The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between

A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????=????????, denoted by pur(R) . In this work we studied some new properties of pur(R) finally we defined the complement of pur(R) and studied some of it is properties

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

In this paper, various aspects of smart grids are described. These aspects include the components of smart grids, the detailed functions of the smart energy meters within the smart grids and their effects on increasing the awareness, the advantages and disadvantages of smart grids, and the requirements of utilizing smart grids. To put some light on the difference between smart grids and traditional utility grids, some aspects of the traditional utility grids are covered in this paper as well.

Background: Periodontal disease is a chronic bacterial infection that affects the gingiva and bone supporting the teeth. Smoking, which is an important risk factor for periodontitis, induce oxidative stress in the body and cause an imbalance between reactive oxygen species (ROS) and antioxidants, such as superoxide dismutase (SOD). This study aimed to evaluate the influence of smoking on periodontal health status by estimating the levels of salivary SOD level in non-smokers (controls) and light and heavy smokers and to test the correlation between the SOD enzyme level and the clinical periodontal parameters in each group. Materials and Methods: The study sample consisted of 75 male, with age ranged from 35 to 50 years. Clinically, the perio

This research explores the concept of cruel optimism in the context of challenging patriarchal, cultural, and social traditions in Ayad Akhtar’s The Who and the What. Cruel optimism, a term coined by Lauren Berlant, refers to the paradoxical attachment to positive aspirations that may ultimately obstruct personal fulfillment and well-being. This study examines how individuals who resist patriarchal norms and entrenched cultural traditions often face significant emotional, psychological, and social challenges. Through a multidisciplinary approach, including literary analysis, sociological perspectives, and psychological insights, the research delves into the lived experiences of those who strive for autonomy, equality, and self-realization

Bipedal robotic mechanisms are unstable due to the unilateral contact passive joint between the sole and the ground. Hierarchical control layers are crucial for creating walking patterns, stabilizing locomotion, and ensuring correct angular trajectories for bipedal joints due to the system’s various degrees of freedom. This work provides a hierarchical control scheme for a bipedal robot that focuses on balance (stabilization) and low-level tracking control while considering flexible joints. The stabilization control method uses the Newton–Euler formulation to establish a mathematical relationship between the zero-moment point (ZMP) and the center of mass (COM), resulting in highly nonlinear and coupled dynamic equations. Adaptiv