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.

In the new era characterized by the modernization of national governance, fair competition is the inherent requirement of building a modern market system. However, the abuse of administrative power by administrative organs to excessively interfere in free-market competition is widespread, seriously damaging the market competition order in China. To avoid the unreasonable intervention of administrative organs in the market economy, restrain the administrative acts of administrative organs, and form a highly “competitive” market environment, the fair competition review system came into being. With the rapid development of blockchain technology, new ideas are provided for the research of fair-trade protocols. Aiming at the system performance bottleneck and high-cost problems caused by centralized processing in traditional fair transaction schemes based on trusted third parties, a fair transaction scheme based on fuzzy signature is proposed. In the proposed scheme, the signature model uses concurrent signature, and both parties hold their own key numbers, which are released through blockchain transactions to bind their signatures. In the whole process, both parties can complete the contract signing without the assistance of a centralized third party. Based on analyzing the security of the proposed scheme, the performance of the proposed scheme is further compared with other similar schemes of the same kind, which shows that the proposed scheme has higher computational efficiency.

Selecting the user comment information of short videos with top 2 likes in the top 50 topics about public cultural services in Shake App as the research object, and facilitating video platforms to identify the high and low quality of the videos and make reasonable promotion arrangements by predicting the short-term playback volume of pop-up videos and analyzing the influencing factors, which is conducive to improving the platform’s pop-up video services and economic benefits. The data related to B station videos are captured, and feature selection and different algorithms are combined to construct random forest model, XG Boost model and LSTM model to predict the playback volume of the pop-up videos, and compare and analyze the effects of different feature combinations on the experimental results. The results show that the prediction accuracy of the random forest model is higher than that of the XG Boost model and the LSTM model, and the features of the pop-up video itself have the greatest influence on the playback volume, while the features of the video markup text have a smaller degree of influence on the playback volume.

The rapid economic progress and widespread use of sophisticated technology elevate the output value per kWh of electricity consumed, underscoring the paramount importance of maintaining an uninterrupted and dependable power supply to avoid substantial economic losses for consumers and society. Investigating the reliability of urban distribution systems emerges not only as a pivotal factor in enhancing power supply quality but also as a cornerstone of electric power modernization, significantly impacting production, technology, and management within the industry while bolstering its economic and social benefits. This study adopts a multifaceted approach: firstly, establishing a methodology for grid-side storage capacity distribution to mitigate substation load factors and implement peak shaving, thereby minimizing load discrepancies. Secondly, it develops a mathematical model encompassing diverse user distributions, employing analytical techniques to derive reliability indices and optimal segment numbers tailored to different user distributions. The research proposes segment optimization based on user distributions, considering both economic viability and reliability, showcasing an interdisciplinary amalgamation of combinatorial principles and scientific computing methodologies. This approach aims to optimize segment distribution, enhancing the reliability and economic feasibility of urban distribution networks through advanced mathematical and computational techniques.

This study introduces a novel approach to address deficiencies in prior teaching quality assessment systems by establishing a mathematical model for evaluation. Utilizing a neural network trained via a particle swarm optimization algorithm (PSO), the method develops a BP (Backpropagation) model fine-tuned by PSO to capture the intricate relationships among diverse indicators influencing teachers’ teaching quality assessment and resulting evaluations. Empirical findings highlight the effectiveness of artificial neural networks in constructing a comprehensive evaluation framework accommodating a wide spectrum of systematic assessments. This approach not only optimizes teaching methodologies but also augments overall teaching efficacy and the quality of educational delivery in a holistic manner. Moreover, it fosters the cultivation of multifaceted individuals proficient in English application skills, contributing to the development of high-quality talent in practical and complex domains. The convergence of advanced mathematical modeling techniques and computational methods, alongside the utilization of numerous indicators, aligns with combinatorial principles, exploring the permutations and relationships of diverse factors impacting teaching quality assessment.

In this paper, we addresses the growing importance of enterprise equipment asset management efficiency. Proposing an advanced approach rooted in combinatorial principles and scientific computing, the study introduces a comprehensive evaluation model for equipment value. Overcoming the limitations of traditional models, a fuzzy algorithm establishes a three-dimensional cross-compound element, encompassing equipment reliability, stability, and accuracy. Hierarchical analysis and the entropy power method determine weights for evaluation indexes, facilitating a quantitative assessment of measurement and production equipment health. Validation through a real energy meter production line demonstrates the model’s effectiveness in comparison to real defect rates. This innovative evaluation model not only offers asset managers a new method for assessing equipment assets but also presents a forward-looking strategy for enterprises to enhance their asset management proficiency, emphasizing the synergies between combinatorics and scientific computing in addressing contemporary economic challenges.

Let \(G = (V, E)\) be a graph with \(n\) vertices. A bijection \(f : V \to \{1, 2, \dots, n\}\) is called a distance magic labeling of \(G\) if there exists an integer \(k\) such that \(\sum_{u \in N(v)}f (u) = k\) for all \(v \in V\), where \(N(v)\) is the set of all vertices adjacent to \(v\). Any graph which admits a distance magic labeling is a distance magic graph. The existence of regular distance magic graphs of even order was solved completely in a paper by Fronček, Kovář, and Kovářová. In two recent papers, the existence of \(4\)-regular and of \((n-3)\)-regular distance magic graphs of odd order was also settled completely. In this paper, we provide a similar classification of all feasible odd orders of \(r\)-regular distance magic graphs when \(r=6,8,10,12\). Even though some nonexistence proofs for small orders are done by brute force enumeration, all the existence proofs are constructive.

A good set on \(k\) vertices is a vertex induced subgraph of the hypercube \(Q_n\) that has the maximum number of edges. The long-lasting problem of characterizing graphs that are cover graphs of lattices is NP-complete. This paper constructs and studies lattice theoretic properties of a class of lattices whose cover graphs are isomorphic to good sets.

Combinatorial mathematics is a versatile field that can provide valuable insights and techniques in various aspects of artificial intelligence and educational research. We focus our attention on the exploration of the mechanism of the role of teachers’ emotional labor In this paper, we merge two parts of data, predicted and formally administered, based on the optimization and management of artificial intelligence English teachers’ emotional labor for the corresponding statistical analysis. Yes individual college English teachers are working for non-interpersonal issues for emotional regulation, temporarily restraining anger and cursing impulses, and communicating with students in a pleasant manner. In the case study of this paper, a teacher repeatedly failed in teaching, but he restrained his frustration and continued to work hard, and finally finished.

In order to determine the optimal scale for urban ride-hailing services and taxis while promoting their sustainable growth, we have developed a Lotka-Volterra evolutionary model that accounts for the competitive, cooperative, and mixed dynamics between these two entities. This model is rooted in the theory of synergistic evolution and is supported by data simulation and analysis. By employing this model, we can identify the appropriate size for urban ride-hailing services and taxis when they reach equilibrium under different environmental conditions. The study’s findings reveal that the evolutionary outcomes of online ride-hailing services and traditional taxis are closely linked to the competitive impact coefficient and the cooperative effect coefficient. In highly competitive environments, intense rivalry can lead to the elimination of the less competitive party, while the dominant player ultimately attains a specific size threshold. As competition moderates, both entities can achieve a balanced and stable coexistence in the market. In cooperative environments, both online ride-hailing services and traditional taxis have more room for development, which facilitates the integration of existing and innovative business models. In environments marked by competition, the development trends of both entities mirror those in competitive settings, but cooperation can slow down the decline of the less competitive party. In conclusion, we propose strategies to foster fair competition between online ride-hailing services and traditional taxis, consider the coexistence of old and new business models, and promote their integrated development.

A vertex labeling \(\xi\) of a graph \(\chi\) is referred to as a ‘vertex equitable labeling (VEq.)’ if the induced edge weights, obtained by summing the labels of the end vertices, satisfy the following condition: the absolute difference in the number of vertices \(v\) and \(u\) with labels \(\xi(v)= a\) and \(\xi(u)= b\) (where \(a,\ b\in Z\)) is approximately \(1\), considering a given set \(A\) that consists of the first \(\lceil \frac{q}{2} \rceil\) non negative integers. A graph \(\chi\) that admits a vertex equitable labeling (VEq.) is termed a ‘vertex equitable’ graph. In this manuscript, we have demonstrated that graphs related to cycles and paths are examples of vertex-equitable graphs.

Network theory is the study of graphs such as representing equilibrium relationships or unequal relationships between different objects. A network can be defined as a graph where nodes and / or margins have attributes (e.g. words). Topological index of a graph is a number that helps to understand its topology and a topological index is known as irregularity index if it is greater than zero and topological index of graph is equal to zero if and only if graph is regular. The irregularity indices are used for computational analysis of nonregular graph topological composition. In this paper, we aim to compute topological invariants of some computer related graph networks. We computed various irregularities indices for the graphs of OTIS swapped network \(OP_a\) and Biswapped Networks \(Bsw(Pa).\)