This paper develops a Legendre neural network method (LNN) for solving linear and nonlinear ordinary differential equations (ODEs), system of ordinary differential equations (SODEs), as well as classic Emden-Fowler equations. The Legendre polynomial is chosen as a basis function of hidden neurons. A single hidden layer Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials. The improved extreme learning machine (IELM) algorithm is used for network weights training when solving algebraic equation systems, and several algorithm steps are summed up. Convergence was analyzed theoretically to support the proposed method. In order to demonstrate the performance of the method, various testing problems are solved by the proposed approach. A comparative study with other approaches such as conventional methods and latest research work reported in the literature are described in detail to validate the superiority of the method. Experimental results show that the proposed Legendre network with IELM algorithm requires fewer neurons to outperform the numerical algorithm in the latest literature in terms of accuracy and execution time.

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Thermal transport and energy dissipation are important for a material in both thermoelectric and electronic devices. Here, we investigate the lateral and interfacial thermal transport of two-dimensional (2D) Bi2O2Se by Raman spectroscopy. It is found that thin Bi2O2Se flakes have a low in-plane thermal conductivity while maintaining an appropriate interfacial thermal conductance. The in-plane thermal conductivity of Bi2O2Se decreases with decreasing thickness, to as low as 0.92 ± 0.18 W⋅m−1⋅K−1 at a thickness of ∼8 nm. Such a low thermal conductivity is derived from the low phonon group velocity, strong anharmonicity, and large surface scattering of acoustic phonons of the Bi2O2Se thin layer. Simultaneously, thinner Bi2O2Se presents a higher thermal dissipation to the substrate than the thicker counterparts in the device. The interfacial thermal conductance increases with decreasing thickness, and reaches ∼21 MW⋅m−2⋅K−1 at ∼8 nm. These results provide critical information for the design of thermoelectric devices with high figures of merit and electronics with low-power consumption based on 2D materials.

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In order to investigate the high altitude effect on dc corona inception voltage of power transmission lines, a mobile corona cage test system was constructed. The experiments were carried in Wuhan, Xining, Geermu, and Nachitai, respectively. Photons released as a result of corona discharge on the conductors were detected by the ultraviolet image detector. Both positive and negative corona inception voltages could be acquired by the "tangent method" based on the measured data. The approximate linear altitude correction formulas were suggested.