Nonlocal Boundary Conditions Are Applied to the Analysis of Curve Equations

The traditional curve equation solution method has a low accuracy, so the non-local boundary conditions are applied to the curve equation solution. Firstly, the solution coordinate system is established, and then the key parameters are determined to solve the curve equation. Finally, the curve equation is solved by combining the non-local boundary conditions. The experiment proves that the method of this design is more accurate than the traditional method in solving simple curve equation or complex curve equation.

On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model

In this research, an elastic model based on the continuum mechanics is developed to study the static behaviors of functionally graded (FG) arbitrary straight-sided quadrilateral nanoplates. The model is constructed in the framework of Gurtin-Murdoch’s surface and Mindlin’s plate theories to account for the surface energy and shear deformation effects, simultaneously. The variational differential quadrature (VDQ) method is used along with a mapping technique to do the discretization process in a variational framework by means of differential and integral operators. Consequently, a weak form of governing equations is obtained from the energy quadratic representation of the problem. The solution method is of a distinguished feature as it involves just the first-order derivative of the field components in the mapping and discretization. After assuring the effectiveness of presented model by doing comparative studies, the critical buckling load and static deflection of the FG nanoplates with different shapes in geometry are investigated considering the surface effects. It is found that the surface energies effect on the static behavior of the rectangular nanoplates is more significant as compared to the non-rectangular nanoplates.

Intelligent System for Training and Assessment of Basketball Referee in Sports Event Using Intelligent Sensor

Aiming at the problem of the fairness of the judgment results in the traditional basketball referee training and evaluation process affected by external factors, an intelligent system for training and assessment of basketball referees in sports events based on intelligent sensors is proposed. We collect the judged poses of basketball referees by wearing intelligent sensor devices, store the collected information in the database using the converter, and analyze the pose data with the quaternion pose solution method based on complementary filters. According to the comparator, the analysis result is compared with the standard judgment information, and the action is judged whether the action conforms to the basketball judgment rules of the sports event. The judge’s action pose score is evaluated according to the judgment result, and the training assessment result is outputted. The results show that the system can clearly simulate the acceleration and pose angle data of the referee’s complex actions, the recognition rate of various basketball penalty poses is high, and the error of the pitch, yaw, and roll pose calculations is small. The response time of this system is 4 ms, when the number of requests sent by the client is 200 which is unanimously approved by the referees.

Some Results on the q-Calculus and Fractional q-Differential Equations

In this paper, we first discuss some important properties of fractional q-calculus. Then, based on these properties and the q-Laplace transform, we translate a class of fractional q-differential equations into the equivalent q-differential equations with integer order. Thus, we propose a method for solving some linear fractional q-differential equations by means of solving the corresponding integer order equations. Several examples are provided to illustrate our solution method.

Optimization Problem of Pricing and Seat Allocation Based on Bilevel Multifollower Programming in High-Speed Railway

This paper studies the multistage pricing and seat allocation problems for multiple train services in a high-speed railway (HSR) with multiple origins and destinations (ODs). Taking the maximum total revenue of all trains as the objective function, a joint optimization model of multistage pricing and seat allocation is established. The actual operation constraints, including train seat capacity constraints, price time constraints in each period, and price space constraints among products, are fully considered. We reformulate the optimization model as a bilevel multifollower programming model in which the upper-level model solves the seat allocation problem for all trains serving multiple ODs in the whole booking horizon and the lower optimizes the pricing decisions for each train serving each OD in different decision periods. The upper and lower are a large-scale static seat allocation programming and many small-scale multistage dynamic pricing programming which can be solved independently, respectively. The solving difficulty can be significantly reduced by decomposing. Then, we design an effective solution method based on divide-and-conquer strategy. A real instance of the China’s Wuhan-Guangzhou high-speed railway is employed to validate the advantages of the proposed model and the solution method.

Mössbauer investigation of Co-doped Bismuth Ferrite prepared by the solution method

In this work, [Formula: see text] ([Formula: see text] = 0, 0.08) nanoparticles were synthesized by the solution method and their structural differences were studied. X-ray diffraction results show that the rhombohedral R3c space group and perovskite structures are detected in both samples, accompanied by an impurity phase. The (104) and (110) peaks merge when cobalt ions are doped. The decrease in lattice parameters indicates that the microstructure of the nanoparticles becomes gradually distorted. Mössbauer spectroscopy analysis at room temperature reveals an additional doublet due to the oxygen vacancies in [Formula: see text]. Hyperfine interactions, spatial spin-modulated structures and oxygen deficiencies around iron ions are also reflected in the observed spectra and variations in hyperfine parameters.