The term ‘context’ was first used in linguistics and semiotics to refer to the contextual relationship of the parts and the whole within a thing. Since the middle of the last century, the concept of context has been introduced into the field of urban research, and urban context has become an important vocabulary to understand cities better. It represents the unique aura of cities, whose essence is a cultural gene and social connection, and is embodied in the physical space of cities, such as buildings and blocks. The construction of Guangzhou City, which has historical value, dates back to more than two thousand years. The ZhaoTuo City, having experienced the BuZhi City and the Song, formed a relatively stable city pattern in the Ming and Qing Dynasties whose influence continues. The Old Town, centred on the outline of the city of Guangzhou in the Ming and Qing dynasties, is a concentrated reflection of Guangzhou's urban culture as a thousand-year-old merchant capital and is also a gathering area for the city's historical buildings, which is of great significance to the inheritance of urban culture. Since the founding of the People's Republic of China, Guangzhou has maintained a rapid pace of urban development, but based on economic functions, urban construction focusing on physical space has to some extent led to the rupture of the urban context, and the urban pattern of ‘green hills half entering the city and six veins all leading to the sea’ has no longer existed, with many reconstruction problems in this old city . The city is a unity of function and structure, and the prerequisite for a well-functioning city is a deep cognition of the structure . While previous qualitative studies on urban structure and context have accumulated rich results, urban space has not received sufficient attention as the spatial form and fabric are often regarded as the backdrop of social and economic activities in a certain region, and the analysis method is more traditional, perceptual and experiential. Understanding the relationship between space and social activities in it is essential to form a correct concept of spatial planning, which can contribute to the inheritance of urban context in the process of urban development. Therefore, exploring new methods for the study of urban structure is a topic that needs to be discussed by urban researchers.
Space syntax theory was created by Bill Hiller and Julienne Hanson et al. from UCL Bartlett Faculty of the Built Environment in the 1970s. Syntax refers to the structure of language grammar. Hiller et al., using ‘syntax’, provided the perception of spatial structure with a theoretical explanation and an approach to quantitative analysis. The urban structure is the classical research of space syntax, and it elaborates the space forms through indicators such as closeness (reachability), betweenness (the possibility of being passed; it refers to the ability to bear the passage capacity), degree of intelligence (degree of fitting for both the local closeness and the overall closeness; it refers to the degree of perception and understanding of space), etc., and is an attempt to explain and quantify the representation of space in terms of its inherent self-organising forces [1, 2]. sDNA is an operational software of space syntax embedded in GIS which was developed by the team from Cardiff University. It redefined the node and the link in the traditional graph theory of space syntax, and transferred dual topology into classical topology, thus getting closer to the network analysis of the traffic conceptually [11, 13]. Space cognition and space syntax can be complementary to the spatial information metrology of GIS; the former can calculate and visualise the spatial structure based upon the topological relationship of spatial grouping, while the latter can overcome the shortcomings of traditional spatial syntax which cannot perform advanced spatial analysis, spatial measurement and produce standard maps. Therefore, the analytic statistics of space syntax can be improved to give an in-depth reveal of the spatial layout . Research, which is based on spatial syntax theory has become more and more diversified; speaking in terms of the context of the era of network big data, the rapid development of analysis technology and the reduction of data acquisition costs, spatial syntax in urban research, architecture, landscape space research, geographical research and even space-related sociological research and other fields gradually emerged. Combined with multi-source big data, it can be combined with spatial configuration analysis to establish a forward-looking and predictive spatial model and can test it, thereby improving the evaluation system, and can provide reference or guidance for planning and design work, which is conducive to a better understanding of space and transformation space. Given this, the paper took the preservation and utilisation of historic buildings in the old district of Guangzhou as an example to explore the new approach based on both space syntax and GIS to study the urban structure.
The old district of Guangzhou was chosen as the research scope. ‘Old district’ was given a detailed description in Technical Regulations on Urban and Rural Planning of Guangzhou Municipality (2012): the urban scope built over 30 years, including the regions of ‘Huanshi Road; Hengfu Road; South from Yongfu Road, West from Guangzhou Avenue, Changgang Road; North from Xingang Road, Zhujiang watercourse of Bai’e’tan; Hedong Bridge; East from Tong Deyong, with an area of about 54 sq.km.’ (Seen in Figure 1). The historic regions delimited by the city wall in the Ming-Qing Dynasty play an important role in the old district and affect the layout of the old district deeply, and therefore is specially marked.
Urban forms and historic buildings of the old district of Guangzhou were studied based on the space syntax analysis of the road network structure. The road data of the old district were from Amap. Since the road network obtained in the modelling is prone to failure of sDNA calculation due to the inevitable fracture, the paper drew the road network of the old district manually according to the high-definition street map, and there were 16545 roads in the region. Historical buildings refer to buildings and structures that have certain protection values, can reflect historical features and local characteristics, and are not announced as cultural relics protection units or registered as immovable cultural relics after being determined and announced by the people's governments of cities and counties. Under normal circumstances, historical buildings are not evenly distributed in the city, but are affected by the economic and social development of the city, and are closely related to the history of the city. The historic buildings were obtained by the spider tool from the open API of Amap; a list of the historic buildings published by Guangzhou Municipal Bureau of Planning and Natural Resources six times were referred. Data were summarized and integrated using comparison between the ancient and modern map, analysis of historic effects and literature and history, and information retrieval. The included old district has certain cultural deposits and representativeness, and there were 150 regions of the old district in total, with the distribution shown in Figure 2.
The research includes two aspects: one is the analysis of space syntax of the old district with space syntax as the theory and tool. The old district was analysed from the perspective of urban form based on space statistics, closeness, and betweenness so as to explore the spatial layout. The other is thinking about the preservation and utilisation of the historic buildings. According to the distribution features of the historic buildings in the spatial layout, suggestions and strategies were put forward for the preservation and utilisation. The framework and idea of the research are seen in Figure 3.
Integration, also called closeness, is the core parameter of the space syntax theory. It represents how closely a small-scale space in a certain radius is connected to other space . High integration means better centrality, accessibility, and integration, and often represents an area that is more attractive to the gathering of people and traffic in the region. In a city, areas with high closeness correspond to urban cores at a certain scale, and such areas are the first consideration in urban studies and perception of the urban structure . In sDNA, closeness is denoted by
A distance of 800 metres is usually considered the radius of a walking trip in the city. Compared with other scales, the urban structure is more dispersed in the closeness analysis of an 800 m radius. The fishing net graph (aggregating the values onto a raster) can clarify the visualisation of the arithmetic results. In the east of the historic area of the city, there emerges a significant core of closeness, and the crossroad consisting of Dongfeng Road, Xiaobei Road, and Cangbian Road expands around; the second core consisting of Dezheng Road and Wenming Road expand horizontally in east and west. Both cores are connected through Cangbian Road, Dezhengbei Road, and Yuexiubei Road. Another significant core is nearby Sun Yat-sen University, forming a well-shaped structure with high closeness through Jiefangzhong Road, Huifuxi Road, Haizhuzhong Road, and Zhongshanliu Road, but no compact network structure is formed inside, nor a core of closeness for the active scope. The above characteristics of the spatial layout can explain the integrated urban core of the old district within the walking distance. In terms of spatial function, the above area is the gathering area of the community, and the spatial pattern is suitable for activities within the community .
A travel distance of 1500m generally indicates that people's travel mode would change and they prefer to bicycle or public transportation such as subway and bus. So, the core of closeness in the old district begins to gather towards the historical district, and the two cores on the 800m radius gradually merge to expand around the core of Beijing Road and Zhongshan Road, while the advantage of the high closeness in the south bank decreases. In terms of spatial functions, business offices have emerged along these axes, such as Pedestrian Street along Beijing Road, Commercial Centre at Dama Station, and Yinhu Building, etc., which coincides with the results of space syntax closeness on a larger radius.
When for a radius of 3000m and 5000m, the core of closeness centres on the historic district to further assemble and expand with a significant increase of the values, and the peak emerges at the banks of the Pearl River. This indicates that areas along the river, at a large scale, are the ‘golden area’ of the old district. The fishing net graph shows that the core of closeness at a radius of 5000m assembles more than that at a radius of 3000m. Both have a similar position with the historic district as the core of closeness. Detailed results show that the horizontal axis with the high closeness of the historic district includes Dongfeng Road, Zhongshan Road, Huifuxi Road, and Wenming Road; the vertical axis with the high closeness of the historic district includes Haizhuzhong Road, Liurong Road - Mishi Road, Jiefangzhong Road, Jixiang Road, Beijing Road, Wende Road, and Dezheng Road. The criss-crossed roads constitute the framework of the whole historic district. This indicates the dominant position of the historic district in the old district. It is worth mentioning that among the above high-value axes are there many arterial streets since the Ming-Qing dynasty, such as Huifu Road, Wenming Road, and Dezheng Road. These roads were all recorded in the local chronicles and other historical materials, manifesting their deep effects in that time. Besides, short and thin road networks with low values are distributed in the grid of axes, indicating that the area is accessible from the outside but ‘closed’ from the inside for ‘strangers’. In this way, it attracts people and protects internal communication from being interrupted. The area has its own social logic: easy to reach from the outside, but with its own internal network, which results from a long historical evolution.
The radius of n is the analysis of the over closeness. Here, no obvious core of closeness within the old district emerges, and the area along the river is more clustered than other areas, but no core is formed either. Globally, the linear pattern is significant, and the clustered core centred on the historic district becomes a long well-shaped axis extending to the whole area. In the front ground network of overall closeness (road network whose values are top 10%), this pattern is more significant. Unlike the regional closeness, the overall closeness has a larger scope of axis extending to east and west while the extension in south and north is a little fragmented. Yuexiu Garden – People Park – Haizhu Square – Jiangnanxi is the vertical long axis, and Dongfeng Road, Zhongshan Road, Huifu Road – Donghua Road is the horizontal long axis. As per the values, the average of regional closeness and overall closeness at a radius of 5000m is 14.011 and 21.873, respectively, with a great improvement. This indicates that the grid structure, at the global scale, replaces the urban structure with the historic district as the core, and the structure of the urban road network is better developed. However, the foreground network reveals that the grid structure in the eastern region and the southern bank of the Pearl River is less developed and no high-value closeness axes have emerged.
Intelligibility (comprehensibility) is another important index of space syntax theory for the interpretation of large-scale space configurations, and users of characterisation build up the whole space cognition by observing the local area. Intelligibility is defined as the degree of fitting of the local and the global analyses results, i.e., the degree of linear correlation between the two . Results show that the value of R2 increases from 800m to 5000m as the radius increases, and is 0.20, 0.36, 0.47, and 0.53, respectively. If the value of R2 on the 5000m radius is greater than 0.5, i.e., significantly correlated, then the city has a higher level of comprehensibility on the public transportation to vehicular scale. Therefore, it can be inferred that the urban operation speed of the old district matches the level of urban development on the 5000m and larger radius scales.
Betweenness(TPBt) is another important parameter provided by sDNA. It is highly correlated with the total depth of space and indicates the probability that a spatial node is passed. Higher TPBt represents the higher probability that the road network will be passed through and accordingly carries a higher calming capacity of the traffic . Unlike closeness which emphasises reachability, TPBt represents passability and is calculated as:
The figure shows that TPBt at a radius of 800m and 1500m does not show a coherent long axis, and it is basically irregular, mostly fine line segments. Therefore, it can be assumed that the old district has poor traffic circulation ability at the radius scale of 800m to 1500m. The shaped axis only emerges at a large radius scale of 3000m to 5000m. In terms of the foreground network, the network structure of TPBt is most obvious at the global scale, supporting almost the whole area of the old district. From the 3000m radius to the global scale, the results of TPBt analysis become more and more clustered, with the highest values located along the river areas. The horizontal axis includes Yanjiang Road, Zhongshan Road, and Dongfeng Road, and the vertical axis includes Jiefangzhong Road, Jiangnan Avenue, Donghu Road, Haiyin Bridge, and Dongxiao Road. But this structure is not balanced and perfect, and fractures emerge along the axis from the fringe areas to the central area; also, the axis along the connection of the old district and the new district also has fractures, indicating that the road access from outside to outside and from inside to inside are both relatively good, but the access from outside to inside is relatively poor. In addition, there may be some problems in fusion between the old and the new district.
In line with the above illustration, the fitting results also show that the radius below 3000m is almost uncorrelated with the global, while the 3000m radius and 5000m radius are highly correlated locally and globally, and TPBt results at the 5000m radius are even almost identical to the global results (R2 from 800m to 5000m is 0.11, 0.35, 0.74, and 0.91, respectively). As seen from the whole old district, the radius that best fits the urban TPBt is from 3000m to 5000m. Among the four radii, 3000m is a node for whether the passing structure appears, indicating that the scale suitable for the operation of the existing urban structure in the old district is no less than 3000m, while the fitting degree of 0.91 indicates that the limit of the operation scale is roughly around 5000m. Based on the basic perception of urban efficiency, this scale represents that the urban flow is also at a high level, and the urban structure has been elevated to the benchmark of a fast road network, while the high-value axis of TPBt has many overlaps with the above TPBt axis. Singly seen from the urban operation speed, we should consider how to match the high-speed urban movement with the low-speed activities of people, and how the urban flow of people and vehicles is compatible. Seen from the practical situations, the congestion problems that occur from time to time within the old district are consistent with the arithmetic results .
Geostatistical analysis has many advantages over ArcGIS spatial analysis though they are often intertwined. Geostatistical analysis, often based on a variety of statistical inference methods, analyses the spatial pattern of ground objects, and the good statistical characteristics of the space syntax allow researchers to carry out various geostatistical analyses on the results of their calculations . The results of space syntax of the old district – closeness and TPBt – have been described above, and preliminary analysis has been carried out based on the actual situations of the old district. The following will use the statistical tools of ArcGIS to further analyse the results and discuss the deeper urban pattern.
Standard Deviational Ellipse is often used to identify the central and directional trends of spatial elements and to characterise the core and direction of distribution of spatial elements. If the Basic spatial pattern of the elements is a spatial normal distribution (scattered from the centre to the periphery), a standard deviational ellipse surface will contain about 68% of the elements in the cluster. The formula is as follows:
Results show that the standard deviational ellipses of closeness and TPBt have a high contact ratio, which is consistent with the above analysis, and characteristics of the directional distribution of both are more obvious, roughly in east-west, slightly inclined along the northwest-southeast direction. Both ellipses include the entire range of the historic urban area, in which characteristics of the pattern of the old urban road network in TPBt are more clustered. This indicates that the historic district and its east areas are the reachability centre and high-value core of passability within the whole area of the old district. This once again verifies the profound effect of the historic district on the urban pattern, and also shows that the construction of eastern areas from the historic district has good integration with the historic district after the founding of New China. But the standard deviational ellipse with a high contact ratio still suggests that solving the contradiction between passability and reachability in terms of the crow and vehicle flow is still a consideration.
The above description summarises the spatial pattern of the old district. Further analysis of the internal spatial pattern requires more accurate identification of spatial heterogeneity, which requires verification of spatial autocorrelation, i.e., spatial dependence, which refers to the potential interdependence between observations of spatial elements in the same distribution area. Moran's I coefficient is an important tool to measure spatial autocorrelation, and its formula is as follows:
With the existence of spatial autocorrelation clarified, we hope to further analyse the clustering pattern. Local Moran's I is an important measurement for spatial clustering and spatial outliers. Local Moran's I values, z scores, pseudo p values, and codes indicate the type of clustering for each statistically significant element. Z scores and pseudo p values indicate the statistical significance of the calculated index. The formula is as follows:
Local Moran's I can reveal four patterns of HH, HL, LH, and LL, representing the local high values around the high values, the low values around the high values...and so on. It can be seen that closeness and TPBt are two different patterns. Analysis of local Moran's I of closeness has significant structure extending from the centre to outside; HH pattern mainly locates within the historic district, and has a high contact ratio; LH pattern, although has spatial outliers, is surrounded by high values, thus providing a guarantee to the internal social communication of areas of high reachability, that is, the “social logic” of the historic district mentioned above. At the same time, the spatial difference within the historic district is small, and HH and HL are complementary. With a long time of natural evolution and modern construction, the historic district has formed a good layout. HL pattern mainly emerges around the marginal area, indicating that the road network in the non-centre area of the old district has a certain centre, but is poorly integrated with the surrounding areas and fails to improve its spatial pattern. Analysis of local Moran's I of overall TPBt is more fragmented with inconspicuous clustering and rules. The original high-value axis of TPBt fails to maintain the continuous HH pattern and fractures in many places emerge. In addition, the LL pattern and the road network structure without significant clustering are scattered in the whole area, and the spatial distribution is more random with many spatial outliers. The originally obvious network of high-value TPBt may be interrupted by too many nodes around, thus losing characteristics of the spatial clustering. Optimisation of the TPBt pattern of the old district needs more consideration, and this paper will not discuss it for the time being.
800m (walking scale) is used as the search radius to analyse the kernel density of historic buildings in the old district, and the results are shown in the figure. It is obvious that the historic district is the core of the distribution of historic buildings. Based upon the spatial analysis of the old district above, the strategies for the conservation and utilisation of historic buildings in the old district are proposed as follows.
The historic buildings around Yuexiu Mountain, People Park and Haizhu Bridge have a high level of clustering, which can improve the accessibility of the whole axis by adding urban greenbelt and reducing nodes that has weak functions. Based on the features of the historic buildings, the natural scene in the north – Yuexiu Mountain, and the revolutionary sites – Ye Jianying's uprising site, Guangzhou Uprising Memorial Hall, and the historic buildings in the south – Haizhu Bridge, and Zhaoqing Hall can be integrated. With the historic buildings along the river as supplementary, the cultural axis of the old district can be created, echoing with the middle axis of the new district, and enriching the cultural deposits of the modern city.
According to Bill Hiller's research, traditional communities have a different ‘spatial DNA’ from modern communities, and the spatial grouping is a reflection of the social connection. For historic buildings, fenced-in preservation can lead to a gradual loss of vitality, and integration into the surrounding social ecology is necessary to maintain such vitality . These communities are based on neighbourhoods, and their form of social association is different from that of modern cities, and it is their unique social logic that highlights the ‘urban fabric’. As mentioned above, the spatial pattern of the historic district has its own unique ‘social logic’: the exterior is easily accessible while the interior activities are not easily disturbed. Based on this feature, the urban fabric can be protected through the optimisation of the pattern of the public service, so that visitors and residents of the community do not interfere with each other. For example, community activity centrer, service centrer, small commercial sites, community health services and education services are provided within the walking distance of the community residents to fulfil their living needs, and meanwhile, space is provided to support their social behaviour. Large-volume urban complexes such as commercial centres should be avoided. This kind of urban function tends to attract pedestrians and vehicles, exacerbating the contradiction between aggregation and reachability. This strategy can be adopted around Guangxiao Temple, Beijing Road, Zhongshan Road, and Wende Road.
This strategy is applicable to historic buildings located outside the historic district or the high-closeness core, such as Xiguandawu and Yongqingfang in the western part of the old district . According to the analysis of spatial structure, if it is not in the core of the city, the road adjustment plan can be prepared according to the field research to improve the accessibility of the area. These areas are located in regions with low-value closeness and TPBt in the old district and are in a weak position in the spatial network of the whole area, but local Moran's I reveal that spatial heterogeneity exists around, i.e. HL pattern. This indicates that it is not that difficult to improve the regional spatial pattern, and reasonable planning, as well as adjustment of the road network structure, can topologically reduce the degree of isolation and improve the spatial pattern; it is also integrated into the spatial network in a manner of ‘darning’.
Urban structure and morphology are hot issues in the field of urban research. Previous studies tend to focus on the analysis of society and culture, with less discussion on the mechanism of spatial function. This paper combines the spatial syntax method with the spatial statistics of GIS to analsze the urban pattern of the old city, and proposes a strategy for the preservation and utilisation of historical buildings in conjunction with their distribution, which means, there is a connection between urban spatial ontology and contextual attributes, aiming to explore a new approach to the study of the urban structure by spatial syntax, for providing a reference for the rational arrangement of urban elements. In the era of big data, urban research or spatial research is increasingly inclined to the comprehensive analysis of multi-source data, and the complexity of cities is increasing, so the research tools need to be upgraded, and the analysis results of combining GIS and different urban data are more refined and diversified compared to the traditional spatial syntax research. The research tool combining spatial syntax and big data technology is worth exploring and has a wide range of application prospects.
Above all, we must mention that the spatial syntax method has some limitations, with insufficient ability to explain the unnatural flow of pedestrian and road networks without a historical development structure. The study of urban structure is complex and comprehensive, where spatial ontology and socio-economic development cannot be ignored and requires multidisciplinary and multi-source data. This paper is a new attempt, and the study of space syntax based on urban research needs more in-depth exploration.
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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 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 of p-groups The 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 H2-N2 atmosphere Algorithm 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