In the major cities with many high-rise buildings in contemporary China, land resources are becoming more and more scarce, and the urban ecological environment is in urgent need of recycling, and due to the blind imitation of Western culture and design mode and the neglect of China traditional regional culture, the urban landscape lacks interaction, resonance, and sense of belonging with citizens, and the phenomenon of landscape similarity emerges in various cities, focusing on the landscape space of urban complexes. There are also these problems. Urban residents urgently need a third space that can adjust their physical, mental, and spiritual needs. How to design an urban complex landscape that meets the aesthetic needs and humanistic needs of contemporary cities and has regional characteristics has become the first important task of my research. Folk art is an artistic treasure created by the working people in their production and life. Folk art is the embodiment of cultural regionality and the foundation of national culture. It awakens people’s awareness of the importance of local culture, awakens people’s sense of belonging, and is closer to the local public life. Today, the living soil and social and humanistic environment of folk art are in the process of urbanization in China, and there is a trend of gradual disappearance of lifestyle changes. How to make the contemporary urban complex landscape an organic soil for the survival, expression, application, and development of folk art is an important task in contemporary urban landscape design. Based on optimization, related concepts such as symbols, folk art symbols, urban complexes, urban complex landscape design, etc. have been sorted out. The relevant experimental results show that the construction land accuracy of the logistic regression model based on genetic algorithm has increased from 78.0% to 85.3%. kappa increased from 74.5% to 81.2%. Research shows that the logistic regression parameter optimization method based on genetic algorithm has better simulation effect than the conventional logistic regression method and is more suitable for the situation of unbalanced data distribution and many data features in the simulation of large-scale urban land dynamic changes.

Digital services, including healthcare, among others, have recently seen a massive volume of complicated data that arrives rapidly due to a rapid increase in the number of smart devices, focusing on the needs of regional emerging economic development and industrial structure adjustment, this paper explores the dynamic adjustment of a major in which schools, governments, enterprises and international cooperation participate in the development of regional emerging economies. mechanism. Based on the concept of future-oriented development, formulate a development plan for the legal profession, build a community of government, school, enterprise and international cooperation, promote the vigorous implementation of engineering practice education, and cultivate high-quality, high-level, international graduates, and to form the school-running characteristics of law majors in local application-oriented undergraduate colleges.

Given a connected simple undirected graph \(G=(V,E)\), a subset \(S\) of \(V\) is \(P_3\)-convex if each vertex of \(G\) not in \(S\) has at most one neighbor in \(S\). The \(P_3\)-convex hull \(\langle S\rangle\) of \(S\) is the smallest \(P_3\)-convex set containing \(S\). A Carathéodory set of \(G\) is a set \(S\subseteq V\) such that \(\langle S \rangle \setminus \bigcup_{w\in S} \langle S\setminus \{w\} \rangle\) is non-empty. The Carathéodory number of \(G\), denoted by \(C(G)\), is the largest cardinality of a Carathéodory set of \(G\). In this paper, we settle the conjecture posed by Barbosa et al. appeared in [SIAM J. Discrete Math. 26 (2012) 929–939] in the affirmative, which states that for a claw-free graph \(G\) of order \(n(G)\), the Carathéodory number \(C(G)\) of the \(P_3\)-convexity satisfies \(C(G) \leq \frac{2n(G)+6}{5}\). Furthermore, we determine all graphs attaining the bound.

The key factor that promotes Vocational students development is the development of movement, which requires children to have excellent motor skills to develop their intellectual level, physical function and social adaptability in daily study and life. Data mining technology is an economical and practical core technology, which obtains useful information for the service system from a large amount of data. However, many teaching deficiencies in this area are prevalent in the field of early childhood education. In the current research on the content of Vocational students physical activities, a large amount of data information needs the support of data mining technology. This paper aims at how to combine data mining technology to study the content of Vocational students sports activities from the perspective of movement development, establish a decision support system for Vocational students sports activities, and conduct experiments on Vocational students sports activities from the perspective of action scientific arrangement and implementation of activity content, carry out empirical research on the content of Vocational students sports activities.

When using airborne LiDAR point clouds for city modelling and road extraction, point cloud classification is a crucial step. There are numerous ways for classifying point clouds, but there are still issues like redundant multi-dimensional feature vector data and poor point cloud classification in intricate situations. A point cloud classification method built on the fusing of multikernel feature vectors is suggested as a solution to these issues. The technique employs random forest to classify point cloud data by merging colour information, and it extracts feature vectors based on point primitives and object primitives, respectively. In this study, a densely populated area was chosen as the study area. Light airborne LIDAR mounted on a delta wing was used to collect point cloud data at a low altitude (170 m) over a dense cross-course. The point cloud data were then combined, corrected, and enhanced with texture data, and the houses were vectorized on the point cloud. The accuracy of the results was then assessed. With a median inaccuracy of 4.8 cm and a point cloud data collection rate of 83.3%, using airborne LIDAR to measure house corners can significantly lighten the labour associated with external house corner measurements.This test extracts the texture information of point cloud data through the efficient processing of high-density point cloud data, providing a reference for the application of texture information of airborne LIDAR data and a clear understanding of its accuracy.

One of the fundamental properties of the hypercube \( Q_n \) is that it is bipancyclic as \( Q_n \) has a cycle of length \( l \) for every even integer \( l \) with \( 4 \leq l \leq 2^n \). We consider the following problem of generalizing this property: For a given integer \( k \) with \( 3 \leq k \leq n \), determine all integers \( l \) for which there exists an \( l \)-vertex, \( k \)-regular subgraph of \( Q_n \) that is both \( k \)-connected and bipancyclic. The solution to this problem is known for \( k = 3 \) and \( k = 4 \). In this paper, we solve the problem for \( k = 5 \). We prove that \( Q_n \) contains a \( 5 \)-regular subgraph on \( l \) vertices that is both \( 5 \)-connected and bipancyclic if and only if \( l \in \{32, 48\} \) or \( l \) is an even integer satisfying \( 52 \leq l \leq 2^n \). For general \( k \), we establish that every \( k \)-regular subgraph of \( Q_n \) has \( 2^k, 2^k + 2^{k-1} \) or at least \( 2^k + 2^{k-1} + 2^{k-3} \) vertices.

Coded caching technology can better alleviate network traffic congestion. Since many of the centralized coded caching schemes now in use have high subpacketization, which makes scheme implementation more challenging, coded caching schemes with low subpacketization offer a wider range of practical applications. It has been demonstrated that the coded caching scheme can be achieved by creating a combinatorial structure named placement delivery array (PDA). In this work, we employ vector space over a finite field to obtain a class of PDA, calculate its parameters, and consequently achieve a coded caching scheme with low subpacketization. Subsequently, we acquire a new MN scheme and compare it with the new scheme developed in this study. The subpacketization \(F\) of the new scheme has significant advantages. Lastly, the number of users \(K\), cache fraction \(\frac{M}{N}\), and subpacketization \(F\) have advantages to some extent at the expense of partial transmission rate \(R\) when compared to the coded caching scheme in other articles.

We continue the study of Token Sliding (reconfiguration) graphs of independent sets initiated by the authors in an earlier paper [Graphs Comb. 39.3, 59, 2023]. Two of the topics in that paper were to study which graphs \(G\) are Token Sliding graphs and which properties of a graph are inherited by a Token Sliding graph. In this paper, we continue this study specializing in the case of when \(G\) and/or its Token Sliding graph \(\mathsf{TS}_k(G)\) is a tree or forest, where \(k\) is the size of the independent sets considered. We consider two problems. The first is to find necessary and sufficient conditions on \(G\) for \(\mathsf{TS}_k(G)\) to be a forest. The second is to find necessary and sufficient conditions for a tree or forest to be a Token Sliding graph. For the first problem, we give a forbidden subgraph characterization for the cases of \(k=2,3\). For the second problem, we show that for every \(k\)-ary tree \(T\) there is a graph \(G\) for which \(\mathsf{TS}_{k+1}(G)\) is isomorphic to \(T\). A number of other results are given along with a join operation that aids in the construction of \(\mathsf{TS}_k\)-graphs.

In this paper, we introduce graceful and near graceful labellings of several families of windmills. In particular, we use Skolem-type sequences to prove (near) graceful labellings exist for windmills with \(C_{3}\) and \(C_{4}\) vanes, and infinite families of \(3,5\)-windmills and \(3,6\)-windmills. Furthermore, we offer a new solution showing that the graph obtained from the union of \(t\) 5-cycles with one vertex in common (\(C_{5}^{t}\)) is graceful if and only if \(t \equiv 0, 3 \pmod{4}\) and near graceful when \(t \equiv 1, 2 \pmod{4}\).

We study groups generated by sets of pattern avoiding permutations. In the first part of the paper, we prove some general results concerning the structure of such groups. In particular, we consider the sequence \((G_n)_{n \geq 0}\), where \(G_n\) is the group generated by a subset of the symmetric group \(S_n\) consisting of permutations that avoid a given set of patterns. We analyze under which conditions the sequence \((G_n)_{n \geq 0}\) is eventually constant. Moreover, we find a set of patterns such that \((G_n)_{n \geq 0}\) is eventually equal to an assigned symmetric group. Furthermore, we show that any non-trivial simple group cannot be obtained in this way and describe all the non-trivial abelian groups that arise in this way. In the second part of the paper, we carry out a case-by-case analysis of groups generated by permutations avoiding a few short patterns.