{"title":"An Investigation on µ-Deferred Triple Ideal Statistically Convergent Sequences in Credibility Space","authors":"Binod Chandra Tripathy, Ömer Kişi, Mehmet Gürdal","doi":"10.1007/s40010-025-00951-w","DOIUrl":"10.1007/s40010-025-00951-w","url":null,"abstract":"<div><p>The primary objective of this paper is to explore various forms of deferred convergence for triple sequences of fuzzy variables (<i>FV</i>), incorporating the concepts of ideal convergence and <span>(mu )</span>-density. We also establish a number of instances to illustrate our definitions. In this study, we also present important findings that reveal the connections between these definitions. The if and only if condition for the <span>(mu )</span>-deferred <span>(mathcal {I}_{3})</span>-statistically pre-Cauchy (<span>(pmathfrak {Ca})</span>) triple sequence of <i>FV</i> is also examined.</p><p><i>Significance of the work in broad context:</i> Summability theory and the convergence of sequences have numerous applications in mathematical analysis. However, the exploration of sequence convergence in credibility space is still in its early stages with limited progress. This paper contributes to the field by introducing the concept of <span>(mu )</span>-deferred <span>(mathcal {I}_{3})</span>-statistical convergence for sequences in credibility space. This novel approach opens up a new direction for researchers in the field.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 1","pages":"43 - 64"},"PeriodicalIF":1.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147611965","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}
Gunisetty Ramasekhar, Shaik Jakeer, Seethi Reddy Reddisekhar Reddy, Harshit Verma, P. Jayasri, P. Durgaprasad, Pankaj Shukla
{"title":"Homotopy Semi-numerical Modeling of Williamson Nanofluid Flow Over a Cone and Wedge with Entropy Generation","authors":"Gunisetty Ramasekhar, Shaik Jakeer, Seethi Reddy Reddisekhar Reddy, Harshit Verma, P. Jayasri, P. Durgaprasad, Pankaj Shukla","doi":"10.1007/s40010-025-00945-8","DOIUrl":"10.1007/s40010-025-00945-8","url":null,"abstract":"<div><p>This study investigates the application of copper-zirconium oxide nanofluids combined with engine oil to improve energy efficiency in renewable energy systems. This study examines the characteristics and performance of a hybrid nanofluid, considering several elements such as thermal radiation, heat generation, porous media effects, and magnetic fields. The present study utilizes the homotopy perturbation technique (HPM) as a computational method to solve the governing equations that describe the flow over cone and wedge geometries. The accuracy of the HPM is then compared with that of the Runge-Kutta method. The findings suggest that the use of HPM yields higher levels of accuracy. Furthermore, we observed that different parameters have a substantial impact on the velocity and temperature profiles, as well as the development of entropy generation. The results of this study are significant because they can help improve the efficiency of heat transfer and find the best shapes for installing renewable energy systems.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"491 - 507"},"PeriodicalIF":1.2,"publicationDate":"2025-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730245","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}
{"title":"Studies of Structural, Dielectric, Electrical, and Optical Properties of Sr3CuZr4O12 Ceramic for Photovoltaic Applications","authors":"S. K. Parida, Amruta Sahu, R. N. P. Choudhary","doi":"10.1007/s40010-025-00952-9","DOIUrl":"10.1007/s40010-025-00952-9","url":null,"abstract":"<div><p>In this paper, synthesis (solid-state reaction) and characterizations of the strontium copper zirconate (Sr<sub>3</sub>CuZr<sub>4</sub>O<sub>12</sub>, SCZO) ceramic are reported. The XRD analysis suggests an orthorhombic crystal structure with average crystallite size and lattice strain found to be 87.8 nm and 0.00135 respectively. The analysis of the Raman lines confirms the presence of all constituent elements. The UV visible spectrum shows a higher potentiality of absorbing visible light at a wavelength of 629 nm and provides a bandgap energy of 1.98 eV, which may find suitable for photovoltaic applications. The dielectric study reveals the presence of Maxwell-Wanger type of dielectric dispersion. The study of impedance spectra supports the negative temperature coefficient resistance (NTCR) character. The modulus study suggests the presence of short-range mobility of the charge carriers at low frequency and oxygen vacancy, defect, and impurity may cause long-range mobility of charge carriers at a higher frequency. A thermally generated activated relaxation process is confirmed by the increase of the activation energies with frequency. The presence of the semi-circular arcs in Nyquist plots suggests a semiconductor nature; which found applications in spintronics and energy storage devices. The study of the polarization–electric field (P-E) loop opens up the possibility of the ferroelectric property in the studied sample. <i>Novelty</i>: Synthesis (solid-state reaction) and characterization (XRD, RAMAN, UV, LCR, PE) of a Sr<sub>3</sub>CuZr<sub>4</sub>O<sub>12</sub> ceramic are reported. An orthorhombic structure with an average crystallite size of 87.8 nm and lattice strain of 0.00135 is formed. UV visible study provides an energy bandgap of 1.98 eV, which is a good range for photovoltaic applications. A study of impedance spectroscopy confirms the NTCR behavior and a P-E loop study suggests the ferroelectric nature.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"547 - 557"},"PeriodicalIF":1.2,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730243","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}
{"title":"Optimized Learning Framework Approaches for Early Detection and Classification of Parkinson’s Disease","authors":"Pooja, Karan Veer, S. K. Pahuja","doi":"10.1007/s40010-025-00948-5","DOIUrl":"10.1007/s40010-025-00948-5","url":null,"abstract":"<div><p>In recent years, progress monitoring and diagnosis devices for evaluation of Parkinson’s disease (PD) are becoming important. The early detection and rehabilitation of PD can improve the treatment consistency of patients from which may allow a fast decision of diagnosis. Broadly, the whole work is categorized in two sections, one is feature extraction and selection. This first section depicts how feature selection techniques can affects the accuracy of individual model. The second is early detection of disorder. For it, ANFIS + GWO model is proposed for early detection of Parkinson’s disease where parameters of ANFIS model are adjusted by exploiting grey wolf optimization (GWO). Different optimization methods are compared using different evaluation metrices like MSE, accuracy, computation time, iterations and number of epochs using a gait dataset of 166 people from Physionet repository. It demonstrate the superiority of ANFIS + GWO model against neural network (NN), adaptive neuro-fuzzy inference system (ANFIS), hybridization of ANFIS with genetic algorithm (GA), and partical swarm optimization (PSO). Here, maximum accuracy is attained ANFIS + GWO i.e. 99.8% that is compared with other optimization techniques used in recent literature for prediction of PD.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"509 - 524"},"PeriodicalIF":1.2,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730263","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}
{"title":"Approximate Solution of Hyperbolic Telegraphic Equation Using Modified Deep Galerkin Method","authors":"Harender Kumar, Neha Yadav","doi":"10.1007/s40010-025-00949-4","DOIUrl":"10.1007/s40010-025-00949-4","url":null,"abstract":"<div><p>This paper employs the Deep–Galerkin–Method (DGM) to approximate solutions to the hyperbolic telegraphic equation (hTE), a significant hyperbolic partial differential equation (hPDE) that models various phenomena in applied sciences. hPDEs are fundamental in describing structural vibrations and form the basis for atomic physics equations. The DGM utilizes a deep neural network (DNN) that satisfies initial conditions (ICs), boundary conditions (BCs), and the differential operator (DO). Training occurs on randomly selected batches of time and space points, eliminating the need for mesh formation. The Adam optimizer is used to optimize the DNN parameters. To enhance DGM efficiency, we propose a novel DNN architecture resembling a multiplicative long short-term memory (mLSTM) network. Additionally, we implement neuron-wise locally adaptive activation functions instead of traditional activation functions. Our experimental results demonstrate significant improvements compared to recent methods, including the B-spline method, the Polynomial scaling functions method, and the Interpolating scaling functions method.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"525 - 539"},"PeriodicalIF":1.2,"publicationDate":"2025-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730262","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}
Pawan Kumar, Prosenjit Sarkar, Nisha, Ram S. Katiyar
{"title":"Influence of Post-Deposition Heat Treatment on Microstructural, Topographical, and Optical Properties of ZnSe Thin Film on c-plane Sapphire Substrate","authors":"Pawan Kumar, Prosenjit Sarkar, Nisha, Ram S. Katiyar","doi":"10.1007/s40010-025-00944-9","DOIUrl":"10.1007/s40010-025-00944-9","url":null,"abstract":"<div><p>In the current study, the primary emphasis is placed on investigating the impact that annealing has on the microstructural and optical properties of ZnSe thin films on a c-plane sapphire (Al<sub>2</sub>O<sub>3</sub>) substrate. Atomic force microscopy (AFM) and X-ray diffraction (XRD) have been utilized to investigate the influence of post-growth annealing treatment on the structural and morphological characteristics of ZnSe thin films. XRD confirms the cubic crystal structure of all annealed thin films. The annealing temperature improved the crystallinity of thin films with a (111) orientation. The RMS surface roughness changed as the annealing temperature increased. From the optical measurements, ZnSe thin films annealed at 300 °C exhibit comparably high transmittance (> 68%) in the visible range with an energy band gap of 2.82 eV. The good optical quality of ZnSe thin film after annealing makes it very suitable as a buffer layer for thin film photovoltaic (TFPV) devices.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"483 - 489"},"PeriodicalIF":1.2,"publicationDate":"2025-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730259","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}
Masood Ahmad, Raghvendra Pratap, Satish Kumar Maurya, Malik Shahzad Ahmed Iqbal, Satish Kumar
{"title":"A Unified Framework for Classifying Big Data Security Algorithms: A Healthcare Perspective","authors":"Masood Ahmad, Raghvendra Pratap, Satish Kumar Maurya, Malik Shahzad Ahmed Iqbal, Satish Kumar","doi":"10.1007/s40010-025-00958-3","DOIUrl":"10.1007/s40010-025-00958-3","url":null,"abstract":"<div><p>Cloud computing technology has enabled easy and anytime access to healthcare services. This is more apparent in the use of cloud computing for storing and processing data generated from wearable medical devices. Daily wearable medical devices generate a large amount of data. This large amount of data is also known as “big data.” Data analytics of the big data generated by medical devices enables the early detection of diseases while facilitating the prompt provision of the required medical care, particularly in the case of patients affected by critical or chronic health debilities. In this context, the study analyzes the challenges in big data security and privacy for accurate diagnosis and treatment of diseases by medical devices, and also discusses possible solutions for healthcare service providers to make the data secure. The authors have designed a Machine Learning (ML)-based framework for selecting the best security algorithm based on their security parameters. The authors classify the algorithms and find that the triple encryption technique is more secure than other hybrid security algorithms. This study uses a Support Vector Machine (SVM)-based classifier for selecting the best security algorithm and compares the selection results with the Decision Tree classifier. Furthermore, the study also focuses on the rapidly emerging security technologies in healthcare that could facilitate better healthcare services and future prospects in this context.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 1","pages":"127 - 137"},"PeriodicalIF":1.2,"publicationDate":"2025-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147612871","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}
{"title":"Fifth Degree Mixed Moment of Kloosterman Sums, Supercharacter Theory, and Elliptic Curves","authors":"Fahim Sayed, Gautam Kalita","doi":"10.1007/s40010-025-00950-x","DOIUrl":"10.1007/s40010-025-00950-x","url":null,"abstract":"<div><p>The Kloosterman sums appear as supercharacter values of a supercharacter theory induced by the group action of a subgroup of GL<span>(_2(mathbb {F}_p))</span> on <span>(mathbb {F}_p^2)</span>. Using this, we here express the fifth degree mixed moment of Kloosterman sums in terms of trace of Frobenius endomorphism of certain families of elliptic curves.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"541 - 545"},"PeriodicalIF":1.2,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145730359","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}
{"title":"Flow Study of a Power-Law Hybrid Nanofluid Using Spectral Method: Local Non-Similarity Approach","authors":"Abhinava Srivastav, Ramreddy Chetteti","doi":"10.1007/s40010-025-00943-w","DOIUrl":"10.1007/s40010-025-00943-w","url":null,"abstract":"<div><p>This article describes the study of a power-law hybrid nanofluid with truncated cone as a geometry in a non-Darcy porous medium. The aqueous Titanium alloy (Ti6Al4V) with multi wall Carbon nanotubes (MWCNTs) is taken as hybrid nanofluid. An efficient algorithm involving approach of local non-similarity and spectral local linearization method (SLLM), is incorporated to deal with the modified flow equations subject to the associated boundary conditions. An error analysis is established to display SLLM convergence. The insertion of nanoparticle volume fraction makes temperature of the system higher because of greater thermal conductivity of nanoparticles. Rate of heat transfer along with skin friction coefficient for this flow over truncated cone are observed between full cone and vertical plate.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"469 - 481"},"PeriodicalIF":1.2,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729715","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}
{"title":"On the Hydromagnetic Stability of Weakly Compressible Flows to Axisymmetric Near-Neutral Modes","authors":"S. Prakash, M. Subbiah","doi":"10.1007/s40010-025-00939-6","DOIUrl":"10.1007/s40010-025-00939-6","url":null,"abstract":"<div><p>The linear hydromagnetic stability of inviscid compressible annular flows with magnetic Mach number <span>(M_{mag}<<1)</span>, corresponding to weak compressibility and a strong azimuthal magnetic field, is studied with respect to the class of near neutral magneto-subsonic axisymmetric normal modes. The method of integral relations is used to obtain general analytical results that give instability regions and growth rate estimates for unstable modes. For basic flows with positive minimum Richardson number <span>({tilde{J}}_{m})</span> it is shown that a necessary condition for instability is that <span>({tilde{J}}_{m})</span> is small. For unstable flows a semielliptical instability region depending on <span>({tilde{J}}_{m})</span> is obtained and this is further improved to get semielliptical-type regions depending on the wave number of the disturbance and the width of the annular channel. It is shown further that the growth rate of an arbitrary unstable mode is bounded and growth rate bounds depending on <span>({tilde{J}}_{m})</span> and width of the channel are given. It follows that the growth rate becomes small as the width of the annulus becomes small.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"95 4","pages":"401 - 419"},"PeriodicalIF":1.2,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729793","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}