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.

Kai Shang1, Fang Wang2
1School of Economics and Management, Voronezh National University of Engineering and Technology, Voronezh, Voronezh State, 394036, Russia
2School of Management, Suzhou University, Suzhou, Anhui, 234000, China
Abstract:

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.

S. Beatrice1, Janaki Meena M1, Dhivviyanandam I2
1School of Computer Science and Engineering Department, Vellore Institute of Technology, Chennai-600127
2Department of Mathematics, North Bengal St. Xavier’s College, Rajganj, West Bengal, India
Abstract:

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.

Zhour Oumazouz1
1Laboratory of mathematics, computer science and applications, Faculty of Science and Technology, Hassan II university, Mohammedia, Morocco
Abstract:

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.

Bijo S. Anand1, Arun Anil2, Manoj Changat2, Prasanth G. Narasimha-Shenoi3,4, Sabeer S. Ramla5
1Department of Mathematics, Sree Narayana College, Punalur, Kollam, Kerala, India – 691305
2Department of Futures Studies, University of Kerala,Thiruvananthapuram, Kerala, India – 695581
3Department of Mathematics, Government College Chittur, Palakkad, Kerala, India – 678104
4Department of Collegiate Education, Government of Kerala, Thiruvananthapuram, Kerala, India – 695033
5Department of Mathematics, Thangal Kunju Musaliar Institute of Technology, Musaliar Hills, Karuvelil P.O., Ezhukone, Kollam, Kerala, India – 691505
Abstract:

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.

Yang Zhang1, Liwei Zeng2
1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
Abstract:

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.

Zijuan Su 1
1School of Foreign Languages and Culture, Geely University of China, Chengdu, Sichuan, 641423, China
Abstract:

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”.

Jie Zhang 1
1Xi’an Fanyi University, Xi’an, Shaanxi, 710105, China
Abstract:

Along with the development of the times, online classroom teaching activities have been carried out in different degrees and frequencies in various schools, and the gradual advancement of education informatization has improved the software and hardware environment of online classroom and other forms of teaching. The study designed a 21-item questionnaire related to English online classroom learning and selected all the students who participated in English online classroom teaching in a school for the survey. After collecting the questionnaire data, factor analysis and multiple stepwise regression model were used to conduct multivariate statistical analysis on the English online classroom data. And on this basis, the teaching plan was adjusted according to the actual learning behaviors of the high, medium and low risk level students themselves respectively to achieve personalized teaching. The results show that students’ satisfaction with the English online classroom is high, and that pre-course homework analysis, group learning, formative learning evaluation, students’ independent learning ability and online learning resources are the key positive factors affecting the learning effect of the English online classroom, with the influence coefficients of 0.036, 0.055, 0.048, 0.044, and 0.062, respectively. At the same time, after the optimization of teaching strategies, the students’ logged-in learning behavior, participation rate in interactive test questions and grades were significantly improved, proving the effectiveness of the strategy.

Mingxing Zhu 1, Xin Guo 1
1Zhixing College, Hubei University, Wuhan, Hubei, 430011, China
Abstract:

In today’s era, the transformative power of computing is highlighted, and computational thinking has become the core literacy and essential ability of learners, while computer education is an effective carrier for cultivating computational thinking. The article firstly researches the theory related to collaborative filtering and generative adversarial recommender system. Then it combines SeqGAN with traditional CF algorithms, proposes to use sequence generative adversarial network for missing data prediction, and makes appropriate improvements to SeqGAN to make it suitable for generating scoring data, and then further designs a computer teaching system based on this model. The article launches performance testing experiments on Ali’s real dataset UserBehavior, and conducts experiments on the effect of computer education with the students of computer application major in a secondary school as the research object. The results of the study show that in the comparative analysis of the pre-test and post-test of computational thinking of the experimental class, the mean of the total score of computational thinking of the experimental class in the pre-test and post-test is 71.17 and 78.35, respectively, and the post-test is more than 7 points higher than the pre-test. It can be concluded that the teaching model of multilevel computational modeling designed in this paper promotes the development of students’ computational thinking and academic performance, improves students’ learning attitudes, and increases classroom participation.

Biao Guo 1, Mengxu Li 1
1School of Accounting and Finance, Anhui Xinhua University, Hefei, Anhui, 230088, China
Abstract:

With economic globalization and the increasing complexity of inter-enterprise business linkages, corporate financial systems have gradually taken on the characteristics of complex networks. This paper firstly gives an overview of the complex network and introduces its basic topological properties, such as clustering coefficient and path length. After that, through the principal component analysis method, the enterprise financial risk early warning indicators are identified, and the key indicators are screened to improve the early warning accuracy. Based on these properties, the financial risk conduction network model of complex enterprises is constructed, the characteristics of the network are analyzed, including network density, centrality distribution, etc., and the effect of financial efficiency enhancement of complex enterprises under the optimization of topology computation is verified in real cases. The results show that most of the financial risk indicators of enterprises have strong correlation, and the degree of centrality of 9 indicators such as “gearing ratio and quick ratio” is more than 50%. In addition, the indicators of “current asset turnover ratio, interest coverage multiple, net profit growth rate” can play the role of intermediary and bridge, and the risk transmission effect among the indicators is high. The threshold value of 0.65 is the watershed of the changes in the financial structure of enterprises, and most of the financial risks in the network have a high degree of similarity in the financial structure when the degree value is 70, and it is negatively correlated with the coefficient of agglomeration, and the coefficient of agglomeration decreases with the increase in the intensity of the points.

Huaying Yu 1
1Linyi Vocational College, Linyi, Shandong, 276000, China
Abstract:

In order to explore the deficiencies in the teaching process of marketing majors in higher vocational colleges and further improve the teaching quality of marketing majors in higher vocational colleges. This paper utilizes the improved ID3 algorithm to construct the SLIQ data mining algorithm to improve the teaching quality of teachers of marketing majors in higher vocational colleges and universities. Using ID3 algorithm to build a decision tree to get the portraits of teachers and students, at the same time, in order to reduce the computational complexity of ID3 algorithm and the problem of multi-value bias, the concept of sample structure vector similarity is introduced, and the degree of information gain is optimized to get a more reasonable decision tree. On this basis, based on the improved ID3 data mining algorithm, a teaching quality assessment system for senior marketing majors based on SLIQ algorithm is designed, which identifies important factors affecting teachers’ teaching quality by mining a large amount of data in the teaching process.The AUC value of the SLIQ data mining algorithm is 0.98, which can effectively improve the algorithm’s generalization ability, and it has an excellent performance in the teaching quality assessment task. The performance is excellent. In this paper, we systematically identify “the principles of marketing” and “the degree of seriousness of teachers’ homework correction” as the key factors to improve the teaching quality of marketing teachers. It provides a scientific basis for improving the quality of teachers’ teaching.

Special Issues

The Combinatorial Press Editorial Office routinely extends invitations to scholars for the guest editing of Special Issues, focusing on topics of interest to the scientific community. We actively encourage proposals from our readers and authors, directly submitted to us, encompassing subjects within their respective fields of expertise. The Editorial Team, in conjunction with the Editor-in-Chief, will supervise the appointment of Guest Editors and scrutinize Special Issue proposals to ensure content relevance and appropriateness for the journal. To propose a Special Issue, kindly complete all required information for submission;