http://irgu.unigoa.ac.in/drs/handle/unigoa/27 2026-10-15T09:10:30Z http://irgu.unigoa.ac.in/drs/handle/unigoa/8057 A Study of Boundary Value Problems for Differential Equations with Deviating Arguments Aiya, Heramb B. 2025-02-01T00:00:00Z http://irgu.unigoa.ac.in/drs/handle/unigoa/8040 Integrated AI and image processing frameworks for structural monitoring, mechanical performance, and engineering optimization Senthilkumar, V.; Pattanayak, B.; Anly Antony M.; Brahm Prakash; Gawas, M.M.; Patel, D.B. India requires frameworks for condition assessment and material design that are both infrastructure-scaled and budget-conscious while retaining engineering accountability. This study presents an artificial-intelligence and image-processing decision framework that connects road-damage monitoring, concrete compressive-strength modelling, and observed-space engineering optimisation at an analytical level. A field-scale proof-of-concept is not attempted; instead, three connected modules with demonstrated value are presented using Indian data. For the monitoring task, the India subset of the RDD2022 database is used, which consists of 9,665 road images; the training set contains 6,831 damage annotations. Of these annotations, potholes dominate the frequency at 46.7 percent compared with 1.0 percent for transverse cracks, a 46.9:1 ratio. Bounded region classification was piloted on the 1,221-image India data subset allocated with N-RDD2024. Histogram-of-oriented gradients, local texture, intensity, colour, and bounding-box descriptors yielded 1,826 features. An RBF support-vector machine, selected using five-fold stratified group validation, achieved 79.7 percent accuracy, 0.682 balanced accuracy, and 0.727 macro-F1 on the supplied held-out validation split. The recall for transverse cracking was low at 0.375. For mechanical performance, 188 experimental recycled-aggregate concrete records from IIT Bhubaneswar were grouped into 60 composition groups. With five-fold group-wise validation, Extra Trees were chosen as the regressor, with an out-of-fold R sup(2) of 0.893, an RMSE of 5.85 MPa and an MAE of 4.23 MPa. Curing age, fly ash, total cementitious material, and water-to-total-cementitious ratio were the most influential variables. For the optimisation task, a retrospective search was conducted within the subset of measured 28-day compressive strengths to screen conservative minimum-cement concrete recipes for 35, 45, and 55 MPa targets. It is concluded that a viable Indian framework would combine vision-based low-cost triage, material models with reduced leakage, observed-space optimisation with a transparent safety margin, and mandatory engineer acceptance, rather than relying on black-box AI to replace established inspection, testing, and design practices. 2026-01-01T00:00:00Z http://irgu.unigoa.ac.in/drs/handle/unigoa/8041 Advanced mathematical models for scalable big data analytics: Integrating optimization algorithms and predictive intelligence in complex data environments Manoj, P.K.; Amit Prakash; Sawant, S.; Gawas, M.M.; Chauhan, R.; Jadhav, D.; Thakkar, P.L. In industrial big-data applications, the ability to transform very complex sensor streams into accurate maintenance information is crucial. The challenge with Remaining Useful Life prediction remains, however, because of the non-linearity of degradation, the fact that operating conditions are often variable, and the balance between model performance and computational time. This paper introduces a predictive intelligence framework for RUL prediction of turbofan engines that is scalable and optimized. The method consists of capped RUL target construction, multivariate sensor preprocessing, baseline predictive modeling, XGBoost learning, and hyperparameter optimization through Random Search, Optuna/Bayesian Optimization, Genetic Algorithm and Particle Swarm Optimization. NASA C-MAPSS FD001 and FD004 were used for the experiments; FD001 was employed for baseline development and FD004 was employed for complex environment validation. The results indicated that the non-linear model was better than the statistical regression. The use of the Random Search optimized XGBoost gave the lowest error RMSE 15.566 and R2 0.682 for FD001 and low but acceptable errors RMSE 16.621 and R2 0.574 for FD004 for XGBoost. The test of scalability showed that the RMSE was not affected by increasing amount of FD004 data, while robustness testing showed sensitivity to sensor noise. The novelty of this work is the reproducible mathematical analytics workflow for optimized and scalable industrial RUL prediction for practical industrial decision support. 2026-01-01T00:00:00Z http://irgu.unigoa.ac.in/drs/handle/unigoa/7899 Characterizations of additively graceful signed paths and cycles D'Souza, B.; Pereira, J. A (p,m,n) signed graph S, is a signed graph of order p with m positive edges and n negative edges. In this paper, we first prove a few basic results on vertex labelings of paths. We use these results and a sequence of lemmas to obtain a characterization of additively graceful signed paths. We prove that, apart from exactly 4 exceptions, additively graceful signed paths are characterized by the signed paths containing at most one negative section with n less than or equal to 2. We also establish a characterization of additively graceful signed cycles. We prove that a (p,m,n) signed cycle S is additively graceful if and only if one among the following 4 conditions are satisfied, (a) n=0 and m identical to 0 or 3 (mod 4), (b) n = 1 and m identical to 1 or 2 (mod 4), (c) n = 2, or 2 (mod 4) and S contains a single negative section, (d) S is the all negative signed cycle on C sub(3). 2026-01-01T00:00:00Z