With the rapid development of network communication and the arrival of big data, it has entered the human brain step by step. The Internet is flooded with hard data, and the traffic of information on the Internet is constantly increasing. This vast amount of information has become the key to answering consumer questions. Most SEO searches by keyword. While this retrieval method makes it easier for users to store data, it returns some search results and does not affect users. It is difficult for users to quickly find the answers they are looking for. How to obtain accurate data to meet most of the big data needs of consumers is the goal of scientists in the information age. In recent years, the development of question answering systems has gradually attracted the attention of researchers. Intelligent question answering system is a new research in natural language processing and data recovery. It allows users to ask questions in natural sentences and uses natural language tools to get short and accurate answers for users. It was created by humans to find information quickly and accurately. In addition to comparing user queries with existing search queries, smart queries have the best results in understanding queries compared to search engine contextual comparison methods and can directly improve answers. Users want them to be presented to the user in a certain way. Answering these smart answers plays an important role in answering distance learning questions and solving challenges [1].

Data ontology is the basis for users to “answer questions”, and appropriate answers to these questions are stored in the database. When a user asks a question, the question answering system usually deletes the common question and returns it to the user to see similar answers. If the system cannot find enough answers from the FAQ database, the system will switch to the ontology database. Among them, algorithms are techniques for answering key questions for finding similar questions by understanding the ontology database. After counting the similarity between the user's question and the question answer stored in the ontology information, select the answer similar to the user's question and submit the answer similar to the user [2].

Phrase similarity algorithms are now widely used in practice. Research status affects research progress in other relationships. Sentence algorithms play an important role in many query answering systems. For example, my country's query answering, ontology question answering system, OTC question answering system, multi-question-based machine question answering system, sentence-like algorithm, etc. are all important technologies in answering questions. Based on this, this document uses the similar sentence algorithm in the original English intelligent question answering system to design and implement the English intelligent question answering system. The sentence-like program completely solves the vocabulary and content of English questions, not only improving the performance of English intelligent answering, but also improving the level of students. Start answering English questions correctly. The system meets the requirements of primary school students' question and answer, and helps primary school students learn English better [3].

K. Boten et al. believe that Key Answer Questions (also known as Intelligent Question Answering Robots) is a new retrieval system that allows users to ask questions in any language without sharing the questions as keywords. The system integrates tools that work in a good language and preserves similar answers by understanding the question [4]. Shi M et al. found that the key questions can be divided into knowledge-based question answering, query-based database query, query-based query, question answering, knowledge-based answering and answering. System based Ontology [5] Nandy S et al found that the key question answering system generally includes three parts: question analysis, data recovery and retrieval. There are several practical answering techniques in restricting the answering of key questions, such as FAQ databases, writing ontology databases and corpus queries, and semantic understanding methods based on multiple equivalence metrics [6].

The English Language Proficiency Test is a great tool for finding information in a natural environment. The goal is to help elementary school students ask questions about simple English sentences in their daily life and then get the correct answers. In short, the intelligent English question answering system examines the English questions raised by students, understands the meaning of the questions, and then sends the answers to the students, so that students can learn to learn. As shown in Figure 1, the English intelligent question answering system has four modules: one is the question analysis module, which has only five parts: answer words, voice annotation, question sample analysis, calculation, question and answer analysis, and keywords. analyze. depending on. The second module is a similar counting module and is the core of the query. This chapter usually includes counting similar words and counting similar sentences. The third module decomposes answers and is often used to partition consistency, filter answers, and create answers. The ultimate module is to gain experience. This often provides answers to users in multiple ways by understanding their different experience levels, stressors, and user choices.

The English Intelligence Questionnaire is data on the use of technology in natural environments. Its goal is to hope that elementary school students can ask questions about simple English sentences in their daily life and then get the correct answers. In short, the English intelligent answering system analyzes the English questions given by the students, understands the meaning of the questions, and then sends the answers to the students. As shown in Figure 1, the English intelligent answering system consists of four modules: one is the query analysis module, which usually has five parts: word correction, partial voice annotation, query type analysis, question-and-answer type analysis and keywords. Delete. The second module is a similar calculation and is essentially a quiz. This is usually similar Chinese and similar sentences. The third module, field extraction, is only used to identify connections, filter answers, and publish answers. The ultimate module is advancing knowledge. This usually provides answers for different types of users by understanding the level of knowledge of different users, the difficulty of previous experiences, and users' preferences for different types.

Error correction modules are usually based on machine language models and similar measurement models. The technical model accepts the standard model. The standard measurement model usually uses a query vector generation model to measure the query statement input by the user through intelligent error correction. It will correct the error if it matches the default. The grammar used in intelligent error correction is divided into pinyin grammar and grammar. The main function of the Pinyin language model is to correct inaccuracies, inaccuracies, etc. in the query sentences entered by the user, and the main function of the script is to correct incorrect sentences and other problems in the input sentences. By user [7].

The question analysis module is an integral part of the intelligent question answering system. The purpose is for the computer to understand the semantics of the user query and prepare the next answer for the decryption module. Accurate question analysis helps the system use methods and strategies to answer various types of questions in the answering module. When users submit English questions, the question analysis module analyzes and develops them. The development plan includes:

Word reduction changes all the words in the question and answer sentences back to the prototype. For example, the auxiliary verbs had and has become have, the plural word sports becomes sport, and the verbs be become is and was become be.

Part of speech tagging marks the part of speech of each restored word. It includes words with part of speech as verbs, words with part of speech as nouns, words with part of speech as adjectives and words with part of speech as adverbs.

Question type analysis analyzes some common English question types put forward by users, such as “What kind of...,” How do you like...?” “Which is ......?” and so on.

Q&A type review to determine what type of product a user's inventory falls under. Types of questions and answers include answers, discussion questions, etc. Each format has four media formats: audio, video, album and image. It is divided into three levels: hard, medium and easy. Also, users can write a question to benefit. Answer types include answer, sentence, sentence, suffix, etc. Distributing and translating words and questions and answers can not only improve English, but also improve students' motivation and interest in learning. Learning English is for one thing.

Keyword extraction the keywords contained in English questions represent the main meaning of the sentence. In the retrieval process, keywords are given different weights according to different parts of speech. The weights are nouns, restrictive adverbs, adjectives and verbs from large to small.

The process of calculating similar sentences is usually to select the appropriate sentence by calculating the similarity between two sentences. Sentences usually include words, syntax, and semantics. The larger the similarity value in the calculation, the closer the morphological, syntactic and semantic data of the two sentences are. In this study, a distance-based similarity algorithm was used to calculate the similarity of English questions. The algorithm is based on a semantic taxonomy dictionary of pure terms. The similarity of English words is calculated by calculating the similarity of the program. After the similarity of English words is obtained, the similarity of English meaning is obtained by statistical angular cosine similarity [8].

The unpacking module analyzes the lexical, syntactic and semantic aspects of the other answer questions obtained from the data retrieval module and needs to rank the answers. Also, the system must be set to boot. Search results are only available if the sentence similarity is greater than the initial similarity. Extract the results by filtering keywords, remove the content that does not affect the search results, and then refine the results according to the categories of keywords, propose the most suitable answer, and return it to the user. Consumers know the level. The model simply subtracts similar answers from the ontology knowledge base by counting similar questions, then analyzes the answers, ranks the above similar answers, this 0.8 based on a similarity value, and pushes another answer to the familiar push module. Problem types can be obtained from the problem analysis module.

In recent years, scientists have proposed several ellipse detection algorithms, which can be divided into three categories: one is the ellipse fitting method based on Hough transform, the other is the fitting method based on geometric features, and the third is the fitting ellipse method. according to the least squares method. In this paper, an ellipse fitting algorithm combining ellipse symmetry and bisection method is proposed, and Halcon is used as the graph algorithm library. The method utilizes the geometric symmetry of the ellipse itself to calculate the basic control of the ellipse, and then provides the bisection method to calculate the semi-axis length, minor semi-axis and direction. The angle of the ellipse is estimated by the completion. Finally, calculate the actual parameters of the ellipse[9–10].

To solve the elliptic equation, five parameters need to be determined. _{1}, _{1} are the center coordinate of the ellipse;

According to the mathematical model of the ellipse, the ellipse is symmetrical about the central point, that is, as a straight line at any angle, parallel lines are tangent to the ellipse, there are two tangents _{a}_{a}_{b}_{b}_{j}_{j}_{j}_{j}

Firstly, the camera is calibrated to obtain internal and external parameters. The camera collects the image of elliptical hole, and carries out image correction and preprocessing. The pixel edge of ellipse is obtained by Canny operator; The sub-pixel edge of the ellipse is obtained by Gaussian fitting.

The coordinates of the ellipse center can be calculated by equations (2) and (3).
_{1} and _{1} are the estimated ellipse center coordinates; N is the logarithm of the tangent point pair.

Estimate the semi axial length of the ellipse length _{i}_{i}_{i}_{k}_{s}_{n}_{+1} = (_{k}_{s}_{n}_{+1},
_{n}_{+1}. Lock the tangent angle area (_{n}_{+1}, _{n}_{+2}) where the next ellipse's long axis length appears, where: _{n}_{+2} = (_{k}_{n}_{+1})/2. In this way, the real value approximating the ellipse's long axis length is continuously updated in the iteration through the dichotomy method. Suppose that when the iteration reaches the j-th time, the absolute value of the difference between _{n}_{+j} and _{n}_{+j+1} is less than the set iteration threshold

Similarly, calculate the length _{i}_{v}_{p}_{v}_{p}_{n}_{+1} and _{n+m+1} is less than the set iteration threshold

The system takes MySQL database and knowledge ontology database as the background database management system. The data tables used include question table, question answer table, answer table, learning preference table, common word dictionary and word net as semantic dictionary. Adopt (spring MVC + Maven + mybatis) and other architectures under the Eclipse platform.

After the user enters a question, the system first queries the FAQ question set. If the answer is found, it will be filtered and the most appropriate answer will be returned to the user. If the answer to the question is not found in the FAQ database, query the knowledge ontology database. This stage requires a series of syntactic processing, such as word restoration, part of speech tagging and other processes to form a keyword set, then calculate the similarity of the processed English sentences, and finally return the question answer with the highest similarity to the user, presenting diversified answer content according to the user's knowledge level. The answer to the question can query the corresponding ID value in the knowledge ontology database and obtain several attribute values related to the ID value. The user ontology database stores the knowledge level, learning style and other information of each student, and finally recommends appropriate learning content to learners through the knowledge push module.

(1) Knowledge base management

Knowledge base is the knowledge center of intelligent question answering system, which is composed of classification, examples, attributes, standard questions, extended questions and standard answers. Among them, classification refers to the classification information marked by personnel or customers on each question and answer pair of the knowledge base in advance. An example refers to a collection of different questions for the same answer, and the attribute is another kind of classification information. For example, the knowledge base of Liangshan Prefecture Government intelligent question and answer system has attributes such as to-do items, query items and so on. Standard questions and standard answers refer to common knowledge Q & A pairs given by customers, and extended questions refer to different questions provided by tagging personnel for the same tagging answer [11].

(2) Ontology class management

Ontology class is the description and formal expression of real-world concepts and the relationship between concepts. It is divided into entity class and method class. Taking the field of government affairs as an example, the ID card belongs to the entity class, the method class, and the handling belongs to the method class and the ontology class. Knowledge management is realized by summarizing and inheriting ontology classes.

(3) Knowledge Topology

Knowledge Topology visually displays the knowledge in the knowledge base in the form of topology according to different dimensions. Intuitively display the knowledge of different dimensions to customers, which is convenient for customers and developers to observe the system.

(4) Knowledge dimension

The knowledge dimension module classifies, organizes and counts knowledge by defining different dimensions. Knowledge combing usually divides knowledge into four dimensions. Taking the government affairs system as an example, the system is divided into four dimensions: state, county, matters to be handled and specific problems.

(5) Hotspot management

Hot issues refer to issues concerned by users and issues related to current events. Hot issues usually become issues concerned by users. Therefore, the system supports the addition, deletion and modification of hot issues, and hot issues are preferentially recommended in the interface.

Question understanding refers to transforming the intention expressed by the query sentence entered by the user into the semantic structure that can be recognized and understood by the intelligent question answering system through natural language technology. In the intelligent question answering system described in this paper, the question understanding function mainly depends on three sub modules. The preprocessing module passes the query statements entered by the user through intelligent word segmentation.

Name entity annotation and other methods are converted into keywords and word sequences. The session management module defines the questions raised by users. The intelligent question and answer system described in this paper helps users who cannot express their intentions to express their intentions through the session management module. The error correction module allows the user to input the correct expression of the sentence and return the error correction result.

As shown in Table 1, the experimental results are evaluated by accuracy and comprehensive similarity. A total of 453 sentences and 920 words are input in this experiment, the accuracy is 81.23% and 89.23% respectively, and the comprehensive similarity value is greater than 0.8. The test results show that the algorithm can improve the accuracy of the experimental results, and the sentence comprehensive similarity is high, which improves the system efficiency.

System data test results

Input type | Number of tests | Number of correct results | Accuracy (%) | Comprehensive similarity |
---|---|---|---|---|

sentence | 453 | 368 | 81.23 | 0.8173 |

word | 920 | 815 | 89.23 | 0.8018 |

When the user enters an English word in the search box, the system will present various types of answers related to the word, such as the original text sentence, situational paragraph, extended example sentence, etc. In the process of querying words, the system first queries the FAQ database, and if the answer is found, it will be directly presented to the user; If the FAQ database has no answer, query the knowledge ontology database to present the answer to the user. For example, take the input word “ruvier” as an example to query [12].

When the user enters a question in the search box, the system will present various types of answers related to the question, such as answer, situational dialogue, important sentence patterns, after-school words, etc. In the process of query, the system first queries the FAQ database, and if the answer is found, it will be directly presented to the user; If the FAQ database has no answer, query the knowledge ontology database to present the answer to the user. While querying the ontology database, calculate the similarity of the found answers to relevant sentences, and select the question answer with the greatest similarity as the final answer to return to the user.

The system collects and arranges more than 2000 common and universal questions of many primary school students in the process of using the question and answer system. The question answers are imported in batch. The question answers are collected through teaching materials and then stored in the knowledge ontology database. Since the system has been running for three months, it has been used by primary school students in various schools for a total of 3058 times, and the statistical analysis is carried out. As shown in Table 2, where

Proportion of sentence similarity results

λ | Number of sentences | Sentence percentage | Number of words | Percentage of words |
---|---|---|---|---|

0.8 | 953 | 21.4% | 3452 | 89.8% |

0.7 | 2456 | 69.4% | 231 | 4.2% |

0.6 | 283 | 4.0% | 156 | 2.1% |

As can be seen from table 2: (1) When

Although the English answer can directly complete the skill, it depends on whether the user's question can be answered correctly. This paper examines English language similarities, teaches English proficiency answer models and the capabilities and functions of each model within each model, provides design and development processes, and mathematics and uses important English questions. The answer is based on algorithms. Due to previous experience and applications, the system is able to successfully and responsibly answer user questions and provide some insight into customer issues. In addition, the speed of the system's exploration and the distance of the similarity algorithm improve the system's accuracy in answering smart English queries. Further research will improve the consistency of the algorithm and strengthen the functionality of the system to see user needs more quickly. At the same time, we will continue to record the number of clicks and page views of users in the actual use of the system, and provide special training to help users obtain information needs. Follow personal training.

#### Proportion of sentence similarity results

λ | Number of sentences | Sentence percentage | Number of words | Percentage of words |
---|---|---|---|---|

0.8 | 953 | 21.4% | 3452 | 89.8% |

0.7 | 2456 | 69.4% | 231 | 4.2% |

0.6 | 283 | 4.0% | 156 | 2.1% |

#### System data test results

Input type | Number of tests | Number of correct results | Accuracy (%) | Comprehensive similarity |
---|---|---|---|---|

sentence | 453 | 368 | 81.23 | 0.8173 |

word | 920 | 815 | 89.23 | 0.8018 |

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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