Entering the new normal of economy symbolises the innovation of growth mode and continuous optimisation and upgradation of economic structure. Using EG index, this paper measures the agglomeration degree of 31 provinces and cities and 31 manufacturing industries in China from 2012 to 2016; the results show that under the new normal, the degree of industrial agglomeration in China's manufacturing industry remains basically stable, but the overall situation is still in a state of moderate agglomeration, the regions with higher degree of concentration continue to present the pattern of ‘one pole, two domains’. To further reveal the relationship between the concentration of Chinese manufacturing industry and regional economic growth, the GMM method of dynamic panel twostage system was used, and the results showed that industrial agglomeration and economic growth do not have simple linear relationship, but inverted Utype relationship. There was a dynamic continuation effect of regional economic growth, and external factors such as fixed asset investment and government financial expenditure can promote regional industrial economic growth. Finally, the enlightenment of the complete article is given.
Keywords
 manufacturing industry
 industrial agglomeration
 economic growth
 EG index
 GMM analysis
Manufacturing industry is the basis of economic development, and the industrial agglomeration brought by its benefits is generally valued. After entering the new normal state of the economy, China's economy has changed from highspeed growth to mediumhighspeed growth. What are the spatial differences in the concentration of manufacturing industries and whether they are in a downward trend, and whether there is a positive correlation between the economic growth effects that follow are the points to ponder, and the different answers will bring different policy implications, which obviously have very important practical significance.
Industrial agglomeration based on the advantages of external economy, innovation benefits and competitive benefits can become a breakthrough point in economic development and structural adjustment. Industrial agglomeration and its effect on regional economic growth have also become one of the hotspots in academic research [1]. Due to the spatial distribution of the industry and its economic growth effects, the empirical research on industrial agglomeration has provided good practical guidance for scientific decisionmaking [2] and has attracted much attention from scholars.
Early related research started from abroad, and most of them indirectly explored the relationship between economic activity concentration and economic growth from some aspects such as labour productivity, urbanisation and market size. With the deepening of research, people have turned to the direct test of industrial agglomeration and economic growth. For example, Ciccone [3] researched the economic agglomeration of five European countries to regional economic growth and found that the two are mutually reinforcing. Geppert et al. [4] and other empirical tests on industrial agglomeration and economic growth in Germany from 1980 to 2000 showed a positive relationship between the two. In the above research, because the indicators for measuring industrial agglomeration are relatively simple, the endogenous nature of agglomeration is not considered, and the data used are mostly crosssectional in nature; so the dynamic relationship between industrial agglomeration and economic growth cannot be examined. Since then, dynamic analysis based on panel data has gradually increased. For example, Bruhlhart and Sbergami [5] established a dynamic panel data model analysis of 105 countries during 1960–2000 and the European Union in 1975–2000 through a systematic GMM method by considering endogenous issues fully; the results show that the industrial agglomeration of these regions has promoted their economic growth.
Also, in China, there are many studies on industrial agglomeration and its relationship with economic growth. Most conclusions, such as Liu [6], show that there is a mechanism of interaction between industrial agglomeration and economic growth, which is a pair of endogenous processes. From the analysis of China's practical data, there is also a negative correlation [7], insignificant [8] or nonlinear relationship [9, 10]. It can be said that different regions, industries, internal and external conditions, historical evolution, etc. will produce different economic agglomeration characteristics, and their corresponding effects on regional economic growth also have different correspondences.
In general, there are still some shortcomings in the current related research. The first is that most of the research is conducted in a static framework, and the research that reflects the dynamic characteristics of practical development has not yet become mainstream; the second is that some literature have simple setting indicators, which do not reflect the degree of industrial agglomeration well. In addition, in the empirical analysis of building data models, many literature do not pay enough attention to endogenous issues. Traditional panel data models cannot guarantee the unbiasedness of parameter estimates, which affects the acceptance of conclusions. Therefore, some literature have begun to use dynamic panel data model for analysis [11, 12].
China's economy has entered the new normal, which is consistent with the macroeconomic development of other countries. And with the rise of Chinese manufacturing, the new normal has gradually changed in recent years. To reflect the situation of our country's industrial agglomeration after the economy enters the new normal state more accurately, this paper takes the 2012–2016 regional manufacturing data as the object and uses a twostage system method to analyse the regional manufacturing industry agglomeration and its economic growth effects through the construction of EG indexes and dynamic panel data models. Because the GMM model can use the information of the difference and level equation variables to construct instrumental variables to control the endogenous problems of the explanatory variables, it can better reveal the hidden phenomena or problems in economic development.
EG indexes are more commonly used in research because they can more accurately measure and reflect the degree of industrial agglomeration. Under normal circumstances,
Drawing on the practice of Lu and Tao [13], the general calculation formula for EG index is:
In Eq. (1),
In Eq. (2),
In Eq. (3),
This paper calculates the
Industrial agglomeration status of 31 provinces and cities in China's manufacturing industry from 2012 to 2016
Area  

2012  2016  Increase or decrease  Increase  2012  2016  Increase or decrease  Increase  Rank  Rank increase or decrease  
Beijing  0.013  0.016  0.002  18.92  0.013  0.016  0.002  19.08  13  0 
Tianjing  0.011  0.005  −0.006  −58.1  0.011  0.005  −0.006  −58.1  24  −8 
Hebei  0.014  0.018  0.004  26.74  0.014  0.018  0.004  27.09  11  1 
Shanxi  0.017  0.008  −0.01  −56  0.017  0.008  −0.01  −56.1  16  −7 
Neimenggu  0.004  0.006  0.002  59.59  0.004  0.006  0.002  59.77  20  5 
Liaoning  0.044  0.026  −0.018  −41.5  0.044  0.026  −0.018  −41.6  9  −2 
Jilin  0.011  0.018  0.007  66.7  0.011  0.018  0.007  66.76  10  7 
Heilongjiang  0.015  0.005  −0.01  −64.1  0.015  0.005  −0.01  −64.1  23  −12 
Shanghai  0.026  0.028  0.002  9.247  0.026  0.028  0.002  9.628  7  1 
Jiangsu  0.057  0.11  0.053  92.14  0.057  0.11  0.053  93.23  2  3 
Zhejiang  0.140  0.081  −0.06  −42.5  0.141  0.081  −0.06  −42.6  3  0 
Anhui  0.005  0.004  −0.002  −29.2  0.005  0.004  −0.002  −29.5  26  −3 
Fujian  0.158  0.075  −0.082  −52.1  0.158  0.075  −0.083  −52.2  4  −2 
Jiangxi  0.004  0.007  0.003  82.91  0.004  0.007  0.003  83.03  17  9 
Shandu  0.066  0.054  −0.012  −17.9  0.066  0.054  −0.012  −18  5  −1 
Henan  0.011  0.027  0.015  132.8  0.011  0.026  0.015  134.2  8  10 
Hubei  0.013  0.012  −0.001  −9.58  0.013  0.012  −0.001  −9.67  15  −1 
Hunan  0.012  0.007  −0.005  −39.5  0.012  0.007  −0.005  −39.5  18  −3 
Guangdong  0.168  0.429  0.262  156.2  0.169  0.44  0.272  161.2  1  0 
Guangxi  0.009  0.006  −0.002  −25.5  0.008  0.006  −0.002  −25.5  19  1 
Hainan  0.000  0.000  0.000  −22.6  0.000  0.000  0.000  −22.6  30  −1 
Chongqing  0.008  0.006  −0.003  −31.9  0.008  0.005  −0.003  −32.1  22  −1 
Sichuan  0.017  0.016  −0.001  −5.47  0.017  0.016  −0.001  −5.4  12  −2 
Guizhou  0.007  0.004  −0.003  −47.8  0.007  0.004  −0.003  −47.8  27  −5 
Yunnan  0.047  0.044  −0.002  −5.2  0.047  0.044  −0.002  −5.19  6  0 
Xizang  0.000  0.000  0.000  2.598  0.000  0.000  0.000  2.594  31  −1 
0  
Shanxi  0.009  0.012  0.003  33.94  0.009  0.012  0.003  34.07  14  5 
Gansu  0.005  0.006  0.001  15.31  0.005  0.006  0.001  15.39  21  3 
Qinghai  0.001  0.001  0.000  −31.4  0.001  0.001  0.000  −31.4  29  −1 
Ningxia  0.000  0.001  0.000  42.15  0.000  0.001  0.000  42.2  28  3 
Xinjiang  0.004  0.004  0.000  12.51  0.004  0.004  0.000  12.51  25  2 
From Table 1, we can see that after the new normal economy, the agglomeration status of China's manufacturing industry has basically remained stable, and there has been no obvious downward trend, but it is still in a moderate agglomeration status as a whole. In the past five years, the degree of industrial agglomeration in China's manufacturing industry has increased. The average regional
In terms of index changes, most of the provinces with higher levels of industrial agglomeration have declined, while some provinces with a low degree of agglomeration have increased, and the differences in the degree of agglomeration of manufacturing between regions have slowed down, showing an overall favourable development trend.
In addition, the ranking of the degree of manufacturing agglomeration in each region has changed greatly, but the regions with a higher degree of agglomeration still continue to present a ‘one pole, two domains’ pattern, that is, a leading pattern with ‘Guangdong as the pole and supported by the Pearl River Delta and the Yangtze River Delta’. In terms of ranking, the top six provinces have not changed, but the overall ranking has changed significantly. The largest increases were in Henan and Jiangxi, whereas the largest declines were in Heilongjiang, Tianjin and Shanxi. Among the declining provinces, one reason was the rational adjustment made due to the high degree of industrial agglomeration, such as in Fujian and Zhejiang; the other was that the old industrial base was affected by factors such as industrial structure transformation and upgrading, zombie corporate governance policies, and slow industrial transformation and upgrading. Third, the backward manufacturing areas are subject to a variety of internal and external factors, and the aggregation effect of resource elements is low. On the whole, the degree of industrial agglomeration in the Yangtze River Delta and the central and western regions has increased. This situation is basically consistent with the status of regional economic development.
To reveal the spatial changes of manufacturing agglomeration more intuitively, according to the changes of manufacturing industry index of 31 provinces and cities in 2016, a map of manufacturing agglomeration changes in each region was made. It can be seen that the region with a higher concentration of manufacturing industries still presents a ‘one pole, two domains’ pattern; this situation of continuous leading has been in less change.
To reflect the dynamic characteristics of practical development and the endogenous problems of data processing, this paper analyses through the construction of a dynamic panel data model and the application of a twophase system GMM method.
Regional economic growth is the result of the combination of multiple variables such as factor inputs, innovation clusters and natural conditions. Based on the CobbDouglas production function, this paper adds agglomeration variables that reflect spatial factors to reflect the basic conditions of regional economic growth from the perspective of time and space. The model is set as follows:
Among them, the dependent variable
To reduce the estimation bias caused by missing variables, the three corresponding control variables are added to the model. (1) Fixed assets investment (assets): It is an important input factor for manufacturing enterprises in production. Its size reflects the scale and strength of the industry. It is a necessary condition for production and can be used to measure the degree of input of internal factors in manufacturing. (2) Government expenditure (ge): On the one hand, the government directly supports the local manufacturing funds, and on the other hand, the government stimulates demand through expenditure, stimulates production, and promotes the development of manufacturing. The general budgetary expenditures of local governments are generally used to measure the degree of government expenditure and the degree of market pull. (3) Dummy variables: Add dummy variables for year and province to control fixed effects of time and region.
For model's robustness and endogenous problems, to overcome the measurement errors caused by different units, initially, all the variables with economic units were used with their logarithmic values. In addition, to consider the inertia and path dependence of China's economic growth, referring to the practice of Sun et al. [14], without using manual setting of instrumental variables, a systematic GMM method was selected to estimate the effects of economic growth and industrial agglomeration to control endogenous problems. Therefore, based on Eq. (4), the specific model of this study is set as:
In Eq. (5), in addition to using the lag period value of the explanatory variable, relevant dummy variables are added to control the fixed effects of time and region. At the same time, the dimensions of the independent and dependent variables are different, and natural logarithmic processing is performed on all continuous variables.
To more clearly show the situation after the new normal of the economy, the data used in this article are from the China Statistical Yearbook 2012 and the China Industrial Economic Statistical Yearbook 2012–2017, and the samples were checked with the National Bureau of Statistics and other websites. Due to the lack of individual data in Tibet, the arithmetic mean of the previous and subsequent years was used in the study to complete the data to ensure the integrity of the data.
Simple descriptive statistics of each variable are shown in Table 2.
Descriptive statistics of variables
Variable  Observations  Meaning  Unit  Mean  Standard deviation  Minimum value  Max  LLC inspection 

155  Industrial added value  100 million yuan  8.592  1.241  4.014  10.394  −12.186  
155  Index    0.033  0.075  0.000  0.474  −71.246  
155  Exponent square    0.007  0.033  0.000  0.225  −53.053  
155  Manufacturing fixed asset investment (excluding farmers)  100 million yuan  7.947  1.364  3.362  10.060  −4.206  
155  Fiscal General Budget Expenditure  100 million yuan  8.226  0.568  6.762  9.506  −19.127  
155  Timecontrolled variable  year  2014  1.419  2012  2016   
To avoid the nonstationary pseudoregression of the data variables, the LLC method is used for testing. Each variable passes the unit root test at the level of 1% (the last column of Table 2). The variables are
Examining the scatter point relationship between the main variables (see Figure 1), it is found that there is a nonlinear relationship between the industrial added value and the
Model regressions such as intergroup effects, random effects, and fixed effects were performed on
Estimated results of
Explained variable  

Explanatory variables  Fe model  Re model  Be model  A model  B model 
0.83^{***}  0.85^{***}  
14.8  14.02  
−0.10  −0.04  0.97  1.07  2.86^{***}  
−0.38  (−0.13)  −1.04  0.84  3.05  
−5.2^{**}  
−2.18  
0.61^{***}  1.01^{***}  0.94^{***}  0.16^{***}  0.15^{***}  
5.01  9.45  5.17  2.96  2.13  
0.21^{***}  0.30^{***}  0.54^{***}  0.14^{***}  0.13^{***}  
6.00  8.53  8.03  3.25  3.26  
106.66^{***}  196.12^{***}  −3.49^{***}  47.44^{***}  48.40^{***}  
4.40  9.08  (−3.06)  6.17  5.27  
Time control  −0.05^{***}  −0.10^{***}  (omitted)  −0.02^{***}  −0.02^{***} 
−4.17  (−8.90)  (−6.13)  (−5.20)  
Area control  Yes  Yes  
1326.05  1269.25  
0  0  
7.7003  9.0495  
0.3598  0.2491  
0.0483  0.0494  
0.9076  0.8012 
(2) Autocorrelation test uses ArellanoBond secondorder autocorrelation test;
(3) The overidentification test uses the Sargan test. The null hypothesis is that all moment conditions in the model are valid.
Further, to eliminate the possible explanatory variables of the dynamic panel model and its related endogenous problems with random error terms, especially the heteroscedasticity, autocorrelation and individual effects that may exist in the ‘large N small T’ panel model, based on the existing results achieved in the literature, this paper uses a twostage system dynamic GMM method to estimate the model. The specific operation is realised by the STATA15.0 tool. On the one hand, difference equations are used to eliminate fixed effects; on the other hand, the lag term of the difference term is used as the instrumental variable of the horizontal term to increase the number of instrumental variables and solve the problem of weak instrumental variables of the horizontal lagging term. The estimation results are shown in the column ‘A model’ in Table 3.
In terms of robustness test, since the lag term of the difference variable is introduced as a new instrumental variable, in order to prevent transitional identification caused by improper selection of instrumental variables, a
The
This paper uses the calculation of the
The degree of manufacturing agglomeration in various regions of China has changed greatly, but the overall situation has remained stable and is in a state of moderate agglomeration. The regions with higher levels of agglomeration still present a ‘one pole, two domains’ pattern.
After entering the new normal state of the economy, the economic growth effect brought by the agglomeration of manufacturing industries in various regions of China is not a simple linear relationship, and there is still a threshold effect.
It can be seen from Table 3 that after introducing the nonlinear explanatory variable
There is a dynamic continuation effect of regional economic growth. It has a positive linear relationship with fixed asset investment, etc., and the government fiscal expenditure pull is higher than the fixed asset investment pull.
Table 3 shows that the coefficient of
These conclusions can bring some important policy implications:
After the economy enters the new normal, China's manufacturing industry agglomeration status has a large gap between regions, and regional changes are also rapid. This requires the overall control of the reasonable flow of industries between regions. The continuous flow and pooling of resources (such as capital, technology), especially highquality resources, to developed and more developed regions will inevitably cause the industrial economy to intensify in terms of the degree of geographical agglomeration. Industry “manufacturing agglomeration. Under the influence of many factors such as declining demand in the foreign market, accelerating the adjustment and upgrading the domestic industrial structure and increasing environmental pollution, the problems of the decline in the concentration of manufacturing industries in the Northeast and the accumulation of industries in the backward areas in the West should be paid attention to.
The threshold effect of economic growth brought by the agglomeration of manufacturing industries is worth vigilant. For economically underdeveloped regions, the effective allocation of various factors and resources is needed to drive the growth of industrial agglomeration, whereas for economically developed regions, more consideration must be given to the highquality development of industries under the new economy.
In the process of stimulating industrial economic growth, regional authorities should give full play to their own micropolicies, such as the government's active fiscal policy, the vigorous support of technological innovation and the establishment of a healthy economic environment. It can be said that China's economic growth has obvious path dependence, and it is necessary to dig out the ways and methods to solve the structural contradictions in restricting economic transformation and upgrading the problems of uneven and insufficient regional economic development.
At present, with the promotion of innovationdriven role and the rapid growth of new industries, new economies and new kinetic energy in economic growth, China's economy is expected to accelerate the development of high quality and continue to maintain its stable operation development trend, manufacturing under the new normal. Industry agglomeration will also exert its positive effects due to the continuous adjustment and upgrading of the industrial structure.
Estimated results of EG indices and economic growth
Explained variable  

Explanatory variables  Fe model  Re model  Be model  A model  B model 
0.83 
0.85 

14.8  14.02  
−0.10  −0.04  0.97  1.07  2.86 

−0.38  (−0.13)  −1.04  0.84  3.05  
−5.2 

−2.18  
0.61 
1.01 
0.94 
0.16 
0.15 

5.01  9.45  5.17  2.96  2.13  
0.21 
0.30 
0.54 
0.14 
0.13 

6.00  8.53  8.03  3.25  3.26  
106.66 
196.12 
−3.49 
47.44 
48.40 

4.40  9.08  (−3.06)  6.17  5.27  
Time control  −0.05 
−0.10 
(omitted)  −0.02 
−0.02 
−4.17  (−8.90)  (−6.13)  (−5.20)  
Area control  Yes  Yes  
1326.05  1269.25  
0  0  
7.7003  9.0495  
0.3598  0.2491  
0.0483  0.0494  
0.9076  0.8012 
Industrial agglomeration status of 31 provinces and cities in China's manufacturing industry from 2012 to 2016
Area  

2012  2016  Increase or decrease  Increase  2012  2016  Increase or decrease  Increase  Rank  Rank increase or decrease  
Beijing  0.013  0.016  0.002  18.92  0.013  0.016  0.002  19.08  13  0 
Tianjing  0.011  0.005  −0.006  −58.1  0.011  0.005  −0.006  −58.1  24  −8 
Hebei  0.014  0.018  0.004  26.74  0.014  0.018  0.004  27.09  11  1 
Shanxi  0.017  0.008  −0.01  −56  0.017  0.008  −0.01  −56.1  16  −7 
Neimenggu  0.004  0.006  0.002  59.59  0.004  0.006  0.002  59.77  20  5 
Liaoning  0.044  0.026  −0.018  −41.5  0.044  0.026  −0.018  −41.6  9  −2 
Jilin  0.011  0.018  0.007  66.7  0.011  0.018  0.007  66.76  10  7 
Heilongjiang  0.015  0.005  −0.01  −64.1  0.015  0.005  −0.01  −64.1  23  −12 
Shanghai  0.026  0.028  0.002  9.247  0.026  0.028  0.002  9.628  7  1 
Jiangsu  0.057  0.11  0.053  92.14  0.057  0.11  0.053  93.23  2  3 
Zhejiang  0.140  0.081  −0.06  −42.5  0.141  0.081  −0.06  −42.6  3  0 
Anhui  0.005  0.004  −0.002  −29.2  0.005  0.004  −0.002  −29.5  26  −3 
Fujian  0.158  0.075  −0.082  −52.1  0.158  0.075  −0.083  −52.2  4  −2 
Jiangxi  0.004  0.007  0.003  82.91  0.004  0.007  0.003  83.03  17  9 
Shandu  0.066  0.054  −0.012  −17.9  0.066  0.054  −0.012  −18  5  −1 
Henan  0.011  0.027  0.015  132.8  0.011  0.026  0.015  134.2  8  10 
Hubei  0.013  0.012  −0.001  −9.58  0.013  0.012  −0.001  −9.67  15  −1 
Hunan  0.012  0.007  −0.005  −39.5  0.012  0.007  −0.005  −39.5  18  −3 
Guangdong  0.168  0.429  0.262  156.2  0.169  0.44  0.272  161.2  1  0 
Guangxi  0.009  0.006  −0.002  −25.5  0.008  0.006  −0.002  −25.5  19  1 
Hainan  0.000  0.000  0.000  −22.6  0.000  0.000  0.000  −22.6  30  −1 
Chongqing  0.008  0.006  −0.003  −31.9  0.008  0.005  −0.003  −32.1  22  −1 
Sichuan  0.017  0.016  −0.001  −5.47  0.017  0.016  −0.001  −5.4  12  −2 
Guizhou  0.007  0.004  −0.003  −47.8  0.007  0.004  −0.003  −47.8  27  −5 
Yunnan  0.047  0.044  −0.002  −5.2  0.047  0.044  −0.002  −5.19  6  0 
Xizang  0.000  0.000  0.000  2.598  0.000  0.000  0.000  2.594  31  −1 
0  
Shanxi  0.009  0.012  0.003  33.94  0.009  0.012  0.003  34.07  14  5 
Gansu  0.005  0.006  0.001  15.31  0.005  0.006  0.001  15.39  21  3 
Qinghai  0.001  0.001  0.000  −31.4  0.001  0.001  0.000  −31.4  29  −1 
Ningxia  0.000  0.001  0.000  42.15  0.000  0.001  0.000  42.2  28  3 
Xinjiang  0.004  0.004  0.000  12.51  0.004  0.004  0.000  12.51  25  2 
Descriptive statistics of variables
Variable  Observations  Meaning  Unit  Mean  Standard deviation  Minimum value  Max  LLC inspection 

155  Industrial added value  100 million yuan  8.592  1.241  4.014  10.394  −12.186  
155  Index    0.033  0.075  0.000  0.474  −71.246  
155  Exponent square    0.007  0.033  0.000  0.225  −53.053  
155  Manufacturing fixed asset investment (excluding farmers)  100 million yuan  7.947  1.364  3.362  10.060  −4.206  
155  Fiscal General Budget Expenditure  100 million yuan  8.226  0.568  6.762  9.506  −19.127  
155  Timecontrolled variable  year  2014  1.419  2012  2016   
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statistical analysis Application of SobolevVolterra 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 Btheory for numerical method of functional differential equations in the analysis of fair value in financial accounting Badminton players’ trajectory under numerical calculation method Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audiovisual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Differenceindifferences test for micro effect of technological finance cooperation pilot in China Application of multiattribute decisionmaking 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 AtanKA 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 Research on the influencing factors of agricultural product purchase willingness in social ecommerce situation Study of a linearphysicalprogrammingbased approach for web service selection under uncertain service quality A mathematical model of plasmidcarried antibiotic resistance transmission in two types of cells Burnout of frontline city administrative lawenforcing personnel in new urban development areas: An empirical research in China Calculating university education model based on finite element fractional differential equations and macrocontrol 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 Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Good congruences on weakly Uabundant semigroups Research on the processing method of multisource heterogeneous data in the intelligent agriculture cloud platform Mathematical simulation analysis of optimal detection of shotputters’ best path Internal control index and enterprise growth: An empirical study of Chinese listedcompanies 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 BSM model in the pricing of derivatives in financial markets Nonlinear Differential Equations in the Teaching Model of Educational Informatisation FedUserPro: A user profile construction method based on federated learning The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education Firstprinciples calculations of magnetic and mechanical properties of Febased nanocrystalline alloy Fe_{80}Si_{10}Nb_{6}B_{2}Cu_{2} 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 in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption MCM of Student’s Physical Health Based on Mathematical Cone Attitude control for the rigid spacecraft with the improved extended state observer 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 nonsampled contourlet transform Nonlinear Differential Equations in ComputerAided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Application of HigherOrder Ordinary Differential Equation Model in Financial Investment Stock Price Forecast 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 Informatisation of educational reform based on fractional differential equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis 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 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with DiamondSquare Algorithm 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 Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Crossborder Ecommerce Platform Operation Based on Fractional Differential Equations Research on Stability of Timedelay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of AirConditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression System dynamics model of output of ball mill Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on shortterm human movement Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement 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 Design of Morlet wavelet neural network to solve the nonlinear influenza disease system Nonlinear Differential Equations in Crossborder Ecommerce 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 Motion about equilibrium points in the JupiterEuropa system with oblateness Fractional Differential Equations in Electronic Information Models Badminton players’ trajectory under numerical calculation method BIM Engineering Management Oriented to Curve Equation Model Optimal preview repetitive control for impulsefree continuoustime descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Value Creation of Real Estate Company Spinoff Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multiregression Model of Informationbased Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centreofmass 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 eyemovement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm} −x +δ )^{s} +ax ^{pm} +bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decisionmaking Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Crossborder Ecommerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model