Advances in Nonlinear Variational Inequalities最新文献

{"title":"Integral Solutions for the Diophantine Equation of Higher Degree with Six Unknowns x⁶ − y⁶ − 3456z³ = 800(p² − q²)R⁸","authors":"J. S. R. Anbuselvi","doi":"10.52783/anvi.v27.412","DOIUrl":"https://doi.org/10.52783/anvi.v27.412","url":null,"abstract":"Our focus in this paper has been on solving high-power Diophantine equations - those with variables raised to a high degree. These types of equations can be particularly challenging as they involve finding integer solutions that satisfy the given polynomial equation. We have utilized various techniques such as brute force methods and substitution strategies to solve these high power Diophantine equations, successfully deriving their solutions. Furthermore, our investigation has led us to uncover intriguing relationships among these solutions, which manifest in four distinct patterns. The equation x⁶ − y⁶ − 3456z³ = 800(p² − q²)R⁸ is analysed with properties. Some of the special numbers are discussed in properties. Special numbers are unique and have special qualities that set them apart from other numbers. Learning about these special qualities helps us understand how numbers work and their significance in different areas of math and science.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"22 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140396605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear Elliptic Equations on the Sierpiński Carpet","authors":"Dahmani Abdelkarim, Kaoutar Lamrini Uahabi, Siham Elhabib","doi":"10.52783/anvi.v27.413","DOIUrl":"https://doi.org/10.52783/anvi.v27.413","url":null,"abstract":"This paper deals with a semilinear elliptic equation for a properly defined Laplace operator on the Sierpiński carpet. We investigate the existence of solutions, under Dirichlet boundary conditions, for the problem∆u+a(x)u=f(x,u).This work is motivated by previos studies established for such problems on the Sierpiński gasket by many authors: Kenneth J. Falconer, Jiaxin Hu, G.Bonanno and others (more details can be found in Introduction). The approach used in this study is based on variational methods, more specifically, the the mountain pass theorem of Ambrosetti and Rabinowit, and Sobolev type inequality, which was of principal use for achieving other results.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"20 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140396429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Hosoya and Schultz Polynomials of Chain of Pentagonal Graph","authors":"Mamoon Fattah Khalf, Habib Azanchiler, Nabeel E. Arif, Sara Eslameian","doi":"10.52783/anvi.v27.411","DOIUrl":"https://doi.org/10.52783/anvi.v27.411","url":null,"abstract":"In order to connect a chain of vertices of rings of a pentagonal graph with a path of length one, we introduce in this work the concepts of Wiener, Schultz, and Modified Schultz indices, as well as Schultz, modified Schultz, and Hosoya polynomials. Along with changing the multiplicities of Schultz and Hosoya, some of Schultz's attributes are also presented.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"19 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140396436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Simulation and Mathematical Analysis of Meta Heuristic MPPT System for Solar Photovoltaic Applications Under Non-Linear Operational Conditions","authors":"Ravinder Singh Maan, Alok Kumar Singh, Ashish Raj","doi":"10.52783/anvi.v27.387","DOIUrl":"https://doi.org/10.52783/anvi.v27.387","url":null,"abstract":"As a sustainable energy source, the use of solar photovoltaic (PV) systems has significantly increased. Environmental elements, especially partial shadowing circumstances, have a considerable impact on how well solar PV systems function. In such cases, the various local maxima in the power-voltage curve make it difficult for conventional Maximum Power Point Tracking (MPPT) methods to maintain peak efficiency. Heuristic Maximum Power Point Tracking (MPPT) system for solar photovoltaic (PV) applications, employing the cuckoo search algorithm. The primary objective of the research is to enhance the efficiency and reliability of solar PV systems by optimizing the MPPT process, which is crucial for maximizing energy extraction under varying environmental conditions. The model is used to simulate the performance of the system under various environmental conditions, such as changes in temperature and irradiance levels. The simulation results are then statistically analyzed to evaluate the effectiveness of the cuckoo search algorithm in tracking the maximum power point accurately and rapidly. The algorithm demonstrates a robust ability to converge to the maximum power point efficiently, thereby enhancing the overall energy yield of the solar PV system.. The performance of the hybrid PSO-CSA  MPPT algorithm in contrast to traditional MPPT techniques is assessed through simulations and tests under various shading circumstances. The findings show that the hybrid strategy regularly outperforms conventional methods by enhancing the total energy production of partially shadowed solar PV installations through faster convergence, less oscillations, and greater tracking accuracy. The proposed hybrid algorithm also demonstrates stability and flexibility in real-world settings, making it a potential option for boosting the dependability and efficiency of solar PV systems when shade is present. This study advances the field of renewable energy and prepares the path for the use of sophisticated optimization methods to the problems of solar PV power generation under changing environmental circumstances.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"373 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140281520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Modeling and Analysis of Energy Aware Probabilistic Distribution Based Cluster Head Selection Algorithm for Wireless Sensor Networks","authors":"Amit Gupta Rakesh Kumar Yadav","doi":"10.52783/anvi.v27.386","DOIUrl":"https://doi.org/10.52783/anvi.v27.386","url":null,"abstract":"From a mathematical perspective, Wireless Sensor Networks (WSNs) are increasingly recognized for their utility across multiple sectors such as environmental oversight, healthcare monitoring, and process automation within industries. A paramount obstacle within WSNs is the management of energy efficiency, given that the sensor nodes are typically powered by batteries with finite energy reserves. The criticality of developing efficient routing protocols cannot be overstated, as they are instrumental in extending the operational lifespan of the network and guaranteeing dependable data communication. This study is centered around the mathematical modelling and performance evaluation of an innovative routing methodology that integrates machine learning algorithms to augment energy efficiency within WSNs. The novel routing strategy dynamically adjusts its operations in response to the immediate environmental and network states, aiming to minimize energy expenditure and elevate the network's overall efficiency. Through comprehensive numerical simulations, this research scrutinizes the efficacy of the machine learning-enhanced routing protocol against conventional routing methodologies, accentuating its advantages in energy savings and reliability in data transmission. The simulation framework encompasses a variety of network configurations, traffic distributions, and environmental contexts, employing metrics such as energy utilization, network longevity, packet delivery ratio, and latency to offer an in-depth examination of the machine learning-based routing approach's performance. Findings from the simulations affirm the algorithm's enhanced energy efficiency, which contributes to prolonged operation of sensor nodes and steadfast data communication across dynamically changing network landscapes. The implications of this study highlight the transformative potential of machine learning in redefining routing protocol design and optimization within energy-restricted WSNs. By elevating both energy efficiency and network functionality, this research marks a significant stride towards realizing sustainable and dependable WSNs, paving the way for their broader application in essential services.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"45 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140271516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of Resource Allocation Problem with Different Techniques: A Comparative Study","authors":"Et al. N. Kalaivani","doi":"10.52783/anvi.v27.365","DOIUrl":"https://doi.org/10.52783/anvi.v27.365","url":null,"abstract":"Assigning n’s entities to m’s other entities in an invertible manner is a challenging task that arises in various circumstances. In combinatorial optimisation, assignment problems are a heavily researched area. These problems have many applications in different domains like production planning, VLSI design for telecommunications, economics, etc. The assignment problem plays a crucial role in assigning things to machines so as to reduce assignment costs. To achieve this purpose, this paper examines many ways for solving assignment problems, including Game theory, choice under uncertainty and Graph theory approaches. In order to demonstrate the efficacy of these models, the results were evaluated against one another. Throughout the study, modifications and special situations of the assignment problem and its applications are also examined. The simulation of the proposed WAP approaches is carried out using MATLAB software. The computational findings for a collection of randomly created problems of varying sizes demonstrate that the proposed methods are capable of locating solutions of high quality.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"77 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140459270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Modeling and Comparative Assessment of Centroid Based Leach Routing Protocol for Wireless Sensor Network","authors":"Et al. Dharmendra Yadav","doi":"10.52783/anvi.v27.355","DOIUrl":"https://doi.org/10.52783/anvi.v27.355","url":null,"abstract":"This research evaluates the performance of two key routing protocols, LEACH and an enhanced version of Centralized LEACH, in Wireless Sensor Networks (WSNs). The study sets initial simulation parameters, gathers data over numerous rounds, and presents results through diagrams. Additionally, it conducts a comparative analysis with existing research. In WSNs, nodes within transmission range communicate directly, while distant nodes rely on intermediaries. The study introduces hierarchical clustering with cluster heads for network efficiency. The number of cluster heads significantly impacts energy consumption .LEACH is explored, emphasizing its two phases: setup and steady-state. The setup phase involves autonomous cluster formation without central control. Cluster heads are selected based on thresholds and advertise their presence. Nodes then choose clusters based on signal strength. TDMA scheduling optimizes data transmission. In the steady-state phase, nodes follow a timetable to send data to cluster heads. Uneven node distribution among cluster heads may lead to varying data loads. Power control minimizes energy usage, and TDMA scheduling maximizes bandwidth use. Cluster heads forward aggregated data to the base station. The paper includes an energy model detailing communication components. Findings offer insights into LEACH and its enhanced variant, contributing to energy-efficient routing protocols in WSNs.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140478436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Extension of Combination of Linear and Bilinear Generating Relations in Function Spaces Associated with Hypergeometric Polynomials; Some New Applications of Two Signals in Special Functions","authors":"Et al. Madhav Prasad Poudel","doi":"10.52783/anvi.v27.332","DOIUrl":"https://doi.org/10.52783/anvi.v27.332","url":null,"abstract":"For a certain class of generalized hypergeometric polynomials, the first derive some special cases on linear and bilinear generating functions and then apply these generating functions in order to reduce the corresponding results for the classical Jacobi, Hermite, Laguerre and Gegenbauer Polynomials, hypergeometric functions of Gauss and functions of Bessel and Kelvin. They also consider several linear generating functions for these polynomials as well as for some multivariable Jacobi and multivariable Laguerre polynomials which were investigated in recent years. Some of the linear and bilinear generating functions, presented in this paper, are associated with the hypergeometric polynomials.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"662 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140479389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Modeling for Non-Linear Behaviorial Analysis of Job Embeddedness on Organization with Improved Statistical Tools","authors":"Et al. Swati Singh","doi":"10.52783/anvi.v27.354","DOIUrl":"https://doi.org/10.52783/anvi.v27.354","url":null,"abstract":"This research endeavors to enhance our understanding of job embeddedness within organizations by employing advanced mathematical modeling and statistical tools to analyze its non-linear behavioral dynamics. Job embeddedness refers to the extent to which an individual feels deeply connected to their job, colleagues, and the organization, which has significant implications for employee retention, performance, and organizational success. Our study applies cutting-edge statistical techniques, such as nonlinear regression models, machine learning algorithms, and network analysis, to decipher the complex interplay of factors that contribute to job embeddedness. By examining various intrinsic and extrinsic factors, including job satisfaction, organizational culture, social networks, and employee engagement, our mathematical models aim to provide a comprehensive perspective on the phenomenon. Through a rigorous analysis of large-scale organizational datasets, we uncover hidden patterns, nonlinear relationships, and critical tipping points that influence job embeddedness. This research not only contributes to a deeper theoretical understanding of job embeddedness but also offers practical insights for organizational leaders and human resource professionals to design targeted strategies for fostering employee commitment and reducing turnover. Ultimately, our mathematical modeling approach improves the accuracy of predicting and managing job embeddedness within organizations, thereby assisting businesses in creating more engaged, satisfied, and embedded workforces.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"324 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140471998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical Modeling and Statistical Analysis of Elederly Fall Detection System Using Improved Support Vector Machine","authors":"Et al. Manoj Kumar Tiwari","doi":"10.52783/anvi.v27.323","DOIUrl":"https://doi.org/10.52783/anvi.v27.323","url":null,"abstract":"This research focuses on enhancing the safety of elderly individuals through early fall detection using  mathematical modelling and statistical analysis of machine learning techniques for the application and effectiveness of elderly fall detection. Falls among the elderly can lead to severe consequences, necessitating timely intervention. Leveraging machine learning algorithms, this innovative open-source project analyses sensor data from wearable sensors like accelerometers, gyroscopes, and magnetometers, along with environmental data such as temperature and humidity, to promptly identify fall patterns. The project uses a dataset containing 14 variables, including age, sex, medical indicators, and more, collected from diverse subjects and activities. The results obtained during the testing phase underscore the importance of refining the model through dataset adjustments. As the physical, cognitive, and sensory functions decline with age, the risk of falls increases, highlighting the need for fall detection and prevention systems. This research reviews the latest machine learning-based systems for fall detection and prevention, analyzing them based on various parameters. It identifies support vector machines and wearable devices as common tools, but emphasizes the need for broader studies in different contexts. The paper also visualizes the performance metrics of ML algorithms in conjunction with various wearables and outlines future research directions, including energy efficiency, sensor fusion, context awareness, and wearable design, to advance fall detection and prevention for the elderly.","PeriodicalId":40035,"journal":{"name":"Advances in Nonlinear Variational Inequalities","volume":"6 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}