Journal Vol – 21 No – 9, September 2026

Abstract:

A cutting procedure that uses heat energy to cut materials without coming into direct contact with the workpiece is laser cutting. Galvanized steel is favored because of its remarkable durability, which combines steel's strength and formability with resistance to corrosion. The Taguchi technique and TOPSIS, a multi-criteria decision-making model, are applied in this work to determine the optimal laser cutting parameters for enhancing surface quality. This study investigates how Cutting Speed (CS), Laser Power (LP), and Gas Pressure (GP) affect kerf width, surface roughness, and cutting time. To ascertain the influence of each input parameter on the output responses, an ANOVA is performed. The best set of parameters, according to the data, is a gas pressure of 8 bar, a power of 1000 W, and a cutting speed of 18 m/min. After laser cutting under optimal conditions, SEM was employed to view the material's surface topography. Furthermore, the results reveal that the grooves and surface marks are less apparent, which is indicative of a rather stable melting and material removal process when the conditions are optimal.

Keywords:

Laser cutting,Process Innovation,Galvanised Iron,TOPSIS method,Scanning Electron Microscopy,

References:

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Abstract:

The prospective arrival of a cryptanalytically relevant quantum computer (CRQC) threatens the asymmetric primitives that protect smart grid communications, protection signalling and identity assertions. Migration to the NIST-standardised post-quantum cryptography (PQC) suite — ML-KEM (FIPS 203) and ML-DSA (FIPS 204) — is unavoidable, but distribution substations cannot be taken offline, intelligent electronic devices (IEDs) operate under millisecond-class deadlines, and PQC key, ciphertext and signature sizes invalidate protocol assumptions embedded in IEC 61850 and DNP3 Secure Authentication. This paper proposes and evaluates TwinPQC, a digital-twin framework in which a cyber-physical replica of a distribution substation is used to simulate, validate and stage PQC adoption before any physical deployment. The environment integrates OpenDSS power simulation, ns-3 network emulation, QEMU-virtualised ARM-class IED firmware and a crypto-agility broker built on the Open Quantum Safe stack. Four cryptographic configurations are evaluated over 480 simulation runs on the IEEE 13-bus and 34-bus distribution feeders. Relative to the classical baseline, the hybrid X25519+ML-KEM-768 / ECDSA+ML-DSA-65 configuration increases MMS association latency by 52.0 ± 1.4 % and GOOSE publication latency from 0.80 ± 0.04 ms to 2.10 ± 0.12 ms, retaining 97.2 % IEC 61850 Type 1A compliance on Cortex-A53 IEDs. On the emulated 120 MHz Cortex-M4 profile, Type 1A compliance falls to 62.4%, and peak heap allocation reaches 148.2 ± 1.8 KB. A frame-level analysis shows that the dominant obstacle for GOOSE is not queueing delay, which contributes under 3 µs on a 1 Gbit/s station bus, but the fact that a 3,501-byte authentication object cannot be carried in a single IEC 61850-8-1 GOOSE frame. A comparison against published pqm4 Cortex-M4 cycle counts further shows that ML-DSA-44 signing alone requires approximately 32.9 ms at 120 MHz, so the emulated constrained-device results must be read as an optimistic bound rather than a timing measurement. The twin flags migration and adversarial faults on 88 to 98 % of injected episodes per scenario, against 0 to 45 % for isolated bench testing, using deterministic predicates that policy-conforming benign traffic cannot satisfy for three of the four scenarios. A five-stage migration playbook with explicit go/no-go criteria and a rollback path is derived from these results.

Keywords:

post-quantum cryptography,digital twin,smart grid,IEC 61850,IEC 62351,crypto-agility,critical infrastructure.,

References:

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Abstract:

The present investigation entails the integrated optimization and modelling of the Wire Electro-Discharge Machining (WEDM) process for the stir-cast AA7050 alloy reinforced with graphite particles, forming metal matrix composites. Because of the composite's high strength and heterogeneous nature with a very fine microstructure, machining parameters must be carefully controlled for an improved process capability. A Taguchi-based design is practically followed so that important process variables-pulse-on time, pulse-off time, and peak current are effectively evaluated for their effects on important performance measures such as material removal rate (MRR), surface roughness (SR), and Dimensional Deviation (DD), and form/orientation tolerances. Grey Relational Analysis (GRA) techniques optimize the multi-objectives to analyse the best possible settings that will maximize overall performance. For modelling and prediction of the process behaviour, an Adaptive Neuro-Fuzzy Inference System (ANFIS) was developed with the Grey Relational Grade (GRG) as the output response. The ANFIS model is developed to capture the nonlinear interactions between the input variables and has a very high prediction accuracy, proving its usefulness for modelling the WEDM process. The synergistic application of Taguchi, Grey, and ANFIS modelling is a robust structure for improving the machinability of AA7050-graphite composites and aiding intelligent decision-making in advanced manufacturing applications.

Keywords:

WEDM,MMC,Taguchi Design,Analysis,MCDM,Grey Theory,ANFIS,

References:

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XXXIII. Thejasree, P., et al. “Application of ANFIS Approach for Prediction of Performance Measures in Wire Electric Discharge Machining of SAE 1010.” Interactions, vol. 245, no. 1, 2024. 10.1007/s10751-024-02030-9.

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Abstract:

Response Surface Methodology (RSM) is a powerful statistical and mathematical tool in designing experiments, modeling, and optimizing the heat transfer efficiency in nanofluids. This paper provides a detailed review of the use of Response Surface Methodology in nanofluids-based heat transfer systems, particularly in experimental design, modeling, interaction between factors, and optimization. Some of the common design techniques used for establishing a relationship between second-order polynomials with operating parameters and thermal response include Box-Behnken Design (BBD) and Central Composite Design (CCD). Applications of RSM in thermal conductivity, heat transfer augmentation, flow analysis, entropy generation, and hybrid nanofluids are covered in this paper. Comparison with artificial neural networks (ANN) suggests that ANN gives more accurate prediction results in the case of a highly non-linear system, while RSM gives explicit correlation between the operating parameters and the thermal responses along with sensitivity analysis. Some of the important areas requiring more research include experimental validation, multi-objective optimization, transient analysis, and uncertainty analysis, among others.

Keywords:

Nanofluid,Hybrid Nanofluid,Response Surface Methodology,Artificial Neural Networks,Machine Learning,AI,

References:

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Abstract:

We generalize the Laplace Adomian Decomposition Method (LADM) to solve both linear and nonlinear stochastic integro-differential equations that are constructed on arbitrary time scales. The presented method implements the time-scale Laplace transform to transform delta-derivative terms into the Laplace domain and build an Adomian series of the nonlinearities, and uses the inverse transform to obtain time-domain solutions; the stochastic integrals not in closed form are approximated by Physics-Informed Neural Networks (PINNs) trained to satisfy Ito-type integral equations. On illustrative linear and nonlinear Volterra problems, we validate the method where the LADM series recovers solutions to the ADM equations within the truncation error (examples show agreement to ?10?^(-3)in mean absolute error) with fewer explicit evaluations of integrals than ADM (reduction in the number of convolution/evaluation steps, approximately 4070 of examples). At points where stochastic integrals are approximated, PINNs give path-wise means that are similar to Monte-Carlo estimates (Table 3). We make the following contributions: (i) we provide a time-scale compatible LADM formulation of Ito-type stochastic forcing; (ii) we show computational savings of LADM over classical ADM on nonstandard time scales; and (iii) we provide a viable LADM-PINN hybrid that computes non-closed-form stochastic integrals. Rigorous convergence and variance-reduction constraints and guidelines are mentioned.

Keywords:

Stochastic Integro-differential equations,Laplace Adomian decomposition method,Laplace transform,Adomian polynomial,Physics-Informed Neural Networks (PINNs).,

References:

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Abstract:

The diagnosis of ophthalmic diseases such as glaucoma, diabetic retinopathy, hypertension, and cardiovascular disorders can be recognized through retinal vessel segmentation from fundus images. The low contrast, noise, blurred boundaries, and substantial variations in vessel thickness make the vessel segmentation a challenging task for semantic segmentation of retinal vessels. To mitigate these limitations, an enhanced U-Net variant is proposed. The framework integrates an initial Inception block, a sequential Global-Local (GL) feature engineering module utilizing zooming and shrinking operations, parallel 1×1 and 3×3 skip paths coupled through element-wise addition, and a terminal Atrous Spatial Pyramid Pooling (ASPP) stage. Internal representations across these stages were systematically profiled using Mutual Information (MI) metrics. Quantitative evaluations demonstrate the network's strong performance across standard benchmarks, recording an mIoU of 80.87%, a Mean BF-score of 91.89%, a center-line Dice (clDice) of 80.83%, and an 84.6% vessel classification accuracy alongside a reduced 15.4% false-negative rate. Ablation trials validate the individual architectural contributions: introducing the Inception layer increases IoU from 50.84% to 59.59%, whereas employing element-wise addition over concatenation in the GL module raises clDice to 81.04% (versus 80.72%). Additionally, MI profiling confirms that average pooling and multi-rate ASPP convolutions retain vital spatial entropy and micro-vascular geometry far more effectively than standard operations.

Keywords:

Retinal Vessel Segmentation,U-Net,ASPP,CLAHE,Fundus Image.,

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XXXI. Ouyang, J. et al. (2023) ‘LEA U-Net: a U-Net-based deep learning framework with local feature enhancement and attention for retinal vessel segmentation’, Complex & Intelligent Systems, 9(6), pp. 6753–6766. 10.1007/s40747-023-01095-3.
XXXII. Pizer, S.M. et al. (1987) ‘Adaptive histogram equalization and its variations’, Computer Vision, Graphics, and Image Processing, 39(3), pp. 355–368. 10.1016/S0734-189X(87)80186-X.
XXXIII. Prajna, Y. and Nath, M.K. (2022) ‘Efficient blood vessel segmentation from color fundus image using deep neural network’, Journal of Intelligent & Fuzzy Systems, 42(4), pp. 3477–3489. 10.3233/JIFS-211479.
XXXIV. Ramos-Soto, O. et al. (2021) ‘An efficient retinal blood vessel segmentation in eye fundus images by using optimized top-hat and homomorphic filtering’, Computer Methods and Programs in Biomedicine, 201, p. 105949. 10.1016/j.cmpb.2021.105949.
XXXV. Sanjeewani Arun Kumar; Akbar, Mohd; Kumar, Mohit; Yadav, Divakar, N.Y. (2024) ‘Retinal blood vessel segmentation using a deep learning method based on modified U-NET model’, Multimedia Tools and Applications, 83(35), pp. 82659–82678. 10.1007/s11042-024-18696-w.
XXXVI. Shang, Z. et al. (2024) ‘DCNet: A lightweight retinal vessel segmentation network’, Digital Signal Processing, 153, p. 104651. 10.1016/j.dsp.2024.104651.
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L. Zafar, A. et al. (2022) ‘A Comparison of Pooling Methods for Convolutional Neural Networks’, Applied Sciences, 12(17). 10.3390/app12178643.
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Abstract:

Inventory management is an integral part of a country’s economic development. Many goods are perishable and gradually worsen over time. Therefore, degradation has a negative effect on perishable goods. If deterioration is not managed properly, it leads to significant inventory loss. Therefore, we propose an EOQ model that incorporates two warehouses and preservation technology to reduce total inventory loss. This proposed model has a constant demand rate with a linearly time-dependent deterioration rate and shortages that are completely backlogged. Goods are first placed in the owned warehouse, and when it is full, the remaining goods are placed in a rented warehouse. For both warehouses, the holding cost is taken as constant. A numerical case and sensitivity analysis table are used to validate the model and examine the behavior of the model under varying parameters.

Keywords:

Two warehouses,Preservation technology,deterioration,shortages with complete backlogging.,

References:

I. Bansal, K. K., O. Singh, S. Kumar, and P. Chaudhary. “Inventory System with Shortages and Weibull Deterioration Purpose.” International Journal of Engineering and Advanced Technology, vol. 9, no. 4, 2020, pp. 107–112. 10.35940/ijeat.C6299.049420
II. Das, A. K., and T. K. Roy. “An Imprecise EOQ Model for Non-Instantaneous Deteriorating Item with Imprecise Inventory Parameters Using Interval Number.” International Journal of Applied and Computational Mathematics, vol. 4, no. 2, 2018, pp. 79–94. 10.1007/s40819-018-0510-1.
III. Garg, G., S. Singh, and V. Singh. “A Two Warehouse Inventory Model for Perishable Items with Ramp Type Demand and Partial Backlogging.” International Journal of Engineering Research & Technology, vol. 9, no. 6, 2020, pp. 1504–1521. 10.17577/IJERTV9IS060999.
IV. Goswami, A., and K. S. Chaudhuri. “On an Inventory Model with Two Levels of Storage and Stock Dependent Demand Rate.” International Journal of Systems Science, vol. 29, 1998, pp. 249–254. 10.1080/00207729808929518.
V. Harris, F. W. “How Many Parts to Make at Once.” Factory, The Magazine of Management, vol. 10, no. 2, 1913, pp. 135–136, 152. 10.1287/opre.38.6.947.
VI. Harris, F. M. Operations and Cost. A. W. Shaw Company, 1915, pp. 48–54. Internet Archive – Operations and Cost.
VII. Hartley, R. V. Operations Research: A Managerial Emphasis. Good Year Publishing Company, 1976, pp. 315–317. CiNii Books – Operations Research: A Managerial Emphasis.
VIII. Kumar, P., A. Saxena, and K. Kumar. “A Two-Warehouse Inventory System with Time-Dependent Demand and Preservation Technology.” Communications on Applied Nonlinear Analysis, vol. 31, no. 2, 2024. doi:10.52783/cana.v31.539
IX. Nath, B. K., and N. Sen. “A Completely Backlogged Two-Warehouse Inventory Model for Non-Instantaneous Deteriorating Items with Time and Selling Price Dependent Demand.” International Journal of Applied Computational Mathematics, vol. 7, 2021, article 145, pp. 1–22. 10.1007/s40819-021-01070-x
X. Nath, B. K., and N. Sen. “A Partially Backlogged Two-Warehouse EOQ Model with Non-Instantaneous Deteriorating Items, Price- and Time-Dependent Demand and Preservation Technology Using Interval Number.” International Journal of Mathematics in Operational Research, vol. 20, no. 2, 2021. 10.1504/IJMOR.2021.118744.
XI. Pathak, K., A. S. Yadav, and P. Agarwal. “Optimizing Two-Warehouse Inventory for Shelf-Life Stock with Time-Varying Bi-Quadratic Demand under Shortages and Inflation.” Mathematical Modelling of Engineering Problems, vol. 11, no. 2, 2024. 10.18280/mmep.110216.
XII. Rathore, H., A. Singh, and G. Singh. “A Two-Warehouse for Deteriorating Items with Advertisement Dependent Demand and Preservation Technology Investment.” International Journal of Pure and Applied Mathematics, vol. 118, no. 22, 2018, pp. 1505–1512.

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Abstract:

Delivering tailored agricultural advice for efficient use by farmers requires precise, localized crop production forecasts under data-constrained conditions. Most AI-based tools that are currently available are only useful at the state or national level and don't show validation metrics, which makes it harder to reproduce scientific results and trust them in real life. In order to estimate crop yields at the district level in all 75 districts of Uttar Pradesh (UP), India, this research suggests a hybrid ensemble machine learning framework that combines an XGBoost regressor and a Random Forest regressor through optimized linear blending. A carefully selected multi-source dataset covering eight agricultural years (2018–2025), 23 engineered features, and four main crop categories—rice, wheat, sugarcane, and pulses—is used to train the framework. While integrated modules provide soil-test-based fertilizer recommendations, crop disease and lodging risk alerts, and thorough economic profitability analysis, a triple-score intelligence layer assesses soil suitability, weather appropriateness, and growth-stage readiness to convert predictive outputs into practical farm decisions. In order to directly address the digital literacy and connectivity issues that 72% of UP's smallholder agricultural population faces, the system is implemented as a privacy-preserving progressive online application with multilingual voice support in Hindi, Awadhi, and English. According to a simulated economic analysis, there might be an annual benefit of about ?15,220 per hectare, which would increase to ?2,905.19 crore with 10% adoption throughout UP (based on 23.86 million smallholder farmers with an average holding of 0.8 ha). Publishing the whole methodology, hyperparameters, and validation metrics makes this work a clear and repeatable standard for AI-driven agricultural decision support in smallholder settings in South Asia.

Keywords:

XGBoost,crop yield prediction,Precision agriculture,smallholder farming,Uttar Pradesh,agricultural artificial intelligence,Random Forest,fuzzy suitability scoring,ensemble learning.,

References:

I. Ministry of Statistics and Programme Implementation, Government of India. : ‘India's Food Grain Production by State in 2024–25’. National Accounts Division, New Delhi, 2025.
II. Invest Uttar Pradesh. : ‘Uttar Pradesh Agriculture Sector Overview’. Industrial Development Department, Government of UP, Lucknow, 2024.
III. Food and Agriculture Organization (FAO). : ‘Precision Agriculture for Smallholder Farmers: Opportunities and Challenges in South Asia’. FAO Regional Office for Asia and the Pacific, Bangkok, 2024.
IV. Indian Council of Agricultural Research (ICAR). : ‘Package of Practices for Kharif Crops – Uttar Pradesh 2023–24’. New Delhi: ICAR, 2023.

V. S. Patel, V. Gupta, K. S. Reddy. : ‘An analysis of AI solutions for precision agriculture in India: A comparative study of DeHaat, BharatAgri, Plantix, and Fasal’. International Journal of Recent Research and Review. Vol. 35, No. 2, pp. 89–104, 2024.
VI. X. Li, Y. Zhang, J. Wang. : ‘Crop yield prediction using machine learning: An extensive and systematic review’. Computers and Electronics in Agriculture. Vol. 218, Article 108726, 2024.
VII. M. Singh, A. Kumar, R. Yadav. : ‘Crop yield prediction using Random Forest algorithm and XGBoost machine learning techniques’. International Journal of Research and Innovation in Social Science. Vol. 8, No. 4, pp. 156–169, 2024.
VIII. R. Kumar, A. K. Singh, P. Sharma. : ‘Crop yield prediction accuracy using XGBoost and Random Forest ensemble learning’. International Journal of Scientific Research in Engineering and Technology. Vol. 14, No. 6, pp. 234–248, 2025.
IX. Indian Council of Agricultural Research (ICAR). : ‘Agro-Climatic Zoning and Crop Production Guidelines for Uttar Pradesh’. ICAR-IIFSR, New Delhi, 2024.
X. Ministry of Agriculture and Farmers Welfare, Government of India. : ‘District, Season and Crop-wise Area, Production and Yield Statistics for Uttar Pradesh’. Directorate of Economics and Statistics, New Delhi, 2025.
XI. India Meteorological Department (IMD). : ‘Agro-Meteorological Advisory Services for Uttar Pradesh’. IMD, Pune, 2024.
XII. International Rice Research Institute (IRRI). : ‘Rice Knowledge Bank: Best Practices for Rice Cultivation in South Asia’. IRRI, Los Baños, Philippines, 2023.
XIII. Ministry of Consumer Affairs, Food and Public Distribution, Government of India. : ‘Minimum Support Price and Procurement Policy for Kharif Crops 2025–26’. Department of Food and Public Distribution, New Delhi, 2025.
XIV. World Economic Forum. : ‘Farmers in India Are Using AI for Agriculture’. WEF Agriculture Innovation Report, 2024.
XV. T. Johnson, K. Williams. : ‘Applying machine learning algorithms for the scientific prediction of crop yields: A global meta-analysis’. SSRN Working Paper, 2024.
XVI. P. Reddy, M. Rao. : ‘Crop yield prediction using deep learning algorithm based on remote sensing data’. Indian Journal of Agricultural Research. Vol. 58, No. 6, pp. 712–720, 2024.
XVII. L. Thompson, D. Harris. : ‘Crop yield and water productivity modeling using nonlinear growth functions’. Scientific Reports. Vol. 15, Article 16096, 2025.
XVIII. A. Ogunleye, Q. Wang. : ‘A comparative study of ensemble learning algorithms for high-dimensional crop yield prediction’. Heliyon. Vol. 10, No. 8, Article e29384, 2024.
XIX. International Journal of Intelligent Systems and Applications in Engineering. : ‘K-fold validation of multi-models for crop yield prediction with ensemble methods’. IJISAE. Vol. 11, No. 3, pp. 145–158, 2023.
XX. Sardar Vallabhbhai Patel University of Agriculture and Technology. : ‘Agro-Climatic Zones of Uttar Pradesh’. SVPUAT, Meerut, 2019.
XXI. Water SA. : ‘Application of logistic model to estimate eggplant yield and water productivity under drip irrigation’. Water SA. Vol. 46, No. 3, pp. 456–465, 2020.
XXII. Extension Journal. : ‘A hybrid machine learning model for crop yield prediction based on remote sensing and ground data’. International Journal of Extension Research. Vol. 8, No. 9, pp. 112–125, 2024.
XXIII. International Journal of Advanced Science and Engineering. : ‘Crop yield prediction and fertilizer usage using logistic regression and machine learning’. IJRASET. Vol. 12, No. 7, pp. 234–247, 2024.
XXIV. Ministry of Statistics, Government of India. : ‘Census 2011 and 2021 Agricultural Holdings Data’. National Sample Survey, New Delhi, 2021.
XXV. Farooqui, U. K., Bharti, A. K. : ‘A privacy preserving upload model for crowd sourced health care monitoring system’. International Journal of Engineering and Advanced Technology (IJEAT). Vol. 1, No. 1, pp. 3337-3346, 2020.

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Abstract:

This study introduces an efficient high-order wavelet quadrature technique for computing highly oscillatory integrals affected by endpoint singular behavior of the form: $latex \int_{0}^{1} f(x)\sin \left(\frac{\omega}{x^r}\right) dx \text{ and } \int_{0}^{1} f(x)\cos \left(\frac{\omega}{x^r}\right) dx, \omega \gg 1, r > 0,$ where standard numerical methods often lose stability and accuracy due to infinite oscillation frequency as x?0^+. The method applies sixth-order Genocchi wavelets within a multiresolution structure to approximate the smooth component of the integrand, while the singular boundary region is treated separately using analytical asymptotic approximations and interval decomposition. Closed-form expressions for the oscillatory kernels are obtained through appropriate transformations. Tests on several benchmark examples demonstrate very high precision, with errors ranging from 10^(-9)to 10^(-13), and show clear improvements in both accuracy and efficiency compared to existing wavelet and hybrid approaches. A practical application to radar cross-section computation is presented.

Keywords:

Highly oscillatory integrals,Genocchi wavelets,singular oscillations,numerical integration,adaptive resolution.,

References:

A. Iserles, S. P. Nørsett, and S. Olver, Highly oscillatory quadrature: The story so far, in Numerical Mathematics and Advanced Applications, Springer, 2006, pp. 97–118. 10.1007/978-3-540-34288-5_6
D. Huybrechs and S. Olver, Highly oscillatory integrals: Analytic continuation and deformation of contours, Contemporary Mathematics, 497 (2009), 59–80. 10.1090/conm/497/09787
Daubechies, Ten Lectures on Wavelets, SIAM, 1992. 10.1137/1.9781611970104.
G. Hariharan, K. Kannan, and K. R. Sharma, Haar wavelet method for solving Fisher’s equation, Applied Mathematics and Computation, 211(2) (2009), 284–292. 10.1016/j.amc.2008.12.089
M. Razzaghi and S. Yousefi, The Legendre wavelets operational matrix of integration, International Journal of Systems Science, 32(4) (2001), 495–502.
10.1080/00207720120227
G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Communications on Pure and Applied Mathematics, 44(2) (1991), 141–183. 10.1002/cpa.3160440202
Aziz, Siraj-ul-Islam, and W. Khan, Quadrature rules for numerical integration based on Haar wavelets and hybrid functions, Computers & Mathematics with Applications, 62 (2011), 2770–2781. 10.1016/j.camwa.2011.03.043.
Siraj-ul-Islam, I. Aziz, and W. Khan, Numerical integration of multidimensional highly oscillatory, gently oscillatory and non-oscillatory integrands based on wavelets and radial basis functions, Engineering Analysis with Boundary Elements, 36 (2012), 1284–1295. 10.1016/j.enganabound.2012.01.008.
Siraj-ul-Islam and S. Zaman, New quadrature rules for highly oscillatory integrals with stationary points, Journal of Computational and Applied Mathematics, 280 (2015), 75–89. 10.1016/j.cam.2014.09.019.
A. Aly, G. A. Evans, and J. Hyslop, The evaluation of integrals within finite limits, Journal of Computational Physics, 13 (1973), 433–438.
10.1016/0021-9991(73)90047-8
M. Blakemore, G. A. Evans, and J. Hyslop, Comparison of some methods for evaluating oscillatory integrals, Journal of Computational Physics, 22 (1976), 352–376. 10.1016/0021-9991(76)90054-1
K. T. Shivaram, Umesha V. et al., Chebyshev and block pulse wavelet approach for the non-linear quasi-singular integral equation, Indian Journal of Natural Sciences, 13(76) (2023), 52994–53000.
K. T. Shivaram, Generalised Gaussian quadrature rules over an arbitrary tetrahedron in Euclidean three dimensional space, International Journal of Applied Engineering Research, 8 (2013), 1533–1538.
K. T. Shivaram, Numerical integration of highly oscillating functions using quadrature method, Global Journal of Pure and Applied Mathematics, 12 (2016), 2683–2690.
K. T. Shivaram, Numerical evaluation of integrals with weight function x^kusing Gauss Legendre quadrature rule, IOSR Journal of Mathematics, 11 (2015), 59–64.
G. S. Teodoro, J. T. Machado, and E. C. De Oliveira, A review of definitions of fractional derivatives and other operators, Journal of Computational Physics, 388 (2019), 195–208. 10.1016/j.jcp.2019.03.008
C. Li, D. Qian, and Y. Q. Chen, On Riemann–Liouville and Caputo derivatives, Discrete Dynamics in Nature and Society, 2011 (2011), Article ID 562494. 10.1155/2011/562494
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. 10.1016/S0304-0208(06)80001-0
Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, 1999.
R. P. Agarwal, C. Cuevas, and H. Soto, Pseudo-almost periodic solutions of a class of semilinear fractional differential equations, Journal of Applied Mathematics and Computing, 37(1–2) (2011), 625–634. 10.1007/s12190-010-0455-y
M. Ur Rahman, M. Arfan, and D. Baleanu, Piecewise fractional analysis of the migration effect in plant pathogen herbivore interactions, Bulletin of Biomathematics, 1(1) (2023), 1–23. 10.59292/bulletinbiomath.2023001
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Abstract:

Bhubaneswar, the smart city of Odisha, is where water quality deterioration is a major concern due to the huge population growth and rural-to-urban migration. This study includes three types of land use patterns, such as high population density areas, industrial areas, and the vicinity of solid waste dumping sites. Five samples were collected from each category of vulnerable areas, totalling fifteen samples. Physico-chemical parameters such as pH, Electrical Conductivity (EC), DO, Hardness, Alkalinity, Cl-, TDS, F-, NO3-, SO42-, Fe2+, Ca²?, Mg²?, Na?, K? and HCO?? were tested for each sample. The concentration of iron is exceeding the permissible limit at 45% of the sample locations due to geogenic processes. Most of the parameter’s concentration is within the permissible limit as stated in IS:10500 (2012). Factor 1 of Principal Component Analysis (PCA) suggests positive loadings for Ca²? (0.962), total hardness (TH) (0.946), TDS (0.894), and HCO?? (0.876), indicating that this factor is predominantly associated with groundwater mineralisation and water–rock interaction. Factor 2 of PCA indicates strong positive loadings of Na? (0.952) and Cl? (0.952), inferring the influence of salinity-related processes and ion exchange. Factor 3 of PCA interprets strong positive loadings for NO?? (0.907) and SO?²? (0.813), inferring a possible influence of anthropogenic activities such as domestic wastewater and other surface-derived inputs. Factor 4 was dominated by Mg²? (0.866) and F? (0.716), suggesting geochemical interactions. Factor 5 shows strong positive loadings for K? (0.866) and pH (0.532. This component may reflect a relatively distinct influence of potassium-bearing minerals and anthropogenic sources, especially where potassium is associated with domestic inputs. Hierarchical cluster analysis (HCA) recommends classification of the physicochemical parameters into five groups at a phenon line at 0.65, which is mostly related to the mineralisation and hardness characteristics of groundwater. The current study suggests that the government needs to develop a policy for the consumption of groundwater in view of rapid urbanization and protect the fresh water from anthropogenic contamination.

Keywords:

: Factor analysis,Bivariate correlation matrix,Groundwater contamination,Hierarchical cluster analysis,

References:

I. Brindha, K., Vaman, K.V.N., Srinivasan, K., Babu, M.S., Elango, L., Identification of surface water-groundwater interaction by hydrogeochemical indicators and assessing its suitability for drinking and irrigational purposes in Chennai, southern India, Appl. Water Sci. 4 (2) (2013) 159–174. 10.1007/s13201-013-0138-6.
II. Central Ground Water Board (CGWB). (2023/2025). Dynamic Ground Water Resources of India / Ground Water Resource Assessment. Ministry of Jal Shakti, Government of India.
III. Das, T.K., Ahmed, S., Hossen, A., Rahaman, M.H., Rahman, M.M., Multivariate statistics and hydrogeochemistry of deep groundwater at southwestern part of Bangladesh, Heliyon 8 (10) (2022) e11206. 10.1016/j.heliyon.2022.e11206.
IV. Di Giacomo, M., et al. (2020). Methodology for the assessment of diffuse pollution background levels in urban groundwater. Frontiers in Environmental Science, *8*, 525469. 10.3389/fenvs.2020.525469
V. Foster, S., Chilton, J., Nijsten, G.J., Richts, A., Groundwater—A global focus on the ‘local resource’, Curr Opin Env. Sustain 5 (6) (2013) 685–695.
VI. Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (8th ed.). Cengage.
VII. Hajigholizadeh, M., Melesse, A.M., Assortment and spatio temporal analysis of surface water quality using cluster and discriminant analyses, CATENA 151 (2017), 247-2.
VIII. Hamid, A., Bhat, S.A., Bhat, S.U., Jehangir, A., Environmetric techniques in water quality assessment and monitoring: a case study, Environ. Earth Sci. 75 (2016) 321. 10.1007/s12665-015-5139-3.
IX. Hota, S. R., Hota, R. N., & Goswami, S. (2023). Statistical appraisal of major ion chemistry of groundwater: A Case study from a river-bounded rural area. Journal of the Geological Society of India, *99*(9), 1253-1262. 10.1007/s12594-023-2459-x
X. Igboama, W.N., Hammed, O.S., Fatoba, J.O., Aroyehun, F.T., Ehiabhili, J.C., Review article on impact of groundwater contamination due to dumpsites using geophysical and physicochemical methods, Appl. Water Sci. 12 (6) (2022) 130. 10.1007/s13201-022-01653-z.
XI. Jianqin, M., Jingjing, G., Xiaojie, L., Water quality evaluation model based on PCA and information entropy. Application in Jinshui River, J. Resour. Ecol. 1 (3) (2010) 249–252.
XII. Khan, M.S., Paul, S.K., Groundwater quality assessment and health issues in coastal zone of Bangladesh, Journal of Hazardous Materials Advances 10 (2023) 100278. 10.1016/j.hazadv.2023.100278.
XIII. Navaneeth, A., Sreeda, P., Maya, T.V., Surendran, U., Harikumar, P.S., Unlocking sustainable groundwater governance in secondary cities: lessons from the assessment of groundwater vulnerability in a coastal City of India, in: Urban Clim., 57, 2024 102116.
XIV. Niedbalska, K., Parametric assessment of groundwater vulnerability to pollution within an open pit reclaimed by gangue, Appl. Water Sci. 12 (12) (2022). 10.1007/s13201-022-01783-4.

XV. Rajan, M., Karunanidhi, D., Jaya, J., Preethi, B., Subramani, T., Aravinthasamy, P., A comprehensive review of human health hazards exposure due to groundwater contamination: a global perspective, Phys. Chem. Earth Parts A/B/C (2024) 103637.
XVI. Rao, N.S., Spatial distribution of quality of groundwater and probabilistic non-carcinogenic risk from a rural dry climatic region of South India, Environ. Geochem. Health 43 (2) (2020) 971–993. 10.1007/s10653-020-00621-3.
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Abstract:

An emergency department (ED) is a network: patient streams are sorted by acuity, queued, and routed through a finite pool of physicians and beds toward admission or discharge. We study admission-risk screening on 558,029 adult ED visits from the Yale-New Haven Health System, using the information present at the triage node: the Emergency Severity Index (ESI) and six triage vital signs, with age and sex retained for stratified validity checks. A gradient-boosted classifier ranks admission with AUC = 0.809, accuracy = 0.760, and Brier score = 0.157 on a held-out set of 111,607 visits. The methodological contribution is a Mondrian (per-acuity) split-conformal layer with a finite-sample, class-conditional coverage guarantee (Theorem 1) and a matching upper bound. Empirical coverage is 0.910 against a nominal 0.90, with mean prediction-set size 1.43. Residual audits show that ESI-level coverage can conceal within-class gaps, most clearly for abnormal vital signs inside ESI-4 (coverage 0.549 versus 0.943 when vitals are not abnormal). A joint Mondrian on ESI x age restores those cells to the nominal band whenever the calibration count meets n_c >= 99, the size that keeps the additive slack 1/(n_c+1) at most 0.01 (Proposition 1). We map each prediction set to an explicit routing action and a three-term decision loss (false preparation, delayed request, unresolved hedge). At a five-to-one delay-to-false-prep cost ratio, the conformal policy has mean cost 0.544, against 0.899 for a hard 0.50 threshold. Theorem 4 places the predictor in the queueing dynamics: committed false bed requests occur at a rate at most alpha, and MaxWeight stability is preserved when the oracle bed load plus that extra load stays below one. Scheduling and surge rules (Theorems 2 and 3) remain framework theory pending timestamped data. Every number is computed from real records.

Keywords:

Patient-flow network,Hospital admission prediction,Conformal prediction,calibration,Queueing models,Clinical decision support.,

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