At present, many companies have recognized the importance of tax issues, and a few have recognized the existence of tax risks, and have tried their best to reduce their tax risks by improving the financial staff's business quality and employing tax consultants. The famous “Hain's Law” states: There are signs behind the accident, and there are signs behind the signs.

It is precisely because companies do not pay much attention to tax risks that have caused serious consequences. The early warning of tax risks is to find potential tax risks of the enterprise by judging the signs and signs before the occurrence of tax risks, and ask the enterprise management authorities to take corresponding measures to prevent problems before they occur [1].

According to PwC survey data, China is the country with the biggest tax challenges in Asia. In addition to traditional financial risks and operational risks, each enterprise faces different levels of tax risks. Due to the complexity of China's tax law, the tax risks of enterprises have been increased, which has proposed for the construction of tax risk research and early warning mechanisms. For urgent needs. The research on tax risks can be viewed from the perspective of tax authorities or from the perspective of enterprises. This article is from the perspective of the enterprise, analyses the possible tax risks of the enterprise, and uses relevant indicators and models to establish a scientific and effective early warning mechanism for tax risks [2].

This paper uses a combination of quantitative analysis and qualitative analysis. On the one hand, it analyses various tax risks and sizes of enterprises from a qualitative perspective; on the other hand, it uses a quantitative value to measure tax risks, and establishes a tax risk early warning mechanism through early warning indicators. In the specific analysis, the marginal analysis of classical economics is used to illustrate the principle of achieving the goal of the early warning mechanism. The method of geometric figures is used to discuss the impact of risk appetite on the early warning mechanism of tax risk. The form of scoring is used to directly display the operation of early warning of tax risk. Process [3]. The original meaning is to recognize the logical sequence of things as the basic structure. Based on the definition of legal risk and early warning, the mechanism analysis of the tax risk early warning mechanism was carried out based on this. Under the condition that the preparatory work was completed, the core part of this article introduced the tax risk early warning indicators and established the corresponding Tax risk early warning mechanism. Finally, the article verifies the construction of the tax risk early warning mechanism with a specific case, and concludes the full text with this.

Tax risk belongs to the category of risk. Before understanding tax risk, it is necessary to clarify what is risk. In 1895, the American scholar Hayes gave a definition of risk from the perspective of economics. He believed that risk is “the possibility of loss”; uncertainty of probability random events is risk. Risks will only occur when there are two or more possibilities for an activity, and the occurrence of risks usually brings some form of loss. Therefore, tax risk is an uncertainty faced by enterprises in all tax-related activities, such as enterprises being inspected by tax authorities, bearing excessive tax liabilities, or incurring liabilities for tax reimbursement and fines. For the production and operation of an enterprise, the pursuit of profit is an eternal theme, but the profit of the enterprise must be controlled within an acceptable risk range. If the profit has a high risk, the enterprise will have the hidden danger of failure [4].

Tax risk has tax uncertainty. Uncertainty is the basis for tax risks. Without uncertainty, risks will not arise, and tax risks will be even more difficult to talk about. In the process of production and operation, enterprises are faced with a variety of decisions. Each decision is the result of a cost-benefit balance. The tax liability is the embodiment of each decision in tax law. Different decisions cause different tax burdens, and even the same decision will have different tax burdens due to different subjective reasons of the taxpayer and objective reasons of the external environment [5]. It should be noted that less tax and delayed taxation have tax risks, and more taxation and early taxation also have tax risks. Less tax payment and delayed tax payment means that failure to pay taxes on time and amount will be punished by tax authorities for late fees and fines, resulting in outflow of economic benefits and reduction of corporate value. By the same token, multiple taxation and early taxation will directly lead to the outflow of economic benefits and time value, reduce corporate value, and cause tax risks.

The generation of corporate tax risks is not caused overnight, but is a process of long-term accumulation and gradual development. In the entire development process of corporate tax risks, although these risks will show different tax characteristics, this performance may not be very significant and clear, and some may even be potential, but once it develops rapidly, it will It may enter a complete tax risk state immediately, leading to serious consequences, so the tax risk early warning requires research on the tax-related characteristics exhibited by the enterprise at different stages [6].

The formation of corporate tax risks should be divided into the following four main stages, and exhibit different characteristics. That is: tax risk incubation stage, tax risk development stage, tax risk deterioration stage and tax risk explosion stage. The different characteristics of these four stages can be described with the following figure.

In college physical education, martial arts have attracted more and more college students because of its unique charm and exercise value. In martial arts, it is easy to cause ligament damage and meniscus injury and aging. After severe meniscus injury or aging degeneration, a total meniscectomy is required. In order to prevent the degeneration of articular cartilage and subchondral bone in meniscectomy patients, try their best to maintain the normal biomechanical function of the knee joint. Plate transplantation has gradually become a new treatment approach. In this meniscus transplantation, in addition to the type matching of the meniscus transplantation, the reasonable fixation of the meniscus transplantation is another key issue in the transplantation operation. Related studies have confirmed that insufficient fixation of the anterior and posterior angles of the meniscus transplantation will cause Knee function degeneration after meniscus transplantation [7].

Tax risk belongs to the category of risk. Before understanding tax risk, it is necessary to clarify what is risk. In 1895, the American scholar Hayes gave a definition of risk from the perspective of economics. He believed that risk is “the possibility of loss”; uncertainty of probability random events is risk. Risks will only occur when there are two or more possibilities for an activity, and the occurrence of risks usually brings some form of loss. Therefore, tax risk is an uncertainty faced by enterprises in all tax-related activities, such as enterprises being inspected by tax authorities, bearing excessive tax liabilities, or incurring liabilities for tax reimbursement and fines. For the production and operation of an enterprise, the pursuit of profit is an eternal theme, but the profit of the enterprise must be controlled within an acceptable risk range. If the profit has a high risk, the enterprise will have the hidden danger of failure [8].

Tax risk has tax uncertainty. Uncertainty is the basis for tax risks. Without uncertainty, risks will not arise, and tax risks will be even more difficult to talk about. In the process of production and operation, enterprises are faced with a variety of decisions. Each decision is the result of a cost-benefit balance. The tax liability is the embodiment of each decision in tax law. Different decisions cause different tax burdens, and even the same decision will have different tax burdens due to different subjective reasons of the taxpayer and objective reasons of the external environment. It should be noted that less tax and delayed taxation have tax risks, and more taxation and early taxation also have tax risks. Less tax payment and delayed tax payment means that failure to pay taxes on time and amount will be punished by tax authorities for late fees and fines, resulting in outflow of economic benefits and reduction of corporate value. By the same token, multiple taxation and early taxation will directly lead to the outflow of economic benefits and time value, reduce corporate value, and cause tax risks.

The generation of corporate tax risks is not caused overnight, but is a process of long-term accumulation and gradual development. In the entire development process of corporate tax risks, although these risks will show different tax characteristics, this performance may not be very significant and clear, and some may even be potential, but once it develops rapidly, it will It may enter a complete tax risk state immediately, leading to serious consequences, so the tax risk early warning requires research on the tax-related characteristics exhibited by the enterprise at different stages [9].

The formation of corporate tax risks should be divided into the following four main stages, and exhibit different characteristics. That is: tax risk incubation stage, tax risk development stage, tax risk deterioration stage and tax risk explosion stage. The different characteristics of these four stages can be described with the following figure.

Through the description of the above four stages of tax risk, although not all the companies used have behaved this way most of the companies in financial crisis are similar, and they are widely universal. It's just that different enterprises have different reasons for generating tax risk crises, so the performance of these crisis characteristics are different, or they focus more on the performance of one or more crisis characteristics.

The stochastic model originated from the study of optimal cash holdings in financial management. In tax risk early warning, this model is also instructive. In the random mode shown in the figure below, the horizontal axis represents time, and the vertical axis represents the size of tax risk. As time changes, tax risk is high and low. For enterprises, risk and return are positively related. The higher the risk, the better, and not the lower the better. Theoretically, there should be an optimal level of tax risk. The constant degree of tax risks can only control tax risks within a feasible range. Assume that the straight-line R is the optimal amount of tax risk for the enterprise, the straight-line H is the upper limit of the tax risk allowed by the enterprise, and the straight-line L is the lower limit of the tax risk that the enterprise is willing to bear. When the tax risk reaches H, the early warning system issues a warning, and the enterprise adjusts the tax risk to the optimal position R. When the tax risk reaches L, the early warning system also issues an alarm, and the enterprise adjusts the tax risk to the state R.

As a kind of management behaviour of an enterprise, the tax risk early warning mechanism should serve the overall objective of the enterprise-maximizing the value of the enterprise. As mentioned earlier, because the situation of each enterprise is different, it is impossible to force each enterprise to establish a sound tax risk early warning mechanism. When considering whether and how to establish a tax risk early warning mechanism, we should pay attention to the actual situation of the enterprise and Consider the cost-benefit principle. In order to understand the realization of the objectives of the tax risk early warning mechanism, the following three questions need to be answered: First, should the enterprise establish a tax risk early warning mechanism? Second, how complete should the tax risk warning mechanism itself be? Third, what level should the tax risk early-warning mechanism control the tax risk of the enterprise? Figure 3 shows the scheme of tax risk early warning mechanism [10].

Convergence and Stability of Ordinary Differential Equation Algorithm

The general form of the explicit one-step method of the above formula is

Where
_{n}_{n}_{n}_{n}_{n}_{n}

Approach

It is possible to approximate the solution to the problem. Therefore, we expect that for any fixed

If the increment function

If relation

If it is true, it is said that the one-step method (3) is compatible with the initial value problem of differential equations, as shown in Figure 4 [11].

It is easy to verify that both the Euler method and the improved Euler method satisfy the compatibility conditions. In fact, for the Euler method, the incremental function is

The compatibility condition is naturally satisfied, and the incremental function of the improved Euler method is

Because

So, Euler's method and modified Euler's method are compatible with the initial value problem. Generally, if the single-step method is shown to have p-order accuracy (

Divide both ends of the above equation by h to get _{n + 1} → 0 and

Therefore, the display single-step method of

Where

The convergence of a numerical method needs to be determined based on the global truncation error _{n + 1} of the method. The global truncation error of the known Euler method has an estimated formula

When _{n + 1} → 0,, the Euler method converges.

It is assumed that the explicit single-step method has p-order accuracy, and its incremental function _{0}) = _{0}, the overall truncation error of the explicit single-step method is

Assuming that the increment function

If there are normal numbers _{0} and C, such that for any initial starting value _{0}, _{0}, the corresponding exact solution _{n}_{n}_{0}, there is always

It is said that the single step method is stable.

If _{0}], and all real numbers y, with respect to lip satisfying the Lipschitz condition, then the one-step method (19) is stable.

For a given differential equation and a given step size h, if there is an error of size _{n}_{m}

Generally limited to typical differential equations

Consider the absolute stability of the numerical method, where

The Euler method, improved Euler method, and Runge-Kutta were used to solve the initial value problem.

Take equal scores as N = 12, 24, 36, 120, respectively, and calculate the maximum error from the real solution. Euler's method algorithm: After calculation, we can get the maximum error between the numerical solution and the real solution when the initial value problem is not taken as shown in Table 1.

Maximum error between Euler method numerical solution and real solution

N (Equal score) | Maximum error | N (equal fraction) | Maximum error |
---|---|---|---|

12 | 0.026320 | 72 | 0.004052 |

24 | 0.012547 | 84 | 0.003465 |

36 | 0.008233 | 96 | 0.003027 |

48 | 0.006126 | 108 | 0.002687 |

60 | 0.004878 | 120 | 0.002416 |

From the running results of the program recorded in Table 1, when the equal score N becomes larger, its error is decreasing. According to the definition we can prove that the method is convergent.

Improved Euler's method: After calculation, we can get the maximum error between the numerical solution and the real solution when the initial value problem is not taken as shown in Table 2.

Maximum error between the numerical solution and the true solution of the improved Euler method

N (Equal score) | Maximum error | N (Equal score) | Maximum error |
---|---|---|---|

12 | 0.001023 | 72 | 0.000028 |

24 | 0.000255 | 84 | 0.000021 |

36 | 0.000113 | 96 | 0.000016 |

48 | 0.000063 | 108 | 0.000013 |

60 | 0.000041 | 120 | 0.000010 |

From the program running results recorded in Table 2, when the equal score N becomes larger, its error is decreasing. According to the definition, we can prove that the method is convergent.

Runge-Kutta algorithm: After calculation, we can get the maximum error between the numerical solution and the real solution when the initial value problem is not taken as shown in Table 3.

Maximum error between Runge-Kutta numerical solution and real solution

N (Equal score) | Maximum error | N (Equal score) | Maximum error |
---|---|---|---|

12 | 0.000001 | 72 | 0.000000 |

24 | 0.000000 | 84 | 0.000000 |

36 | 0.000000 | 96 | 0.000000 |

48 | 0.000000 | 108 | 0.000000 |

60 | 0.000000 | 120 | 0.000000 |

From the program running results recorded in Table 3, when the equal score N becomes larger, its error is decreasing. According to the definition, we can prove that the method is convergent.

In order to compare the convergence speeds of the above three methods, we have calculated their minimum equal fraction N with an error accuracy of 10-5 as shown in Table 4 below.

Convergence speed comparison

Method | N (Minimum grade) | Error accuracy |
---|---|---|

Euler method | 2900 | 10-5 |

Improved Euler's method | 40 | 10-5 |

Runge-Kutta method | 5 | 10-5 |

From the running results of the programs recorded in Table 4, the Runge-Kutta method has the fastest convergence speed, followed by the improved Euler method, and the Euler method is the worst. From this point, the Runge-Kutta method is the most ideal numerical solution among them.

The author believes that the relationship between the tax risk attitude of corporate managers or shareholders and the early warning of tax risks is reflected in the following: Tax risk appetite is willing to accept higher tax risk levels and expect higher returns, and usually sets the threshold for tax risk early warning. Slightly higher; on the contrary, tax risk aversion is willing to bear a lower level of tax risk and can get lower expected returns, generally the tax risk early warning threshold is determined to be more conservative; while the tax risk neutral is between the two [14].

If the management of a company ignores tax risk management or believes that there is no tax risk if it operates legally, then the company loses its management basis for tax risk control. Therefore, the support of the manager is the fundamental condition for the company to carry out tax risk management.

The company's business process determines the company's applicable taxes, tax rates, tax methods, etc. Therefore, the company's financial staff must analyse the company's business process with the business staff, including: 1, tax analysis of various sales processes; 2, various purchases Analysis of the tax situation of the process; 3. Analysis of the tax situation of special business processes.

Only by regularly auditing the company's tax, the company can discover the tax issues facing the company in advance, and control the tax risks in the bud. Including: 1, auditing sales and collection business processes; 2, auditing procurement and payment business processes; 3, auditing the authenticity and legality of related documents; 4, auditing the use of related tax benefits; 5, special taxes (personal income tax Stamp duty).

The audit of the company's tax before the annual settlement can adjust the accounting for the problems found in the audit before the annual settlement. The impact of this process on corporate income tax is far-reaching. From the analysis of some previous cases, we have found that cases of overpayment of income tax by the company are not uncommon in practice due to the failure to implement the annual tax pre-check procedures.

Don't think that the tax bureau is a bad thing to check the accounts, you must know that the tax staff is responsible for checking the accounts, just like the company employees must go to work. Only by understanding and supporting their work can tax risks be better reduced. In some laws and regulations dealing with ambiguous tax issues, strengthening communication can better solve this problem.

The requirements and changes of the macro-environment are the important reasons that cause enterprises to face tax risks. Therefore, companies should:

Study the macro environment. Although the external macro-environment exists outside the enterprise and cannot be changed, the enterprise can adapt to changes in the environment by adjusting its own operating behaviour. For example, analysis and research on the changing external macro environment, especially analysis and research on national industrial policies, industry policies, relevant laws and regulations, market changes, new products, new technologies, and changes in the international situation, and keep abreast of changes. Understand the trends and laws of the environment, understand and analyse the impact of environmental changes on the production and operation of the enterprise, and fully consider the possibility, severity and impact of changes in the macro environment that make the enterprise face tax risks. If it affects the overall tax burden of the enterprise, how long will the existence of tax risks affect its performance How much influence the indicator has, and so on [15].

Take effective measures. Aiming at the various risks that enterprises may face, on the premise of being proficient in grasping relevant tax-related laws and regulations, and understanding the taxpayer's financial situation and requirements, timely formulate various contingency measures[16], and monitor the development form and status of their production and operation behaviours, Timely feedback. Reflect situations that may occur or are not in line with expectations, and adjust their business goals and implementation processes in a timely manner, in order to reduce the tax risks brought to the enterprise due to the uncertainty of the macro environment through risk prevention and management, and improve risk prevention benefit[17].

When each early-warning indicator shows different evaluation values, tax risks are in different areas. Enterprises should adopt different strategies to deal with tax risks and control tax risks within an acceptable range. The early warning of tax risks is not the goal of an enterprise. The real purpose of an enterprise is to discover the operating situation of corporate tax risks in a timely manner by means of early warning of tax risks, and use various effective measures to deal with tax risks, and ultimately maximize the value of the enterprise. Of course, the above-mentioned tax risk early-warning mechanism is not a panacea and cannot be applied to every enterprise. Enterprises should make appropriate changes based on the above-mentioned core early-warning indicators according to their own special circumstances, so that the tax risk early-warning mechanism is stubborn. Vitality and broad applicability.

#### Maximum error between Euler method numerical solution and real solution

N (Equal score) | Maximum error | N (equal fraction) | Maximum error |
---|---|---|---|

12 | 0.026320 | 72 | 0.004052 |

24 | 0.012547 | 84 | 0.003465 |

36 | 0.008233 | 96 | 0.003027 |

48 | 0.006126 | 108 | 0.002687 |

60 | 0.004878 | 120 | 0.002416 |

#### Maximum error between the numerical solution and the true solution of the improved Euler method

N (Equal score) | Maximum error | N (Equal score) | Maximum error |
---|---|---|---|

12 | 0.001023 | 72 | 0.000028 |

24 | 0.000255 | 84 | 0.000021 |

36 | 0.000113 | 96 | 0.000016 |

48 | 0.000063 | 108 | 0.000013 |

60 | 0.000041 | 120 | 0.000010 |

#### Maximum error between Runge-Kutta numerical solution and real solution

N (Equal score) | Maximum error | N (Equal score) | Maximum error |
---|---|---|---|

12 | 0.000001 | 72 | 0.000000 |

24 | 0.000000 | 84 | 0.000000 |

36 | 0.000000 | 96 | 0.000000 |

48 | 0.000000 | 108 | 0.000000 |

60 | 0.000000 | 120 | 0.000000 |

#### Convergence speed comparison

Method | N (Minimum grade) | Error accuracy |
---|---|---|

Euler method | 2900 | 10-5 |

Improved Euler's method | 40 | 10-5 |

Runge-Kutta method | 5 | 10-5 |

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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 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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 Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language 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 Design and evaluation of intelligent teaching system on basic movements in PE 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 Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function 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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 Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System 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 Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -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 Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on 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Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network