For the comprehensive mechanised coal mining technology, the support design of the main withdrawal passage in the working face is an important link to achieve high yield and efficiency. Due to the impact of mining, the roof movement of the withdrawal passage is obvious, the displacement of the coal body will increase significantly, and it is easy to cause roof caving and serious lamination problems, and even lead to collapse accidents, which will affect the normal production of the mine. In this paper, the mining pressure development law of the main withdrawal passage support under the influence of dynamic pressure is designed, the most favourable roof failure form of the withdrawal passage is determined, and the action mechanism and applicable conditions of different mining pressure control measures are studied. The pressure appearance and stress distribution in the final mining stage of fully mechanised coal face are studied by numerical simulation. The deformation and failure characteristics and control measures of roof overburden in the last mining stage of fully mechanised coal face are analysed theoretically. Due to the fact that periodic pressure should be avoided as far as possible after the full-mechanised mining face is connected with the retracement passage, some auxiliary measures such as mining height control and forced roof blasting are put forward on this basis. The relative parameters of the main supporting forms are calculated. The main retracement of a fully mechanised working face in a coal mine channel is put forward to spread the surrounding rock grouting reinforcement, reinforcing roof, and help support and improve the bolt anchoring force, the main design retracement retracement channels in the channel near the return air along the trough for supporting reinforcing surrounding rock control optimisation measures, such as through the numerical simulation analysis, the optimisation measures for coal mine fully mechanised working face of surrounding rock is feasible. Numerical simulation results also show that the surrounding rock control of fully mechanised working face of coal mine design improvements, its main retreat channel under the roof subsidence, cribbing shrank significantly lower, and closer, to better control the deformation of surrounding rock, achieved significant effect, to ensure the safety of coal mine main retracement channel of fully mechanised working face support.

#### Keywords

- numerical simulation
- fully mechanised caving coal mine
- main retracement channel
- supporting design

#### MSC 2010

- 76U05

As a major energy consumer, fossil energy occupies an important position in China’s energy structure, among which coal energy accounts for 75% of China’s fossil energy consumption. With the continuous development of China’s industrial upgrading and energy diversification, the proportion of coal in the whole energy structure will decline, but for a period of time to come, coal will still play an irreplaceable role in the manufacturing, chemical and other industries [1]. Being China’s strategic energy, to maintain the stable development of China’s coal has important safety and economic significance; the relevant data shows that China’s coal has proven total reserves of >900 billion tons; with the rapid development of the market economy, China’s coal output accounts for more than one-quarter of the world’s coal output. In order to better adapt to the requirements of the rapidly developing market economy, China’s coal enterprises take the initiative to seek change and actively carry out technological innovation. In the process of continuous development of coal mining technology, comprehensive mechanised coal mining technology has been gradually replaced in order to meet the limitations of different mining conditions. Comprehensive mechanised coal mining technology, referred to as fully mechanised mining, refers to the coal breaking, loading, transporting, supporting and other construction in coal mining operations on the working face [2]. The adoption of fully mechanised mining construction technology can greatly improve the coal mining rate. Fully mechanised mining face moving face is an important link in mine production, but also an important determinant of mine production efficiency. However, due to the loss mechanism of the main retracement channel supporting the design and mining stage at the end of the pressure control measures are of insufficient understanding. The existing coal mining stage at the end of the process design of fully mechanised working face there are many unreasonable factors, and these may cause instability of roadway, crushing accidents, and so moving the job not only leads to high cost, low working efficiency, but also hidden danger of big security, leading to great restriction in the coal mine production [3]. With improvement in the overall coal mining technology, this kind of constraint is becoming more and more obvious. In order to give full play to the superiority of fully mechanised coal mining technology and realise the maximisation of coal mining benefit, it is necessary to fully guarantee the stability and safety of the withdrawal passage. For the fully mechanised coal mining technology, the main backout passage in the working face is a necessary link and an important preparation for mine production, which is of great significance to realise safe and efficient production. In order to give full play to the technical advantages of a fully mechanised caving coal mine, so that the work efficiency and mine benefits are steadily improved, it is necessary to ensure the stability of the surrounding rock of the main withdrawal channel, make the moving face smooth and safe. Combined with the characteristics of roof breaking in the final mining stage and the numerical simulation technology of the withdrawal passage, an optimisation scheme for the support design of the withdrawal passage in the fully mechanised top-coal caving face is put forward, based on the actual geological conditions of the coal mine.

Based on the simulation purpose and model construction, the ground stress conditions were set, and the coal rock surrounding rock conditions were combined to carry out the parameters [4]. Given or limited boundary mechanics conditions and displacement conditions, and completing the initial stress field (unexcavated disturbance) calculation balance, to ensure the authenticity of the calculation results, arrange and excavate the retreating roadway, simulate the surrounding rock deformation and failure process and evolution of the retreating roadway, which then simulates the progressive influence of the working face and studies the supporting design of the main withdrawal passage under dynamic pressure mining, including the process and evolution of surrounding rock deformation and failure.

The pressure step of the main roof is a key parameter to describe the motion state of the rock beam. In the mechanical model of the pressure step of the main roof, the hinged rock beam is composed of fractured rock mass [5]. The composition of the rock mass can be approximated as being under force on a cantilever beam, regardless of the deflection of the beam. Then the structural forces on the rock mass include the dead weight of the rock beam as:

The thrust pressure and the corresponding friction force at the hinge point of the fractured rock mass are:

The couple moment generated by shifting the force at the hinge point to the centre of the rock beam is as:

The support reaction force is not considered before the end of the rock beam is not fractured. If the fractured part of the rock beam is in equilibrium, the couple moment of the rock beam at the point is zero:

In the limit condition, the formula can be substituted into:

When the working face comes under periodic pressure, the mechanical conditions of rock beam cracking from the end under the action of structural forces are as follows:

The bending moment value at the end of the beam is:

The actual tensile stress is:

According to _{t}

Above the retracement passage, when the suspension length of the main roof reaches the period to press the step distance, the main roof may be above the roadway it ruptures and turns down. In this case, the motion state of the rock block has obvious influence on the stability of the surrounding rock of the main retractable passage, and the length of the rock block is the periodic pressure step of the support design of the main retractable passage [6].

L shall be designed to be in the cantilever beam state as:

Numerical simulation analysis of the surrounding rock stress failure under the influence of dynamic pressure is as shown in Figure 2A. With the gradual progress of the working surface, vertical stress concentration of the surrounding rock of withdrawn roadway increases significantly. Stress redistribution of the surrounding rock of multiple roadway is superimposed with the influence of mining dynamic pressure of working face, and supporting load of bearing structure of surrounding rock of main withdrawal passage is severe. Position the face to stop mining line between retracement channels for vertical stress concentration of surrounding rock and dynamic pressure in the working face vertical peak should focus entirely overlay, the retracement help department between surrounding rock of roadway vertical stress concentration peak 16.2 MPa, and in the central word retracement lord bearing stress distribution of surrounding rock is most prominent, surrounding rock bearing burden that lane position is located in the main retracement channel which department of surrounding rock, the location of the main retreat for skiving of surrounding rock and deformation of roof and floor is most severe, so optimisation design, it is necessary to improve the support load of support strength in order to maintain the stability of surrounding rock during the retreat [7] as

Dynamic pressure under the influence of roadway surrounding rock stress redistribution and the mining face more pressure superposition effect, the main vertical stress concentration effect of surrounding rock are the most significant retreat channel up to 16.3 MPa, the level of surrounding rock stress concentration up to 9.05 MPa, shows that dynamic pressure under the influence of vertical stress superposition effect on roadway and its corresponding main retracement retracement tunnel surrounding rock of mine pressure appear ‘deepening’ role, and its bearing structure of roadway surrounding rock stability is the key to the retreat channel lane to help the broken ends and the working face of coal wall rock shallow position, the position is at the end of the fully mechanised working face of coal mine mining period for most prominent position and horizontal deformation [8]. In order to maintain the bearing capacity of the surrounding rock in the broken roadway, more attention should be paid to the maintenance of surrounding rock and the improvement of supporting strength of roof and floor. In a retreat on the distribution of damage evolution of roadway surrounding rock, with face advance to stop mining line, retreat of surrounding rock of roadway affected by dynamic pressure under the influence of vertical stress superposition of roadway and its corresponding main retracement retracement tunnel surrounding rock pressure appeared violently, between surrounding rock destruction through most affected. This also causes the retracement bearing structure to be one of the reasons for the instability of surrounding rock of roadway. Combined with numerical value in the face to stop mining line position, the main retracement channel vertical stress concentration with the help of between surrounding rock dynamic pressure of working face of vertical peak should focus entirely on the overlay, surrounding rock damage, since the shear failure of overburden rock roadway surrounding rock damage fracture and retreat, at the same time between retracement coupon lane surround rock bearing structure since central gradual destruction, eventually go against the main retreat channel bearing structure stability of surrounding rock, Figure 2B is the surrounding rock stress distribution and shape distribution [9].

According to the study of regional geological conditions established for the numerical simulation model, studying the retracement channel is affected by face abutment pressure in the model first excavation main retreat channel and retracement auxiliary lane, three-dimensional calculation by pillar between two roadways model size 40 m × 150 m × width direction long direction high direction 50 m model a hexahedral unit divided into 97419 grid nodes. Mohr criterion is used in model calculation. Coal pillars are left on the left side of the model during excavation. When the working face is far from the stop-mining line, each 10-m excavation step is pushed to the retracement passage. Every 5 m of excavation is when the working face is separated from the stop-mining line. When the working face is away from the stop-mining line, each 1 m excavation step will be excavated for a total of 70 m. Based on the above mechanical formulas and data values, the support design optimisation of the numerical three-dimensional model of the main retracement passage is as follows.

When the distance between the working face and the main retracement passage is >30 m, the axial force and borehole stress of the bolt are always at a low level and hardly change with mining of the working face. The roof subsidence of the retracement passage, the subsidence of the column of the stacking support and the wall moving close of the roadway increase, but the change is small. The maximum principal stress, vertical stress, plastic zone and displacement deformation of surrounding rock have little change in the process of pushing and mining in the main retracement channel. This shows that the surrounding rocks of the main withdrawal passage in this range are relatively stable and the deformation is small, and the ore pressure is not obvious, so it can be used normally. When the distance between the fully mechanised coal mining face and the main withdrawal passage is <30 m, the axial force and borehole stress of the bolt increase significantly. As shown in Figure 3, the roof subsidence, the stacking support column subsidence and the change rate of the roadway wall proximity in the main withdrawal passage all increase significantly. Master retreat channel within the maximum principal stress and vertical stress of surrounding rock were significantly increased, in the main between retracement channel and working face has significant effects in the coal pillar stress, high in advance, the Lord retreat channel increase significantly vertical settlement deformation rate and deformation, face the plastic zone and the main retreat channel, forming a continuous plastic damage area, see Table 1.

Statistical table of roof settlement of working face

Mining help | The vertical stress | 4.61 | 10.02 | 11.41 | 11.05 | 2.36 | - |

Maximum principal stress | 9.68 | 10.36 | 11.80 | 11.05 | 2.43 | - | |

Minimum principal stress | 3.53 | 3.77 | 4.31 | 4.11 | 0.79 | - | |

Non-mining side | The vertical stress | 8.99 | 9.35 | 11.06 | 12.36 | 11.65 | 3.94 |

Maximum principal stress | 9.04 | 9.38 | 11.09 | 12.43 | 11.75 | 4.29 | |

Minimum principal stress | 3.32 | 3.44 | 4.11 | 4.11 | 4.34 | 1.50 |

Combined with coal mine retracement of fully mechanised working face, the failure characteristics of surrounding rock support design of the numerical simulation analysis, put forward retracement of fully mechanised working face of roadway surrounding rock anchor + double metal net + + anchor plate of shotcrete support improved design scheme: the deputy retreat channel and its retreat coupon lane roof and the two sides adopt phi 000 18 mm × 2 mm metal bolt, row spacing between 1,000 mm × 1,000 mm, and tightening torque should reach 100 n. m. The roof of the main and auxiliary roadway is arranged with a row of anchor cables (three sets), and the two sides and the roof of the 308 retraction-joint roadway are arranged with a row of anchor cables (two sets), which all adopt 15.24 mm × 7600 mm pre-stressed steel hinge line for reinforcement support. At the same time, the top is supported by a steel ladder beam with a diameter of 14 mm, and the top is supported by a steel ladder beam with a diameter of 12 mm for reinforcement. The surrounding rocks of the withdrawal link roadway are all supported by double-layer metal mesh. The specification of the metal mesh is 5,500 mm × 1,200 mm, the mesh is 50 mm × 50 mm, and the spacing is 200 mm. Anchor force of bolt shall be no <50 kN, and torque shall be no <100 N m. The bottom plate is made of C30 concrete, 150 mm thick. In the final mining period, the decision should be made according to the actual situation. If necessary, the single hydraulic prop should be taken to cooperate with the active supporting measures.

Working face area average pressure continuous step distance 4.12 m, area average cycle pressure step distance 13.2 m; The bolt anchorage force in the main retracting passage of working face is insufficient, and the stress of the bolt in some areas has exceeded the design value of the bolt anchorage force in this mine. The ore pressure in the middle area of the main withdrawal passage (50–200 m) is more serious than that at both ends. The ore pressure of auxiliary retracement channel is not obvious, the surrounding rock is relatively stable and the deformation is small, so it can be used normally. When the distance between the fully mechanised mining face and the main withdrawal passage is <30 m, the main withdrawal passage is significantly affected by the mining movement of the working face at the beginning, and the on-site ore pressure is severe. The surrounding rock failure and deformation amount are large, and the deformation rate is significantly increased. The surrounding rock stress of the main withdrawal passage gradually concentrates and reaches its peak value. The vertical settlement deformation rate and deformation amount of the main withdrawal passage increase significantly. The plastic zone of the main withdrawal passage is connected with the plastic zone of the working face to form a continuous plastic failure zone. It shows that the stability of surrounding rock is obviously affected by mining in this range. In coal mine retracement auxiliary channel of fully mechanised working face and its retreat sanlian lane roadway position as an engineering test section, can be seen from Figure 4, tunnelling advance good Lord retreat channel combination supporting scheme and layout, eventually retreat of fully mechanised working face roof and floor of roadway surrounding rock deformation in 150~ 185 mm, the deformation of surrounding rock of two sides in the 160~ 180 mm, The design effect of shotcrete support of anchor cable and bimetal mesh and bolt plate is remarkable.

In conclusion, through to the coal mine fully mechanised working face mining control effect and surrounding rock deformation and failure laws of surrounding rock during field measurement analysis and improvement by using numerical simulation methods to analyse the main retracement channel supporting design, including the existing supporting conditions of fully mechanised working face of coal mine main retracement channel when affected by mining move pressure of surrounding rock stress distribution, plastic zone and displacement deformation.

#### Statistical table of roof settlement of working face

Mining help | The vertical stress | 4.61 | 10.02 | 11.41 | 11.05 | 2.36 | - |

Maximum principal stress | 9.68 | 10.36 | 11.80 | 11.05 | 2.43 | - | |

Minimum principal stress | 3.53 | 3.77 | 4.31 | 4.11 | 0.79 | - | |

Non-mining side | The vertical stress | 8.99 | 9.35 | 11.06 | 12.36 | 11.65 | 3.94 |

Maximum principal stress | 9.04 | 9.38 | 11.09 | 12.43 | 11.75 | 4.29 | |

Minimum principal stress | 3.32 | 3.44 | 4.11 | 4.11 | 4.34 | 1.50 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Nonlinear Differential Equations in the Teaching Model of Educational Informatisation The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology