Proceedings of the National Academy of Sciences, India Section A: Physical Sciences最新文献

The enhanced power graph ({mathcal {P}}_E(G)) of a group G is a simple undirected graph with the vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup of G. In this paper, we have obtained the metric dimension and the resolving polynomial of the enhanced power graph of the non-abelian group of order p³, where p is an odd prime. We also study the coloring and detour distance properties of the graph ({mathcal {P}}_E(G)).

The COVID-19 pandemic has emerged as one of the most devastating infectious disease in the history of mankind. Though the collective efforts of various institutions across the globe have potentially managed to control the pandemic, the infection still continues to pose a public health risk. In this paper, we develop a modified SEIQHRD model to study the transmission dynamics of the COVID-19 across a region. The basic reproduction number, which measures the potential spread of the virus is computed. Disease free equilibrium point for the model is shown to be locally as well as globally asymptotically stable whenever (R_0 le 1). Further, existence of endemic equilibrium along with its local and global asymptotic stability is proved when (R_0>1). Sensitivity analysis is performed for the associated parameters in the model. Finally, numerical simulation is done for the formulated model that demonstrates and validates the theoretical results derived in the paper.

Using the Fibonacci matrix, we introduce the Fibonacci sequence of fuzzy variables in four directions of credibility theory: almost surely, credibility, mean, and (p-) distance. We also discuss the (p-)distance convergence of a sequence of fuzzy variables in terms of credibility. In this context, we demonstrate some relationship between the aforementioned Fibonacci convergence and the existent ones.

Free space optical system (FSO) is a wireless communication system which offers unlicensed spectrum with low cost of deployment. Losses caused by atmospheric turbulence are an enormous challenge for FSO systems. The Gamma–Gamma model is used to represent moderate to strong turbulence. This model considers wind velocity, but does not consider rainfall parameter for the calculation of refractive index structure parameter C_n². In this research paper, we have considered effect of heavy rainfall as well as rms value of strong wind velocity which exist in hilly terrains. This modified model for the proposed spectrum-sliced wavelength division multiplexing (SS-WDM) communication link incorporates differential quadrature phase shift keying (DQPSK) between the popular high altitude Nilgiris mountains from the state of Tamilnadu, India. Simulation of conventional model and the modified model by considering rainfall parameter as well as wind velocity has been demonstrated using meteorological data. The impact of pointing errors in the presence of fog is studied. The results in terms of eye diagrams, and performance metrics such as bit error rate (BER), log (BER), Q-factor, and maximum eye height indicate that the modified model is more accurate for maintaining foolproof and efficient communication link. Data rate increases four times by implementing SS-WDM.

A NASICON-type solid electrolyte Li_1.3Al_0.3Ti_1.7(PO₄)₃(LATP) ceramic was prepared using the sol–gel synthesis technique. To improve the ionic conductivity of LATP ceramic, Sb₂O₃ was added. The effect of Sb₂O₃ on the structural, microstructural, and ionic conductivity of the LATP ceramic was investigated. IR spectra were studied to determine the structural groups present in the ceramic samples. The highest bulk conductivity of 3.95 × 10^–3 Scm⁻¹ at room temperature, a relative density of 84.01%, and a low activation energy of 0.17 eV is obtained for the 1wt% Sb₂O₃ added LATP ceramic. The Sb₂O₃ added LATP ceramics can be a promising electrolyte material for solid-state lithium-ion battery applications.

Edge colouring for crisp graphs is a well-defined topic. However, fuzzy graph edge coloring was very recently developed. In a m-polar fuzzy network, however, we have to take into account m components for each node and edge. Since this idea has just one component, we cannot handle this kind of circumstance with a fuzzy model for we consider m components for both nodes and edges in our consideration. Again, we cannot utilize the bipolar or intuitionistic models because every edge or node in the fuzzy network consists of simply two components. Therefore, these mPFG models yield fuzziness discoveries more effectively than earlier fuzzy models. Additionally, creating and examining these kinds of mPFGs with instances and associated theorems is quite intriguing. Considering all those things together, defining edge colouring for mPFG needs some new ideas. In this article, we studied edge colouring for mPFG along with many interesting associated properties. Here, the chromatic index as well as its generalizations and interconnected facts are thoroughly investigated. Here, we also find chromatic numbers as well as strong chromatic numbers on some well-known mPFG. A relation between chromatic numbers and the strong chromatic number has been discussed here. We also give an alternative form of edge colouring with the help of node colouring based on the mPF line graph. Both processes have been discussed thoroughly in step-by-step methods along with prescribed examples. We introduced an algorithm for edge colouring on mPFG. Lastly, a real-life application based on edge colouring for mPFG has been discussed to show the usefulness of the proposed method.

The Himalayan regions are encountering substantial challenges in managing spring water quality, driven by rapid urbanization, changing land use patterns, and insufficient management and regulatory oversight. The present research focuses on the use of the Water Quality Index (WQI) and geospatial techniques to assess the spring water quality in a Himalayan district, with 49 samples collected from Rudraprayag district for analysis. The study includes entropy weighted and weighted arithmetic WQI and their comparison to assess potability of spring water samples. The requirement of data for calculating WQI and geospatial mapping is applied after analyzing the physico-chemical parameters of all samples. The physico-chemical parameters were analyzed applying APHA standard method. Only one sample demonstrates that spring water quality is non-potable for drinking due to high Fe contamination (28.40 mg/L). Fe concentration in that location exceeds 93 times than the WHO permissible limit (0.3 mg/L). The Mg (10.20–72.41 mg/L) and Ca (14–142 mg/L) concentrations in 18% and 8% of samples exceeded the WHO standard limit. The existence of higher igneous rocks and rapid groundwater pumping increases the Fe content in spring water. Results of WQI suggest that spring water quality in most of the monitoring locations is suitable for drinking. The outcomes of EWWQI and WAWQI reveal that 98% and 82% of samples have excellent water quality. Applying the procedures of identification and management, geospatial mapping is acquired depending on data ranges including all relevant criteria. Therefore periodical monitoring of physico-chemical parameters is necessary to protect waterbodies from pollution and a cost-effective treatment method must be adopted to reduce Fe contamination in spring water. Moreover, the spring water must be free from bacterial infections to safeguard human health and living organisms.

The proposed analysis contribute an essential analysis towards comprehensive and theoretical grasp the how the existing gradient descent algorithm (GDA) beneficial efficiently on homotopy analysis technique. To illustrate the idea, we consider the fundamental Burgers’ equation which is one the simplest nonlinear model. The majority of PDEs has been evaluating by considering either an approximate analytical approach or numerical owing to the occurrence of severe nonlinearity. Further, among several approximation techniques, the HAM, shows better results and regulate the region of convergence of computed closed form solution due to presence of auxiliary parameter (hslash). In HAM, choosing (hslash) values is based on trial and error approach and due to this solution might be diverges. Therefore, it is necessary to determine convergence to the correct solution and ensure correctness. To do so, the well established GDA is the proper choice for obtaining the precise solution by establish the accurate values of (hslash). The results of obtained from GDA are validated with already-reported analytical and numerical results from the literature in order to confirm the efficacy of the proposed method. The work proposed here would be advantageous for solving the different kinds of nonlinear models.

In the present paper, we investigate three theorems of the Volterra type containing (k, p-k) and (p,s,k) Mittag–Leffler functions. Moreover, the Laplace transforms of the (k, p-k) and (p,s,k) Mittag–Leffler functions are derived here. The solutions to these problems were obtained by the Laplace transform method. In some special cases, new and known results are also obtained here. The acquired results are suitable in the fields of applied science, physics, engineering, and technology. The novelty of this work lies in their enhanced modeling capabilities, improved solution methods, and interdisciplinary applicability, making them a powerful tool for understanding complex systems across various fields. Also, the special function involved here can be reduced to simple functions; those have a variety of applications in different areas of science and technology. In the future, researchers can do more work on Volterra-type integrals and differential equations using various types of special functions.

The Kumbh Mela, one of the world’s largest religious gatherings, poses significant public health and logistical challenges due to the influx of millions of pilgrims. This study employs a comprehensive Failure Modes and Effects Analysis (FMEA) and a resource allocation model to identify and address potential risks associated with infectious disease transmission during the event. The FMEA model was developed to systematically evaluate the key processes involved in managing infectious diseases during the Kumbh Mela 2025. The FMEA was conducted across five critical areas: sanitation facilities, healthcare services, security and crowd management, food safety and inspection, and public awareness and communication. The process involved mapping key activities, identifying potential failures, assessing their impact, and prioritizing mitigation strategies based on Risk Priority Numbers (RPN). Key findings reveal high-risk failure modes, such as insufficient sanitation facilities and inadequate food safety inspections, which necessitate strategic interventions. The resource allocation model was developed to optimize the distribution of 5,000 available resource units, aiming to minimize the deviation between allocated resources and actual demand. Results indicate significant shortfalls in sanitation and food safety, highlighting the need for innovative solutions and strategic partnerships to enhance service delivery. The study recommends leveraging technological innovations, such as AI-driven analytics and telemedicine, and engaging community volunteers as health ambassadors to mitigate risks and improve resource management. These insights provide a robust framework for enhancing preparedness and response capabilities, offering valuable implications for the management of future mass gatherings worldwide. By integrating data-driven decision-making and collaborative strategies, event organizers can ensure the health and safety of attendees, delivering a successful and safe Kumbh Mela 2025.