Advances in Mathematical Physics

Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph is a subset of the vertices such that every vertex not in is adjacent to at least one member of . The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of -Regular vague dominating set and provide some examples to explain various concepts introduced. Also, some results were discussed. Additionally, the -Regular strong (weak) and independent strong (weak) domination sets for vague domination set (VDS) were presented with some theorems to support the context.

This article gives some essential scopes to study the characterizations of the antineutrosophic subgroup and antineutrosophic normal subgroup. Again, several theories and properties have been mentioned which are essential for analyzing their mathematical framework. Moreover, their homomorphic properties have been discussed.

In this paper, we report the effect of classical and quantum superposition of atomic states on quantum correlations. Coupled photon pairs generated in a ladder quantum beat laser using coherent-induced classical field and atomic state coherent superposition are considered. Once the quantum coherence get sufficient time, it can generate quantum correlations that include quantum discord, quantum entanglement, and quantum steering, which quickly increase with time until they get their maximum strength. Their strength can be improved further by increasing the number of superposed atoms per unit time, selecting an appropriate amplitude of the classical fields, and managing the amount of temperatures and phase fluctuations. In particular, two-way quantum steering, which is a guarantee for the existence of quantum discord and quantum entanglement, can be achieved by increasing the rate of atomic injection from 2 kHz to 25 kHz even if the mean temperature of the heat bath is considered. The maximum achievable strength of quantum correlations is enhanced by increasing the rate of atomic injection and choosing an appropriate parameters of the coherent-induced classical field in the open quantum system which is treated by using the density operator approach.

The concept of the natural mate and the conjugate curves associated to a smooth curve in Euclidian 3-space were introduced initially by Dashmukh and others. In this paper, we give some extra results that add more properties of the natural mate and the conjugate curves associated with a smooth space curve in . The position vectors of the natural mate and the conjugate of a given smooth curve are investigated. Also, using the position vector of the natural mate, the necessary and sufficient condition for a smooth given curve to be a Bertrand curve is introduced. Moreover, a new characterization of a general helix is introduced.

This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of immunity by recovered individuals. The analytic solutions, which are given as series solutions, are derived using the fractional power series method (FPSM) and the residual power series method (RPSM). In comparison, the series solution for the number of susceptible members, using the FPSM, is proportional to the series solution, using the RPSM for the first two terms, with a proportional constant of , where is the natural birth rate of the baby into the susceptible population, is the gamma function, is the th term of the series, and is the fractional order as the initial number of susceptible individuals approaches the population size of Ghana. However, the variation in the two series solutions of the number of members who are susceptible to the COVID-19 disease begins at the third term and continues through the remaining terms. This is brought on by the nonlinear function present in the equation for the susceptible subgroup. The similar finding is made in the series solution of the number of exposed individuals. The series solutions for the number of deviant people, the number of nondeviant people, the number of people quarantined, and the number of people recovered using the FPSM are unquestionably almost identical to the series solutions for same subgroups using the RPSM, with the exception that these series solutions have initial conditions of the subgroup of the population size. It is observed that, in this paper, the series solutions of the nonlinear system of fractional partial differential equations (PDEs) provided by the RPSM are more in line with the field data than the series solutions provided by the FPSM.

The informatization construction of the power grid is becoming increasingly popular, business application systems are constantly emerging, and power-related data is rapidly expanding. These discrete power data are scattered in various application systems, and it is not easy to directly provide advanced enterprise applications. The establishment of intelligent power statistical model is an urgent need for constructing power grid informatization. This paper proposes a model of an electric energy metering system based on intelligent sensor data and introduces the existing digital metering system. This model is the integration and promotion of business integration based on the digital metering system. It is the first time to apply new metering equipment, such as measurement and control devices with integrated metering functions, and new metering technologies, such as IEC 61850 electricity meter reading applications. It is hoped that this paper can lay a foundation for further research.