The dissolution characteristics of glycerol derivatives in solvents at different temperatures and pressures were studied. The effects of solvent structure on gas absorption capacity and separation selectivity were analyzed. The absorption thermodynamics and kinetics were discussed. The experimental results show that as the temperature increases, the solubility of glycerin derivatives decreases, and the separation selectivity between gases also decreases. At the same temperature, the more carbon atoms of the glycerin derivative, the easier the dissolution process in the ionic liquid. The thermodynamic parameters of each gas do not change much with increasing temperature. At the same time, the spectral clustering algorithm can be used to obtain the characteristics of the global optimal solution, which solves the problem that the traditional hybrid data clustering algorithm is easy to fall into the local optimal solution.

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A motion object extraction algorithm based on the active contour model is proposed. Firstly, moving areas involving shadows are segmented with the classical background difference algorithm. Secondly, performing shadow detection and coarse removal, then a grid method is used to extract initial contours. Finally, the active contour model approach is adopted to compute the contour of the real object by iteratively tuning the parameter of the model. Experiments show the algorithm can remove the shadow and keep the integrity of a moving object.

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The use of mathematical methods has become an indispensable research tool and method in the establishment and improvement of many disciplines. Therefore, mathematical methods have also been included in the intelligence analysis system of public security information science. Intelligence is a summary of information that exists in all aspects of our lives. This information is distributed according to time based on certain rules. The application of mathematical analysis methods can more accurately extract effective information and predict future trends. As we all know, classical calculus is a powerful tool for dealing with many dynamic processes in the field of applied science. However, there are many complex systems in nature that cannot be characterized by classical integer-order calculus models, especially in information processing analysis. The fractional-order system model can better describe its system performance. This paper introduces the time series analysis method into the public security intelligence analysis system, combines the fractional differential operator to construct the mathematical model, analyzes the network intelligence, predicts the future occurrence of the case, and compares the predicted data with the actual data to verify. The method is predictive of the true credibility of the results.

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