This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics.

The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in quantum calculus is a field of mathematics that has been gaining considerable attention recently. Despite the fact of its application in discrete calculus, it can be applied in fractional calculus as well. In this paper, some new Anderson type q-integral and h-integral inequalities are given using a Feng Qi integral inequality in quantum calculus. These findings are highly beneficial for basic frontier theories, and the techniques offered by technology are extremely useful for those who can stimulate research interest in exploring mathematical applications. Due to the interesting properties in the field of mathematics, integral inequalities have a tied correlation with symmetric convex and convex functions. There exist strong correlations and expansive properties between the different fields of convexity and symmetric function, including probability theory, convex functions, and the geometry of convex functions on convex sets. The main advantage of these essential inequalities is that they can be converted into time-scale calculus. This kind of inevitable inequality can be very helpful in various fields where coordination plays an important role.

Currently, indoor renovation construction technology is developing towards intelligence and automation, creating an urgent need for mobile robots to participate in high-pollution and high-risk construction operations. To address the issues of insufficient robustness and accuracy in indoor construction robot positioning due to relatively small indoor spaces and weak signals, this paper proposes a monocular vision indoor construction positioning and distance measurement method. It designs an improved YOLOv5 target detection algorithm with Canny edge detection operator for distance measurement and positioning. Experiments were conducted in a specific indoor construction environment by measuring the distance between the cross point projected by the laser emitter on the construction robot and the cross point generated by the laser level. The experimental results indicate that the calculated values from the algorithm differ from the actual measurements by no more than 8 mm, achieving an accuracy of 96%. This demonstrates that the proposed method has good performance in indoor construction positioning.

In order to reduce the certain number of oil film bearing burning accident, this paper proposes a novel method used to test static pressure pipes and measure the assembling clearance between sleeve and bush inside the bearing. On account of the theory of lubrication and the working mechanism for oil film bearing, through the development of a new set of hydrostatic oil supply system and test platform, provide the static supporting pressure and the disassembling and locking pressure. And based on this method, the assembling clearance measuring was carried out. The results show that the proposed measuring method has the ability to support the disassembling and assembling process of the oil film bearing. In addition, this method provides an important basis for the engineers of cold rolling mill on site to adjust the assembling clearance of oil film bearing. The application of this method effectively reduces the online burning accidents of the oil film bearing.