When searching for data on the internet, every user has their own personal context for doing so. The job of a search engine is to find the most relevant content from all the blogs on the internet based on the user's query. Information retrieval systems, both locally and globally, have been profoundly affected by the advent of the internet, and this includes the value of information left as comments on a page of SNS (Social Network Services). The concept of emotional and social connections is translated into a logical framework using the terms "node" and "link" to describe the structure of a social network. Efficient semantic models are more extensive training and evaluation materials, are needed to improve social network search capabilities. When compared with machine learning algorithms, the efficacy of traditional keyword-based search engines at understanding users' intentions is low. Recently, neural networks have gained popularity in the field of information retrieval because of their impressive vector representation learning capabilities. The usage of deep learning techniques for this purpose has recently been seen, and they have proven to be more effective than traditional machine learning techniques such artificial neural networks (ANNs). Improved results have been seen specifically using deep-learning techniques like long short-term memory (LSTM) & Recurrent Neural Network (RNN). In order to create a more personalized Information Retrieval(IR) system, this research suggests using a deep learning Hybrid RNN - LSTM model. Finally, the suggested method takes user comments into account and uses a hybrid RNN - LSTM to re-rank the data so that everyone is happy. Web search contest dataset is used for the implementation. Statistics like accuracy, precision, & recall are used to evaluate the data set on Bing and Duckduck go, two of the most prominent search engines. According to the findings, the proposed Hybrid method outperformed more traditional methods.
{"title":"An Improved Information Retrieval System using Hybrid RNN LSTM for Multiple Search Engines","authors":"B. Sangamithra, Dr. M. Sunil Kumar","doi":"10.52783/cana.v31.1011","DOIUrl":"https://doi.org/10.52783/cana.v31.1011","url":null,"abstract":"When searching for data on the internet, every user has their own personal context for doing so. The job of a search engine is to find the most relevant content from all the blogs on the internet based on the user's query. Information retrieval systems, both locally and globally, have been profoundly affected by the advent of the internet, and this includes the value of information left as comments on a page of SNS (Social Network Services). The concept of emotional and social connections is translated into a logical framework using the terms \"node\" and \"link\" to describe the structure of a social network. Efficient semantic models are more extensive training and evaluation materials, are needed to improve social network search capabilities. When compared with machine learning algorithms, the efficacy of traditional keyword-based search engines at understanding users' intentions is low. Recently, neural networks have gained popularity in the field of information retrieval because of their impressive vector representation learning capabilities. The usage of deep learning techniques for this purpose has recently been seen, and they have proven to be more effective than traditional machine learning techniques such artificial neural networks (ANNs). Improved results have been seen specifically using deep-learning techniques like long short-term memory (LSTM) & Recurrent Neural Network (RNN). In order to create a more personalized Information Retrieval(IR) system, this research suggests using a deep learning Hybrid RNN - LSTM model. Finally, the suggested method takes user comments into account and uses a hybrid RNN - LSTM to re-rank the data so that everyone is happy. Web search contest dataset is used for the implementation. Statistics like accuracy, precision, & recall are used to evaluate the data set on Bing and Duckduck go, two of the most prominent search engines. According to the findings, the proposed Hybrid method outperformed more traditional methods.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141830080","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}
Dr. L. Kuladeep Kumar, Dr. D.Venkatesh, Dr.J. Katyayani, Dr.Sreenivasulu Sunkara, Dr Gowthami
The banking industry, inherently customer-focused, relies on understanding and fulfilling the diverse needs of its clientele for success. Customization of offerings is crucial for banks serving individuals, families, or businesses across various financial stages. Client segmentation stands out as a primary strategy in achieving this customization. By categorizing customers based on shared characteristics, banks can deploy targeted marketing efforts, allocate resources efficiently, and deliver tailored banking experiences. In the contemporary banking landscape, where vast amounts of data are generated daily, thorough analysis is indispensable. Customized business strategies have become increasingly vital amidst intensifying industry competition. Customer segmentation serves as a pivotal aspect of market research, facilitating the grouping of customers based on common characteristics and behaviors. This segmentation enables banks to tailor marketing campaigns to suit the distinct requirements and preferences of each segment. This study focuses on employing cluster analysis, a statistical technique for organizing data points, to achieve efficient client segmentation in the banking sector. Specifically, we utilize the K-means algorithm, a popular clustering method, to categorize clientele into discrete groups based on transaction history, banking preferences, and demographic data. To ensure the accuracy and robustness of our segmentation methodology, sophisticated machine learning techniques like the Elbow and Silhouette methods are employed. These techniques enable the evaluation of clustering effectiveness and determination of the optimal number of clusters. Our objective is to utilize machine learning to identify meaningful and actionable customer groups, guiding banks' strategic decision-making processes. The segmentation approach outlined in this study empowers banks to optimize services and elevate customer satisfaction levels. By aligning offerings with the specific needs of each segment, banks can cultivate stronger customer relationships, drive revenue growth, and gain a competitive advantage in the dynamic banking landscape.
{"title":"A Study on Customer Segmentation for Banking Sector Through Cluster Analysis: Ethical Implications","authors":"Dr. L. Kuladeep Kumar, Dr. D.Venkatesh, Dr.J. Katyayani, Dr.Sreenivasulu Sunkara, Dr Gowthami","doi":"10.52783/cana.v31.999","DOIUrl":"https://doi.org/10.52783/cana.v31.999","url":null,"abstract":"The banking industry, inherently customer-focused, relies on understanding and fulfilling the diverse needs of its clientele for success. Customization of offerings is crucial for banks serving individuals, families, or businesses across various financial stages. Client segmentation stands out as a primary strategy in achieving this customization. By categorizing customers based on shared characteristics, banks can deploy targeted marketing efforts, allocate resources efficiently, and deliver tailored banking experiences. In the contemporary banking landscape, where vast amounts of data are generated daily, thorough analysis is indispensable. Customized business strategies have become increasingly vital amidst intensifying industry competition. Customer segmentation serves as a pivotal aspect of market research, facilitating the grouping of customers based on common characteristics and behaviors. This segmentation enables banks to tailor marketing campaigns to suit the distinct requirements and preferences of each segment. This study focuses on employing cluster analysis, a statistical technique for organizing data points, to achieve efficient client segmentation in the banking sector. Specifically, we utilize the K-means algorithm, a popular clustering method, to categorize clientele into discrete groups based on transaction history, banking preferences, and demographic data. To ensure the accuracy and robustness of our segmentation methodology, sophisticated machine learning techniques like the Elbow and Silhouette methods are employed. These techniques enable the evaluation of clustering effectiveness and determination of the optimal number of clusters. Our objective is to utilize machine learning to identify meaningful and actionable customer groups, guiding banks' strategic decision-making processes. The segmentation approach outlined in this study empowers banks to optimize services and elevate customer satisfaction levels. By aligning offerings with the specific needs of each segment, banks can cultivate stronger customer relationships, drive revenue growth, and gain a competitive advantage in the dynamic banking landscape.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141831032","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}
The Conjugate Gradient Methods(CGM) are well-recognized techniques for handling nonlinear optimization problems. Dai and Liao (2001) employ the secant condition approach, this study utilizes the modified secant condition proposed by Yabe-Takano (2004) and Zhang and Xu (2001), which is satisfied at each iteration through the implementation of the strong Wolf-line search condition. Additionally, please provide three novel categories of conjugate gradient algorithms of this nature. We examined 15 well-known test functions. This novel approach utilises the existing gradient and function value to accurately approximate the goal function with high-order precision. The worldwide convergence of our novel algorithms is demonstrated under certain conditions. Numerical results are provided, and the efficiency is proven by comparing it to other approaches.
{"title":"A New Modified Secant Condition for Non-linear Conjugate Gradient Methods with Global Convergence","authors":"Farhan Khalaf Muord, Muna M. M. Ali","doi":"10.52783/cana.v31.1056","DOIUrl":"https://doi.org/10.52783/cana.v31.1056","url":null,"abstract":"The Conjugate Gradient Methods(CGM) are well-recognized techniques for handling nonlinear optimization problems. Dai and Liao (2001) employ the secant condition approach, this study utilizes the modified secant condition proposed by Yabe-Takano (2004) and Zhang and Xu (2001), which is satisfied at each iteration through the implementation of the strong Wolf-line search condition. Additionally, please provide three novel categories of conjugate gradient algorithms of this nature. We examined 15 well-known test functions. This novel approach utilises the existing gradient and function value to accurately approximate the goal function with high-order precision. The worldwide convergence of our novel algorithms is demonstrated under certain conditions. Numerical results are provided, and the efficiency is proven by comparing it to other approaches.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":"170 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141834556","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}
In this paper, we investigate topologies produced by simple connected graphs. In particular, we will present the type of relations on the vertices set. It is converted to an adjacent matrix and through this matrix, whose elements represent the relationship between each vertex to the rest of the vertices adjacent to it, where sets are produced through which they represent the basis for topology. On the graph is the vertex set.
{"title":"On Finite Topological Spaces Generated by Connected Simple Graphs","authors":"Noor Nouman, F. Mayah","doi":"10.52783/cana.v31.982","DOIUrl":"https://doi.org/10.52783/cana.v31.982","url":null,"abstract":"In this paper, we investigate topologies produced by simple connected graphs. In particular, we will present the type of relations on the vertices set. It is converted to an adjacent matrix and through this matrix, whose elements represent the relationship between each vertex to the rest of the vertices adjacent to it, where sets are produced through which they represent the basis for topology. On the graph is the vertex set.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":"73 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664429","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}
Chandra Sekhar Mishra, Dr. Ranjan Kumar, Dr. Asit Mohanty, Dr. Prakash K Ray, Dr. Pragyan P Mohanty, Dr. Sunil Kumar Gupta
Recent advancements in distributed generation (DG) systems interfaced with microgrids necessitate robust regulatory mechanisms to manage inherent power fluctuations, particularly from renewable sources like photovoltaics. These fluctuations can significantly impact the stability and efficiency of microgrids. This paper introduces a novel mathematical framework for simultaneous voltage and frequency regulation, aimed at addressing power quality and stability challenges in DG-grid interfaced systems. Utilizing a combination of algebraic topology and dynamical systems theory, we develop a model that incorporates an adaptive virtual frequency-impedance control loop. This mathematical approach allows for the analytical examination of the stability properties of the system and the design of control strategies that guarantee optimal operational thresholds. We extend the conventional droop control mechanisms with a rigorously defined Simultaneous Voltage and Frequency Correction Scheme (SVFCS), providing a theoretical underpinning that supports experimental observations. The efficacy of the proposed model is validated through numerical simulations that demonstrate adherence to the IEEE 519 standard, ensuring reduced harmonic distortion and enhanced system reliability. Our results highlight the potential for these mathematical methods to provide foundational insights into the control and optimization of microgrid operations.
{"title":"A Mathematical Framework for Simultaneous Voltage and Frequency Regulation in Distributed Generator (DG) Grid-Interfaced Systems","authors":"Chandra Sekhar Mishra, Dr. Ranjan Kumar, Dr. Asit Mohanty, Dr. Prakash K Ray, Dr. Pragyan P Mohanty, Dr. Sunil Kumar Gupta","doi":"10.52783/cana.v31.981","DOIUrl":"https://doi.org/10.52783/cana.v31.981","url":null,"abstract":"Recent advancements in distributed generation (DG) systems interfaced with microgrids necessitate robust regulatory mechanisms to manage inherent power fluctuations, particularly from renewable sources like photovoltaics. These fluctuations can significantly impact the stability and efficiency of microgrids. This paper introduces a novel mathematical framework for simultaneous voltage and frequency regulation, aimed at addressing power quality and stability challenges in DG-grid interfaced systems. Utilizing a combination of algebraic topology and dynamical systems theory, we develop a model that incorporates an adaptive virtual frequency-impedance control loop. This mathematical approach allows for the analytical examination of the stability properties of the system and the design of control strategies that guarantee optimal operational thresholds. We extend the conventional droop control mechanisms with a rigorously defined Simultaneous Voltage and Frequency Correction Scheme (SVFCS), providing a theoretical underpinning that supports experimental observations. The efficacy of the proposed model is validated through numerical simulations that demonstrate adherence to the IEEE 519 standard, ensuring reduced harmonic distortion and enhanced system reliability. Our results highlight the potential for these mathematical methods to provide foundational insights into the control and optimization of microgrid operations. ","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141668652","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}
Stochastic Differential Equations (SDEs) are powerful mathematical tools used to model systems subject to random fluctuations. In physics, SDEs find widespread applications ranging from statistical mechanics to quantum field theory. This paper provides an in-depth exploration of the theoretical foundations of SDEs in physics, their applications, and their implications in understanding complex physical phenomena. We delve into the mathematical framework of SDEs, their numerical solutions, and their role in modeling various physical processes. Furthermore, we present case studies illustrating the practical relevance of SDEs in different branches of physics.
{"title":"Stochastic Differential Equations in Physics","authors":"Dr Nand Kumar","doi":"10.52783/cana.v31.937","DOIUrl":"https://doi.org/10.52783/cana.v31.937","url":null,"abstract":"Stochastic Differential Equations (SDEs) are powerful mathematical tools used to model systems subject to random fluctuations. In physics, SDEs find widespread applications ranging from statistical mechanics to quantum field theory. This paper provides an in-depth exploration of the theoretical foundations of SDEs in physics, their applications, and their implications in understanding complex physical phenomena. We delve into the mathematical framework of SDEs, their numerical solutions, and their role in modeling various physical processes. Furthermore, we present case studies illustrating the practical relevance of SDEs in different branches of physics.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141676312","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}
Network theory is going to analyse the set of techniques. But in a complex system network in a network of complex it has techniques to analyse the structure in a system of interacting agents. The graph theoretic representation means the system is made to apply network. The problem may be converted into graph by two components namely nodes and edges nodes are called as entities and interactions between edges are called as edges.
{"title":"Connected Graph with Bacterial Graphs and Network Distance","authors":"T. Selvaraj, Dr. S. Subramanian","doi":"10.52783/cana.v31.830","DOIUrl":"https://doi.org/10.52783/cana.v31.830","url":null,"abstract":"Network theory is going to analyse the set of techniques. But in a complex system network in a network of complex it has techniques to analyse the structure in a system of interacting agents. The graph theoretic representation means the system is made to apply network. The problem may be converted into graph by two components namely nodes and edges nodes are called as entities and interactions between edges are called as edges.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141675215","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}
Coupled Schrödinger equations with fractional damping represent a complex yet fascinating area of study in quantum mechanics. This research paper delves into the analytical investigation of such systems, focusing on deriving decay solutions and conducting stability analysis. By combining theoretical frameworks with numerical methods, we explore the behavior of these coupled equations under varying parameters and conditions. Through a thorough analysis, we aim to deepen our understanding of the dynamics and stability properties of quantum systems subject to fractional damping, with potential implications for diverse fields ranging from quantum mechanics to condensed matter physics.
{"title":"Analytical Study of Coupled Schrödinger Equations with Fractional Damping: Decay Solutions and Stability Analysis","authors":"Dr. Eric Howard, Vikas Kumar, Dr Nand Kumar","doi":"10.52783/cana.v31.941","DOIUrl":"https://doi.org/10.52783/cana.v31.941","url":null,"abstract":"Coupled Schrödinger equations with fractional damping represent a complex yet fascinating area of study in quantum mechanics. This research paper delves into the analytical investigation of such systems, focusing on deriving decay solutions and conducting stability analysis. By combining theoretical frameworks with numerical methods, we explore the behavior of these coupled equations under varying parameters and conditions. Through a thorough analysis, we aim to deepen our understanding of the dynamics and stability properties of quantum systems subject to fractional damping, with potential implications for diverse fields ranging from quantum mechanics to condensed matter physics.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141676691","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}
This paper proposed a general formulation of the stochastic solid transportation problem (SSTP) with mixed constraints such as supply, demand and conveyance capacity taken as uncertain under stochastic environment, following the Weibull distribution (WD). The aim of this study is to minimize the transportation cost includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). SSTP with probabilistic constraints is represented as a chance constrained programming problem. Obtain alpha cut representation from cost coefficient of the fuzzy objective function. We have developed four models for stochastic solid transportation problem. The suggested models are demonstrated by taken as numerical example. A sensitivity analysis is performed to understand parameter’s sensitivity in the proposed model. Introduction: In system of transportation, goods are moved from various sources to destinations using different vehicles and organizational systems, involving both technology and human efforts. Efficient resource allocation in transportation system is crucial for industries and imprecision from factors like fluctuating demand, unreliable supply chains and unpredictable traffic. To address these complexities, advanced mathematical models are needed to manage stochasticity, fuzziness and mixed constraints. The study explores the stochastic solid fuzzy transportation problem with mixed constraint by utilizing the Weibull distribution to model uncertainties inherent in transportation systems. This research addresses the complexity introduced by stochastic variables and fuzzy parameters, particularly in situations where demand, supply and cost of transportation are not deterministic. Objectives: The aim of this study is to minimize the cost of transportation includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). Methods: Obtain alpha cut representation form the cost coefficient of the fuzzy objective function and four models are developed for stochastic solid transportation problem. These models are demonstrating by using a numerical example and a sensitivity analysis is conducted to understand the sensitivity of the parameters in the propose model. Results: Obtained optimal solutions for developed four models of SFSTPMC and sensitivity analysis shows that cost of transportation and flow of unit are sensitive to change in probabilities of demand. Improve transportation system by understanding sensitivity patterns that help decision maker choose appropriate supply availability probabilities. Conclusions: This study presented an approach for solving the SFSTPMC using the Weibull distribution for probabilistic constraints and fuzzy objective functions for transportation cost. Developed and optimized four models, focusing on stochastic parameters. Sensitivity analysis demonstrated the impact of these parameters on transportation cost and unit flow. The results validate
{"title":"Analyze the Stochastic Solid Fuzzy Transportation Problem with Mixed Constraints through Weibull Distribution","authors":"Rashi Arya, Dr. Vipin Kumar, Dr. Abhinav Saxena","doi":"10.52783/cana.v31.949","DOIUrl":"https://doi.org/10.52783/cana.v31.949","url":null,"abstract":"This paper proposed a general formulation of the stochastic solid transportation problem (SSTP) with mixed constraints such as supply, demand and conveyance capacity taken as uncertain under stochastic environment, following the Weibull distribution (WD). The aim of this study is to minimize the transportation cost includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). SSTP with probabilistic constraints is represented as a chance constrained programming problem. Obtain alpha cut representation from cost coefficient of the fuzzy objective function. We have developed four models for stochastic solid transportation problem. The suggested models are demonstrated by taken as numerical example. A sensitivity analysis is performed to understand parameter’s sensitivity in the proposed model. \u0000Introduction: In system of transportation, goods are moved from various sources to destinations using different vehicles and organizational systems, involving both technology and human efforts. Efficient resource allocation in transportation system is crucial for industries and imprecision from factors like fluctuating demand, unreliable supply chains and unpredictable traffic. To address these complexities, advanced mathematical models are needed to manage stochasticity, fuzziness and mixed constraints. The study explores the stochastic solid fuzzy transportation problem with mixed constraint by utilizing the Weibull distribution to model uncertainties inherent in transportation systems. This research addresses the complexity introduced by stochastic variables and fuzzy parameters, particularly in situations where demand, supply and cost of transportation are not deterministic. \u0000Objectives: The aim of this study is to minimize the cost of transportation includes probabilistic constraints have inequalities of stochastic solid transportation problem (SSTP). \u0000Methods: Obtain alpha cut representation form the cost coefficient of the fuzzy objective function and four models are developed for stochastic solid transportation problem. These models are demonstrating by using a numerical example and a sensitivity analysis is conducted to understand the sensitivity of the parameters in the propose model. \u0000Results: Obtained optimal solutions for developed four models of SFSTPMC and sensitivity analysis shows that cost of transportation and flow of unit are sensitive to change in probabilities of demand. Improve transportation system by understanding sensitivity patterns that help decision maker choose appropriate supply availability probabilities. \u0000Conclusions: This study presented an approach for solving the SFSTPMC using the Weibull distribution for probabilistic constraints and fuzzy objective functions for transportation cost. Developed and optimized four models, focusing on stochastic parameters. Sensitivity analysis demonstrated the impact of these parameters on transportation cost and unit flow. The results validate","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674876","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}
Iftekher S. Chowdhury, Dr. Eric Howard, Dr Nand Kumar
This paper embarks on a thorough analytical and numerical exploration of coupled Schrödinger equations under the influence of fractional order damping mechanisms. By integrating fractional damping, which introduces memory effects and non-local dissipative interactions, into the coupled Schrödinger framework, we aim to dissect and understand the nuanced dynamics that govern these complex quantum systems. The research delves into the mathematical underpinnings, stability characteristics, and the dynamical behaviors that emerge from the intricate balance between quantum coupling and fractional damping effects. Through a blend of analytical rigor and sophisticated numerical simulations, this study unveils new insights into the complex interplay among quantum entanglement, dissipation, and non-linear dynamics, offering potential implications for quantum computing, optical systems, and beyond.
{"title":"Advanced Analytical and Numerical Studies on Coupled Schrödinger Equations with Fractional Order Damping","authors":"Iftekher S. Chowdhury, Dr. Eric Howard, Dr Nand Kumar","doi":"10.52783/cana.v31.932","DOIUrl":"https://doi.org/10.52783/cana.v31.932","url":null,"abstract":"This paper embarks on a thorough analytical and numerical exploration of coupled Schrödinger equations under the influence of fractional order damping mechanisms. By integrating fractional damping, which introduces memory effects and non-local dissipative interactions, into the coupled Schrödinger framework, we aim to dissect and understand the nuanced dynamics that govern these complex quantum systems. The research delves into the mathematical underpinnings, stability characteristics, and the dynamical behaviors that emerge from the intricate balance between quantum coupling and fractional damping effects. Through a blend of analytical rigor and sophisticated numerical simulations, this study unveils new insights into the complex interplay among quantum entanglement, dissipation, and non-linear dynamics, offering potential implications for quantum computing, optical systems, and beyond.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674794","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}
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