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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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 Application of regression function model based on panel data in financial risk management of bank resource allocation 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 Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus 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 Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform 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 Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new 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 environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media 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 Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities 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 transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis 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 Application of regression function model based on panel data in bank resource allocation financial risk management Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality 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 A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling 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 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 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 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 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 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 The trend and influence of media information Propagation based on nonlinear Differential 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 Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model