This paper analyzed the components of the connotation of innovation ability, then constructs a linear spatial model of innovation and entrepreneurship ability, proposes a multi-objective function model of the utilization efficiency and allocation efficiency of education resources, and uses the grey correlation algorithm The experimental simulation and model solution are carried out. The simulation results show that, through the optimization, the utilization efficiency and allocation efficiency of the educational resources for innovation and entrepreneurship for all are increased by 18.72% and 20.98% respectively, and tend to be in equilibrium, which can achieve the optimization of educational resources allocation. Among all people, the correlation value with ideal entrepreneurship is 0.3177, achieving the most excellent innovation and entrepreneurship education.

IMO Member State audits aim to identify non-compliant behavior with the requirements of relevant instruments, enabling the implementation of corrective measures to enhance performance. However, the complexity and diversity of IMO instruments’ requirements result in low evaluation effectiveness and efficiency in current assessment methods of implementation of IMO instruments. To address this challenge, this study proposes a meta-learning model based on prototype networks, focusing on the corrective measures outlined in consolidated audit summary reports approved and issued by the IMO Secretariat. The suggested model conducts meta-learning using small samples, offering a swift and straightforward assessment method. It facilitates the fine classification of corrective measures, providing a way for the consistent and effective assessment of various countries’ current implementation practices. Empirical results of two strategies demonstrate improved classification accuracy. In comparison with traditional manual evaluation, the proposed method achieves accuracy value 71.61% and 65.78% in two strategies respectively. Furthermore, the model exhibits varying prediction accuracy across different articles and demonstrates robust generalization capabilities, highlighting its practicality.

A mapping \(l : E(G) \rightarrow A\), where \(A\) is an abelian group written additively, is called an edge labeling of the graph \(G\). For every positive integer \(h \geqslant 2\), a graph \(G\) is said to be zero-sum \(h\)-magic if there is an edge labeling \(l\) from \(E(G)\) to \(\mathbb{Z}_{h} \backslash \{0\}\) such that \(s(v) = \sum_{uv\in E(G)}l(uv) = 0\) for every vertex \(v \in V(G)\). In 2014, Saieed Akbari, Farhad Rahmati and Sanaz Zare proved that if \(r\) \((r\not= 5)\) is odd and \(G\) is a \(2\)-edge connected \(r\)-regular graph, \(G\) admits a zero-sum 3-magic labeling, and they also conjectured that every 5-regular graph admits a zero-sum \(3\)-magic. In this paper, we first prove that every 5-regular graph with every edge contained in a triangle must have a perfect matching, and then we denote the edge set of the perfect maching by \(EM\), and we make a labeling \(l : E(EM) \rightarrow {2}\), and \(E(E(G) – EM) \rightarrow {1}\). Thus we can easily see this labeling is a zero-sum 3-magic, confirming the above conjecture with a moderate condition.

Let \(\Gamma_{G}\) be the orbit graph of \(G\), with non-central orbits in the subset of order two commuting elements in \(G\), and the vertices of \(\Gamma_{G}\) connected if they are conjugate. The main objective of this study is to compute several topological indices for the orbit graph of a dihedral group, including the Wiener index, the Zagreb index, the Schultz index, and others. We also develop a relationship between the Wiener index and the other indices for the dihedral group’s orbit graph. Furthermore, their polynomial has been computed as well.

\(Y_k\)-tree is defined as \((v_1, v_2,\ldots, v_{k-1};\, v_{k-2} v_k)\) by taking their vertices as \((v_1,\,v_2,\ldots,\,v_k)\) and edges as \(\{(v_1v_2, v_2v_3,\ldots, v_{k-2}v_{k-1})\cup (v_{k-2}v_k)\}\). It is also represented as \((P_ {k-1} +e)\). One can obtain the necessary condition as \(mn(m-1)(n-1)\equiv 0 \pmod {2(k-1)}\), for \(k \geq 5\) to establish a \(Y_k\)-tree decomposition in \(K_m \times K_n\). Here the tensor product is denoted by \(\times\). In this manuscript, it is shown that a \(Y_5\)-tree (gregarious \(Y_5\)-tree) decomposition exists in \(K_m \times K_n\), if and only if, \(mn(m-1)(n-1)\equiv 0 \pmod8\).

For graphs \(F\) and \(H\), the proper Ramsey Number \(PR(F,H)\) is the smallest integer \(n\) so that any \(\chi'(H)\)-edge-coloring on \(K_n\) contains either a monochrome \(F\) or a properly colored \(H\). We determine the proper Ramsey number of \(K_3\) against \(C_3\) and \(C_5\).

We have constructed Block structured Hadamard matrices in which odd number of blocks are used in a row (column). These matrices are different than those introduced by Agaian. Generalised forms of arrays developed by Goethals-Seidel, Wallis-Whiteman and Seberry-Balonin heve been employed. Such types of matrices are applicable in the constructions of nested group divisible designs.

The primary challenge in credit analysis revolves around uncovering the correlation between repayment terms and yield to maturity, constituting the interest rate term structure-an essential model for corporate credit term evaluation. Presently, interest rate term structures are predominantly examined through economic theoretical models and quantitative models. However, predicting treasury bond yields remains a challenging task for both approaches. Leveraging the clustering analysis algorithm theory and the attributes of an insurance company’s customer database, this paper enhances the K-means clustering algorithm, specifically addressing the selection of initial cluster centers in extensive sample environments. Utilizing the robust data fitting and analytical capabilities of the Gaussian process mixture model, the study applies this methodology to model and forecast Treasury yields. Additionally, the research incorporates customer credit data from a property insurance company to investigate the application of clustering algorithms in the analysis of insurance customer credit.

In this paper, we propose a method for effectively evaluating the quality of business English teaching in colleges and universities. The approach is based on a multimodal neural network model integrated with grey correlation analysis. By employing the optimal data clustering criterion, we identify teaching quality evaluation indices. Subsequently, we establish a teaching quality evaluation index system using a genetic algorithm (GA) optimized Radial Basis Function (RBF) neural network. Grey correlation analysis is then applied to assess the quality of business English teaching by considering the relationship between the correlation degree and the evaluation level. The results indicate a correlation degree exceeding 0.90, signifying excellent teaching quality. The reliability of the selected evaluation indicators, assessed through retesting, surpasses 0.700, validating the evaluation results.

A crucial component of kindergarten instruction, collective teaching activities are a good way to educate young children on their overall development. The language field is one of the subjects taught in kindergarten, and it has to do with how kids learn to read, write, and speak. In order to improve teachers’ comprehension of children’s emotional reactions and language, this paper combines quantitative and qualitative methods to observe and analyze the quality of current language collective teaching activities in kindergartens. It also suggests knowledge logic and psychological logic for grasping the content of language collective teaching in kindergartens. To improve the quality of language teaching in kindergartens, it is crucial to adopt a variety of teaching strategies and organizational techniques, provide the proper tools and materials for language learning, pay attention to the key experiences of children learning the language, and enhance learning quality.