Science and technology are the primary productive forces, and technological innovation is the driving force for enterprise development. The key to the development and growth of an enterprise lies in its core competitiveness, and the core support for an enterprise to adapt to the development and changes of the environment is technological innovation. High-tech enterprises are emerging enterprises with huge potential for technological innovation and development. Under the background of technological revolution and technological innovation on a global scale, high-tech enterprises should seize business opportunities and seek innovative development[1]. The unique characteristics of high-tech enterprises make them different from ordinary enterprises in terms of production, operation and growth, they are high in technology, knowledge-intensive, high-input, high-growth, high-risk, and high-income, the development of technological innovation has led to great changes in corporate performance [2]. Therefore, the author chooses high-tech enterprises as the research object, and then discusses how to enhance their core competitiveness and improve their performance through technological innovation. Digital signal processing technology has been widely used in various industries in recent years, mainly due to its ability to convert many analog information, such as sound or pictures, to digital information, it can meet the digital development requirements in the field of computer or other industrial machinery and equipment [3]. At the same time, after the emergence of DSP processor, the processed information can also be output in the form of analog information, which has strong practicability [4]. Therefore, it is of great significance to analyze the application and development of digital signal processing technology. In response to this research problem, Dewanthikumala, Jasruddin and others took pharmaceutical companies in listed companies as the research object, collected their patent application data, and concluded that the increase in the number of patent applications will lead to the continuous improvement of corporate profitability [5]; Kumar D G et al. used the annual number of patent applications to measure the impact of technological innovation on enterprise performance, and empirically found that the two are significantly positively correlated [6]; When Liu J et al. studied the impact of technological innovation of listed manufacturing companies on enterprise performance, they used invention patents, design patents and utility model patents to reflect technological innovation indicators, the results show that different types of patents have different effects on performance, and the impact of utility model patents on enterprise performance is weaker than that of the other two types of patents [7]. Based on the current research, the author proposes to use digital signal processing, and multiple regression analysis to study the financial distressed company forecasting system. Firstly, the research method is designed, Logistic regression model is the most commonly used multivariate statistical method when modeling binary dependent variables, it can solve the problem of nonlinear classification, there is no specific requirement for the distribution of variables, and the accuracy of judgment is high. The author selects 32 financial ratios from the perspectives of solvency, operating ability, profitability, development ability, per share index, and risk level. Taking special treatment (ST) due to abnormal financial status as a sign of financial distress in listed companies, when selecting samples, the matching principle is adopted to select non-ST companies as matching samples. Two methods of logistic regression and support vector machine are used for empirical testing, and both in-sample testing and out-of-sample prediction are performed.

In the study of financial distress forecasting, domestic and foreign scholars have adopted a variety of methods and techniques, it is mainly divided into two categories: one is the discriminant classification method based on statistical model, such as linear discriminant analysis, Logistic regression, Probit regression, etc.; The second is artificial intelligence methods, such as decision trees, artificial neural networks, support vector machines, evolutionary computing, etc. In order to examine the role of the textual quantitative indicators constructed by the authors in predicting financial distress, in order to ensure the robustness of the research conclusions, the authors chose the above two types of methods, the most widely used and most representative logistic regression and support vector machines are used for empirical analysis [8].

Logistic regression model

(1) Among the traditional statistical methods of credit risk early warning, logistic regression is the most commonly used multivariate statistical method for modeling binary dependent variables, which can solve the problem of nonlinear classification, there are no specific requirements for the distribution of variables, and the accuracy of the judgment is relatively high. The general form is as follows:

Where _{i}_{i}

(2) Support vector machine

Support vector machine is a classification method based on statistical learning theory, it has many advantages in solving small sample, nonlinear and high-dimensional pattern recognition, its purpose is to construct a hyperplane, maximize the margins between the two classes in the high-dimensional feature space, its advantage is to use the kernel function to provide a classification model with high accuracy, and to avoid the over-adaptation of the model with the help of regular terms, while avoiding the influence of local optima and multiple collinearity [9]. The optimization problem solved by the support vector machine is as follows:

Where i=1, 2,., M, _{i}_{i}_{i}^{T} · _{j}_{i}_{j}

Financial ratios are the basic variables for predicting the financial distress of listed companies, on the basis of combining existing literature and considering the availability of data, the author selects 32 financial ratios from the perspectives of solvency, operating ability, profitability, development ability, per share index, risk level, etc, including fixed asset ratio (FIX), current ratio (CURRENT), quick ratio (ACID), working capital (WC), interest coverage ratio (INTEREST), net cash flow from operating activities/current liabilities (CASH), cash flow interest coverage multiple (CINTEREST), asset-liability ratio (LEV), tangible asset-liability ratio (TLEV), equity multiplier (EM), equity Ratio (EQUITY) Equity/Liability (ED), Total Assets Growth Rate (AGROWTH), Equity Growth Rate (EGROWTH), Financial Leverage (FL), Operating Leverage (OL), Comprehensive Leverage (CL), operating cycle (0C), total asset turnover (TAT), earnings per share (EPS), operating income per share (OIPS), operating profit per share (OPPS), net assets per share (BPS), retained earnings per share (REPS), net cash flow from operating activities per share (CPS), net cash flow per share (NCPS), return on invested capital (RIA), return on assets (ROA), net interest rate on assets (JROA), return on Equity (ROE), Operating Profit Margin (OPM) and Total Operating Cost Ratio (OCR) [11].

(1) Extraction method of feature words

Due to the company's operating and financial conditions, the wording and style of its disclosure text will be affected, the author uses the R language open source segmentation tool JiebaR to perform word segmentation, and then uses the chi-square test method to select feature words that can distinguish financial distressed companies from normal companies. N represents the total number of documents in the training corpus, and A represents the frequency of documents belonging to the _{j}_{i}_{j}_{i}_{j}_{i}

According to the critical value of one degree of freedom of the chi-square distribution, it can be determined whether the feature word _{i}

(2) Weight setting of feature words

Considering the relative importance of feature words in classification, the weights are set by extending the term frequency inverse document frequency (TFHDF, Term Frequency Inverse Document Frequency). The weight _{i}_{i}

Where j represents documents, k and l represent categories, _{ijk}

(3) Construction of Default Propensity Index Based on Text Analysis

By selecting feature words and setting their weights, the feature words contained in each information disclosure text can be counted, from this, the Tendency toward Default (TTD, Tendency toward Default) indicator based on text analysis can be constructed:

Where _{j}_{i}_{i}_{i}_{i}

In the fields of test instruments and measuring instruments, digital signal processing technology can also be used, which can improve the function of products. High-end single-chip microcomputer in traditional equipment, gradually replaced by this technology, the rapid development of digital signal processing technology, its internal resources are now very rich, which can not only simplify the hardware circuit on the instrument, but also further improve the reliability, precision and accuracy of instrument measurement. Programmable digital signal processing technology is widely used in the field of personal computers, which can combine Motion Picture Experts Group and high-speed communication technology, and can convert audio and video formats. The computers we usually use are based on digital signal processing technology, handles a variety of versatile, multi-modal digital signal processors. The application of this technology in the field of shortwave communication is mainly manifested in analyzing link quality, processing audio signals, detecting and scanning channels, and realizing channel digitization. The principle is that after processing the front-end RF signal, the digital signal module will analyze and process the intermediate frequency signal of the input digital signal, then output the audio signal, and ensure that the AGC control signal and the baseband signal are digitally quantized. The AGC control signal can reflect the digital baseband signal and the gain of the amplifier signal, providing a reference for the analysis of spectrum and waveform, and the terminal equipment can also make full use of the signal to achieve the goal of reducing the noise of the analog signal. The mode adopted in the design of hardware structure in the module mainly combines AD, PDC and DSP, after completing the amplification and filtering process, the intermediate frequency signal is input into the high-speed modulus to complete the quantization purpose, when the programmable inverter is used to filter and decelerate the signal, it will output a spectrum of a certain component, at this time, through the conversion of the signal, the analog signal for the end user will be output.

The author takes special treatment (ST) due to abnormal financial status as a sign of financial distress in listed companies, and adopts the matching principle to select non-ST companies as matching samples when selecting samples. In order to ensure the robustness of the empirical results, the authors follow the same industry, based on the principle of similar asset size, non-ST companies are selected as matching samples, and the matching ratios are selected according to 1:1 and 1:2 respectively. Since the annual report of a listed company is prepared and released within 4 months of the end of the year, the release of the annual report of year t-1 occurs at the same time as whether it is specially treated in year t, to this end, the author uses the data of listed companies in t-2 years to build a model to predict whether they will have credit risk in year t. Based on the above conditions, the author selected 199 listed companies that were listed by ST from 2016 to 2021 as a sample of financially distressed companies, according to the principle of similar industries and similar scales, 398 non-ST companies were selected as matched normal company samples, the corresponding data period is from 2014 to 2020. Considering that enough samples should be considered for the selection of feature words, regardless of whether the ratio of financially distressed companies to normal companies in the empirical analysis is 1:1 or 1:2, the author selects feature words based on all samples. After preprocessing and word segmentation, when selecting feature words, since the chi-square test is difficult to exclude some words that cannot distinguish financially distressed companies from normal companies, such as “cash flow”, “operating activities”, “investors”, “management measures”, “suppliers”, “subsidiaries” and other common accounting or industry terms, therefore, the author screened the words that passed the chi-square test, finally, 93 characteristic words of financial distressed companies and 98 characteristic words of normal companies were selected, then calculate the weight of each feature word.

The financial data in this article are all from the Guotai'an database, and the annual report is from the

Regarding the role of default propensity index in predicting financial distress, the author uses two methods of logistic regression and support vector machine to conduct empirical test, and conducts in-sample test and out-of-sample prediction at the same time. First, the training set and the test set are not distinguished, and the in-sample test is carried out with all samples (in two ratios of 1:1 and 1:2), the models are modeled according to the two situations before and after adding the default propensity indicator (TTD); Then, 139 ST companies and paired samples from 2016 to 2021 were selected as the training set, and two methods were used for modeling, taking the samples of 60 ST companies and paired normal companies from 2016 to 2017 as the test set, the accuracy of the model in predicting financial distress is compared and analyzed. There are three main judgment criteria: First, whether the addition of TTD can improve the overall accuracy of classification (Accuracy); The second is whether the addition of TTD can reduce the probability of Type I error (Type I error, identifying ST company as a normal company) and Type II error (Type II error, identifying a normal company as ST company); The third is whether the addition of TTD can improve the AUC (Area Under Curve) of the receiver operating characteristic curve (ROC, Receiver Operating Characteristic Curve), AUC is calculated according to the probability that the sample is predicted to be ST based on the modeling result, and the value ranges from 0.5 to 1, the larger the value, the better the fitting effect of the in-sample model or the accuracy of the out-of-sample prediction.

When using Logistic regression analysis, the author applies stepwise regression method to eliminate insignificant variables, firstly, the Tendency to Default Index (TTD) is not considered, and then this index is added to compare and analyze the fitting degree and predictive ability of the mode, at the same time, according to whether the propensity to default indicator (TTD) will be eliminated in the process of gradual regression, we can judge its role in the construction of financial distress model.

Table 1, Figure 1 shows the out-of-sample prediction results of the logistic stepwise regression. It can be seen from Table 1 that when the ratio of ST company to normal company is 1:1, the addition of the Tendency to Default Index (TTD) has improved the AUC and overall accuracy to a certain extent, both the first and second types of errors have been reduced, and the reduction of the first type of errors is more obvious; After increasing the matching ratio and increasing the number of normal companies, the improvement of the prediction effect by the addition of the propensity to default indicator (TTD) decreased, but it can also improve the overall accuracy and AUC, reduce the first type of error and the second type of error, again, the reduction in Type 1 error is more pronounced. It can be seen that when using the logistic regression method, the propensity to default indicator (TTD) reflected in the text content, it can indeed improve the out-of-sample prediction accuracy of the financial distress prediction model, and it is consistent with the in-sample test, this is mainly reflected in the reduction of the first type of error, that is, the probability of misjudging a financial distressed company as a normal company.

Out-of-sample prediction results of Logistie regression

1:1 ratio | 1:2 ratio | |||
---|---|---|---|---|

Do not join TTD | Join TTD | Do not join TTD | Join TTD | |

AUC | 91.80% | 93.05% | 90.01% | 90.14% |

Type I error | 13.32% | 6.66% | 18.32% | 13.32% |

Type II error | 18.32% | 16.66% | 15.82% | 15.01% |

Accuracy | 84.16% | 88.32% | 83.32% | 85.55% |

When using support vector machine modeling and analysis, in order to judge the relative importance of the propensity to default indicator (TTD) and financial ratio variables to model financial distress forecasts, the author introduces sensitivity analysis method to calculate the relative importance of each variable before and after adding TTD, and conducts in-sample test, then, the out-of-sample prediction ability of SVM before and after adding TTD is compared and analyzed.

Table 2, Figure 2 presents the results of the SVM within-sample test. As can be seen from Table 2, when the sample ratio is small, the overall accuracy of the support vector machine is higher, mainly because the probability of the first type of error is relatively much lower, after the sample ratio is enlarged, the probability of Type 1 error is significantly improved; After adding the propensity to default indicator (TTD), regardless of the proportion, the probabilities of both the first type of error and the second type of error have been reduced, and the reduction of the first type of error will be relatively more significant, at the same time, the overall accuracy and AUC also have a certain degree of improvement. From the results of the sensitivity analysis, the change of the proportion of the ratio has little effect on the relative importance of the financial ratio variable when using support vector machine modeling, the propensity to default indicator (TTD) entered the top ten important variables in both proportions, and when the ratio is 1:2, it ranks fourth in all indicators, and the importance increases significantly. It can be seen that when the support vector machine is used to build a financial distress prediction model, the propensity to default indicator (TTD) has played an important role.

In-sample test results of support vector machines

1:1 ratio | 1:2 ratio | |||
---|---|---|---|---|

Do not join TTD | Join TTD | Do not join TTD | Join TTD | |

AUC | 95.73% | 96.82% | 94.70% | 96. 32% |

Type I error | 6.02% | 4.51% | 16.07% | 14.56% |

Type II error | 9.03% | 8.53% | 8.28% | 7.53% |

Accuracy | 92.45% | 93.46% | 89.10% | 90.11% |

Table 3, Figure 3 presents the results of SVM out-of-sample prediction. As can be seen from Table 3, also, when the sample proportion is small, the overall accuracy of the support vector machine is higher, and after the sample proportion is enlarged, the probabilities of both types of errors are significantly improved; From the impact of the addition of propensity to default (TTD), when the ratio is 1:1, significantly reduces the probability of type 2 errors, AUC has also been significantly improved, and the overall accuracy has been greatly improved, however, after the proportion is enlarged, its impact is reduced, and the impact on Type II errors is small, it just reduces the probability of type 1 error. Overall, in the case of using the support vector machine method, add the Tendency to Default Index (TTD) reflected by the text information, it can also improve the accuracy of financial distress prediction models.

Out-of-sample prediction results of support vector machines

1:1 ratio | 1:2 ratio | |||
---|---|---|---|---|

Do not join TTD | Join TTD | Do not join TTD | Join TTD | |

AUC | 92.96% | 99.82% | 92.11% | 92.14% |

Type I error | 3.32% | 3.32% | 16.65% | 15.01% |

Type II error | 12.51% | 3.32% | 12.51% | 12.51% |

Accuracy | 90, 82% | 96.66% | 86.10% | 86.65% |

The author proposes a study on the prediction of corporate financial distress by digital signal processing and multiple regression analysis, the authors used the chi-square test method, through a comparative analysis of the content of the management discussion and analysis texts of financial distressed companies and normal companies' annual reports, feature words reflecting financial distressed companies and normal companies are extracted, by extending the term frequency-inverse document frequency (TF-IDF), the feature word weights are set to construct the company manager's default tendency index (TTD), the default propensity indicator is then combined with financial variables, logistic regression and support vector machine methods were used, respectively, for empirically test whether the default propensity indicator can improve the accuracy of financial distress prediction, the results show, default propensity indicator reflected by text content, it can indeed improve the fit and prediction accuracy of the financial distress prediction model, reduce the Type 1 error rate and Type 2 error rate where false positives occur. However, the author's research is limited to listed companies, and it is difficult to apply to non-listed companies, but for these companies, it can be achieved by mining and analyzing the text content of news reports, social media and other channels, of course, since the text information of these channels comes from outside the enterprise, further research is needed on the selection of specific methods and technologies.

#### Out-of-sample prediction results of Logistie regression

1:1 ratio | 1:2 ratio | |||
---|---|---|---|---|

Do not join TTD | Join TTD | Do not join TTD | Join TTD | |

AUC | 91.80% | 93.05% | 90.01% | 90.14% |

Type I error | 13.32% | 6.66% | 18.32% | 13.32% |

Type II error | 18.32% | 16.66% | 15.82% | 15.01% |

Accuracy | 84.16% | 88.32% | 83.32% | 85.55% |

#### In-sample test results of support vector machines

1:1 ratio | 1:2 ratio | |||
---|---|---|---|---|

Do not join TTD | Join TTD | Do not join TTD | Join TTD | |

AUC | 95.73% | 96.82% | 94.70% | 96. 32% |

Type I error | 6.02% | 4.51% | 16.07% | 14.56% |

Type II error | 9.03% | 8.53% | 8.28% | 7.53% |

Accuracy | 92.45% | 93.46% | 89.10% | 90.11% |

#### Out-of-sample prediction results of support vector machines

1:1 ratio | 1:2 ratio | |||
---|---|---|---|---|

Do not join TTD | Join TTD | Do not join TTD | Join TTD | |

AUC | 92.96% | 99.82% | 92.11% | 92.14% |

Type I error | 3.32% | 3.32% | 16.65% | 15.01% |

Type II error | 12.51% | 3.32% | 12.51% | 12.51% |

Accuracy | 90, 82% | 96.66% | 86.10% | 86.65% |

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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