Volume 02, Issue 8
Published on: August 2026
KL ANALYSIS FOR MULTI-SCALE PROBLEMS IN ARTIFICIAL INTELLIGENCE AND RESILIENT LOGISTICS
VA Sharma
Dept. of mathematics ,Arts, commerce and science college, Amravati
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Abstract
We have completed and professionalized the classical theory of the Kontorovich–Lebedev transform that was sketched in the attached notes. The essential analytic ingredients definition of the operator as a Lebedev integral, the formally adjoint operator, analytic continuation of the Macdonald kernel of purely imaginary order into a complex strip, the uniform estimate the three principal asymptotic regimes (large argument, near the origin, and large order), and the characterization of the natural domain have been stated in full professional mathematical format and placed on a rigorous functional-analytic footing.
A literature review has situated this analytic apparatus within the contemporary applied corpus on artificial intelligence, quantum computing, digital twins, resilient logistics and high-performance computing infrastructures. Building on that foundation, four theoretical models were constructed that map each of the above analytic ingredients onto concrete technological settings: spectral approximation of kernels in large language models, radial heat and load diffusion in data centre geometries, spectral analysis of GPU cluster load, and continuum polar-flow models of infrastructure supply chains.
In every model the uniform bound, the large order decay , and membership in the natural domain furnish precise a-priori estimates and stability statements that are independent of any particular numerical discretisation. These results demonstrate that the classical theory of the Kontorovich–Lebedev transform continues to supply a powerful and rigorous language for multi-scale problems arising in modern computational and logistical infrastructures.
A literature review has situated this analytic apparatus within the contemporary applied corpus on artificial intelligence, quantum computing, digital twins, resilient logistics and high-performance computing infrastructures. Building on that foundation, four theoretical models were constructed that map each of the above analytic ingredients onto concrete technological settings: spectral approximation of kernels in large language models, radial heat and load diffusion in data centre geometries, spectral analysis of GPU cluster load, and continuum polar-flow models of infrastructure supply chains.
In every model the uniform bound, the large order decay , and membership in the natural domain furnish precise a-priori estimates and stability statements that are independent of any particular numerical discretisation. These results demonstrate that the classical theory of the Kontorovich–Lebedev transform continues to supply a powerful and rigorous language for multi-scale problems arising in modern computational and logistical infrastructures.
How to Cite this Paper
Sharma, V. (2026). KL Analysis for Multi-Scale Problems in Artificial Intelligence and Resilient Logistics. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-9. https://doi.org/10.55041/ijcope.v2i8.172
Sharma, VA. "KL Analysis for Multi-Scale Problems in Artificial Intelligence and Resilient 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.v2i8.172.
Sharma, VA. "KL Analysis for Multi-Scale Problems in Artificial Intelligence and Resilient 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.v2i8.172.
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