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Fuzzy Korovkin Type Theorems for Periodic Continuous Functions via Statistical ((C,1) (E,mu )) Product Summability Method 周期连续函数的统计模糊Korovkin型定理((C,1) (E,mu ))积可求和法
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-04-06 DOI: 10.1007/s40010-026-01001-9
Purshottam Narain Agrawal, Behar Baxhaku
{"title":"Fuzzy Korovkin Type Theorems for Periodic Continuous Functions via Statistical ((C,1) (E,mu )) Product Summability Method","authors":"Purshottam Narain Agrawal,&nbsp;Behar Baxhaku","doi":"10.1007/s40010-026-01001-9","DOIUrl":"10.1007/s40010-026-01001-9","url":null,"abstract":"<div><p>This study addresses a specific problem in fuzzy approximation: classical Korovkin-type theorems often fail when operator sequences show constant noise or oscillations. To fix this, we combine <span>((C,1)(E,mu ))</span> product summability with statistical convergence. This method lets us find stable limits in sequences that would usually be seen as divergent. We prove a new fuzzy Korovkin-type theorem under this framework and use the fuzzy modulus of continuity to find convergence rates. Our numerical results show that this approach works for cases where the standard Anastassiou–Gal theorem does not, making it a useful option for modeling uncertainty in periodic systems.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 3","pages":"401 - 411"},"PeriodicalIF":1.3,"publicationDate":"2026-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927083","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
Norm Inequalities of Pseudo-differential Operators associated with Fractional Hankel Transform on Beurling Like Spaces 类Beurling空间上与分数阶Hankel变换相关的伪微分算子的范数不等式
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-02-04 DOI: 10.1007/s40010-025-00979-y
Kanailal Mahato, Durgesh Pasawan
{"title":"Norm Inequalities of Pseudo-differential Operators associated with Fractional Hankel Transform on Beurling Like Spaces","authors":"Kanailal Mahato,&nbsp;Durgesh Pasawan","doi":"10.1007/s40010-025-00979-y","DOIUrl":"10.1007/s40010-025-00979-y","url":null,"abstract":"<div><p>The continuous fractional Hankel transform and its inverse are studied on certain Beurling type spaces. Various mapping properties of pseudo-differential operators are discussed exploiting the theory of fractional Hankel transform on suitably designed Beurling type spaces. Statement of relevance: Pseudo-differential operators are the generalization of partial differential operators. Pseudo-differential operators can sometimes be used to find solutions of certain differential equations; more frequently, they are used to find estimates on the size of solutions through the boundedness properties of the operator on certain function spaces. In this article, we have obtained boundedness results of Pseudo-differential operator on Beurling type spaces.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 3","pages":"365 - 375"},"PeriodicalIF":1.3,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926476","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
Soft Computing-Enabled Optimization of Multi-Choice Stochastic Transportation Problem Involving Exponential and Logistic Distributions 包含指数分布和逻辑分布的多选择随机运输问题的软计算优化
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-27 DOI: 10.1007/s40010-025-00978-z
Saptadeep Biswas, Kamana Mishra, Uttam Kumar Bera
{"title":"Soft Computing-Enabled Optimization of Multi-Choice Stochastic Transportation Problem Involving Exponential and Logistic Distributions","authors":"Saptadeep Biswas,&nbsp;Kamana Mishra,&nbsp;Uttam Kumar Bera","doi":"10.1007/s40010-025-00978-z","DOIUrl":"10.1007/s40010-025-00978-z","url":null,"abstract":"<div><p>This study presents a novel approach to solving complex transportation models characterized by multi-choice parameters and stochastic constraints using soft computing techniques. The transportation problem under investigation involves random availability and demand parameters following continuous distributions such as exponential and logistic. The primary objective is to derive optimal solutions by transforming probabilistic constraints into deterministic ones and utilizing Evolutionary Algorithms (EAs) for optimization. Leveraging Lagrange’s Interpolation Method, the study identifies the most favourable choices from the multi-choice parameters, facilitating the subsequent conversion of probabilistic constraints into deterministic equivalents. The research introduces a range of soft computing algorithms, including a real-parameter Genetic Algorithm, a variant of Differential Evolution, an Evolution Strategy, and a Particle Swarm Optimization. Two numerical illustrations are employed to evaluate the proposed techniques, allowing for a thorough comparison of algorithmic efficiency and solution quality. A comprehensive performance metric tracks the evolution of optimum solutions, the non-dominated solution sets generated in each iteration, and the convergence rate of the algorithms. The study’s contributions lie in addressing intricate transportation problems marked by uncertainty in parameter values. Combining EAs with soft computing strategies offers a robust framework for optimizing multi-choice transportation models. The research sheds light on various soft computing algorithms’ effectiveness and suitability for solving similar challenges in diverse domains.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 3","pages":"341 - 363"},"PeriodicalIF":1.3,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148928028","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
Correction: Analysis of COVID-19 Model Using Atangana-Baleanu Variable Order Operator 更正：使用Atangana-Baleanu变量阶算子分析COVID-19模型
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-20 DOI: 10.1007/s40010-025-00977-0
Pratibha Verma, Surabhi Tiwari
{"title":"Correction: Analysis of COVID-19 Model Using Atangana-Baleanu Variable Order Operator","authors":"Pratibha Verma,&nbsp;Surabhi Tiwari","doi":"10.1007/s40010-025-00977-0","DOIUrl":"10.1007/s40010-025-00977-0","url":null,"abstract":"","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"339 - 339"},"PeriodicalIF":1.3,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496695","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
A Ranked Set Generalized Procedure for Computing Mean Using Searls Technique: Applications to Real Data 一种利用Searls技术计算平均值的排序集广义方法：在实际数据中的应用
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-17 DOI: 10.1007/s40010-025-00976-1
Abhishek Singh, Bavita Singh, Sweta Shukla
{"title":"A Ranked Set Generalized Procedure for Computing Mean Using Searls Technique: Applications to Real Data","authors":"Abhishek Singh,&nbsp;Bavita Singh,&nbsp;Sweta Shukla","doi":"10.1007/s40010-025-00976-1","DOIUrl":"10.1007/s40010-025-00976-1","url":null,"abstract":"<div><p>The Searls technique has been used in this article to build a generalized class of estimators for estimating a finite population mean under a ranked set sampling strategy. To the first order of approximation, the equations for bias and mean square error (MSE) of the proposed class of estimators have been derived. Many specific estimators from the suggested class are displayed. Using the MSE, percentage relative efficiency criterion, the suggested class of estimators has been compared to the corresponding generalized class and to its other existing estimators. It has been established under what circumstances the suggested class performs better. Ranked set sampling is better substitute of simple random sampling, is also proved. Two real-world studies using real-world data on cost-effective gasoline sample, and sleeping patterns of elderly people have been used in efficiency comparisons, in empirical study. The simulation studies have also been carried for the same.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"299 - 311"},"PeriodicalIF":1.3,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496677","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 Shively’s Pseudo Laguerre Type Matrix Polynomials 关于Shively的伪拉盖尔型矩阵多项式
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-13 DOI: 10.1007/s40010-025-00980-5
Vinod Kumar Jatav, Ankit Pal, Ajay Kumar Shukla
{"title":"On Shively’s Pseudo Laguerre Type Matrix Polynomials","authors":"Vinod Kumar Jatav,&nbsp;Ankit Pal,&nbsp;Ajay Kumar Shukla","doi":"10.1007/s40010-025-00980-5","DOIUrl":"10.1007/s40010-025-00980-5","url":null,"abstract":"<div><p>In this paper, we introduce Shively’s Pseudo Laguerre type matrix polynomials and obtain some properties, including the hypergeometric matrix function representation, the <span>({}_pR_q(mathcal {P},mathcal {Q};z))</span> matrix function representation, and the generating matrix functions. Furthermore, we establish the composition of generalized fractional calculus operators with the Shively’s Pseudo Laguerre type matrix polynomials, and some special cases have also been discussed. The proposed generating function provides advanced tools for analyzing and solving matrix-based systems encountered in quantum mechanics, control theory, and numerical analysis.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 3","pages":"377 - 384"},"PeriodicalIF":1.3,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927698","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
Simulation and Analysis of Fractional Model of Human Liver with Real Data Comparison via Caputo Derivative 基于Caputo导数的人体肝脏分数模型的仿真与分析
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-09 DOI: 10.1007/s40010-025-00969-0
Lalit Mohan, Amit Prakash
{"title":"Simulation and Analysis of Fractional Model of Human Liver with Real Data Comparison via Caputo Derivative","authors":"Lalit Mohan,&nbsp;Amit Prakash","doi":"10.1007/s40010-025-00969-0","DOIUrl":"10.1007/s40010-025-00969-0","url":null,"abstract":"<div><p>In this work, we have examined the fractional model of the human liver based on BSP test. A hybrid numerical technique namely Natural transform homotopy perturbation technique is utilised for solving the given model. This technique is an excellent combination of Natural transform and a semi-analytical technique. The Ulam–Hyers stability of the solutions of the given model is analysed. The existence of a unique solution is established by using fixed-point theorem. Finally, the efficiency of the presented technique is validated by comparing the numerical results with the existing methods and clinical data.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"203 - 212"},"PeriodicalIF":1.3,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496741","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 q-New Laplace Type Integral Transform of Three Variables with Applications 三变量的q-新拉普拉斯型积分变换及其应用
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-05 DOI: 10.1007/s40010-025-00973-4
Srikumar Panda, Arvind Kumar Sinha
{"title":"On q-New Laplace Type Integral Transform of Three Variables with Applications","authors":"Srikumar Panda,&nbsp;Arvind Kumar Sinha","doi":"10.1007/s40010-025-00973-4","DOIUrl":"10.1007/s40010-025-00973-4","url":null,"abstract":"<div><p>We introduce the definition of triple new Laplace type integral transform in q-calculus namely q-triple new Laplace type integral transform, by using the functions of several variables and establish some properties. Furthermore, several theorems dealing with the properties of the q-triple new Laplace type Integral transform are proved. We also give some applications of q-triple new Laplace type Integral transform for solving non-homogeneous Mboctara partial differential equation and diffusion partial differential equation with initial and boundary values problems to its effectiveness and performance of the proposed method.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"269 - 278"},"PeriodicalIF":1.3,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496691","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
Microbial Fuel Cells: Sustainable Energy Solutions for Wastewater Treatment-A Mini Review 微生物燃料电池：废水处理的可持续能源解决方案综述
IF 1.2 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-03 DOI: 10.1007/s40010-025-00960-9
Morteza Esfandyari, Dariush Jafari
{"title":"Microbial Fuel Cells: Sustainable Energy Solutions for Wastewater Treatment-A Mini Review","authors":"Morteza Esfandyari,&nbsp;Dariush Jafari","doi":"10.1007/s40010-025-00960-9","DOIUrl":"10.1007/s40010-025-00960-9","url":null,"abstract":"<div><p>Microbial fuel cells (MFCs) have been emerging as a promising technology for efficient and sustainable energy production from wastewater. MFCs produce electricity by controlling the metabolic activity of microorganisms present in wastewaters. Such a process is not only used for the conversion of wastes to energy, but also it is considered as an environmentally friendly strategy for wastewater treatment. Several feasibility studies have been carried out on the application of MFCs for wastewater treatment which have approved the potential of this technology for energy production and resource recovery. However, further investigations should be carried out on optimization of MFCs real application and finding appropriate solutions to their technical and economic challenges related to their scale-up.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 1","pages":"155 - 164"},"PeriodicalIF":1.2,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147614777","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
Estimation of the Plastic Area Around the Crack Tip Using a New Mixed Finite Element Approach 用一种新的混合有限元法估计裂纹尖端周围的塑性面积
IF 1.3 4区 综合性期刊
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Pub Date : 2026-01-03 DOI: 10.1007/s40010-025-00971-6
Ahmed Bougueroua, Hamoudi Bouzerd, Mohamed Kezzar
{"title":"Estimation of the Plastic Area Around the Crack Tip Using a New Mixed Finite Element Approach","authors":"Ahmed Bougueroua,&nbsp;Hamoudi Bouzerd,&nbsp;Mohamed Kezzar","doi":"10.1007/s40010-025-00971-6","DOIUrl":"10.1007/s40010-025-00971-6","url":null,"abstract":"<div><p>The present article presents a numerical model for analyzing interfacial fracture in ductile materials exhibiting perfectly elastoplastic behavior, taking into account the ductility induced by the increase in tension at the crack tip. The analysis of structures with cracked interfaces requires the satisfaction of interface continuity conditions—namely, the continuity of displacement and the continuity of the stress vector. To address this, a mixed finite element, designated RMQ-7, is employed to determine the size of the plastic zone (PZ) around the crack tip under both mode I and mixed-mode (I + II) loading conditions. The calculations are performed according to the Von Mises plasticity criterion, implemented within the mixed finite element framework, which incorporates the elastoplastic constitutive law of the material. The results obtained using the RMQ-7 element show good agreement with both numerical and analytical results, as verified by the maximum crack opening displacement and the classical Irwin formula. In addition, this paper addresses the problem of slant and kinking cracks. The proposed special mixed finite element, combined with the virtual crack extension technique, has been developed to evaluate the energy release rate within a single finite-element analysis. The element is defined from a parent element in the natural coordinate plane (ξ, η), which simplifies the numerical computation within each element of the simulation. Finally, an example problem involving slant cracks in a homogeneous material, drawn from the literature, is presented to assess the computational accuracy of the proposed approach.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":"96 2","pages":"233 - 246"},"PeriodicalIF":1.3,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148496679","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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