Little Flower College is a women's Catholic college in Guruvayur, India, and is affiliated with the University of Calicut. The administration of the college falls under the Assisi Province of the Franciscan Congregation. In 2017, the college was ranked 49th in India by the National Institutional Ranking Framework (NIRF).
The Collatz or 3x + 1 conjecture asserts that repeated application of the map for even n and for odd n eventually reaches 1 from every positive integer. Although unproven, it is supported by a heuristic random-walk model which predicts that the total stopping time σ(n), the number of iterations needed to reach 1, has mean approximately 6.952 ln n and a standard deviation proportional to √(Inn ). This study computes σ(n) exactly for every integer up to 10⁷ and tests these predictions. Trajectories were computed in C using memoisation and validated against direct iteration and known records. The longest trajectory below 10⁷ begins at 8,400,511 and takes 429 steps of T (685 steps of the standard map), and the highest point reached, 3.02 × 10¹³, occurs in the trajectory of 6,631,675. A least-squares fit of binned mean stopping times against ln n over 10³ to 10⁷ gives a slope of 6.817 (R² = 0.9996), within 2 per cent of the predicted 6.952. The variance of σ(n) grows in proportion to ln n, with a coefficient of 91 to 97 compared with the predicted 101.4. The standardised stopping times are close to Gaussian in the centre, with 68.7 per cent within one standard deviation, but are positively skewed, with skewness about 0.6 and a long right tail. The results support the random-walk model as a first approximation while identifying systematic departures in the variance and the tail.
This study explores the role of Artificial Intelligence (AI) in smart traffic monitoring and road accident prevention. The main objective is to understand how AI can improve road safety by monitoring traffic, reducing congestion, and preventing accidents. The study discusses the importance of AI-based traffic management systems, common causes of road accidents, and the challenges involved in implementing these technologies. Information was collected from research articles, government reports, and other reliable sources. The findings show that AI technologies, such as smart traffic signals, real-time monitoring, and data analysis, can improve traffic flow and help reduce accidents. The study also highlights the need for public awareness, proper infrastructure, and government support for the successful implementation of AI-based traffic systems. In conclusion, Artificial Intelligence has the potential to make transportation safer and more efficient by supporting better traffic management and reducing road accidents. Keywords: artificial intelligence; Smart Traffic Management; Road Safety; Traffic Monitoring; Accident Prevention; Intelligent Transportation Systems
Spatial domain image steganography has emerged as one of the most widely adopted information-hiding techniques due to its simplicity, high embedding capacity, low computational complexity, and ability to preserve the visual quality of digital images. It plays a significant role in secure communication by concealing confidential information within digital images, thereby protecting sensitive data from unauthorized access in applications such as healthcare, military communication, banking, cloud computing, digital forensics, and multimedia systems. Despite these advantages, spatial domain techniques face several challenges, including vulnerability to steganalysis, limited robustness against image processing operations, and the trade-off between embedding capacity and imperceptibility. This paper presents a comprehensive review of spatial domain image steganography by examining its historical development, fundamental concepts, classification, and major techniques, including Least Significant Bit (LSB), Adaptive LSB, Pixel Value Differencing (PVD), Pixel Indicator Technique (PIT), Optimal Pixel Adjustment Process (OPAP), edge-based methods, and other adaptive spatial approaches. The reviewed techniques are comparatively analyzed based on embedding capacity, imperceptibility, robustness, computational complexity, and practical applicability, and are further illustrated through a quantitative case study that evaluates PSNR, SSIM, and MSE for LSB substitution on a standard test image. The study identifies existing research gaps and highlights future research directions aimed at improving robustness, visual quality, and embedding capacity. By providing a structured and critical synthesis of existing literature, this review serves as a valuable reference for researchers, academicians, and practitioners working in the field of digital image security and information hiding. Keywords: Least Significant Bit (LSB); Pixel Value Differencing (PVD); Information Hiding; Digital Image Security; Steganalysis
The increasing demand for heating and cooling in buildings, driven by rapid urbanization and climate change, has led to higher energy consumption and carbon emissions. Improving thermal energy efficiency has therefore become an important objective in sustainable building design. This paper proposes the conceptual design of an Artificial Intelligence (AI)-assisted Phase Change Material (PCM) thermal panel for residential and commercial buildings. The proposed system combines encapsulated PCMs with embedded temperature sensors and an AI-assisted control framework to improve indoor thermal regulation. During periods of high temperature, the PCM absorbs and stores excess heat, while during cooler conditions it releases the stored heat, thereby maintaining a more stable indoor temperature and reducing dependence on conventional heating, ventilation, and air-conditioning (HVAC) systems. The AI component continuously analyzes environmental parameters such as indoor and outdoor temperature, humidity, occupancy, and weather conditions to support intelligent thermal management and optimize panel operation under different climatic conditions. This paper presents the conceptual architecture, operating principle, and expected performance of the proposed system based on existing research in PCM technology and AI-assisted energy management. The proposed design is expected to enhance thermal comfort, improve building energy efficiency, reduce electricity consumption and carbon emissions, and support the development of sustainable and smart building infrastructure. Keywords: sustainable construction; Artificial Intelligence (AI); energy efficiency; Phase Change Material (PCM); Thermal Panel; Thermal Energy Storage; Smart Buildings
Artificial Intelligence in Education Focused on Standardized Learning: A Learning Analytics Review Artificial Intelligence (AI) has emerged as a transformative force in education, reshaping teaching, learning, assessment, and educational management. Recent research highlights the growing integration of AI technologies such as machine learning, deep learning, natural language processing, learning analytics, recommendation systems, and generative AI across diverse educational contexts. While standardized learning seeks to ensure consistency in curriculum delivery and learning outcomes, AI-driven educational systems provide opportunities to enhance learner engagement, academic performance, and instructional effectiveness through data-driven insights. This analytical review synthesizes findings from recent studies on AI applications in education, including personalized learning, learning analytics, self-regulated learning, agentic AI, inclusive education, recommendation systems, AI literacy, and K–12 educational environments. The review examines key analytical indicators such as student achievement, engagement, learning behavior, retention, assessment performance, and adaptive learning outcomes. Findings indicate that AI-powered learning analytics can support standardized learning by enabling continuous monitoring, predictive modeling, personalized feedback, and evidence-based decision-making while maintaining common educational standards. The analysis further reveals that AI technologies contribute to improved accessibility, inclusiveness, and learning efficiency. However, challenges related to ethical concerns, data privacy, algorithmic bias, transparency, and digital equity remain significant barriers to implementation. The study concludes that the integration of AI and learning analytics has the potential to strengthen standardized learning systems by balancing educational consistency with learner-centered support, thereby improving overall educational quality and outcomes. Keywords: education; generative AI; Personalized Learning; Keywords: Artificial Intelligence; Recommendation Systems; AI literacy; Learning Analytics; Standardized Learning
