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In this article, a novel image de-noising method is proposed. This method is based on spherical coordinates system. First, spherical transform is re-defined in wavelet domain, and the properties of the spherical transform in wavelet domain are listed. Then, a new adaptive threshold in spherical coordinate system is presented. It has been proved based on Besov space norm theory. After that, a novel curve shrinkage function is proposed to overcome the limitation of the traditional shrinkage functions. The new function can reach and exceed the true value and enhance the edge of the image. Finally, the multi-scale product in wavelet domain is introduced to spherical coordinates system. This article names the multi-scale product in spherical coordinates system as Multi-Scale Norm Product. The experimental results compared the improved algorithm with other methods from the peak signal-tonoise ratio, mean square error, and running time. The results indicate that improved algorithm is simple and effective.

Predicting the viscosity of ionic liquids (ILs) is crucial for their applications in chemical and related industries. In this study, a large data set of experimental viscosity data of ILs with a wide range of viscosity (7.83–142 000 cP), pressure (1–3000 bar), and temperature (258.15–395.32 K) are employed to build predictive models. The structures of cations and anions for 89 ILs are optimized, and the S σ‑profiles descriptors are calculated using the quantum chemistry method.Two new models are developed by using extreme learning machine (ELM) intelligence algorithm with the temperature, pressure, and a number of S σ‑profiles descriptors as input parameters. The coefficient of determination (R 2) and average absolute relative deviation (AARD %) of the total sets of the two predictive models are 0.982, 2.21% and 0.951, 4.10%, respectively. The results show that the two ELM models are reliable for predicting the viscosity of ILs.

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