With the advancement of communication technology and the development of the Internet, the dissemination of information and the application of network resources are becoming more and more extensive, which not only impact some traditional industries but also bring new development and opportunities. Among them, the traditional education industry has also spawned new education models in the wave of technological innovation. Especially since the outbreak of the new crown epidemic in 2020, the education industry has gradually shifted to an online model. According to a report released by the China Internet Network Information Center, as of June 2020, the scale of online education in China reached 623 million users, a 110.2% increase in the number of users compared with 2018. In the context of the epidemic, many learning channels, including universities, primary and secondary schools, and international education, have converted to online education models to avoid the spread of the epidemic due to offline education [1, 2, 3]. Therefore, it can be seen that online education is the general trend of today's Internet globalisation and the new crown epidemic, with huge demand and wide application background [4, 5, 6, 7]. With the economic development of various countries, people all over the world are paying more and more attention to the needs of the spiritual field of entertainment. Driven by the upsurge of learning piano, the number of piano learners has risen sharply. Most of the traditional piano teaching models are offline models. Although they have the advantages of good effect and strong experience, due to the new crown epidemic, the piano education industry is vulnerable to huge risks, and the traditional offline one-to-one teaching mode is expensive. The inefficiency further hinders the popularisation of piano education.

The application of the Internet can improve the shortcomings of the traditional piano teaching mode, avoid the risk of epidemic spread, and reduce the cost of piano education. In major colleges and universities, online piano teaching has become an important teaching method since the epidemic. Teachers can teach and students can learn through the Internet, which means that remote wireless network communication technology needs to be applied in the teaching process. The long-distance wireless network communication technology is a technical means to monitor and control the object at a long distance, and it is a remote-control system interacted by computer technology, automatic control technology and communication technology [8, 9]. Long-distance wireless network communication technology has been widely and profoundly applied in many fields. According to the available literature, the amount of literature expression in the field of remote wireless network communication technology is increasing year by year (see Figure 1). Lv

To cope with the impact of the new crown epidemic on piano teaching in colleges and universities and to seize the general trend of Internet popularisation, this paper designs an application and a remote piano teaching method based on remote wireless network communication for piano teaching in colleges and universities. The functional requirements of the system are analysed, the overall structure of the system is designed, including software and hardware systems, the communication mode is selected according to the characteristics of online piano teaching, and the advantages and disadvantages of different protocol algorithms are compared.

Before carrying out the system design, we first conduct research on the piano teaching situation in colleges and universities to understand the most basic user needs of teaching. The summary of the survey results is shown in Figure 2. The functions required for piano teaching are networking, intelligent piano equipment control, and remote management. The networking function is the basic guarantee of human–computer interaction and a necessary condition for realising the online to offline mode of piano teaching, which can provide a basic approach for cloud management of teaching topics and updating of teaching materials. The purpose of the networking function is to allocate all intelligent terminals reasonably through a unified network approach, which is convenient for piano teaching to manage and check the students’ devices. The intelligent piano device control function is to run and upload the teaching-end device through a pre-set programme, and conducts information induction and cloud management of teaching materials, such as videos and music scores, to increase the availability of the teaching and learning ends and to improve the user experience. The remote management function can help teaching to achieve equipment control, practice inspection, and improve teaching quality.

After summarising the system functions, the development goals of the intelligent piano teaching system can be determined: to provide piano video lesson recording, online live teaching functions, visual and auditory effects collection and recording, remote control equipment, online interactive platform, homework inspection and submit the Q&A feature. The system design will be based on the STM32 single-chip microcomputer platform, network the video acquisition equipment and audio acquisition equipment, and cooperate with the software and hardware design of the motor module to achieve comprehensive control of the online piano teaching classroom. Through the coupling of mobile network, wireless Wi-Fi technology and ZigBee communication technology, remote wireless network college piano classroom teaching can be realised, so that teachers can realise non-contact remote teaching; and students can learn in the front-end web page or mobile APP and upload the exercises and other related exercises. Teachers and students communicate with each other. In addition, it is also equipped with visual system maintenance conditions. Through the computer Internet platform, the communication status and connection status of piano teaching equipment can be displayed, so that developers and users can maintain the equipment status and better grasp the system operation status. Most of the mechanical structures adopted in the system are additional structures, and corresponding matching mechanisms are used for application.

Judging from the current communication technology, due to the different communication environments and needs of each part of the online piano teaching in colleges and universities, the communication technology adopted will also be different, and the relevant software and hardware technical requirements and choices are also different [18, 19, 20]. To realise the complete online piano teaching communication, the system communication can be divided into two modules: (1) module 1 is the sensor signal transmission with STM32 microcontroller as the core and (2) module 2 is the information between the teacher terminal and the user terminal and the local piano teaching system Interactive communication. In the needs of sensor signal transmission, the current technical direction can be roughly divided into wired and wireless communications. Although wired communication runs stably, the complex wiring operation not only affects the appearance but also is not easy to maintain and care. Therefore, we abandoned the wired communication method and switched to the construction of the underlying structure of the wireless communication method. At present, the most used wireless communication technologies on the market include Wi-Fi technology, ZigBee technology, Bluetooth technology and NFC technology [21, 22, 23, 24]. Among them, Wi-Fi technology has the advantages of wide signal coverage and fast signal transmission, but it may have an impact on piano teaching due to network fluctuations, especially in live teaching. ZigBee technology has the advantages of low cost and low power consumption, but the transmission rate is slow. Bluetooth technology has high security, but it has poor fault tolerance in embedded development and poor compatibility with various technical architectures. NFC technology also has high security, but its transmission distance is too short. Therefore, combined with the needs of online piano teaching and the characteristics of signal transmission at the bottom perception layer, we have selected two communication methods to ensure the safety and effectiveness of information interaction. Among them, ZigBee technology is used as the main communication method of the signal sensing layer, which can meet the data volume of the bottom signal sensing layer. Wi-Fi technology is used as an auxiliary communication method to meet the communication detection function requirements due to the addition of a computer interface in the design.

In the second choice of information exchange communication, to realise the information cross-linking between the online teaching system and the user terminal, and considering that the huge online teaching market in colleges and universities needs to be promoted in a low-cost way, the controller signal and cloud server need to be promoted first. The connection is realised by using the Wi-Fi routing network with the technical route of the computer, and with the development of the mobile APP client and the web port to meet the operation and learning needs of different users.

Based on the needs of online piano teaching, the system functions need to have the functions of uploading and downloading teaching materials and remote control. Among them, the remote-control function is that the processor with the STM32 as the core controls the piano equipment remotely through logical operations such as analysis, calculation, arrangement, etc. after receiving the signal from each terminal sensor, combined with the instructions required by the teacher. Both teachers and students can debug the equipment in the piano classroom through the mobile phone APP client and teach after the performance. The teaching screen is recorded and uploaded by the multi-angle cameras arranged in the classroom. The uploading method can be connected to Wi-Fi, ≥ 10 m, it can also be the full coverage area of the signal after connecting to the 4G communication network. In general, the priority of user-based remote control is higher than the automatic control of the STM32 microcontroller. When the user does not perform remote control, the automatic control will be carried out spontaneously. The overall system structure diagram is shown in Figure 3.

The implementation process of the specific communication process is as follows:

The development process of the software programme can be determined from the hardware structure of all levels of remote wireless network communication. Among them, the first thing that needs to be done is the interaction between the information obtained by the underlying sensors and the work orders of the mechanical structure. After that, the information is translated through the logic layer and then transmitted to the network communication module [25]. Because the work coordination of the Zigbee communication protocol and each terminal module in the system are the most basic information exchange process in the whole system and the largest development workload, the IAR Embedded Workbench development environment is selected for the software development of the STM32 microcontroller.

IAR Embedded Workbench is a top-level integrated development environment in the industry, referred to as ‘IAR’. It is an integrated software programme development environment developed by the world-renowned Swedish company IAR Systems for microprocessors. It enjoys high authority in the industry. The software development integrated environment supports ARM, AVR, MSP430 and other chip platforms, and also supports C/C++ language and other functions such as development, debugging, and online simulation.

In the funny piano teaching system based on remote wireless network communication technology, the control programme loaded into the microcontroller and other terminal control modules has three tasks to be completed [26].

Control the recording start or stop of the audio and video equipment required for the recording of piano lessons, and control the recorded video to be uploaded to the cloud server through the Wi-Fi routing network or 4G communication network.

Control the ESP8266 module to connect with the cloud server to obtain the operation state of the remote user controls the motor to debug and play according to the instructions issued by the user on the APP or web page.

The developer schedules the work of each terminal device based on the information of various sensors, that is, in the case of no manual operation, each terminal device can also operate normally and self-monitor the working status.

To realise the above three control tasks, modular programming is carried out through C language, which is divided into ZigBee communication, W-Fi communication, sensor signal acquisition, generating PWM waveform to control the motor, remote/automatic working state switching, and other programme modules. The composition and control flow are shown in Figure 4.

The model of the Wi-Fi module used in this design is ESP8266, which can be connected to the router equipment in the school classroom to realise remote control of motors, audio and video equipment, etc. The specific control steps are as follows:

The ZigBee wireless communication network sends the signal to the STM32 master for data processing.

After the STM32 main control chip processes the signal, it sends the data to the Wi-Fi module through serial communication.

The STM32 main control chip sends control commands to let the network module join the router local area network.

Connect the router to the server in the cloud by adding the port mapping of the router.

The ESP8266Wi-Fi module supports three working modes: STA, AP, and STA+AP. The STM32 master sends the corresponding AT command to the ESP8266 module through serial communication to convert it to the corresponding working mode. By comparing the functions and characteristics of the three working modes, it is determined to adopt the STA working mode. The specific steps and sending AT commands are:

Convert to STA working mode: AT+CWMODE=1;

Restart the ESP8266 module: AT+RST;

Connect to router Wi-Fi: AT+CWJAP=“Wi-Fi name” “Wi-Fi password”;

Start multiple connections: AT+CIPMUX=1;

Establish micro server: AT+CIPSERVER=1;

Set the IP and port number of the connection server: AT+CIPSTART=0, “192.XXX.2.176”, 10011;

Specify the length of the data to be sent: AT+CIPSEND=0.8;

Send data.

ZigBee is a short-range wireless communication technology. It is essentially a two-way wireless networking technology with a relatively low transmission rate. As a communication protocol, it can wirelessly network different digital devices so that they can communicate with each other and provide standardised instructions for the communication process [27]. To network through the ZigBee communication protocol, you can use the ZigBee protocol stack. The so-called protocol stack is the specific implementation form of the protocol, and it is the interface for developers to standardise the use of the protocol. Developers can programme through the API interface provided by the ZigBee protocol stack to efficiently implement ZigBee networking, which can greatly reduce the workload while ensuring standardisation [28].

The workflow of the ZigBee protocol stack can be roughly divided into several steps: system startup, driver initialisation, operating system abstraction layer initialisation and startup, and entering task polling. System initialisation is realised by the function osal_init_system, which realises the initialisation of hardware abstraction layer, network layer, tasks, etc. Among them, isalInitTasks is the initialisation function of the operating system task. After the system is initialised, the function osal_start_znp is called to poll the processing tasks. This function is a loop structure that continuously processes the task with the highest priority among all the tasks currently in the ready state.

In the long-distance wireless network communication system, the ZigBee wireless communication network usually needs to be connected to many devices, sensors, actuators and other nodes, because each node will generate energy loss during the routing process, and there will be new nodes in the process of use. It is added to the ZigBee communication network, so it is necessary to optimise the ZigBee routing structure through algorithms, reduce the path length, reduce network bottleneck nodes, and improve the reliability and stability of the entire network in the communication process. At present, there are two kinds of optimisation algorithms commonly used in ZigBee routing protocol: one is the Cluster-tree algorithm and the other is the On-demand Distance Vector (AODVjr) algorithm. The Cluster-tree algorithm is the most traditional and direct ZigBee routing protocol optimisation algorithm. It starts from the main coordinator, performs layering and traversal according to the tree structure, and forms a cluster tree network topology.

The address assignment of the Cluster-tree algorithm follows the following method:

The main coordinator establishes a new communication network, its own address is 0, and the depth _{0} = 0 in the network;

If node

Node _{skip}

The routing strategy of Cluster-tree is a routing node calculates the next hop of the packet according to the destination network address of the received packet. Suppose the router network address is

In the C4.5 algorithm in the Cluster-tree algorithm, for a given data set

For the desired information needed:
_{i}_{1},_{2},…,_{v}_{1},_{2},…,_{v}_{j}_{A}

Choose a fitness function:
_{1} represents the classification accuracy of the rule set; _{2} represents the number of all rules in the rule set; _{3} represents the number of “attribute name = attribute value” in the rule set, that is, the complexity of the rule set; _{1}, _{2}, _{3} represent the impact factor of _{1}, _{2}, _{3}.

Denote the fitness of each selection of the algorithm as _{i}

To compare the different ZigBee routing protocol algorithms, compare the reliability of the C4.5 and the GAC algorithms, the accuracy of the piano recognition classification based on the decision trees constructed by the two algorithms, the number of rules (i.e., the number of leaf nodes) and the complexity of the rule set (i.e., the number of all “attribute name = attribute value” in the rule set) to compare and analyse the performance of the algorithm. The specific experimental results are shown in Table 1.

Correlation factors of decision tree constructed by C4.5 and GAC algorithms, respectively

C4.5 decision tree | 94.93 | 8 | 17 |

GAC decision tree | 91.84 | 5 | 8 |

As can be seen from Table 1, the classification accuracy of the decision tree constructed by the genetic optimisation classification algorithm based on C4.5 is 94.93%, the number of rules is 8, and the complexity of the rule set is 17. The classification accuracy of the decision tree constructed by the optimised classification algorithm is 91.84%, the number of rules is 5, and the complexity of the rule set is 8, which means that although the complexity of the C4. Compared with the GAC decision tree, the accuracy rate is improved by 3.09%, so the algorithm has better performance. In this paper based on the remote wireless network communication in the application of piano teaching in colleges and universities, this algorithm is adopted as the ZigBee routing protocol optimisation.

Further, to compare the performance of the GAAR decision tree algorithm, the experimental data adopts two classic data sets in machine learning Iris and Breast-cancer. The 150 sample information of the Iris data set contains four conditional attributes and one category attribute, and the 683 sample information of Breast-cancer contains nine conditional attributes and one category attribute. The traditional C4.5 and the GAAR algorithms are used to conduct experiments on these two data sets, respectively. Finally, the data mining software ‘Weka’ is used to construct a decision tree, the cross-validation is used to verify the accuracy of its classification, and the corresponding results are obtained. From the classification accuracy (Correctly Classified Instances), the number of classification condition attributes (Number of Classified Con-Attributes), the size of the tree (Size of the tree) and the number of leaf nodes (Number of Leaves) to compare the performance of the two algorithms is analysed, and the specific experimental results are given in Table 2.

Correlation factors of decision tree constructed by C4.5 and GAAR algorithms, respectively

Iris | C4.5 decision tree | 96.67 | 4 | 11 | 6 |

GAAR decision tree | 96.67 | 1 | 6 | 3 | |

Breast-cancer | C4.5 decision tree | 96.08 | 9 | 21 | 12 |

GAAR decision tree | 97.09 | 5 | 14 | 8 |

The experimental results show that the GAAR algorithm maintains the classification accuracy greater than or equal to the C4.5 algorithm in the calculation of different data sets, and the size of the decision tree and the number of leaf nodes are significantly smaller than the latter. It shows that the GAAR algorithm can correctly and effectively reduce the attributes of the data set, and the optimised decision tree can effectively reduce the scale of the decision tree without reducing the classification accuracy, thereby improving the prediction accuracy of the decision tree model. The speed and efficiency of data have more practical value.

As shown in Figure 5, the energy consumption of a single node of the system increases with the increase of traffic under different algorithms. Although the energy consumption of the GAC algorithm is small at the beginning, its increase with the increase of traffic is very significant. It is obviously not suitable to use this algorithm in the online piano open class. The growth of the C4.5 algorithm is relatively gentle, and the improved GAAR algorithm can achieve the lowest overall power consumption.

As shown in Figure 6, in the comparison of the node survival rate between the GAAR and the traditional C4.5 algorithms, the node survival rate of the GAAR algorithm is significantly higher than that of the C4.5 algorithm, and with the increase of the number of nodes, the survival rate increases, while the survival rate of the C4.5 algorithm increases with the increase of the number of nodes. As the number of nodes increases, it first increases and then decreases. It shows that in the multi-node wireless network communication transmission, the GAAR algorithm is more excellent, and the execution energy consumption and packet loss rate are optimised.

The structure of the Cluster-tree algorithm determines that there is no route discovery process, and nodes do not need to maintain routing tables. Therefore, the control consumption of the routing protocol and the energy consumption of nodes can be reduced. In addition, the storage capacity requirements of nodes are also greatly reduced. It can save node cost. In the comparison of different Cluster-tree algorithms, the GAAR algorithm has a higher node survival rate and lower energy consumption. If the constructed communication network needs to collect a large amount of information, it can bear the underlying nodes with a large business volume. Reduce the information transmission delay and unbalanced network traffic caused by the allocation strategy.

Given the new crown epidemic and the background of the Internet, this paper designs an application of remote wireless network communication for piano teaching in colleges and universities. The functional requirements of the system are analysed, the overall structure of the system is designed, including software and hardware systems, the communication mode is selected according to the characteristics of online piano teaching, and the advantages and disadvantages of different protocol algorithms are compared. The specific conclusions are as follows:

The survey results show that the functions required for piano teaching are networking, intelligent piano equipment control, and remote management. To realise the information cross-linking between the online teaching system and the user terminal, considering that the huge online teaching market in colleges and universities needs to be promoted in a low-cost way, the Wi-Fi routing network is used in the connection between the controller signal and the cloud server to cooperate with the computer. The technical route is realised, and the mobile APP client and web port are developed to meet the operation and learning needs of different users.

In the hardware system, the development environment of the main control chip STM32 is IAR Embedded Workbench. The design logic of the whole system software is roughly divided into Wi-Fi module and setting steps, ZigBee protocol stack and its development process. After the ZigBee wireless communication network is constructed, the ZigBee routing protocol optimisation algorithm is introduced, and the characteristics and defects of different Cluster-tree algorithms are compared.

Among different Cluster-tree algorithms, the improved GAAR algorithm can achieve the lowest overall power consumption, and the energy consumption of the GAC algorithm increases significantly with the increase of traffic, which is not suitable for applications similar to online public courses. The GAAR algorithm has a higher node survival rate and lower energy consumption. If the constructed communication network needs to collect a large amount of information, the underlying nodes that can bear a large amount of business can reduce the information transmission delay caused by the allocation strategy.

#### Correlation factors of decision tree constructed by C4.5 and GAC algorithms, respectively

C4.5 decision tree | 94.93 | 8 | 17 |

GAC decision tree | 91.84 | 5 | 8 |

#### Correlation factors of decision tree constructed by C4.5 and GAAR algorithms, respectively

Iris | C4.5 decision tree | 96.67 | 4 | 11 | 6 |

GAAR decision tree | 96.67 | 1 | 6 | 3 | |

Breast-cancer | C4.5 decision tree | 96.08 | 9 | 21 | 12 |

GAAR decision tree | 97.09 | 5 | 14 | 8 |

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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 ofp -groupsStudy on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method 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 sentiment analysis method based on bidirectional long short-term memory networks 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