Volume 02, Issue 8
Published on: August 2026
KARHUNEN–LOèVE EXPANSION THEORY IN AI–BLOCKCHAIN SUPPLY CHAINS, AND SUSTAINABLE LOGISTICS
V. A. Sharma
Department of Mathematics, Smt. Narsamma Arts, Commerce and Science college, Amravati 444606
Article Status
Plagiarism Passed
Peer Reviewed
Open Access
Available Documents
Abstract
The Karhunen–Loève (KL) expansion provides an optimal orthogonal series representation of second-order stochastic processes and random fields. This paper presents a complete mathematical formulation of the KL theory using native Office Math Markup Language (OMML) equations, covering the governing Fredholm integral eigenvalue problem, the expansion and its coefficients, truncation error bounds, and the normalized representation. Building upon this theoretical foundation, we systematically explore practical applications of the KL expansion in contemporary supply-chain research themes: quantum-inspired optimization and uncertainty quantification in logistics networks; construction of resilient and adaptive digital twins for global supply chains; stochastic modelling supporting artificial-intelligence and blockchain integration for transparency, traceability and resilience; and uncertainty-aware modelling in sustainable and green logistics. The KL expansion emerges as a rigorous, computationally tractable tool for dimensionality reduction, random-field generation and risk quantification across these domains, thereby bridging classical stochastic process theory with the emerging requirements of Industry 4.0 and quantum-era logistics systems.
Keywords— Karhunen–Loève expansion; stochastic processes; uncertainty quantification; digital twin; supply chain resilience; quantum logistics; green logistics; AI–blockchain integration.
Keywords— Karhunen–Loève expansion; stochastic processes; uncertainty quantification; digital twin; supply chain resilience; quantum logistics; green logistics; AI–blockchain integration.
How to Cite this Paper
Sharma, V. A. (2026). Karhunen–Loève Expansion Theory in AI–Blockchain Supply Chains, and Sustainable Logistics. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.192
Sharma, V.. "Karhunen–Loève Expansion Theory in AI–Blockchain Supply Chains, and Sustainable Logistics." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-9. doi:https://doi.org/10.55041/ijcope.v2i8.192.
Sharma, V.. "Karhunen–Loève Expansion Theory in AI–Blockchain Supply Chains, and Sustainable Logistics." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-9. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.192.
Search & Index
References
- Akarshan Gulhane, “Distributional Extension of the FKF Transform and Its Relevance to Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026 , DOI: https://doi.org/10.55041/ijcope.v2i8.137
- Akarshan Gulhane,“Sequential Convergence in the Testing Function Space of the Two-Sided FKF Transform,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.138
- Akarshan Gulhane,“ Spectral Analysis for Multi Scale Supply Chain Dynamics and ResidueBased Resonance Extraction in Hybrid-Vehicle Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.141
- Akarshan Gulhane,“ Shift-Invariant Spectral Analysis of Multi-Echelon Supply-Chain Lead Times via the FKF Transform,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.136
- Akarshan Gulhane,“ Spectral Framework Based on the FKF Transform for Supply Chain Dynamics and Resilience,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.140
- Akarshan Gulhane,“ Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.139
- Akarshan Gulhane,“ FKL Transform Key Properties, And Applications To Supply-chain Analysis,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 596-605, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3816
- Akarshan Gulhane,“ Expanded Treatment Of The Time-Shift Property Of FKF Transform With Supply-Chain Applications,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 606 – 616, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3817
- Akarshan Gulhane,“ The FKF Transform: Exponential Modulation Properties And Applications To Secure Digital Supply-Chain Networks,” International journal of Engineering sciences and Advanced Technology, Published:11-12-2025, Issue: Vol. 25 No. 12 (2025), Page Nos: 617 – 623, DOI: Https://doi.org/10.64771/ijesat.2025.v25.i12.3818
- Akarshan Gulhane, “Spectral Differential Properties of the Distributional FKF Transform with Applications to Resilient Supply-Chain Systems,” International Journal of Creative and Open Research in Engineering and Management ISSN: 3108-1754 (Online) Volume 02 Issue 08 Augustl-2026, DOI: https://doi.org/10.55041/ijcope.v2i8.139.
Ethical Compliance & Review Process
- •All submissions are screened under plagiarism detection.
- •Review follows editorial policy.
- •Authors retain copyright.
- •Peer Review Type: Double-Blind Peer Review
- •Published on: Aug 24 2026
CCBYNC
This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. You are free to share and adapt this work for non-commercial purposes with proper attribution.