Volume 9 | Issue 6 | June-2021

 Abstract

Ordinary Differential Equations (ODEs) are fundamental in modeling a wide range of phenomena in science, engineering, economics, and various other fields. However, finding exact analytical solutions to ODEs is not always possible, especially for complex, non-linear, or high-dimensional systems. In such cases, numerical methods offer a practical approach to approximating solutions. This paper explores various numerical techniques for solving ODEs, including the Euler method, Runge-Kutta methods, and multistep methods. It highlights the advantages and limitations of each approach in terms of accuracy, stability, and computational efficiency. The paper also discusses the concept of step size selection, error analysis, and the impact of discretization on the convergence of solutions. Additionally, we investigate specialized methods for stiff ODEs, which pose unique challenges due to the presence of rapidly changing variables alongside slow dynamics. Methods like the backward Euler and implicit Runge-Kutta schemes are reviewed for their effectiveness in handling stiffness. Finally, the paper presents several examples and applications to demonstrate the practical implementation of these methods and their ability to approximate solutions for real-world problems. We conclude by emphasizing the importance of choosing appropriate numerical techniques based on the nature of the problem at hand and the desired accuracy of the solution.

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Ordinary Differential Equations, Numerical Methods, Galerkin's Method, Runge-Kutta Methods, Stiff ODEs, Error Analysis, Stability

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This research investigates the impact of ERP (Enterprise Resource Planning) cloud integration on organizational agility and decision-making processes. As businesses increasingly adopt cloud-based solutions, understanding how these systems enhance operational flexibility and support timely, informed decisions becomes crucial. The study employs a mixed-methods approach, combining quantitative surveys and qualitative interviews across various industries to gather data on the effectiveness of cloud-based ERP systems. Preliminary findings indicate that ERP cloud integration significantly improves organizational agility by facilitating real-time data access, enhancing collaboration, and streamlining processes. Additionally, the integration fosters better decision-making through improved information flow and analytical capabilities. This research contributes to the existing literature by elucidating the relationship between cloud ERP adoption and key organizational outcomes, offering practical insights for businesses aiming to leverage technology for competitive advantage. The findings underscore organizations' need to embrace cloud ERP solutions to enhance agility and elevate decision-making effectiveness in an increasingly dynamic business environment.

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 Keywords

ERP (Enterprise Resource Planning), Cloud Integration, Organizational Agility, Decision-Making, Business Intelligence.

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Transforming legacy systems into modern Enterprise Resource Planning (ERP) systems is a complex but crucial task for large organizations striving to maintain competitiveness and operational efficiency. Legacy systems, often characterized by outdated technologies, limited integration capabilities, and high maintenance costs, pose significant challenges during ERP implementations. This paper explores the strategies that large organizations can employ to ensure successful ERP implementations, focusing on overcoming the unique challenges associated with legacy systems. One of the primary challenges in legacy system transformation is data migration. Organizations must ensure that data from outdated systems is accurately and efficiently transferred to the new ERP system without loss of integrity. This paper highlights best practices for data cleansing, mapping, and validation, which are essential for mitigating the risks associated with data migration. Additionally, the paper discusses the importance of establishing a robust data governance framework to maintain data quality throughout the implementation process. Change management is another critical factor in the success of ERP implementations. The paper emphasizes the need for organizations to develop comprehensive change management strategies that address the cultural and operational shifts required by ERP systems. This includes stakeholder engagement, training programs, and continuous communication to ensure that all levels of the organization are aligned with the transformation objectives. Integration of the ERP system with existing IT infrastructure is another significant challenge, particularly in large organizations with complex technology landscapes. The paper outlines strategies for seamless integration, including the use of middleware, APIs, and microservices architectures to ensure that the new ERP system can interact effectively with other enterprise systems. This section also examines the role of cloud-based ERP solutions in facilitating integration and scalability. The paper further discusses the importance of selecting the right ERP solution that aligns with the organization's strategic goals and operational needs. It provides a framework for evaluating ERP vendors and solutions, considering factors such as scalability, customization capabilities, and support services. The role of external consultants in providing expertise and guidance during the selection and implementation process is also explored. Finally, the paper addresses the post-implementation phase, which is critical for realizing the benefits of ERP systems. It emphasizes the need for continuous monitoring, optimization, and support to ensure that the ERP system evolves with the organization's needs. The paper concludes with a discussion on the future trends in ERP implementations, including the rise of AI and machine learning in enhancing ERP functionalities and decision-making processes.

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 Keywords

ERP implementation, legacy systems transformation, data migration, change management, system integration, cloud ERP, vendor selection, post-implementation optimization, large organizations, enterprise resource planning

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The unification of Kannada-speaking regions into a single state was a transformative movement that began in the late 19th century. This effort, initially driven by cultural and literary figures, evolved into a significant political struggle supported by a range of leaders and organizations. The eventual formation of Karnataka in 1956 was a milestone in this process, reflecting both achievements and ongoing regional disparities. This article provides an in-depth exploration of the historical context, key figures, major milestones, and the enduring impacts of the Kannada unification movement.

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Key words : Kannada Unification , Linguistic Nationalism, Aluru Venkata Rao , Karnataka Gatha Vaibhava , Karnataka Vidya Vardhaka Sangha , Political Mobilization, Regional Disparities , ndian National Congress , Karnataka Ekikarana Sangha , State Reorganization , Post-Independence Challenges

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Social network analysis has gained much attention in recent times. A graph can be used to depict social networks. In the analysis of social networks, every individual is denoted as a node, and the connections between them are represented as edges. Identifying communities and representing the interactions between entities and individuals in real-world network graphs is a difficult task. There are numerous established methods for locating the linked nodes that eventually result in the discovery of communities. This paper presents a novel method for community detection in social networks by integrating unnormalized spectral clustering with the k-nearest neighbors (KNN) algorithm. The approach leverages the strengths of spectral clustering for global structure analysis and KNN for local neighborhood refinement. The primary objective of the algorithm proposed in this study is to identify and eliminate any noisy nodes from the identified communities, hence enhancing the quality of the identified communities. Experimental results on synthetic and real-world datasets demonstrate the method's effectiveness in accurately identifying community structures.

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Community Detection, Social Networks, Spectral Clustering, K-Nearest Neighbors (KNN).

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 Abstract

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Video super-resolution (VSR) aims to enhance the visual quality of low-resolution videos by generating corresponding high-resolution frames. Traditional methods for VSR often suffer from limitations in handling complex motion patterns and preserving temporal consistency across frames. This paper proposes an efficient VSR approach leveraging generative adversarial networks (GANs) and temporal consistency constraints to address these challenges. Our method consists of two key components: a generator network that learns to map low-resolution video frames to their high-resolution counterparts and a discriminator network that distinguishes between generated and real high-resolution frames. Additionally, we introduce temporal consistency constraints to ensure smooth transitions between consecutive frames in the super-resolved video sequence. Experimental results on benchmark datasets demonstrate that our proposed approach achieves state-of-the-art performance in quantitative metrics and visual quality, effectively enhancing low-resolution videos' resolution and temporal coherence

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Component, formatting, style, styling, insert

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The global entrepreneurial landscape is witnessing a paradigm shift with startups emerging as pivotal players in economic development. This research paper conducts a comparative analysis of entrepreneurial ecosystems in leading global startup hubs, aiming to unravel the key success factors that entrepreneurs navigate. With a focus on regions such as Silicon Valley, Tel Aviv, Berlin, and Bangalore, the study employs a multidimensional approach, encompassing funding landscapes, government policies, talent availability, network density, and cultural nuances. By synthesizing qualitative interviews, surveys, and secondary data, the paper elucidates the intricacies of each ecosystem. Findings are anticipated to provide policymakers, entrepreneurs, and stakeholders with actionable insights, fostering informed decisions to bolster local ecosystems and contribute to sustained economic growth and innovation.

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Entrepreneurial Ecosystems, Startup Hubs, Economic Development, Entrepreneurial Strategies, Funding Landscape, Sustainable Growth, Global Comparative Analysis

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Numerical analysis is a critical branch of mathematics and computer science that provides methods and algorithms for solving mathematical problems arising in various fields, including engineering, physics, finance, and computer science. This abstract explores the fundamentals of numerical analysis, emphasizing the core algorithms and their diverse applications. The foundation of numerical analysis lies in the development and analysis of numerical algorithms, which are step-by-step procedures designed to approximate solutions to mathematical problems that may be challenging or impossible to solve analytically. These algorithms are essential for tackling real-world problems where analytical solutions are often impractical due to complexity or nonlinearity. This abstract delves into the key components of numerical analysis, starting with the basics of approximation theory and error analysis. It highlights the importance of understanding the limitations and sources of error in numerical computations, emphasizing the trade-offs between accuracy and computational efficiency. Numerical stability, an essential concept, is explored to ensure that algorithms produce reliable results in the presence of rounding errors and computational imprecisions. The abstract then explores various numerical techniques, including interpolation, numerical integration, and solution of linear and nonlinear equations. The focus extends to iterative methods and optimization algorithms, illustrating their role in solving large-scale problems encountered in scientific and engineering applications. Additionally, the abstract discusses the numerical treatment of differential equations, a crucial aspect with widespread applications in physics, engineering, and biology. To illustrate the practical significance of numerical analysis, this abstract presents a selection of applications across different domains. Examples include finite element analysis for structural engineering, numerical simulation of fluid dynamics, and financial modeling for risk assessment. The role of numerical algorithms in image processing, machine learning, and data analysis is also highlighted, showcasing the interdisciplinary nature of numerical analysis. In conclusion, this abstract provides an overview of the fundamentals of numerical analysis, emphasizing the development, analysis, and application of numerical algorithms. By understanding these fundamentals, researchers, engineers, and practitioners can employ robust numerical techniques to address complex problems in a wide range of scientific and engineering disciplines. The abstract encourages further exploration of advanced numerical methods and their integration into emerging technologies, contributing to ongoing advancements in computational science.

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Numerical Analysis, Algorithms and Applications

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As the number of companies continues to grow, there arises a need for establishing a mechanism that accurately portrays the structure and operations of any business entity. In this regard, the concept of corporate governance plays a crucial and indispensable role. Numerous stakeholders are invested in the performance of these companies, and shareholders, in particular, seek assurance that the company operates with transparency in all its business actions and critical decisions. While companies are artificial entities, it is unjust to hold the entire corporate responsible for any fraud committed by an insider. Corporate governance addresses this issue by providing provisions to uncover the truth and hold the real individuals behind corporate frauds accountable. In India, SEBI has introduced clause 49, which outlines mandatory and non-mandatory parameters that every listed company must adhere to. The main focus of this paper is to comprehensively understand the concept of corporate governance and its significance in the Indian market. Furthermore, the paper will discuss the major opportunities and challenges faced in implementing corporate governance in India.

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Corporate Governance, India, Challenges, Opportunity, SEBI Clause 49

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