Cities are highly concentrated areas of human civilization, the contradiction between urban development and resources and environment has become increasingly prominent. Inefficient use of energy and land resources, shortage of water resources, and environmental pollution are threatening the healthy development of cities. In this paper, the signal reconstruction algorithm and measurement matrix design in the compressed sensing theory are mainly studied. Aiming at the problems of green city environmental monitoring and landscape design, signal underestimation or overestimation caused by the fixed selection step in the iterative process of sparse adaptive matching tracking algorithm, The threshold idea is introduced into atomic selection, and a variable step size strategy is proposed based on the change of step size. The experimental results show that the establishment of the green city environment monitoring and landscape design model system dynamically changes the network topology, so that data can be transmitted in the mobile ad hoc network.

Deep learning is based on scientific educational psychology theory and is an important concept in contemporary learning theory. Therefore, combining in-depth learning with teaching of political courses, to explore teaching strategies of college political courses based on students’ in-depth learning, requirements for implementing new curriculum standards for cultivating students’ core literacy of disciplines, and cultivating students who meet development requirements of times. High-quality talents are of great value and significance. Through questionnaires and sample interviews, this paper focuses on analyzing specific measures for improvement from four aspects: sufficient teaching preparation, effective teaching implementation, scientific teaching evaluation and normalized teaching reflection. It is highly effective and feasible to increase level of students’ deep learning ability to more than 14.65%.

The development of information society requires the reform of traditional English education. The progress of science and technology, especially the progress of Internet information technology, has penetrated into the English teaching system, reconstructed the relationship between the elements of the English teaching system, and provided technical support for the reform of English teaching. These two aspects are the internal and external impetus of English teaching reform. According to the theory of knowledge construction and multimodal information fusion, this research establishes a user-centered knowledge space, which can respond to user needs quickly, emphasizes the integration and integration of multimodal subject knowledge in resource organization, and expresses multi-dimensional relevance in functional form. The experimental results show that the optimized BOPPPS English teaching model is conducive to improving students’ participation in English classroom interaction. In the new information integration technology environment, students are more likely to put forward opinions or suggestions, and the transformation relationship of students’ interactive behavior becomes more complex.

At present, countries all over the world attach great importance to cultural works. These works have become an important engine of economic development and can make good contributions to economic growth. The traditional tracing control scheme of cultural creation works has some problems, such as incomplete information collection, critical point of unit tracing, information fraud, centralized data storage and so on. At the same time, there seems to be a series of problems that can be solved. This paper analyzes the current situation of the review data of cultural creation products, and puts forward the review and analysis scheme of cultural creation works based on large-scale data algorithm and block chain technology. In addition, by combining department chain technology with intranet and traditional database system, an information database about the supply chain of cultural products in crop departments is established. The processing, logistics and sales information and the information of participants are interrelated.

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 \(C_5\).