The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

The present study investigates the effect of two parameters of process type and tool offset on tensile, microhardness, and microstructure properties of AA6061-T6 aluminum alloy joints. Three methods of Friction Stir Welding (FSW), Advancing Parallel-Friction Stir Welding (AP-FSW), and Retreating Parallel-Friction Stir Welding (RP-FSW) were used. In addition, four modes of 0.5, 1, 1.5, and 2 mm of tool offset were used in two welding passes in AP-FSW and RP-FSW processes. Based on the results, it was found that the mechanical properties of welded specimens with AP-FSW and RP-FSW techniques experience significant increments compared to FSW specimens. The best mechanical and microstructural properties were observed in the samples welded by RP-FSW, AP-FSW, and FSW methods, respectively. Welded specimens with the RP-FSW technique had better mechanical properties than other specimens due to the concentration of material flow in the weld nugget and proper microstructure refinement. In both AP-FSW and RP-FSW processes, by increasing the tool offset to 1.5 mm, joint efficiency increased significantly. The highest weld strength was found for welded specimens by RP-FSW and AP-FSW processes with a 1.5 mm tool offset. The peak sample of the RP-FSW process (1.5 mm offset) had the closest mechanical properties to the base metal, in which the Yield Stress (YS), ultimate tensile strength (UTS), and elongation percentage (E%) were 76.4%, 86.5%, and 70% of base metal, respectively. In the welding area, RP-FSW specimens had smaller average grain size and higher hardness values than AP-FSW specimens.

The innovative way of enterprise development depends on many issues in the framework of legislation, financing, infrastructure, human resources, technological base, information, and other areas. The current study analyzes the factors that determine the manifestations of labor opportunism and its forms based on functional and resource approaches, taking into account institutional and economic constraints among workers in the energy industry. The results of a sociological study on the forms of opportunistic behavior at the enterprises of the energy industry are presented. The results of the study indicate that labor opportunism is one of the significant factors that block the innovative development of an enterprise. It has a major impact on labor relations as long as one of the conditions for the emergence of opportunism is a conflict of interests between the employee and the employer. It occurs when the interests of one economic agent run counter to the interests of another. This is proved by the results of assessing the influence of various factors on the opportunism level of employees of energy enterprises and is based on correlation and regression analysis. In the framework of this study, labor opportunism is understood as a form of selfish behavior of an employee pursuing personal gain as a response to a conflict of interests between economic agents in the course of labor activity. The conclusions reached suggest that labor opportunism should be considered as a blocking factor when designing the innovative development of an industrial enterprise. Measures aimed at overcoming labor opportunism, building trust in the team and raising the level of innovation in enterprises are proposed.

Breast cancer is one of the most dreaded diseases that affects women worldwide and has led to many deaths. Early detection of breast masses prolongs life expectancy in women and hence the development of an automated system for breast masses supports radiologists for accurate diagnosis. In fact, providing an optimal approach with the highest speed and more accuracy is an approach provided by computer-aided design techniques to determine the exact area of breast tumors to use a decision support management system as an assistant to physicians. This study proposes an optimal approach to noise reduction in mammographic images and to identify salt and pepper, Gaussian, Poisson and impact noises to determine the exact mass detection operation after these noise reduction. It therefore offers a method for noise reduction operations called Quantum Inverse MFT Filtering and a method for precision mass segmentation called the Optimal Social Spider Algorithm (SSA) in mammographic images. The hybrid approach called QIMFT-SSA is evaluated in terms of criteria compared to previous methods such as peak Signal-to-Noise Ratio (PSNR) and Mean-Squared Error (MSE) in noise reduction and accuracy of detection for mass area recognition. The proposed method presents more performance of noise reduction and segmentation in comparison to state-of-arts methods. supported the work.