With the increasingly fierce market competition, independent innovation has become the only means for enterprises to survive and progress, and enterprises pay more and more attention to product R&D investment [1]. The subsidy provided by the government can not only alleviate the problem of insufficient R&D funds in enterprises, but can also serve as a signal to convey to investors the government's expectation of R&D and innovation activities of enterprises and affirmation of the future development of enterprises, which will help enterprises attract more investment and promote the sustainable development and value enhancement of enterprises [2]. However, government subsidy is one of the most commonly applicable ways for the industrial chain to apply the current policies [3], and the effectiveness of its implementation results varies from scholar to scholar.

Scholars generally believe that government subsidies play a positive role in creating value for enterprises. Dongmin and Tianshang [4] studied the listed companies in Shanghai and Shenzhen, and found that government subsidies play a positive role in improving corporate economic performance and social responsibility. The fund use efficiency of private enterprises in terms of operating performance and social responsibility increases with increase in the scale of government subsidies. Ye et al. [5] found that the operating results of enterprises can be improved through the transmission mechanism of government financial subsidies. Shaoxiu et al. [6] found that government subsidies have a significant impact on the enterprise value, which can help enterprises improve their value to a certain extent. For the information technology industry, government subsidies can help enterprises alleviate the difficulties of capital shortage, improve production efficiency and promote the promotion of enterprise value. Chunmei and Pei [7] took 331 listed high-tech enterprises on the gem as samples for empirical analysis. Their research results show that government subsidies have a significant positive incentive effect on both scientific and technological performance and the economic performance of enterprise innovation. Jiahui et al. [8] show that enterprises need to allocate resources reasonably and increase their R&D investment to improve their scientific and technological strength, so as to increase the value of enterprises. By using R&D expenditure, enterprises can introduce advanced production equipment, enterprise management experience, improve the R&D and innovation ability of the whole team, improve enterprise production efficiency, and realise enterprise value. In Fogarty and Simon [9], the relationship between tax preference and RD capital investment in the pharmaceutical manufacturing industry is first established to provide reference for government departments to formulate and regulate tax policies and the independent innovation ability of the pharmaceutical manufacturing industry. Based on co-integration analysis, Granger causality test, impulse response and variance decomposition, this paper empirically analyses the relationship between tax preference and R&D capital investment in the pharmaceutical manufacturing industry. The results show that the comprehensive tax burden of the industry decreased by 1% and the internal R&D expenditure increased by 8.293%. The conclusion is that the current preferential tax policies in China have a significant incentive effect on the R&D capital investment of the manufacturing industry, and the continuous preferential tax policies are reasonable for the scientific R&D and design capital investment of the pharmaceutical manufacturing industry. According to the actual situation of the company's development, government departments further strengthen the relevant tax incentives, encourage enterprises to participate in R&D activities and propose to maintain the long-term stability of tax policies as far as possible.

This paper studies the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry, and analyses the mechanism of government subsidies on R&D investment of Chinese enterprises, in order to improve the acceptability of government subsidies to promote the R&D policy of the manufacturing industry. The quantile regression model is constructed to reduce the constraints, make it more inclusive to heterogeneity, make the estimation more robust, make the estimated coefficients more significant and make the regression analysis results more reliable.

Government subsidies can not only reduce the burden on enterprise assets, but also carry out enterprise credit evaluation on enterprises of financial institutions, which is conducive to enterprises to obtain loans from financial institutions and maintain their long-term development trend. When government subsidies are used for the production and operation of enterprises, they will be affected by the completion process of market value, causing a lag effect on the use value of enterprises [10].

With the gradual improvement of China's market economic system and fierce market competition, there is no doubt that if the manufacturing industry wants to survive and seek the development trend, it must obtain the core competitiveness through independent innovation. The improvement of manufacturing innovation capability requires rational allocation of R&D resources. Product R&D should increase project investment and create enterprise use value [11]. At the same time, it takes a period of time for enterprise product R&D from project approval to successful R&D, and then to market promotion, and the benefits may not be immediately reflected in the enterprise value.

In recent years, the research on enterprise independent innovation shows that the key for government departments to apply enterprise product R&D is the harm to R&D activities. Some enterprises' product R&D and activities are found to be at a high risk for small-scale taxpayers, which hinders the improvement of the enterprise's R&D capability [12]. At this time, government subsidies support the innovation activities of enterprise product R&D investment, improve the expected rate of return and independent R&D can promote work ability [13].

In the context of independent and mass entrepreneurship, competition among enterprises is becoming more and more fierce, and R&D investment is an important factor related to the sustainable development of enterprises. The Chinese government has formulated a series of support plans for development of the information technology industry, and also provided necessary financial support for the creation industry [14]. Government subsidies alleviate the problem of capital shortage faced by enterprises and provide financial guarantee for their R&D investment. The implementation of R&D activities is related to the future development of enterprises. Government subsidies can reduce the cost and income risks brought by R&D activities, encourage enterprises to actively carry out R&D activities, provide guarantee for the long-term development of enterprises and promote the value of enterprises [15]. Therefore, the R&D investment of enterprises links the government subsidy with the enterprise value, and has an intermediary effect on the two.

The standard mean function of any variable is analysed by traditional least square regression. In other words, some variables are used to describe the mean value of relevant variables [16]. However, in the discussion of social economics and investment, the quantile of any variable at any probability level has attracted more and more attention. To fully consider the real valued random variables

For

If there is only one solution, and if there are multiple solutions
_{t}

For the calculation sample

Given information set _{y}

Setting _{1}, ⋯, _{n}_{τ}^{−1}(_{τ}

Objective function

Basis of _{n}_{n}

The expected value of

The variance of

According to the definition of variance [22]:

So there are:

If ^{2} = ^{2} (_{τ}

It can be concluded that:

Assume ^{2} = ^{2} (_{τ}_{τ}

Considering the linear regression model [24], the expression is:
_{i}^{−1}(_{0} is a positive definite matrix, MP dimensional vector estimation of multiple quantile regression

If error term _{i}

^{2} = ^{2} (_{τ}^{−1}(^{−1}. It can be called quantile density function [25]. Knowable ^{−1}(

So the sparse function is a quantile function ^{−1}(^{−1} experience estimates, _{n}_{n}

Usually,

Send ^{−1}(^{−1} (

Quantile function for sample

The empirical quantile function is:

In general, the number of zero residuals in quantile regression is exactly
^{−1} the potential factor in the approach is the need to ensure adequate window width [28]. Obviously, when _{n}^{−1} the method is:

Existence

Of which, ^{2}(^{2} (^{−1}(

According to the traditional regression analysis ^{2} a goodness-of-fit statistic [29], the scoring function is:

The optimal value of the objective function with unconstrained parameters is:

Null hypothesis _{0} : _{1}(

According to the goodness-of-fit criterion, the formula is:

^{1} (

Set vector ^{′} (_{1}), ⋯ ^{′} (_{m}

The statistics of Wald test are:
_{n}

Compared with the general least square method, it can only show the influence of independent variable parameters on the partial change of variables [31]. Quantile regression can more accurately show the variable transformation category of independent variables and the harm of independent variables to the standard spread pattern. It can capture various features of the spread. When the main parameters cause different harm to the spread of variables in different parts (such as left or right), it can more comprehensively describe the features of the spread, and then obtain comprehensive results.

The variables to consider the compressive strength of enterprises' independent innovation investment are basically the expenditure on innovation activities or the investment in independent innovation human resources [32]. The variables to consider the size of enterprises include the number of employees, sales, and property. When setting up the entity model, this paper selects the compressive strength of the budget input of the enterprise's independent innovation funds (the ratio of the internal structure expenditure of the enterprise's activity funds budget to the sales volume) as the expression variable [33]. Taking full account of the independent innovation budget input, the compressive strength variable is applied to the enterprise sales. The enterprise scale variable set here will select the total number of employees in the enterprise. In addition to the scale of the enterprise, there are also many manipulation variables added to the presentation variables.

Schumpeter's economic growth theory holds that enterprises pursuing perfect monopoly rights and interests are the main energy to promote independent innovation and technological progress. Therefore, the acquisition of enterprise profits at this stage, that is, enterprise profitability will do great harm to the next innovation technology. It is also effective to select the early operating profit margin as the expression variable [34].

In order to better determine whether there is an optimal control correlation between the enterprise scale and the compressive strength of independent innovation investment, the quadratic term of enterprise scale is also added to the entity model as an expression variable [35].

As the main body of innovation activities, its expenditure cost immediately affects the transformation of enterprise product cost. On the one hand, the rise of labour cost has increased the working pressure of enterprise management, on the other hand, it has driven enterprises to adopt proactive methods, select innovative technology capabilities and maintain the continuous development trend of enterprises. Here, we choose the average salary as the key variable to consider the labour cost.

The level of independent innovation equity financing ability can directly harm the independent innovation investment of enterprises. Because of the high risk of innovation activities and the difficulty of enterprise equity financing, enterprises with strong equity financing ability also relatively increase the innovation activity investment. Therefore, the variable of total amount of equity financing in the creative industry was selected to clarify the relationship between equity financing ability and R&D investigated the compressive strength of investment.

For many years, enterprises have been harmed by various national economic policies, rules and regulations, environmental damage and other complex reasons, and the compressive strength of independent innovation investment will vary. Therefore, the variable duration can be added to get the harm to enterprise innovation activities for many years. Based on the above comprehensive analysis and demonstration, the definition of entity model variables is shown in Table 1.

Variable definition

Innovation spending intensity | % | Internal expenditure of scientific and technological activity funds/sales income |

Last period sales profit margin | % | Profit/Sales Revenue |

Salary per capita | Million | Total salary/number of employees |

Years | Year | 2013–2020 |

Enterprise size | People | Number of employees |

Size | Big | >1000 |

Small | >1000 |

The data used in this paper are the 8-year data of large, medium and small industrial production enterprises in Shanghai from 2014 to 2021 [36]. In the sample selection process, some enterprises were removed according to the database security and reliability standards. Finally, the year-end data information (mixed cross-sectional data) of 1308 enterprises was selected as the analysis sample. The mixed cross-section data obtains several random samples from a population at different points to carry out mixing. Therefore, while increasing the number of samples, more accurate prediction values can be obtained, thus giving resource advantages to the determination and analysis in this paper.

As shown in Table 2, descriptive statistical analysis is carried out on the sample information expressed as independent innovation expenditure variables in the sample.

Statistical description of explained variables

Mean | 0.025 |

Median | 0.002 |

Maximum | 0.796 |

Minimum | 0.000 |

Std.Dev | 0.042 |

Skewness | 6.73 |

Kurtosis | 77.65 |

JB | 3.12 + E05 |

Sample size | 1280 |

According to Table 2, this variable is not normal, and JB statistics greatly exceed the threshold, which fully tests the non-normality and asymmetry of sample information. Therefore, the possible multiple regression analysis with OLS may lead to serious deviation of the index, which is unfavourable for further analysis based on the reversion conclusion. Therefore, in order to get a more effective and efficient conclusion, quantile regression is used.

Quantile regression was carried out on the constructed detection entity model using the R software, and the corresponding regression estimation conclusions shown in Table 3 were obtained.

Quantile regression results

ren | 6.78E−06 (0.874) | 5.73E−09^{″} (1.303) | 1.34E−08 (0.012) | 4.99E−06^{**} (1.342) | 1.46E−05^{***} (2.503) | 7.67E−07 (0.098) |

ren2 | 6.03E−11 (0.438) | 5.21E−11^{**} (1.668) | 1.44E−10^{***} (9.997) | 1.29E−10^{***} (4.744) | 9.12E−11^{***} (2.097) | −7.53E−41^{***} (−2.925) |

wage | −5.59E−05^{**} (−1.874) | 2.43E−08^{″} (1.392) | 6.82E−08 (0.023) | −9.35E−07 (−0.086) | 1.12E−06 (0.058) | −1.12E−05 (−0.749) |

pr-1 | 8.98E −04 (0.294) | −1.12E−06 (−1.233) | −3.361E−06 (−0.005) | −1.26E−04 (−0.12) | 8.44E−04 (0.212) | 4.72E−03 (0.683) |

big | 1.51E−02^{***} (2.217) | 3.73E−06 (0.698) | 1.44E −05 (0.014) | 4.82E−03^{*} (1.489) | 9.23E−03^{**} (2.007) | 9.91E−03 (1.010) |

big Xren | −9.03E−06 (−1.106) | −5.86E−09′ (−1.314) | −1.54E−08 (−0.104) | −5.59E−06 (−1.491) | −1.54E−05^{***} (−2.614) | −4.01E−06 (−0.476) |

big Xren2 | −1.26E −10 (−0.383) | 2.85E−11 (0.913) | 1.49E −11 (0.122) | −6.67E−11 (−0.100) | −1.12E −10 (−0.602) | −9.33E−11 (−0.868) |

Yoo | −3.61E −03 (−0.539) | −4.55E−06′ (−1.409) | −6.68E−06 (−0.005) | −2.21E −04 (−0.062) | 3.94E −04 (0.094) | 7.8E −03 (0.864) |

Yor | −3.45E −03 (−0.518) | −2.56E−06 (−0.805) | −5.18E −07 (−0.0003) | 3.03E−03 (0.828) | 4.13E−03 (1.038) | 3.18E−03 (0.380) |

Y02 | −2.01E −03 (−0.294) | −1.03E−06 (−0.268) | 3.87E −03^{*} (1.615) | 5.22E−03^{*} (1.417) | 5.82E−03^{*} (1.439) | 9.06E−03 (1.106) |

Y03 | 3.18E −03 (0.463) | 7.28E−07 (0.173) | 1.58E−03 (1.189) | −8.85E−04 (−0.255) | 2.7E−03 (0.596) | I.IIE−02 (1.128) |

You | 2.36E−03 (0.341) | −2.95E−06 (−0.737) | −7.35E−06 (−0.007) | −4.01E−03^{*} (−1.523) | −2.99E−03 (−0.582) | 1.11E−02 (1.309) |

Yo (pseudo) | 2.14E−03 (0.300) | −7.23E −06′ (−1.274) | −1.24E−05 (−0.013) | −4.28E−03^{**} (−1.800) | −6.59E−03^{*} (−1.338) | 115E−02^{*} (1.404) |

R-squared | 0.684 | 7.03 | 14.08 | 17.25 | 19.26 | 19.40 |

Table 3 sets the price index as the weighted average value of consumer price index and fixed asset investment price index, with weights of 0.55 and 0.45, respectively, so as to obtain the actual value.

It can be seen that the regression conclusion of OLS is only 0.684, the goodness of linear fitting is extremely low, only the average salary and the type of enterprise scale are prominent at the level of 5% and 1%, respectively, and the necessity of some independent variables is low. This means that because of the non-regular expression and asymmetry of sample information, the application of OLS method has an important harm to the determination results. In OLS mode, there is no ‘U’ or ‘inverted U’ correlation between enterprise size and expenditure intensity, so large enterprises exceed the innovation expenditure intensity of key companies. However, with increase of the company's total volume, its effect is very different. The increase in scale of large enterprises will reduce the intensity of expenditure, and increase in the scale of small- and medium-sized enterprises will increase the intensity of expenditure. At the same time, the increase in average salary is likely to significantly reduce the intensity of capital investment.

According to the quantile regression data, the overall innovation expenditure intensity of large enterprises is higher than that of small- and medium-sized enterprises, and the regression coefficient is positive. With the increase of stores, it slowly expands. Among them, the coefficient conclusion is more significant at 0.5 and 0.6 loci. This shows that when the innovation expenditure intensity is at the medium level, large enterprises can have stronger innovation ability than the backbone companies with the relatively sufficient fund utilisation and good reputation. Here, the key factors are the high level of asset concentration in the internal structure of large enterprises, the strong overall strength of innovative talents, and the strong immunity to the hidden dangers of unsuccessful product research and development. Therefore, the diligence of innovation expenditure is generally very large. Backbone companies encounter practical problems of enterprise scale expansion, take out part of internal structure assets to expand production scale, and the innovation expenditure is less than that of large enterprises. The details are shown in Figures 1 and 2.

It can be seen from Figure 1 that the total number of employees of the enterprise scale has also changed greatly with the type of business scale. The marks of the first and second reversion coefficients of small and medium-sized enterprises are basically positive. Only when the score is high (0.8), the primary and secondary new project coefficients are obviously negative from the 1% level, but the key new project coefficients are significantly reduced, and there is a less significant ‘inverted U’ type correlation on the whole. On the other hand, apart from 0.8 points, between 0.2 and 0.6 points, the first coefficient shows a relatively significant growth trend, and the second coefficient shows the characteristic of first adjustment. The higher the expenditure intensity, the higher the total amount of the company, indicating a stronger active effect. However, the ‘rate’ of this increase increased again at the bottom point, and the high score in the middle gradually decreased. On the other hand, large enterprises have obtained quite different conclusions in the chain stores. The coefficient mark of key new items is negative from beginning to end. The coefficient mark of primary and secondary new items changes from low scores (0.2–0.5) to positive numbers, and from higher scores (0.6–0.8) to negative numbers.

Based on the conclusion in Table 3, it can be found that large enterprises have a significant ‘U’ correlation between the low quantile (0.2–0.5) and enterprise size and innovation expenditure intensity. However, at high score points, this kind of correlation disappears, and the order coefficient may be marked as all negative numbers, resulting in lower data. This is not a simple linear correlation between the change in business scale and expenditure intensity of large enterprises at the middle score of low expenditure intensity. On the contrary, the larger the enterprise size, the less the innovation expenditure. However, after exceeding a certain threshold, the company's innovative product R&D shows that the theme activities increase with the increase in business scale. However, from a high score (0.6–0.8), if large enterprises expand again, it will have an important adverse impact on the intensity of innovation expenditure. The primary factor is that the larger the enterprise scale, the greater the operation and management ability, the slower the reaction rate of the operation leaders, the more traditional the company's innovation concept, the larger the operation scale, the greater the company's operation cost and the lower the management decision-making efficiency.

Figure 2(a) and 2(b) describes large enterprises. The increase in their scale will reduce the intensity of expenditure. Figure 2(c) and 2(d) describes small- and medium-sized enterprises. The increase in their scale will increase the intensity of expenditure. At the same time, the increase in average salary is likely to significantly reduce the intensity of capital investment.

It can be seen that in the adjustment variables, the independent variable of average salary is repeatedly marked by the correlation coefficient in each branch, but only in the low branch, there is a need for a 10% level. In general, the low index is positive, and the higher in the middle is negative. Because the low budget expenditure has low compressive strength, the company introduces high-tech talents, offers high salary positions, and increases investment in innovation and R&D. Therefore, increasing the average salary can improve the compressive strength of expenditure. However, with increase in high scores and the continuous growth of labour costs, the manufacturing industry must take all kinds of restrictions into account. Only by reducing the expenditure on independent innovation can the additional expenditure of costs be filled.

The coefficient estimates were not significant at each quantile, and the estimated values were only 10% significant at 0.4 quantile. The coefficient estimates were only significantly lower at the low quantile (0.2), and there were significant positive correlations in different degrees at the other quantiles. Except for the 0.9 quantile, in other quantiles, the manufacturing industry will increase R&D investment as time changes.

This paper makes an in-depth study on the relationship between government subsidies, R&D investment and high-quality development of the manufacturing industry. The quantile regression entity model is created, and the asymmetric linear loss function is introduced to obtain the point estimation of quantile. The asymptotic distribution is obtained according to the Moivre–Laplace limit value law. The sample quantile function is calculated, and the asymptotic covariance matrix is estimated by the fitting residual of quantile regression. The solid model is tested according to the goodness-of-fit specification. The experimental results show that the coefficient conclusion is more significant at the 0.5 and 0.6 quantiles, and this method is efficient and widely applicable.

#### Quantile regression results

ren | 6.78E−06 (0.874) | 5.73E−09^{″} (1.303) |
1.34E−08 (0.012) | 4.99E−06^{**} (1.342) |
1.46E−05^{***} (2.503) |
7.67E−07 (0.098) |

ren2 | 6.03E−11 (0.438) | 5.21E−11^{**} (1.668) |
1.44E−10^{***} (9.997) |
1.29E−10^{***} (4.744) |
9.12E−11^{***} (2.097) |
−7.53E−41^{***} (−2.925) |

wage | −5.59E−05^{**} (−1.874) |
2.43E−08^{″} (1.392) |
6.82E−08 (0.023) | −9.35E−07 (−0.086) | 1.12E−06 (0.058) | −1.12E−05 (−0.749) |

pr-1 | 8.98E −04 (0.294) | −1.12E−06 (−1.233) | −3.361E−06 (−0.005) | −1.26E−04 (−0.12) | 8.44E−04 (0.212) | 4.72E−03 (0.683) |

big | 1.51E−02^{***} (2.217) |
3.73E−06 (0.698) | 1.44E −05 (0.014) | 4.82E−03^{*} (1.489) |
9.23E−03^{**} (2.007) |
9.91E−03 (1.010) |

big Xren | −9.03E−06 (−1.106) | −5.86E−09′ (−1.314) | −1.54E−08 (−0.104) | −5.59E−06 (−1.491) | −1.54E−05^{***} (−2.614) |
−4.01E−06 (−0.476) |

big Xren2 | −1.26E −10 (−0.383) | 2.85E−11 (0.913) | 1.49E −11 (0.122) | −6.67E−11 (−0.100) | −1.12E −10 (−0.602) | −9.33E−11 (−0.868) |

Yoo | −3.61E −03 (−0.539) | −4.55E−06′ (−1.409) | −6.68E−06 (−0.005) | −2.21E −04 (−0.062) | 3.94E −04 (0.094) | 7.8E −03 (0.864) |

Yor | −3.45E −03 (−0.518) | −2.56E−06 (−0.805) | −5.18E −07 (−0.0003) | 3.03E−03 (0.828) | 4.13E−03 (1.038) | 3.18E−03 (0.380) |

Y02 | −2.01E −03 (−0.294) | −1.03E−06 (−0.268) | 3.87E −03^{*} (1.615) |
5.22E−03^{*} (1.417) |
5.82E−03^{*} (1.439) |
9.06E−03 (1.106) |

Y03 | 3.18E −03 (0.463) | 7.28E−07 (0.173) | 1.58E−03 (1.189) | −8.85E−04 (−0.255) | 2.7E−03 (0.596) | I.IIE−02 (1.128) |

You | 2.36E−03 (0.341) | −2.95E−06 (−0.737) | −7.35E−06 (−0.007) | −4.01E−03^{*} (−1.523) |
−2.99E−03 (−0.582) | 1.11E−02 (1.309) |

Yo (pseudo) | 2.14E−03 (0.300) | −7.23E −06′ (−1.274) | −1.24E−05 (−0.013) | −4.28E−03^{**} (−1.800) |
−6.59E−03^{*} (−1.338) |
115E−02^{*} (1.404) |

R-squared | 0.684 | 7.03 | 14.08 | 17.25 | 19.26 | 19.40 |

#### Variable definition

Innovation spending intensity | % | Internal expenditure of scientific and technological activity funds/sales income |

Last period sales profit margin | % | Profit/Sales Revenue |

Salary per capita | Million | Total salary/number of employees |

Years | Year | 2013–2020 |

Enterprise size | People | Number of employees |

Size | Big | >1000 |

Small | >1000 |

#### Statistical description of explained variables

Mean | 0.025 |

Median | 0.002 |

Maximum | 0.796 |

Minimum | 0.000 |

Std.Dev | 0.042 |

Skewness | 6.73 |

Kurtosis | 77.65 |

JB | 3.12 + E05 |

Sample size | 1280 |

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optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape 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and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of 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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 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 Research on evaluation system of cross-border E-commerce platform based on the combined model 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 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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 Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsStudy on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method 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 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 Evaluation and prediction of regional human capital based on optimised BP neural network 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 A study of local smoothness-informed convolutional neural network models for image inpainting 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 Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System 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 Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences 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 An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area 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 Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network