes identification. Martin Crimp (b. 1956) defines his off-stage characters in Attempts on Her Life (1997), Anne, or whatever the name is, as a 'BwO', upon which