Risk transmission has three elements: risk source, risk flow and risk carrier. The paper quotes the asymmetric model and the joint asymmetric model to analyse the conduction effects of financial risks. At the same time, the article uses the elasticity coefficient to quantitatively calculate the risk transmission effect of the two supply chain financial financing modes. The research results prove that the risk transmission ability of each financial market has individual differences, and the foreign exchange market does not have significant risk transmission ability to other markets during the rising stage. The joint asymmetric model is more effective in predicting corporate financial risks.

#### Keywords

- risk transmission
- asymmetry
- financial risk
- mathematical modelling
- linear regression

#### MSC 2010

- 62J05

Since 2012, Chinese financial system reform has been further deepened, and the regulatory authorities have gradually loosened financial control. In particular, the interest rate marketisation reform has the most direct impact on Chinese financial institutions in two aspects: First, it can promote the transformation of traditional financial institutions from a single deposit and loan, premium and other business to various innovative profit models that can be harnessed by businesses. And through mergers and acquisitions, reorganisation of financial institutions and other means aimed at promoting the current financial system based on separate operations, the change is gradually being made towards mixed operations [1]. Second, it can promote the rapid development of various financial innovations and financial derivative products and connect different market participants such as banks, securities companies and insurance companies more closely. This significant change in the financial sector has brought about extensive relevance and crossover of financial service businesses, dramatically increasing systemic financial risks. At this stage, Chinese systemic financial risks are becoming increasingly prominent.

In contrast, the risk prevention awareness of relevant market entities is relatively weak, and the level of risk management is weak. Which sector of the Chinese financial market has the most substantial contagion effect on other markets? Which sector contributes the most to overall financial risk? What are the internal risk transmission laws and internal mechanisms of the financial system? These issues help investors make optimal investment portfolio decisions based on the correlation of sectors and provide a theoretical basis and practical guidance for policymakers and market regulators on preventing systemic risks more effectively.

Some scholars believe that the market volatility is positively correlated with the value at risk, while the stock price in the financial market has a significant volatility clustering effect. Then the value at risk closely related to volatility should also have similar properties. For this reason, the author proposes a CAViaR model with autocorrelation characteristics based on the idea of quantile regression to directly measure the value at risk of financial markets [2]. However, the CAViaR model is mainly suitable for analysing the dynamic risk characteristics of a single sector. Still, it cannot capture the complex relationship of risk contagion between different sectors (or different markets). Some scholars have extended the traditional CAVi-aR model to the MVMQ-CAViaR model to overcome the shortcomings of the above models. This model extends the idea of single-equation quantile regression to the structured equation of vector autoregression. At the same time, the model reveals that the value at risk of a single sector (or a single market) is affected by its market and risk spillovers from other markets. The specific expression is as follows:

_{it}_{it−1} under the _{it−1}| represents the absolute value of the return rate of the market index i. This parameter represents a market shock item and implies that a positive shock and a negative shock lagging have the same effect on the current VAR. _{it−1} represents the lagged conditional quantile, which can well describe the autocorrelation of the financial market tail distribution. Taking the banking sector and the securities sector as examples, suppose _{1t} represents the Var of the bank and _{2t} represents the Var of the securities. Eq. (1) shows that the bank’s risk value _{1t} is affected by its market and the extreme risk _{2t−1} of the securities sector and the market shock item |_{2t−1}|.

Model (1) assumes that the market shock item does not have a ‘leverage effect’. The positive shocks and adverse shocks of this market and other markets have equivalent effects on the value at risk. In real life, the investor’s utility function often puts a greater weight on the negative utility of losses while giving a smaller weight to the positive utility of returns. Therefore, this paper expands Eq. (1) to the asymmetric MVMQ-CAViaR model. The model is expressed as follows:

(_{1t−1})^{+} and (_{1t−1})^{−}, respectively, represent the positive and negative part of the slow rate of return. When the two plates negatively impact, it is likely to be a joint impact [3]. This kind of shock will undermine public investment confidence and investors’ panic, amplifying the original market risk. To further study the asymmetric effects on Var when different financial sectors are simultaneously subjected to adverse shocks, we further extend model (2) into a joint asymmetric MVMQ-CAViaR model. The specific model is as follows:

From Eqs (1)–(3), we can see that risks between different financial industry sectors will be transmitted to each other. The market shock item (namely _{it}_{t}_{t}

First, suppose that the formation process of the return rate data of two different sector indexes satisfies

Second, at time t, a one-time positive or negative impact of 1 unit of new interest _{1t} will make the actual rate of return _{it}_{1t} and _{2t}.

Finally, the Δ_{it}

The MVMQ-CAViaR model belongs to the category of multiple quantile regression. We can use the Least Absolute Deviation Method (LAD) estimation, and the objective function it needs to optimise is:

_{i}_{i}_{it}_{it}_{i}, a

This article takes the conditional quantile of _{i}_{1} and use the simplex algorithm and the quasi-Newton algorithm to optimise the model. This paper adopts a two-step estimation method to improve the estimation efficiency of the structured model [7]. The first step is to estimate the univariate quantile SAV model and use the estimated result as the initial trial estimated coefficient of the second step optimisation. In the second step, we optimise the multivariate quantile model (1)–(3) as a whole to minimise the objective function (4).

The in-sample performance of the model cannot simply be extended outside the sample. To further demonstrate the effect of this model on predicting VAR, we must also perform an out-of-sample robustness test. Some scholars have assumed that the model can effectively predict risk, proving that the sequence of ‘hit events’ obeys the Bernoulli distribution. Scholars construct unconditional test statistics of likelihood ratio as the following:

where p is the significance level, N is the total number of predicted samples and n is the number of hits in the prediction sample. When the LR statistic is greater than the critical value of the chi-square distribution under a given confidence level, the original model is rejected. On the contrary, when the statistic is less than the critical value, the model is accepted.

Eq. (5) shows that the Kupiec likelihood ratio test quantity is an index that characterises the degree to which the actual number of hits is close to the theoretical number of hits. In addition to testing the failure rate, it should also be tested whether there is a correlation between hit events. If there is a significant correlation between the observations that fail to predict the VaR, then a loss that continuously exceeds the VaR may occur. This will bring huge losses to investors [8]. The hit sequence of an accurate and reliable risk measurement model should be unbiased and non-autocorrelation. Therefore, some scholars proposed a dynamic quantile test. They used the bullish risk as an example to define a new hit sequence:

_{t}_{t}_{θ, t}_{t}_{t}_{θ, t}_{θ, t}_{t−1}) = 0. This shows that _{θ, t}_{θ, t−k} and predicted _{t−k}. We construct the following regression equation:

We express the above model as a matrix form, _{θ, t}_{t}

From the results in Table 1, we can see that in the sample interval selected in this article, the average yields of banks and securities are both positive. Among them, the average yield of securities reached 0.033, while the insurance industry was hostile. Thus, if the stock price index changes reflect the overall expectations of the industry’s operating performance, from this perspective, the securities industry is more prosperous than the insurance industry. At the same time, the standard deviation of the securities sector is relatively the largest, and the high risk also brings a higher risk premium [9]. This is in line with the ‘small-cap stock effect’ in finance.

Descriptive statistical results of the sample

bank | 0.026 | 9.551 | -10.506 | 6.32 | 0 | 0 |

Securities | 0.033 | 9.531 | -10.537 | 4.685 | 0 | 0 |

Insurance | -0.006 | 9.545 | -10.536 | 5.196 | 0 | 0 |

Furthermore, the three plate indices all have typical ‘negative bias’ and ‘sharp peaks and thick tails.’ Finally, according to the P-value of the J-B statistic and the ADF statistic, we further found that all the index returns are non-normal and stationary time series. Thus, the trends of banking, securities and insurance remained the same.

Table 2 shows the mutual risk transmission results of banks and securities, securities and insurance, and banks and insurance at the 5% quantile level. All the coefficients _{11} and _{22} reject the null hypothesis at the 1% significance level, and the coefficient values are all greater than 0.8. This shows that the risk levels of different financial sectors have a high degree of serial correlation. Other specific results are as follows:

Estimated results of the MVMQ-CAViaR model in the financial industry

c1 | -0.013 | -0.162 | c1 | 0.005 | -0.035 | c1 | -0.006 | -0.031 |

a11 | -0.106 | -0.08 | a11 | -0.091 | -0.05 | a11 | -0.068 | -0.038 |

a12 | -0.028 | -0.04 | a12 | -0.007 | -0.033 | a12 | -0.053 | -0.068 |

b11 | 0.952 | -0.161 | b11 | 0.961 | -0.028 | b11 | 0.949 | -0.082 |

b12 | 0.011 | -0.142 | b12 | 0.003 | -0.027 | b12 | 0.031 | -0.023 |

c2 | -0.042 | -0.131 | c2 | -0.013 | -0.033 | c2 | -0.022 | -0.037 |

a21 | -0.042 | -0.033 | a21 | -0.039 | -0.041 | a21 | 0.01 | -0.043 |

a22 | -0.089 | -0.048 | a22 | -0.047 | -0.045 | a22 | -0.087 | -0.083 |

b21 | 0.041 | -0.022 | b21 | 0.022 | -0.012 | b21 | 0.022 | -0.133 |

b22 | 0.96 | -0.114 | b22 | 0.973 | -0.029 | b22 | 0.934 | -0.179 |

First, the coefficient _{11} in the multiple regression model of banks and securities reaches a significance level of 10%. This shows that the bank’s previous yield has a significant negative impact on Var, and the coefficient _{22} is also significantly different from zero. This shows that the market impact of the securities sector will also increase the risk value of the market. In addition, we also found that the coefficients _{21} and _{21} have reached the 10% significance level. This shows that the banking sector’s extreme risks and market shocks will be transmitted to the securities sector, and the direction of influence will be harmful [10]. However, the securities sector does not have a significant risk transmission effect on the banking sector.

Second, for the regression results of banking and insurance, we can find that the coefficient _{22} is not statistically significant. This shows that the insurance sector risk is not affected by previous market shocks. Coefficient _{21} significantly indicates that extreme risks of banks will be transmitted to the insurance sector, while risks in the insurance industry have not been transmitted to banks.

Third, from the empirical results between securities and insurance, it can be seen that the extreme risks of insurance have a significant one-way spillover effect on securities, and securities do not have the function of actively transmitting risks.

Table 2 does not distinguish between the different effects of the rise and fall of the sector index on Var. To further explore the leverage effect of VaR in the financial industry, Table 3 gives the empirical results of the asymmetric MVMQ-CAViaR model. It can be seen from this that the estimation results of the three multi-quantile regression models are consistent with Table 2, and the main difference is reflected in the asymmetric coefficient. From the significance of the coefficients _{11}, _{12} and _{21}, _{22}, it is easy to know that the risk of the banking sector is significantly affected by its own negative market shock. In contrast, the impact of the positive market shock is not wholly significant. The securities sector was significantly affected by both positive and negative market shocks [11]. In addition, the insurance sector is also occasionally affected by adverse market shocks. And the absolute values of all parameters are not correspondingly equal. This means that the market shock of the Chinese financial industry has apparent asymmetric effects on the Var of different sectors, and the impact of the decline of the sector index is more significant than the rise of the sector index. From the estimation results of the coefficients _{21}, _{22} and _{11}, _{12}, it can be seen that the negative market impact of banks will spread to the securities sector and the insurance sector and significantly increase the risk value of these two sectors. However, the positive market shock coefficients are not significant. Negative insurance information will also spread to the securities sector, and there is no risk spillover effect on other markets.

Estimated results of the asymmetric MVMQ-CAViaR model

c1 | 0.082 | -0.245 | c1 | -0.013 | -0.027 | c1 | -0.003 | -0.023 |

a11 | -0.058 | -0.055 | a11 | -0.047 | -0.03 | a11 | 0.016 | -0.013 |

a12 | -0.178 | -0.106 | a12 | -0.129 | -0.078 | a12 | -0.072 | -0.03 |

d11 | -0.039 | -0.035 | d11 | 0.02 | -0.026 | d11 | -0.011 | -0.04 |

d12 | -0.076 | -0.128 | d12 | -0.052 | -0.049 | d12 | -0.067 | -0.04 |

b11 | 0.824 | -0.112 | b11 | 0.856 | -0.011 | b11 | 0.865 | -0.022 |

b12 | 0.078 | -0.182 | b12 | -0.005 | -0.021 | b12 | 0.018 | -0.013 |

c2 | -0.666 | -0.419 | c2 | -0.025 | -0.041 | c2 | -0.037 | -0.032 |

a21 | 0.029 | -0.147 | a21 | 0.007 | -0.049 | a21 | -0.019 | -0.038 |

a22 | -0.065 | -0.043 | a22 | -0.073 | -0.055 | a22 | 0.028 | -0.031 |

d21 | -0.026 | -0.02 | d21 | -0.054 | -0.061 | d21 | 0.001 | -0.051 |

d22 | -0.086 | -0.029 | d22 | -0.038 | -0.035 | d22 | -0.113 | -0.069 |

b21 | 0.037 | -0.022 | b21 | -0.015 | -0.011 | b21 | -0.001 | -0.034 |

b22 | 0.849 | -0.09 | b22 | 0.905 | -0.03 | b22 | 0.881 | -0.047 |

Figures 1 and 2 show the quantile impulse response results of the banking and securities sectors, respectively. Whether it is a standard deviation information shock from the banking sector or the securities sector, we find that a negative information shock has a more significant impact on the original market than a positive information shock. The positive impact of the banking sector has an initial positive effect on securities and then quickly decays to negative [12]. Comparing Figures 1 and 2, we can find that when there is a joint negative information shock, the intensity of this shock is significantly greater than the negative shock of a single market. The risk expansion value of the more volatile securities sector is significantly greater than that of the bank.

To summarise, this part explains the significant asymmetry of risk transmission between different sectors of the Chinese financial industry according to the two methods of coefficient value and quantile impulse response of the regression results. It is further discovered that Chinese banks have significant risk contagion effects on other sectors, while securities are at a disadvantageous position to receive risks from other sectors passively.

The estimation results of the joint asymmetric MVMQ-CAViaR model

c1 | 0.001 | -0.045 | c1 | -0.001 | -0.034 | c1 | -0.021 | -0.04 |

a11 | -0.04 | -0.053 | a11 | -0.035 | -0.02 | a11 | 0.023 | -0.015 |

a12 | -0.173 | -0.12 | a12 | -0.134 | -0.044 | a12 | -0.075 | -0.041 |

d11 | -0.032 | -0.033 | d11 | 0.015 | -0.02 | d11 | -0.03 | -0.048 |

d12 | -0.053 | -0.056 | d12 | -0.072 | -0.033 | d12 | -0.084 | -0.045 |

e1 | -0.081 | -0.066 | e1 | -0.078 | -0.05 | e1 | 0.003 | -0.013 |

b11 | 0.847 | -0.023 | b11 | 0.839 | -0.009 | b11 | 0.869 | -0.06 |

b12 | -0.013 | -0.015 | b12 | -0.024 | -0.016 | b12 | -0.016 | -0.011 |

c2 | -0.013 | -0.034 | c2 | -0.032 | -0.033 | c2 | -0.004 | -0.109 |

a21 | 0.004 | -0.045 | a21 | 0.013 | -0.029 | a21 | -0.08 | -0.062 |

a22 | -0.178 | -0.047 | a22 | -0.093 | -0.062 | a22 | -0.04 | -0.09 |

d21 | -0.012 | -0.025 | d21 | -0.022 | -0.017 | d21 | 0.106 | -0.095 |

d22 | -0.062 | -0.048 | d22 | -0.046 | -0.058 | d22 | -0.140 | -0.084 |

e2 | -0.123 | -0.074 | e2 | -0.095 | -0.071 | e2 | -0.011 | -0.033 |

b21 | -0.028 | -0.016 | b21 | -0.023 | -0.011 | b21 | 0.093 | -0.09 |

b22 | 0.851 | -0.017 | b22 | 0.820 | -0.013 | b22 | 0.862 | -0.092 |

Table 5 shows the backtest results of different sectors under the 5% quantile. At the 5% significance level, the Kupiec likelihood ratio results of the three models all passed the robustness test. Judging from the accuracy of prediction, the asymmetric

Backtest results of the model

Bank-securities | Bank | 0.641 | 0.016 | 0.641 | 0.112 | 0.838 | 0.258 |

Securities | 0.289 | 0.146 | 0.838 | 0.249 | 0.836 | 0.898 | |

Bank- insurance | Bank | 0.838 | 0.428 | 0.838 | 0.562 | 0.838 | 0.862 |

Insurance | 0.289 | 0.003 | 0.289 | 0.013 | 0.641 | 0.222 | |

Securities-insurance | Securities | 0.678 | 0.16 | 0.678 | 0.351 | 0.678 | 0.331 |

Insurance | 0.199 | 0.001 | 0.289 | 0.195 | 0.289 | 0.076 |

The relevant research conclusions have important policy implications for suggesting the means to prevent Chinese systemic financial risks. First, we conduct differentiated monitoring and prevention of financial institutions of different systems importance. Second, we view the risks of the entire Chinese financial system from a global perspective, strengthen macro-prudential regulatory requirements and establish an early warning system for different industries to respond to risks jointly. Finally, we must focus on monitoring the impact on the entire financial system when negative news is encountered in different financial industry sectors at the same time, and the impact of local risks is relatively small. However, the simultaneous occurrence of risk events in different financial sectors will severely damage the public’s investment confidence, thus easily causing market panic. It will drastically expand the risk level of the market.

#### The estimation results of the joint asymmetric MVMQ-CAViaR model

c1 | 0.001 | -0.045 | c1 | -0.001 | -0.034 | c1 | -0.021 | -0.04 |

a11 | -0.04 | -0.053 | a11 | -0.035 | -0.02 | a11 | 0.023 | -0.015 |

a12 | -0.173 | -0.12 | a12 | -0.134 | -0.044 | a12 | -0.075 | -0.041 |

d11 | -0.032 | -0.033 | d11 | 0.015 | -0.02 | d11 | -0.03 | -0.048 |

d12 | -0.053 | -0.056 | d12 | -0.072 | -0.033 | d12 | -0.084 | -0.045 |

e1 | -0.081 | -0.066 | e1 | -0.078 | -0.05 | e1 | 0.003 | -0.013 |

b11 | 0.847 | -0.023 | b11 | 0.839 | -0.009 | b11 | 0.869 | -0.06 |

b12 | -0.013 | -0.015 | b12 | -0.024 | -0.016 | b12 | -0.016 | -0.011 |

c2 | -0.013 | -0.034 | c2 | -0.032 | -0.033 | c2 | -0.004 | -0.109 |

a21 | 0.004 | -0.045 | a21 | 0.013 | -0.029 | a21 | -0.08 | -0.062 |

a22 | -0.178 | -0.047 | a22 | -0.093 | -0.062 | a22 | -0.04 | -0.09 |

d21 | -0.012 | -0.025 | d21 | -0.022 | -0.017 | d21 | 0.106 | -0.095 |

d22 | -0.062 | -0.048 | d22 | -0.046 | -0.058 | d22 | -0.140 | -0.084 |

e2 | -0.123 | -0.074 | e2 | -0.095 | -0.071 | e2 | -0.011 | -0.033 |

b21 | -0.028 | -0.016 | b21 | -0.023 | -0.011 | b21 | 0.093 | -0.09 |

b22 | 0.851 | -0.017 | b22 | 0.820 | -0.013 | b22 | 0.862 | -0.092 |

#### Descriptive statistical results of the sample

bank | 0.026 | 9.551 | -10.506 | 6.32 | 0 | 0 |

Securities | 0.033 | 9.531 | -10.537 | 4.685 | 0 | 0 |

Insurance | -0.006 | 9.545 | -10.536 | 5.196 | 0 | 0 |

#### Estimated results of the asymmetric MVMQ-CAViaR model

c1 | 0.082 | -0.245 | c1 | -0.013 | -0.027 | c1 | -0.003 | -0.023 |

a11 | -0.058 | -0.055 | a11 | -0.047 | -0.03 | a11 | 0.016 | -0.013 |

a12 | -0.178 | -0.106 | a12 | -0.129 | -0.078 | a12 | -0.072 | -0.03 |

d11 | -0.039 | -0.035 | d11 | 0.02 | -0.026 | d11 | -0.011 | -0.04 |

d12 | -0.076 | -0.128 | d12 | -0.052 | -0.049 | d12 | -0.067 | -0.04 |

b11 | 0.824 | -0.112 | b11 | 0.856 | -0.011 | b11 | 0.865 | -0.022 |

b12 | 0.078 | -0.182 | b12 | -0.005 | -0.021 | b12 | 0.018 | -0.013 |

c2 | -0.666 | -0.419 | c2 | -0.025 | -0.041 | c2 | -0.037 | -0.032 |

a21 | 0.029 | -0.147 | a21 | 0.007 | -0.049 | a21 | -0.019 | -0.038 |

a22 | -0.065 | -0.043 | a22 | -0.073 | -0.055 | a22 | 0.028 | -0.031 |

d21 | -0.026 | -0.02 | d21 | -0.054 | -0.061 | d21 | 0.001 | -0.051 |

d22 | -0.086 | -0.029 | d22 | -0.038 | -0.035 | d22 | -0.113 | -0.069 |

b21 | 0.037 | -0.022 | b21 | -0.015 | -0.011 | b21 | -0.001 | -0.034 |

b22 | 0.849 | -0.09 | b22 | 0.905 | -0.03 | b22 | 0.881 | -0.047 |

#### Estimated results of the MVMQ-CAViaR model in the financial industry

c1 | -0.013 | -0.162 | c1 | 0.005 | -0.035 | c1 | -0.006 | -0.031 |

a11 | -0.106 | -0.08 | a11 | -0.091 | -0.05 | a11 | -0.068 | -0.038 |

a12 | -0.028 | -0.04 | a12 | -0.007 | -0.033 | a12 | -0.053 | -0.068 |

b11 | 0.952 | -0.161 | b11 | 0.961 | -0.028 | b11 | 0.949 | -0.082 |

b12 | 0.011 | -0.142 | b12 | 0.003 | -0.027 | b12 | 0.031 | -0.023 |

c2 | -0.042 | -0.131 | c2 | -0.013 | -0.033 | c2 | -0.022 | -0.037 |

a21 | -0.042 | -0.033 | a21 | -0.039 | -0.041 | a21 | 0.01 | -0.043 |

a22 | -0.089 | -0.048 | a22 | -0.047 | -0.045 | a22 | -0.087 | -0.083 |

b21 | 0.041 | -0.022 | b21 | 0.022 | -0.012 | b21 | 0.022 | -0.133 |

b22 | 0.96 | -0.114 | b22 | 0.973 | -0.029 | b22 | 0.934 | -0.179 |

#### Backtest results of the model

Bank-securities | Bank | 0.641 | 0.016 | 0.641 | 0.112 | 0.838 | 0.258 |

Securities | 0.289 | 0.146 | 0.838 | 0.249 | 0.836 | 0.898 | |

Bank- insurance | Bank | 0.838 | 0.428 | 0.838 | 0.562 | 0.838 | 0.862 |

Insurance | 0.289 | 0.003 | 0.289 | 0.013 | 0.641 | 0.222 | |

Securities-insurance | Securities | 0.678 | 0.16 | 0.678 | 0.351 | 0.678 | 0.331 |

Insurance | 0.199 | 0.001 | 0.289 | 0.195 | 0.289 | 0.076 |

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stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement 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 Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest 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 optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics 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 Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology 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 Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching 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 Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation 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 Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance 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 Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology