We use the panel data of innovation and entrepreneurship for global spatial autocorrelation and model selection testing. At the same time, we applied the Spatial Dubin Model (SDM) to empirically study the knowledge spillover effects of higher education campuses on regional innovation capabilities. Experimental research found that there are significant spatial differences in the innovation efficiency of universities. Specialized agglomeration can effectively improve the innovation efficiency and scale efficiency of colleges and universities. At the same time, the diversified agglomeration has no obvious effect on the innovation efficiency of colleges and universities. The accumulation of high-tech industries can effectively promote the innovation efficiency of universities. Human capital and opening to the outside world can effectively improve the innovation efficiency of universities.

#### Keywords

- Higher education
- Knowledge spillover
- Innovation and entrepreneurship
- Spatial Dubin model

#### MSC 2010

- 62H20

Universities are the main body of knowledge creation and transmission, and they are also important gathering places for scientific research talents. Since China implemented the strategy of “rejuvenating the country through science and education,” the R&D (Research and Experimental Development) activities of universities have played an important role in the implementation of social development, economic construction, and independent innovation strategies [1]. Moreover, the products invested by R&D have typical characteristics of public goods. It acts on the micro-level to show strong externalities to the regional industrial structure and total output. The final manifestation is the overall improvement of the industry and the improvement of the overall technical level.

From a realistic perspective, the output of university R&D activities is the intermediate knowledge output and many market-based outputs closely related to enterprises' business behavior [2]. Because although university R&D focuses on basic research, basic research as a public product will stimulate technological innovation. This positive externality benefits various enterprises and manufacturers in the form of knowledge spillovers. Therefore, the impact of university R&D on regional innovation capabilities should also include the two aspects mentioned above. But judging from the existing literature, it mainly revolves around the knowledge spillover of the intermediate output of university R&D, even if there is little literature involving two aspects of regional innovation capabilities. The main reason is that it has not adopted a reasonable empirical method and has a relatively large limitation. Therefore, the use of practical analytical tools and standardized empirical analysis is of great significance to clarify the R&D knowledge spillovers in universities.

The theoretical analysis foundation of the spillover effect of university R&D on the regional economy is based on the conceptual framework of the knowledge production function [3]. In essence, the knowledge production function is still a typical Cobb-Douglas production function [4]. Since university R&D investment involves two aspects: expenditure and personnel input, we give a revised knowledge production function based on related theories:
^{μ}

The SAR model is mainly used to measure the spatial spillover effects of dependent variables, and its setting form is as follows:
_{it}_{ij}_{it}_{it}_{ij}τ_{jt}

SEM does not consider the spatial spillover effects of dependent variables. The previous research literature on the knowledge spillover effects of R&D in Chinese universities is mainly based on the estimation results of the SEM model. The SAR model ignores the spatial dependence in the error term, which reduces the effectiveness of the estimation. Because of the characteristics and limitations of the SAR and SEM models, some scholars have proposed an SDM model that can simultaneously measure the spatial spillover effect of the dependent variable and the spatial dependence of the error term [6]. The characteristic of this model is that it contains both the spatial lag term of the dependent variable and the spatial lag term of the explanatory variable. Whether the real data generation process is SEM or SAR, the SDM model has relatively general and robust estimation results. Its form is as follows:
_{ij}X_{ijt}

Only in 2008 did university R&D expenditures. Since 2011, the statistical caliber of industrial enterprises has been changed from large and medium-sized to large-scale [7]. Relative quantities cannot examine the overall scale of university R&D expenditures and personnel input knowledge spillovers in various regions, so all variables in models (3) and (4) are absolute numbers. In 1994, China implemented the tax-sharing system reform, so we set the 1994 CPI index as the base price. Table 1 shows the running results of STATA12.0, and the rest are obtained by Matlab R2012b.

LMsarsem test

π | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

LM-LAG | 1.126 | 3.002 | 5.865 | 9.739 | 14.61 | |

P | 0.289 | 0.083 | 0.015 | 0.002 | 0 | |

LM-ERROR | 56.01 | 56.15 | 55.76 | 54.46 | 51.75 | |

P | 0 | 0 | 0 | 0 | 0 | |

π | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

LM-LAG | 11.94 | 10.20 | 8.519 | 6.92 | 5.433 | |

P | 0.001 | 0.001 | 0.004 | 0.009 | 0.02 | |

LM-ERROR | 13.39 | 11.90 | 10.11 | 8.012 | 5.647 | |

P | 0 | 0.001 | 0.001 | 0.005 | 0.017 |

First, select the spatial weight matrix. In the past, the research literature of university R&D knowledge spillover only considered the geographical distance between regions and did not consider the gap in economic growth between regions [8]. This paper adds the regional economic distance weight matrix to the geographical distance weight matrix:
_{ij}_{ij}_{i}_{j}_{i}_{j}_{ij}_{ij}_{ij}

Some scholars have proposed that the LM statistic obeys the asymptotic χ^{2}(1) distribution. In this way, it is judged whether to choose a space measurement model and what form of the space measurement model to choose. This model is more concise and convenient than Moran's I statistics.

When the explained variable is lnPatent, regardless of the value of π, the LM-ERROR statistic is very significant. Explain that the data generation process is in SEM format. But with the increase of the geographic distance share, the significance of the LM-ERROR statistics diminishes. At this time, the model completely uses geographic distance as the weight matrix. When π=0.1, the SAR model is not suitable. When π=0.2, the LM-LAG statistic is significant at the 1% level. SAR models can be selected starting from π=0.3. When the explained variable is lnNewRevenue, when π takes a value of 0 to 0.6, both SAR and SEM models are suitable. It shows that the data generation process conforms to both the SAR format and the SEM format. At this time, it is very necessary to choose the SDM model. Otherwise, the validity and consistency of the parameter estimation will be biased. When the explained variable is LnPatent, the π values are 0.7, 0.7, and 0.6, respectively. When the explained variable is LnNewReveue, π is 0.3, 0.6, and 0.3, respectively.

The results of the hybrid OLS estimation show that regardless of whether the explained variable is lnPatent or ln New Revenue, the expenditure and personnel input of university R&D and enterprise R&D are significant. Hybrid OLS is the benchmark and reference model for subsequent spatial measurement model estimation. The LM space autoregressive-error test is based on the OLS model. The table also shows the estimated results of the ordinary panel's fixed effects and random-effects models. LnPatent and ln New Revenue reject the assumption that there is no difference between fixed effects and random effects at the significance levels of 1% and 5%, respectively [10]. The estimation method of the fixed effect model is better, so the fixed effect model is also used to estimate the spatial measurement model. When the explained variable is lnPatent, the effect of university R&D personnel input is uncertain. When the explained variable is ln New Revenue, the explanatory variables are significant, and the degree of fit is relatively higher. The DW value under the mixed OLS model is also close to 2, which shows that heteroscedasticity does not affect the model.

The SEM model measures the error impact of the R&D expenditure and personnel input of universities in a region on the region's innovation capability. At the same time, it also reflects the extent of its impact on the changes in innovation capabilities in other regions. Tables 2 and 3 show the parameter estimation results of the SAR and SEM models of the knowledge spillover effects of university R&D on regional innovation capabilities as the explained variables ln Patent and ln New Revenue respectively.

The knowledge spillover effect of university R&D when the explained variable is lnPatent

lnPatent | ||||||
---|---|---|---|---|---|---|

SAR | SEM | |||||

Regional fixed | Fixed time | Double fixation | Regional fixed | Fixed time | Double fixation | |

− 0.1061 | 0.1495 | − 0.2030 | − 0.1549 | 0.1984 | − 0.2071 | |

(− 2.8704) | −3.3179 | (− 4.3726) | (− 3.2648) | −4.2377 | (− 4.1984) | |

− 0.1433 | 0.1595 | −0.1322 | − 0.1493 | 0.1182 | −0.1278 | |

(− 1.8661) | −2.1488 | (− 1.5826) | (− 1.7383) | −1.525 | (− 1.4396) | |

0.2418 | 0.6328 | 0.1634 | 0.1591 | 0.7266 | 0.1691 | |

−5.7823 | −11.0594 | −3.2596 | −3.0969 | −12.0784 | −3.1735 | |

0.1205 | −0.0379 | 0.1545 | 0.0984 | − 0.1156 | 0.1653 | |

−2.7329 | (− 0.634) | −3.3443 | −2.0245 | (− 1.8273) | −3.3719 | |

0.7510 | 0.5060 | 0.2080 | ||||

−19.0213 | −8.8495 | −1.6646 | ||||

0.9220 | 0.2700 | 0.2604 | ||||

−62.9079 | −2.2429 | −2.1436 | ||||

^{2} |
0.9726 | 0.9047 | 0.9732 | 0.8871 | 0.8944 | 0.973 |

^{2} |
0.8782 | 0.8714 | 0.8696 | 0.8672 | 0.8687 | 0.8623 |

−2.0509 | −242.1127 | 10.6244 | −2.0134 | −254.54 | 9.8759 |

The knowledge spillover effect of university R&D when the explained variable is ln New Revenue

ln New Revenue | ||||||
---|---|---|---|---|---|---|

SAR | SEM | |||||

Regional fixed | Fixed time | Double fixation | Regional fixed | Fixed time | Double fixation | |

0.1895 | 0.2529 | 0.1893 | 0.2565 | 0.3005 | 0.1886 | |

−3.4387 | −4.8188 | −3.0238 | −5.1687 | −5.6397 | −2.8485 | |

0.2960 | 0.1432 | 0.2253 | 0.2025 | 0.1120 | 0.2281 | |

−2.8203 | −1.6604 | −1.9983 | −1.7871 | −2.2665 | −1.9115 | |

0.3786 | 0.8486 | 0.3258 | 0.3679 | 0.9332 | 0.3269 | |

−6.1334 | −12.3513 | −4.8205 | −5.5543 | −13.0891 | −4.5652 | |

− 0.1013 | − 0.2566 | − 0.1162 | −0.0662 | − 0.3292 | − 0.1181 | |

(− 1.6818) | (− 3.6053) | (− 1.8667) | (− 1.0265) | (− 4.4152) | (− 1.7947) | |

0.4820 | 0.4390 | 0.1139 | ||||

−9.4609 | −8.3856 | −1.6582 | ||||

0.8660 | 0.2540 | 0.1068 | ||||

−33.3533 | −5.2703 | −1.6751 | ||||

^{2} |
0.9665 | 0.9158 | 0.9681 | 0.906 | 0.9013 | 0.9681 |

^{2} |
0.8917 | 0.8724 | 0.8741 | 0.8733 | 0.8614 | 0.8542 |

−121.1745 | −300.0728 | −105.3039 | −149.3385 | −316.9979 | −101.2397 |

When the explained variable is lnPatent, the π value of the SAR and SEM spatial weight matrices are both 0.7. This shows that the influence of geographic distance is greater than that of economic distance. From the LM inspection in Table 1, it can be seen that the data generation process at this time is both SAR and SEM forms. In the SEM model, when they are 0.1691% and 0.1653%, respectively, the effect of capital investment in enterprise R&D is only slightly higher than the effect of personnel input. For every increase of 1% of the knowledge spillover effect of the innovation capability level of the region on the innovation capability of the surrounding area, the innovation capability of the surrounding area will increase by 0.208%.

When the explained variable is ln New Revenue, the π value in the SAR model is 0.3. The impact of economic distance is 70%, and the value of π in the SEM model is 0.6. The impact of geographic distance is greater than that of economic distance. Although the value of π is different, the data generation process is still in both SAR and SEM formats. Both university R&D expenditures and personnel input are significantly conducive to the increase in sales revenue of new products in the region. In SAR, every 1% increase in university R&D funding will increase sales revenue by 0.1893%. For every 1% increase in staff full-time equivalent, new product sales revenue will increase by 0.2253%. The relevant data in SEM were 0.1886% and 0.2281%. This is not much different from SAR. Corporate R&D expenditures and personnel inputs have different effects on new product sales revenue. Expenditures are significantly conducive to the increase in sales revenue of new products. The SAR and SEM models are 0.3258% and 0.3269%, respectively, which are significantly greater than the contribution of college R&D expenditures. However, the personnel investment of enterprise R&D is not conducive to the increase of sales revenue of new products.

When the explained variable is lnPatent or ln New Revenue, the data generation process is both in the form of SAR and SEM. Therefore, it is necessary to use the SDM model. It can be seen from Table 4 that when the explained variable is lnPatent or ln New Revenue, the fitting degree of the SDM model under the double fixed effects is higher than that of the SAR and SEM models. When the explained variable is lnPatent, university R&D expenditure and personnel input are still not conducive to improving regional basic innovation capabilities. This point is consistent with the estimated results of SAR and SEM, and the spatial spillover effects of the two to other regions are not significant. Enterprise R&D expenditure and personnel input have a significant positive effect on improving regional basic innovation capabilities. The effect of capital investment is greater than the effect of personnel investment. The elasticity is 0.1739% and 0.1257%, respectively. The SAR and SEM models respectively underestimate the former and significantly overestimate the role of enterprise R&D personnel input in promoting regional basic innovation capabilities. The spatial spillover effect of the dependent variable is −0.3860%.

Spatial Dubin model estimation results

SAR | SEM | |||||
---|---|---|---|---|---|---|

Regional fixed | Fixed time | Double fixation | Regional fixed | Fixed time | Double fixation | |

−0.1607 | 0.0998 | −0.1636 | 0.1695 | 0.1811 | 0.1762 | |

(−3.6828) | −2.0982 | (−3.6731) | −2.7025 | −3.3192 | −2.7827 | |

−0.1291 | 0.2047 | −0.0949 | 0.2978 | 0.2179 | 0.2768 | |

(−1.6639) | −2.6456 | (−1.1611) | −2.6684 | −2.455 | −2.3919 | |

0.1707 | 0.6013 | 0.1739 | 0.3742 | 0.8327 | 0.3454 | |

−3.6306 | −9.8824 | −3.6084 | −5.5388 | −11.775 | −5.0811 | |

0.1274 | −0.0121 | 0.1257 | −0.1263 | −0.2361 | −0.1170 | |

−2.8754 | (−0.1927) | −2.7945 | (−1.9710) | (−3.1813) | (−1.8350) | |

0.0618 | −0.1944 | −0.1554 | −0.2507 | −0.2236 | −0.0996 | |

−0.5387 | (−0.6875) | (−0.7059) | (−1.9035) | (−1.1171) | (−0.5241) | |

−0.0451 | −0.408 | 0.5391 | 0.6837 | 0.2259 | 0.5859 | |

(−0.2282) | (−1.0500) | −1.2123 | −2.7406 | −0.7605 | −1.4445 | |

0.5128 | 2.0471 | 0.5202 | 0.5288 | 1.2255 | 0.7136 | |

−3.2092 | −6.7424 | −1.8907 | −2.9566 | −5.0426 | −2.839 | |

0.7663 | −1.3748 | 0.9643 | −0.3629 | −1.3439 | −0.3925 | |

−5.0543 | (−4.5872) | −4.4216 | (−2.3054) | (−5.8152) | (−2.0111) | |

−0.3040 | 0.104 | −0.3860 | 0.2680 | 0.3450 | 0.0249 | |

(−2.2383) | −0.9781 | (−2.5783) | −3.0599 | −4.2713 | −1.6621 | |

^{2} |
0.9755 | 0.915 | 0.9762 | 0.967 | 0.9218 | 0.9686 |

^{2} |
0.8917 | 0.8943 | 0.8752 | 0.8973 | 0.8831 | 0.8667 |

27.5879 | −214.061 | 32.514 | −114.031 | −283.615 | −102.539 |

When the explanatory variable is ln New Revenue, university R&D expenditures and personnel input are conducive to improving regional secondary innovation capabilities. The improvement ratio was 0.1762% and 0.2768%, respectively. The SAR and SEM models overestimate the former and significantly underestimate the role of university R&D personnel input. Personnel investment is also not conducive to improving regional secondary innovation capabilities, which are close to the estimated results of SAR and SEM models. The spatial spillover effect of the dependent variable is positive. This shows that the increase in sales revenue of new products in this region is conducive to improving secondary innovation capabilities in surrounding areas. This effect is 0.0249%.

This paper uses China's provincial data from 2018 to 2020 and uses the Spatial Dubin Model (SDM) to study the knowledge spillover effect of R&D in Chinese universities on regional innovation capabilities. The results show that (1) University R&D expenditures are not conducive to improving basic innovation capabilities in the region, and the impact of personnel input is not significant. (2) Expenditure and personnel input have a significant role in promoting the secondary innovation capabilities of the region, and the promotion effect of personnel input is greater than the effect of expenditures. (3) The expenditure and personnel input of university R&D did not produce direct knowledge spillover effects on surrounding areas. This spillover effect is more indirectly realized through changes in the region's innovation capabilities.

#### The knowledge spillover effect of university R&D when the explained variable is lnPatent

lnPatent | ||||||
---|---|---|---|---|---|---|

SAR | SEM | |||||

Regional fixed | Fixed time | Double fixation | Regional fixed | Fixed time | Double fixation | |

− 0.1061 | 0.1495 | − 0.2030 | − 0.1549 | 0.1984 | − 0.2071 | |

(− 2.8704) | −3.3179 | (− 4.3726) | (− 3.2648) | −4.2377 | (− 4.1984) | |

− 0.1433 | 0.1595 | −0.1322 | − 0.1493 | 0.1182 | −0.1278 | |

(− 1.8661) | −2.1488 | (− 1.5826) | (− 1.7383) | −1.525 | (− 1.4396) | |

0.2418 | 0.6328 | 0.1634 | 0.1591 | 0.7266 | 0.1691 | |

−5.7823 | −11.0594 | −3.2596 | −3.0969 | −12.0784 | −3.1735 | |

0.1205 | −0.0379 | 0.1545 | 0.0984 | − 0.1156 | 0.1653 | |

−2.7329 | (− 0.634) | −3.3443 | −2.0245 | (− 1.8273) | −3.3719 | |

0.7510 | 0.5060 | 0.2080 | ||||

−19.0213 | −8.8495 | −1.6646 | ||||

0.9220 | 0.2700 | 0.2604 | ||||

−62.9079 | −2.2429 | −2.1436 | ||||

^{2} |
0.9726 | 0.9047 | 0.9732 | 0.8871 | 0.8944 | 0.973 |

^{2} |
0.8782 | 0.8714 | 0.8696 | 0.8672 | 0.8687 | 0.8623 |

−2.0509 | −242.1127 | 10.6244 | −2.0134 | −254.54 | 9.8759 |

#### Spatial Dubin model estimation results

SAR | SEM | |||||
---|---|---|---|---|---|---|

Regional fixed | Fixed time | Double fixation | Regional fixed | Fixed time | Double fixation | |

−0.1607 | 0.0998 | −0.1636 | 0.1695 | 0.1811 | 0.1762 | |

(−3.6828) | −2.0982 | (−3.6731) | −2.7025 | −3.3192 | −2.7827 | |

−0.1291 | 0.2047 | −0.0949 | 0.2978 | 0.2179 | 0.2768 | |

(−1.6639) | −2.6456 | (−1.1611) | −2.6684 | −2.455 | −2.3919 | |

0.1707 | 0.6013 | 0.1739 | 0.3742 | 0.8327 | 0.3454 | |

−3.6306 | −9.8824 | −3.6084 | −5.5388 | −11.775 | −5.0811 | |

0.1274 | −0.0121 | 0.1257 | −0.1263 | −0.2361 | −0.1170 | |

−2.8754 | (−0.1927) | −2.7945 | (−1.9710) | (−3.1813) | (−1.8350) | |

0.0618 | −0.1944 | −0.1554 | −0.2507 | −0.2236 | −0.0996 | |

−0.5387 | (−0.6875) | (−0.7059) | (−1.9035) | (−1.1171) | (−0.5241) | |

−0.0451 | −0.408 | 0.5391 | 0.6837 | 0.2259 | 0.5859 | |

(−0.2282) | (−1.0500) | −1.2123 | −2.7406 | −0.7605 | −1.4445 | |

0.5128 | 2.0471 | 0.5202 | 0.5288 | 1.2255 | 0.7136 | |

−3.2092 | −6.7424 | −1.8907 | −2.9566 | −5.0426 | −2.839 | |

0.7663 | −1.3748 | 0.9643 | −0.3629 | −1.3439 | −0.3925 | |

−5.0543 | (−4.5872) | −4.4216 | (−2.3054) | (−5.8152) | (−2.0111) | |

−0.3040 | 0.104 | −0.3860 | 0.2680 | 0.3450 | 0.0249 | |

(−2.2383) | −0.9781 | (−2.5783) | −3.0599 | −4.2713 | −1.6621 | |

^{2} |
0.9755 | 0.915 | 0.9762 | 0.967 | 0.9218 | 0.9686 |

^{2} |
0.8917 | 0.8943 | 0.8752 | 0.8973 | 0.8831 | 0.8667 |

27.5879 | −214.061 | 32.514 | −114.031 | −283.615 | −102.539 |

#### LMsarsem test

π | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

LM-LAG | 1.126 | 3.002 | 5.865 | 9.739 | 14.61 | |

P | 0.289 | 0.083 | 0.015 | 0.002 | 0 | |

LM-ERROR | 56.01 | 56.15 | 55.76 | 54.46 | 51.75 | |

P | 0 | 0 | 0 | 0 | 0 | |

π | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | |

LM-LAG | 11.94 | 10.20 | 8.519 | 6.92 | 5.433 | |

P | 0.001 | 0.001 | 0.004 | 0.009 | 0.02 | |

LM-ERROR | 13.39 | 11.90 | 10.11 | 8.012 | 5.647 | |

P | 0 | 0.001 | 0.001 | 0.005 | 0.017 |

#### The knowledge spillover effect of university R&D when the explained variable is ln New Revenue

ln New Revenue | ||||||
---|---|---|---|---|---|---|

SAR | SEM | |||||

Regional fixed | Fixed time | Double fixation | Regional fixed | Fixed time | Double fixation | |

0.1895 | 0.2529 | 0.1893 | 0.2565 | 0.3005 | 0.1886 | |

−3.4387 | −4.8188 | −3.0238 | −5.1687 | −5.6397 | −2.8485 | |

0.2960 | 0.1432 | 0.2253 | 0.2025 | 0.1120 | 0.2281 | |

−2.8203 | −1.6604 | −1.9983 | −1.7871 | −2.2665 | −1.9115 | |

0.3786 | 0.8486 | 0.3258 | 0.3679 | 0.9332 | 0.3269 | |

−6.1334 | −12.3513 | −4.8205 | −5.5543 | −13.0891 | −4.5652 | |

− 0.1013 | − 0.2566 | − 0.1162 | −0.0662 | − 0.3292 | − 0.1181 | |

(− 1.6818) | (− 3.6053) | (− 1.8667) | (− 1.0265) | (− 4.4152) | (− 1.7947) | |

0.4820 | 0.4390 | 0.1139 | ||||

−9.4609 | −8.3856 | −1.6582 | ||||

0.8660 | 0.2540 | 0.1068 | ||||

−33.3533 | −5.2703 | −1.6751 | ||||

^{2} |
0.9665 | 0.9158 | 0.9681 | 0.906 | 0.9013 | 0.9681 |

^{2} |
0.8917 | 0.8724 | 0.8741 | 0.8733 | 0.8614 | 0.8542 |

−121.1745 | −300.0728 | −105.3039 | −149.3385 | −316.9979 | −101.2397 |

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techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional 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variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor 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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 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 The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Nonlinear Differential Equations in Preventing Financial Risks 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 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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 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 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 Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Image denoising model based on improved fractional calculus mathematical equation The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Evaluation and Verification of Patent Value Based on Combination Forecasting Model Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations The Law of Large Numbers in Children's Education 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 Good congruences on weakly U-abundant semigroups Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Fed-UserPro: A user profile construction method based on federated learning 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 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 Computer Vision Communication Technology in Mathematical Modeling 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 The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics 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 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 Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations 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 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 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 Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method 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 Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model 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 The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model