Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

In this study the adsorption of cefixime on to selected Iraqi clay bentonite. The aim of this study is to search for selective active surface in adsorption of the drug and to act as physical antidotes in treatment of poisoning if the drug is taken in quantities higher than the recommended dosages. Quantitative estimation of the drug adsorption has been done by utilizing the technique of UV spectrophotometry in λmax (273) nm at different conditions of temperature (25, 37, 45) ˚C found the adsorption decrease with increase the temperature. Study of clay weight of bentonite (0.1-1.5) gm found the adsorption increase with increase of clay weight, study effect of pH (1.2, 3, 5, 7) on adsorption of bentonite found the optimum adsorption

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

This narrative review focused on research investigating the impact of loneliness on the prevalence of dementia and its relationship with other risk factors. A comprehensive and rigorous search was conducted using a variety of scientific databases with specific keywords to identify all prior studies that examined the correlation between dementia and loneliness. The inquiry was confined to articles published in English from January 2017 to March 2024. The narrative review identified a consensus regarding the role of loneliness in enhancing the risk of all‐cause dementia, with a particular emphasis on the subjective perception of loneliness. This phenomenon may be caused by the sensations of exclusion, discrimination, and alienation that are

Abstract Introduction: Aphthous stomatitis is a recurring oral ulceration condition that affects a significant proportion of the population. While several factors have been proposed to contribute to its occurrence, the link between caffeine consumption, anxiety levels, and the development of aphthous stomatitis remains unknown. This survey-based study aimed to understand the association between coffee, anxiety, and the development of aphthous stomatitis in this specific demographic, which can provide useful insights for medical management as well as preventive strategies. Material and methods: A structured online questionnaire was distributed via various social media platforms targeting a sample of the Armenian population. The quest

International relations scholars have increasingly debated the evolving landscape of actors that challenge the traditional state-centric world order. A key element of this transformation is the rise of sub-state actors, which engages in alternative diplomacy parallel to the state, transcending traditional state-centric frameworks. This paper explores the significant shifts in international actorness over the late 20th century, focusing on the emergence and implications of sub-state diplomacy, or "paradiplomacy." First, the study introduces sub-state actors and their role in challenging the dominant state-centric discourse. It then examines the dynamic evolution of paradiplomacy, highlighting how sub-states have expanded their global