Inversion of the Poisson-Hankel transform by C. Nasim

“…The Poisson-Hankel transform is defined as an integral transform of the initial temperature function, with the kernel as the source solution of the generalized heat equation. …”
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Recent developments on the Stieltjes transform of generalized functions by Ram Sankar Pathak, Lokenath Debnath

Subjects: “…Stieltjes transforms of ordinary and generalized functions…”
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On The Mean Convergence of Biharmonic Functions

“…Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . …”
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N-harmonic extensions of weighted integrable distributions by Josefina Alvarez, Martha Guzmán-Partida, Salvador Pérez-Esteva

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CIRCULAR PUNCH INDENTATION INTO CONTINUOUSLY INHOMOGENEOUS THERMOELASTIC HALF-SPACE UNDER GIVEN CONSTANT TEMPERATURE AT ITS FLAT BOTTOM by Leonid Ivanovich Krenev, Sergey Mikhaylovich Aizikovich, Boris Igorevivich Mitrin

“…The original problem is r educed to the system of dual integral equations. The properties of the dual integral equations kernel transforms allow applying a well - grounded bilateral asymptotic technique which is being actively developed at present. …”
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DETERMINATION OF SURFACE DEFORMATION OF CONTINUOUSLY INHOMOGENEOUS THERMOELASTIC HALF-SPACE UNDER LOCAL HEATING by Leonid Ivanovich Krenev, Sergey Mikhailovich Aizikovich, Boris Igorevich Mitrin

“…The axially symmetric quasistatic problem on thermoelasticity for the functionally graded half-space, with elasticity modulus, Poisson ratio, heat conduction, and linear expansion coefficients varying continuously in the near-surface layer is considered. …”
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Dirichlet Problem for the Schrödinger Operator in a Half Space by Baiyun Su

“…Meanwhile, a solution of the Poisson integral for any continuous boundary function is also given explicitly by the Poisson integral with the generalized Poisson kernel depending on this boundary function.…”
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Solution of Helmholtz eigenvalue problems with non-regular domains using the direct interpolation technique by Carlos Friedrich Loeffler, Luciano de Oliveira Castro Lara, Hercules de Melo Barcelos, João Paulo Barbosa

“…Using the radial basis functions, the Direct Interpolation Method approximates the non-self-adjoint kernel of the domain integral equations, which appear in many partial differential equations of mathematics, physics, and engineering. …”
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A Novel Multi-Fidelity Support Vector Classification Method for Boundary Prediction in Engineering Applications by Jinliang Luo, Lingzhi Liu, Youwei He, Kuan Tan

“…The key points of the proposed method include the design of a reasonable kernel function to effectively describe the relationship between the input and output of multiple fidelities, and the determination of the optimal hyperparameters. …”
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High-Throughput 3D Rice Chalkiness Detection Based on Micro-CT and VSE-UNet by Zhiqi Cai, Yangjun Deng, Xinghui Zhu, Bo Li, Chenglin Xu, Donghui Li

“…Through comprehensive training optimization strategies, including the Dice focal loss function and dropout technique, the model achieves robust and accurate segmentation of both kernels and chalky regions in continuous CT slices. …”
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