In this paper, a class of successive permutation iterative methods for solving three-dimensional diffusion equations is constructed based on full-implicit discretization. The growth matrix of the method is given in this paper, and the convergence is analyzed. The new method can avoid solving large linear equations, and thus significantly improve the calculation speed. Compared with the full-implicit method and the Gauss-Seidel method, the new method not only has the same approximate accuracy as the full-implicit method but also is faster and more accurate than the Gauss-Seidel method.

Quaternion matrix equations have widespread applications in signal processing, image processing, control systems, etc. By using the real representation, determinant, inverse matrix definition and properties of quaternion matrices, and based on the Kronecker product of quaternion matrices, a class of coupled Sylvester quaternion matrix equations is transformed into equivalent real linear equations. The Cramer's rule for the solution of the equations with a unique solution is studied. Finally, the Cramer's rule for the coupled Sylvester quaternion matrix equations is derived by using the isomorphic relationship between quaternions and their real representations. Through the analysis of the method, the theoretical validity and feasibility are proved. Numerical examples demonstrate that the proposed theoretical method has good computational performance and practicality.

In natural world, many biological populations exist in a hierarchical structure which is similar to human societies, both the age and size of individual populations are important factors to influence the hierarchical structure of populations, and the dominance of the individual size in the hierarchical structure of biological populations has more pronounced and widespread. Therefore, based on the fact that individuals with larger size in a population have a greater advantage in obtaining food and reproducing offspring, this paper researches the existence of positive equilibria state and the stability of zero equilibria state of a nonlinear predator-prey model with hierarchical size-structured. A non-zero fixed point theorem is used to show that there is at least one positive equilibrium state in the model. The stability criterion of the zero equilibrium state is obtained by deriving the characteristic equation of the zero equilibrium state and constructing the Lyapunov function. Finally, present some numerical experiments of zero equilibrium state to verify the conclusions.

A dynamic model of echinococcosis in livestock, domestic dogs, stray dogs and eggs in the environment is established, and the influence of stray dogs on the transmission of echinococcosis is discussed. Firstly, by using the fundamental theorem of differential equation, the adaptability of the model solution is obtained, including non-negative and boundedness. Secondly, the equilibrium point and the basic regeneration number of the model are obtained. By analyzing the characteristic equation and the Lyapunov function, it is obtained that when the basic regeneration number is less than 1, the disease-free equilibrium point is asymptotically stable, namely, the echinococcosis tends to be extinct. When the basic regeneration number is greater than 1, the disease-free equilibrium point is unstable, and the endemic equilibrium point is asymptotically stable, namely, the echinococcosis persists.

This paper explores optimal control strategies for target benefit pension plans in the presence of inflation risk. It proposes a premium refund clause to protect members who pass away during the accumulation phase. The pension fund can invest in a risk-free asset, an inflation-indexed bond, and a stock. By maximizing the expected utility of benefits and final wealth using the Cobb-Douglas utility function, the optimal investment and benefits strategies are determined through Hamilton-Jacobi-Bellman (HJB) equations. Numerical analyses examine the influence of important parameters on benefit payment and fund wealth.

Real estate prices are affected by locational heterogeneity, locational autocorrelation and nonlinearity of locational distribution, which makes it challenging to evaluate housing prices quickly, massively and accurately under complex urban locations in China. Based on trend surface analysis and Bayesian optimization modeling, this paper constructs the BO-TSA-XGBoost model, which converts the valuation problem into an attribute space partitioning problem, to achieve the identification and learning of locational information of real estate mass appraisal in a complex data environment. In this paper, 34 460 second-hand house transaction data from all 16 administrative districts of Shanghai from 2020 to 2021 are collected for empirical analysis. The research results show that the BO-TSA-XGBoost model can accurately identify and learn location information under complex data, effectively solve the problem of evaluation accuracy degradation caused by complex locality characteristics, and achieve a high level of accuracy in multiple price intervals and multiple complex locations; The trend surface analysis and Bayesian optimization algorithm significantly improve the evaluation accuracy and evaluation robustness of the original ensemble learning model; housing location information is the key to the mass appraisal model.

With the rapid development of 3D scanning and processing technologies, point cloud surface reconstruction has become a significant research focus in the fields of computer graphics and computer vision. The goal of point cloud surface reconstruction is to recover a continuous surface of an object or scene from discrete and irregular point cloud. In recent years, implicit function has gained increasing attention for their robustness and flexibility. Notably, the introduction of deep learning has significantly improved their performance in reconstructing complex geometries. A growing body of research on the application of implicit functions for point cloud surface reconstruction has emerged, making it increasingly challenging to track and understand the broader landscape. Therefore, there is an urgent need for a comprehensive review to summarize the fundamental principles, key techniques, and developmental trajectories of these methods. This paper first reviews the fundamental principles and historical development of implicit functions in point cloud surface reconstruction. It then systematically surveys existing methods from six perspectives: the definition of implicit functions, types of implicit functions, technological advancements, loss functions, datasets and evaluation metrics. Finally, the paper identifies critical challenges in this field, such as handling low-quality point clouds, ensuring real-time performance and addressing sequential point cloud reconstruction. It also provides an outlook on future research directions. This review aims to serve as a comprehensive technical reference for researchers engaged in point cloud reconstruction and related fields, helping them gain an in-depth understanding of the field's dynamics and efficiently identify frontier problems.

Federated learning is a new distributed learning framework to deal with data isolation and privacy protection. This paper focuses on the second-order gradient federated learning algorithm. It carries out the research on the federated learning Newton's algorithm for the more practical scheme that only some users can participate in the federated learning task. The convergence of the algorithm is proved theoretically. By using the McDiarmid inequality, the trade-off of the number of participating users, the convergence speed of the algorithm and the final convergence error are theoretically explained. The experimental results show that the algorithm can converge quickly and efficiently, effectively reduce the communication cost of federated learning, and prove the effectiveness, practicality and theoretical correctness of the algorithm.

Warehouse layout design is an important factor affecting the walking distance of picking operations and picking efficiency. On the basis of the fishbone layout and the flying-V layout, this paper takes the shelf placement angle and the angle of the diagonal cross-aisle as the starting points to study the leaf layout, constructs the effective storage area utilization model of the leaf warehouse layout, and investigates the influence of the shelf placement angle and the angle of the diagonal cross-aisle on the effective storage area. Then, we construct the stochastic model of S-shape and return routing strategies in leaf layout and complete the approximate calculation and simulation to verify it. The numerical experimental results show that in the leaf layout, the improvement of the layout has a small impact on the actual storage area, with a difference of 1.6\% and 2.7\% with the fishbone layout and flying-V layout, respectively, and the routing strategy of the leaf layout can be further studied. For specific angles of the shelf and the diagonal cross-aisle, both the return strategy and the S-shape strategy can achieve better values. The S-shape strategy is superior to the return strategy.

Restoring the true image from a degenerated version is a classical ill-posed inverse problem. Regularization technique is one of the mainstream methods to solve this problem. It restricts the solution image into a regularization space, and the restored image is the projection of the degenerated image in this space. However, it is difficult to choose a proper regularization space for different images. In order to improve the adaptability of the regularization model and model images with different features more precisely, an adaptive hybrid regularization model based on fuzzy set theory is proposed in this paper. Firstly, learning algorithm is used to calculate the membership degree of the images in different regularization spaces. And then the first s spaces with the largest membership degree are selected to establish an adaptive hybrid regularization model with membership degree as the weights. Finally, ADMM (Alternating Direction Method of Multipliers) based algorithm is used to numerically solve the model. The experimental results validate the proposed model. For different synthetic and real images, the proposed model can effectively choose the appropriate regularization spaces and obtain satisfactory results.

This paper studies the waiting time distributions of customers in an $M/M/1/m+1$ queueing system with customer interjections and server's single vacation. The customers who enter the system are divided into regular customers and interjection customers according to whether they interject the queue or not. After entering the system, the regular customers queue up at the end of the waiting line and wait for service, while the interjection customers queue up as close as possible to the head of the waiting line to receive service. There is one server who takes single vacation in the system. By using the properties of negative exponential distribution, the phase type distribution and the Markov chain with absorbing state, the matrix expressions of waiting time distribution of customers in waiting queue position $n$, regular customers and interjection customers are derived. Further, the waiting time distributions with time $t$ are plotted.