‘Catalyst’ is originally a concept in chemistry, which refers to a low-dose substance that can change or accelerate the reaction speed without being consumed in the chemical reaction. In urban development, ‘catalyst’ refers to a construction project that can trigger a ‘chain reaction’ and promote the maturity of urban construction conditions, so as to promote the sustainable and gradual development of the city according to the will of the people [1]. There are two modes of urban development in China. One is ‘leapfrog’ development which is the development of new towns at a certain distance from the old city; the other one is ‘sprawl’ development which is based on the gradual outward expansion of the existing urban area. However, no matter what kind of development model, it is necessary to set up a strong development ‘catalyst’ to drive the development of surrounding areas and new towns. Usually, important public buildings or cluster commercial facilities are used as the catalyst for the development of new towns.

‘Sports Centre’ is one of the important catalysts in the development of new towns. The construction of sports buildings and supporting facilities in the sports centre is conducive in creating a good urban environment, greatly improving the urban image and function, so as to catalyse the development of surrounding areas, drive the development of urban areas, expand the urban spatial structure and accelerate the development of urban economy [2]. For example, the construction of Guangzhou Tianhe Sports Centre became the catalyst for the eastward expansion of Guangzhou in the 1990s. Its construction triggered the development of Tianhe area, which was a farmland till the 1980s, into the economic and commercial core area of Guangzhou in 10 years. Then considering the Asian Games as an opportunity and venue construction as the core driving force, Guangzhou has expanded and improved the urban spatial structure, sublimating the traditional urban pattern of ‘cloud mountain and Pearl water’ into a characteristic multi centre cluster network pattern of ‘mountain, water, city, field and sea’. The construction of the sports centre of London 2012 Olympic Games transformed the old industrial area and polluted area into an attractive large-scale sports park, activating the construction and development of this area and improving the living standards of the city and the country.

Since entering the new century, with the deepening of social reforms, the process of national industrialisation and urbanisation has increased exponentially. The transformation and expansion of the original urban areas are not enough to meet the needs of urban development. Many cities carry out urban expansion or new town construction outside the existing urban areas. A large number of sports centre projects with high hopes as urban catalysts have been carried out one after another. However, in the construction of these sports centres, due to the one-sided emphasis on the ‘high, large and superior’ of the sports centre itself and the neglect of the relationship between the sports centre and the sustainable development of the city, the following problems are often prone to occur:

Scale problem – the lack of rational feasibility study and design positioning in the planning of the sports centre leads to the blind and excessive construction scale. Under the realistic background of China where the development of sports industrialisation is immature and the utilisation rate of large-scale stadiums and gymnasiums is generally less after games; once the construction and operation cost of stadiums and gymnasiums exceeds the city's affordability, it will be detrimental to the development of the new town and it is difficult to play its corresponding promoting role.

Accessibility issues - accessibility issues include two aspects. From the supporting level of urban public transport, as the sports centre is located in the new urban area, private cars are often expected to be the main traffic in planning; insufficient consideration is given to the public transport system, the supporting facilities are imperfect, and the connection capacity is not strong enough. Even if it is fully planned, sometimes the construction of public transport network is delayed due to neglect in construction, which makes the accessibility of new town sports centre weak. From the perspective of urban spatial structure, the plot scale of sports centre is often too large, and the surrounding plots fail to form a grid system, so urban traffic forms congestion easily. This will have a greater impact after the development of the new town.

Vitality problem – due to the influence of the national sports policy, the sports centre must focus on the sports function and restrict the setting of other functions such as commercial function, resulting in insufficient attraction to the target population and lack of popularity and vitality of the place. Therefore, to solve the vitality problem of the sports centre can only rely on the functional complementarity with the surrounding plots. Therefore, if the functional positioning of the surrounding areas at the planning level is ignored, there are no rich and diversified functional clusters, or the spatial layout of the surrounding plots is not dynamic at the urban spatial level, it is difficult to form a strong complementarity with the functions of the sports centre and create a dynamic urban centre.

As the ‘catalyst’ of urban development, the sports centre must meet the requirements of ‘sustainable development’ in order to play a positive role in its own and the long-term development of the city. In the construction process of sports centre from scratch, planning is the initial intervention stage. It will be the most effective and fundamental means to guide and design its sustainability from the planning level. This study hopes to analyse the practical cases of stadiums and gymnasiums by using cluster analysis [3] and spatial syntax, combined with the design practice and using feedback experience of stadiums and gymnasiums, and in view of the misunderstandings in the construction of domestic existing sports centres, so as to get some suggestions for the sustainable development of sports centres.

Cluster analysis is to establish a classification method to automatically classify a batch of sample data (or variables) according to their affinity in nature without prior knowledge [4]. In the design of sustainable sports centre, the strategy of venue merger design is often adopted to make efficient use of resources. Among them, the size and functional efficiency of venues are important parameters for the merger of venues. Therefore, this paper attempts to judge whether it is suitable for the combined design by cluster analysis of the two elements of venue scale and functional efficiency of the sports centre. According to the distance-based cluster analysis algorithm, the venues of the sports centre are numbered respectively, and the size of the venues is set as the x-value parameter and the function efficiency is set as the y-value parameter. In terms of size parameters, if 100 seats are assigned as 1 point, 10000 seats will be 100 points. In terms of function parameters, the high frequency of function use is 100-80 points, generally frequency is 80-60 points and the low frequency is less than 60 points. After assignment, cluster calculation is carried out according to the square educated distance equation:

That is,

The distance between two samples (x, y) is the sum of squares (k variables) of the difference between each variable value of each sample. Through calculation, it is concluded whether there is obvious clustering effect between the venues of the sports centre, which is suitable for combined design.

The main theory of spatial analysis using spatial syntax is called ‘spatial syntax theory’. This theory was proposed by Bill Hillier and others. Taking spatial ontology as the research object, it makes quantitative analysis and visual expression of spatial form through indicators such as integration, traversal and intelligence. It is a method that attempts to explain and quantitatively express space from the behaviour of people in space and the topology structure of spatial ontology [5]. Years of empirical studies have shown that space syntax as an algorithm for the quantitative description of street space topology has a good correlation with the distribution of various traffic movements and active functions in the city [6].

SDNA is a spatial syntax calculation software embedded in GIS developed by the research team of Cardiff University. It improves the traditional spatial syntax graph theory, emphasising the dual topological relationship between ‘points’ and ‘lines’ in spatial networks, and when calculating, the road network deflection angle and Euclidean distance can be weighted at the same time, so that the calculation method is conceptually closer to the urban road network analysis with a certain scale and complexity. Combined with the analysis ability of GIS, it has a wide range of application prospect in the field of urban planning [7]. Among them, the key evaluation indexes are closeness degree and betweeness degree, and the evaluation index related to space is Moran index. Combined with yolo-v3 and DeepSnRh algorithms of deep learning, spatial syntax can also provide a broader perspective for environmental space research [8].

Closeness degree represents the difficulty of a road network to the rest of the road network within the search radius. The road network with high integration usually has a high integration ability in the region and has greater attraction to the crowd. In SDNA, the closeness degree is expressed by NQPDAn (n represents the calculated road network radius), and its calculation equation is as follows:

Betweeness degree is also an important parameter (hPBt) provided by SDNA. It is usually used to measure the probability that the road network has been through the traffic flow within the search radius. The higher the betweeness degree, the greater the probability that the road network has been selected to pass through, bearing the role of rapid traffic rather than stay aggregation. Different from the integration degree, the former emphasises the arrival, while the betweeness degree represents trafficability. Its calculation equation is:

Moran's I coefficient is an important means to measure spatial correlation, and its operation equation is:
_{i} is the deviation between the attribute of element i and its average value
_{i,j} is the spatial weight between elements i and j, n is equal to the total number of elements, and S0 is the aggregation of all spatial weights.

With the analysis of spatial syntax, we can verify the relationship between the urban spatial closeness degree and betweeness degree of sports centre and its contribution to the sustainable development of urban public space, so as to provide reference for the design of Sports Centre in the future.

Urban stadiums and gymnasiums often need a large volume to meet their needs as urban landmarks; However, too large volume and scale will cause waste of construction cost and future operation cost. Therefore, how to coordinate the contradiction between them is a problem that needs to be solved in design.

In recent years, the scale setting of new sports centres in China has been blindly greedy. Taking the seat size of stadiums as an example, this paper analyses the case data of 13 new town sports centres newly built in recent years. More than half of the stadiums have more than 50,000 seats, 1/3 have between 40,000 and 50,000 seats, and only about 15% have less than 40,000 seats. This is particularly evident in the construction of the Sports Centre Gymnasium in the new city. These large-scale sports centres are difficult to hold events matching their scale and specifications in practical use. On the contrary, they are vacant for a long time, affecting urban development. Therefore, the venue scale of the Sports Centre shall be reasonably formulated according to the needs of urban development.

The Kunming Mingxing Sports Centre is an earlier case of adopting the design idea of ‘all-in-one venues’ to solve this contradiction. In addition, there is also the Shenyang Olympic Sports Centre. The former includes a stadium and a gymnasium. In view of the high use of gymnasium and the low utilisation rate of stadiums, the seat size of the easier-to-operate gymnasium was adjusted to 10,000, and the seat size of the stadium was reduced to 10,000. On this basis, the stadium and the gymnasium were combined. The Shenyang Olympic Sports Centre combined a natatorium with a tennis stadium because of a similar scale and low utilisation rate.

Number and assign virtual values to the four types of venues with high frequency set in the sports centre. Among them, No. 01 is the stadium, No. 02 is the stadium, No. 03 is the natatorium and No. 04 is the tennis stadium. With reference to the venues of Kunming Xingyao sports centre and Shenyang Olympic Sports Centre, and combined with the scale and universal functional use of four types of venues, the clustering elements (x, y) of venues are assigned. Based on years of research experience, the utilisation rate of gymnasiums in sports centres is generally higher than that of stadiums and tennis courts; The utilisation rate of natatoriums is related to the regional characteristics of the South and the north. Generally, the utilisation rate of natatoriums in the south is high while in the north it is low. As Shenyang is located in the north and the sports centre is located in the suburbs, the accessibility is low, so the functional parameters of the natatorium need to be assigned a lower value. Finally, 01 (100, 60), 02 (100, 90), 03 (20, 60), 04 (40, 50) are assigned. After clustering calculation, it is concluded that the clustering effect between natatorium and tennis hall is the most obvious, only 500; The clustering distance between small stadiums and large stadiums is 900, which are obvious and suitable for combined setting (Table 1).

Educlidean Distance of Stadiums in Sports Centres

01 (stadium) | 900 | 6400 | 4600 | |

02 (Gym) | 900 | 7300 | 5200 | |

03 (natatorium) | 6400 | 7300 | 500 | |

04 (Tennis Hall) | 4600 | 5200 | 500 |

The design starting point of Kunming Xingyao sports centre is ensuring the ability to hold large-scale activities by improving the scale of the gymnasium with high utilisation rate; Reduce the construction scale of stadiums with low utilisation rate to reduce the construction cost and daily operation consumption; The combined design of large gymnasium and small stadium further ensures the landmark of the sports centre needed by the city. Shenyang Sports Centre also combines the natatorium and tennis hall with low utilisation rate in order to improve the overall utilisation efficiency. Through the cluster analysis in calculations, it can be concluded that the two designs are quite reasonable. It has been proved by practice; the reasonable venue scale control and the combination of venues enable Kunming Xingyao sports and Shenyang Olympic Sports Centre to maintain their sustainable development with lower daily operating expenses and higher operating income under a small land scale [9]. However, if the venue integration design is not appropriate, the expected purpose may not be achieved. Therefore, the use of cluster analysis in the integrated design and planning of stadiums and gymnasiums will help to provide effective judgement support on how to merge stadiums and gymnasiums, and ensure the feasibility of merging stadiums and gymnasiums and the sustainability of the development of sports centres in the future.

Verifying the accessibility of sports centres that promote urban development through spatial syntax, it can be found that high accessibility is an important feature of these sports centres. Take Tianhe Sports Centre as an example. Tianhe Sports Centre is an important case that has a positive effect on urban development in China, making the area around the sports centre in Tianhe District of Guangzhou from farmland in the 1980s to the current urban core area. Through the spatial algorithm calculation of different metric radius (800m, 1500m, 2000m and 3000m) of Tianhe Sports Centre and surrounding street network, the results show that the sports centre is located in the high accessibility area of the area under different scales of walking radius, public transport travel radius and vehicle travel radius (Figure 1). Taking the global closeness degree and global betweeness degree as indicators, the standard deviation ellipse is created to summarise the spatial characteristics of geographical elements (central trend, dispersion and direction characteristics, including 68% of the calculation results). It is found that Tianhe Sports Centre is located in the centre of the two indicators and is completely included, indicating that the sports centre is the centre point of arrival traffic in the region, and it dominates the surrounding street network (Figure 2).

Based on the algorithm and combined with the surrounding traffic conditions, it is found that there are 4 rail transit passing by and 6 subway stations; the ground public transportation is also convenient. There are 22 urban bus stops around, including 10 BRh stops on Tianhe Road, the main urban transportation road in the south. The accessibility is improved through convenient public transport distribution, which strengthens the convenience and willingness of citizens to reach the area.

It can be said that high accessibility is a necessary means to ensure the effective role of sports centres. Due to the large area of the sports centre, with the development of the city, the high land price in the old urban area is obviously difficult to support the construction of the new sports centre. Therefore, new sports centres are often located at the periphery of the city or in the start-up area or core area of the new city. However, regardless of the site selection, the sports centre is often far away from the existing mature urban areas, and the development degree of the surrounding plots is often not high when it is put into use. Therefore, accessibility is an important problem that must be solved to realise the sustainable coupling between sports centre and city. During the planning of the new sports centre in the future, it is necessary not only to ensure accessibility through urban space design and road network design, but also to introduce large or medium volume public transport through the improvement of transportation supporting facilities, so as to improve accessibility and meet the needs of daily operation when the sports centre undertakes large-scale competitions and after competitions.

Urban function combination refers to the compatible state of multiple urban functions in a certain space and time range. It is the result of the mixing of different land use modes, functional layout, business forms and spatial forms. Its significance lies in the provision of supportive services between functions [10]. The city is an organism, and each plot will be related to the surrounding plots. Compound function and symbiosis are a basic concept followed by modern cities. In the planning stage, the residential, commercial and office facilities around the Sports Centre shall be provided, and other supporting facilities shall be improved. On the one hand, the users of the surrounding facilities are the potential users of the sports centre, on the other hand, these facilities can attract flow of people from other places together with the sports centre. The compound plot design strategy is conducive to the exertion of the sports function of the sports centre. For example, when Guangzhou built Tianhe Sports Centre, a large number of surrounding commercial and financial functional plots were designed. These plots also brought people flow to Tianhe Sports Centre, making Tianhe Sports Centre become the regional centre and development core of Tianhe District, driving the development of the whole urban area.

On the other hand, in addition to the composite function setting of sports, commerce, residence and other functions, from the perspective of spatial layout, the grid like spatial vitality pattern is conducive to the role of public services and can play an important role in promoting regional development. Using spatial syntax, this paper analyses the Moran index of Tianhe Sports Centre and its surrounding urban space. First, through the spatial autocorrelation analysis of the closeness degree operation value, the p value is 0, indicating that the result has statistical significance, and it can be considered that the regional network is clustered in the concept of closeness degree (Figure 3). Based on this, through the analysis of local Moran's index (local Moran's I, which is measured to identify statistically significant hot spots, cold spots and spatial outliers), it can be found that the sports centre is the core of gathering in the region, but the road network with high characteristics in the region is not completely attached to the sports centre, but also has a high degree of correlation with the surrounding grid plots, indicating that the surrounding areas have high vitality (Figure 4). Therefore, when there is no way to form a finer plot division within the sports centre, the efficient grid plot division of surrounding plots can make up for this deficiency.

The construction of sports centre can improve the surrounding environmental value and attract popularity, so as to drive the vitality of the area and even the whole city [11]. However, we must also see that there are positive and negative effects in the interactive relationship between stadiums and cities, which can form a positive interactive relationship or a negative interactive relationship [12]. An effective sustainable development strategy from the planning level will promote the good interaction between the sports centre and the city in the whole life cycle and realise its ‘catalyst’ planning vision [13]. With the help of mathematical algorithm analysis, this paper verifies the design characteristics of the sports centre that forms a good relationship with the city for sustainable development, and draws the following conclusions: the combined design of venues under the intensive principle can resolve the negative impact caused by the huge volume requirements of urban stadiums, Maintaining the high accessibility of the sports centre and ensuring that the surrounding plots and the sports centre plots form a composite functional area and a high vitality zone of grid streets can ensure the sustainable development of the sports centre and the city.

#### Educlidean Distance of Stadiums in Sports Centres

01 (stadium) | 900 | 6400 | 4600 | |

02 (Gym) | 900 | 7300 | 5200 | |

03 (natatorium) | 6400 | 7300 | 500 | |

04 (Tennis Hall) | 4600 | 5200 | 500 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Industrial transfer and regional economy coordination based on multiple regression model Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation 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 Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Research on sustainable design of sports centre based on algorithm verification Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Institutional investor company social responsibility report and company performance Research on multi-dimensional optimisation design of user interface under Rhino/GH platform 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 A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Informatisation of educational reform based on fractional differential equations Application research on piano teaching in colleges and universities based on remote wireless network communication 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 Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation 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 Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model 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}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis 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 The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model 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 Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling 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 Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A 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 Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation 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 Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics 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 Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection 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 Calculating university education model based on finite element fractional differential equations and macro-control analysis 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 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 Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets 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 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 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 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 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 Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model 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 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 -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion 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 Research on threat assessment problems of island air defence system based on the leader-follower model 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 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 Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model