To put it simply, principal component analysis is a mathematical transformation method that transforms a given set of related variables into another set of unrelated variables in linear transformation, and rearranges the new variables in descending order of decreasing variance. Under the condition that the overall variance remains unchanged, the first variable has the maximum variance, which is regarded as the first component. The variance value ranked second, and the variable not associated with the first variable was regarded as the second principal component. By analogy, a variable has a principal component. There are multiple variables in the data, and there is correlation between the variables, then there may be problems such as variable duplication or information intersection, and there are many subsequent problems caused by the unprocessed data[1].

Assuming that there are n sample units and all sample units have P indicators, construct the matrix X= (X_{ij}) n*p, where represents the JTH financial indicator of the ith company, as shown below^{[2].}:

In order to achieve standardized data, it is necessary to solve the differences between the original financial data and build a standardized matrix, as shown below:

Standardized data information is regarded as the basis, and statistical indicators of the close relationship between standardized data are presented after the covariance matrix is constructed. The larger the value is, the more principal component analysis is required. The matrix formula of z-correlation coefficient is as follows:

The equation for calculating the eigenvalue and eigenvector of R is as follows:

Obtaining characteristic values

Generally speaking, the first principal component contains the largest amount of information, and F1 represents the first component. Only when the information contained in the first principal component cannot fully explain the original variable, the second component can be selected, and there is no correlation between the two. The principal component score is calculated as follows:

There is a direct proportional relationship between the variance contribution rate of the principal component and the information contained. The larger the actual value is, the more information contained is. The variance contribution rate of the ith principal component is as follows:

By multiplying the principal component score by the variance contribution rate, the weight value can be obtained and the composite score for each sample can be obtained.

In the early 1940s, American statistician stone using the principal component analysis (pca), to the United States during the period of 1929 to 1938, the data information of system research, the variable elements of original research involves 17, and principal component analysis (pca) only need three variables, including the total income, the rate of change of total revenue, economic development and the trend of decline, The actual calculation accuracy can reach 97.4%. Based on the research results of this event, it can be seen that principal component analysis is to comprehensively simplify the actual multi-variable cross-section data table under the principle of minimizing the loss of data information. In other words, it is to reduce the dimension of high-dimensional variable space.[4]

Suppose we are discussed the practical problems contained in the p index, the index as a p a random variables, principal component analysis is to the index, converted to discuss the linear combination of multiple indexes, and these new indicators, need according to the principle of reserves the main information, fully show the information of original indexes, and independent of each other.

And this study meets the following conditions:

First, the sum of the square coefficients of all principal components is 1, and the specific formula is:

Secondly, the principal components are independent of each other and there is no overlapping information. The specific formula is as follows:

Finally, the variance of principal components will decrease successively, and their importance will also decrease. The corresponding formula is as follows:

According to the geometric interpretation diagram of the principal component analysis shown in FIG. 1 below, if the x1 and x2 axes are first shifted and θ angles are rotated counterclockwise, new coordinate axes F1 and F2 can be obtained, which are then two new variables.

In the above formula, U ‘represents the rotation transformation matrix, which belongs to the orthogonal matrix, and it can be obtained:

The purpose of rotation transformation is to maximize the discretization degree of N sample points along the F1 axis, in other words, to maximize the variance of variable F1. The variable F1 represents the vast majority of the original data. When studying corporate financial strategy and performance management, there will be no significant change even if the variable F2 is not studied. The rotation changes allow more information to be concentrated in axis F1, thus reducing the information contained in the data.^{[5]}

In the above formula, _{i}

The unit eigenvector corresponding to the eigenroots of the above matrix is U1... Up, Assuming that

It can be clear that the real symmetric matrix A represents the orthogonal relationship between the corresponding feature vectors of different features, and it can be obtained as follows:

Because it represents a nonnegative definite symmetric matrix, it can be obtained by using the knowledge of linear algebra, and there must be an orthogonal matrix U, thus:

_{1}, _{2},…, _{p}_{x} Eigenroots, you can assume that _{1} ≥ _{2} ≥ … ≥ _{p}

Based on the imperfect information of the first principal component, we should search for the second principal component. Under constraint cov(_{1}, _{2}) = 0 Below, find the second component as shown below:

Because in accordance with

This condition, so can be obtained:

Then for the p-dimension vector U2, it can be obtained:

So assume a curvilinear change:

Then F2 will have the second largest variance, and so on:

The corresponding matrix form is:

Since the selection of evaluation indicators directly affects the overall evaluation results, the influence of evaluation indicators on the results should be fully studied in the selection. In this paper, when an enterprise chooses its financial indicators, it will study the four abilities of the enterprise, the first is the solvency, the second is the profitability, the third is the operation ability, and the last is the growth ability. The actual selected financial indicators are shown in Table 1 below:[6].

The meaning of financial indicators

Indicators | Meaning |
---|---|

Return on equity X1 | Net profit/average balance of shareholders’ equity *100% |

Net margin on sales X2 | Net profit/net operating income *100% |

Gross margin on sales X3 | Gross profit on sales/net operating income *100% |

Asset-liability ratio X4 | Liabilities/Assets *100% |

Current ratio X5 | Current assets/current liabilities |

Quick ratio X6 | (Current assets - Inventory)/current liabilities |

Inventory turnover X7 | Cost of sales/average inventory balance |

Accounts receivable turnover X8 | Net credit sales/average balance of accounts receivable |

Profit growth rate X9 | (Net profit of current period - net profit of the same period of last year)/Net profit of the same period of last year *100% |

Growth rate of assets X10 | (Asset ending value of current period - initial value of asset of current period)/Initial value of asset of current period *100% |

First, the possibility of principal component analysis of the original data should be judged. Both bartlett test and K MO test can be used to judge whether the original data conforms to the principal component analysis method, and its application principle is to check the correlation between variables. The larger the value of K mo obtained, the greater the correlation between variables is proved, so it is very suitable for principal component analysis. Generally speaking, there is a definite limit to this value. When the value is above 0.5, principal component analysis can be used, otherwise it is not suitable. According to the analysis of the test results shown in the table below, the value of the selected variables obtained in this study is equal to 0.630, which exceeds the defined value of the applicable method. Therefore, principal component analysis can be used in this study. However, the significance of Bartlett's sphericity test is equal to zero, which proves that the value is lower than the actual limit value of 0.05, proving that a small number of principal components can be obtained from the proposed variable.

Test results

0KMO sampling suitability quantity | .630 | |
---|---|---|

Badlett sphericity test | The approximate chi-square | 355.037 |

Degrees of freedom | 46 | |

significant | .000 |

Second, make clear the degree of commonality of variables. The initial value and proposed value of this content can be listed according to variance in the software calculation, which can intuitively present the information number contained in the original variable and the information number after extraction, and intuitively determine whether the proposed principal component can explain the large amount of information of the original data. According to the analysis of the common factor variance table as shown in Table 3 below, except for the low degree of commonality of the variables of asset growth rate, the commonness of the variables of profit growth rate is even 97.4%, which proves that the obtained principal components can directly explain the original variables.

Common factor variance table

The initial | Extract | |
---|---|---|

X1 | 1.000 | .846 |

X2 | 1.000 | .811 |

X3 | 1.000 | .877 |

X4 | 1.000 | .853 |

X5 | 1.000 | .911 |

X6 | 1.000 | .804 |

X7 | 1.000 | .867 |

X8 | 1.000 | .892 |

X9 | 1.000 | .973 |

X10 | 1.000 | .562 |

Third, rubble map. The horizontal coordinate contains 10, corresponding to each serial number of the principal component studied in this paper. The vertical axis refers to the size of the characteristic value, and the value closer to the horizontal axis, the smaller it is. This graph can intuitively show the characteristics of which principal component, and the largest value represents the stronger the actual importance. Based on the results shown in Figure 2 below, the first four main variables can be considered important in explaining all the variables.

Fourth, extract the principal component. In the reduction analysis, the conclusion of the total variance interpretation table can show whether the variance contribution rate of the principal component and the cumulative variance contribution rate meet the requirements. Generally speaking, if the cumulative variance contribution rate exceeds 70%, it means that it can prove the core information of the original index. According to the research results shown in the following table, the cumulative variance contribution rate of the first four principal components reached 80.710%.

Total variance interpretation table

Initial eigenvalue variance percent | Extract load square and variance percentage | Rotational load square and variance percent | |||||||
---|---|---|---|---|---|---|---|---|---|

composition | A total of | than | Cumulative % | A total of | than | Cumulative % | A total of | than | Cumulative % |

1 | 3.861 | 36.999 | 36.999 | 3.862 | 36.999 | 36.999 | 2.720 | 24.939 | 24.939 |

2 | 2.112 | 19.277 | 56.376 | 2.111 | 19.377 | 56.376 | 2.403 | 18.967 | 51.706 |

3 | 1.278 | 12.769 | 69.145 | 1.279 | 12.769 | 69.145 | 1.933 | 17.069 | 68.775 |

4 | 1.047 | 11.565 | 80.710 | 1.047 | 11.565 | 80.710 | 1.096 | 11.935 | 80.710 |

5 | .694 | 6.998 | 88.391 | ||||||

6 | .383 | 3.847 | 93.307 | ||||||

7 | .285 | 2.698 | 95.979 | ||||||

8 | .154 | 1.530 | 97.533 | ||||||

9 | .128 | 1.268 | 98.684 | ||||||

10 | .113 | 1.154 | 100.000 |

Fifth, independence test. According to the analysis of component score covariance matrix table as shown in Table 5 below, the difference of covariance between the four components is 0, which proves that there is no correlation between them.

Matrix table of component score covariance

Composition | 1 | 2 | 3 | 4 |
---|---|---|---|---|

1 | 1.000 | .000 | .000 | .000 |

2 | .000 | 1.000 | .000 | .000 |

3 | .000 | .000 | 1.000 | .000 |

4 | .000 | .000 | .000 | 1.000 |

Sixth, principal component function analysis. The principal component of solvency is regarded as F1, the principal component of profitability as F2, the principal component of operating capacity as F3, and the principal component of growth capacity as F4. According to the score coefficient matrix of standardized processing of original variables, the matrix of calculation function is shown as Table 6 follows:

Coefficient matrix table of component scores

1 | 2 | 3 | 4 | |
---|---|---|---|---|

X1 | .079 | −.302 | −.321 | .167 |

X2 | −.017 | .363 | .004 | −.114 |

X3 | .225 | .255 | .208 | .089 |

X4 | −.339 | −.023 | −.003 | .007 |

X5 | .401 | .411 | .191 | .064 |

X6 | .396 | .115 | .253 | .030 |

X7 | .113 | −.008 | −.493 | .057 |

X8 | −.004 | −.289 | .377 | −.177 |

X9 | .104 | .216 | .098 | .899 |

X10 | −.043 | −.109 | .597 | .199 |

The corresponding score calculation function is:

Finally, after summary and analysis, the variance contribution rate of the four principal components is regarded as the coefficient of the evaluation score, and the weight is linearly weighted to the comprehensive, thus obtaining the following function:

According to the ranking results of the research enterprise among the peer listed enterprises, the details are shown in Table 7 below. An enterprise ranked 11th in the comprehensive score last year, which proves that the financial performance of the enterprise is at a low level among these companies. In addition to the principal component ranking of the growth ability, the principal components of the other three capabilities are in the middle and lower reaches of the industry. For example, in the principal component analysis of profitability, the average score of the enterprise studied in this paper is −0.0633, far lower than the average score of other enterprises, and accounts for 18.967% in the four principal component analysis, thus proving that the principal component analysis of profitability is also the main factor affecting the financial performance of enterprises. In the principal component analysis of enterprise growth ability, the actual score can reach 0.145, which is in the middle and lower reaches of the industry ranking, but there is a large room for improvement of the actual growth ability[7.8].

Score statistics of sample enterprises in 2020

The company referred to as | F1 | F2 | F3 | F4 | F | Comprehensive ranking |
---|---|---|---|---|---|---|

Sanhua intellectual control | 4.9681 | 2.2115 | 4.5898 | 0.026 | 3.0294 | 1 |

Han clock precision machine | 4.0291 | 3.0532 | 3.3143 | 1.0355 | 2.8166 | 2 |

Good try to | 3.5571 | 3.4277 | 2.561 | 0.0784 | 2.3579 | 3 |

Double liang energy-saving | 4.5730 | 2.6331 | 3.7981 | −2.9552 | 2.3981 | 4 |

Ice cold or hot | 2.8285 | 1.7479 | 5.1566 | −0.7148 | 2.2697 | 5 |

The vic | 2.6417 | 3.2867 | 3.0437 | 0.0047 | 2.2331 | 6 |

Moon co | 3.0747 | 2.8874 | 3.0775 | −2.092 | 1.9701 | 7 |

In accordance with the meters | 0.7784 | 0.1396 | 4.6653 | 0.0643 | 1.2696 | 8 |

Company | 0.9165 | 0.2155 | 1.7859 | 0.3764 | 0.7672 | 9 |

The peak of electronic | 2.9744 | −0.0583 | 2.7993 | −6.3473 | 0.5587 | 10 |

The snowman shares | 0.7498 | −0.0268 | 0.9747 | −0.8154 | 0.3109 | 11 |

First of all, to build a sound financial performance evaluation department. During financial performance appraisals, most of the data information is derived from financial statements, so it is considered the business of the accounting department. However, from the perspective of the development of enterprise organizational structure, based on the requirements of enterprise strategic management, the establishment of a comprehensive financial center, including the management of securities department, audit department, financial department and other staff, can effectively integrate and use department resources, and jointly participate in the evaluation of enterprise financial performance. The specific structure is shown in Figure 3 below:

Secondly, it is necessary to strengthen the professional quality of enterprise performance appraisal personnel. Financial performance evaluation work to by finance department personnel to carry out, so if the finance department personnel lack of professional knowledge and professional quality, so the actual financial performance evaluation work is bound to be problems, such as unscientific indicators, financial performance evaluation result is not accurate, etc., finally it is difficult to achieve the requirements of performance management. Therefore, enterprises should conduct comprehensive assessment when recruiting professionals, pay attention to regular training of internal financial personnel, encourage and support employees to learn professional knowledge and skills in salty fish time.

Finally, to strengthen the management level of enterprise financial performance. On the one hand, we must constantly optimize the capital structure. The capital structure of an enterprise will be affected by internal and external factors, among which internal factors involve enterprise scale, profit level, site capacity, asset structure and other contents. External factors include national economy, economic cycle, industry competition and so on. Generally speaking, the capital structure should put forward two levels of standards, one should be set according to their own development, and the other should pay attention to the target of leading enterprises in the industry, pay attention to the concept of building dynamic capital structure, so as to increase the current assets of enterprises, control the proportion of current liabilities, and control the debt ratio within a reasonable range. On the other hand, we should put forward a unified asset management system. It is necessary to not only put forward a perfect post responsibility system for fixed assets, but also arrange special personnel for control during use, integrate relevant maintenance indicators into performance assessment, and conduct regular or irregular inspection and management. Meanwhile, regular maintenance should be carried out for fixed equipment, and application equipment should be updated and optimized in time, so as to improve the application efficiency and overall operation level of fixed assets.[9]

To sum up, according to the research results and performance evaluation of enterprise financial system, find the problems existing in the enterprise financial performance management, optimizing the performance evaluation of enterprise financial system, promoting the comprehensive qualities of the performance evaluation of financial personnel, strengthen the application research of principal component analysis (pca), help enterprise during the period of construction management into a debt crisis, and to obtain more economic benefits in the practice exploration.

#### Score statistics of sample enterprises in 2020

The company referred to as | F1 | F2 | F3 | F4 | F | Comprehensive ranking |
---|---|---|---|---|---|---|

Sanhua intellectual control | 4.9681 | 2.2115 | 4.5898 | 0.026 | 3.0294 | 1 |

Han clock precision machine | 4.0291 | 3.0532 | 3.3143 | 1.0355 | 2.8166 | 2 |

Good try to | 3.5571 | 3.4277 | 2.561 | 0.0784 | 2.3579 | 3 |

Double liang energy-saving | 4.5730 | 2.6331 | 3.7981 | −2.9552 | 2.3981 | 4 |

Ice cold or hot | 2.8285 | 1.7479 | 5.1566 | −0.7148 | 2.2697 | 5 |

The vic | 2.6417 | 3.2867 | 3.0437 | 0.0047 | 2.2331 | 6 |

Moon co | 3.0747 | 2.8874 | 3.0775 | −2.092 | 1.9701 | 7 |

In accordance with the meters | 0.7784 | 0.1396 | 4.6653 | 0.0643 | 1.2696 | 8 |

Company | 0.9165 | 0.2155 | 1.7859 | 0.3764 | 0.7672 | 9 |

The peak of electronic | 2.9744 | −0.0583 | 2.7993 | −6.3473 | 0.5587 | 10 |

The snowman shares | 0.7498 | −0.0268 | 0.9747 | −0.8154 | 0.3109 | 11 |

#### Total variance interpretation table

Initial eigenvalue variance percent | Extract load square and variance percentage | Rotational load square and variance percent | |||||||
---|---|---|---|---|---|---|---|---|---|

composition | A total of | than | Cumulative % | A total of | than | Cumulative % | A total of | than | Cumulative % |

1 | 3.861 | 36.999 | 36.999 | 3.862 | 36.999 | 36.999 | 2.720 | 24.939 | 24.939 |

2 | 2.112 | 19.277 | 56.376 | 2.111 | 19.377 | 56.376 | 2.403 | 18.967 | 51.706 |

3 | 1.278 | 12.769 | 69.145 | 1.279 | 12.769 | 69.145 | 1.933 | 17.069 | 68.775 |

4 | 1.047 | 11.565 | 80.710 | 1.047 | 11.565 | 80.710 | 1.096 | 11.935 | 80.710 |

5 | .694 | 6.998 | 88.391 | ||||||

6 | .383 | 3.847 | 93.307 | ||||||

7 | .285 | 2.698 | 95.979 | ||||||

8 | .154 | 1.530 | 97.533 | ||||||

9 | .128 | 1.268 | 98.684 | ||||||

10 | .113 | 1.154 | 100.000 |

#### Common factor variance table

The initial | Extract | |
---|---|---|

X1 | 1.000 | .846 |

X2 | 1.000 | .811 |

X3 | 1.000 | .877 |

X4 | 1.000 | .853 |

X5 | 1.000 | .911 |

X6 | 1.000 | .804 |

X7 | 1.000 | .867 |

X8 | 1.000 | .892 |

X9 | 1.000 | .973 |

X10 | 1.000 | .562 |

#### Coefficient matrix table of component scores

1 | 2 | 3 | 4 | |
---|---|---|---|---|

X1 | .079 | −.302 | −.321 | .167 |

X2 | −.017 | .363 | .004 | −.114 |

X3 | .225 | .255 | .208 | .089 |

X4 | −.339 | −.023 | −.003 | .007 |

X5 | .401 | .411 | .191 | .064 |

X6 | .396 | .115 | .253 | .030 |

X7 | .113 | −.008 | −.493 | .057 |

X8 | −.004 | −.289 | .377 | −.177 |

X9 | .104 | .216 | .098 | .899 |

X10 | −.043 | −.109 | .597 | .199 |

#### Matrix table of component score covariance

Composition | 1 | 2 | 3 | 4 |
---|---|---|---|---|

1 | 1.000 | .000 | .000 | .000 |

2 | .000 | 1.000 | .000 | .000 |

3 | .000 | .000 | 1.000 | .000 |

4 | .000 | .000 | .000 | 1.000 |

#### The meaning of financial indicators

Indicators | Meaning |
---|---|

Return on equity X1 | Net profit/average balance of shareholders’ equity *100% |

Net margin on sales X2 | Net profit/net operating income *100% |

Gross margin on sales X3 | Gross profit on sales/net operating income *100% |

Asset-liability ratio X4 | Liabilities/Assets *100% |

Current ratio X5 | Current assets/current liabilities |

Quick ratio X6 | (Current assets - Inventory)/current liabilities |

Inventory turnover X7 | Cost of sales/average inventory balance |

Accounts receivable turnover X8 | Net credit sales/average balance of accounts receivable |

Profit growth rate X9 | (Net profit of current period - net profit of the same period of last year)/Net profit of the same period of last year *100% |

Growth rate of assets X10 | (Asset ending value of current period - initial value of asset of current period)/Initial value of asset of current period *100% |

#### Test results

0KMO sampling suitability quantity | .630 | |
---|---|---|

Badlett sphericity test | The approximate chi-square | 355.037 |

Degrees of freedom | 46 | |

significant | .000 |

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the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in 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 Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model