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-518
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9469-9481
- Published Online: 16/04/2025
In recent years, with the rapid development of information technology, the traditional single-threaded processing method can no longer meet the rapid growth of digital media data volume. In this paper, based on the digital media data processing system based on BS structure, the GPGPU parallel processing architecture is used for optimization. The access efficiency of massive parallel multithreading is ensured by executing a multilevel storage architecture composed of behavior decision unit, branch merge unit and branch recovery stack. The study designs the computational resource pool as well as the storage resource pool to form an infrastructure solution to the data processing problem. The query performance of the digital media data processing system using the GPGPU microarchitecture with multithreaded parallel processing is improved by about 81% and 69% or so compared to the Ocelot and prototype systems, respectively. And the average execution time for performing dynamic data allocation is 5.17s less than that of the original system. It shows that the optimized digital media data processing system has better data processing efficiency.
- Research article
- https://doi.org/10.61091/jcmcc127b-517
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9443-9468
- Published Online: 16/04/2025
The problems of debt value and optimal capital structure of enterprises are the main issues in corporate finance research. Under the ESG rating mechanism, the article first utilizes the real option theory to study the optimal capital structure and investment and financing decision-making methods of enterprises. Then it puts forward model assumptions and combines the jump diffusion model for the construction of enterprise project investment and financing decision-making model and the dynamic planning adjustment of capital structure. Finally, through specific numerical experiments, the influence process of each variable in the model on the enterprise investment and financing decision is analyzed, and the agency problem is analyzed.Through the experiment, it can be obtained that when the residual value after stopping production, the risk-free interest rate, the variable production cost and the tax rate are set to γ = 1, r = 0.1, ξ = 0.1, θ = 0.2, respectively, with the increase of the frequency of the jump, the investment price of the positive-jump model gradually decreases, and the investment price of the negative-jump model gradually increases, which can be obtained that the reasonable simulation estimation of the relevant parameters has an important impact on the enterprise’s investment strategy, so the enterprise should make a more accurate assessment of the parameters, otherwise they will lose part of the benefits or lose good investment opportunities.
- Research article
- https://doi.org/10.61091/jcmcc127b-516
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9423-9441
- Published Online: 16/04/2025
Analyzing the interaction strategies of international relations helps to understand and predict changes in the international landscape, so as to develop and optimize international interaction strategies. Firstly, a single-layer multi-temporal network is modeled for political events, scientific cooperation and international trade in international relations, and added to a multi-layer aggregation network. On this basis, a simulation and analysis method for simulating international relations interaction strategies based on deep learning and multi-intelligence body reinforcement learning methods is proposed. Applying the method of this paper to the arithmetic simulation analysis, it is found that the international relations in the last 10 years have shown the small-world characteristics, and cooperation and conflict coexist. Economic dependence is an influencing factor of conflict between two countries, when the economic and trade links are close, the two countries are less prone to conflict, so the optimization of the international relations interaction strategy should focus on the economic and trade relations.
- Research article
- https://doi.org/10.61091/jcmcc127b-515
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9405-9422
- Published Online: 16/04/2025
Objective and comprehensive teaching effectiveness assessment is a strong guarantee for the quality of English teaching in colleges and universities. This paper establishes an index system for evaluating the teaching effectiveness of English in colleges and universities from the levels of students, teachers and classroom teaching. The particle swarm algorithm is used to optimize the convolutional neural network, the SGD formula is used to improve the calculation accuracy, the Adam optimizer is improved to improve the model operation efficiency, and the optimization algorithm of convolutional neural network, PSO-CNN, is proposed. The PSO-CNN algorithm is introduced into the system and the logic design is carried out to realize the evaluation of the teaching effect of English teaching and to build up the English teaching effect evaluation system based on the intelligent algorithm. Evaluation system based on intelligent algorithm. The performance of the system is examined and analyzed with the help of PCA method, which shows that the cumulative contribution rate of the first six indicators, such as learning acquisition and teaching ability, reaches 91.08%. In the mean square error of model training, the PSO-CNN algorithm applied in this paper’s system has a lower mean square error than other algorithms after 35 iterations, and has better evaluation accuracy. In the application practice of English majors in a higher education institution in B city, after applying the system of this paper to evaluate the effectiveness of English teaching, the English test scores of the regular and experimental classes with improved teaching were significantly improved.
- Research article
- https://doi.org/10.61091/jcmcc127b-514
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9385-9403
- Published Online: 16/04/2025
Traditional learning path planning methods often fail to meet the individualized needs of learners. In this paper, a dynamic learning path planning method based on neural network is studied by constructing a student model. Firstly, the construction method of the student model is designed, and the Item Response Theory (IRT) is used as a test method for the cognitive level of students, which realizes the dynamic acquisition of student information. A neural network-based cognitive collaborative filtering model was constructed, which models learners’ learning behaviors and interests, and customizes personalized dynamic learning paths for learners after assessing their cognitive levels and learning difficulties. The collaborative filtering algorithm in this paper performs better than the other four algorithms in terms of accuracy and coverage, and the accuracy and coverage rate of the generated knowledge point sequences reach 98.9% and 93.6% respectively, and the performance of the students in the experimental group has been significantly improved under the application of the dynamic learning path generation model of blended teaching in this paper, indicating that the effectiveness and feasibility of the personalized learning path generation model in this paper are excellent and are expected to be further promoted.
- Research article
- https://doi.org/10.61091/jcmcc127b-513
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9371-9384
- Published Online: 16/04/2025
The monitoring of training load and recovery cycle of Wushu Sanshou athletes is a long-term and fundamental work for sports teams. The article introduces the parameters of resting heart rate, ventricular muscle contractility, arterial wall and maximal oxygen uptake VO2max as monitoring indexes, and designs a real-time monitoring method of physical training load data based on graph convolution network. Subsequently, through the flow level variables (BFL, TLQ, BRQ), flow rate variables (BFLI, BFLD, TLQI, BRQI), auxiliary variables (TT, TI, RT, RM), exogenous variables (RYN), and the causal relationship between the elements of each variable of the Wushu sparring training function monitoring system, we constructed a nonlinear system of the training load and recovery cycle of the Wushu sparring athlete Dynamics model. Using the real-time monitoring model of this paper to monitor the wushu sparring athletes, in the third minute of the experiment, the real-time monitoring system predicted that the heart rate was 90, and the adjusted heart rate using the model of this paper was 90, which was consistent with the actual monitored heart rate. It can be concluded that the model of this paper can well monitor the training load of martial arts sparring athletes. Through experimental simulation, the article concludes that both the strong physical fitness program and the strong training program can be beneficial to the training of wushu sparring athletes.
- Research article
- https://doi.org/10.61091/jcmcc127b-512
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9353-9369
- Published Online: 16/04/2025
Least Squares Support Vector Regression (LSSVR) machine has the advantages of small sample, nonlinearity and high dimensionality, which can solve the problem of predicting the compressive strength of green concrete with oil palm shell aggregate. In this paper, the error sum of squares instead of the error sum is used as the objective function, IFFA is used to find the optimization of the kernel function parameters and penalty factors of LSSVR, and the PWLCM-based chaotic search is used to initialize the population, and ultimately the improved auricular fox algorithm is realized for the optimization of the least squares support vector regression algorithm, which makes it have strong fitting and generalization abilities, and significantly reduces the burden of computation, thus improving the Computational efficiency. Application of the designed combined algorithm for compressive strength prediction of concrete reveals that the R², MAPE and RMSE values obtained by this paper’s model on the training dataset are 98.71%, 5.92% and 1.0823 MPa, respectively. The correlation coefficients predicted by the model are much closer to 1 as compared to that of the baseline model, which suggests that this paper’s model possesses a superior generalization capability, making it more effective in dealing with complex and invisible data. The adopted method is practical and innovative, and is of guiding significance for practical engineering.
- Research article
- https://doi.org/10.61091/jcmcc127b-511
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9337-9352
- Published Online: 16/05/2024
Starting from the essence of dynamic programming algorithms, the terminology in dynamic programming algorithms, the applicability conditions of the algorithms, and common sub-problem models are summarized. The Belman optimal algorithm is used to split the multilevel problems in dynamic planning into simple single-level problems and solve them one by one, combined with the function approximation structure to approximate the performance index function, to construct the adaptive dynamic planning algorithm, and to apply it in the resource balancing optimization of integrated teaching. The results show that the adaptive dynamic programming algorithm has better resource balancing effect than other algorithms, and the number of convergence and running time are reduced by 6-53 times and 48.92-90.34 seconds respectively. The introduction of the adaptive dynamic programming algorithm improved the resource balancing accuracy of university teaching and learning management by 4.0%-17.4% in each subject group. As the number of resources increased, the time consumption required when balancing resources decreased by 50%-83.33% for test groups 3, 4 and 5, and the efficiency of the test improved by 75%-100%. This shows that the algorithm proposed in this paper is effective when dealing with balancing online and offline teaching resources in higher education.
- Research article
- https://doi.org/10.61091/jcmcc127b-510
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9321-9335
- Published Online: 16/04/2025
Grasping economic behavior is a foothold of market optimization, this paper combines game theory ideas with deep learning technology to explore the laws of economic behavior. Firstly, different payment strategies are considered and payment matrices are constructed, and replicated dynamic equations are used to describe the dynamic adjustment process of the game and simulate the game process of market economic transactions. The MS-RCNN model that can be used to predict economic behavior is constructed by extracting data features using CNN and processing the feature matrix using GRU. The results of the game simulation simulation show that when the government regulation of the market is in place, it is easier for the trading parties to reach a deal. In addition the MS-RCNN model can more accurately reflect the fluctuation of the market when making long-term and short-term predictions, and the predicted price is closer to the real market price. Therefore a better understanding of economic behavior through game theory and its prediction through deep learning helps to achieve the optimization of market strategies.
- Research article
- https://doi.org/10.61091/jcmcc127b-509
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 9303-9320
- Published Online: 16/04/2025
The change of landscape pattern is closely related to the quality of ecological environment, and the study of urban and rural landscape pattern, especially three-dimensional landscape pattern, is of great significance for urban-rural integration spatial planning. Based on the theory of landscape pattern, this study constructs a numerical simulation method for the characteristics of urban and rural threedimensional landscape pattern, and explores the formation of optimization strategies for the threedimensional development of urban and rural areas. Taking Chengdu City as an example, firstly, based on multi-source remote sensing data, the landscape pattern index method and gradient analysis method are utilized to explore the spatial and temporal coupling characteristics of urban and rural three-dimensional landscape patterns. Then the CA-Markov coupling model is used to predict the landscape pattern of future land use, so as to provide a reference for decision-making. The results of the study show that the landscape type changes in Chengdu City from 2005 to 2020 are dominated by the transformation between cultivated land, forest land and construction land, and the reasons for the changes are closely related to the urban development plan. In addition, the accuracy indices of the CAMarkov model all reached more than 80%, and the simulation results were reliable. The model prediction results show that construction land and cropland are the largest transformed landscape types, with a large-scale increase in the landscape area of construction land and a large-scale decrease in the landscape area of cropland. Spatially, the degree of fragmentation of the landscape pattern in Chengdu City gradually decreases, the landscape patches are more regularized, and the overall pattern shows a highly aggregated trend. The research results of this paper can be used as a reference for the optimization policy of three-dimensional landscape pattern in urban and rural areas, and provide data support and innovative ideas for the innovative development of urban and rural three-dimensional landscapes




