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

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Impact of Online Education: an Artificial Intelligence-Based analysis 网络教育的影响:基于人工智能的分析
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-02 DOI: 10.1007/s40010-025-00975-2
R. Sujatha, Gali Yaswanth, Jyotir Moy Chatterjee, Ishaani Priyadarshini
{"title":"Impact of Online Education: an Artificial Intelligence-Based analysis","authors":"R. Sujatha,&nbsp;Gali Yaswanth,&nbsp;Jyotir Moy Chatterjee,&nbsp;Ishaani Priyadarshini","doi":"10.1007/s40010-025-00975-2","DOIUrl":"10.1007/s40010-025-00975-2","url":null,"abstract":"<div><p>Online education is one of the educational solutions for students during the COVID-19 pandemic. Worldwide, most universities have shifted much of their learning frameworks to an online learning model to limit physical interaction between people and slow the spread of COVID-19. The effectiveness of online learning depends on multiple factors, including student and instructor self-efficacy, attitudes, and confidence in using the technology involved; the educational strategies employed; the ability to monitor and evaluate educational outcomes; and student motivation, among many others. Therefore, in the present work, we will be assessing the performance and student condition in the online mode of education by predicting the degree to which students are satisfied in online mode depending on factors like internet facility, interaction in online mode, etc. We will be evaluating the data, which is collected using a survey method with almost 1000 records with 22 attributes by applying various machine learning models (XGBoost, Random Forest, Catboost, Gradient Boosting) and a deep learning model named TabNet to predict the impact of online education among the students. To enhance the accuracy of the prediction model, we have ensembled the machine learning and deep learning models. The ensemble model gave an accuracy of 86.6%, with an F1 score of 0.863 on the dataset.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"287 - 297"},"PeriodicalIF":1.3,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coinfection Dynamics of Tuberculosis with Other Infectious Diseases—A Mathematical Study 结核病与其他传染病共感染动力学的数学研究
IF 1.2 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-02 DOI: 10.1007/s40010-025-00946-7
Aditya Pandey, Archana Singh Bhadauria
{"title":"Coinfection Dynamics of Tuberculosis with Other Infectious Diseases—A Mathematical Study","authors":"Aditya Pandey,&nbsp;Archana Singh Bhadauria","doi":"10.1007/s40010-025-00946-7","DOIUrl":"10.1007/s40010-025-00946-7","url":null,"abstract":"<div><p>This study investigates the SEIR mathematical model to examine the co-dynamics of tuberculosis and other infectious diseases. Tuberculosis patients are known to have a higher susceptibility to additional infections due to compromised immunity. As such, understanding the dynamics of co-infections involving tuberculosis is critical, given their significant contribution to the overall disease burden in a population. In this paper, we propose an SEIR model that accounts for saturated treatment and incidence rates. A local stability analysis of the model is conducted, along with the calculation of the basic reproduction number. We also perform a sensitivity analysis of the reproduction number. Furthermore, an optimal control problem is formulated to enhance prevention strategies and minimize the costs associated with managing co-infectious diseases. The findings highlight that providing effective treatment to the infected population is the most impactful and cost-efficient strategy for disease control.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 1","pages":"15 - 31"},"PeriodicalIF":1.2,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147611963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical Solution of Third-Order Singularly Perturbed Boundary Value Problems Via Quartic B-Spline Method 三阶奇摄动边值问题的四次b样条法数值解
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-29 DOI: 10.1007/s40010-025-00974-3
Hradyesh Kumar Mishra, Ram Kishun Lodhi
{"title":"Numerical Solution of Third-Order Singularly Perturbed Boundary Value Problems Via Quartic B-Spline Method","authors":"Hradyesh Kumar Mishra,&nbsp;Ram Kishun Lodhi","doi":"10.1007/s40010-025-00974-3","DOIUrl":"10.1007/s40010-025-00974-3","url":null,"abstract":"<div><p>This manuscript presents a Quartic B-spline Method (QBSM) for the accurate estimation of numerical solutions to singularly perturbed third order boundary value problems (SPTOBVPs). The technique leverages a piecewise uniform mesh, constructed through the Fitted Mesh Technique (FMT), to enhance nodal point distribution within boundary layer regions. The convergence of proposed method are thoroughly investigated and found that it gives second-order convergence results. The efficacy of proposed method is demonstrated through the numerical examples, substantiating its theoretical results.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"279 - 286"},"PeriodicalIF":1.3,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Efficient Supply Management in Water Flow Network Using Graph Spectral Techniques Based on a Distance Laplacian Matrix 基于距离拉普拉斯矩阵的图谱技术在水流网络中的高效供应管理
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-22 DOI: 10.1007/s40010-025-00972-5
Tamilselvi Gopalsamy, Vasanthi Thankappan, Sundar Chandramohan
{"title":"An Efficient Supply Management in Water Flow Network Using Graph Spectral Techniques Based on a Distance Laplacian Matrix","authors":"Tamilselvi Gopalsamy,&nbsp;Vasanthi Thankappan,&nbsp;Sundar Chandramohan","doi":"10.1007/s40010-025-00972-5","DOIUrl":"10.1007/s40010-025-00972-5","url":null,"abstract":"<div><p>The efficient management of water distribution networks (WDNs) is crucial for ensuring sustainable urban water supply. In this paper, we present a novel framework that utilizes the Distance Laplacian Matrix (DLM) to analyze and optimize WDNs. The DLM integrates distance information into the Laplacian matrix, offering valuable insights into network connectivity and dynamics. We introduce a comprehensive methodology that employs spectral analysis techniques based on the DLM to tackle key challenges in WDN management, such as critical node identification, network resilience assessment, and structural optimization. Through case studies and practical implementations, we illustrate the effectiveness of our approach in improving decision-making processes and enhancing the efficiency and resilience of WDNs. The framework offers a novel suite of Distance Laplacian Matrix techniques tailored to enhance core water management tasks and streamline the identification of water losses through optimal network partitioning. This study proposes a novel framework using the Distance Laplacian Matrix (DLM) for efficient water distribution network management. The DLM incorporates distance metrics into spectral analysis, which provides enhanced network connectivity and performance insights. Through the application of DLM-based spectral clustering, critical nodes, resilience assessments, and network optimization tasks are handled effectively. Case studies demonstrate the applicability of the framework in urban water networks, ensuring improved decision making for network partitioning and resource distribution.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"247 - 268"},"PeriodicalIF":1.3,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Machinability of Tungsten Carbide Through Electrical Discharge Machining: State of Art and Future Perspectives 电火花加工碳化钨的可加工性:现状与展望
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-22 DOI: 10.1007/s40010-025-00964-5
Mayank Choubey, Kalipada Maity, Sandeep Bansal, Pushpinder Kumar
{"title":"Machinability of Tungsten Carbide Through Electrical Discharge Machining: State of Art and Future Perspectives","authors":"Mayank Choubey,&nbsp;Kalipada Maity,&nbsp;Sandeep Bansal,&nbsp;Pushpinder Kumar","doi":"10.1007/s40010-025-00964-5","DOIUrl":"10.1007/s40010-025-00964-5","url":null,"abstract":"<div><p>The ability to machine complex components in hard and difficult-to-machine materials with great geometrical accuracy has made electrical discharge machining (EDM) the most prevalent unconventional machining method. Recently, EDM has proven beneficial in machining complex 3D objects, employing composites made of tungsten carbide, which is difficult to cut, and in manufacturing dies, cavities, and intricate moulds. The prime objective of this review is to provide the most recent developments in electrical discharge machining of tungsten carbide and its composites. A quick introduction to the EDM and micro-EDM processes sets the stage for the review. This research categorizes conventional electrical discharge machining and the recent hybrid methods used with tungsten carbide into two basic categories. This review also highlights the difficulties and challenges of machining tungsten carbide using micro-EDM and the significance of combined and hybrid machining methods. The conclusion summarizes the recommendations for further studies based on the review.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 3","pages":"515 - 529"},"PeriodicalIF":1.3,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Green Synthesis of Covellite CuS Nanoparticles for BLEDs 用于BLEDs的covelite cu纳米颗粒的绿色合成
IF 1.2 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-19 DOI: 10.1007/s40010-025-00947-6
Yukti Gupta, Neena Jaggi
{"title":"Green Synthesis of Covellite CuS Nanoparticles for BLEDs","authors":"Yukti Gupta,&nbsp;Neena Jaggi","doi":"10.1007/s40010-025-00947-6","DOIUrl":"10.1007/s40010-025-00947-6","url":null,"abstract":"<div><p>In the present study, tulsi extract mediated hydrothermal method is utilized for the synthesis of Covellite CuS nanoparticles. To optimize the synthesised nanoparticles for their application in Blue Light Emitting Diode (BLEDs), the effect of reaction time on their structural and optical properties, was studied at 100 °C for 8 h, 12 h, and 16 h. Here, a biomolecule eugenol present in tulsi extract acted as a good reducing, stabilizing, and catalytic agent. The diffraction and morphological studies were conducted using X-Ray Diffraction and Field Emission Scanning Electron Microscopy analysis respectively. The particle size decreases with the increase in reaction time and the structural parameters matched well with the covellite CuS hexagonal phase prepared at 12 h reaction time. Ultraviolet-visible absorption studies reveal that the bandgap of nanoparticles was found in the range of 3.64–3.8 eV. The Photoluminescence spectroscopy and CIE chromaticity plot reveal that the sample synthesized at 12 h has a low recombination rate and emits light in the blue region which suggests that it can be utilized in devices like blue LEDs and lamps. Statement of relevance. In the present study, the green synthesis approach is adopted by using Tulsi extract as a solvent for synthesizing Covellite CuS nanoparticles via the hydrothermal route. The optical properties of synthesized sample reveal that the sample can be a potential n-type material for Blue LEDs.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 1","pages":"33 - 41"},"PeriodicalIF":1.2,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147611964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical Investigation of Liquefaction Behavior in Poorly Graded Fine Sand Reinforced by Stone Columns 石柱加筋差级配细砂液化特性数值研究
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-18 DOI: 10.1007/s40010-025-00970-7
Md Naseem Ahamad, Neelu Patel, V. P. Singh
{"title":"Numerical Investigation of Liquefaction Behavior in Poorly Graded Fine Sand Reinforced by Stone Columns","authors":"Md Naseem Ahamad,&nbsp;Neelu Patel,&nbsp;V. P. Singh","doi":"10.1007/s40010-025-00970-7","DOIUrl":"10.1007/s40010-025-00970-7","url":null,"abstract":"<div><p>Bahraich district (Uttar Pradesh, India) falls under seismic zone IV. The subsoil deposits in the Bahraich region consist of uniformly graded sand with a loose to medium-density profile and water tables vary at shallow depth. All these geological, compositional and state criteria lead to liquefaction during earthquakes. One particular ground improvement approach that lowers the risk of liquefaction and associated ground deformation is the installation of stone column in loose soil. Numerical analysis for implementation of stone columns in this region provides a better and efficient insight for the implementation of this technique to enhance ground condition and decrease the risk of liquefaction. In this study, (3D) finite element (FE) numerical analysis has been performed to simulate the stone column (SC). For 3D FE analysis an open-source computational platform OpenSeesPL is used. OpenSeesPL has a robust user interface that simplifies the effort-intensive pre and post processing phases. Initially, a liquefaction susceptibility analysis (LSA) was conducted, considering local geological, compositional, state, and historical criteria. The LSA indicates that the site under consideration is susceptible to liquefaction up to a significant depth (7.50 m), with a very high level of severity. Following that, a comparative analysis was performed between unimproved liquefiable soil and improved soil to demonstrate the impact of stone columns (SC) on the response of liquefiable soil to earthquake of 6.8 Mw. It was found that lateral displacement was reduced by 83.36% and excess pore pressure was reduced by 27.91%. The results of the present study were compared with other investigations, and it was found that the results are closely matching. Subsequently, a parametric study was also conducted to assess the influence of each factor such as area replacement ratio (A<sub>rr</sub> = 9%, 13%, 20%), diameter of stone column (D = 0.4 m, 0.8 m, 1.0 m, 1.2 m ) and stone column (SC) permeability (k<sub>sc</sub> = 0.01 m/s, 0.1 m/s, 1.0 m/s) on lateral surface displacement and excess pore pressure (EPP). The results show that increasing A<sub>rr,</sub> D, and k leads to reduction in lateral displacement and EPP. The maximum reduction in lateral displacement was 83.38%, 86.46% and 93.73% and maximum reduction in EPP was 10%, 26.65% and 94.43% respectively at A<sub>rr</sub> = 20%, D = 1.2 m and k<sub>sc</sub> = 1.0 m/sec. The outcomes of the study demonstrate that the installation of stone column is an effective measure for ground improvement and the mitigation of liquefaction in loose, saturated fine sand deposits.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"213 - 232"},"PeriodicalIF":1.3,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Implications of Exponentially Decaying Internal Heat Generation on Mixed Convection Flow from a Vertical Porous Plate Influenced by Hydrodynamics and Thermal Partial Slip 指数衰减内生热对流体力学和热偏滑影响下垂直多孔板混合对流流动的影响
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-15 DOI: 10.1007/s40010-025-00967-2
Basant K. Jha, Gabriel Samaila
{"title":"On the Implications of Exponentially Decaying Internal Heat Generation on Mixed Convection Flow from a Vertical Porous Plate Influenced by Hydrodynamics and Thermal Partial Slip","authors":"Basant K. Jha,&nbsp;Gabriel Samaila","doi":"10.1007/s40010-025-00967-2","DOIUrl":"10.1007/s40010-025-00967-2","url":null,"abstract":"<div><p>This article contains crucial details about how internal heat generation affects mixed convection slip flow past a vertical plate. The simplified first-order differential equations are integrated with Maple Software 2022. One of the most important discoveries is that internal heat generation acts as a barrier to stop heat from flowing from the left to the right plate edge. However, this could be averted by considering strong mixed convection to covect away the heat conducted through the left plate surface and the internal heat generated. But for weak mixed convection, the movement of the fluid from the left to the right surface is achievable even with minimal internal heat generation. Since the right plate surface temperature is warmer (higher) than the left plate surface, the flow properties, in this case, are also affected by the internal heat generation, which also causes the reverse heat flow from the plate. Particle injection could also be used to avert unwanted reversed flow for various hydrodynamic slip conditions considered. <i>Research relevance</i> Internal heat generation can be used in heat transmission, nuclear reactors, post-accident heat removal operations, modeling of the combustion process, production of metal waste from nuclear fuel, and phase transition. However, the analysis of internal heat generation is influenced by the plate surface. The constant or convective boundary conditions were taken into account by various previous researchers. In this communication, momentum and thermal partial slip conditions are applied to the plate surface. The fundamental novelty of this article is the combination of internal heat generation, hydrodynamics, and thermal partial slip conditions.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"185 - 191"},"PeriodicalIF":1.3,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fuzzy Deductive Systems in Sheffer Stroke Hilbert Algebras Sheffer Stroke Hilbert代数中的模糊演绎系统
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-15 DOI: 10.1007/s40010-025-00968-1
Young Bae Jun, Tahsin Oner
{"title":"Fuzzy Deductive Systems in Sheffer Stroke Hilbert Algebras","authors":"Young Bae Jun,&nbsp;Tahsin Oner","doi":"10.1007/s40010-025-00968-1","DOIUrl":"10.1007/s40010-025-00968-1","url":null,"abstract":"<div><p>With the aim of discussing the deductive system in Sheffer stroke Hilbert algebras using fuzzy sets, the notions of fuzzy deductive system and positive subset in Sheffer stroke Hilbert algebras are introduced, and their properties are investigated. Conditions under which a fuzzy set can be a fuzzy deductive system are explored, and characterizations of a fuzzy deductive system are considered. The situation in which a positive subset will be a deductive system with respect to the conditions that fuzzy sets have is discussed. Also, the situation in which <i>t</i>-level set and <span>(Q_{t})</span>-set of a fuzzy set will be deductive systems with respect to the conditions that fuzzy sets have is explored. Finally, fuzzy deductive systems by their level deductive systems are classified.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"193 - 202"},"PeriodicalIF":1.3,"publicationDate":"2025-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the (A_{alpha }) matrix over finite metacyclic groups 有限亚环群上(A_{alpha })矩阵
IF 1.2 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2025-12-12 DOI: 10.1007/s40010-025-00933-y
Aditya Singh, Yogendra Singh, Anand Kumar Tiwari, S. Pirzada
{"title":"On the (A_{alpha }) matrix over finite metacyclic groups","authors":"Aditya Singh,&nbsp;Yogendra Singh,&nbsp;Anand Kumar Tiwari,&nbsp;S. Pirzada","doi":"10.1007/s40010-025-00933-y","DOIUrl":"10.1007/s40010-025-00933-y","url":null,"abstract":"<div><p>The <span>(A_{alpha })</span> matrix of a graph <i>G</i> is defined as <span>(A_{alpha }(G) = alpha D(G) + (1-alpha )A(G))</span>, where <i>D</i>(<i>G</i>) and <i>A</i>(<i>G</i>) denote the degree diagonal matrix and adjacency matrix of the graph <i>G</i>, respectively. In this article, we determine the eigenvalues of <span>(A_{alpha })</span> matrix for the power graph of a class of metacyclic groups. We set upper and lower bounds for the largest eigenvalues of <span>(A_{alpha })</span> matrix associated with the power graphs of the finite cyclic group of order <i>n</i> and the metacyclic group.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 1","pages":"1 - 13"},"PeriodicalIF":1.2,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147612872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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