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-488
- Full Text
In natural orchard environments, tangerines are susceptible to being shaded by foliage and to overlapping with multiple fruits. Varying weather conditions can cause inconsistent levels of illumination, and these unstable factors combined with complex backgrounds can diminish the efficiency of tangerine recognition and localization. Consequently, this paper utilizes images of tangerines captured under various weather conditions within a tangerine orchard as a dataset, and a method based on the YOLOv8n object detection algorithm is proposed. The dataset was trained using BiFPN, MCA attention mechanism, and PConv. An improvement in the algorithm resulted in an accuracy rate of 94.4% for tangerine target detection, a recall rate of 92.7%, an F1 score of 93.5%, and a mAP of 98.3%, with each metric showing an increase of 0.7%, 0.6%, 0.7%, and 1.3% respectively over the original model.
- Research article
- https://doi.org/10.61091/jcmcc127b-487
- Full Text
As the throat of transportation system, bridge structure is a lifeline project related to the coordinated development of society and economy. Based on fuzzy mathematical theory, this paper adopts Gaussian subordinate degree function to quantitatively characterize the damage detection information of articulation joints, combines Latin hypercubic sampling method and response surface method, and proposes a reliability assessment method for bridges integrating transversely distributed damage information, and analyzes the bridge of a certain structure as an engineering case, compares the failure probability corresponding to the model outputs and the real damage degree under different damage degrees, and analyzes the change of reliability indexes with the damage degree under articulation joint damage and main plate damage conditions, respectively. Under the conditions of articulation joint damage and main plate damage, the changes of reliability indexes with the damage degree are analyzed. The results show that the narrower the width of the damage interval is, the closer the failure probability is to the value corresponding to the real damage degree, and the reliability of the bridge decreases with the increase of the articulation damage and the main plate damage, which illustrates the objectivity and reasonableness of the method proposed in this paper.
- Research article
- https://doi.org/10.61091/jcmcc127b-486
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8853-8867
- Published Online: 16/04/2024
Intelligent power preservation automation terminal is an important part of the smart grid, which plays an important role in improving the power supply quality of the power system. In this study, the CAB module is utilized to extract the multimodal features of visible images and infrared images during distribution network line operation. The weighted feature maps of each part of the distribution network operation are obtained by fusing different modal features through the average fusion strategy to realize line quality monitoring and fault detection and localization. The batch normalization layer and Relu function are also used to improve the image feature quality extraction performance of the model, which is then piggybacked on the model to construct a digital platform for intelligent power protection. The empirical analysis of the case found that the power supply reliability rate of L power supply company increased from 85.060% to 99.87% after the application of the smart power protection digital platform, the average power supply restoration time of non-faulty sections in the grid can be shortened to 3.24 minutes, and the line loss rate in the distribution network has been reduced to a certain extent. This study carries out the exploration of the practical application of the intelligent power preservation digital platform system, which lays the foundation for the stable operation of the distribution network and the improvement of power supply reliability.
- Research article
- https://doi.org/10.61091/jcmcc127b-485
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8833-8851
- Published Online: 16/04/2025
Distribution network line project acceptance is a key link in the quality control of distribution network line project, an important factor affecting the safe and stable operation of the distribution network, which directly determines the level of safe operation of the distribution network. In this paper, for the distribution network line manual acceptance time-consuming and laborious, rare quality defects found rate identification rate is low and other issues, to carry out visual positioning and image recognition based on the distribution network drone automated acceptance technology research. In order to optimize the spatial positioning, attitude sensing and target tracking of the UAV, five coordinate systems, including the world coordinate system, body coordinate system, and photocentric coordinate system, are selected for spatial transformation. Based on the visual localization of the UAV, the path planning algorithm for UAV distribution line inspection combined with the path acquisition scheme is proposed. Gaussian denoising and histogram equalization are performed on the UAV inspection collected images, and Sarsa reinforcement learning algorithm is applied to train the samples to improve the automatic identification capability of safety hazards and other security hazards in the distribution network inspection. Visualization and analysis of UAV distribution line inspection path. Combine the distribution network defects dataset for optimal training strategy selection for distribution networks. The automatic identification algorithm for distribution network defects proposed in this paper achieves a mAP value of 79.60% in the target detection experiment. And in multiple dynamic path planning, the UAV nodes are able to accomplish the path planning tasks in different environments.
- Research article
- https://doi.org/10.61091/jcmcc127b-484
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8815-8832
- Published Online: 16/04/2025
With the construction and development of new power system, grid business presents high reliability, high security protection, high flexibility, massive access level characteristics, 5G as the frontier technology of wireless network access, with high speed, wide connectivity, low latency features and advantages, and diversified grid business communication needs are highly compatible. Based on the characteristics of 5G communication technology, this paper analyzes its practicality in the power system. The main two protocols of the current autonomous network routing protocol for power system are proposed, and the inter-cluster routing optimization of OLSR is carried out by using AO algorithm. Simulate the predation behavior of skyhawk, develop the search strategy in the optimization process of AO algorithm, and construct the mathematical model of AO optimization algorithm. A quasi-inverse solution is used on the basis of the inverse solution to further increase the population diversity and convergence speed of the AO algorithm, while an adaptive weight factor strategy is used to balance the global search and local exploration capabilities of the AO algorithm. Simulation experiments are utilized to investigate the performance of the IAO algorithm as well as the PDR and delay in the mobile scenario of the power system. Comparing the PDR of the three protocols at different expected delivery distances, IOLSR still maintains a delivery rate of about 28% at a distance of 350m-500m. The optimized IOLSR shows further reduction in delay compared to OLSR in most of the cases with an average delay of 10829.43ns.
- Research article
- https://doi.org/10.61091/jcmcc127b-483
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8797-8813
- Published Online: 16/04/2025
Wide-area protection systems are capable of eliminating or mitigating the consequences of disturbances by obtaining multi-point information about the grid system through measurement and communication techniques, and power system control and protection systems. In this study, distribution data in the grid system is collected and preprocessed, the distribution state of the grid system is estimated using data fusion methods, and an optimization method for distribution state estimation based on distributed computing methods is proposed. Then the grid wide-area protection system is designed by combining the grid system fault diagnosis method. Simulation and example analysis results show that the grid wide-area protection system based on data fusion and distributed computing has good performance in processing grid data and detecting and localizing grid faults, and the maximum localization error of faulted line points is maintained within 0.770%. In addition, this grid wide-area protection system is able to accurately detect a certain circuit fault in a regional grid system where faults are frequent, avoiding large-scale power outages and ensuring the stable operation of the grid system. This study has important scientific significance and application value for grid multivariate data fusion modeling and real-time fault detection, and provides an effective widearea protection scheme for the grid system.
- Research article
- https://doi.org/10.61091/jcmcc127b-482
- Full Text
Reservoir dams are highly susceptible to unstable conditions under the long-term action of water flow. In this paper, we mainly investigate the effect of water flow on the stability of reservoir dams under the conditions of complex boundaries. Through the advection orthogonal curve generation network and the use of the adjustment factor on the sparsity of the grid range of values, to achieve the mesh division of the reservoir dam body. The control volume method is used to discretize the control equations of the planar two-dimensional water flow model under the complex boundary conditions, and the SIMPLEC method is used for numerical calculations at the same time. For the treatment of complex boundaries, this paper reduces the error between the simulated and real water margins by comparing and selecting the diagonal Cartesian method. The limit equilibrium method is introduced and combined with the strength reduction method to solve the problem together and comprehensively analyze the stability of the reservoir dam under the action of water flow. Reservoir dam A is selected as the object of numerical calculation in this paper, and the input information of the model is set by setting parameters and selecting working conditions. The model is used to calculate the stability of the reservoir dam under the action of water seepage and water pressure. Compared to the static condition, the value of displacement and deformation of the dam body is increased by about 52.00% under the water flow action condition. The stability of the reservoir dam body under the action of water flow infiltration and pressure decreases significantly.
- Research article
- https://doi.org/10.61091/jcmcc127b-481
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8763-8774
- Published Online: 16/04/2025
Fractal geometry is an emerging discipline that has developed rapidly in recent decades, and its study of irregular geometric shapes can be used to describe objects in nature that cannot be described by traditional geometry, and it has a broad space for development and application prospects. In this paper, the theory of fractal geometry is applied to industrial design to realize the refinement and analysis of surface features. The study includes an in-depth analysis of the theory of fractal geometry, the Koch curve as an example to illustrate the principle of fractal geometry. The study also investigates different dimension calculation methods, such as Hausdorff dimension, box dimension, correlation dimension, information dimension, generalized dimension, and self-similarity dimension of fractal geometry, and proposes a dimension calculation method for the refinement of structural surface features for industrial design. After the fractal geometry surface feature refinement simulation analysis, the porosity of the fractal map based on this paper’s method ranges from 16% to 38%, and the comparison with the Serpinski method proves that the presently selected fractal model is more effective in the refinement of structural surface features for industrial design. As shown by the surface feature simulation results, there is indeed a certain degree of similarity between the roughness topography of the real structural surface of the two surface processing methods in industrial design and the roughness topography simulated by the fractal function. The above study proves that the method of refining the structural surface features of industrial design based on fractal geometry in this paper is scientific and feasible.
- Research article
- https://doi.org/10.61091/jcmcc127b-480
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8747-8762
- Published Online: 16/04/2025
This topic discusses the problem of maximizing the interests of multiple participants in the trading market based on game theory. Taking the electric power market as a study case, an interest maximization model of multi-party trading strategy in the electric power market is constructed, and the ADMM algorithm is used to solve the model. The rationality and effectiveness of the described model are verified through experimental analysis and arithmetic simulation. Compared with other algorithms, the ADMM algorithm in this paper has a faster convergence speed, and the benefits of the grid company, the benefits of the new entities and the benefits of the users under different numbers of users are all closest to the ideal Nash equilibrium state, which shows the superiority of the ADMM algorithm in this paper. The constructed model is used to solve the conflict of interests among the grid company, new entities and users, and the existence and uniqueness of the game equilibrium is proved through analysis and derivation, and has good convergence results. After the optimization of the strategy in this paper, the revenue of the added entity increases by 6.76%, the power purchase cost of the users decreases by 10.29%, and the consumption surplus increases by 4.50%. Through price-guided output, the load curve is realized to shift peaks and fill valleys, so that the grid company, the added entities and the users get higher benefits.
- Research article
- https://doi.org/10.61091/jcmcc127b-479
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 8723-8745
- Published Online: 16/04/2025
The large number of accesses of distributed power supplies changes the distribution network from a passive network to an active network with small and medium-sized power supplies all over the network, which brings important impacts on all aspects of the distribution network, such as planning, operation, and power quality. The study analyzes the types of distributed power nodes and the traditional trend model of distribution network, studies the changes of voltage and network loss after the integration of distributed power sources into the distribution network, and analyzes the impact of different numbers, capacities and access locations of distributed power sources on the reactive power optimization of the distribution network by means of IEEE33 nodes. Analyze the impact of distributed power supply on distribution network. Firstly, the characteristics of distributed power supply are analyzed, distributed photovoltaic and distributed wind power operation models are established, and the influencing factors of the two power supply outputs are analyzed to generalize the distributed power supply output model. The basic principle of weighted least squares state estimation and its algorithmic process are introduced, and on its basis, an equation-containing constrained state estimation model for dealing with zero-injection nodes in the distribution network is introduced, and finally, the feasibility and validity of the proposed constrained state estimation model’s state estimation method for the distribution network are verified through the analysis of an example of the IEEE 33-node system. Combining the sequence quadratic programming method and the idea of trust domain, the trust domain sequence quadratic programming method is proposed, and the use of the effective set method to quickly solve the sub-quadratic programming problem after downsizing is the key that the algorithm in this paper can solve the optimization problem relatively quickly. The optimization results show that distributed power sources participate in active distribution network reactive power optimization and cooperative control to provide a theoretical basis, and the effectiveness of the method is verified through simulation cases.




