We use a dynamic programming algorithm to establish a new lower bound on the domination number of complete cylindrical grid graphs of the form \(C_n\square P_m\), that is, the Cartesian product of a path and a cycle, when \(n\equiv 2\pmod{5}\), and we establish a new upper bound equal to the lower bound, thus computing the exact domination number for these graphs.

In this paper, we address computational questions surrounding the enumeration of non-isomorphic André planes for any prime power order \(q\). We are particularly focused on providing a complete enumeration of all such planes for relatively small orders (up to 125), as well as developing computationally efficient ways to count the number of isomorphism classes for other orders where enumeration is infeasible. André planes of all dimensions over their kernel are considered.

We use a dynamic programming algorithm to establish a lower bound on the domination number of complete grid graphs of the form \(C_n\square P_m\), that is, the Cartesian product of a cycle \(C_n\) and a path \(P_m\), for \(m\) and \(n\) sufficiently large.

With the increasingly frequent exchanges between countries, my country’s demand for high-quality English translators has greatly increased. However, an important problem we are currently facing is that China’s translation talents are far behind the demand. An important reason for this phenomenon is that the traditional translation teaching is difficult to cultivate translators who can meet the market demand. Therefore, it is necessary to improve the traditional translation teaching mode. Translation teaching for English majors is an important part of translation teaching. Therefore, after evaluating the speech characteristics and speech data, this document first proposes a translation classification error detection model based on mfcc-rf. The acoustic function of the extracted 39 dimensional Mel inverse spectral coefficient is the input of the random forest classifier, and a classification error detection model is established. By analyzing the experimental results, the MFCC radio frequency translation error detection model has achieved high classification error detection accuracy under three types of errors (rising, falling and shortening). The experimental results show that, with semantic similarity as the design principle of distractors, using the word vector training method of the context word prediction model to automatically generate distractors can ultimately improve the comprehensive training efficiency of college English majors’ translation ability.

A node in the \(n\)-dimensional hypercube \(Q_n\) is called an odd node (resp. an even node) if the sum of all digits of the node is odd (resp. even). Let \(F\subset E(Q_n)\) and let \(L\) be a linear forest in \(Q_n-F\) such that \(|E(L)|+|F|\leq n-2\) for \(n\geq 2\). Let \(x\) be an odd node and \(y\) an even node in \(Q_n\) such that none of the paths in \(L\) has \(x\) or \(y\) as internal node or both of them as end nodes. In this note, we prove that there is a Hamiltonian path between \(x\) and \(y\) passing through \(L\) in \(Q_n-F\). The upper bound \(n-2\) on \(|E(L)|+|F|\) is sharp.

As a product of the revolutionary war years, red culture, with its strong vitality, strong cohesion and extraordinary charm, with its incomparable positive energy, resists vulgar and flattering culture, promotes people to rebuild their faith, purify their minds, stimulate their motivation, and promote the process of cultural power. Yan’an, represented by red culture, is rich in resources. This is the holy land of Chinese revolution, the first batch of famous historical and cultural cities named by the State Council, and the three major education bases of patriotism, revolutionary tradition, and Yan’an spirit. The development and utilization of such resources have great political, cultural, educational and economic values. This research is based on the development of red culture, and uses the distributed machine learning system to realize in the system architecture of parameter server. In the distributed system set in this study, node downtime and network interruption are random. When the parameter server system adopts static scheduling, it leads to poor scalability and robustness. The experimental results show that under the intelligent simulation of machine learning system, the development of red culture resources meets the expected assumptions, and the accuracy of the model is relatively high.

In this paper, we introduce a class of restricted symmetric permutations, called half-exceeded symmetric permutations. We deduce the enumerative formula of the permutations of \(\{1,2,\ldots,2n\}\) and give it a refinement according to the distribution of the inverse pairs. As a consequence, we obtain new combinatorial interpretations of some well-known sequences, such as Stirling numbers of the second kind and ordered Bell numbers. Moreover, we introduce the ordered Stirling number of the second kind and establish a combinatorial proof of the recursive relation of the sequence.

The total labeling of a graph \(G=(V,E)\) is a bijection from the union of the vertex set and the edge set of \(G\) to the set \(\{1,2,\dots,|V(G)|+|E(G)|\}\). The edge-weight of an edge under a total labeling is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex under a total labeling is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total labeling is called edge-magic or vertex-magic when all the edge-weights or all the vertex-weights are the same, respectively. When all the edge-weights or all the vertex-weights are different then a total labeling is called edge-antimagic or vertex-antimagic total, respectively.

In this paper we deal with the problem of finding a~total labeling of some classes of graphs that is simultaneously vertex-magic and edge-antimagic or simultaneously vertex-antimagic and edge-magic, respectively.
We show several results for stars, paths and cycles.

This study presents a pioneering federated multi-modal data classification model tailored for smart optical cable monitoring systems. By harnessing federated learning techniques, the model ensures data privacy while achieving performance on par with centralized models. Through comprehensive experiments spanning various modalities, including vision and auditory data, our approach showcases promising outcomes, as evidenced by accuracy and precision metrics. Furthermore, comparative analyses with centralized models highlight the superior data security and reduced network strain offered by federated learning. Moreover, we delineate the design and deployment of a smart optical cable monitoring system leveraging edge computing, accentuating the pivotal role of information technology in elevating operational efficiency within the cable monitoring domain. Through meticulous analysis and simulations, our proposed system adeptly monitors environmental variables, thereby bolstering safety and efficiency in smart optical cable monitoring applications.

The created public art sculpture is a material form that expresses the public spirit of the city. This paper proposes a deep model capable of enhancing the aesthetic quality of public art sculptures. The model uses the inverse mapping network of the augmented network to weaken the restriction of paired data sets required for training, and at the same time designs an effective loss function, that is, constructs the color and texture losses that are actively learned in training through generative adversarial rules, and enhances generative sculpture. The total variational loss of smoothness that improves the aesthetic quality of the sculpture to some extent. On this basis, this paper improves the design idea of content consistency loss. Experiments on the interaction between public art sculptures and the urban environment and the enhancement of aesthetics.

With the increasing scale of college enrollment and the increasing complexity of college teaching management, college finance department should innovate the traditional financial management mode while adapting to the reform of teaching management, and make use of the openness and real-time characteristics of Internet to improve the quality of college financial management and reduce the risk of college financial management. To this end, this paper designs a university financial system based on multi-scale deep learning. In the hardware design, the system adds multiple sensors and scans all the information in the financial database using a coordinator. In the software design, the weights that can connect the financial information of the same attribute are set by establishing a database form; according to the multilayer perceptual network topology, a full interconnection model based on multi-scale deep learning is designed to realize the system’s deep extraction of data. The experimental results show that the financial risk is based on the risk warning capability for university finance, and compared with the system under the traditional design, the university finance system designed in this time has the most categories of financial information parameters extracted.

This work suggests predicting student performance using a Gaussian process model classification in order to address the issue that the prediction approach is too complex and the data set involved is too huge in the process of predicting students’ performance. In order to prevent overfitting, a sample set consisting of the three typical test outcomes from 465 undergraduate College English students is divided into training and test sets. The cross-validation technique is used in this study. According to the findings, Gaussian process model classification can accurately predict 92% of the test set with a prediction model, and it can also forecast students’ final exam marks based on their typical quiz scores. Furthermore, it is discovered that the prediction accuracy increases with the sample set’s distance from the normal distribution; this prediction accuracy rises to 96% when test scores with less than 60 points are taken out of the analysis.

Fix integers \(k, b, q\) with \(k \ge 2\), \(b \ge 0\), \(q \ge 2\). Define the function \(p\) to be: \(p(x) = kx + b\). We call a set \(S\) of integers \emph{\((k, b, q)\)-linear-free} if \(x \in S\) implies \(p^i(x) \notin S\) for all \(i = 1, 2, \dots, q-1\), where \(p^i(x) = p(p^{i-1}(x))\) and \(p^0(x) = x\). Such a set \(S\) is maximal in \([n] := \{1, 2, \dots, n\}\) if \(S \cup \{t\}, \forall t \in [n] \setminus S\) is not \((k, b, q)\)-linear-free. Let \(M_{k, b, q}(n)\) be the set of all maximal \((k, b, q)\)-linear-free subsets of \([n]\), and define \(g_{k, b, q}(n) = \min_{S \in M_{k, b, q}(n)} |S|\) and \(f_{k, b, q}(n) = \max_{S \in M_{k, b, q}(n)} |S|\). In this paper, formulae for \(g_{k, b, q}(n)\) and \(f_{k, b, q}(n)\) are proposed. Also, it is proven that there is at least one maximal \((k, b, q)\)-linear-free subset of \([n]\) with exactly \(x\) elements for any integer \(x\) between \(g_{k, b, q}(n)\) and \(f_{k, b, q}(n)\), inclusively.

Nanoparticles have potential applications in a wide range of fields, including electronics, medicine and material research, because of their remarkable and exceptional attributes. Carbon nanocones are planar carbon networks with mostly hexagonal faces and a few non-hexagonal faces (mostly pentagons) in the core. Two types of nanocone configurations are possible: symmetric and asymmetric, depending on where the pentagons are positioned within the structure. In addition to being a good substitute for carbon nanotubes, carbon nanocones have made an identity for themselves in a number of fields, including biosensing, electrochemical sensing, biofuel cells, supercapacitors, gas storage devices, and biomedical applications. Their astonishing chemical and physical attributes have made them well-known and widely accepted in the fields of condensed matter physics, chemistry, material science, and nanotechnology. Mathematical and chemical breakthroughs were made possible by the concept of modeling a chemical structure as a chemical graph and quantitatively analyzing the related graph using molecular descriptors. Molecular descriptors are useful in many areas of chemistry, biology, computer science, and other sciences because they allow for the analysis of chemical structures without the need for experiments. In this work, the quotient graph approach is used to establish the distance based descriptors of symmetrically configured two-pentagonal and three-pentagonal carbon nanocones.

A kite \(K\) is a graph which can be obtained by joining an edge to any vertex of \(K_3\). A kite with edge set \(\{ab,\,bc,\,ca,\,cd\}\) can be denoted as \((a,\,b,\,c;\,cd)\). If every vertex of a kite in the decomposition lies in different partite sets, then we say that a kite decomposition of a multipartite graph is a gregarious kite decomposition. In this manuscript, it is shown that there exists a decomposition of \((K_m \otimes \overline{K}_n) \times (K_r \otimes \overline{K}_s) \) into gregarious kites if and only if
\[
n^2 s^2 m(m-1)r(r-1) \equiv 0 \pmod{8},
\]
where \(\otimes\) and \(\times\) denote the wreath product and tensor product of graphs respectively. We denote a gregarious kite decomposition as \(\it GK\)-decomposition.

With the rapid development of my country’s socialist market economy, the system of joint and several liability has been established in my country’s civil and commercial law and is playing an increasingly important role. There are also problems such as scattered regulations and contradictory laws and regulations at the level. Since there is no unified application principle established in judicial practice, the litigation burden caused by the recovery lawsuit also wastes a lot of trial resources. Dimensional key features distinguish confusing charges. Use regular expression technology to extract key content such as fact descriptions, defendants’ charges, relevant laws and regulations in legal documents and create JSON format documents; use stammer word segmentation and stop word list to remove stop words; use Word2Vec algorithm to represent text into vector form , establish a judicial judgment prediction model and an optimization model, and through experimental comparison, it is concluded that the performance of the model after adding focal loss is improved by 1.82%, 0.45%, 1.62%, and 1.62% compared with the cross entropy loss, and the final accuracy of the optimized model is 84.78%. , the precision rate is 87%, the recall rate is 85%, and the F1 value is 85%. The system is expected to assist judicial workers in classifying crimes with joint liability and reduce the burden of judicial workers reading many legal documents to classify crimes.

The evolution of computer science and the innovations in language teaching methodologies have paved the way for computer-assisted language learning (CALL) technology to tackle pertinent challenges. While existing CALL systems primarily emphasize vocabulary and grammar acquisition, their evaluation mechanisms often rely on a limited set of criteria, resulting in a simplistic assessment of learners’ pronunciation skills. This oversight underscores the need for a more comprehensive approach. In response, this study targets Chinese college students’ English oral proficiency and aims to enhance the conventional computerized evaluation method. Our approach involves integrating multiple assessment parameters, including pitch, speed, rhythm, and intonation. For instance, pitch assessment is grounded on frequency central feature parameters, while speech speed evaluation considers speech duration, thus enriching the evaluation framework. Through experimental validation, the efficacy of our method in evaluating pitch, speed, rhythm, and intonation has been substantiated, reaffirming its reliability.

The common bills in life include VAT invoices, taxi invoices, train invoices, plane itineraries, machine-printed invoices, etc. Most of these common bills are presented in the form of fixed form templates, so template matching can be used. , for a certain fixed template bill, manually set the rules to determine the spatial position of the key area, extract the corresponding text information, or build a model with logical semantic relationship and spatial relative relationship between the bill texts of different attributes, from the global image of the image. Identify the required key text information in the text information. However, these methods are either limited by fixed ticket templates, or cannot guarantee considerable accuracy. The electronicization of paper invoices mainly needs to go through the steps of text detection, bill recognition and text recognition. Based on this, this paper adopts the DL method. Construct a financial bill recognition model and combine experiments to explore the effectiveness and superiority of the model. The results show that our model can achieve a recognition accuracy rate of up to 91\%, and also achieve a 26\% improvement in recognition speed.

The maximum-weight perfect matching inverse issue in graph theory and text clustering are the two primary topics of this study. We suggest a novel approach to text clustering that makes use of self-encoders and BERT embeddings for feature extraction in order to increase clustering accuracy. According to experimental results, our technique enhances the clustering results greatly and performs well on numerous short text datasets. In the context of graph theory, we examine the unit paradigm inverse issue of maximum-weight perfect matching with value constraints and provide a robust polynomial-time method for its solution. In addition to effectively solving the maximum-weight perfect matching inverse issue, our technique can also produce the best weight vector configuration scheme for real-world uses. In conclusion, our work has advanced the domains of text clustering and graph theory significantly, offering fresh approaches and theoretical underpinnings for future investigations.

A brief survey on mutually orthogonal resolutions of some combinatorial designs is presented. Some \((2,w)\)-threshold schemes from mutually orthogonal resolutions of these designs are also obtained.

In the era of social media platforms like Douyin, preserving the essence of traditional Chinese culture while adapting it to contemporary trends is crucial for its continued relevance and vitality. This paper delves into the practical implications of leveraging social media for cultural communication, emphasizing communication strategies tailored to platforms like Douyin. It introduces two novel algorithms for generating Douyin information dissemination trees: one based on retweeting relationships and another optimized for rapid dissemination. Comparative experiments assess the performance of these algorithms and analyze the node distribution within dissemination trees, aiming to enhance the dissemination power of traditional culture and foster its inheritance and innovation.

The “Three Rural Issues” has always been the top priority of my country’s economic development, which related to the construction process of modern agriculture, the development effect of agricultural economy and the development speed of the national economy. In recent years, the state and local governments have taken the construction of new countryside as the starting point, seriously discussed many problems faced by the agricultural economy in the process of development, and took targeted measures to effectively solve them, which better promoted the construction of new countryside. Agriculture plays an important role in the national economy and is the foundation of national economic development. Under the background of new rural construction, we must strengthen the management of agricultural economy. This paper analyzes the main contents, characteristics and existing problems of agricultural sustainable development under the background of new rural construction, and puts forward solutions that hope to be discussed by a wide range of partners.

Zhou, Xu and Sun [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional \((a,b,k)\)-critical covered graphs, Information Processing Letters 152(2019)105838] defined the concept of a fractional \((a,b,k)\)-critical covered graph, namely, a graph \(G\) is a fractional \((a,b,k)\)-critical covered graph if after removing any \(k\) vertices of \(G\), the remaining graph of \(G\) is a fractional \([a,b]\)-covered graph. In this paper, we prove that a graph \(G\) with \(\delta(G)\geq2+k\) is fractional \((2,b,k)\)-critical covered if \(bind(G)>\frac{b+k}{b-1}\), where \(k\geq0\) and \(b\geq2+k\) are two integers.

In this paper, we study the submodular hitting set problem (SHSP), which is a variant of the hitting set problem. In the SHSP, we are given a supergraph \(H = (V, \mathcal{C})\) and a nonnegative submodular function on the set \(2^{V}\). The objective is to determine a vertex subset to cover all hyperedges such that the cost of submodular covering is minimized. Our main work is to present a rounding algorithm and a primal-dual algorithm respectively for the SHSP and prove that they both have the approximation ratio \(k\), where \(k\) is the maximum number of vertices in all hyperedges.

In recent years, there is a lot of interest in the topic of conveying the groups of planar graphs with an unvarying metric dimension. A few types of planar graphs have recently had their locating number (or metric dimension) determined, and an outstanding problem concerning these graphs was brought up that: Illustrate the types of planar graphs \(\Upsilon\) that can be generated from a graph \(\Phi\) through the addition of more edges to \(\Phi\), such that \(dim(\Phi)=dim(\Upsilon)\) and \(\mathbb{V}(\Phi)=\mathbb{V}(\Upsilon)\). While proceeding in a similar directives, we identify two families of radially identical planar graphs with unaltered metric dimension in this study: \(\digamma_{n,m}\) and \(\gimel_{n,m}\). We do this by establishing that \(dim(\digamma_{n,m})=dim(\gimel_{n,m})\) and \(\mathbb{V}(\digamma_{n,m})=\mathbb{V}(\gimel_{n,m})\), respectively. We acquire another family of a radially symmetrical plane graph (i.e., \(\daleth_{n,m}\)) with a constant metric dimension. We show that all the vertices of these classes of the plane graphs can potentially be identified with just three well-chosen nodes.

The purpose of this work was to use machine learning classification models and hyperspectral camera technologies to create a model of surface damage to garlic. 140 of the 184 garlic plants of which 44 were used for test validation were pre-treated for surface damage. First, we examined the data in ENVI under various damage scenarios using the normalised vegetation index (NDVI) approach. 579 pixels were then chosen for the training of the logistic regression model. Finally, we used 54 garlic bulbs to practically validate the model. Although tiny regions could not be precisely identified, the mouldy portion of the garlic’s surface could be identified using the NDVI technique. 90% accuracy was attained using the 90% classification model constructed using the logistic regression approach. Garlic’s surface damage, even at first mild ones, was correctly identified. The creation of this model for identifying garlic damage lowers the cost of detecting garlic damage and broadens the use of hyperspectral technologies in garlic detection.

In this paper, the sensor is applied to the collection of rock parameter data. Aiming at the classification and evaluation of stability (i.e. rock quality), an attribute recognition model for the classification and evaluation of surrounding rock quality of underground engineering is established. Using multi-source data fusion and orthogonal numerical simulation test methods, the effects of rock mechanics parameters on the horizontal convergence of the tunnel, the settlement of the vault and the plastic zone coefficient are studied. Six factors (elastic modulus, Poisson’s ratio, internal friction angle, tensile strength, cohesion and density) and three levels of orthogonal experimental solutions were selected. The method of defining similar weight by using similar number to determine the weight of evaluation index, so as to calculate the comprehensive attribute measure, and apply confidence criteria to identify the stability of rock samples. Through the analysis and evaluation of rock mass quality classification of underground engineering, the application of the model and the evaluation method of rock mass quality classification are explained. The test results match the orthogonal test results; Considering the stability of tunnel envelope, the horizontal convergence, vault settlement and plastic zone coefficient after excavation should be comprehensively considered.

This paper proposes a comprehensive framework for testing and evaluating automatic ambulances, crucial for ensuring their reliability and safety in real-world scenarios. The framework includes designing test scenarios with varying complexity, covering environmental factors like road conditions, weather, and obstacles. An evaluation index system is introduced, comprising driving security, ride comfort, intelligence, and efficiency. Methodologies for calculating indicator weights, using the CRITIC and AHP methods, are presented to ensure fair evaluation. Additionally, evaluation methods including qualitative and quantitative techniques, such as grey correlation theory, are discussed. The test results show that the assessment results of the traditional fuzzy comprehensive evaluation method and the grey correlation theory evaluation method are highly consistent. The change in vehicle speed has less of an effect on accuracy during the real-time assessment process when the time interval is set to 0.1s, and the evaluation time of 0.098s can satisfy the requirement that the planning time of autonomous driving vehicles be shorter than 200 ms.

In recent years, the use of smart data analysis method to predict the stock price is financial technology; important issues in the field of finch. However, there are many technical indicators and human subjective factors will affect the stock price forecast, so we must effectively grasp the important influence indicators to improve the accuracy of stock price forecast. Therefore, this study uses four machine learning algorithms to predict and analyze the stock price fluctuation through the screening process of technical indicators, and then selects the important technical indicators. In addition, due to the uncertainty and fuzziness of the attributes of technical indicators and human subjective judgment, this study uses the fuzzy inference method to construct the fuzzy inference system to predict the rise and fall of stock price, and proposes the prediction method of the range of the rise and fall of stock price. Finally, this paper makes an empirical analysis on the stock price data of three companies. The results show that the accuracy of stock price forecast is more than 82.13%, and the average accuracy of stock price forecast is more than 83%. Therefore, the fuzzy inference prediction system proposed in this study not only has the theoretical basis, but also can effectively predict the trend and range of stock price, which has practical value and contribution to investors.

Removing clouds is an essential preprocessing step in analyzing remote sensing images, as cloud-based overlays commonly occur in optical remote sensing images and can significantly limit the usability of the acquired data. Deep learning has exhibited remarkable progress in remote sensing, encompassing scene classification and change detection tasks. Nevertheless, the appli-cation of deep learning techniques to cloud removal in remote sensing images is currently con-strained by the limited availability of training datasets explicitly tailored for neural networks. This paper presents the Remote sensing Image Cloud rEmoving dataset (RICE) to address this challenge and proposes baseline models incorporating a convolutional attention mechanism, which has demonstrated superior performance in identifying and restoring cloud-affected regions, with quantitative results indicating a 3.08% improvement in accuracy over traditional methods. This mechanism empowers the network to comprehend better the spatial structure, local details, and inter-channel correlations within remote sensing images, thus effectively addressing the diverse distributions of clouds. Moreover, by integrating this attention mechanism, our models achieve a crucial comparison advantage, outperforming existing state-of-the-art techniques in terms of both visual quality and quantitative metrics. We propose adopting the Learned Per-ceptual Image Patch Similarity metric, which emphasizes perceptual similarity, to evaluate the quality of cloud-free images generated by the models. Our work not only contributes to advancing cloud removal techniques in remote sensing but also provides a comprehensive evaluation framework for assessing the fidelity of the generated images.

Let \(g,f:V(G)\rightarrow\{0,1,2,3,\cdots\}\) be two functions satisfying \(g(x)\leq f(x)\) for every \(x\in V(G)\). A \((g,f)\)-factor of \(G\) is
defined as a spanning subgraph \(F\) of \(G\) such that \(g(x)\leq d_F(x)\leq f(x)\) for every \(x\in V(G)\). An \((f,f)\)-factor is simply called
an \(f\)-factor. Let \(\varphi\) be a nonnegative integer-valued function defined on \(V(G)\). Set
\[
D_{g,f}^{even}=\Big\{\varphi: g(x)\leq\varphi(x)\leq f(x) \text{ for every } x\in V(G) \text{ and } \sum\limits_{x\in V(G)}\varphi(x) \text{ is even}\Big\}.
\]
If for each \(\varphi\in D_{g,f}^{even}\), \(G\) admits a \(\varphi\)-factor, then we say that \(G\) admits all \((g,f)\)-factors. All \((g,f)\)-factors
are said to be all \([1,k]\)-factors if \(g(x)\equiv1\) and \(f(x)\equiv k\) for any \(x\in V(G)\). In this paper, we verify that for a connected multigraph
\(G\) satisfying \(N_G(X)=V(G) \text{ or } |N_G(X)|>\Big(1+\frac{1}{k+1}\Big)|X|-1\) for every \(X\subset V(G)\), \(kG\) admits all \([1,k]\)-factors, where
\(k\geq2\) is an integer and \(kG\) denotes the graph derived from \(G\) by replacing every edge of \(G\) with \(k\) parallel edges.

We consider finitely presented groups \(G_{mn}\) as follows:
\[
G_{mn}=\left\langle x, y \mid {x^{m}}={y^{n}}=1, {[x, y]^{x}}=[x, y], {[x, y]^{y}}=[x, y] \right\rangle m, n\ge 2.
\]
In this paper, we first study the groups \(G_{mn}\). Then by using the properties of \(G_{mm}\) and \(t-\)Fibonacci sequences in
finitely generated groups, we show that the period of \(t-\)Fibonacci sequences in \(G_{mm}\) are a multiple of \(K(t, m)\). In particular for \(t \geq 3\) and \(p=2\), we prove \({{LEN}_{t}({{G}_{pp}})}= 2K(t,p)\).

In this paper, we consider a degree sum condition sufficient to imply the existence of \(k\) vertex-disjoint chorded cycles in a graph \(G\).
Let \(\sigma_4(G)\) be the minimum degree sum of four independent vertices of \(G\).
We prove that if \(G\) is a graph of order at least \(11k+7\) and \(\sigma_4(G)\ge 12k-3\) with \(k\ge 1\),
then \(G\) contains \(k\) vertex-disjoint chorded cycles.
We also show that the degree sum condition on \(\sigma_4(G)\) is sharp.

This study addresses challenges in rural planning amid economic growth and the implementation of rural revitalization policies. The aim is to enhance the integration of cultural and ecological elements in rural areas, combating issues such as the fading village atmosphere and incomplete agricultural chains. The research focuses on optimizing the random forest algorithm to explore innovative approaches to landscape planning and design for rural human settlements. Using the moving window method, the study computes two-dimensional and three-dimensional landscape indices in surrounding villages of Beijing, conducting a multi-scale analysis of the living environment. Power function fitting indicates an optimal window size of approximately 700 meters for studying the relationship between art patterns and three-dimensional landscape patterns in the rural area. The findings offer insights into improving rural living environments through effective landscape planning and design influenced by artistic modes.

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.