In this paper, we introduce and study the concept of S-coprime submodules, where a proper submodule N of an R-module M is called S-coprime submodule if M N is S-coprime Rmodule. Many properties about this concept are investigated.

  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

The global food supply heavily depends on utilizing fertilizers to meet production goals. The adverse impacts of traditional fertilization practices on the environment have necessitated the exploration of new alternatives in the form of smart fertilizer technologies (SFTs). This review seeks to categorize SFTs, which are slow and controlled-release Fertilizers (SCRFs), nano fertilizers, and biological fertilizers, and describes their operational principles. It examines the environmental implications of conventional fertilizers and outlines the attributes of SFTs that effectively address these concerns. The findings demonstrate a pronounced environmental advantage of SFTs, including enhanced crop yields, minimized nutrient loss, improved nut

Roller compacted concrete (RCC) is a material with no slumps and is made from the same raw materials as conventional concrete. The roller compacted dam method, the high paste technique, the corps of engineers method, and the maximum density method are all ways of designing RCC. The evolution of RCC has resulted in a substantial change in construction projects, most notably in dams, because of the sluggish pace of conventional placement, consolidation, and compacting. The construction process was accelerated by incorporating RCC into dams, resulting in a shorter construction period. Research shows that the dams that used RCC had completed one to two years sooner than the dams that used regular concrete (Bagheri an

African-American writers during the 19th century wrote in the shadow of the prominent romance, sentimental, and domestic fiction. Harriet Wilson’s Our Nig (1859) reflects an “alternative social character”, for the female protagonist suffers racism in the free North, because she is a mulatto child. Through depicting the life of free blacks, who supposedly lives a better life than Southern slaves, Wilson exposes how she has actually lived and sensed life in antebellum America. According to Raymond Williams (2011), there are two kinds of literary writings. The first represents the general tendency of the age, and he calls it “dominant social character”; representing the majority content of both the public writing and speaking. But, a

Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

The issue of freedom is the most prominent and distinctive issue of Western thought, which it reached after a long struggle. The English thinker John Stuart Mill is considered the most prominent Western thinker who elaborated on the issue of freedom, until his ideas on the issue of freedom became the semi-final formula for issues of freedom in Western thought, which revolve in their entirety on The individual has complete freedom as long as it does not harm others, and this freedom is controlled by law.

And if the freedoms he offered were not considered an achievement in Western thought; Freedom in Islam is a central and fundamental issue, and the details of freedoms in Islam have not been accomplished by anyone, but rather came

The main objective of this work is to propose a new routing protocol for wireless sensor network employed to serve IoT systems. The routing protocol has to adapt with different requirements in order to enhance the performance of IoT applications. The link quality, node depth and energy are used as metrics to make routing decisions. Comparison with other protocols is essential to show the improvements achieved by this work, thus protocols designed to serve the same purpose such as AODV, REL and LABILE are chosen to compare the proposed routing protocol with. To add integrative and holistic, some of important features are added and tested such as actuating and mobility. These features are greatly required by some of IoT applications and im

In this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control