With the gradual enhancement of scientific research capabilities around the world, new technologies continue to emerge, and the current momentum of VR technology development is strong. The source of China’s VR industry development is based on the development and application of a computer repair training platform. In the context of computer repair training platform, VR technology can be applied to the display of computer parts to achieve the development and design of a training platform combined with virtual reality. Therefore, it can be foreseen that ‘VR industry + practical training platform’ has great potential and will certainly promote the upgrading of the display industry. Universities are actively thinking about how to carry out teaching reform, and today, with the rapid development of technology, using information technology to implement teaching reform is undoubtedly the best choice [1–3]. In order to accelerate the process of teaching reform, various interactive online learning platforms using multimedia computer technology and network technology have emerged. To a certain extent, this will weaken students’ motivation to participate in teaching [4, 5]. Therefore, based on this situation, a new technology, VR, has entered the education field with its rapid development. The basic principle of virtual reality (VR) technology is to construct a corresponding three-dimensional virtual space with the help of computer graphics rendering technologies to give users sensory perceptions, including visual, auditory and tactile sensations, so that users can feel as if they are in a virtual environment, and at the same time, users can feel the information from the virtual reality world and interact with it [6, 7]. The products based on VR technology are listed in Table 1, and the analysis shows that with the development of science and technology, VR technology has gradually penetrated into all aspects of life . The main reason is that the virtual reality technology allows people to create a real feeling of being there and to perform corresponding activities and communication [9, 10]. The main feature of VR technology is the perfect match between virtual and reality, which gives people a sensory experience . VR technology mainly includes sensing technology, stereoscopic display technology, network technology, voice recognition, stereo sound technology and data communication technology .
Percentage of VR technologies in each application area
|Product name||VR technology share (%)|
In recent years, the development of virtual reality technology has advanced rapidly due to, firstly, the rapid progress of computer technology and computer graphics processing technology, and secondly, the application of virtual reality technology to many industries, and has reached very high achievements. People are more and more favourable to virtual reality technology [13, 14]. At this stage, VR technology has started to be applied in many fields, such as education, entertainment, medical, military and heritage conservation. The application of VR in the field of education first originated in some major developed countries, like Europe and the United States, and has been developed for nearly three decades. The pioneer in VR teaching is the electrical engineering department of MIT in the United States, which brought VR technology to the classroom soon after its emergence [15, 16]. Based on these analyses, Zhang  proposed new ideas on how to use VR technology in teaching and learning, and Damiani et al.  presented a typical case study on the use of VR technology in teaching and learning, called ‘The Book of the Future’. Fealy et al.  built a Web-based exploratory virtual physics laboratory using JAVA technology, which contains three main research directions: firstly, research on experimental courses; secondly, research on virtual experimental apparatus and facilities; and third, research on collaborative learning. Burova et al.  used QuickTime technology to conduct research and a complete demonstration of the VR Potala Palace. Cassidy et al.  effectively proposed the technique of expression and lip sync in VR-related projects, which contributed to the great development of VR technology. Burova et al.  focused on virtual roaming and used virtual modelling and virtual driver training in urban planning. In a theoretical sense, the computer maintenance training platform itself is a very important part of the vocational training of students, and it is an essential part for them. The introduction of VR technology into practical training can theoretically bring new developments to the teaching of practical training and make up for the lack of theoretical guidance. Education informatisation has become the tone of education in the whole society, and on top of that, how to improve the existing computer repair practical training platform through VR technology to develop a more complete teaching model is under discussion [23–25]. In addition, the current status of the computer maintenance practical training platform is more limited to the theoretical level, and the practical scenarios are extremely limited. How to combine the current situation of practical training teaching and the limitations suffered at the current stage, through VR technology to optimise the teaching mode, can perfectly match the teaching needs of the current computer maintenance practical training platform and effectively improve the quality of practical training teaching [26, 27]. In a practical sense, the current educational information reform conducted by the computer maintenance training platform requires the use of VR technology, and VR technology in the classroom is of great practical importance for the development of practical training courses.
VR technology in the practical training courses can effectively solve the drawbacks of the traditional teaching model. At present, due to the expansion of students and effective funding, traditional practical training courses are bound to have limited training stations and outdated equipment, coupled with the danger of some practical training projects, and students need to take greater risks in the process of experience. These problems can be solved through VR technology so that students can get a lot of practical training experience through VR technology, avoiding the problem of high risk of practical training projects. These problems can be solved by VR technology, which allows students to get a lot of practical training experience through VR technology and avoid the problem of high danger of the project [28, 29]. At the same time, VR technology also allows students to practice a project several times to improve the effect of practical training [30, 31]. Secondly, for students attending computer maintenance practical training courses, technology learning requires long-term and repeated practice, and VR technology can provide an opportunity for them to repeatedly practice a project through VR technology, and with a small amount of real experience, the students’ practical training ability can be greatly improved, which can not only reduce the error rate of students in real operation but also develop practical skills for students. This practice not only reduces the error rate of students in real operation but also cultivates a sense of achievement in practical operation for students and improves their interest in learning and self-confidence [32, 33]. Finally, the wide application of VR technology in practical training courses not only allows students to gain fresh experiences through VR technology but also allows teachers to supplement their teaching methods by attending conferences and trainings of some specialised courses without leaving home, improving their teaching level, obtaining richer teaching resources and, at the same time, mastering the latest information on teaching methods and professional technologies and cultivating teachers’ developmental awareness [34, 35].
Therefore, this research uses VR technology as the theoretical basis and conducts an in-depth study on the demand of VR technology application in the computer maintenance practical training platform development design and application by establishing a neural Turing machine (NTM) algorithm model, and quantitative and qualitative analyses of the platform development design according to the application of VR technology.
For the development, design and application of the computer maintenance practical training platform, perfect integration with VR technology is the difficulty and the key point, which is related to the operability of the practical training platform and the improvement of teaching quality. To improve the matching of VR technology in the computer maintenance practical training platform, a VR model based on the NTM algorithm is established.
An NTM is a neural network architecture with the addition of an external storage matrix. The external storage matrix enhances the neural network’s ability to remember long input sequences, forming an attention mechanism similar to the
The controller in the NTM is equivalent to the CPU in the computer, its external memory is equivalent to the memory of the computer, and its read/write terminal is equivalent to the IO device of the computer. The controller modifies and reads the memory block through the read/write terminal. During the operation of the computer, the CPU addresses the data information according to the control signal from the controller and determines the location in the memory to read and write the data information. Unlike the actual machine, there is no derivable concept for computer operations on memory, whereas in the NTM, all read and write operations on the memory block matrix are derivable.
The addressing of the NTM, that is, the process of calculating the weights corresponding to all the vectors in the external matrix, includes addressing by content and addressing by position. Addressing by content requires first calculating the similarity between the target vectors given by the controller and all the vectors in the external matrix of the NTM, while addressing by position makes some adjustments to the results of the addressing by the content process according to their position coordinates in the memory matrix. Addressing by content and addressing by position jointly realise the addressing of the NTM and form the effect of attention mechanism. The general addressing formula of the NTM is as follows:
The key for content addressing part of the NTM is very similar to the role of the attention mechanism. Addressing by content requires a normalised weight value for all vectors in the memory, and when reading and modifying the external memory matrix in the NTM, it needs to be modified to varying degrees depending on the result of the addressing. This process attention mechanism is very similar. In the addressing process of the NTM, the output vector
The part of computing similarity can be computed using the Luong attention mechanism, which is widely used in sequence applications and has achieved effective enhancements in several areas of natural language processing. This attention mechanism belongs to one of the implementations of the global attention mechanism, in which the hidden state vector of the target is compared with all the output states of the encoder during the computation of the intermediate semantic vector, and a weight vector of length equal to the time step of the encoder is computed. The weights of this attention are calculated as given in the following Eq. (5):
There are many ways to calculate the
In this study, the
In the decoder part enhanced with the external memory matrix, after addressing by content, it is still necessary to use addressing by position to further obtain more accurate different weights of each vector in the external memory matrix. This part mainly includes three processes: linear interpolation, transfer and sharpening, which are calculated as follows:
The output of the NTM controller controls the workflow of the entire NTM-VR model. The controller is implemented as a neural network, which means it can be a recurrent neural network or a fully connected or convolutional network, and the neural network controller interacts with the whole system input and output. The read and write sides of the NTM-VR model calculate the weights of each vector in the external memory matrix in the current state based on the control signals from the controller and then perform read and write operations on the external memory based on the weights. The NTM-VR model needs to calculate a set of weight coefficients for both the read and write operations of the external memory matrix, and this process of finding the weight coefficients is the addressing process of the NTM-VR model.
The moment in the previous formula is
The decoder is another NTM-VR model parameter module with weights separate from the NTM-VR model. The advantage of this model is that the input data and output data are in different data distributions, and their respective data distributions can be represented by their respective NTM-VR model neurons separately, and the network is easier to converge and can achieve better training results, but the total number of weights is twice that of the encoder or decoder when the dimensions of their hidden states are the same, which may affect the working efficiency of the system in some scenarios.
This subsection shares the weights of the decoder and the encoder, as in Eq. (13), so that the parameters of the whole NTM-VR model are reduced by half by sharing the weights of the NTM-VR model, but the processes of encoding and decoding in the
After merging the weights, the model eliminates the attention layer in
Each weight in the neural network is a parameter value of the floating point type during the participation in the calculation, and the gradient of the quantised value is calculated by the reverse transfer of the gradient. But at this time, this gradient value is used to update the previously saved up floating point type of parameter value. The process of the reverse transfer of gradient is shown in Eq. (15).
Following this process, both forward inference and gradient back propagation of the model can be completed. When the model is fully trained, a final quantisation operation can be performed using the latest floating point parameters to form the quantised neural network and weights with the following Eqs (16) and (17):
The replacement of value types in the quantisation process of the network model requires a uniform transformation of the original range of values into a new range of integer-type values, and there is a conversion process of scales and zeros in this process. The quantisation process is shown in Eq. (16), where
The corresponding process of finding the floating point number corresponding to each quantised value during the training process is called inverse quantisation, in which can be carried out using the following Eq. (19):
The quantisation method using zeros makes the quantised results symmetrically distributed, but the introduction of zeros increases the computational effort in the quantisation process exponentially. The design can be quantised using a quantisation process with a fixed value of zero. This quantisation process can be simplified using the following Eqs (20) and (21):
This fixed zero point corresponds to the inverse quantisation, as given in the following Eq. (22):
For the sequence generation model and sequence classification model, the quantisation method in this subsection is used to compress the weights of the NTM-VR model in the feature extraction network, which can further obtain a more lightweight network structure.
In the current computer maintenance training platform teaching in colleges and universities, the teaching and teaching content of the practical training courses as well as the actual social work cannot meet the needs of course teaching and actual social work mainly because the computer network courses emphasise theoretical teaching and ignore the practical training, and because of the low utilisation rate of laboratory equipment. The maintenance training platform teaching content is too old, which is away from the actual needs of society. The content of experimental training cannot be perfectly combined with the theoretical course, and the mode of practical training is too single. Therefore, it is urgent to build a reasonable structure and perfect function of the practical training teaching platform to meet the needs of practical training and better cultivate network technology talents in line with the needs of society. And the use of traditional computer network experimental rooms to carry out network experiments, often using direct plugging and unplugging line connection equipment experimental methods, has several major drawbacks: first of all, a lot of students’ experimental time is wasted in plugging and unplugging lines, rather than in the experimental content, which results in poor learning. Secondly, a large number of students plug and unplug lines at the same time; the scene is chaotic; the teacher’s energy is wasted in maintaining order in the classroom, so they cannot concentrate on counselling students to perform experiments; thus, the teaching effect is poor. Thirdly, the loss of equipment in the experimental process is very serious. The use of simulation technology in the teaching of the computer maintenance training platform can effectively avoid the aforementioned problems.
Therefore, factoring in the needs of teachers and students and the existing training platform as a parameter, we used the NTM-VR model for simulation analysis. The analysis results are shown in Figure 1. Analysis of Figure 1 shows that students’ acceptance of the VR training platform is 67.4%, which is much higher than 32.6% acceptance for the traditional platform; and teachers’ acceptance of the VR training platform is as high as 71.5%. The calculation results show that the VR technology-based computer maintenance practical training platform can not only connect the real equipment integrated network practical training environment into the Internet but also connect each laboratory bench unit of the practical training platform. With the open design, students can break through the limitation of time and space to carry out practical training exercises using this module. Students can configure the equipment in the experimental environment by simply logging onto the access controller of the practical training system through the Internet and entering the name of the corresponding equipment to access the unit for experiments, which greatly enhances students’ participation and improves teachers’ teaching quality.
The teaching resource library is designed to categorise scattered and messy teaching resources, store them in an orderly manner, and provide students and teachers with uploading, retrieving and downloading functions so that students can obtain teaching resources and practice topics conveniently through the Internet when they need them and realise the sharing of teaching resources. This will change the traditional teaching concept, teaching style and learning style, combining task-based learning and project-based teaching methods, turning students from being indoctrinated in learning to being inquirers in learning, highlighting the position of students as the main body and centre in the learning process. At the same time, the use of teaching resources library can also realise fragmented learning, students can carry out independent learning when they have free time, choose teaching resources according to their needs, selectively choose learning resources according to their learning situation and learning progress and realise personalised learning. Therefore, the learning intensity, learning outcomes and practical training platform approach are brought into the NTM-VR model for simulation analysis, and the results are shown in Figure 2. From Figure 2, it can be seen that under the uniform learning intensity, the learning outcome based on the VR computer repair practical training platform is 76%, which is much higher than the learning outcome based on the traditional computer repair practical training platform of 24%. This shows that VR technology connects the practical training platform to the real virtual, and at the same time, it can make the computer-related parts real in front of students so that they can master computer repair skills more quickly. Under the unified learning outcome, the learning intensity of the VR-based computer repair practical training platform is only 32%, which is much lower than the learning intensity of 68% based on the traditional computer repair practical training platform. This shows that VR technology brought into the classroom can drive students’ motivation and improve the acquisition of students’ learning skills while reducing the learning intensity. The aforementioned data calculation results show that the open computer network implementation platform uses a combination of virtual and real experimental environment and online teaching mode, introduces advanced teaching concepts and teaching modes, builds shareable computer network course practical training teaching resources and creates a teaching platform that fully supports online practical training. It can build an experimental teaching system that unites knowledge and ability. The goal of the computer maintenance training platform is not simply to master the network foundation of computers and practical training tools but also to develop computer network courses and computational thinking skills around ‘computing’.
According to the aforementioned calculation results and field research, it is known that the computer maintenance practical training platform is developed and designed for the purpose of enriching the types of experiments for students because students can only carry out the networking practice in the network practical training course through the real practical training environment and cannot create a fault scenario. The virtual simulation technology can create a fault scenario for students and exercise their ability to apply their knowledge flexibly. Therefore, in order to make the VR computer maintenance practical, the training platform designed in this study must have the following four major functions for more realistic use: Update the experimental teaching content, which requires computer network courses in the framework of the complete knowledge and ability of the curriculum system, a comprehensive update of teaching content consistent with the computer subject planning. To explore the ‘‘computational thinking skills, computer network technology application skills, multidisciplinary cross-fertilization’’ of the unity of knowledge and ability training system, and to establish a practical training system to adapt to it, from the training program to fully support the unity of knowledge and ability of the course, the establishment of a new curriculum system in line with the development of the times and social needs. Open-type virtual and real experimental environment supports the reform of teaching methods. Computer science is supported by information technology, and the flow and changes of information are invisible, which is a difficult problem plaguing the development and teaching reform of computer science. A key problem yet to be solved is presenting new structures and new content experiments. Online shared resource library construction: In order to solve the shortage of teaching resources, the open computer network practical training platform is required to provide resource-rich and diverse forms of teaching resource library[ to realise the teaching resource library, open computer network practical training platforms and teaching resource interoperability; and to provide support tools for teaching and experimental teaching of computer network courses. Fully support the whole process of practical training teaching: The practical training platform needs to track the whole process of experimental teaching, including the maintenance of experimental project library of experimental courses, practical training teaching arrangement, intelligent guidance of experimental process, automatic evaluation of experimental reports, experiments into the multi-colour statistics query, digital resource management, teacher-student interactive communication and other functions.
Update the experimental teaching content, which requires computer network courses in the framework of the complete knowledge and ability of the curriculum system, a comprehensive update of teaching content consistent with the computer subject planning. To explore the ‘‘computational thinking skills, computer network technology application skills, multidisciplinary cross-fertilization’’ of the unity of knowledge and ability training system, and to establish a practical training system to adapt to it, from the training program to fully support the unity of knowledge and ability of the course, the establishment of a new curriculum system in line with the development of the times and social needs.
Open-type virtual and real experimental environment supports the reform of teaching methods. Computer science is supported by information technology, and the flow and changes of information are invisible, which is a difficult problem plaguing the development and teaching reform of computer science. A key problem yet to be solved is presenting new structures and new content experiments.
Online shared resource library construction: In order to solve the shortage of teaching resources, the open computer network practical training platform is required to provide resource-rich and diverse forms of teaching resource library[ to realise the teaching resource library, open computer network practical training platforms and teaching resource interoperability; and to provide support tools for teaching and experimental teaching of computer network courses.
Fully support the whole process of practical training teaching: The practical training platform needs to track the whole process of experimental teaching, including the maintenance of experimental project library of experimental courses, practical training teaching arrangement, intelligent guidance of experimental process, automatic evaluation of experimental reports, experiments into the multi-colour statistics query, digital resource management, teacher-student interactive communication and other functions.
In the past, schools paid more attention to the theoretical education of computer maintenance than to practical education, which is largely due to the fact that it is time-consuming and costly to provide practical education to students. The introduction of VR technology can simulate the actual situation for students, and the VR display can not only enhance students’ interest but also deepen their impressions. Therefore, this research has used VR technology as the theoretical basis, established the NTM algorithm model and conducted an in-depth study on the demand, development design and application of VR technology in the computer maintenance practical training platform.
The demand of teachers and students and the existing practical training platform are taken as the parameters and incorporated into the NTM-VR model for simulation analysis. The calculation results show that the acceptance of the VR practical training platform by university students is quite high at 67.4%, which is much higher than the traditional platform acceptance of 32.6%, and the acceptance of VR practical training platform by teachers is as high as 71.5%. The aforementioned calculation results show that with the open design, students can break through the time and space constraints to carry out practical training exercises using this module.
Including the learning intensity, learning outcomes and the way of practical training platform into the NTM-VR model for simulation analysis, the results show that the learning outcomes based on the VR computer repair practical training platform are 76% under the uniform learning intensity, which is much higher than the learning outcomes based on the traditional computer repair practical training platform of 24%. This means that VR technology is able to build an experimental teaching system that unifies knowledge and energy. It is also able to introduce advanced teaching concepts and teaching modes, build shareable teaching resources for practical training of computer network courses and create a teaching platform that fully supports online practical training.
In order to make the VR computer maintenance practical training platform designed in this study more realistic for use, it must have the following four major functions: updating experimental teaching content, an open virtual-real experimental environment, building an online shared resource library and supporting the whole process of comprehensive practical training teaching.
Percentage of VR technologies in each application area
|Product name||VR technology share (%)|
|Supermarket shopping||85%|Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on 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intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Symmetry Analysis and Exact Solutions of Extended Kadomtsev-Petviashvili Equation in Fluids Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on 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process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric 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on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G) on the set of maximal subgroups of p-groups Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network