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/jcmcc127a-250
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4411-4427
- Published Online: 15/04/2025
People’s performance requirements for air conditioning along with people’s requirements for indoor air quality also continue to improve, air conditioning heat exchanger as an important part of the refrigeration system in the air-conditioning products in the largest proportion of space. Therefore, this paper is based on ϐinite element analysis of air conditioning heat exchanger optimization design, oriented to the needs of air conditioning heat exchanger, heat transfer to the mechanism of depth analysis. The ϐinite element analysis is used to study the heat transfer simulation theory of air conditioning heat exchanger, and the heat transfer optimization design method is proposed, and the heat transfer model based on ϐinite element analysis is constructed. Through the physical model and its numerical simulation method for veriϐication, the numerical simulation value and experimental value of the pressure drop and convective heat transfer coefϐicient error of ± 6.50W/m² ℃ and ± 12.7Pa, respectively, which veriϐies the model of this paper and the feasibility of numerical simulation method for. Comparing the performance of the optimized air conditioning heat exchanger, the optimized heat exchanger in this paper improves the cooling capacity by 0.04~0.50kW and the total pressure drop by 11.19~50.84kPa compared with the comparative models, which proves that the optimized heat exchanger in this paper has better performance and can meet the performance and reliability index requirements of engineering applications.
- Research article
- https://doi.org/10.61091/jcmcc127a-249
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4395--4410
- Published Online: 15/04/2025
Currently, the severity of information leakage is increasing, and attacks and protection against cryptographic devices have become a research hotspot in the ϐield of information security. In order to increase the security of SM4 algorithm structure against side channel attack, the paper focuses on the protection scheme of adding masks to cryptographic circuits to resist DPA attack, and proposes a cipher algorithm design method of ϐinite domain additive coding. Experimentally, it is proved that the additive coding SM4 algorithm used in this paper can correctly and efϐiciently perform encryption, and the encryption efϐiciency is improved by 56.54%~82.42% than the general SM4 algorithm. Meanwhile, it has the security against 1st-order and 2nd-order side-channel attacks, and the success rate against attacks reaches 93.67%, which is higher than that of the compared algorithms by 5.34%~21.00%. It also proves that the scheme has high security against side channel attacks and can provide a reliable solution for the information security of wireless LAN.
- Research article
- https://doi.org/10.61091/jcmcc127a-248
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4379--4394
- Published Online: 15/04/2025
Ceramics have many applications, covering scientiϐic research, medical, industrial, jewelry, etc. Ceramic materials are stable and have a silk-like touch. Ceramic 3D printing technology is based on laser curing molding as a rapid manufacturing technology. This paper proposes a personalized design strategy for ceramic artwork, determines the degree of inϐluence of ceramic process parameters on the quality of laser 3D printed ceramic artwork by calculating the Pearson’s correlation coefϐicient, and adopts numerical simulation to obtain the ceramic 3D printing quality data, calculates the error of the number of printed layers, and controls the quality of the printed ceramic artwork. The ceramic quality parameter optimization model is established. Five algorithms of SVR support vector regression, BP neural network, RF random forest, RBF radial basis function, and Kriging model are used to set up the relevant parameters of 3D printing, input the six ceramic process parameters that have been processed by the uniϐied magnitude, and complete the optimization of the quality ceramic process parameters of laser 3D printing. Through the investigation and analysis of the effect of ceramic artwork design, the ceramic color designed in this paper makes the user generate positive emotions; a total of 235 positive emotions were generated, accounting for nearly 60%. The mean value of user preference for ceramic samples is analyzed. The samples with the highest user preference are sample 4, sample 6, and sample 1, and the mean values of preference are 3.425, 3.245, and 3.148, respectively.
- Research article
- https://doi.org/10.61091/jcmcc127a-247
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4359--4378
- Published Online: 15/04/2025
Graph neural networks are widely used in image recognition. This paper introduces a two-node graph neural network DouN-GNN model based on a traditional graph neural network. By constructing two nodes, the features in the sample image that are difficult to extract by the shallow embedding network are extracted so that the network model can incorporate more multi-dimensional information about the sample image, thus enhancing image recognition accuracy. Aiming at the problem of the overall performance of the DouN-GNN model not reaching the ideal state, this paper adds three optimization modules to improve the DouN-GNN model and form the IGNN model. The optimized IGNN model is trained, tested, and applied to real-world scenarios such as agricultural weed recognition, natural resource enforcement, and video surveillance to explore the performance of the IGNN image recognition model constructed in this paper in real-world applications. The model achieves the highest accuracy of 98.39% in agricultural weed image recognition, and the classification accuracy for weeds is also high. In natural resources law enforcement and video surveillance, the model in this paper performs better than other image recognition models and can effectively meet the requirements of image recognition in practical application scenarios.
- Research article
- https://doi.org/10.61091/jcmcc127a-246
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4343--4358
- Published Online: 15/04/2025
In the current information age, image tampering detection technology is crucial to ensure the integrity and authenticity of digital media, and remote image tampering detection technology combined with deep neural networks has become a research hotspot. This paper adopts convolutional neural network as the main detection tool, and on the improved DPN network model, the feature fusion module based on the attention mechanism is used to fuse the two features in this paper. In this way, the image tampering detection technique based on dual-stream feature fusion is proposed in this paper. The precision, recall and F value of the detection algorithm in this paper are better than the comparison algorithm. When the image compression quality factor is reduced to 20, the precision rate, recall rate, and F value of this paper’s algorithm do not appear to be greatly reduced, and the reduction is only 0.028, 0.041, and 0.042. This paper’s image tampering detection algorithm, which fuses the frequency domain branching module and the attention mechanism feature fusion module, has a higher detection efficiency. And the Accuracy rate, Recall rate and F Value of this paper’s algorithm on image level detection are 17.8%, 15.3% and 16.3% higher than that of DCT algorithm respectively. In conclusion, the remote image tampering technique combined with deep neural network provides an effective solution to ensure the authenticity and integrity of images.
- Research article
- https://doi.org/10.61091/jcmcc127a-245
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4325--4341
- Published Online: 15/04/2025
In order to improve the impact toughness and service life of GF/EVE composites, this paper applies the thermoplastic nonwoven fabric structure to the preparation of GF/EVE composites. The thermoplastic polyurethane was used as the raw material, and the meltblown method was used for the preparation of thermoplastic nonwoven fabrics, and then the prepared thermoplastic nonwoven fabrics were used for the preparation of GF/EVE composites through the VARTM device. For the properties of GF/EVE-TPU composites, specific test methods are given to define the moisture absorption rate and the erosion performance based on the consideration of the stress change of its hygrothermal properties, and the determination of the interlaminar fracture toughness is given.The critical damage threshold load of GF/EVE-TPU composites is 1.57kN, and its contact force increases with time, and the composites are aging in After 60 days, its moisture absorption and erosion weight loss in alkaline environment were 0.736% and 81.19%, respectively.The optimum fracture toughness value of 9g/m² thermoplastic nonwoven structure incorporated into GF/EVE composite was 0.97kJ/m², and the GIIC value of GF\EVE-TPU30 was increased compared with the GF/EVE material without interlaminar toughening by 183.83%. Combining the thermoplastic nonwoven fabric structure with GF/EVE composites can enhance the erosion resistance and interlaminar toughness of the composites and improve the service life of GF/EVE composites.
- Research article
- https://doi.org/10.61091/jcmcc127a-244
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4309--4323
- Published Online: 15/04/2025
With the continuous development of virtual reality technology, its application in the digitization of cultural heritage has been constantly emphasized and applied, which has an important role and significance for the protection and inheritance of cultural heritage. This paper proposes a rendering algorithm that combines LOD algorithm and occlusion rejection algorithm. The article firstly carries out theoretical research on the relevant theories and rendering processes of LOD algorithm and occlusion removal algorithm, and finally takes the cultural heritage of Shennongjia as the research object to analyze the performance of this paper’s algorithm in rendering different landscape scenes of the cultural heritage of Shennongjia. This paper concludes that in the high configuration machine, the algorithm of this paper improves the rendering performance by 587% in the resolution of 1280*720, and improves the rendering performance by 1061% in the resolution of 1920*1080. In the low configuration machine, the algorithm in this paper improves the performance by 653% in 1280*720 resolution and 770% in 1920*1080 resolution. Rendering frame rate LOD combined with occlusion culling algorithm (132.65fps) > occlusion culling algorithm (79.88fps) > LOD method (18.02fps) > without any optimization algorithm (5.32fps). The total number of rendering triangles is without any optimization algorithm (55.65) > LOD algorithm (16.78) > occlusion culling algorithm (3.64) > algorithm of LOD combined with occlusion culling (1.05).
- Research article
- https://doi.org/10.61091/jcmcc127a-243
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4295--4307
- Published Online: 15/04/2025
Teaching digitalization and integration of industry and education are developing deeply in the field of education, this study designs and constructs the digital practical training system, innovates the teaching mode of school-enterprise collaboration, and applies it to the teaching practice of tourism specialty. The performance of the digital training system for tourism majors is tested by concurrency test, business success rate test and target system thing test. Design teaching experiments to verify the teaching effect of the digital practical training system and the school-enterprise collaboration model by comparing the gaps and changes between the experimental group and the control group in the competitiveness of students’ employment, the utilization rate of resources, the tourism market research, the tourism marketing, the results of the digital practical training, and the development of tourism projects. The maximum number of users in concurrent testing of the digital practical training system for tourism majors is 20, the average number is 10.182, and all the operations of users are processed, achieving good test results. Before the experiment, there is basically no difference between the two groups in the six aspects of employment competitiveness, resource utilization, tourism market research, tourism marketing, digital practical training results and tourism project development. After the experiment, the two groups showed large differences. The scores of the experimental group were higher than those of the control group in all 6 dimensions, and the difference in the scores of each dimension was more than 5 points. The teaching effectiveness of the experimental group rose more than 4.9 points in all 6 dimensions. And the score difference between the pre- and post-test of the control group is not more than 0.5 points. In this paper, digital practical training system and schoolenterprise collaboration model have better teaching effect.
- Research article
- https://doi.org/10.61091/jcmcc127a-242
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4275--4293
- Published Online: 15/04/2025
The study firstly introduces the reinforcement learning theory, and proposes a decision-making method based on reinforcement learning to build a robot for autistic children, centered on autonomous human-robot interaction, with the purpose of serving the task of concentration training for autistic children. Among them, the goal task in the current environment is formulated based on imitation learning in the high level, and the robot’s action selection is realized based on interactive Qlearning in the low level. The decision making based on reinforcement learning to build a robot is applied to train the robot to interact with the training, and the simulation results verify the effectiveness and generalization of the designed algorithm in solving the concentration training path. Using the KANO model to analyze the needs of autistic children, based on which we design a multimodal human-computer interaction system for autistic children’s concentration training, and carry out a personal concentration intervention containing academic tasks for an 8-year-old autistic child, to verify the effectiveness of the multimodal human-computer interaction system in intervening in the concentration behaviors of autistic children, and the results of the study show that: the children’s concentration behaviors of the academic tasks in the intervention period are significantly improved compared with the baseline period compared with the baseline, and the mean value increased to 88.42%.
- Research article
- https://doi.org/10.61091/jcmcc127a-241
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 4257-4273
- Published Online: 15/04/2025
This paper takes the native vegetation in Hanzhong City as the research object, and constructs a multiobjective linear programming model to optimize the distribution of the suitability of the native vegetation in Hanzhong City. The ArcGIS software was used to test the sample consistency and screen the environmental variables of the native vegetation data in Hanzhong City represented by alfalfa, and the model in the software was used to predict the distribution of alfalfa’s suitability area. Based on the prediction results, this paper constructs a multi-objective linear planning model with economic and ecological benefits as the objective function and the land area of different utilization types as the decision variables to optimize the distribution of the suitability of native vegetation in Hanzhong. At the same time, the fuzzy mathematical planning method was used to solve the constructed model. After the model optimization, the area of fitness distribution of native vegetation in Hanzhong City increased significantly, and the growth of the fitness distribution area of each vegetation by 2080 was 49.61%, 35.51%, 36.41%, 28.11%, 15.36%, 24.75%, 27.92%, 28.40%, 31.22%, and 31.52%, respectively. In addition, the optimization of the distribution of native vegetation suitability using the model of this paper can produce obvious economic and ecological benefits, which fully demonstrates the effectiveness of the model of this paper.




