The absolute majority of modern studies dealing with the interpretation of experimental data on the basis of the Freundlich isotherm ignore the fact that the data obtained for regions of low and moderate adsorbate concentration/pressure can be analytically continued within the Freundlich adsorption model to the adsorptive saturation area with coverages tending to 100%. Needless to say, this would give valuable extended information about the corresponding adsorption process. This message proposes a framework to comprehensively analyse experimental data first recognised as complying with the Freundlich adsorption model. An algorithm-driven method is presented which enables one to translate the data obtained in the area of small and moderate the coverages of the area of adsorptive saturation regime. As examples, three sets of experimental data for adsorption of mercury (II) on N-rich porous organic polymers and of protein on carrier nano-Mg(OH)₂ have been processed and presented according to the framework developed.

This paper describes a modification of the method of power series for the construction of approximate solutions of the Lorenz system. The results of a computer-aided simulation are presented. Also,...

This paper presents a study on a memristive two-neuron-based Hopfield neural network with fractional-order derivatives. The equilibrium points of the system are identified, and their stability is analyzed. Bifurcation diagrams are obtained by varying the magnetic induction strength and the fractional-order derivative, revealing significant changes in the system dynamics. It is observed that lower fractional orders result in an extended bistability region. Also, chaos is only observed for larger magnetic strengths and fractional orders. Additionally, the application of the fractional-order model for image encryption is explored. The results demonstrate that the encryption based on the fractional model is efficient with high key sensitivity. It leads to an encrypted image with high entropy, neglectable correlation coefficient, and uniform distribution. Furthermore, the encryption system shows resistance to differential attacks, cropping attacks, and noise pollution. The Peak Signal-to-Noise Ratio (PSNR) calculations indicate that using a fractional derivative yields a higher PSNR compared to an integer derivative.

When patients perform musculoskeletal rehabilitation exercises, it is of great importance to observe the correctness of their performance. The aim of this study is to increase the accuracy of recognizing human movements during exercise. The process of monitoring and evaluating musculoskeletal rehabilitation exercises was modeled using various tracking systems, and the necessary algorithms for processing information for each of the tracking systems were formalized. An approach to classifying exercises using machine learning methods is presented. Experimental studies were conducted to identify the most accurate tracking systems (virtual reality trackers, motion capture, and computer vision). A comparison of machine learning models is carried out to solve the problem of classifying musculoskeletal rehabilitation exercises, and 96% accuracy is obtained when using multilayer dense neural networks. With the use of computer vision technologies and the processing of a full set of body points, the accuracy of classification achieved is 100%. The hypotheses on the ranking of tracking systems based on the accuracy of positioning of human target points, the presence of restrictions on application in the field of musculoskeletal rehabilitation, and the potential to classify exercises are fully confirmed.