rss_2.0Applied Mathematics and Nonlinear Sciences FeedSciendo RSS Feed for Applied Mathematics and Nonlinear Sciences Mathematics and Nonlinear Sciences Feed Analysis and Exact Solutions of Extended Kadomtsev-Petviashvili Equation in Fluids<abstract> <title style='display:none'>Abstract</title> <p>The extended Kadomtsev-Petviashvili (eKP) equation in fluids is investigated by using Lie symmetry analysis. The symmetry reductions, together with the simplest equation method, are used to obtain exact solutions of the eKP equation. Finally, we derive the conservation laws of eKP by using multiplier approach.</p> </abstract>ARTICLEtrue on the Largo and architectural landscape of Macau from the perspective of historical layering<abstract> <title style='display:none'>Abstract</title> <p>With the research of urban historical landscape, its definition has been continuously deepened. The development of a city is regarded as the result of the accumulation of cultural and natural values in different periods, that is, the historical landscape of a city is the result of historical ‘layering.’ This paper takes the historical dynamic layering process of the Largo and the architectural landscape of Macau as the research content and uses the layering method to take the economy, society and culture of Macau in each historical period as the internal cause of its layering value, relating its explicit characteristics so as to explore the ways and rules of its historical layering. Moreover, in the historical layering of various dimensions, the harmonious Chinese and Western cultural values of Macau are always linked, and it is concluded that ‘the characteristics of pluralism and symbiosis have created the present Macau.’ This paper advocates that in the protection and inheritance of the urban context of Macau, we should focus on the effective protection and promotion of the multi-symbiotic culture and pass on the unique flavour of the city jointly created by the Chinese and Portuguese people.</p> </abstract>ARTICLEtrue of the current situation and influencing factors of information technology education in middle school<abstract> <title style='display:none'>Abstract</title> <p>The development of science and technology is becoming more and more rapid, and the educational empowerment of information technology (IT) in middle schools is becoming more and more obvious. The interesting and operational aspects of IT are suitable for middle school students, who are gradually becoming more rational in their thinking and problem-solving skills, and who are curious to discovering new things. This paper analyses the factors influencing the acceptance of IT education among middle school students by reviewing a large amount of literature and compiling technology-related theories. The research variables are determined by combining the characteristics of middle school students, and a structural equation model is constructed to select the factors influencing the acceptance of technology in secondary school IT classrooms, and the hypothesis is proposed, tested and revised, and then the scientific and effective measures are proposed according to the model. By the statistical analysis of variables, it can be seen that the average values of perceived ease of use and social influence (SI) are relatively high, which are 3.9899 and 4.1933, respectively, indicating that SI and subjective initiative have significant positive correlations with the behavioural intentions of middle school students in learning IT. As technological literacy is low, with an average value of only 3.4966, the influence of the technological literacy of IT on middle school students’ learning ability is not significant. This reflects the degree of middle school students’ mastery of the knowledge of IT, which is not enough. Further, the initiative of learning in the network is low and the needs of teachers in IT classes indirectly affect students’ learning initiative. It is hoped middle school students learn IT through the network by their initiative and provide guidance for teachers in teaching, to promote the application and deep popularity of IT in secondary school education.</p> </abstract>ARTICLEtrue study of immersive technology for product usability improvement design based on comprehensive value evaluation<abstract> <title style='display:none'>Abstract</title> <p>The combined value of any product design method depends on the design benefits and costs of use, determining the need to put the method into practice. In this study, a virtual reality design system was constructed to support the widely adopted user interview method for the usability improvement design of an existing product, using an industrial remote control as example. The combined value of the method was verified to be superior to the use of user interviews alone, in terms of the number and importance of usability questions mined by users, the level of styling of improved design solutions guided by usability questions, and the willingness of designers to use the method. It provides a useful reference for the promotion of immersive technology in the field of product design and the search for new focus points.</p> </abstract>ARTICLEtrue of hybrid kernel function in economic benefit analysis and evaluation of enterprises<abstract> <title style='display:none'>Abstract</title> <p>The economic benefit of enterprises is an effective index to measure the economic activities, which forms the basis and starting point. Therefore, in this paper, the traditional analysis methods of enterprise in terms of economic benefits are compared and based on its evaluation principles, the advantages, theory and realisation process of the kernel function in enterprise economic benefits analysis are analysed. Then, different kernel functions are selected to analyse the total output value, product sales rate, sales revenue, total profit and total profits after taxes of five enterprises, and their economic benefits are evaluated by the cumulative contribution rate of principal components. Finally, the mixed kernel function based on the combination of polynomial kernel function and Gaussian kernel function is used to optimise the analysis effect, which is meant to help enterprise leaders make more scientific decisions and lay a foundation for the sound development of enterprises.</p> </abstract>ARTICLEtrue and application of the ‘Learning in Zhejiang University City College’ platform, integrating teaching evaluation and management<abstract> <title style='display:none'>Abstract</title> <p>In view of the isolation of the software and hardware teaching environment, isolation of various online teaching platforms and lack of coordination of data, it is not conducive for further promotion of ‘Internet Plus Teaching’ and the improvement of online teaching. The Trinity teaching platform, namely ‘Learning in Zhejiang University City College’ is built against the background of digitalisation reform in colleges and universities. The teaching platform integrates the smart classroom, the Zhiyun Classroom (online classroom) and the curriculum platform. The platform breaks through the limitation of time and space, connects the teaching process and implements the integrated ‘teaching, learning, evaluation and management’ based on data collaboration. It is fully applied in Zhejiang University City College, and is stable, efficient and convenient, with a high access rate and better interaction between teachers and students. It effectively implements closed-loop management of the teaching process, changes the educational form of teacher education, student learning and school management. It also adapts to the cultivation of innovative and individualised talents under the new situation, and further deepens reforms of ‘Internet Plus Teaching’. It provides a solid support for the whole process management of student learning.</p> </abstract>ARTICLEtrue and prediction of regional human capital based on optimised BP neural network<abstract> <title style='display:none'>Abstract</title> <p>With the increasing role of knowledge and technology in the economy, human capital has become the decisive factor for economic development and social progress. Measuring, evaluating or predicting the level of regional human capital within a country can grasp the investment policy of human capital as a whole. Therefore, in this paper, a prediction model of regional human capital level based on optimised BP neural network is built. First, the evaluation system of the regional human capital is constructed by selecting 15 evaluation indexes in 5 categories, such as educational training, development of science and technology, medical care, labour migration and social security. Then, the PSO algorithm is used to optimise the BP neural network, and the core problems in the optimisation process are solved. Finally, the model is tested and analysed by the MATLAB simulation platform. The results show that the prediction accuracy of the model is high, and the output results are basically consistent with the reality, which is conducive to promoting the structural upgrading of human capital.</p> </abstract>ARTICLEtrue and evaluation of intelligent teaching system on basic movements in PE<abstract> <title style='display:none'>Abstract</title> <p>For a long time, the situation of students’ learning in physical education (PE) was not optimistic, especially the basic movement learning after class, which lacked effective online learning tools. With the in-depth research of deep neural network and the rapid development of computer hardware, the artificial intelligence technology based on deep learning has performed well in the field of basic teaching. Therefore, in this paper, an intelligent teaching system of basic movements in PE is designed. First, the information of coordinate points is collected according to the Gaussian model, and the pose of students is estimated by OpenPose. Second, the overall architecture and functional modules of the system are designed. Finally, the deviation limbs that affect the standard of overall movements are identified by the matching algorithm, which realises the evaluation and feedback of basic movements in PE. Through this teaching system, teachers can obtain the learning situation of students’ movements, and students can adjust their movements through the feedback, which achieves the convenient interaction of PE teaching.</p> </abstract>ARTICLEtrue nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model<abstract> <title style='display:none'>Abstract</title> <p>Researching the past empirical studies, we find that the empirical results of using data from the same or similar stages of economic development tend to be very close; however, there will be some discrepancies when comparing the empirical results of data samples at different stages of development. In order to explain this phenomenon, a theoretical analysis is made on the regional differences in the impact of population ageing on national saving. By analysing the areas considered in this paper as being in different stages of economic development, the combined effects of population ageing on the national saving rate are different. In order to verify the above conclusions, the thresholds and threshold effects are estimated and tested through the threshold model. The results show that the impact of population ageing on the savings rate will be different due to different levels of economic development. When per capita income is below the threshold of 9001.69, population ageing has a greater negative impact on the national savings rate. When per capita income is above the threshold of 9001.69, the negative impact of population ageing on the national saving rate is smaller.</p> </abstract>ARTICLEtrue on classification of e-commerce customers based on BP neural network<abstract> <title style='display:none'>Abstract</title> <p>With the development of e-commerce technology, the relationship between enterprises and customers has been completely changed. The core management concept of enterprises has gradually transformed from ‘product-centred’ to ‘customer-centred’. Adopting effective methods to classify customers, implementing different management and marketing schemes of customer retention and customer upgrading will play an important role in promoting the development of e-commerce enterprises. Therefore, the classification of e-commerce customers based on Back Propagation (BP) neural network is studied in this work. Firstly, the theoretical basis of customer classification is summarised in the Introduction and theoretical part. Then, a classification index system of the e-commerce customer is constructed, and on this basis, a classification model of the e-commerce customer based on the BP neural network is constructed. Finally, the results of classification are analysed with related data.</p> </abstract>ARTICLEtrue algorithm-based congestion control optimisation for mobile data network<abstract> <title style='display:none'>Abstract</title> <p>Mobile data network is featured by long delay and moving terminals, which affect the user service quality performance of transmission control protocol’s (TCP) congestion control algorithm Vegas. To solve this problem, this paper first proposed to optimise the congestion control algorithm using a genetic algorithm, build ns-3 network topology structure and adopt mobile data network trace for optimisation and simulation; and the Vegas optimisation problem as a multivariate dual-objective problem was solved with Non-dominated Sorting Genetic Algorithm II (NSGA-II). The ns-3 simulation results indicate that Vegas with optimised parameters have high throughput and short delay, which significantly promotes TCP Vegas’s QoS under a mobile scene.</p> </abstract>ARTICLEtrue on innovative strategies of college students’ English teaching under the background of artificial intelligence<abstract> <title style='display:none'>Abstract</title> <p>Today, corresponding to the new wave of internationalisation and integration, education is also subject to rapid and innovative changes. Accordingly, detailed research is undertaken in the present study on innovative teaching strategies that can be developed, under the background of artificial intelligence, to familiarise college students with the ability to fluently express their ideas in English. The research shows that among the factors affecting the quality of English teaching, teachers’ teaching methods, English teaching environment and students’ independent learning ability account for high weightage, which are 54%, 31% and 11%, respectively. Through the model of college students’ English teaching innovation strategy, it can be seen that the teaching method, teaching environment and autonomous learning method are the most feasible methods that can be employed in crafting a students’ English teaching innovation strategy.</p> </abstract>ARTICLEtrue of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF<abstract> <title style='display:none'>Abstract</title> <p>As China’s agriculture has developed towards modern agriculture, agricultural finance has played a crucial role in promoting China’s rapid agricultural development. Due to the ineffective interpretation of policy support of agricultural finance, poor agricultural areas cannot benefit from the current policy. The purpose of this paper is to propose a model that combines the ELECTRA model with a bi-directional long- and short-term memory network, BiLSTM and conditional random field (CRF) for identifying agricultural finance policy information. The first step is to convert the plain text of agricultural finance policy into word vectors using ELECTRA’s pre-trained language model. By incorporating zigzag character substitution in the generator, the adaptability of the pre-training target to the annotation task on agricultural finance policy is improved. Next, the BiLSTM neural network is used to obtain the contextual abstract features of the serialised text. Finally, the global optimisation sequence decoding annotation is combined with the CRF to extract the structured agricultural finance policy information. The results indicate that the agricultural finance policy information extraction model is more effective than other models in capturing agricultural finance policy information and has excellent information extraction capabilities.</p> </abstract>ARTICLEtrue on the construction of rural interface style based on aesthetic rules<abstract> <title style='display:none'>Abstract</title> <p>The form and overall style of rural settlements are the carrier of the rural regional context and aesthetics. At present, China’s rural areas are facing a disorderly style and urbanisation. This study is based on similarity aesthetic regularity and visual aesthetic regularity; on the one hand, this work researches the method of building interface coordination from the aspects of form, material and colour, and puts forward the interface construction method of strong contrast, medium contrast and weak contrast according to the rural areas. On the other hand, this study analyses people’s perception characteristics of the style from the visual psychological level, explains the skills for the rural interface and sequence arrangement based on the relationship between visual matching and the bottom of the picture and constructs the aesthetic image under the new overall relationship of the place. Finally, this study puts forward a series of strategies for rural style construction, such as symbol concatenation, contrast reconstruction and aesthetic conflict transformation, to constructing a new aesthetic image of place so as to provide ideas and methods for the development of the rural style in the future.</p> </abstract>ARTICLEtrue on location algorithm of new energy vehicle charging station based on multi-objective decision<abstract> <title style='display:none'>Abstract</title> <p>Under the influence of the new energy strategy, the new energy vehicle has developed vigorously. As an important supporting infrastructure, the rationality of its location construction has become the key factor for the popularization of the cars. In this paper, the influence of economy, environmental protection and convenience is comprehensively considered in the model. The comprehensive optimization objective is to minimize the annual cost of construction and operation of the stations, minimize the additional carbon emissions caused by charging, and maximize the service capacity. Considering the layout and capacity constraints of charging facilities in charging stations, the AHP is used to weight each objective function. Thus, the multi-objective optimization model can be simplified, and the chicken swarm algorithm is used to settlement this question.</p> </abstract>ARTICLEtrue transmission of simultaneous wireless information and power transfer system for Internet of things<abstract> <title style='display:none'>Abstract</title> <p>Due to the excellent broadcasting characteristics of radio signals, simultaneous wireless information and power transfer (SWIPT) can transmit both information and energy, and provide users with stable power supply. Wireless channel has the characteristics of openness, which will lead to the leakage of information in the SWIPT system. It is one of the research hotspots in the industry to ensure the secure transmission of information in SWIPT system where there are differences in the transmission of energy and information. This paper proposes an ‘information-energy’ dynamic switching opportunistic secure transmission scheme. First, a model considering three factors of multi-cell, multi-user and multiple eavesdropper is established which assumes that the user adopts a time-domain switching receiver that collects energy in a nonlinear model. Then, combined with the time-varying wireless channel, a dynamic information energy switching transmission scheme based on signal-to-interference noise ratio threshold is proposed. Finally, the energy and information transmission performance of the scheme are comprehensively analysed.</p> </abstract>ARTICLEtrue on the evaluation of historical building values based on historic building mapping<abstract> <title style='display:none'>Abstract</title> <p>Historic buildings carry the history of human civilisation, and their conservation and utilisation are widely valued by countries around the world. At present, the lack of qualitative and quantitative assessment and evaluation methods for the preservation status and attachment value of historic buildings poses a challenge to the smooth implementation of the conservation and utilisation of historic buildings. The development of a set of system standards for the assessment and evaluation of historic buildings is an urgent task for the conservation and utilisation of historic buildings. This paper proposes a set of comprehensive mapping assessment and evaluation system for historical buildings through the analysis and sorting out of the current situation of preserving historical buildings and their development lineage, architectural style, building type, society and art. Finally, based on the above mapping evaluation system, 20 historical buildings are graded according to the requirements of historical building classification, and according to the different levels. Corresponding conservation measures are proposed and different planning schemes are formulated to better utilise the historical, scientific, cultural and economic values of historical buildings.</p> </abstract>ARTICLEtrue Necessary Conditions for Feedback Functions of de Bruijn Sequences<abstract> <title style='display:none'>Abstract</title> <p>De Bruijn sequence is an important kind of nonlinear shift register sequence, which has a very wide range of applications in the fields of communication and cryptography. From the perspective of the relationship between linear terms, quadratic terms and cubic terms in the feedback functions of de Bruijn sequences, some new necessary conditions for feedback functions of de Bruijn sequences are obtained. Some examples show that the known necessary conditions cannot deduce the proposed necessary conditions.</p> </abstract>ARTICLEtrue on tourism development income index calculation of finite element ordinary differential mathematical equation<abstract> <title style='display:none'>Abstract</title> <p>The development of tourism promotes the rapid development of regional economy. Balancing the relationship between investment and income of tourism is important, which affects the speed of economic development. Based on the background of tourism economy, to a specific mode of regional tourism, the first step is to collect information, for the coupling analysis between the subsystems of the tourism industry and regional economy of synergy, through the tourism development index of income differential mathematical equations of finite element calculation, a mathematical model built for the tourism income. By solving the finite element ordinary differential mathematical equation, the relationship between tourism maximum income, effective income and investment cost is obtained. Finally, the stability of the mathematical model is analysed. This study evaluates and predicts the income index of tourism development in a specific region and provides countermeasures for the development of tourism economy in this region.</p> </abstract>ARTICLEtrue on product process design and optimisation model based on IoT intelligent computing<abstract> <title style='display:none'>Abstract</title> <p>In this article, some complex parameters of the product and design processes, how to match and optimise the sub-parts of related industrial products and how to improve the quality of the corresponding products and the competitiveness of the product in the international market are discussed in this article. We also build an algorithm based on the particle swarm and XGBoost algorithms, combined with the intelligent computing of the Internet of Things (IoT). We transform some uncertain factors in the process of the industrial product design process through the fuzzy matrix, select the optimal design through the optimised intelligent computing of the IoT scheme and compare the influence of the scheme before and after optimisation on production efficiency. The results show that the method proposed in this article can reduce the time-consumption of optimal solution selection by 42.85%–52.94%. In addition, selecting the optimal solution for each field in a targeted manner can increase the overall production efficiency of the product by about 5%, reaching between 93.6% and 96.5%, which may save raw materials and create more economic value.</p> </abstract>ARTICLEtrue