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-154
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 2731--2744
- Published Online: 15/04/2025
Shallow loess landslides, as one of the widely distributed and high-frequency geologic hazards, have brought great economic losses and ecological damage to human society. In this study, Qinzhou District, Tianshui City, Gansu Province, is taken as the study area, and the Scoops3D model is used to predict the occurrence of loess landslides in the area based on the DEM data of the area. Bishop’s simplified method and box search method were used to calculate and analyze the landslide stability in the study area. The landslide prediction results of the Scoops3D model of this paper are compared and analyzed under different DEM data resolutions. Subsequently, local environmental data are collected to study the correlation between environmental impact factors and shallow loess landslides. Finally, the prediction accuracy of the shallow loess landslide prediction model based on Scoops3D in this paper is tested by comparing the difference between the prediction results of the Scoops3D model of this paper and other prediction models with the actual results. The resolution of the DEM data has an important influence on the prediction results of the Scoops3D model, and the accuracy of the high-resolution DEM prediction results is higher than that of the low-resolution prediction results. There is a significant correlation between landslide displacement and humidity and cumulative precipitation, and the difference between the predicted and measured values of the GA-BP and GA-Elman models is within 8 mm, and the difference gradually increases. The difference between the predicted and measured values of the Scoops3D model in this paper is between 0.00 and 2.30 mm, and the prediction effect is optimal.
- Research article
- https://doi.org/10.61091/jcmcc127a-153
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 2713-2730
- Published Online: 15/04/2025
The inheritance and protection of urban cultural heritage faces the dilemma of narrow coverage and lack of change in form, and to solve this dilemma, we need to find a breakthrough in cultural creation and animation design, and carry out creative activities and popularisation among all people. The article proposes a feature extraction model that integrates multi-scale features and housing element information mining, and applies it to the feature extraction of housing elements in urban cultural heritage. A hybrid attention module is embedded in the ResNet-18 backbone network to enhance housing element features and suppress redundant information, and a CEB module and learnable parameters are combined to filter out the background information of the low-level features, so as to obtain finer architectural housing element features. The extracted housing elements are used as the basis for the design of creative products and animation scenes, and the feasibility of the programme is investigated through questionnaires. The overall evaluation mean value of the research respondents on the design of cultural and creative products for the housing was 7.64 points, and more than 95% of the evaluation respondents indicated that the housing elements were more suitable for the animation scene design. Relying on modern technology to extract housing elements from urban cultural heritage and realising the innovative application of cultural heritage in the form of cultural creation and animation provides a new path for the revitalisation and inheritance of urban cultural heritage.
- Research article
- https://doi.org/10.61091/jcmcc127a-152
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 2695--2712
- Published Online: 15/04/2025
According to the connotation of traditional and modern design elements in rural landscape beautification, multi-dimensional data cube mining method is adopted to construct the research data set of this paper. According to the ratio of 2:8, the data set is divided into test set and training set. The data of traditional and modern design elements are used as inputs, substituted into the decision tree model for training and classification, and the CART algorithm is used to construct a decision tree model for traditional and modern design elements in rural landscape beautification. Combining the dataset and the model in this paper, the simulation analysis of traditional and modern design elements in rural landscape beautification is carried out. The data show that based on the Gini index calculation formula of CART algorithm, it is concluded that the Gini index of X9 (0.9581) is the largest, so X9 is chosen as the root node for decision making, and the decision tree is derived downward until the leaf node, and the decision tree oriented to the countryside landscaping is obtained, and the rural landscape beautification scheme is induced based on the results of the analysis and the effect of the rural landscaping is found to have the difference between the before and after mean values of 3.36 ( 20.11-16.75=3.36), while there is a significant difference between the two, similarly, there is also a significant difference in the building living comfort above. This study enhances the effect of rural landscape beautification, which is of great significance in promoting rural revitalisation and architectural design development.
- Research article
- https://doi.org/10.61091/jcmcc127a-151
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127a
- Pages: 2675--2694
- Published Online: 16/04/2025
In today’s increasingly stringent sewage discharge standards, the construction of a new generation of wastewater treatment plants more and more urgent. This paper adopts MBBR as the main process to treat wastewater, the pretreatment process of wastewater treatment plant adopts coarse and fine grating + cyclone sand sedimentation tank, and the secondary treatment process selects AAO process. Through the reasonable calculation of water volume and hydraulics, and then calculate the size of each structure. Based on the ASM2 model, combined with the conversion rate equation of the AOO reaction tank, the kinetic model of the wastewater treatment system was constructed. Analyzing the inlet and outlet water quality monitoring data of the high-efficiency wastewater treatment plant for one year of operation, it was found that the average values of inlet and outlet water COD concentration in one year of operation were 255.437 and 10.556 mg/L, respectively, and the annual average removal rate was 94.37%. The average values of ammonia nitrogen in and out of the water for the whole year were 32.085 and 1.107mg/L, and the average ammonia nitrogen removal rate was 96.98%. All the effluent indicators have reached the “urban sewage treatment plant pollutant discharge standards” level A discharge standards and environmental protection departments on the effluent indicators, indicating that the overall operational efficiency of the research-designed high-efficiency wastewater treatment plant is good, and has reached the expected goals, with significant environmental and social benefits.
- Research article
- https://doi.org/10.61091/jcmcc127-01
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127
- Pages: 3-17
- Published Online: 19/04/2025
Optimizing regional economic resources is a crucial aspect of the Belt and Road initiative. This paper develops a multi-objective optimization model to objectively evaluate the development level of regional economic resource optimization in Belt and Road countries and to identify the key influencing factors. The model maximizes regional economic and social benefits under constraints of resource availability, output capacity, and coordinated regional development, and it incorporates a synergy measure to ensure robust progress. Our findings show that the regional economic benefits index increased from 0.264 in 2017 to 0.575 in 2023 (a growth rate of 117.8%), while social benefits grew by 14.29%. Additionally, panel regression analysis reveals that merchandise trade, foreign direct investment, road traffic mortality, and industrial development all have significant negative impacts on the optimization of economic resources, at the 1% significance level.
- Research article
- https://doi.org/10.61091/jcmcc126-04
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 126
- Pages: 73-91
- Published Online: 19/04/2025
Alzheimer’s disease (AD) is a progressive neurodegenerative condition that affects the elderly population. The early detection and diagnosis of AD is critical for achieving effective treatment, as it can greatly improve the patient experience. AD can be viewed through imaging techniques like MRI, PET, and SPECT, providing valuable information about structural and functional changes. These findings are important in understanding this area. However, each imaging modality offers a different perspective. This information can be better collected from several of the other modalities as well as from some others to improve accuracy and reliability in AD detection. By combining information from different imaging modalities, such as MRI, PET, DTI, and fMRI, automated multimodal medical image frameworks aim to create a fused representation that preserves the relevant features from each modality. Convolutional neural networks (CNNs) and generative adversarial networks (GANs), among other deep learning techniques, have been prevalent in these frameworks for learning discriminative and informative features from multi-modal data. In this paper, The Alzheimer’s Disease Neuroimaging Initiative (ADNI) is used for experimental analysis. The proposed work gives 98.94% of accuracy and 1.06% of error which is greater than the existing approaches.
- Research article
- https://doi.org/10.61091/jcmcc126-03
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 126
- Pages: 29-72
- Published Online: 19/04/2025
The power of the public key cryptosystem based on Paley graphs is due to several mathematical problems namely quadratic residuosity, local equivalence, and identification of the graphs induced by a sequence of local complementations of the Paley graphs. The classification in terms of degree of these induced graphs can be useful in the cryptanalysis part of the proposed public-key cryptosystem based on these algebraic graphs. This work aims to give the exact value of the minimum and maximum degree by local complementation, then the possible classifications in terms of degree to the graphs induced by a sequence of local complementations of Paley graphs of degree p less than or equal to 13 and some information about the equivalence problem.
- Research article
- https://doi.org/10.61091/jcmcc126-02
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 126
- Pages: 11-27
- Published Online: 19/04/2025
Given a graph \(G \), a set is \(\Delta \) convex if there is no vertex \(u\in V(G)\setminus S \) that forms a triangle with two vertices of \(S \). The \(\Delta \)-convex hull of \(S \) is the minimum \(\Delta \)-convex set containing \(S \). This article is an attempt to discuss the Carath\’eodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and lexicographic products of graphs.
- Research article
- https://doi.org/10.61091/jcmcc126-01
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 126
- Pages: 3-9
- Published Online: 19/04/2025
Directed strongly regular graphs were introduced by Duval in 1998 as one of the possible generalization of classical strongly regular graphs to the directed case. Duval also provided several construction methods for directed strongly regular graphs. In this paper, an infinite family of directed strongly regular graphs is constructed, as generalized Cayley graphs.
- Research article
- https://doi.org/10.61091/jcmcc127b-218
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 127b
- Pages: 3929-3944
- Published Online: 16/04/2025
With the need of international dissemination of Chinese culture, the problem of translating traditional Chinese texts gradually emerges. The study embeds a computer semantic model into the English translation of The Analects of Confucius, and constructs a natural language understanding model based on S-LSTM network through semantic representation of natural language processing. In order to explore the performance of the S-LSTM model, it is compared with RNN, LSTM, I-LSTM and other models in terms of training time and accuracy, so as to validate the superiority of the S-LSTM model in this paper. This paper deeply explores the philosophical connotation of the character “body” in The Analects, and studies the structural complexity of the translation of the character “body” through the S-LSTM model. Finally, the English translation strategy of The Analects and other classics is proposed. Among all the comparison models, the S-LSTM model has the fastest training speed and the highest accuracy. The translation of the word “body” in The Analects and the local complexity of the ministry are characterized by complication. The local complexity of the noun and the subject in the source English language, and the overall complexity of the “be-passive” structure have obvious effects on the structure of the translated Chinese character “body”.




