This paper applies smart technologies to urban rain garden design and analyzes the hydrological effects based on urban smart rain garden technologies. The SWMM model is used to simulate runoff water quantity and quality under the environment of long-term and continuous rainfall events in urban areas. Building area A is selected as the case study object of this paper, and its geographic location and precipitation data are analyzed to preliminarily explain the hydrological conditions of the case study area. Based on the SWMM model, the model pipe network generalization and other operations are carried out to establish the SWMM model of the study area. The SWMM model is calibrated in terms of the calibration of the model’s parameters and the feasibility of the structured network SWMM model to verify the validity of the SWMM model of the study area and its catchment delineation method. Based on the urban smart rain garden technology, the LID module is added to the SWMM model of the study area and the hydrological effects under different scenarios such as combined LID are analyzed. Each LID measure can have a certain reduction effect on the combined runoff coefficient and total runoff. The combined LID measures in this paper have the best reduction effect, with the reduction rate of the integrated runoff coefficient over 35% and the total runoff over 50% in the 2h rainfall event. The combined LID scheme has the best reduction effect on the flood peak, and the reduction rate can reach more than 40% in both 2h rainfall events.
Curriculum Civics refers to the integration of Civics elements into the teaching of professional courses, so that courses other than Civics courses can also play the role of Civics teaching. In this paper, we study a knowledge mapping-based content generation technology for teaching course Civics and Politics, so that the knowledge of Civics and Politics courses can be integrated and visualized. The knowledge points, concepts, definitions and other information of the course Civics and Politics are extracted in the form of Civics and Politics knowledge triples. Through the extraction of the knowledge entity of curriculum Civics and politics, the relationship between semi-structured data and unstructured data is extracted to realize the integration of knowledge and content generation. After achieving content generation, the generated content is personalized through a deep reinforcement learning recommendation algorithm based on diversity optimization. Taking the two courses of Engineering Cost Management and Engineering Economics in the engineering management specialty as an example, it is found that the proposed knowledge graph construction method has an accuracy rate of 96.2%, which is able to effectively establish the knowledge association between the civic elements and the elements of professional knowledge, and realize the mining and generation of the civic elements. Meanwhile, the DDRL-Base recommendation algorithm achieves the optimum in accuracy, recall and F1 value indexes, and optimizes the problems such as cold start and sparse data in resource matrix, which improves the effect of recommending the Civics and Politics teaching content of the course.
The technical analysis of conventional tennis sports basically focuses on individual studies, with less research on the basic theory of tennis, and the theoretical analysis of tennis trajectory is even rarer. In this study, based on the calculation equations of the main forces during tennis movement, the dynamics analysis of tennis serve movement is carried out, and the three-dimensional trajectory equations of tennis serve are established. Then, based on the ODE dynamics engine technology, the simulation platform of tennis serve is built to realize the simulation and visualization analysis of tennis trajectory. Since the simulation system beat frequency is 1000Hz, the time difference between tennis simulation and actual movement is the smallest, so the frequency of 1000Hz is chosen for the simulation study of tennis serve trajectory. The simulation results show that under the same hitting height and ball angle, the larger the initial velocity of the tennis ball is, the farther the X-axis landing point is from the center line. In addition, under the consideration of air resistance and Malnus force, the difference between the Y-axis landing point of tennis ball when the initial serve angle is 30° and 60° is 1.81098 m. The present study provides a certain reference for the in-depth study of the serving strategy of tennis ball, and at the same time, it also provides a certain theoretical basis for the improvement of the tennis players’ training method and technical playing style.
The temperature gradient formed by cooling and heat dissipation after shutdown of aero-engine will lead to thermal bending of rotor, which is also the main reason for bending vibration of rotor after engine secondary start-up. In this paper, the rotor system model of a GTF motor considering the gearbox structure is established, and the thermal bending deformation of the fan-gearbox-low pressure rotor caused by temperature gradient is analyzed. The critical speed of the rotor system considering the temperature field is calculated and the vibration characteristics of the engine after the second start are analyzed, which provides a reference for the design of the rotor system of GTF engine. The results show that the rotor mainly appears hot bending deformation in the direction of vertical axis, especially in the joint of disc axis. The large bearing stiffness of the gearbox has obvious inhibition on the hot bending deformation of the rotor, and the effect is obvious when the bearing stiffness is above 1E6. The vibration characteristics of rotor are greatly affected by temperature field. The amplitude of rotor system is larger and the sensitivity of gearbox structure is higher under the influence of temperature field. The amplitude is also the largest when the thermal bending amount is maximum about 10min, and the amplitude decreases by 50% after 40min. The bearing stiffness of the gearbox has a great influence on the vibration characteristics of the rotor system with hot bending deformation, and the vibration suppression effect is best when the bearing stiffness is between 1E6 and 1E8, and the peak point above 1E8 is close to the operating speed of the fan, which is bad for the safe operation of the engine.
The Cascaded Integrator Comb (CIC) decimation filter is a pivotal technology extensively employed in digital signal processing (DSP). This paper delves into a comprehensive examination of the CIC algorithm within software-defined radio (SDR) systems from the perspective of parallel computing and introduces a novel Non-Recursive Implementation (NR-I) on an NVIDIA GPU using CUDA. The NR-I approach significantly reduces computational load by unfolding the recursive CIC structure with pre-derived Unfold Factors. Further optimization was achieved through data-transfer enhancements using PM Implementation (PM-I) and ODT Implementation (ODT-I). Experimental results demonstrate that NR-I achieves a speedup of over 449.48. Additionally, the data-transfer optimizations resulted in substantial performance improvements, with PM-I and ODT-I reducing execution time by 43.24% and 64.22%, respectively. The GPU implementation’s speedup is significantly greater than that of OpenMP, ranging from 3.34 to 10.22 times. These results underscore the effectiveness of the proposed Non-Recursive Implementation in accelerating time-intensive and data-intensive computations.
Sustainable agricultural development is a key component of the rural revitalization strategy, and strengthening the guidance and support for sustainable agricultural development is an inevitable choice for improving agricultural production capacity and realizing rural revitalization. The study constructs an evaluation system of sustainable agricultural development based on four dimensions: economic opportunity, social well-being, environmental quality, and climate action, selects relevant index data of each province from 2004 to 2022, and adopts a multi-level factor analysis method to comprehensively evaluate the sustainable agricultural development as well as the dynamic distribution of 31 provinces in China. The results show that Henan leads other provinces in economic opportunities with a score of 1.21, and Hebei ranks first in social well-being with abundant human resources and policy support. In the level of regional sustainable agricultural development, there is an uneven distribution pattern of “North > Central > South”. From the dynamic distribution of agricultural sustainable development in 31 provinces from 2004 to 2022, it is concluded that the development trend of agricultural sustainable development in China is better, and the gap between provinces has been narrowed. Finally, policy recommendations are put forward based on the situation of agricultural sustainable development to provide reference for the subsequent work on agricultural sustainable development.
The integration of Civics elements into the EFL classroom is an organic supplement and deepening of the teaching content and materials, while EFL Civics classroom teaching is a powerful means to strengthen the deep and longitudinal development of students’ critical thinking. This paper discusses the relationship between EFL Civics classroom teaching and the development of critical thinking ability from the theoretical and practical levels respectively. On the basis of existing research, the evaluation index of students’ critical thinking ability is proposed. The CVM coefficient of variation method is improved, and the ICVM and BP neural network algorithm are combined to constitute the evaluation model of students’ critical thinking ability based on ICVM and BP neural network. According to the evaluation process, the level of students’ critical thinking ability after EFL-based Civics classroom teaching is derived. It also integrates teachers’ and students’ evaluation of the effect of English Civics elements integrated into the EFL classroom, and finally obtains the practical teaching effect of the EFL Civics classroom. The overall mean value in the teacher’s side is greater than 3.5 points, which indicates that teachers are basically positive about the effect of integrating Civics in EFL courses, and basically agree with the positive impact of English Civics elements on EFL classroom teaching. Based on the evaluation results of ICVM and BP model, the evaluation scores of students’ critical thinking skills and critical thinking monitoring are higher than the evaluation scores of critical thinking tendency, i.e., the elements of English Thinking can be effectively integrated into the EFL classroom and promote the development of students’ critical thinking skills.
Digital teaching strategies can significantly stimulate students’ interest in learning and provide personalized learning pathways. This paper proposes a multimodal action recognition method that integrates the word vector method, and designs a teaching decision optimization strategy based on this idea. Firstly, we compare the information of different modalities, complete the construction of multimodal action recognition network through the processing of image information and optical flow information, and combine the word vector method to guide the semantic learning of students’ actions. Then the design and realization process of the teaching decision aid system is introduced. Based on the above proposed action recognition method to collect students’ classroom behavior data for model training to be used in the system, the system consists of four modules: model training, classroom data collection, behavior recognition and data presentation. After the data collection, the action recognition of student behavior is carried out to provide teachers with feedback on student behavior information and assist them in making teaching decisions. In this paper, the above algorithms and systems have been verified by relevant experiments. After comparison with other algorithms, it is verified that the multimodal action recognition method designed in this paper, which incorporates the word vector method, has a high accuracy rate. In the comparison of the overall quality of instructional design decisions, the average value of the instructional decision aid system in this paper is 17.35, which is higher than the average score of excellent human teachers in the overall quality of instructional design decisions, indicating that the instructional decision aid system designed in this paper achieves the optimization of instructional decisions and reaches the level of excellent decisions.
This paper proposes a user electricity data mining method based on deep learning and improved locust optimization algorithm, and at the same time adopts the Pearson correlation coefficient method to reduce its dimension to improve the data mining effect of linear weighted KFCM algorithm. In order to deal with the electricity demand of massive electricity customers, the user electricity demand forecasting model is constructed based on the Extreme Learning Machine ELM algorithm by combining the relationship between short-term loads and factors of electricity customers. Construct the service optimization model with the maximization of benefit index as the objective function, and use the BAS algorithm to solve the optimal solution in order to achieve the effect of user service optimization. Determine the experimental platform and model parameters, and carry out an example analysis of demand forecasting and service optimization for electricity users.C class users have a small electricity load except for breakfast and dinner, and the maximum time period of the electricity load is from 18:00 to 20:00 hours. Combined with MAPE, the ELM model improves 4.57% than SVR, 21.9% than LSTM, and 34.37% than ARIMA, which indicates that the ELM model is more effective and higher in demand forecasting for electricity users. In addition, the optimal solution of the effect of the BAS algorithm is 69 yuan, 102 yuan and 49 yuan higher than that of the GA algorithm in terms of dividend transmission benefit, energy saving and emission reduction benefit, and electricity right trading benefit, respectively, and the optimal solution based on the BAS algorithm is closer to the actual benefit value, which fully proves the effectiveness of the service optimization model based on the BAS algorithm.
Smart contract technology based on artificial intelligence background is gradually becoming a brand-new path to improve the efficiency of economic transactions due to its unique advantages. This paper initially explores the impact of smart contract technology on economic transaction efficiency through empirical analysis of models and data. The credit mechanism is introduced as an intermediate variable to analyze its mediating effect in the process of improving economic transaction efficiency by smart contract technology. The optimization of Fabric transaction mechanism is realized by using the improved credit model, which further exerts the role of smart contract technology in enhancing economic transaction efficiency. The principal component analysis is used to calculate the comprehensive score of economic transaction efficiency before and after the optimization of smart contract trading mechanism to show the effect of the development of smart contract technology on the improvement of economic transaction efficiency. This paper concludes that the development of smart contract technology will significantly and positively promote the improvement of economic transaction efficiency through benchmark regression analysis, mediation effect test and other methods. After the optimization of smart contract transaction mechanism, the comprehensive score of economic transaction efficiency produces significant improvement compared with the pre-optimization period, in which the average value of the comprehensive score of transaction efficiency in Guangdong, Jiangsu, Shanghai, and Beijing is improved by 20.18%, 24.52%, 33.77%, and 35.54%, respectively. It further indicates that smart contract technology is an effective path to improve economic transaction efficiency.
In the context of globalization where market competition is becoming more and more intense, strategic human resource management (SHRM) plays an important role in enhancing corporate competitiveness. Through structural equation modeling and multiple linear regression methods, this paper reveals the complex paths of SHRM perceptions on employee proactive behaviors, and uses convolutional neural network pairs to explore the nonlinear relationships in the model and validate the results of SEM analysis. Overall, SHRM perception has a significant positive effect on employee proactive behavior (β=0.254, p<0.001). The indirect effect values of job self-efficacy and conceptual psychological contract as mediators were 0.1043 and 0.1726, respectively, which were both positive, i.e., they played a mediating role in the mechanistic effect of SHRM perceptions on employees' proactive behaviors. Insider identity perception, on the other hand, has a significant positive moderating effect between SHRM perception and employee-initiated behavior (β=0.09, p<0.01). The importance of independent variables using CNN model was ranked in descending order as: conceptual psychological contract, job self-efficacy, SHRM perception, job category, and insider identity perception, which was consistent with the results of SEM analysis, revealing the significance of convolutional neural network in optimizing human resource management strategies and enhancing employee motivation.
The rapid development of information technology makes intelligent decision support system play an increasingly important role in economic standardized management. The Intelligent Decision Support System (IDSS) constructed in this paper includes interaction layer, analysis layer and data layer. The system standardizes the management of enterprise economy through strategic forecasting and decision analysis, economic planning and control, and economic analysis. The study combines the fuzzy hierarchical analysis method (FAHP) and the fuzzy comprehensive evaluation method (FCE) to evaluate the standardized level of economic management of enterprise A. The evaluation score of the standardized level of enterprise A’s economic management is , which is greater than 80, and it belongs to the grade of “good”. It shows that the intelligent decision support system constructed based on this paper can effectively help standardize the management of enterprise economy.
With the development of renewable energy technology and the pursuit of sustainable development in the construction industry, the design of direct-soft photovoltaic systems integrated with buildings has become an important research direction. In this paper, a variety of photovoltaic power generation modules are selected and combined with building roof functions to design a solar photovoltaic building integration system. In addition, this paper constructs a multi-objective optimization configuration model, improves the multi-objective particle swarm algorithm, and analyzes the optimization effect of the improved particle swarm algorithm on the photovoltaic building integration system by using multiple sets of test functions and evaluation indexes, combined with a number of experiments. The improved particle swarm algorithm in this paper converges to the optimal value of 0.21 when iterating to 25 rounds. And with the increase of the number of nodes, the optimized particle swarm algorithm, the distribution of node voltages in the vicinity of the standard voltage. The PV building integrated system designed in this paper still has a generation output efficiency higher than 85% after 20 years, which shows good stability of power generation. And the power generation in its whole life cycle is about 1645710kwh, which greatly reduces the consumption of conventional energy. In conclusion, the PV building integrated system in this paper not only has significant advantages in terms of capacity efficiency, but also shows strong potential for environmental protection.
As the birthplace of national culture, traditional villages can convey cultural and social natures through spatial configuration. Based on the theory of spatial syntax, this paper combines the genetic algorithm to design the fitness function for optimization, and selects the streets and lanes of Wengji Village as the research sample, focusing on the analysis of its morphological evolution mechanism from 1975 to 2020. Through quantitative analysis, it is found that although the streets and alleys of Wengji Village show spatial scale expansion due to social and economic development, the village streets and alleys can still maintain the original spatial texture and style. The integration degree, selectability, synergy (0.4273~0.6395) and comprehensibility (0.3744~0.5761) of the streets and alleys in Wengji Village are all characterized by increasing, indicating that the spatial accessibility, spatial openness and spatial wholeness of the streets and alleys in Wengji Village have been improved. However, the degree of synergy and comprehensibility are still lower than 0.7, and there is some room for optimization of the wholeness and cognizability of the streets and lanes of Wengji Village. It is necessary to protect and continue the overall structure of the village, optimize and integrate the key spaces of the village, and rationally control the development process of the village, so as to promote the protection of the spatial form of the streets and lanes of Wengji Village and the continuation of the cultural lineage.
In the context of big data, many problems connected with usage of classical techniques in computing large and complicated data have emerged. For a true disruption of silicon and computational power, there is quantum computing which is poised to redefine itself in the future. Quantum computing is the area of study for this research; real-time big data processing with a specific emphasis on speed. In a sequence of experiments, the performance of quantum algorithms was compared to the performance of classical algorithms regarding large-scale data processes. These findings imply that the compared quantum algorithm has enhanced the processing time while providing on average 70%-time reduction as well as 30 percent improvement of the computational efficiency. Besides, the scalability of quantum computing is also better; it remains effective when used on large datasets, and it has an accuracy of 95% that is higher than classical one. This outcome depiction the power of quantum computing in the alteration of data processing tactics. However, there are some issues like quantum decoherence and error rates, which are guaranteeing the non-stability of quantum computing, but they are expecting more improvements in the field of quantum hardware and error correction. From this study, it consequently becomes clear why the advancement of quantum technology should continue and for what; to meet the challenges of big data.
Let \(G\) be a \((p,q)\) graph. Let \(f\) be a function from \(V(G)\) to the set \(\{1,2,\ldots, k\}\) where \(k\) is an integer \(2< k\leq \left|V(G)\right|\). For each edge \(uv\) assign the label \(r\) where \(r\) is the remainder when \(f(u)\) is divided by \(f(v)\) (or) \(f(v)\) is divided by \(f(u)\) according as \(f(u)\geq f(v)\) or \(f(v)\geq f(u)\). \(f\) is called a \(k\)-remainder cordial labeling of \(G\) if \(\left|v_{f}(i)-v_{f}(j)\right|\leq 1\), \(i,j\in \{1,\ldots , k\}\) where \(v_{f}(x)\) denote the number of vertices labeled with \(x\) and \(\left|\eta_{e}(0)-\eta_{o}(1)\right|\leq 1\) where \(\eta_{e}(0)\) and \(\eta_{o}(1)\) respectively denote the number of edges labeled with even integers and number of edges labeled with odd integers. A graph with admits a \(k\)-remainder cordial labeling is called a \(k\)-remainder cordial graph. In this paper we investigate the \(4\)-remainder cordial labeling behavior of Prism, Crossed prism graph, Web graph, Triangular snake, \(L_{n} \odot mK_{1}\), Durer graph, Dragon graph.
Behera and Panda defined a balancing number as a number b for which the sum of the numbers from \(1\) to \(b – 1\) is equal to the sum of the numbers from \(b + 1\) to \(b + r\) for some r. They also classified all such numbers. We define two notions of balancing numbers for Farey fractions and enumerate all possible solutions. In the stricter definition, there is exactly one solution, whereas in the weaker one all sufficiently large numbers work. We also define notions of balancing numbers for levers and mobiles, then show that these variants have many acceptable arrangements. For an arbitrary mobile, we prove that we can place disjoint consecutive sequences at each of the leaves and still have the mobile balance. However, if we impose certain additional restrictions, then it is impossible to balance a mobile.
For a graph G and for non-negative integers p, q, and r, the triplet \((p, q, r)\) is said to be an admissible triplet if \(3p + 4q + 6r = |E(G)|\). If G admits a decomposition into p cycles of length 3, q cycles of length 4, and r cycles of length 6 for every admissible triplet \((p, q, r)\), then we say that G has a \(\{C_{3}^{p}, C_{4}^{q}, C_{6}^{r}\}\)-decomposition. In this paper, the necessary conditions for the existence of \(\{C_{3}^{p}, C_{4}^{q}, C_{6}^{r}\}\)-decomposition of \(K_{\ell, m, n} (\ell \leq m \leq n)\) are proved to be sufficient. This affirmatively answers the problem raised in Decomposing complete tripartite graphs into cycles of lengths 3 and 4, Discrete Math. 197/198 (1999), 123-135. As a corollary, we deduce the main results of Decomposing complete tripartite graphs into cycles of lengths 3 and 4, Discrete Math., 197/198, 123-135 (1999) and Decompositions of complete tripartite graphs into cycles of lengths 3 and 6, Austral. J. Combin., 73(1), 220-241 (2019).
A graph G(V, E) is Γ-harmonious when there is an injection f from V to an Abelian group Γ such that the induced edge labels defined as w(xy) = f(x) + f(y) form a bijection from E to Γ. We study Γ-harmonious labelings of several cycles-related classes of graphs, including Dutch windmills, generalized prisms, generalized closed and open webs, and superwheels.
If Γ is a finite group and G a graph such that Aut(G) ≡ Γ acts regularly on V(G), then we say that G is a graphical regular representation (GRR) of Γ. The question asking which finite groups have at least one GRR was an important question in algebraic graph theory and it was completely solved as a result of work done by several researchers. However, it remains a challenge to discern whether a group known to have GRRs has GRRs with specific properties, such as being trivalent. In this paper, we shall be deriving simple conditions on the parameters of a subset of a dihedral group for easily constructing trivalent graphical regular representations (GRR) of the group. Specifically, we shall prove the following:
Let n be an odd integer greater than 5 and let r, s, and t be integers less than n such that the difference of any two of them is relatively prime to n. If 3r – 2s = t (mod n), then Cay(Dn, {abr, abs, abt}) is a GRR of Dn.
We will also be looking at very convenient corollaries of this result. But another main aim of this paper is to show how a simple use of Schur rings can be used to derive such results. This paper therefore also serves as a review of some basic results about Schur rings which we feel should be among the standard armory of an algebraic graph theorist.
This paper presents an investigation of a modified Leslie-Gower predator-prey model that incorporates fractional discrete-time Michaelis-Menten type prey harvesting. The analysis focuses on the topology of nonnegative interior fixed points, including their existence and stability dynamics. We derive conditions for the occurrence of flip and Neimark-Sacker bifurcations using the center manifold theorem and bifurcation theory. Numerical simulations, conducted with a computer package, are presented to demonstrate the consistency of the theoretical findings. Overall, our study sheds light on the complex dynamics that arise in this model and highlights the importance of considering fractional calculus in predator-prey systems with harvesting.
For a set \( S \) of vertices in a connected graph \( G \), the multiplicative distance of a vertex \( v \) with respect to \( S \) is defined by \(d_{S}^{*}(v) = \prod\limits_{x \in S, x \neq v} d(v,x).\) If \( d_{S}^{*}(u) \neq d_{S}^{*}(v) \) for each pair \( u,v \) of distinct vertices of \( G \), then \( S \) is called a multiplicative distance-locating set of \( G \). The minimum cardinality of a multiplicative distance-locating set of \( G \) is called its multiplicative distance-location number \( loc_{d}^{*}(G) \). If \( d_{S}^{*}(u) \neq d_{S}^{*}(v) \) for each pair \( u,v \) of distinct vertices of \( G-S \), then \( S \) is called an external multiplicative distance-locating set of \( G \). The minimum cardinality of an external multiplicative distance-locating set of \( G \) is called its external multiplicative location number \( loc_{e}^{*}(G) \). We prove the existence or non-existence of multiplicative distance-locating sets in some well-known classes of connected graphs. Also, we introduce a family of connected graphs such that \( loc_{d}^{*}(G) \) exists. Moreover, there are infinite classes of connected graphs \( G \) for which \( loc_{d}^{*}(G) \) exists as well as infinite classes of connected graphs \( G \) for which \( loc_{d}^{*}(G) \) does not exist. A lower bound for the multiplicative distance-location number of a connected graph is established in terms of its order and diameter.
Earlier optimal key pre\(-\)distribution schemes (KPSs) for distributed sensor networks (DSNs) were proposed using combinatorial designs via transversal designs, affine, and partially affine resolvable designs. Here, nearly optimal KPSs are introduced and a class of such KPSs is obtained from resolvable group divisible designs. These KPSs are nearly optimal in the sense of local connectivity. A metric for the efficiency of KPSs is given. Further, an optimal KPS has also been proposed using affine resolvable \( L_{2} \)-type design.
We study the nonzero algebraic real algebras \( A \) with no nonzero joint divisor of zero. We prove that if \( Z(A) \neq 0 \) and \( A \) satisfies one of the Moufang identities, then \( A \) is isomorphic to \( \mathbb{R} \), \( \mathbb{C} \), \( \mathbb{H} \), or \( \mathbb{O} \). We show also that if \( A \) is power-associative, flexible, and satisfies the identity \( (a,a,[a,b])=0 \), then \( A \) is isomorphic to \( \mathbb{R} \), \( \mathbb{C} \), \( \mathbb{H} \), or \( \mathbb{O} \). Finally, we prove that \( \mathbb{R} \), \( \mathbb{C} \), \( \mathbb{H} \), and \( \mathbb{O} \) are the only algebraic real algebras with no nonzero divisor of zero satisfying the middle Moufang identity, or the right and left Moufang identities.
The metric dimension of a graph is the smallest number of vertices such that all vertices are uniquely determined by their distances to the chosen vertices. The corona product of graphs \( G \) and \( H \) is the graph \( G \odot H \) obtained by taking one copy of \( G \), called the center graph, \( |V(G)| \) copies of \( H \), called the outer graph, and making the \( j^{th} \) vertex of \( G \) adjacent to every vertex of the \( j^{th} \) copy of \( H \), where \( 1 \leqslant j \leqslant |V(G)| \). The Join graph \( G + H \) of two graphs \( G \) and \( H \) is the graph with vertex set \( V(G + H)=V(G) \cup V(H) \) and edge set \( E(G + H)=E(G) \cup E(H) \cup \{uv :u \in V(G),v \in V(H)\} \). In this paper, we determine the Metric dimension of Corona product and Join graph of zero divisor graphs of direct product of finite fields.
The secure edge dominating set of a graph \( G \) is an edge dominating set \( F \) with the property that for each edge \( e \in E-F \), there exists \( f \in F \) adjacent to \( e \) such that \( (F-\{f\})\cup \{e\} \) is an edge dominating set. In this paper, we obtained upper bounds for edge domination and secure edge domination number for Mycielski of a tree.
In this paper we contribute to the literature of computational chemistry by providing exact expressions for the detour index of joins of Hamilton-connected (\(HC\)) graphs. This improves upon existing results by loosening the requirement of a molecular graph being Hamilton-connected and only requirement certain subgraphs to be Hamilton-connected.
The geometrical properties of a plane determine the tilings that can be built on it. Because of the negative curvature of the hyperbolic plane, we may find several types of groups of symmetries in patterns built on such a surface, which implies the existence of an infinitude of possible tiling families. Using generating functions, we count the vertices of a uniform tiling from any fixed vertex. We count vertices for all families of valence \(5\) and for general vertices with valence \(6\), with even-sized faces. We also give some general results about the behavior of the vertices and edges of the tilings under consideration.
This study extends the concept of competition graphs to cubic fuzzy competition graphs by introducing additional variations including cubic fuzzy out-neighbourhoods, cubic fuzzy in-neighbourhoods, open neighbourhood cubic fuzzy graphs, closed neighbourhood cubic fuzzy graphs, cubic fuzzy (k) neighbourhood graphs and cubic fuzzy [k]-neighbourhood graphs. These variations provide further insights into the relationships and competition within the graph structure, each with its own defined characteristics and examples. These cubic fuzzy CMGs are further classified as cubic fuzzy k-competition graphs that show competition in the \(k\)th order between components, \(p\)-competition cubic fuzzy graphs that concentrate on competition in terms of membership degrees, and \(m\)-step cubic fuzzy competition graphs that analyze competition in terms of steps. Further, some related results about independent strong vertices and edges have been obtained for these cubic fuzzy competition graph classes. Finally, the proposed concept of cubic fuzzy competition graphs is supported by a numerical example. This example showcases how the framework of cubic fuzzy competition graphs can be practically applied to the predator-prey model to illustrate the representation and analysis of ambiguous information within the graph structures.
A graph \( X \) is \( k \)-spanning cyclable if for any subset \( S \) of \( k \) distinct vertices there is a 2-factor of \( X \) consisting of \( k \) cycles such that each vertex in \( S \) belongs to a distinct cycle. In this paper, we examine the \( k \)-spanning cyclability of 4-valent Cayley graphs on Abelian groups.
A path \(x_1, x_2, \dots, x_n\) in a connected graph \( G \) that has no edge \( x_i x_j \) \((j \geq i+3)\) is called a monophonic-triangular path or mt-path. A non-empty subset \( M \) of \( V(G) \) is a monophonic-triangular set or mt-set of \( G \) if every member in \( V(G) \) exists in a mt-path joining some pair of members in \( M \). The monophonic-triangular number or mt-number is the lowest cardinality of an mt-set of \( G \) and it is symbolized by \( mt(G) \). The general properties satisfied by mt-sets are discussed. Also, we establish \( mt \)-number boundaries and discover similar results for a few common graphs. Graphs \( G \) of order \( p \) with \( mt(G) = p \), \( p – 1 \), or \( p – 2 \) are characterized.
This note presents a counterexample to Propositions 7 and 8 in the paper [1], where the authors determine the values of \( V \) and \( W \). These values are crucial in determining the Hamming distance and MDS codes in the family of certain constacyclic codes over \(\mathbb{F}_{p^m}[u]/\langle u^3 \rangle\), which implies that the results found in [2] are incorrect. Furthermore, we provide corrections to the aforementioned results.
For a graph \( G \) and for non-negative integers \( p, q \) and \( r \), the triplet \( (p, q, r) \) is said to be an admissible triplet, if \( 3p + 4q + 6r = |E(G)| \). If \( G \) admits a decomposition into \( p \) cycles of length \( 3 \), \( q \) cycles of length \( 4 \), and \( r \) cycles of length \( 6 \) for every admissible triplet \( (p, q, r) \), then we say that \( G \) has a \( \{C_{3}^{p}, C_{4}^{q}, C_{6}^{r}\} \)-decomposition. In this paper, the necessary conditions for the existence of \( \{C_{3}^{p}, C_{4}^{q}, C_{6}^{r}\} \)-decomposition of \( K_{\ell, m, n}(\ell \leq m \leq n) \) are proved to be sufficient. This affirmatively answers the problem raised in \emph{Decomposing complete tripartite graphs into cycles of lengths \( 3 \) and \( 4 \), Discrete Math. 197/198 (1999), 123-135}. As a corollary, we deduce the main results of \emph{Decomposing complete tripartite graphs into cycles of lengths \( 3 \) and \( 4 \), Discrete Math., 197/198, 123-135 (1999)} and \emph{Decompositions of complete tripartite graphs into cycles of lengths \( 3 \) and \( 6 \), Austral. J. Combin., 73(1), 220-241 (2019)}.
The λ-fold complete symmetric directed graph of order v, denoted λKv*, is the directed graph on v vertices and λ directed edges in each direction between each pair of vertices. For a given directed graph D, the set of all v for which λKv* admits a D-decomposition is called the λ-fold spectrum of D. In this paper, we settle the λ-fold spectrum of each of the nine non-isomorphic orientations of a 6-cycle.
In this paper, we provide a correction regarding the structure of negacyclic codes of length \(8p^s\) over \(\mathcal{R} = \mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) when \(p^m \equiv 3 \pmod{8}\) as classified in [1]. Among other results, we determine the number of codewords and the dual of each negacyclic code.
The multiplicative sum Zagreb index is a modified version of the well-known Zagreb indices. The multiplicative sum Zagreb index of a graph \(G\) is the product of the sums of the degrees of pairs of adjacent vertices. The mathematical properties of the multiplicative sum Zagreb index of graphs with given graph parameters deserve further study, as they can be used to detect chemical compounds and study network structures in mathematical chemistry. Therefore, in this paper, the maximal and minimal values of the multiplicative sum Zagreb indices of graphs with a given clique number are presented. Furthermore, the corresponding extremal graphs are characterized.
Let \( G = (V, E) \) be a graph. A subset \( S \subseteq V \) of vertices is an \textit{efficient dominating set} if every vertex \( v \in V \) is adjacent to exactly one vertex in \( S \), where a vertex \( u \in S \) is considered to be adjacent to itself. Efficient domination is highly desirable in many real-world applications, and yet, in general, graphs are often not efficient. It is of value, therefore, to determine optimum ways in which inefficient graphs can be changed in order to make them efficient. It is well known, for example, that almost no \( m \times n \) grid graphs have efficient dominating sets. In this paper, we consider the minimum number of vertices that can be removed from an \( m \times n \) grid graph so that the remaining graph has an efficient dominating set.
Let \( G = (V, E) \) be any graph. If there exists an injection \( f : V \rightarrow \mathbb{Z} \), such that \( |f(u) – f(v)| \) is prime for every \( uv \in E \), then we say \( G \) is a prime distance graph (PDG). The problem of characterizing the family of all prime distance graphs (PDGs) with chromatic number 3 or 4 is challenging. In the fourth part of this series of articles, we determined which fans are PDGs and which wheels are PDGs. In addition, we showed: (1) a chain of \( n \) mutually isomorphic PDGs is a PDG, and (2) the Cartesian product of a PDG and a path is a PDG. In this part of the series, we improve (1) by showing that there exists a chain of \( n \) arbitrary PDGs which is a PDG. We also show that the following graphs are PDGs: (a) any graph with at most three cycles, (b) the one-point union of cycles, and (c) a family of graphs consisting of paths with common end vertices.
Let \(P_n\) and \(K_n\) respectively denote a path and complete graph on \(n\) vertices. By a \(\{pH_{1}, qH_{2}\}\)-decomposition of a graph \(G\), we mean a decomposition of \(G\) into \(p\) copies of \(H_{1}\) and \(q\) copies of \(H_{2}\) for any admissible pair of nonnegative integers \(p\) and \(q\), where \(H_{1}\) and \(H_{2}\) are subgraphs of \(G\). In this paper, we show that for any admissible pair of nonnegative integers \(p\) and \(q\), and positive integer \(n \geq 4\), there exists a \(\{pP_{4}, qS_{4}\}\)-decomposition of \(K_n\) if and only if \(3p+4q=\binom{n}{2}\), where \(S_4\) is a star with \(4\) edges.
Natural environment protection compensation refers to the legal system that protects the natural ecological environment, protects the natural environment and makes the beneficiaries of the natural environment get compensation by some means, so as to adjust the interests of the relevant subjects of natural ecological environment protection. This paper discusses the ecosystem service function and its type division of newly built areas in Ganjiang, and the emergy evaluation of ecosystem service function of newly built areas in Ganjiang, establishes the regular scheduling and joint optimal scheduling models of natural ecosystem service value single reservoir, intro-duces the corresponding model solving methods, and applies the ant colony algorithm to the optimal schedule is a lesson. According to the ant colony algorithm, the best way to study the region is to determine these algorithms. Combined with the kernel density analysis method, the spatial scope, potential corridors and key recovery points of ecological corridors are identified, and the optimization mode of natural ecological security pattern of Shule River is constructed. The experimental results show that the optimized ant colony algorithm proves that joint scheduling plays a more prominent role in ecological environment protection, mainly in ecological support and ecological regulation. At the same time, it verifies the applicability of ant colony algorithm in joint scheduling, and improves the average protection efficiency of natural ecology to 20.9%.
The semantic function of modern Chinese “negation + X” modal words based on communication technology and big data corpus has gained wide attention. As the basis of SOA architecture, Web services provide the key resources for worldwide information transfer and information sharing with their characteristics of loose coupling, platform independence, and data exchange without additional support from third-party hardware and software. However, along with the popularization and improvement of Web service technology, the number and types of Web services in the Internet are also increasing massively, and there are a large number of Web services with various functions, quality and granularity. Therefore, how to quickly and accurately discover Web services that satisfy users’ query requests from a large and complex set of services has become a critical problem to be solved in the current Web service discovery research. Based on the real corpus, this paper analyzes the similarities and differences in the semantic functions of modern Chinese “negation + X” modal words by combining lexicalization and grammatization, cognitive linguistics, systemic functional grammar and other related theories. The experimental results demonstrate that the model is designed for automatic annotation of semantic word classes, and the annotation algorithm based on the hidden horse model, combined with the Viterbi algorithm based on dynamic programming, achieves a correct rate of 94.3% in the closed test and 89.1% in the open test despite the small size of the training corpus and severe data sparsity, and the model fitting effect meets the dynamic expectations.
The relationship between competition state anxiety, motor motivation and coping styles of adolescent track and field athletes in China was investigated using interview and questionnaire research methods. The results showed that the mean scores of cognitive state anxiety and somatic state anxiety were lower in junior track and field athletes who had entered the echelon for a short period of time than in older athletes, and the opposite was true for state self-confidence; there were highly significant differences and significant differences in the identity regulation and introjection regulation dimensions of motor motivation; and there were significant differences in the focused problem-solving coping dimension of coping style. This paper proposes an algorithm for classifying athletic visual mirrors based on sequential model mining. This paper focuses on two issues – feature extraction and definition of semantic rules. In the feature extraction stage, the track and field video footage is automatically segmented into a series of identifiable sequences of athletic events, and then each type of behavioral event is identified using a mechanically learned algorithm. There were no significant differences between the three age groups in terms of race state anxiety, identity regulation and introjection regulation, and no significant differences in coping styles. There were no significant differences in the anxiety of competition status, motivation and coping styles among youth athletes of different sport levels. The results showed the effectiveness of the present algorithm for classifying track and field video cameras.
A graph labeling is an assignment of integers to the vertices or edges or both, which satisfies certain conditions. The domination cover pebbling number of a graph \( G \) is \( \psi(G) \), which is the minimum number of pebbles required such that any initial configuration of \( \psi(G) \) pebbles can be transformed through a number of pebbling moves so that the set of vertices with pebbles after the pebbling operation forms a dominating set of \( G \). In this paper, we explore the relationship between two graph parameters, namely graph labeling and domination cover pebbling.
In this paper, we study the \( A_\alpha \)-spectral radius of graphs in terms of given size \( m \) and minimum degree \( \delta \geq 2 \), and characterize the corresponding extremal graphs completely. Furthermore, we characterize extremal graphs having maximum \( A_\alpha \)-spectral radius among (minimally) \( 2 \)-edge-connected graphs with given size \( m \).
The metric dimension of a graph \(\Gamma = (V, E)\), denoted by \( \operatorname{dim}(\Gamma) \), is the least cardinality of a set of vertices in \(\Gamma\) such that each vertex in \(\Gamma\) is determined uniquely by its vector of distances to the vertices of the chosen set. The topological distance between an edge \(\varepsilon = yz \in E\) and a vertex \( k \in V \) is defined as \( d(\varepsilon, k) = \min\{d(z, k), d(y, k)\} \). A subset of vertices \( R_{\Gamma} \) in \( V \) is called an edge resolving set for \(\Gamma\) if for each pair of different edges \( e_{1} \) and \( e_{2} \) in \( E \), there is a vertex \( j \in R_{\Gamma} \) such that \( d(e_{1}, j) \neq d(e_{2}, j) \). An edge resolving set with minimum cardinality is called the edge metric basis for \(\Gamma\) and this cardinality is the edge metric dimension of \(\Gamma\), denoted by \( \operatorname{dim}_{E}(\Gamma) \). In this article, we show that the cardinality of the minimum edge resolving set is three or four for two classes of convex polytopes (\( S_{n} \) and \( T_{n} \)) that exist in the literature.
Language learning cannot be separated from the environment, and the environment for second language acquisition is becoming more and more perfect and ideal. It makes the traditional single and limited English learning environment gradually move towards a three-dimensional and diversified learning environment. On the premise of the great development of higher education in China, this study aims to conduct research and discussion on higher English teaching. In combination with other successful or well functioning higher English teaching reforms, it studies and discusses some problems faced in the construction and implementation of vocational English teaching application system in China, and finds solutions and methods. Therefore, this study has practical significance for the reform and development of higher English education in China. This manuscript is based on the design of the college English teaching system module of Web technology to realize the sharing of information resources. In addition, with the deepening understanding of the importance of English teaching in colleges and universities, improving English level and English teaching level is the goal of colleges and universities. English teachers urgently need to understand the factors that affect students’ English level in order to teach students in accordance with their aptitude and find the best teaching methods. The experimental results show that the system realizes the management, query and sharing functions of open level information, and has high security and interactivity. The development of the system conforms to the development trend of network information technology and promotes the informatization and standardization of college English teaching management.
At present, the social economy is entering the information age represented by computer, communication technology and network technology as the core, and the continuous development of modern information technology will certainly have a great impact on the teaching mode, content and methods of traditional accounting computerization. We aim to improve the existing higher vocational accounting teaching mode by building a multi-integrated teaching mode through federated learning based on 5G communication network as an environment for efficient information transfer. In addition, we develop a joint optimization strategy for priority-dependent task offloading, wireless bandwidth, and computational power in a distributed machine learning approach to ensure that more resources are allocated to users with higher priority while protecting user data privacy and reducing learning overhead. We have conducted extensive simulation experiments for both environments, and these simulation results demonstrate the effectiveness of our proposed solutions for different problems from different perspectives.
This study explores the integration of “Internet+” into university education to enhance students’ learning, innovation, and entrepreneurship (I&E) skills. By updating educational concepts and methods, we aim to establish a comprehensive I&E framework that includes mindset development, knowledge acquisition, skill enhancement, and team support. Practical training and network learning communities are emphasized to provide global platforms for skill improvement and project incubation. Through a case study, we analyze the development and effectiveness of an I&E education platform, highlighting the importance of targeted demand surveys and data analysis. Our findings demonstrate the significance of aligning talent training with industry needs, fostering creativity, and promoting entrepreneurial success through collaborative school-enterprise initiatives.
The concept of graph energy, first introduced in 1978, has been a focal point of extensive research within the field of graph theory, leading to the publication of numerous articles. Graph energy, originally associated with the eigenvalues of the adjacency matrix of a graph, has since been extended to various other matrices. These include the maximum degree matrix, Randić matrix, sum-connectivity matrix, and the first and second Zagreb matrices, among others. In this paper, we focus on calculating the energy of several such matrices for the join graph of complete graphs, denoted as \( J_{m}(K_{n}) \). Specifically, we compute the energies for the maximum degree matrix, Randić matrix, sum-connectivity matrix, first Zagreb matrix, second Zagreb matrix, reverse first Zagreb matrix, and reverse second Zagreb matrix for \( J_{m}(K_{n}) \). Our results provide new insights into the structural properties of the join graph and contribute to the broader understanding of the mathematical characteristics of graph energy for different matrix representations. This work extends the scope of graph energy research by considering these alternative matrix forms, offering a deeper exploration into the algebraic and spectral properties of graph energy in the context of join graphs.
Tunnels are essential infrastructure elements, and it is critical to maintain their stability for both operation and safety. Using engineering techniques, this study examines the correlation between rock mass motorized characteristics and tunnel surrounding rock stability. This study utilizes the multi-sensor monitoring data of the surrounding rock mechanical characteristics and tunnel support structure collected during tunnel boring machine construction as its research object. The integrated cuckoo search optimized Upgraded dynamic convolutional neural network (ICSO-UDCNN) has been utilized for predicting the tunnel parameters. In general, the surrounding rock’s hardness correlates with its level, which in turn determines how quickly tunnels are being excavated. There is a stronger correlation of 98\% between the field penetration index (FPI) variables of the rock’s characteristic slope along the conditions surrounding the tunnel. The most significant factor influencing its deformation is the surrounding rock’s mechanical characteristics. For engineers and other decision-makers engaged in tunnel design, building, and maintenance, the study’s findings add a greater understanding of the variables affecting tunnel stability. This research provides an establishment for enhancing security protocols, lowering hazards related to tunneling operation, and optimizing tunnel engineering techniques by quantitatively evaluating the influence of rock mass mechanical factors on solidity.
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