Ayat Waleed Khaled, Najlae Falah, Hameed Al Saffar
The longest process in ECC is the elliptic curve scalar multiplication. The structure of this operation involves three mathematical levels; this work aims to study issues that arise in the efficient implementation of this operation, specifically targeting the point arithmetic level for the Koblitz curve over a binary field. Theorems have been made for a speedy point doubling and point addition operation, in these theorems Jacobian coordinate modification has been considered, where these coordinates represent each point: refers to a point on a curve over . This occurs when a coordinate system represents any point on a Koblitz curve over a binary field. By choosing the right coordinate system, it is possible to speed up the elliptic curve scalar multiplication using this method.
{"title":"Improved Arithmetic on Koblitz Curves over Binary Field","authors":"Ayat Waleed Khaled, Najlae Falah, Hameed Al Saffar","doi":"10.52783/cana.v31.950","DOIUrl":"https://doi.org/10.52783/cana.v31.950","url":null,"abstract":"The longest process in ECC is the elliptic curve scalar multiplication. The structure of this operation involves three mathematical levels; this work aims to study issues that arise in the efficient implementation of this operation, specifically targeting the point arithmetic level for the Koblitz curve over a binary field. Theorems have been made for a speedy point doubling and point addition operation, in these theorems Jacobian coordinate modification has been considered, where these coordinates represent each point: refers to a point on a curve over . This occurs when a coordinate system represents any point on a Koblitz curve over a binary field. By choosing the right coordinate system, it is possible to speed up the elliptic curve scalar multiplication using this method.","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":"141676745","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}
Introduction: The Identity of a user in digital world is an important factor for an individual. Identity management has been handled by various models which, over the period of time have been prone various security breaches. The foremost integral part of any identity model is the centralized storage, access of data. Considering this, in recent years, there has been evolution from centralization to de-centralization of Identity management. With respect to this new aspect, this paper proposes a solution to the centralized management problems, as a decentralized Identity Management System. The said approach utilizes Ethereum blockchain, IPFS, both supporting distributed data accessibility and data storage respectively. This paper also sheds light on the W3C specification of DID (De-centralized Identifier) which supports the Self-Sovereign Identity principles of Identity Management and are vital for de-centralization of Identity Management
{"title":"Decentralization of Identity using Ethereum and IPFS","authors":"S. Lohar, S. D. Babar, P. N. Mahalle, India Pune","doi":"10.52783/cana.v31.917","DOIUrl":"https://doi.org/10.52783/cana.v31.917","url":null,"abstract":"Introduction: The Identity of a user in digital world is an important factor for an individual. Identity management has been handled by various models which, over the period of time have been prone various security breaches. The foremost integral part of any identity model is the centralized storage, access of data. Considering this, in recent years, there has been evolution from centralization to de-centralization of Identity management. With respect to this new aspect, this paper proposes a solution to the centralized management problems, as a decentralized Identity Management System. The said approach utilizes Ethereum blockchain, IPFS, both supporting distributed data accessibility and data storage respectively. This paper also sheds light on the W3C specification of DID (De-centralized Identifier) which supports the Self-Sovereign Identity principles of Identity Management and are vital for de-centralization of Identity Management","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674473","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}
Bi-isotropic media (chiral and non-reciprocal) present an outstanding challenge for the scientific community. Their characteristics have facilitated the emergence of new and remarkable applications. In this paper, we focus on the novel effect of chirality, characterized through a newly proposed formalism, to highlight the nonlinear effect induced by the magnetization vector under the influence of a strong electric field. This research work is concerned with a new formulation of constitutive relations. We delve into the analysis and discussion of the family of solutions of the nonlinear Schrödinger equation, describing the pulse propagation in nonlinear bi-isotropic media, with a novel approach to constitutive equations. We apply the extended -expansion method with varying dispersion and nonlinearity to define certain families of solutions of the nonlinear Schrödinger equation in bi-isotropic (chiral and non-reciprocal) optical fibers. This clarification aids in understanding the propagation of light with two modes of propagation: a right circular polarized wave (RCP) and a left circular polarized wave (LCP), each having two different wave vectors in nonlinear bi-isotropic media. Various novel exact solutions of bi-isotropic optical solitons are reported in this study. Introduction: The investigation of exact solutions for nonlinear partial differential equations (PDEs) holds significant importance in understanding nonlinear physical phenomena. Nonlinear waves manifest across various scientific domains, notably in optical fibers and solid-state physics. In recent years, several potent methodologies have emerged for identifying solitons and periodic wave solutions of nonlinear PDEs. These include the -expansion method [1-6], the new mapping method [9-10], the method of generalized projective Riccati equations [11-16], and the expansion method [17]. Consequently, an original mathematical approach is proposed to evaluate nonlinear effects in bi-isotropic optical fibers, stemming from magnetization under the influence of a strong electric field [19-20]. The extended -expansion method emerges as a potent technique for deriving solution families of the nonlinear Schrödinger equation in bi-isotropic optical fibers. This method employs a perturbation expansion in powers of the dimensionless parameter and is applicable for both weak and strong nonlinearities. It accommodates varying dispersion and nonlinearity, rendering it suitable for modeling a wide array of optical fibers. Results and Conclusion: This investigate is concerned with a new formulation of constitutive relation linking to the magnetic effect, to understand rigorously the physical nature of biisotropic effects and to generalize the main macroscopic models. We inferred the nonlinear Schrodinger equation for a bi-isotropic medium term with a nonlinear term of magnetizing. In this article, the extended -expansion method is a powerful technique for determining a family of solutions of the
{"title":"Application of the G’/G Expansion Method for Solving New Form of Nonlinear Schrödinger Equation in Bi-Isotropic Fiber","authors":"Ourahmoun Abbes","doi":"10.52783/cana.v31.951","DOIUrl":"https://doi.org/10.52783/cana.v31.951","url":null,"abstract":"Bi-isotropic media (chiral and non-reciprocal) present an outstanding challenge for the scientific community. Their characteristics have facilitated the emergence of new and remarkable applications. In this paper, we focus on the novel effect of chirality, characterized through a newly proposed formalism, to highlight the nonlinear effect induced by the magnetization vector under the influence of a strong electric field. This research work is concerned with a new formulation of constitutive relations. We delve into the analysis and discussion of the family of solutions of the nonlinear Schrödinger equation, describing the pulse propagation in nonlinear bi-isotropic media, with a novel approach to constitutive equations. We apply the extended -expansion method with varying dispersion and nonlinearity to define certain families of solutions of the nonlinear Schrödinger equation in bi-isotropic (chiral and non-reciprocal) optical fibers. This clarification aids in understanding the propagation of light with two modes of propagation: a right circular polarized wave (RCP) and a left circular polarized wave (LCP), each having two different wave vectors in nonlinear bi-isotropic media. Various novel exact solutions of bi-isotropic optical solitons are reported in this study. \u0000Introduction: The investigation of exact solutions for nonlinear partial differential equations (PDEs) holds significant importance in understanding nonlinear physical phenomena. Nonlinear waves manifest across various scientific domains, notably in optical fibers and solid-state physics. In recent years, several potent methodologies have emerged for identifying solitons and periodic wave solutions of nonlinear PDEs. These include the -expansion method [1-6], the new mapping method [9-10], the method of generalized projective Riccati equations [11-16], and the expansion method [17]. \u0000 Consequently, an original mathematical approach is proposed to evaluate nonlinear effects in bi-isotropic optical fibers, stemming from magnetization under the influence of a strong electric field [19-20]. The extended -expansion method emerges as a potent technique for deriving solution families of the nonlinear Schrödinger equation in bi-isotropic optical fibers. This method employs a perturbation expansion in powers of the dimensionless parameter and is applicable for both weak and strong nonlinearities. It accommodates varying dispersion and nonlinearity, rendering it suitable for modeling a wide array of optical fibers. \u0000Results and Conclusion: This investigate is concerned with a new formulation of constitutive relation linking to the magnetic effect, to understand rigorously the physical nature of biisotropic effects and to generalize the main macroscopic models. We inferred the nonlinear Schrodinger equation for a bi-isotropic medium term with a nonlinear term of magnetizing. In this article, the extended -expansion method is a powerful technique for determining a family of solutions of the ","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141676840","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}
Dengue is a vector borne disease , which can be fatal at times . Early detection dengue of dengue is vital as no vaccines have been developed for dengue yet..The process of eliminating irrelevant and redundant features from the data set facilitates the optimal features selection . This study is proposed to select the Optimal features by using Opt_Recur algorithm from the Dengue dataset , a hybrid SDR model which makes prediction with better accuracy when compared to the conventional classifiers like the Support Vector Machine (SVM), Decision Tree(DT) and the Random Forest (RF) classifiers.
{"title":"A Novel Hybrid SDR Model for Dengue Prediction using Opt_Recurr Feature Selection Algorithm","authors":"Dr. S. Nagasundaram","doi":"10.52783/cana.v31.857","DOIUrl":"https://doi.org/10.52783/cana.v31.857","url":null,"abstract":"Dengue is a vector borne disease , which can be fatal at times . Early detection dengue of dengue is vital as no vaccines have been developed for dengue yet..The process of eliminating irrelevant and redundant features from the data set facilitates the optimal features selection . This study is proposed to select the Optimal features by using Opt_Recur algorithm from the Dengue dataset , a hybrid SDR model which makes prediction with better accuracy when compared to the conventional classifiers like the Support Vector Machine (SVM), Decision Tree(DT) and the Random Forest (RF) classifiers.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141675729","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 compilation of research studies holds the utmost significance in hardware acceleration for machine learning. In our current era, characterised by the exponential growth of artificial intelligence (AI) applications, these studies tackle crucial challenges in optimising neural network accelerators' performance, energy efficiency, and resilience. The importance lies in their potential to revolutionise AI implementation across various domains. Efficient hardware accelerators are a cornerstone in unlocking the full potential of AI, enabling breakthroughs in deep learning, high-speed train fault detection and isolation, and numerous other applications. By improving memory management, facts placement, bus scheduling, and fault tolerance, that research paves the way for AI structures which are both powerful and sustainable, making AI accessible and impactful in a wide variety of fields. This research is important for fostering the growth and adoption of AI, ultimately remodelling how we interact with technology and facts in our daily lives.
{"title":"Revolutionising Ai Deployment: Survey On Hardware Acceleration for Machine Learning Optimisation and Resilience","authors":"G. Pooja, Dr. S. Malathy","doi":"10.52783/cana.v31.855","DOIUrl":"https://doi.org/10.52783/cana.v31.855","url":null,"abstract":"This compilation of research studies holds the utmost significance in hardware acceleration for machine learning. In our current era, characterised by the exponential growth of artificial intelligence (AI) applications, these studies tackle crucial challenges in optimising neural network accelerators' performance, energy efficiency, and resilience. The importance lies in their potential to revolutionise AI implementation across various domains. Efficient hardware accelerators are a cornerstone in unlocking the full potential of AI, enabling breakthroughs in deep learning, high-speed train fault detection and isolation, and numerous other applications. By improving memory management, facts placement, bus scheduling, and fault tolerance, that research paves the way for AI structures which are both powerful and sustainable, making AI accessible and impactful in a wide variety of fields. This research is important for fostering the growth and adoption of AI, ultimately remodelling how we interact with technology and facts in our daily lives.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":"178 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141674286","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 study investigates the stability and decay properties of solutions to nonlinear Schrödinger equations (NLSEs) with time-dependent coefficients. Employing a blend of analytical and numerical methods, we delve into how temporal variations in coefficients influence the dynamics of wave functions. Our analysis reveals that time-dependent coefficients significantly affect the stability and decay rates of solutions, uncovering conditions that lead to either enhanced stability or accelerated decay. The findings highlight the critical role of coefficient temporality in dictating the behavior of NLSE solutions. These insights not only advance our theoretical understanding of NLSEs but also bear implications for practical applications in fields modeled by these equations. Our research opens avenues for exploiting time-dependent behaviors in designing systems with desired dynamical properties.
{"title":"Analysis of Nonlinear Schrödinger Equations with Time-Dependent Coefficients: Stability and Decay Properties","authors":"Dr. Eric Howard, Dr Nand Kumar","doi":"10.52783/cana.v31.934","DOIUrl":"https://doi.org/10.52783/cana.v31.934","url":null,"abstract":"This study investigates the stability and decay properties of solutions to nonlinear Schrödinger equations (NLSEs) with time-dependent coefficients. Employing a blend of analytical and numerical methods, we delve into how temporal variations in coefficients influence the dynamics of wave functions. Our analysis reveals that time-dependent coefficients significantly affect the stability and decay rates of solutions, uncovering conditions that lead to either enhanced stability or accelerated decay. The findings highlight the critical role of coefficient temporality in dictating the behavior of NLSE solutions. These insights not only advance our theoretical understanding of NLSEs but also bear implications for practical applications in fields modeled by these equations. Our research opens avenues for exploiting time-dependent behaviors in designing systems with desired dynamical properties.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141673661","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, Intuitionistic Fuzzy Threshold Hypergraph (IFTHG) is described with some definitions, such as adjacency level, strength, walk, hyperpath, score values, connected and disconnected IFTHGs. IFTHGs are essential for modeling complex relationships and uncertainties in emergency response scenarios within crowed areas. Furthermore, a novel method for capturing fugitives using IFTHG model is demonstrated. The proposed system initializes robots and implements a step-by-step algorithm upon detecting any intrusion, ultimately determining the nearest robot to capture the fugitives.
{"title":"Intuitionistic Fuzzy Threshold Hypergraphs and Their Role in Chasing Fugitives with Multi-Bots","authors":"Myithili.K.K","doi":"10.52783/cana.v31.826","DOIUrl":"https://doi.org/10.52783/cana.v31.826","url":null,"abstract":"In this paper, Intuitionistic Fuzzy Threshold Hypergraph (IFTHG) is described with some definitions, such as adjacency level, strength, walk, hyperpath, score values, connected and disconnected IFTHGs. IFTHGs are essential for modeling complex relationships and uncertainties in emergency response scenarios within crowed areas. Furthermore, a novel method for capturing fugitives using IFTHG model is demonstrated. The proposed system initializes robots and implements a step-by-step algorithm upon detecting any intrusion, ultimately determining the nearest robot to capture the fugitives.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141673626","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}
Mr. Jagdish Pimple, K. Vhatkar, Rachna K. Somkunwar, Mrs. Shital Wadaganve, Deepali Baghel, Dr. Rajesh Bharti, Dr. Vinod Kimbahune
In this study, we explore how to optimize data center operations by combining Operations Research (OR) and Machine Learning (ML) methodologies with Python-based categorization algorithms. Using Scikit-learn and TensorFlow, two Python libraries, we investigate how ML algorithms might be integrated with OR techniques like queuing theory and linear programming to forecast workloads and allocate resources more effectively. Problems with scheduling workloads, allocating resources, and managing energy consumption are at the heart of our research into data center optimization. The goal of this comprehensive framework is to create more effective and environmentally friendly data centre operations by systematically evaluating Python-based categorization models in response to changing workload demands and environmental circumstances. Introduction: The backbone of our digital infrastructure, data centers stand tall in the ever-changing world of contemporary technology. A vast variety of online services, including social media platforms, e-commerce websites, cloud computing, and big data analytics, rely on the servers, storage devices, networking gear, and other essential components housed in these expansive facilities. Meeting the ever-increasing demands for computational resources while simultaneously enhancing performance, efficiency, and cost-effectiveness is a daunting task for data centers, which are already struggling to keep up with the exponential growth in both the amount and complexity of digital data. Objectives: Our goal in writing this article is to delve into the ways in which data center optimization intersects with Operations Research and Machine Learning. Data center optimization presents a wide range of problems, and this course will explore the theory, methods, and best practices for using OR and ML to solve these problems. To develop an integrated framework that combines operations research (OR) and machine learning (ML) techniques to optimize the performance, energy efficiency, and reliability of data centers. Methods: Optimization strategies that improve data center operations in terms of performance, efficiency, and sustainability. These proposed strategies make use of both OL and ML techniques. Data center operators can optimize resource allocation, workload management, temperature control, energy consumption, and anomaly detection in real-time by formally stating the optimization problem in a mathematical framework. This allows for informed decision-making, systematic analysis of trade-offs, and the implementation of adaptive control strategies. Results: The visualization depicts the projected energy usage in terms of bandwidth for both approaches, compared to the actual values. In general, although both methods demonstrate potential, additional refinement and optimization may be necessary to attain superior outcomes in real-life situations. This discussion presents an analysis of the performance of both proc
在本研究中，我们探讨了如何通过将运筹学（OR）和机器学习（ML）方法与基于 Python 的分类算法相结合来优化数据中心的运营。利用 Scikit-learn 和 TensorFlow 这两个 Python 库，我们研究了如何将 ML 算法与队列理论和线性规划等运营研究技术相结合，以更有效地预测工作负载和分配资源。工作负载调度、资源分配和能耗管理问题是我们数据中心优化研究的核心。这个综合框架的目标是通过系统地评估基于 Python 的分类模型，以应对不断变化的工作负载需求和环境状况，从而创建更有效、更环保的数据中心运营。简介作为数字基础设施的支柱，数据中心在瞬息万变的当代技术世界中傲然挺立。各种在线服务，包括社交媒体平台、电子商务网站、云计算和大数据分析，都依赖于这些庞大设施中的服务器、存储设备、网络设备和其他重要组件。要满足对计算资源日益增长的需求，同时提高性能、效率和成本效益，这对数据中心来说是一项艰巨的任务，因为数据中心已经难以跟上数字数据数量和复杂性的指数级增长。目标：我们撰写本文的目的是深入探讨数据中心优化与运筹学和机器学习的交叉方式。数据中心优化会带来各种各样的问题，本课程将探讨使用运筹学和机器学习解决这些问题的理论、方法和最佳实践。 开发一个综合框架，结合运筹学（OR）和机器学习（ML）技术，优化数据中心的性能、能效和可靠性。方法：从性能、效率和可持续性方面改进数据中心运营的优化策略。这些建议的策略利用了 OL 和 ML 技术。数据中心运营商可以通过在数学框架中正式说明优化问题，实时优化资源分配、工作负载管理、温度控制、能源消耗和异常检测。这样就能做出明智的决策，系统地分析权衡，并实施自适应控制策略。结果可视化描述了这两种方法在带宽方面的预计能源使用量与实际值的比较。总的来说，虽然两种方法都显示出了潜力，但要在实际情况中取得更好的结果，可能还需要进一步的改进和优化。 本讨论分析了这两种方法的性能，并深入探讨了它们各自的优缺点，为进一步研究或改进这两种方法奠定了基础。结论：通过使用综合的多学科方法，我们可以优化数据中心，在提高效率和性能的同时，鼓励数据中心运营的创新性、弹性和可持续性。此外，通过整合优化算法、预测分析和自适应控制策略，数据中心的资源运营商可以获得可观的利用率、能源效率和整体系统性能收益。
{"title":"Scientific Integration of Operations Research and Machine Learning for Data Centre Optimization","authors":"Mr. Jagdish Pimple, K. Vhatkar, Rachna K. Somkunwar, Mrs. Shital Wadaganve, Deepali Baghel, Dr. Rajesh Bharti, Dr. Vinod Kimbahune","doi":"10.52783/cana.v31.948","DOIUrl":"https://doi.org/10.52783/cana.v31.948","url":null,"abstract":"In this study, we explore how to optimize data center operations by combining Operations Research (OR) and Machine Learning (ML) methodologies with Python-based categorization algorithms. Using Scikit-learn and TensorFlow, two Python libraries, we investigate how ML algorithms might be integrated with OR techniques like queuing theory and linear programming to forecast workloads and allocate resources more effectively. Problems with scheduling workloads, allocating resources, and managing energy consumption are at the heart of our research into data center optimization. The goal of this comprehensive framework is to create more effective and environmentally friendly data centre operations by systematically evaluating Python-based categorization models in response to changing workload demands and environmental circumstances. \u0000Introduction: The backbone of our digital infrastructure, data centers stand tall in the ever-changing world of contemporary technology. A vast variety of online services, including social media platforms, e-commerce websites, cloud computing, and big data analytics, rely on the servers, storage devices, networking gear, and other essential components housed in these expansive facilities. Meeting the ever-increasing demands for computational resources while simultaneously enhancing performance, efficiency, and cost-effectiveness is a daunting task for data centers, which are already struggling to keep up with the exponential growth in both the amount and complexity of digital data. \u0000Objectives: Our goal in writing this article is to delve into the ways in which data center optimization intersects with Operations Research and Machine Learning. Data center optimization presents a wide range of problems, and this course will explore the theory, methods, and best practices for using OR and ML to solve these problems. \u0000 To develop an integrated framework that combines operations research (OR) and machine learning (ML) techniques to optimize the performance, energy efficiency, and reliability of data centers. \u0000Methods: Optimization strategies that improve data center operations in terms of performance, efficiency, and sustainability. These proposed strategies make use of both OL and ML techniques. Data center operators can optimize resource allocation, workload management, temperature control, energy consumption, and anomaly detection in real-time by formally stating the optimization problem in a mathematical framework. This allows for informed decision-making, systematic analysis of trade-offs, and the implementation of adaptive control strategies. \u0000Results: The visualization depicts the projected energy usage in terms of bandwidth for both approaches, compared to the actual values. In general, although both methods demonstrate potential, additional refinement and optimization may be necessary to attain superior outcomes in real-life situations. \u0000 This discussion presents an analysis of the performance of both proc","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141673872","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 article, we have derived a new oscillation criteria for a class of conformable Schrodinger equations. Based on the generalized Riccati technique, the results were obtained here. Also we have extended the Hartman-Winter oscillation criteria to conformable Schrodinger equation.
{"title":"On the Oscillation of a Class of Conformable Schrodinger Equations","authors":"N. Sasikala","doi":"10.52783/cana.v31.852","DOIUrl":"https://doi.org/10.52783/cana.v31.852","url":null,"abstract":"In this article, we have derived a new oscillation criteria for a class of conformable Schrodinger equations. Based on the generalized Riccati technique, the results were obtained here. Also we have extended the Hartman-Winter oscillation criteria to conformable Schrodinger equation.","PeriodicalId":40036,"journal":{"name":"Communications on Applied Nonlinear Analysis","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141676596","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}
Shivangni Jat, R. S. Tomar, Santosh Narayankhedkar
Vehicular networks play a crucial role in modern transportation systems, significantly impacting connectivity and safety on highways. This paper explores the application of graph theoretical models to enhance both connectivity and safety in vehicular networks. Graph theory, a branch of discrete mathematics, provides a robust framework for modeling and analyzing complex networks, including those formed by vehicles on highways. Our study begins by defining the vehicular network as a graph where nodes represent vehicles, and edges denote communication links between them. We employ various graph theoretical concepts such as connectivity, centrality, and network flow to evaluate and improve the network's performance. Key metrics, including the degree of nodes, clustering coefficients, and shortest path lengths, are utilized to quantify network connectivity and identify critical nodes and edges that influence overall network efficiency. One of the primary objectives is to ensure uninterrupted connectivity in the presence of dynamic and often unpredictable vehicular movement. To this end, we analyze the network's resilience to node failures and propose strategies to enhance robustness using redundancy and alternative routing paths. By incorporating concepts like k-connectivity and network diameter, we develop models that maintain high levels of connectivity despite the removal or failure of multiple nodes or edges. Safety is addressed through the lens of network stability and reliability. We investigate the impact of vehicular density, speed, and communication range on the network's ability to sustain reliable communication channels. Techniques such as dynamic topology management and adaptive power control are proposed to mitigate the risks associated with network fragmentation and communication delays. Furthermore, we introduce optimization algorithms that leverage graph partitioning and community detection to improve the management of vehicular clusters, facilitating efficient data dissemination and reducing the likelihood of congestion-related incidents. The proposed models are validated through simulations that mimic real-world highway conditions, demonstrating significant improvements in both connectivity and safety metrics. In conclusion, the application of graph theoretical models offers a promising approach to enhancing highway connectivity and safety in vehicular networks
车辆网络在现代交通系统中发挥着至关重要的作用，对高速公路的连通性和安全性产生了重大影响。本文探讨了如何应用图论模型来增强车辆网络的连通性和安全性。图论是离散数学的一个分支，它为复杂网络的建模和分析提供了一个强大的框架，包括高速公路上车辆形成的网络。我们的研究首先将车辆网络定义为一个图，其中节点代表车辆，边代表车辆之间的通信链路。我们采用各种图论概念，如连通性、中心性和网络流，来评估和改进网络的性能。我们利用节点度、聚类系数和最短路径长度等关键指标来量化网络连通性，并识别影响整体网络效率的关键节点和边。我们的主要目标之一是确保在动态且经常不可预测的车辆移动情况下的不间断连接。为此，我们分析了网络对节点故障的恢复能力，并提出了利用冗余和替代路由路径来增强鲁棒性的策略。通过结合 k 连接性和网络直径等概念，我们开发出了在多个节点或边缘被移除或失效的情况下仍能保持高水平连接性的模型。我们从网络稳定性和可靠性的角度来探讨安全性问题。我们研究了车辆密度、速度和通信范围对网络维持可靠通信通道能力的影响。我们提出了动态拓扑管理和自适应功率控制等技术，以降低与网络分裂和通信延迟相关的风险。此外，我们还引入了优化算法，利用图分割和群落检测来改善车辆集群的管理，促进数据的有效传播，降低拥堵相关事故发生的可能性。通过模拟现实世界的高速公路状况，对所提出的模型进行了验证，结果表明连接性和安全性指标均有显著改善。总之，图论模型的应用为提高高速公路的连通性和车辆网络的安全性提供了一种前景广阔的方法。
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