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-167
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2971-2991
- Published Online: 16/04/2025
Under the new situation of continuous and stable development of China’s economy, large products have extremely high requirements on transportation safety due to their high price, complex transportation technical requirements, which determines that large products should be delivered to customers in the safest and most economical way, which poses a difficult problem for decision makers to choose the optimal path. In this paper, we constructed an intelligent approval framework for bulky transportation, made technical and economic analysis of transportation routes, and established a multi-objective optimization mathematical model for path selection of bulky transportation vehicles. A hybrid genetic algorithm incorporating greedy strategy is proposed to solve the problem, which strengthens the ability of the algorithm to jump out of the local extremes and selects the optimal chromosome in the final population as the resulting optimal solution. The results of the approval and optimal route planning for bulky transportation are verified by the method of example experimental analysis. The volume of bulky transportation increases with the increase of years until 2023, and the GDP, value added of tertiary industry, total population, and road mileage are 1015987.54, 553948.15, 140563, and 536.48, respectively. In the instances where the number of orders is 2000 or more, the transportation distance, the maximum number of service bundles of orders on the route, and the maximum service hours of vehicles the mean values are 50, 3.56, and 14.33, respectively. According to the constructed mathematical model, the optimal line for the bulky transportation scheme is 0→2→4→7→8, and the total transportation cost is 670,500,000 yuan, of which the transportation costs are 116,500,000 yuan, 320,000 yuan, 151,000,000 yuan, and 83,000,000 yuan, respectively.
- Research article
- https://doi.org/10.61091/jcmcc127b-166
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2949-2969
- Published Online: 16/04/2025
Aiming at the problems of unfixed switching frequency and complicated calculation in the control of permanent magnet synchronous motor, a permanent magnet switch FNN-PID control strategy based on deep learning technology is proposed. Based on the vector control of permanent magnet synchronous motor, the resonant pole inverter is combined with permanent magnet switch control, and then the fuzzy neural network and incremental PID algorithm are used to construct the optimization strategy of permanent magnet synchronous motor switching frequency FNN-PID control. And combined with the finite element simulation software, the permanent magnet switch finite element model is constructed, and the effectiveness of the FNN-PID control strategy is illustrated by verifying the permanent magnet switch control strategy and the temperature rise curve change. When using the FNN-PID control strategy, the electromagnetic torque quickly reaches stabilization near the given torque of 9 N-m after 0.03 s of startup, and the permanent magnet switch frequency of the FNN-PID control strategy is reduced by 24.04%. The difference between the measured maximum winding temperature and the calculated maximum temperature under rated operating conditions is less than 9°C, and the permanent magnet switching loss is reduced by about 35% with the FNN-PID control strategy compared with the traditional MTPA control strategy. Therefore, the combination of deep learning technology and finite element analysis can explore the optimization effect of PM switches from the strategy and application dimensions and provide research ideas for the stable operation of PM switches.
- Research article
- https://doi.org/10.61091/jcmcc127b-165
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2933-2947
- Published Online: 16/04/2025
The ring network cabinet of the distribution network is an important part of the urban power system, and its operation state directly affects the stability and reliability of the power system. In this paper, a deep learning algorithm is used to analyze and process the partial discharge signal, and a permanent magnet fast ring main unit partial discharge detection and fault identification model based on improved DBN-LSTM is proposed. By analyzing a large amount of local discharge signal data under normal operation and fault conditions of ring main cabinet, and using these data to train a deep learning-based fault prediction model. The performance of the improved DBN-LSTM model is tested by combining the defect spectrograms of four typical ring network cabinet partial discharge models and compared with other algorithms. The proposed model has good effect on fault identification of ring network cabinet, with a combined identification accuracy of 98.41%, and the overall identification performance is better than both BP neural networks and SVM classifiers. The prediction accuracy of the fault prediction model also reaches 88.52%, and the experimental results of the method in this paper are more satisfactory.
- Research article
- https://doi.org/10.61091/jcmcc127b-164
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2911-2931
- Published Online: 16/04/2025
Syntactic analysis is a basic work in the field of natural language processing, which explores the syntactic structures and their interaction relations in sentences. This paper first describes the basic approach of syntactic analysis, and explores the computational method of Chinese syntactic structure classification from large-scale corpus construction. Then, a grid-based large-scale corpus construction and distribution model is constructed. And the word embedding model BERT is used as the pre-trained language model, and the captured semantic features are input into the Bi-LSTM model to extract the contextual bidirectional sequence information, and the results of Chinese syntactic structure classification are obtained by the Conditional Random Field (CRF) processing. Through manual proofreading as well as the calculation of confidence level, the average correct rate of syntactic structure classification of the final Chinese canonical corpus is increased from 94.21% to 99.06%, which is an improvement of 4.85%. The syntactic structure classification accuracy of the BERT-Bi-LSTM-CRF1 and BERT-Bi-LSTM-CRF2 models with “complement structure” and “object structure” were higher than those of the BERT model, the Bi-LSTM-CRF model and the BERT-Bi-LSTM-CRF3 model with all syntactic structures. Meanwhile, the accuracy of the syntactic structure annotation method of BERT-Bi-LSTM-CRF model + manual differs from that of manual annotation by only 0.66%, and the average time spent is reduced by 37.04%, which reduces the workload of the annotators and improves the efficiency of the annotation, which verifies the validity and practicability of this paper’s model in automatic classification of Chinese syntactic structures.
- Research article
- https://doi.org/10.61091/jcmcc127b-163
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2895-2909
- Published Online: 16/04/2025
The construction of dual prevention mechanism is a necessary way to solve the problem of “not recognizing, not thinking, not managing well” in the field of enterprise safety production. This paper combines the elements involved in the theoretical framework of the dual prevention mechanism, constructs two evaluation index systems of safety risk classification and the operation effect of the dual prevention mechanism, and then establishes an evaluation model based on the multi-level analysis method and the fuzzy comprehensive evaluation method, to explore the operation effect of the dual prevention mechanism in the enterprise. The evaluation results show that after the dual prevention mechanism of safety risk classification and hidden danger investigation and management strategy is operated in S enterprises with higher safety risk level (1.50 points), the awareness of safety production and the level of intrinsic safety of the enterprises have been significantly improved, and the average value of the evaluation of the operation effect of the dual prevention mechanism in enterprises is 3.91 points, which reaches a good level. The research results of this paper not only have strong guiding significance and practical help for the optimization of risk management of production safety in enterprises, but also can be used by the same type of enterprises and even other enterprises in optimizing the risk management of production safety and the management of hidden danger investigation.
- Research article
- https://doi.org/10.61091/jcmcc127b-162
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2875-2894
- Published Online: 16/04/2025
Digital auditing has become the key to the transformation and upgrading of the auditing field. Financial audit data anomaly detection needs to combine multiple aspects of information, and it is of great practical significance to utilize the existing technical means to discover financial anomalies in the limited content. In this paper, based on the limitations of the weighted KNN deep neural network algorithm, a multi-branch deep neural network is proposed and a cost-sensitive loss function is designed. Combining the qualitative and quantitative methods of risk assessment, the enterprise audit risk assessment index system is constructed, the indexes are standardized, and the results of enterprise audit risk assessment are analyzed. The specific application effect of the assessment model is analyzed from the aspects of industry status and key financial performance, and the relevant strategies for corporate audit risk response are proposed. In the 1st risk assessment, 8 of the 20 enterprises are above higher risk, 6 are medium risk, and 6 are below lower risk. The results of the 2nd audit risk assessment have varying degrees of reduction between -0.3663 and -0.0119. From 2017, the overall net profit growth rate of enterprises is decreasing year by year, especially in the period from 2019 to 2020, and the net profit growth rate of the industry in 2020 is -24.87%, which predicts that the future development of the industry is not optimistic.
- Research article
- https://doi.org/10.61091/jcmcc127b-161
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2857-2873
- Published Online: 16/04/2025
With the rapid development of blockchain technology, consistency assurance of distributed database has become one of the key issues. In this paper, a blockchain distributed database consistency assurance mechanism based on the practical Byzantine fault tolerance (Rpbft) algorithm and its improved algorithm is studied in depth.The RPBFT algorithm combines the RSA algorithm and the PBFT consensus algorithm, and then performs the signature operation after message encryption in order to increase the system security. Aiming at the shortcomings of the master node selection mechanism of the original algorithm and the RPBFT algorithm, a master node selection mechanism that includes the time factor is proposed, which introduces the role of the recording node, so that the waiting time of the node can be adjusted dynamically. Meanwhile the algorithm changes the conditions of view switching and reduces the system consumption. Through simulation experiments to verify the performance of this paper’s R-PBFT algorithm and OmniLedger and RapidChain two programs in the same network conditions, this paper’s algorithm compared to the comparison algorithm can be more effective in guaranteeing the consistency of the distributed database, when the number of slices is 20, the transaction latency time is 13s, 25s lower than that of RapidChain and OmniLedger, respectively. When the number of shards is 20, the transaction delay time is lower than that of RapidChain and OmniLedger by 13s and 25s respectively, which provides strong support for the application of blockchain technology in the field of distributed database.
- Research article
- https://doi.org/10.61091/jcmcc127b-160
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2833-2856
- Published Online: 16/04/2025
Urban spatial structure and three-dimensional perspective can express personalized city brand image, which is an important feature of city brand form. In this paper, computer graphics technology is applied to design a city 3D modeling algorithm based on point cloud fusion, which transforms city information into city spatial visual symbols, and then carries out the innovation of city brand image morphology. Firstly, on the basis of binocular stereo vision, tilted image generation modeling technology is utilized to realize texture mapping 3D dense point cloud structure network. Aiming at the lack of accuracy of the sparse point cloud and the existence of noise points and mesh voids due to the influence of occlusion and shadows, we design the stereo vision PMVS algorithm based on the faceted slice in order to realize the densification of the point cloud. The algorithm performance is tested on the dataset using standard 3D reconstruction evaluation metrics F-score, chamfer distance (CD), and the application analysis of segmentation and merging execution efficiency for building clusters, optimization effect of rectangle fitting, and height calculation of building clusters, and the study finds that this paper’s algorithm is ahead of the baseline model in 13 categories. When the number of regions reaches 70,000, the traditional RAG method takes 26.9 seconds, while this paper’s algorithm only takes 14.8 seconds. The time consumption reduction reaches more than 40%. The average score of the aesthetic assessment of the city brand design is 83.47 points, and the 10 experts’ evaluation of the spatial aesthetics is above 90 points, and the design is unanimously recognized. The study makes a useful exploration for the innovation of city brand image under the conditions of cutting-edge information technology.
- Research article
- https://doi.org/10.61091/jcmcc127b-159
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2819-2832
- Published Online: 16/04/2025
The study of the impact of climate change on permafrost and the response mechanism in the Upper Irtysh River Basin can help to comprehensively understand the impact of climate change and grasp the development of coping strategies. In this paper, the one-dimensional heat conduction equation is used as the core to propose a model for calculating the distribution of permafrost in the upper Irtysh River Basin and the boundary conditions for solving the model, and the model is simulated and solved by using the general form of partial differential equations in the COMSOL Multiphysics finite element analysis software. Subsequently, the simulation results and regression equations are combined to investigate the driving effect of meteorological data changes on permafrost depth distribution changes. The simulation results found that the meteorological factor regression model could explain 30.6% of the variation in maximum permafrost depth, with mean annual relative humidity driving permafrost depth to the greatest extent (Beta = -0.251). This paper finds that the driving effect of meteorological factors on permafrost depth change provides a new perspective for understanding the dynamical mechanism of permafrost change in the upper Irtysh River Basin, and also provides a scientific basis for predicting and responding to the impact of future climate change on permafrost.
- Research article
- https://doi.org/10.61091/jcmcc127b-158
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 2805-2817
- Published Online: 16/04/2025
In this paper, the basic structure of fuzzy integral-based multi-classifier fusion model is used as a reference to construct Choquet integral vectors, measure the similarity of English sentences, and construct a fast retrieval algorithm for English sentences based on Choquet expectation. Determine the algorithm threshold and compare the running time of similar retrieval algorithms. Deploy the algorithm into the English sentence retrieval model for dataset training and comparison experiments. Verify the model robustness and determine the chosen K value for the model. Further use the test set to compare the retrieval effectiveness of the model with the traditional semantic retrieval model. The algorithm threshold is set to 6 to improve English sentence recall. The running time consumption of the algorithm is 0.827s and 1.941s, which is lower than the other three similar retrieval algorithms. In the dataset comparison experiments, the algorithmic model of this paper scores better than the comparison model in all 5 evaluation metrics. The model has the best robustness when k takes the value of 15. The model check accuracy and check completeness are higher than the semantic retrieval model LM by nearly 8 percentage points. The fast retrieval algorithm for English sentences based on Choquet expectation can improve sentence retrieval timeliness and retrieval accuracy, and reduce retrieval energy consumption.




