S Keerthana, E.Mynavathi

Fuzzy Graph; Fuzzy Connectivity; Strong Fuzzy Graph; Fuzzy Path; Graph Theory.

Fuzzy graph theory is an important extension of classical graph theory introduced to model systems involving uncertainty. In fuzzy graphs, vertices and edges are associated with membership values between 0 and 1. Connectivity is one of the most fundamental structural properties of fuzzy graphs. It helps in understanding the relationship between vertices and the strength of connections between them. In this paper, various types of connectivity in fuzzy graphs are studied. Important definitions, properties, and theorem results related to fuzzy connectivity and strong fuzzy connectivity are presented. The structural properties of connected fuzzy graphs are analyzed. These results help in understanding fuzzy networks and their applications in real-world systems.

[1] N. J. S. Mathew, “Connectivity Analysis of Cyclically Balanced Fuzzy Graphs,” International Journal of Fuzzy Systems, vol. 7, pp. 245–255, 2015.
[2] M. S. Sunitha, “Connectivity in a fuzzy graph and its complement,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 116–125, 2016.
[3] T. Pathinathan and J. Jesintha Rosline, “Characterization of fuzzy graphs into different categories using arcs in fuzzy graphs,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 18–34, 2016.
[4] M. S. Sunitha and S. Mathew, “Fuzzy Graph Theory: A Survey,” International Journal of Fuzzy Systems, vol. vol. 12, no. 3, pp. 234–257, 2016.
[5] M. Muthukani, “Connectivity in a fuzzy graph,” International Journal of Fuzzy Systems, vol. 12, no. 3, pp. 56–81, 2016.
[6] R. J. Wilson, Introduction to Graph Theory, 4th ed. Pearson Education Limited, 2010.
[7] S. K. Yadav, Elements of Graph Theory, Krishna Prakashan Media, 2013.
[8] V. K. Balakrishnan, Graph Theory, McGraw-Hill Education, 2012
[9] S. Arumugam and S. Ramachandran, Invitation to Graph Theory, Scitech Publications, 2011.
R. Balakrishnan and K. Ranganathan, A Textbook of Graph Theory, 2nd ed. Springer, 2012.

G Dharaniselvi, S Hariharan

Compact-Open Topology; Pseudocompactness; Submetrizability; Function Spaces; G-Delta Set; Sigma-Compact Space; Induced Mappings; Uniform Convergence.

Compactness is one of the most fundamental and influential concepts in general topology and functional analysis. Over the past century, various generalizations of compactness have been introduced in order to extend its applicability to broader classes of topological spaces. Among these, pseudocompactness and compact-open structures have played a significant role in the development of function space theory. The aim of this paper is to provide a comprehensive and detailed study of open compactness and open pseudocompactness in topological spaces, particularly in relation to function spaces of continuous real-valued functions. We analyze the structure of C(X), Ck(X), and Cps(X), examine their metrizability and submetrizability properties, study σ-compactness conditions, and investigate compactness-type equivalences. Special attention is given to induced mappings, Gδ-properties, separability, countability conditions, and the structural relationships between compact-open and pseudocompact-open topologies. The results presented here unify several known facts in function space topology and provide a broader structural perspective for further research in advanced topology and functional analysis.

[1] R. F. Arens, “A topology for spaces of transformations,” Annals of Mathematics, vol. 47, no. 3, pp. 480–495, 1946.
[2] E. Hewitt, “Rings of real-valued continuous functions,” Transactions of the American Mathematical Society, vol. 64, no. 1, pp. 45–99, 1948.
[3] D. Gulick, “The σ-compact-open topology,” Transactions of the American Mathematical Society, vol. 161, pp. 275–282, 1971.
[4] S. Kundu and P. Garg, “The pseudocompact-open topology,” Topology Proceedings, vol. 31, no. 1, pp. 279–299, 2007.
[5] S. Warner, “The topology of compact convergence,” Mathematische Annalen, vol. 136, no. 3, pp. 229–246, 1958.
[6] A. Dow, J. R. Porter, R. M. Stephenson, Jr., and R. G. Woods, “Spaces whose pseudocompact subspaces are closed subsets,” Applied General Topology, vol. 5, no. 2, pp. 243–264, 2004.
[7] D. Gulick, “The σ-compact open topology and its relatives,” Mathematica Scandinavica, vol. 30, pp. 159–176, 1972.
[8] S. Kundu and P. Garg, “The pseudocompact-open topology,” Topology Proceedings, vol. 30, pp. 279–299, 2006.
[9] S. Kundu and P. Garg, “The compact-open topology: A new perspective,” Topology and its Applications, vol. 155, no. 7, pp. 686–695, 2008.
[10] S. Warner, “The topology of compact convergence on continuous function spaces,” Duke Mathematical Journal, vol. 25, pp. 265–282, 1958.
[11] R. F. Arens, “A topology for spaces of transformations,” Annals of Mathematics, ser. 2, vol. 47, pp. 480–495, 1946.

Dr.N.Sevugapandi, K.Ponraj

Indian Penal Code (IPC); First Information Report (FIR); Natural Language Processing (NLP); Bi-LSTM; RoBERTa; Hybrid Deep Learning; Text Classification; Legal Text Analysis; IPC Section Prediction; Transformer Model; Sequential Learning; Contextual Embeddings.

This paper presents an intelligent system for automatic prediction of Indian Penal Code (IPC) sections based on FIR (First Information Report) text. The system uses Natural Language Processing (NLP) techniques combined with a hybrid deep learning model consisting of Bi-LSTM and RoBERTa. The model analyzes case descriptions and predicts the most relevant IPC section along with confidence score. Additionally, the system provides automated legal explanation for better understanding. The proposed system improves accuracy compared to traditional machine learning models and helps in faster legal decision support. This solution can assist police departments, legal professionals, and judicial systems in reducing manual effort and improving efficiency. The legal domain involves complex analysis of textual data such as FIR (First Information Reports), which requires expertise and time to determine the appropriate IPC sections. This paper proposes an intelligent system that automates the prediction of IPC sections using Natural Language Processing (NLP) and a hybrid deep learning model combining Bi-LSTM and RoBERTa. The system processes unstructured legal text, extracts meaningful features, and predicts the most relevant IPC sections with a confidence score. Additionally, the system provides automatic IPC explanations from a structured database, improving interpretability. Experimental results demonstrate that the hybrid approach significantly improves prediction accuracy compared to traditional machine learning methods. The proposed system can assist law enforcement agencies, legal practitioners, and judicial systems in enhancing efficiency and reducing manual effort.

[1] Y. Goldberg, “A Primer on Neural Network Models for Natural Language Processing,” Journal of Artificial Intelligence Research, vol. 57, pp. 345–420, 2016.
[2] J. Devlin, M. Chang, K. Lee, and K. Toutanova, “BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding,” in Proceedings of NAACL-HLT, 2019.
[3] Y. Liu et al., “RoBERTa: A Robustly Optimized BERT Pretraining Approach,” arXiv preprint arXiv:1907.11692, 2019.
[4] S. Hochreiter and J. Schmidhuber, “Long Short-Term Memory,” Neural Computation, vol. 9, no. 8, pp. 1735–1780, 1997.
[5] Graves, “Supervised Sequence Labelling with Recurrent Neural Networks,” Springer, 2012.
[6] T. Mikolov et al., “Efficient Estimation of Word Representations in Vector Space,” arXiv preprint arXiv:1301.3781, 2013.
[7] S. Bird, E. Klein, and E. Loper, “Natural Language Processing with Python,” O’Reilly Media, 2009.
[8] D. Jurafsky and J. H. Martin, “Speech and Language Processing,” 3rd ed., Pearson, 2020.
[9] Indian Penal Code, 1860, Government of India.
[10] A.Vaswani et al., “Attention Is All You Need,” in Advances in Neural Information Processing Systems (NeurIPS), 2017.
[11] F. Chollet, “Deep Learning with Python,” Manning Publications, 2018.
[12] T. Brown et al., “Language Models are Few-Shot Learners,” in NeurIPS, 2020.

C.Srimathi,B.Ramkumari

Directed Graph; Even Cycle; Digraph; Characterization; Graph Theory; Connectivity.

Graph theory has emerged as one of the most important areas of discrete mathematics due to its wide range of applications in computer science, communication networks, transportation systems, electrical circuits, and social network analysis. Among various structures in graph theory, directed graphs (digraphs) provide an effective way to model asymmetric relationships where the direction of interaction plays a crucial role. Because of this directional nature, the structural analysis of digraphs becomes both mathematically rich and practically significant. Cycles in directed graphs are fundamental in understanding feedback systems, routing mechanisms, and dependency structures. In particular, even cycles occupy a special position in the study of parity, bipartite properties, and algorithmic behavior of networks. The identification and characterization of even cycles help in solving problems related to deadlock detection, network stability, and circuit design. This study focuses on the structural characterization of directed graphs and investigates the existence and properties of even cycles within them. The work presents essential concepts related to digraphs, examines conditions that guarantee the presence of even cycles, and discusses their theoretical importance. Both standard results and analytical observations are included to provide a clear understanding of the topic. The results of this study contribute to strengthening the theoretical foundation of directed graph analysis and offer useful insights for further research in advanced graph theory and its applications in real-world network systems.

[1] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Macmillan Press Ltd., London, 1976.
[2] J. A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, Springer, New York, 2008.
[3] F. Harary, Graph Theory, Addison-Wesley Publishing Company, Reading, Massachusetts, 1969.
[4] Douglas B. West, Introduction to Graph Theory, 2nd Edition, Prentice Hall, Upper Saddle River, NJ, 2001.
[5] Reinhard Diestel, Graph Theory, 5th Edition, Springer-Verlag, Heidelberg, 2017.
[6] Gary Chartrand and Ping Zhang, Introduction to Graph Theory, McGraw-Hill Education, 2012.
[7] Bela Bollobas, Modern Graph Theory, Springer, New York, 1998.
[8] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest and Clifford Stein, Introduction to Algorithms, MIT Press, 2009.
[9] K. Thulasiraman and M. N. S. Swamy, Graphs: Theory and Algorithms, John Wiley & Sons, 1992.
[10] Alan Gibbons, Algorithmic Graph Theory, Cambridge University Press, 1985.
[11] S. Even, Graph Algorithms, Cambridge University Press, 2011.
[12] Narsingh Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice-Hall of India, 2004.
[13] R. J. Wilson, Introduction to Graph Theory, 5th Edition, Pearson Education, 2010.
[14] Frank Harary and Edgar M. Palmer, Graphical Enumeration, Academic Press, 1973.
[15] Jonathan L. Gross and Jay Yellen, Handbook of Graph Theory, CRC Press, 2004.
[16] Michel Gondran and Michel Minoux, Graphs, Dioids and Semirings, Springer, 2008.
[17] Gary Chartrand, Linda Lesniak and Ping Zhang, Graphs and Digraphs, CRC Press, 2011.
[18] Claude Berge, The Theory of Graphs, Dover Publications, 2001.
[19] Alexander Schrijver, Combinatorial Optimization, Springer, 2003.

A. Kiruthiga, V. Manjubashini, Mohana Priya

Fibonacci numbers; golden ratio; Fibonacci sequence; Q-matrix, Binet’s formula

Fibonacci numbers and the golden ratio are fundamental concepts in number theory and mathematics. The Fibonacci sequence is defined by a recursive relation in which each term is the sum of the two preceding terms. The golden ratio is a mathematical constant closely related to the Fibonacci sequence. This paper presents definitions, properties, identities, and important results related to Fibonacci numbers and the golden ratio. Important identities such as the sum of Fibonacci numbers, sum of squares, Fibonacci Q-matrix, Cassini’s identity, and Binet’s formula are discussed. The relationship between Fibonacci numbers and the golden ratio is analyzed. Applications in nature, computer science, and mathematics are also presented.

[1] Jeffrey R. Chasnov, Fibonacci Numbers and Golden Ratio, Hong Kong University of Science and Technology (HKUST), 2015.
[2] Richard A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 1997.
[3] Keith Devlin, The Man of Numbers: Fibonacci’s Arithmetic Revolution, Walker & Company, 2011.
[4] Thomas Koshy, Fibonacci and Lucas Numbers with Application, John Wiley & Sons Ltd., Volume 2 (second edition series), 2019

A Sivasankari, K Thavamani

Ring Theory; Ideals; Euclidean Rings; Quotient Rings; Polynomial Rings; Abstract Algebra

Ring theory is a central area of abstract algebra that generalizes arithmetic operations and polynomial algebra through algebraic structures equipped with two binary operations: addition and multiplication. This paper presents a systematic study of ring theory, beginning with basic definitions and progressing through important classes of rings such as integral domains, fields, Euclidean rings, and polynomial rings. Special emphasis is given to ideals, quotient rings, maximal ideals, and homeomorphisms, which play a vital role in understanding the structural properties of rings. The paper also discusses Euclidean rings and unique factorization, illustrating how classical number-theoretic results emerge naturally from ring-theoretic concepts. The study aims to provide a clear and rigorous foundation for students and researchers interested in modern algebra and its applications in mathematics, computer science, and related disciplines.

[1] American Mathematical Society. (2022). Mathematics Subject Classification (MSC2020). Retrieved January 10, 2022, from https://mathscinet.ams.org/msc/msc2020.html
[2] Atiyah, M. F., & Macdonald, I. G. (1969). Introduction to Commutative Algebra. AddisonWesley Publishing Company.
[3] Eisenbud, D. (1995). Commutative Algebra: With a View Toward Algebraic Geometry. SpringerVerlag.
[4] Lang, S. (2002). Algebra (3rd ed.). SpringerVerlag.
[5] Matsumura, H. (1989). Commutative Ring Theory. Cambridge University Press.
[6] Rotman, J. J. (2009). Advanced Modern Algebra. American Mathematical Society.
[7] Galaz-García, F., Kerin, M., Radeschi, M., Wiemeler, M.: Torus orbifolds, slice-maximal torus actions, and rational ellipticity. Int. Math. Res. Not. IMRN 18, 5786–5822 (2018)
[8] Guillemin, V., Sabatini, S., Zara, C.: Equivariant -theory of GKM bundles. Ann. Global Anal. Geom. 43(1), 31–45 (2013)
[9] Aberbach, I.M., Enescu, F.: The structure of F-pure rings. Math. Z. 250(4), 791–806 (2005)
[10] Akesseh, S.: Ideal containments under flat extensions. J. Algebra 492, 44–51 (2017).

Jennifer A

Style Drift; Everyday Fashion; Classic Fashion; Clothing.

Style Drifts arise and diminish; in parallel, a society’s values are established and evolving characteristics aligned with their beliefs and culture. Fashion is not just an ambitious portrayal of a reinterpreted traditional value aimed at fulfilling a function or agenda, but rather, it embodies a compelling and invigorating idea deserving of representation for society’s admiration, which further heightens our instinctual behavior. Within society, a person’s appearance acts as a medium to express non-verbal communication signals, such as possible indicators regarding their social standing, values, and lifestyle. Fashion communication has undergone a complete 360-degree shift in its communicable aspects, starting from projecting a basic image of our appearance and feelings, to expressing our emotional experiences through interactive elements in clothing.

[1] www. thinkwithgoogle.com/ spring-2015-fashion-trends-google.
[2] www.teenvogue.com/gallery/spring-summer-2015-beauty-trend-report.
[3] www.wgsn.com/blogs/trends-and-fashion-theyre-not-dead-and-never-will-be.
[4] www.nytimes.com/2015/19/20/fashion.

Mr. Purushothaman

Passenger Transport; Temporary Operational Modification; Cargo Highlights.

The term “Preighter” emerged during the unprecedented disruptions brought about by the COVID-19 pandemic, referring to passenger aircraft that were temporarily adapted for cargo purposes. Among the aircraft utilized in this innovative role was the Airbus A380, recognized as the world’s largest passenger airliner. This report examines the A380 Preighter phenomenon, detailing their definition, usage by carriers such as Emirates and Hi-Fly, the modifications and cargo capacity achieved, the reasons for their deployment, their operational characteristics, future possibilities, and a comparative analysis of their advantages and disadvantages relative to dedicated cargo planes. The investigation suggests that although the A380 significantly enhanced cargo capacity during a pivotal period, its fundamental design as a passenger aircraft imposed operational and financial limitations that indicate its function as a Preighter was largely a temporary solution.

[1] 7–Skyways Eunsu Lee Ph.D., Cpim, Cscp, Gisp Https://Doi.Org/10.1016/B978-0-323-90129-1.00012-2.
[2] Ghostbusters: Hunting Abnormal Flights In Europe During Covid-19 Xiaoqian Sun, Sebastian Wandelt, Anming Zhang Https://Doi. Org/ 10.1016/J.Tranpol.2022.08.020.
[3] Covid-19 And Aviation, Lessons Learned From The Trenches: A Survey Among Participants At The 26th Atrs World Conference Xiaoqian Sun , Changhong Zheng, Anming Zhang Https://Doi.Org/ 10.1016/J.Jatrs.2024.100005.
[4] Exploring Factors Affecting Airport Selection During The Covid-19 Pandemic From Air Cargo Carriers’ Perspective Through The Triangular Fuzzy Dombi-Bonferroni Bwm Methodology Gökhan Tanriverdi, Fatih Ecer, Mehmet Şahin Durak Https://Doi.Org /10.1016/J.Jairtraman.2022.102302
[5] Covid-19 Pandemic And Air Transportation: Summary Of Recent Research, Policy Consideration And Future Research Directions Xiaoqian Sun , Sebastian Wandelt , Anming Zhang Https://Doi.Org/10.1016/J.Trip.2022.100718
[6] How Covid-19 Transformed The Landscape Of Transportation Research: An Integrative Scoping Review And Roadmap For Future Research Milad Haghani , Rico Merkert , Ali Behnood , Chris Degruyter , Khashayar Kazemzadeh , Hadi Ghaderi , Zahra Shahhoseini , Vinh Thai , Elnaz Irannezhad , Behnam Fahimnia , S Travis Waller, David A Hensher Https://Doi.Org/ 10.1080 /19427867.2022.2160294
[7] Converting Passenger Aircraft Into Cargo Planes Under Volatile Market Demand Shiyuan Zheng , Kun Wang , Changmin Jiang Https://Doi.Org/10.1016/J.Tra.2024.104013
[8] Technological And Educational Challenges Towards Pandemic-Resilient Aviation, Xiaoqian Sun, Sebastian Wandelt, Anming Zhang Https://Doi.Org/10.1016/J.Tranpol.2021.09.010
[9] Solving The Mystery Of Discrepancies And Double Counting In Air Cargo Through Demand And Supply Big Data AnalysisVincent Van Bockstaele, Sven Buyle, Wouter Dewulf Https://Doi.Org/ 10.59521/6a961ef46eb809c5.
[10] Airport Pandemic Response: An Assessment Of Impacts And Strategies After One Year With Covid-19 Mohit Arora , Stefan Tuchen, Mohsen Nazemi, Lucienne Blessing Https://Doi.Org/ 10.1016/J.Trip.2021.100449.

Dr.G.Muralikrishnan, Jitenthra N, Ramesh B, Jackson K

LVDN; EV; Battery Charging; THD; FFT.

The increasing magnitude of the Electric vehicles (EV) as part of these global energy transition highlights the necessity to understand their effects of the power quality dispersion networks. This project investigates the distortions caused by power electronic converters in EV battery chargers, which can significantly degrade power quality. The emergence of single-phase intensive loads, such as private EV charging stations, complicates the operation of Low Voltage Distribution Networks. Given the growing adoption of EV, addressing these power quality issues is crucial. This study focuses on evaluating the impact of charging station on key power factors Limits, of particularization Total Harmonic Distortion and electric field. Using MATLAB and Power Simulation simulations, to be the project analyses the power quality impacts associated with EV charging. The results provide insight into the extent to which EV chargers influence power quality and highlight the potential challenges and solutions in integrating EV infrastructure into existing power dispersion systems.

[1] Power factor of the Electric Vehicle Charging Stations and Optimal Placement in the Dispersion Network M. Shadnam Zarbil, A. Vahedi * Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran.
[2] Effects of the Battery Vehicle power St a t i o n on the Quality of the Low Voltage Network Supply Effect Assessment to Electric Vehicle Charging is an AC and DC smart grids: A Comparative Study.
[3] Effects of bidirectional EV power stations on dispersion network: a Power Hardware-In- the-Loop implementation Battery Vehicles Under reduced Temperatures: A Review on Battery Performance, Charging Needs,and Power Grid Impacts
[4] Impact of Hot Arid Climate on ideal Placement of Electric Vehicle power Stations “The impact of the electric vehicle charging on a residential low voltage distribution network in Malaysia”, IEEE Innovate. Smart meter Tech., “Effects of EV battery chargers on the powerfactorsof dispersion systems
[5] “Research on the harmonic characteristics of electric vehicle fast charging station “Current harmonics, voltage distortion, and powers associated with electric vehicle battery chargers distributed on the residential power system”.
[6] “Load management in smart grids considering harmonic distortion and transformer berating”, Innov. Smart Grid “Input current THD reduction via virtual resistant in EV charger”, Optimal location of electric vehicle charging station and its impact on distribution network .
[7] “Impact of electric vehicle chargers on a low voltage distribution system”, Current harmonics, voltage distortion, and powers associated with electric vehicle battery chargers distributed on the residential power system”.

Dr.B.Geetha, Ramya J, Samyutha Ram

Gamification; Higher Education; Learning.

In higher education, gamification has become a potent pedagogical tool that is revolutionizing conventional teaching techniques by adding game-based components to improve learning outcomes, motivation, and student engagement. This Research paper examines the function of gamification in higher education, emphasizing how it affects instructional methods and student involvement. The study also looks at both the benefits and challenges of gamification, emphasizing how it can help students become more collaborative, critical thinkers, and problem solvers. The article also covers the best ways for teachers to successfully incorporate gamification into their lessons. The article also covers the best ways for teachers to successfully incorporate gamification into their lessons. This study highlights the importance of gamification in contemporary education and its role in creating a more dynamic and student-centered learning environment through a thorough examination of case studies and previous research.

[1] Islam Alomari, Hosam Al-Samarraie, Reem Yousef (2019), Universiti Sains Malaysia Al Falah University, “The Role of Gamification Techniques in Promoting Student Learning: https://pureportal.coventry.ac.uk/en/publications/the-role-of-gamification-techniques-in-promoting-student-learning.
[2] José-María Campillo-Ferrer, Pedro Miralles-Martínez, and Raquel Sánchez-Ibáñez (2020),”Gamification in Higher Education: Impact on Student Motivation and the Acquisition of Social and Civic Key Competencies”. https://doi.org/10.3390/su12124822.
[3] Guillermo M. Chans,May Portuguez Castro (2021), “Gamification as a Strategy to Increase Motivation and Engagement in Higher Education Chemistry Students”. https://doi.org/10.3390 /computers 10100132.
[4] Crystal Han-Huei Tsay, Alexander Kofinas, Jing Luo (2018),”Enhancing student learning experience withtechnology-mediatedgamification: An empirical study”.https://doi.org/ 10.1016 /j.compedu.2018.01.009.