As a new school of modern econometrics, spatial econometrics, originally proposed by Jean Paelinck in the 1970s when addressing regional economic problems, for decades, it has been widely used in many traditional economic fields such as real estate economy, agricultural economy, demand analysis and labor economics, as well as in ecology, epidemiology and other disciplines . Anselin (1988) was the first to give a comprehensive solution to the common models, basic concepts, parameter estimation and hypothesis testing of spatial econometrics, since then, many scholars have done a lot of research in this area, such as Cliff, Ord, Lesage and so on. Economic data often have both temporal and spatial dimensions, previous studies only analyzed the spatial dimension as a general factor, resulting in unsatisfactory results . Later, the spatial dimension was considered separately, elevated to the same important position as the time dimension, and a series of analytical methods were developed. This approach greatly expands the application scope of traditional economic models, and also prompts the emergence of a new research direction, namely spatial econometrics. Different from traditional methods, spatial econometrics introduces spatial effects of data and constructs new models. There are two types of spatial effects, spatial heterogeneity and spatial correlation. Spatial correlation refers to certain observations of an economic or geographic phenomenon in a region, usually influenced by surrounding regions. For example, the consumption habits of residents in a county are often consistent with the consumption habits of residents in surrounding counties and cities. This is because consumption habits are affected by many factors, including residents' income, local industrial structure, etc., and these factors usually have the characteristics of geographical concentration. For another example, in the Beijing-Tianjin-Hebei area, the development of ICT related industries in Beijing-Tianjin two cities has driven the development of surrounding Langfang, Tangshan and other places. At present, there are many modeling methods for the analysis of spatial correlation, among which the most popular method is the spatial autoregressive model (also called the spatial lag model). This type of model was proposed by Cliff and Ord (1973, 1981), and for research on its estimation and testing, see Anselin (1988), Kelejian and Prucha (1999) and Lee (2004). Spatial heterogeneity refers to the disequilibrium in geographic space. For example, China's southeast coastal areas are relatively developed economically, but inland provinces are still relatively lacking. Spatial heterogeneity emphasizes that although there are spatial connections in the general environment, there are also special circumstances. At present, there are also abundant research results on spatial heterogeneity.
As far as the international environment is concerned, since the outbreak of the global financial crisis in 2008, the economies of all countries have suffered a huge impact, this led to a sharp decline in global demand and a slow recovery of the global economy. With the increasing trend of global integration, the competition of major economies in the international market has become increasingly fierce, gradually breaking the original market pattern monopolized by one or several countries, the international market faces a new round of reconstruction. In order to protect the development of their own industries, major economies have introduced a variety of trade protection policies to restrict imported goods, the trend of “de-globalization” has begun to surge. With the Brexit of the United Kingdom in 2016 and the inauguration of Trump in the US election, the trend of “de-globalization” has been pushed to a new stage of development, and the uncertainty of trade has greatly increased . The deterioration of the external economic environment has severely impacted the economic development of China, which is highly dependent on foreign countries, causing its exports to continue to decline, it indicates that China's “export-oriented” development advantage is unsustainable, this means that China continues to rely on trade to drive economic growth, and needs to shift to a model that relies on domestic demand to drive economic growth. As far as the Chinese context is concerned, the Chinese economy is in a critical period of transition from high-speed growth to high-quality growth. Due to the inertia of the existing development mode in economic growth, faced with the rigid adjustment of the economic benefit structure during the transition period, the transition is bound to be a slow and difficult process. The transformation of growth drivers requires the continuous promotion of domestic demand, so it is particularly critical to grasp the actual evolution trend of Chinese residents' consumption demand. From the perspective of China's actual economic and social development process, a good foundation has been laid for the realization of domestic demand as a new engine of economic growth. First, the per capita income level of residents has been continuously improved. Tan Q et al. found that according to international experience, when per capita GDP reaches US$3,000, consumption's driving force for economic growth begins to surpass investment and trade; When per capita GDP reaches 4,000 US dollars, consumption will become the strongest support for economic growth . From 1978 to 2016, China's per capita GDP increased from about 227 US dollars to over 8,000 US dollars, gradually moving towards a high-income country. From an objective point of view, the consumption potential of residents will be gradually released, the consumption structure will be continuously optimized, and the role of domestic demand in driving economic growth will become increasingly prominent. Second, China's urbanization is developing rapidly and its scale is expanding. The urbanization rate of China's permanent population increased from 17.9% in 1978 to 56.1% in 2015, according to the general law of urbanization development, it is still in a stage of rapid development. Previous studies by Permai SD and others believed that the urbanization process can promote the formation of regional markets and promote population agglomeration, effectively release the consumption potential of residents. Third, the Chinese government has put forward a series of policy measures to stimulate residents' consumption.
Since the reform and opening-up in 1978, China's national economy has continued to grow rapidly. In particular, great changes have taken place in the consumption sector. The scale of the consumer goods market has continued to expand, the focus of consumption has shifted from physical consumption to service consumption, consumer upgrade products have grown rapidly, and new types of businesses continue to emerge. Since 2014, and especially in 2018, China has been upgrading consumption and transforming its economy from high-speed growth to high-quality development. From 2014 to 2020, final consumption expenditure contributed 51.2%, 66.4%, 64.6%, 58.8%, 76.2%, 59.4%, and 54.3% to GDP growth, respectively, making consumption the first driving force of economic growth for many years in a row . However, Xie L et al. found the status quo of the development of residents' consumption demand, it is difficult to match the goal of enhancing the new kinetic energy of consumption. Facts have proved that the willingness of Chinese residents to consume demand has changed from the pursuit of quantity to the pursuit of quality, and the uneven development among regions has led to a trend of differentiated and stepped evolution of residents' needs. These practical contradictions inhibit residents' willingness to consume to a certain extent, and at the same time are not conducive to the optimization of residents' consumption structure. From the perspective of supply structure, the long-term economic growth model that relies on investment and exports, this leads to the problem of overcapacity in various industries and the lack of independent innovation capability. This shows that the development of the existing supply structure is not very adaptable to the domestic demand structure, and cannot fully meet the individualized and diversified consumption needs of residents. The development and dissemination of information and communication technology (ICT) in various fields of human activities is accelerating global economic and social changes. ICT not only changed the way of doing business, but also changed the way people communicate and consume. The development of information and communication technology (ICT) has become the main driving force of the new world economy. The information and communication industry has made great contributions to the overall economic growth of countries around the world. For example, developed countries and some developing countries especially in China and India. The development of Information and Communication Technologies (ICT) has created broad prospects for the development of China's e-commerce and digital economy and has had a great impact on China's household consumption expenditures. Therefore, under the background of realistic contradictions, it is very important to study the evolution characteristics of residents' consumption demand .
As the main link in macroeconomic operation, consumption plays an important role in economic growth, theoretical analysis and empirical research on consumption are also at the core of economic research. Since the reform and opening up, China has experienced 40 years of rapid economic growth, which has greatly increased the income level of residents, the time taken by this process is much shorter than other countries, and it also means that the problems China has encountered are more complex than other countries. Judging from the evolution of consumer demand of Chinese residents in the past 40 years, the total demand has continued to grow, and the demand structure has continued to change, however, unbalanced and insufficient development has brought about real contradictions such as inequality of residents' income and consumption between regions, mismatch between supply structure and demand structure, and insufficient release of residents' consumption potential. This determines the evolution of Chinese residents' consumption needs and will face new problems that are different from the laws of classical theory. Therefore, the research on the consumption demand of Chinese urban residents, it is not only necessary to learn from modern classic consumption theories, but also to combine China's special economic and social development reality. The consumption effect of differences in regional income distribution is based on the premise of considering regional factors, the impact of income level gap and distribution structure difference on residents' consumption demand is analyzed respectively . First, This paper reviews the relationship between residents' income and consumption in the relevant modern classic consumption theory, and introduces the theoretical point of view to explore the relationship between income and consumption from a regional perspective, then, discuss the relationship between residents' income gap and consumption demand, and the relationship between income distribution and heterogeneous consumption, so as to lay a theoretical foundation for the consumption effect of regional income distribution differences; Secondly, in the context of relevant theoretical foundations, combined with a large number of empirical studies, the theoretical expectation of the consumption effect of regional income distribution differences is expounded from a theoretical perspective.
The consumption theory has roughly gone through four stages. The first stage takes the absolute income hypothesis as the representative theory. The absolute income hypothesis is a theory established by Keynes on the basis of macro analysis, it first explored the relationship between current income and consumption, it is believed that residents' current disposable income determines their current consumption, income and consumption are mainly reflected in a functional relationship, which verifies the “law of diminishing marginal propensity to consume”, that is, an increase in residents' income level will reduce their corresponding propensity to consume, however, this theory has a subjective judgment on consumer psychology and ignores the microeconomic basis, so it has obvious defects . With the gradual recovery of the economies of Western countries after World War II, Keynes's theory has weakened the explanatory power of the actual consumption situation at that time, therefore, Duesenberry (1949) combined with social psychology to supplement and revise the theory, and then put forward the relative income hypothesis, but in general it is still under the analytical framework of Keynes theory. The relative income hypothesis believes that residents' consumption depends not only on their consumption inertia, but also on the consumption level of their environment, the former is called the “ratchet effect” and the latter is called the “demonstration effect”.
The second stage is mainly based on Modiliani's Life Cycle Theory (LCH) and Friedman's Persistent Income Hypothesis (PIH), and a series of researches on consumer behavior based on the theoretical thinking of the micro-foundation of economics. Among them, the life cycle theory believes that the income of residents in their lifetime can be divided into two stages, the first stage is that the income level is higher than the consumption expenditure, the second stage is that the income level is lower than the consumption expenditure, so when the residents are young, there will be a saving motive for old age, so as to optimize the consumption expenditure in the whole life cycle. The consumption function of the life cycle theory is, see formula (1):
In Friedman's permanent income hypothesis, income is divided into two parts: permanent income and temporary income, namely. This theory holds that residents will not adjust consumption due to fluctuations in temporary income, and only fluctuations in permanent income will impact consumption, at this time, the consumption function is shown in Equation (2):
The third stage is mainly represented by Hall's random walk (RWH). On the basis of the life-cycle permanent income hypothesis, Hall (1978) introduced rational expectations and stochastic processes, the conclusion that consumers obey a random walk process is obtained, namely the random walk hypothesis (RWH). But the random walk hypothesis is just an extension of the life cycle permanent income hypothesis under rational expectations, and its essence is the same. These theories clearly point out that the purpose of micro-subject consumption is to increase its utility, so the consumption function must be established on the basis of maximizing the utility of consumers, rational consumers will choose their lifetime consumption paths based on information such as current income and expected future income to maximize utility.
There is no mature theoretical model to analyze the relationship between residents' income gap and consumption demand. Generally, the absolute income hypothesis proposed by Keynes (1936) is used as the reference for the relationship between the two. In the theory of absolute income hypothesis, it is believed that there is a stable linear relationship between income and consumption, and consumption is a linear function determined by income, that is, see formula (3):
In order to analyze the impact of the income gap between regions on the total social consumption demand, under the framework of absolute income theory, two regions are set, low-income and high-income, the income level of residents in low-income areas is lower than that of residents in high-income areas, at this time, the population of low-income areas can be set as
In order to further explore the impact of income distribution on heterogeneous consumption, we first need to consider the impact of different types of saving motives. In existing research, saving motives can be divided into life-cycle saving motives, bequest saving motives, precautionary saving motives, intertemporal alternative saving motives, speculative saving motives and so on. Among them, after removing the motives that obviously depend on psychological and sociological explanations, mainstream economics - the saving motives generally believed to have an impact on consumption mainly include the life cycle saving motive, the legacy saving motive and the precautionary saving motive. According to the research of Musgrave (1980), it can be found that the precondition for the generation of saving motive is that the residents' income reaches a certain level. In his research, the residents' income is divided, part of which is used to meet basic living needs, that is, subsistence income; the other part is income beyond meeting survival needs, that is, additional income. Under the income division, household consumption is mainly affected by additional income. If all income is used to maintain basic living needs, then the residents' propensity to save low. When income is less than subsistence income, residents will not choose to save, only when income is greater than subsistence income, residents have the motivation to save. Residents of different income levels have different savings intensity and quantity, which leads to the generation of heterogeneous consumption. The following chapter will analyze the relationship between income distribution and consumption according to three different types of saving motives: Life-cycle saving motive, legacy saving motive and precautionary saving motive.
The first type is the life cycle savings motive. Under the standard life cycle hypothesis, the purpose of consumer savings is to use it for retirement when the income decreases after retirement, that is, to arrange the consumption trajectory of a lifetime according to the sum of current and expected income, so that the consumption trajectory tends to be as smooth as possible. At this time, the consumer's utility level has nothing to do with the welfare of its offspring, but arranges lifetime income according to the principle of utility maximization. This also means that consumers' long-term average propensity to consume remains unchanged, which is not affected by changes in income levels. Since income is equal to the sum of consumption and saving, the lifetime propensity to save is independent of income level. Groups of different income levels will use a fixed percentage of income for savings, as shown in Figure 1.
The second type is the bequest saving motive. According to the generalized life cycle hypothesis, the level of consumer utility is not only related to the consumption of a lifetime, but also affected by the welfare level of its offspring. In addition to their own life cycle savings, consumers also have savings for bequests. Specifically, consumers' average propensity to consume is inversely proportional to their income level due to the bequest saving motive.
The third type is the precautionary saving motive. The precautionary saving theory mainly adds uncertainty factors into the LCH-PIH-RE analysis framework. Due to the imperfection of the credit market and the uncertainty of the income level of residents, consumers will choose to save to prevent uncertainties. Therefore, the degree of risk aversion of consumers at different income levels will affect the strength of the precautionary saving tendency. As far as China's national conditions are concerned, due to liquidity constraints and other reasons, low-income earners face higher risks than high-income earners, as shown in Figure 2. Where
How to narrow the gap in the consumption demand of residents between regions and fully release the consumption potential of residents? First of all, it is necessary to consider the reasons for the inequality of residents' consumption among regions, this is to narrow the consumption gap between residents in different regions, this will help to expand the premise of effective domestic demand, which is of great significance for effectively releasing consumption potential and solving the contradictions caused by unbalanced development . The development trend of non-equilibrium consumption of residents among regions, first, it reflects the insufficient development of residents' consumption; second, it brings about social contradictions and economic problems such as inequality of residents' welfare and mismatch between consumption demand and supply. As far as the current research methods on the consumption gap are concerned, it is mainly carried out from two aspects. The first is to use the Gini coefficient, Theil index, logarithmic variance, etc. to measure the degree of economic welfare gap, the main purpose of which is to measure the disequilibrium trend. According to the US CEX data, the Gini coefficient, logarithmic variance and the ratio of different consumption quantiles of US residents' consumption were calculated, and it was found that when the inequality of income distribution increased, the role of formal and informal credit and insurance mechanisms in developed countries such as the United States will expand accordingly, reducing the possible accompanying rise in the consumption gap. Although the Gini coefficient and Theil index can intuitively judge the degree of inequality through the size of the index, and the logarithmic variance method can observe the changing law of the degree of disparity, its disadvantage is that it can only provide a limited amount of information. The second is to decompose the degree of disparity and determine its causes. Some scholars use the proposed Gini coefficient component decomposition and regression equation estimation methods to decompose the total consumption imbalance. Through the Gini coefficient component decomposition method, the contribution rate of each consumption to the total consumption gap is obtained according to the data of the US Expenditure Survey. In order to make a more detailed calculation, by expanding the method of Gini coefficient grouping and factor decomposition, we can obtain the marginal impact of Chinese residents' food consumption expenditure on each sub-category on the overall food consumption coefficient. The above methods mainly decompose the total consumption into items, and judge and compare the overall consumption gap of residents, but ignore the information on the changes in the distribution of residents' consumption. It is difficult to measure the overall picture of consumption distribution only by analyzing the gap from the mean value . Although some scholars from the perspective of distribution, conditional quantile regression decomposition method is used to study the gap between consumer groups, but conditional quantile regression will have too many or unnecessary control variables, and the rigor will be weakened. Compared with the conditional quantile regression method, the recentralization influence function (RIF) combined with the unconditional quantile regression decomposition model is proposed, which can effectively solve the problem of excessive or unnecessary control variables. Based on the method of RIF regression decomposition, mainly used in the decomposition and comparison of residents' income and wage gaps, later, it was used to measure the economic and social welfare inequality of various residents such as consumption, therefore, it can be found that the RIF regression decomposition method can judge and measure the welfare gap at different levels, has unique advantages. The method of normalization and decomposition has studied the gap between consumption groups, but the conditional quantile regression will have excessive or unnecessary control variables, and the rigor will be weakened . Compared with the conditional quantile regression method, the recentralization influence function (RIF) combined with the unconditional quantile regression decomposition model is proposed, which can effectively solve the problem of excessive or unnecessary control variables. The method based on RIF regression decomposition is mainly applied to the decomposition and comparison of residents' income and wage gaps, and has since been used to measure various types of residents' economic and social welfare inequality, such as consumption. Therefore, it can be found that the RIF regression decomposition method can judge and measure the welfare gap at different levels, has unique advantages. In view of the consumption inequality of urban residents between regions, this section will use the method of RIF regression decomposition from a micro perspective, characterize and decompose the characteristics of residents' consumption distribution gap between regions, judging the impact of differences in income distribution between regions from different consumption levels, the application of distribution thinking fully considers the heterogeneity of people at different consumption levels .
Table 1 shows the disposable income and total consumption of urban households in 2007 and 2013. From Table 1, it can be found that the per capita consumption and per capita income of eastern households are much higher than other regions, the per capita income of eastern households was 24,900 yuan and 28,800 yuan in 2007 and 2013, respectively. West 64.2% level, by 2013, the gaps had been reduced to 39.3% and 34.6%, respectively, and the average gap had slowed down. At the same time, the per capita consumption gap of urban residents between regions also decreased, the gap between the eastern and central regions decreased from 73.8% to 44.1%, and the gap between the eastern and western regions decreased from 42% to 29.1%.
Descriptive statistics of household disposable income and total consumption
|years||area||Household disposable income (per capita): 10,000 yuan||Total household consumption (per capita): 10,000 yuan|
|mean||standard deviation||minimum||maximum value||mean||standard deviation||minimum||maximum value|
|west||2.14||1.25||0.02||10.87||1.50||0.90||0. 15||5. 97|
Based on the above research results, combined with the analysis of the characteristics of regional consumption distribution gaps from the perspective of consumption levels in the previous section, the consistent results of different main influencing factors of group consumption demand gaps are obtained. No matter from the perspective of income distribution or consumption distribution, the disparity in income level is still the main reason for the consumption inequality among the groups below the middle income among regions. From the perspective of high-income groups among regions, their consumption inequality is weakened by the constraints of income gaps, while the differences in the middle and high-end markets caused by the gaps in the distribution pattern of income groups have a stronger effect on them, this in turn leads to a trend of high-level consumption inequality between regions. For the middle-level consumption group, its heterogeneous consumption propensity helps to alleviate the consumption gap among its regions, at the same time, the polarization of income distribution in the central and western regions is lower than that in the eastern region, households' marginal propensity to consume has weakened, income distribution with less polarization in the central and western regions, it also slowed down the trend of consumption inequality in the middle consumption level among regions.
The disparity in income structure is also reflected in information technology. As of December 2020, the proportion of netizens with a monthly income of 2,001–5,000 yuan accounted for 32.7%, and the balance of netizens with a monthly payment of more than 5,000 yuan accounted for 29.3%. Netizens with no income but a monthly income of 1,000 yuan or less made up 15.3% of the population. Information and communication technology development has created opportunities for balanced regional development. As of December 2020, the number of Chinese netizens reached 989 million. As China promotes the digital village strategy, information and communication technology, represented by the Internet, has also played an essential role in China's poverty alleviation work, with the gap between urban and rural netizens gradually closing. For example, digital technology is fully integrated with Internet applications such as e-commerce and live broadcasting to shape and enhance brand influence, expand sales channels, and increase sales of agricultural products. In 2020, national rural online retail sales will reach 1.79 trillion yuan. Information technology promotes the development of the digital economy and plays a vital role in increasing people's incomes and narrowing regional disparities.
At this stage, China's economy is in a critical period of transition from high-speed growth to high-quality growth. Facing many problems such as tightening international market demand, increasing trade uncertainty, and urgent need to adjust the production capacity structure, how to effectively enhance the endogenous power of economic growth is crucial. From the perspective of demand, with the improvement of residents' income level, the consumption demand has gradually increased, and the consumption structure has been continuously optimized, residents' willingness to consume has changed from the pursuit of quantity to the pursuit of quality. Although the overall consumption level of residents has increased significantly since the reform and opening up, however, there are still practical contradictions such as insufficient consumption demand, slow consumption upgrading, and uneven consumption among regions caused by unbalanced and insufficient development, which at the same time hinder the role of expanding domestic demand in promoting economic growth. From the perspective of supply, the target supply structure is not very adaptable to the demand structure, and cannot fully meet the individualized and diversified consumption needs of consumers, in addition, there are problems of insufficient supply of medium and high-end commodities and excess supply of low-end commodities, which has led to the dislocation of supply and demand and the outstanding contradiction of major structural imbalance. Therefore, how to find a new equilibrium state of supply and demand under the background of objective reality contradictions, it needs to be linked with the growth of residents' income and the evolution of consumer demand. Based on the consideration of practical problems, the author draws on relevant research at home and abroad, according to “unbalanced regional economic development - differences in the distribution of residents' income - regional uneven evolution of consumer demand—regional differences in the optimization of residents' consumption structure—regional heterogeneity in the development of emerging consumer markets “Sex” is the main line of research logic, in the context of income growth, the starting point is the difference in income distribution, such as income inequality and unbalanced income distribution structure, this paper specifically analyzes the evolution characteristics of Chinese urban residents' consumption demand at the current stage, in order to provide a reference for cultivating new consumption momentum, provide a basis for the adaptive adjustment of the supply-side structure. At the same time, with the development of information and communication technology, China's “new infrastructure” has been fully launched. The in-depth advancement of the Internet has created opportunities for balanced regional development. The development of Internet applications and industrial technologies continues to tap into new consumption hotspots, provide consumers with more personalized and diversified needs, and promote the development of the digital economy. Information and communication technologies enable the accelerated development of high technology and assist China's digital transformation. The main research conclusions are summarized as follows: Combined with relevant domestic and foreign classic theories and research foundations, the theoretical connotation of the consumption effect of regional income distribution differences is clarified, this paper analyzes the internal correlation mechanism between income distribution difference and regional consumption demand in detail, and analyzes the deep meaning behind the individual consumption effect and consumption market effect of income distribution difference. At the same time, the development of information and communication technology will help promote the coordinated development of regions and play an important role in the development of consumption structures and the economy.
Descriptive statistics of household disposable income and total consumption
|years||area||Household disposable income (per capita): 10,000 yuan||Total household consumption (per capita): 10,000 yuan|
|mean||standard deviation||minimum||maximum value||mean||standard deviation||minimum||maximum value|
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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 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