Growth: A Journal of Mathematics and Mathematics Education
ISSN: xxxx-xxxx
Growth: A Journal of Mathematics and Mathematics Education aims to provide a publication platform for high quality undergraduate research in mathematics and in mathematical pedagogy. The technical scope of the journal is combinatorial mathematics, broadly interpreted—the editorial board will consider all submissions in their areas of interest. All submitted articles must have an undergraduate research component and must be certified by a senior researcher. All submissions will be peer reviewed according to standard practices in academic mathematics. Precise editorial policies are set by the editorial board.
- Research article
- https://doi.org/10.61091/jcmcc127b-197
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3527-3546
- Published Online: 16/04/2025
Aiming at the many problems in research resource management in private universities, this paper takes the integration of research resources in international business discipline of Xiamen Institute of Technology as an example, proposes a global integration and dynamic allocation model of research resources in distributed computing environment based on mobile agent (DCMA), and designs a dynamic bidirectional matching method of tasks and resources (DBMM) in order to improve the effectiveness of distributed computing. Experiments show that the proposed DBMM algorithm outperforms the LDCP algorithm and the hierarchical node sorting algorithm (SNLDD) in three metrics, namely, scheduling length, acceleration ratio and computational efficiency. Compared with LDCP and SNLDD, the scheduling length of DBMM algorithm is shortened by an average of 19.89% and 11.81%, the acceleration ratio is improved by an average of 19.77% and 9.26%, and the computational efficiency is increased by an average of 10.74% and 3.72%, which further improves the resource utilization rate of distributed computing system. Experiments were conducted using the research resource integration model, which achieved better efficacy in terms of probability value, goodness-of-fit, and stability of research resource integration in international business disciplines compared with the gray correlation analysis method. This paper provides an example reference for distributed computing system to realize research resource integration and efficiency improvement.
- Research article
- https://doi.org/10.61091/jcmcc127b-196
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3509-3525
- Published Online: 16/04/2025
Aiming at the dilemma of corpus-based intelligent English translation, the article proposes an English neural machine translation method based on depth-separable convolution, which combines with the dynamic computation method to improve the semantic consistency of the translation system for semantic alignment and fusion. In order to verify the training effect of the proposed convolutional neural network model combined with the dynamic computation method, comparison experiments with one-way and two-way network models and baseline model with different cut-off granularity are conducted respectively. In order to better examine its performance in practical translation applications, online translation, machine translation and systematic methods are utilized for comparison. The BLUE values of this paper’s model for Chinese-English data translation in four different granularities of words, syllables, subwords and characters are 21.41%, 21.91, 29.25% and 20.40%, respectively. In 100,000, 200,000 and 500,000 training English-Chinese bilingual parallel corpus, the training time consumed by the model in this paper is 9.58 h, 15.94 h and 32.69 h. In practical application, the decibel range of the noise reduction of the translation system method designed by the research is distributed in [1.62 ~ 1.89], the average value of coherence is 91.1%, and the average compression rate and the average stability of the BLEU scores are 93.84% and 98.38%, respectively, and the results are better than the comparison methods.
- Research article
- https://doi.org/10.61091/jcmcc127b-195
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3493-3507
- Published Online: 17/04/2025
This paper constructs a set of models for monitoring and evaluating the effect of Civics education through the research on the evaluation of Civics education based on educational big data environment. First, based on distributed gray cluster analysis, it analyzes and researches students’ Civics learning behavior, and explores learners’ learning characteristics by mining meaningful behavioral features for cluster analysis. The second is to design the Civics teaching quality evaluation model using principal component analysis, test the effects of population size and convolution kernel number on the performance of the Civics teaching quality evaluation model, and optimize the teaching quality evaluation model by using the dimensionality-reduced evaluation data. Distributed gray cluster analysis gets four clusters according to the characteristics of students’ learning behaviors, which are divided into excellent, diligent, average, and negative students.PCA selection of evaluation indexes found that the cumulative contribution rate of the first 10 principal component indexes to the evaluation of the quality of Civic Teaching in colleges and universities has reached 95.63%, which indicates that these 10 indexes can adequately evaluate the quality of Civic Teaching in colleges and universities. When the number of population size is taken as 31 and the number of optimal convolution kernels is taken as 19 values, the RMSE of the evaluation model is 0.01973, and the test time consumed is 0.0783ms, which is the best performance. The constructed Civics education effect monitoring model can effectively assess students’ learning behavior and efficiently and accurately evaluate the quality of Civics teaching.
- Research article
- https://doi.org/10.61091/jcmcc127b-194
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3479-3492
- Published Online: 16/04/2025
This paper proposes knowledge representation based on knowledge graph embedding (TransE model) and based on deep wandering (DeepWalk model) to enhance the level of intelligent recommendation of knowledge points. Synthesize and construct a knowledge graph-based Civic Education model. Analyze the node centrality specifics of the model. Carry out a controlled experiment of model application and investigate student satisfaction on this basis. The three nodes with the highest node centrality are “life view and values”, “morality and law” and “patriotism and nationalism”. The average score of the test questions in the experimental class is 71.25, and the correct rate of the six types of test questions is higher than that of the control class. Most of the students’ satisfaction level with the intelligent teaching mode combined with the model was between 65 and 100 points. 92% of the students found the teaching mode interesting at a level between (75,100]. 90% of the students’ content mastery satisfaction level was between 85 and 100 points. Intelligent teaching using the knowledge graph-based Civics education model can help students improve their interest in learning Civics knowledge and construct Civics knowledge system.
- Research article
- https://doi.org/10.61091/jcmcc127b-193
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3463-3477
- Published Online: 16/04/2025
English children’s literature has strong application value in educational content selection. This study takes classic English children’s literature texts as the research object, and constructs a semantic theme mining model based on the implicit Delicacy Distribution (LDA). Through keyword weight analysis and theme probability distribution calculation, multi-dimensional theme clustering and visual characterization of literary works are realized. According to the 2378 English children’s literature collected in the corpus, the LDA model was used to extract five core themes: “Adventure and Fantasy”, “Friendship and Teamwork”, “Growth and Self-Identity”, “Family and Affection”, and “Nature and Animals”.A semester-long controlled experiment was conducted with third-grade students in an elementary school in Guangdong Province, designing graded English teaching content based on the results of topic distribution. Through the questionnaire survey, vocabulary test and reading ability assessment, it was found that students in the experimental group significantly outperformed the control group in terms of active interest in learning (12.42% increase in mean value) and independent learning ability (15.67% increase in test scores) (p<0.05). The study shows that the educational content adaptation method based on the LDA theme model can effectively optimize the selection strategy of teaching resources, and provide a theoretical basis and practical path for the precise matching of literary themes and cognitive development stages in children's English teaching.
- Research article
- https://doi.org/10.61091/jcmcc127b-192
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3443-3461
- Published Online: 16/04/2025
In this paper, finite element analysis is applied to the mechanical characterization of the foot. A finite element simulation model of the foot is constructed and its material properties are defined. Finite element analysis is applied to calculate the stresses on various tissues of the foot under different touchdown modes. Set up controlled experiments to verify the advantages of FEA technology in sports. The material property values of each tissue in the simulation model differed greatly, which was in line with the actual situation of biological tissues. In the 2 touchdown modes, the change curves of flexion and extension angles of the supporting foot were generally similar in the latter 75% of the supporting phase, and the differences were concentrated in the first 25%. The movement of the foot on the coronal plane showed a general tendency toward eversion. There were 2 peaks in the vertical ground reaction force variation in the heel-touch mode and only 1 peak in the non-heel-touch mode. The resistance impulse and power impulse ratios varied widely. The time of occurrence of the maximum contact stress on the talo-heel joint surface varied. P<0.05, the experimental group was better than the control group in terms of skill level, learning interest and initiative of the two groups of students after the experiment. The use of finite element analysis to assist physical education teaching can enhance students' enthusiasm and skill level.
- Research article
- https://doi.org/10.61091/jcmcc127b-191
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3429-3442
- Published Online: 16/04/2025
The automation system is gradually applied to many fields because of its intelligent and efficient characteristics, and its energy control makes the equipment work in the optimal efficiency zone, however, the actual control effect needs to be further optimized. This paper explains the energy control problem of automation system for its control process, and uses the weighted residual value method to transform the original system into a system dynamics model. On the basis of this model, the optimal control is solved by the variational method, and the energy control algorithm based on the variational method is built by combining Lie algebra. The algorithm of this paper is used to establish the energy optimal control strategy and simulation experiments are carried out as a prerequisite for constructing the driving cycle. In the simulation experiments, the energy optimal control strategy based on this paper’s algorithm saves 4.77% of fuel, which shows that the energy control of the automation system under this paper’s algorithm is better and in line with the environmental protection needs.
- Research article
- https://doi.org/10.61091/jcmcc127b-190
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3413-3428
- Published Online: 16/04/2025
Graph neural networks are widely used in educational research, and have strong application potential in the prediction of students’ comprehensive development and recommendation of personalized educational resources. In this paper, the information and characteristics of students are mined from massive learning data, and the prediction method of multi-topology graph neural network is used to realize the effective prediction of students’ comprehensive development. Through the graph neural network, knowledge graph and cluster search algorithm and other technologies, the personalized learning path planning and optimization are completed, and the personalized learning path is designed. The research shows that the data accuracy of the student development trend prediction model in this paper reaches the qualifying value of 0.1, and the absolute maximum value of the error does not exceed 0.17, so the model constructed in this thesis is effective and robust. It can fulfill the task of student development direction prediction. The usage frequency of generating learning paths are more than 60%, so the learning path generation method proposed in this paper is practical. And the average grade of the users who use this method is 6.17 points higher than the average grade of the users who do not use this method.
- Research article
- https://doi.org/10.61091/jcmcc127b-189
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3397-3412
- Published Online: 16/04/2025
Industrial Internet based on distributed computing and cloud computing platform forms a “cloud-edge-end” cooperative system. Facing the problem of computing task offloading for machine-type communication devices in industrial Internet scenarios, this paper transforms the task offloading problem into a Markov decision process problem, proposes an online task offloading algorithm based on deep Q neural network (DQN), and designs an optimal scheduling method based on iterative optimization for industrial Internet resources. Simulation experiments are conducted by comprehensively considering the network environment and server state during the task offloading process, and compared with other resource optimization scheduling strategies. The results show that the DQN algorithm converges in about 9000 steps and has good convergence performance. The offloading strategy based on the DQN algorithm can effectively reduce the delay, energy consumption and total overhead of the computational task offloading system in the economy.
- Research article
- https://doi.org/10.61091/jcmcc127b-188
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3375-3395
- Published Online: 16/04/2025
Currently, digital libraries face challenges in piracy and illegal distribution, data and privacy security, digital content identification and traceability. In this paper, we design a blockchain-based copyright protection system for digital libraries to provide true and reliable digital copyright information for libraries and users, and to ensure the security of data information stored in the digital copyright registration system. Firstly, we classify blockchain and analyze in detail the three core technical principles of consensus mechanism, cryptography principle, and hash algorithm. Then design the copyright registration protection system that contains the functions of unique authentication of digital work copyright, IPFS distributed storage, and privacy data encryption. The designed algorithm is tested for performance and the service performance of this paper’s scheme is analyzed in real applications, and it is found that the throughput performance of this paper’s algorithm when the number of nodes ranges from 4 to 20 is on average 36.19% more than that of the PBFT consensus algorithm, and 55.92% more than that of the RBFT consensus algorithm. When there are 5000 digital resource feature vectors in the system database, the time required for similarity retrieval is only 0.523s, which meets the requirements of the system’s non-functional needs for similarity retrieval runtime, and realizes a good balance between the operational efficiency of digital libraries and security. The research has practical reference significance for the application of blockchain technology in the field of digital copyright protection.




