We identified, via a computer search, 143 excluded minors of the spindle surface, the space formed by the identification of two points of the sphere. Per our search, any additional excluded minors must have at least 12 vertices and 28 edges. We also identified 847 topological obstructions for the spindle surface. We conjecture that our lists of excluded minors and topological obstructions are complete.

This paper analyzes the prediction model of enterprise human resource demand based on Internet of Things (IoT) technology and data mining technology. It also analyzes the impact of the company’s growth scale and other key factors on the demand for human resources, tries to establish a coupling factor model of enterprise development and economic benefits, and then analyzes and forecasts the enterprise’s personnel structure and quality structure. The experimental results show that the optimized human resource demand forecasting model integrates the advantages of the grey system model in data processing, can mine the inherent laws of unorganized data information, and provides a certain convenience for forecasting. Through the linear mapping and processing of sample data, the input and output reflect a kind of correlation, thus changing the fault tolerance of information, making the prediction in the calculation process more accurate, and its comprehensive accuracy can exceed 92.5%.

Low efficiency and poor accuracy are caused by missing data in traditional 3D reconstruction methods. This study suggests a new 3D point cloud recognition technique for substation equipment based on 3D laser scanning point clouds, which combines the k-nearest neighbour (KNN) classification algorithm and particle swarm optimisation (PSO) algorithm, to address these issues. The particle swarm optimisation algorithm optimises the coefficient weights of each subspace feature. The k-nearest neighbour classification algorithm is then used to finish the classification. To confirm the superiority and accuracy of the suggested approach, the impact of the point cloud subspace’s size and loss rate on the recognition effect is examined experimentally and contrasted with the enhanced iterative nearest point algorithm. With an average recognition time of 0.19 seconds and a recognition accuracy of over 95\%, the experimental results demonstrate the method’s good performance in terms of efficiency and accuracy, opening up a wide range of potential applications.

Users may receive personalised information services and decision support from personalised recommendations. In this paper, a hybrid algorithm-based personalised recommendation approach for learning English is proposed. The user model is created by merging user interest tags, and the Person Rank algorithm is then recommended based on user information. Second, the question-and-answer model is created once the question-and-answer data has been labelled, and the Problem Rank algorithm is suggested in accordance with the question-and-answer data. Then, the approach of tag-based recommendation, comparable user recommendation, and multi-dimensional sliding window are used to construct the recommendation algorithm model. The experimental findings demonstrate that, following the model’s training with the gradient descent technique, the recommendation accuracy is steady at around 0.78, the suggested information can accommodate users who are learning English, and the personalised recommendation effect is enhanced.

In this paper, we introduce the edge version of doubly resolving set of a graph which is based on the edge distances of the graph. As a main result, we computed the minimum cardinality \(\psi_E\) of edge version of doubly resolving sets of family of \(n\)-sunlet graph \(S_n\) and prism graph \(Y_n\).

Consider the simple connected graph G with vertex set V(G) and edge set E(G). A graph \(G\) can be resolved by \(R\) if each vertex’s representation of distances to the other vertices in \(R\) uniquely identifies it. The minimum cardinality of the set \(R\) is the metric dimension of \(G\). The length of the shortest path between any two vertices, x, y in V(G), is signified by the distance symbol d(x, y). An ordered k-tuple \(r(x/R)=(d(x,z_1),d(x,\ z_2),…,d(x,z_k))\) represents representation of \(x\) with respect to \(R\) for an ordered subset \(R={\{z}_1,z_2,z_3…,z_k\}\) of vertices and vertex \(x\) in a connected graph. Metric dimension is used in a wide range of contexts where connection, distance, and connectedness are essential factors. It facilitates understanding the structure and dynamics of complex networks and problems relating to robotics network design, navigation, optimization, and facility location. Robots can optimize their localization and navigation methods using a small number of reference sites due to the pertinent idea of metric dimension. As a result, many robotic applications, such as collaborative robotics, autonomous navigation, and environment mapping, are more accurate, efficient, and resilient. A claw-free cubic graph (CCG) is one in which no induced subgraph is a claw. CCG proves helpful in various fields, including optimization, network design, and algorithm development. They offer intriguing structural and algorithmic properties. Developing algorithms and results for claw-free graphs frequently has applications in solving of challenging real-world situations. The metric dimension of a couple of claw-free cubic graphs (CCG), a string of diamonds (SOD), and a ring of diamonds (ROD) will be determined in this work.

Using blockchain technology to handle the entire chain of digital copyrights in digital libraries not only helps to improve the economy, validity, and fairness of the libraries’ digital resource offerings, but it also increases the revenue of digital copyright subjects in a sustainable manner. In this work, a decentralized, secure, and traceable digital copyright transaction system is designed and implemented using blockchain technology. The system serves creators, administrators, and subscribers through its user layer, business model layer, and Fabric network layer. To guarantee the accuracy and integrity of transaction data, smart contracts are used for the registration of digital works, transaction supervision, and smart contract execution. Fabric Composer is used in the development of the system and offers good scalability. The system still has issues with privacy protection, increasing performance, and complying with laws and regulations. It is anticipated that the digital copyright transaction system will advance in the area of digital copyright protection as blockchain technology develops.

As computer and mechanical automation technologies advance, machine vision-based non-destructive testing technology finds use in a multitude of domains. Non-destructive testing technologies can be used on apple sorting equipment to decrease apple damage while simultaneously increasing sorting efficiency. As a result, the apple sorting machine’s image identification system now incorporates machine vision technology. The automatic classification of apple grades is accomplished by gathering, processing, extracting, and computing the contour features of apple photographs using preset sorting levels. The automatic control system then sorts apples of different grades to designated locations, thus achieving the automation of apple sorting. Tests were run on the sorting machine’s image recognition system to confirm the solution’s viability. The outcomes demonstrate that the sorting machine can effectively classify fruit automatically based on their perimeter, which is important for fruit sorting automation.

The gearbox gearbox transmission system, which is the foundation of a new energy vehicle, is responsible for the crucial duty of power transmission. In reality, the reducer gearbox system is the primary source of noise inside cars because of the design of the system, mistakes made during manufacturing and assembly, and gear engagement impulses. The research target is the second-stage retarder gearbox system of a new energy vehicle. A three-dimensional model of the retarder gearbox system is created using the Romax software.Static and dynamic analyses were carried out in Romax software based on the five typical conditions of start, acceleration, equal speed, deceleration, and stop in order to derive performance data such as maximum contact and bending stresses of the gears, single-position length load distribution, gearbox error, etc. In the NVH analysis, the system’s vibration acceleration was ascertained using the findings of the gearbox error analysis. In order to provide comparative data for vibration and noise reduction of gear modification, the comparative study analyses the data output results under various working conditions and analyses the relationship between gear engagement force and gear vibration.

Let \(G\) be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and the placing one pebble to an adjacent vertex and throwing away the another pebble. A dominating set \(D\) of a graph \(G=(V,E)\) is a non-split dominating set if the induced graph \(\) is connected. The Non-split Domination Cover(NDC) pebbling number, \(\psi_{ns}(G)\), of a graph $G$ is the minimum of pebbles that must be placed on \(V(G)\) such that after a sequence of pebbling moves, the set of vertices with a pebble forms a non-split dominating set of \(G\), regardless of the initial configuration of pebbles. We discuss some basic results and determine \(\psi_{ns}\) for some families of standard graphs.