Coal resources play a decisive role in promoting the rapid development of national economy and the improvement of people’s life [1]. Taking China as an example, the proportion of coal resources in China’s energy structure is calculated, as shown in Table 1. As can be seen from Table 1, the development and utilisation of coal resources account for more than half of China’s primary energy structure [2], and its important position in China’s industrial modernisation and economic prosperity will remain unshakable in the short term. However, when coal resources are exploited in large quantities, various types of coal mine accidents are likely, which will not only cause serious casualties and economic losses but also cause huge hidden dangers to the peace and stability of the society [3]. Therefore, while enjoying coal resources to bring great welfare to people’s life, safety problems in mining cannot be ignored [4].

China’s energy structure from 2017 to 2021

Energy types proportion of energy structure | ||||
---|---|---|---|---|

Coal (%) | Natural gas (%) | Oil (%) | Hydropower and nuclear power (%) | |

2017 | 84 | 9 | 4 | 3 |

2018 | 80 | 11 | 5.5 | 3.5 |

2019 | 75 | 14 | 7 | 4 |

2020 | 73 | 16 | 8 | 6 |

2021 | 65 | 18 | 9 | 8 |

In recent years, the state has paid more and more attention to the work of safety in all industries. In relevant reports, it has been clearly proposed to ‘establish the concept of safety development, promote life first, safety first’ as the guiding ideology and, at the same time, to truly improve the level of safety in production, thereby reducing accident indicators as the ultimate goal of the policy [5, 6]. Yin et al. analysed and studied the characteristics of major gas explosion accidents in China from 2000 to 2014 and systematically expounded the unsafe behaviours leading to coal mine gas explosion accidents. Patterson et al. conducted a systematic analysis and research on the occurrence regularity of 508 coal mine accidents in Queensland, Australia, based on the neural Turing machine (NTM) deep learning network. Ciocal summarised the causes of gas explosion accidents from two aspects of methane–air mixture and ignition source [7]. Through the NTM deep learning network analysis and research, British DADESA W believes that the gas explosion hazard sources should be analysed and studied based on the mechanism of gas explosion. As governments increase coal mine safety supervision and urge coal mining enterprises to deepen their attention to work safety in production, the coal industry safety in the production situation continues to improve, and the accident indexes steadily decline year after year; for example, in China, coal mine accident death toll and gas explosion mortality statistics are shown in Table 2 [8]. However, with the gradual increase in the mining depth of coal resources, the coal mining process inevitably faces many safety problems, such as mine gas, coal dust, rock burst, mine water damage and heat damage. China’s coal industry safety production situation is still grim, with all kinds of major and above coal mine accidents still occurring from time to time. Coal mine gas accident is the biggest and most prominent problem threatening coal mine safety production at present. Gas accidents cause the most serious harm and cause mass death and mass injury of malignant accidents [9]. In 2007, a coal mine accident in China killed >100 people, the root cause of which was a gas explosion. In recent years, under the situation of coal mine safety regulation, safety technology and equipment level have been greatly improved, but still many gas accidents occur in coal mines, especially in the prohibited area, because of mismanagement, illegal operation and blind cross-border mining caused by accident; for example, in the old county of Shanxi Province in 2010 national key coal mine gas explosion mine, 54 people died; in 2011, 73 people were killed in a deadly gas explosion at the Xinxing coal mine of Heilongjiang Longmay Mining Holding Group Hegang Branch [10, 11]; and in 2011, the flood accident of Shanxi Wangjialing coal mine was caused by catching up with the schedule, blindly pursuing the schedule of production engineering and ignoring the pre-detection of disasters. Coal mine gas disaster prevention and control research is still one of the important issues to be solved in coal mine safety. Therefore, how to find the potential risks in coal mine production and how to scientifically identify, evaluate, warn and pre-control possible risks before the occurrence of gas accidents and apply them to the daily production of coal enterprises have become the problems that need to be solved as soon as possible in the current coal mine safety production [12].

Statistics of coal mine accident deaths and gas explosion mortality in China from 2015 to 2021

Year | Accident deaths (persons) | Death rate from gas explosion (%) |
---|---|---|

2015 | 889 | 0.354 |

2016 | 775 | 0.274 |

2017 | 602 | 0.221 |

2018 | 502 | 0.132 |

2019 | 398 | 0.101 |

2020 | 356 | 0.085 |

2021 | 216 | 0.076 |

By analysing Tables 1 and 2, it is found that the number of deaths caused by gas explosion accidents in large and above coal mines decreases year after year on the whole, but it still accounts for a large proportion in all the accidents of large and above coal mines, indicating that gas explosion is still a heavy resistance affecting the safety production of the coal mine industry [13–16]. The NTM deep learning network, one of the most effective theoretical shuttles for expressing and reasoning uncertainty problems, has been widely used in accident risk assessment of natural disasters and health risks. Through retrieval, it is found that since the 21st century, there have been >1000 studies on the ‘NTM deep learning network’ and ‘hazard sources’ as the theme included in CNKI, indicating that the NTM deep learning network has become an important method for hazard management research in the academic world. Therefore, based on the coal mine gas explosion as the research object, to effectively identify the accident hazards, from the source to avoid gas explosion accident happened as the fundamental purpose, in building a scientific and reasonable system of coal mine gas explosion risk or variables based on the established NTM deep learning network hazard warning recognition and prediction model, to research and analyse the hazard variables, The risk factors and early warning factors that may lead to gas explosion accidents in coal mines are excavated in order to provide some decision-making support for coal mine enterprises to effectively prevent gas explosion accidents [17–19].

Coal mine hazard is defined as under certain conditions in the process of coal production as a result of the mine personnel management, control, decision-making, and a series of activities, the influence of gas, water, fire, roof and equipment materials such as accidental and release energy cause personal injury, occupational hazards, equipment and property loss of various risk factors. For instance, if the whole coal mine system is taken as the research object, gas is one of the sources of danger. Gas hazard sources refer to the factors that may cause gas accidents in various operating systems of mines [20]. Gas accident mainly refers to gas explosion, coal and gas outburst, asphyxiation and so on. Gas hazard sources have the following characteristics:

Gas hazard has objective reality and objectively exists, which is not transferred from people’s subjective consciousness. Once the subjective conditions are met, it will turn from potential danger into reality and cause accidents.

Gas hazard has potential that refers to the factors that are not easy to be realised or can be found in time in the process of the upcoming operation, but there is a certain risk; in other words, it refers to the hazard that is clearly exposed in the process of operation but does not become reality.

Gas hazard sources are complex and variable. The complexity of hazard sources is determined by the complexity of operational conditions. In each operation, although the task is the same, personnel participating in the operation, the site of the operation and the use of tools vary; therefore, the operation methods are different, and the possible resultant hazards will be different.

The gas hazard source is knowable and preventable. However, according to the dialectical point of view, all objective things are knowable. As long as importance is attached to the effective and reliable measures taken, hazard sources can be identified and prevented in advance in daily operations, which is also the basis and premise of gas hazard identification.

The identification of gas accident hazard refers to the identification of whether there is a critical gas accident hazard in the research object [21]. The identification of coal mine gas hazard source is mainly to carry out statistics and analysis of all kinds of accidents that may occur in the gas hazard source system. The hazard source of coal mine gas accident is a kind of special hazard mode and the existence form of dangerous energy. The hazard factor is dynamic and nonlinear [22]. The relationship between the hazard sources is fuzzy and random. There are many reasons for coal mine gas accidents, one of which is related to the long-term lack of predictable and effective identification of hazard sources in the coal mine gas accident hazard system. According to the actual situation of coal mine, the traditional identification method of coal mine gas hazard sources mainly relies on experience and accident statistics, and the accident probability model is established to evaluate the hazard sources. The probability of gas hazard accidents can be obtained by quantitative analysis of the accident tree model or by reliability statistical method according to the relevant data of gas hazard accidents [23]. This study refers to the existing standard system of major hazard sources and uses the NTM deep learning network to carry out early warning identification of the hazard sources of gas accidents and excavates the hazard sources that may lead to the occurrence of coal mine gas explosion accidents so as to play a role of timely warning.

The recurrent neural network realises the ‘memory function’ by iteratively using the last hidden layer information. The cyclic neural network is calculated using Eq. (1) as follows:
_{t}_{x}_{h}_{t}

In order to enhance the performance of the RNN on long sequences, some researchers proposed improved RNN structures such as long short-term memory (LSTM) network and gated recurrent unit (GRU) network [24]. The main idea of these structures is to add a memory line to the RNN, and each time step model will interact with the memory. The newly added memory wire ‘penetrates’ sequence iterations, passing information to the remote end of the sequence. Given the _{t}_{t}

The second part of the LSTM model is to judge which information of the input part needs to be retained [25]. This process can be understood as the current output sequence, and its main function is to calculate whether there are critical gas accident hazard sources among the research objects. The specific formula for this process is as follows:
_{t}

A NTM deep learning network uses LSTM as a controller that internally maintains a small amount of information between time steps. The LSTM, as the controller, uses internal storage units for messaging. Outside the controller, the NTM model adds a two-dimensional storage matrix, in which the storage items are separated from each other. The operation of the storage matrix can be completed by the attention mechanism [26] so that a small amount of data can be read and written without disturbing other storage. The addressing operation of the NTM model includes four steps: content-based addressing, continuous addressing, address sliding and address sparse. Firstly, linear transformation is performed on the output of the controller to obtain the operation parameters, as shown in Eq. (7):

Take writing an address as an example, the addressing operation is calculated as follows:
_{t–1} is the content of the storage matrix at the previous time and the storage matrix is calculated in each row. Therefore, the result cost is a one-dimensional sparse vector [27]. Cosine is cosine similarity function and Softmax is normalised exponential function, which are defined as follows:

Continuous addressing refers to addressing on the basis of the address of the last moment. The proportion of content-based addressing and continuous addressing can be controlled by the content/continuous addressing ratio, which can be calculated by using Eqs (11) and (12):
_{t}_{t}

The problem process solved by the NTM deep learning network is similar to a Markov chain. Usually, we focus on the solution of the problem, namely, the strategy, and the problem needs to be transformed into a Markov decision process (MDP). MDP is A quintuple form <

The maximum reward for state action is

It can be seen from Eqs (18)–(20) that the reward function has a recursive form, so the dynamic programming method can be used to solve all known MDP problems of quintuples. As expressed in mathematical formulas, the NTM deep learning network defines the value approximation function

The calculation of the NTM deep learning network is described in the previous section. In application, this model can apply the organisational structure of the recurrent neural network, input sequence tasks into the network in turn and obtain corresponding sequence outputs. The NTM deep learning network used in this study refers to the construction of two NTM deep learning network models with independent training parameters. The sequences are input into the two models in a positive order and a reverse order, respectively, to obtain two sets of sequence outputs

To enhance model generalisation, the dropout method is used at the output layer of the NTM deep learning network. The dropout method reduces the problem of neural network overfitting by randomly shielding some neurons proportionally during training and turning on all neurons for prediction during testing. For the classification task in natural language processing, the model uses the cross-entropy method to calculate the predicted loss of the network, and the calculation formula is as follows:
_{2} are loss learning rate and L2 normal learning rate, respectively.

The calculation of the NTM deep learning network is described in the previous section. In application, this model can apply the organisational structure of the recurrent neural network, input sequence tasks into the network in turn and obtain corresponding sequence outputs [29, 30]. The comprehensive inferential calculation of gas accident must be based on the instance data in the knowledge base of gas accident, and the data set used in this study is the instance database in the knowledge base of gas accident. The content of the instance library is the instance of each disaster-causing event (basic event or intermediate event) in the gas event. The disaster-causing event is structured and standardised to describe the logical relationship of the gas accident through data and object attributes. At the same time, the spatio-temporal attributes are defined to constrain the NTM deep learning network [31].

The commonly used risk source index quantification methods include fuzzy comprehensive evaluation method, expert scoring method, risk grade matrix method and plan review technique method. In the process of quantifying risk early warning indicators, this study considers the occurrence probability of risk variables and the influence degree of risk variables on target variables in combination with NTM deep learning network application characteristics [32]. The probability of occurrence of risk variables is determined by the learning results of parameters. The degree of influence of risk variables on target variables is determined by node sensitivity analysis results. Zero, low, medium and high sensitivity are quantified as 1, 2, 3 and 4, respectively. According to the risk classification standard and risk warning interval determined, specific gas explosion accident cases were selected, and the risk warning model was simulated and analysed based on the Bayesian network model to further verify the effectiveness of the model [33]. According to the different numbers of deaths caused by accidents, the random sampling method is adopted to select one accident of different grades from the collected investigation reports of coal mine gas explosion accidents as the concrete verification cases of risk warning [34]. The selected cases are all examples of each disaster-causing event (basic event or intermediate event) in the gas incident. The NTM deep learning network algorithm under the constraints of multiple disaster factors is studied. According to the NTM deep learning network algorithm, the existing state of risk factors in the case were input into the NTM deep learning network, respectively, and the output results of the coal mine gas explosion node accident grade were observed. The calculation process and warning results of the NTM deep learning network algorithm are shown in Figure 1.

In Figure 1, there is a self-rescuer failure probability of 0.9, ranging from 3 to 10; mine personnel careless probability of 0.6, 2–3 o’clock; coal seam water injection failure, probability of 0.9, with a time interval of 0–16; and stratified mining not relieved probability of 0.5 with a time of 2–8. These four actual events are the disaster-causing conditions of a gas explosion accident. Meanwhile, under the constraints of time and space, the NTM deep learning network algorithm designed in this study is calculated and analysed, and the final probability of gas outburst accident is 0.567 and the hazard source warning level is poor. By comparing the accident level predicted by the NTM deep learning network algorithm with the actual situation, it is found that the prediction result of the NTM deep learning network algorithm is basically consistent with the actual situation.

Based on the aforementioned calculation results, the inferential calculation under the condition of multiple disaster-causing factors and insufficient space-time constraints is studied. According to the NTM deep learning network algorithm, the existing state of risk factors in the case was input into the NTM deep learning network, respectively, and the output results of the coal mine gas explosion node accident grade were observed. The calculation process and warning results of the NTM deep learning network algorithm are shown in Figure 2.

In Figure 2, for self-rescuer failure, mine personnel carelessness, coal seam water injection failure and stratified mining not relieved, the event probability is unchanged, and the occurrence time of the existing facts changes. Self-rescuer failure between 0 and 8, mine personnel carelessness from 9 to 11 am, time interval of coal seam water injection failure was 14–16 and stratified mining not relieved from 22 to 23 o’clock. These four actual events are the disaster-causing conditions of gas explosion accidents, but the space-time constraint conditions are not satisfied. Through the calculation and analysis of the NTM deep learning network algorithm designed in this study, the final probability of gas outburst accident is 0, and the hazard source warning level is good. By comparing the accident level predicted by the NTM deep learning network algorithm with the actual situation, it is found that the prediction result of the NTM deep learning network algorithm is basically consistent with the actual situation.

To sum up, the prediction results of the NTM deep learning network are basically consistent with the actual situation. Therefore, the existing instances calculated by the algorithm are added, the hazard factors of each existing instance are calculated and then the typical samples are tested and trained. The hazard sources and their weights of coal mine gas explosion accidents are shown in Figure 3.

According to Figure 3, through NTM deep learning network algorithm calculation and analysis, gas concentration has the highest weight of risk factors in early warning and identification of risk sources of gas explosion accidents, with a weight of 96. In the early warning identification of hazard sources, the hazard factor next to gas concentration is mine combustibles, with a weight of 75. This means that gas concentration is one of the biggest risk sources, followed by mine combustibles, in the warning of coal mine gas explosion accidents in the future.

In this section, the risk classification standards of node variables are firstly determined, and the accident warning levels and accident incidence are determined with the help of the NTM deep learning network algorithm theory. Secondly, the random sampling idea is adopted to determine specific research cases, and the existing fact states in each case are imported into the NTM deep learning network, and the accident warning level and accident incidence are calculated and analysed through empirical analysis. Finally, the existing examples calculated by the algorithm are added to calculate the hazard factors of each existing instance, and then the typical samples are tested and trained. The risk sources and their weights of coal mine gas explosion accidents are obtained, which has high practicability.

For coal mine gas explosion process concealment, sudden strong, cause complex features, such as taking gas explosion as the research object, the depth of NTM learning network algorithm was applied to a gas explosion hazard management study, expert knowledge and data learning methods, such as construction of coal mine gas explosion NTM deep learning network algorithm, Accurately identify the hazard sources of gas explosion accidents. Through the research, the following conclusions are drawn:

The existing data research mode is adopted to extract and screen the key words of accident cause in the investigation report of gas explosion accident of large or above coal mines. Combined with the application of the NTM deep learning network, the occurrence probability of risk variables and the influence degree of risk variables on target variables are mainly considered. The occurrence frequency of each key word is counted, and the system of coal mine gas explosion hazard is constructed.

Based on the constructed NTM deep learning network algorithm, the coal mine gas explosion accident risk is identified and evaluated. The specific case of coal mine gas explosion accident is selected, and the accident cause data are introduced into the Bayesian network to simulate and analyse the accident warning and predict the accident grade. Through the study of the risk of coal mine gas explosion accidents, it is found that the failure of a self-rescue device, illegal operation of personnel, underground safety management not in place and so on are the important hazard sources that likely lead to the occurrence of gas explosion accidents, with a disaster probability of 0.567.

Based on the constructed NTM deep learning network algorithm, the risk factors and their weights are calculated and analysed in the early warning identification of risk sources of gas explosion accidents. Through calculation analysis, it can be seen that the highest weight of risk factors is gas concentration, with a weight of 96. In the early warning identification of hazard sources, the hazard factor next to gas concentration is mine combustibles, with a weight of 75.

In the prevention and management of coal mine gas explosion accidents in the process of coal mining, enterprises should ensure risk variables are in a normal level, continue to strengthen employee safety education training, improve employee safety consciousness to the maximum extent, avoid downhole staff to work in illegal operations, continuously implement the underground safety management system, put the safety management system into practice, always strengthen the safety management and supervision of coal mine enterprises and resolutely curb the existence of ‘face project’ phenomenon in safety management.

#### China’s energy structure from 2017 to 2021

Energy types proportion of energy structure | ||||
---|---|---|---|---|

Coal (%) | Natural gas (%) | Oil (%) | Hydropower and nuclear power (%) | |

2017 | 84 | 9 | 4 | 3 |

2018 | 80 | 11 | 5.5 | 3.5 |

2019 | 75 | 14 | 7 | 4 |

2020 | 73 | 16 | 8 | 6 |

2021 | 65 | 18 | 9 | 8 |

#### Statistics of coal mine accident deaths and gas explosion mortality in China from 2015 to 2021

Year | Accident deaths (persons) | Death rate from gas explosion (%) |
---|---|---|

2015 | 889 | 0.354 |

2016 | 775 | 0.274 |

2017 | 602 | 0.221 |

2018 | 502 | 0.132 |

2019 | 398 | 0.101 |

2020 | 356 | 0.085 |

2021 | 216 | 0.076 |

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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 -groupsResearch 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