In today's society, with the development of data transmission technology, the reduction of network cost and the improvement in the coverage that mobile devices offer, the development rate of online learning is greatly accelerated, and online learning platforms and massive online courses are constantly updated. The main battlefield for people to learn online has also spread from the website to the massive open online course platform under mobile phone and WeChat applet, even in educational UGC platforms such as forums and blogs [1]. Courses that are free of charge can be classified into audio or video, customised or universal. Among them, language learning, as a major platform of online learning, has blossomed everywhere, whether on the PC or on the mobile device, and nearly 100 English learning software can be downloaded in the mobile application market. At the same time, learners also gradually change their traditional ideas and begin to adapt to the fragmented learning mode with short content and loose structure, and this trend is especially obvious in the case of English vocabulary learning [2]. Online education makes up for the imbalance of educational resources in traditional education, and realises the sharing of educational resources. By making use of wireless mobile communication technology and equipment, learners can acquire educational resources indiscriminately, ignore the limitations of time and space, and obtain the benefit of digital learning anytime and anywhere.

However, the explosive growth of learning resources has a negative impact on both “teaching” and “learning” [3]. It is difficult for users to select the resources suitable for them from the massive data, and the phenomena such as high participation rate, low completion rate, uneven resource quality and homogeneous competition in platform become more and more prominent. Learners took a great effort to register in the platform and try to find high-quality resources, which indirectly led to the situation of low completion rate and low active period of users. For English vocabulary learning, the rigid resource push form leads to the difficulty that users learn words every day, which is largely determined by the selected dictionary, instead of depicting accurate user portraits according to different learners’ vocabulary size and personal abilities [4,5,6]. Therefore, in this paper, artificial intelligence is combined with English vocabulary learning to build an intelligent recommendation model for English vocabulary learning. According to the calculation of similar users and related words, a list of intelligent recommended words is formed, and a resource feature model is constructed. By calculating the correlation between words, an intelligent recommendation system for English vocabulary learning based on crowdsensing is designed and realised.

Adaptive Learning originated in the 1970s, studies and simulates people's learning from the perspective of information processing and is essentially a computer program [7]. This program can generate new rules in the process of problem solving, and add them to the program, so as to solve similar problems more effectively. It mainly includes the following four aspects:

Change what: Adaptive learning can change the learning contents by distinguishing the difficulty level of a task, or change the form of representation and path selection of the content [8].

Why change: It focuses on three levels, namely learning parameters, interaction between learners and systems, and teaching variables.

When to change: The first adjustment is made based on learner characteristics, followed by continuous modelling and further adjustment based on interactive parameters.

How to change: The common adaptation is controlled by the system, including learners’ complete control over learning environment and content, and sharing adaptation.

As shown in Figure 1, the four-dimensional view of adaptive learning very intuitively shows a core problem in the design of adaptive learning system. It can be divided into learner-oriented and educator-oriented adaptive learning. The latter of these is characterised by a big conflict between curriculum management and the existing teaching system, and there are few mature products at present. As for the former, the system is familiar with the functions of acquiring interactive data of learners, creating a learning model, selecting information and displaying information. Learner-oriented adaptive learning can be realised through the cycle of four basic stages: acquisition, analysis, selection and presentation.

Mobile Crowd Sensing (MCS) [9] refers to collecting data by using smart mobile device sensors in physical space and mobile social networks in cyberspace. Owing to its inherent high mobility and scalability, it has been widely used in many sensing applications [10], as shown in Figure 2.

Group intelligence has the following two characteristics [11, 12]: First, there is no central control, but it is distributed in such a manner as to be suitable for the working state under the network environment, and will not affect the solution of the whole problem due to the mistakes of decision-making and data anomalies. Second, groups are self-organised. Each individual in the group can communicate indirectly for information transmission and cooperation, and thus each individual can change the environment. However, the complex behaviour of the group is reflected by the intelligence in the process of individual interaction. This kind of wisdom emerging from the group is beyond the wisdom of its constituent individuals which is called group intelligence [13].

Group intelligence is applied in the educational environment, that is, individual learners have certain rules about their abilities and behaviours to learn specific knowledge, and they can communicate indirectly. Therefore, for new learners, it has great reference and application value. In the teaching process, the conclusion of group intelligence can be used to improve teaching methods, update teaching contents and share learning strategies, so as to help learners optimise the learning process and improve teaching efficiency.

The role of the system is divided into learner and manager. The main functions of learners include: personal information maintenance, uploading corpus, completing tests, and vocabulary learning. The main functions of the administrator are to review corpus, update thesaurus, publish tests, recommend new words and so on.

Corpus update: It is used to solve the problems of singleness and lack of timeliness of professional corpus [14]. Through user-uploaded corpus, system audit, word segmentation, keyword extraction and other technical means, the role of swarm intelligence can be brought into full play to realise real-time updating of corpus.

Accurate recommendation of new words: It is used to solve the problem of low accuracy of intelligent vocabulary recommendation. Similar words of learned words and co-occurrence words are used as important sources of recommended words for mixed recommendation, which improves the efficiency of new word recommendation of the system.

Systematic recommendation strategy: It is used to solve the problem of time-consuming memorisation by users. This system is different from the way in which other memorising software show all usages to users, since it divides the words into resource types, which reduces the presentation of interference information, helps users to improve the efficiency of memorising words and makes personalised adjustments to the source and quantity of words.

As shown in Figure 3, the architecture of intelligent vocabulary recommendation system is divided into three layers: user layer, business layer and data layer. The layer provides data storage services and undertakes the responsibility of ensuring the reliability and security of data. According to the actual demand of the system, data layer stores user information database, user log behaviour database, vocabulary database, corpus, comment data published by users, test data and so on. The business layer implements the core business logic of the recommendation system, including similar words’ mining and adopting a user-based collaborative filtering algorithm to recommend words to learners, where the clustering algorithm is used to locate the learning style of users and adjust the push mode. The user layer is responsible for the interaction between learners and the system, the server response to the user's request and the display of the results, such as word learning, registration, corpus uploading, testing and other functions. Moreover, all data of user behaviour generated by this layer will be recorded in the log database.

The core of English vocabulary learning is word learning [15]. When users recite words, the system will judge whether they are new users who need to complete the test first. Users who have completed a round of tests can choose to take the test again if they have not conducted a new round of tests for a long time or have formed an impression that the results of the previous round of tests do not constitute an accurate reflection of their actual standard. The system will recommend adaptive test questions for users with different needs according to the information registered by users in the early stage of registration, for example, recommending real questions or high-quality prediction questions over the years for users who choose CET-4 and CET-6 as their learning objectives; or selecting foreign original news such as BBCNews or NewYorkTimes for journalism students who need to improve their professional skills [16,17,18]. According to these learning data, the system can find highly relevant words, and form a list of recommended words for users to learn. As shown in Figure 4, when learning a new word, users can choose whether to collect it as a new word, comment on it or directly skip to learning the next word. In this way, the number of users’ new vocabulary books keeps increasing, and every time the software is restarted and the user starts learning, the system will recommend a new batch of words according to the updated vocabulary. If there is a need to review, the user can click on the new word book directly. This function helps users quickly find new words every time they learn, improves the efficiency of memorising words and rapidly expands their vocabulary.

When the user collects words, the system will automatically ask the user whether the words need to be marked as core words. If not marked, the system will judge whether the words belong to proper nouns according to the characteristics of the words themselves. If not, they will be recorded as ordinary words. In the stage of review, users will only be shown basic usages such as definitions and phonetic symbols. If the recorded word is regarded as a core word, not only will the basic usage be displayed but also advanced usage, such as example sentences, will be further developed.

In the process of language learning, students with different professional backgrounds have personalised needs for English vocabulary, for example, students majoring in computer science need to master the latest technological achievements; students majoring in history need to learn a wide range of place-names and toponyms; and students majoring in news need to master the current events to help them develop their ability at news writing [19,20,21]. However, a professional dictionary usually can’t fundamentally solve their needs. The editing of the dictionary needs relevant corpora from different fields to be collected, and combined with opinions of experts, so as to sort out and integrate them. As shown in Figure 5, for students with different professional backgrounds, the system adopts the way in which users can customise the corpus, which allows users to upload different forms of corpus materials, including speech videos, interview recordings, news reports, professional papers, etc., so as to supplement the existing professional corpus. Managers can review the authority and correctness of data. By reviewing a high-quality corpus prepared in this manner, the professional thesaurus can subsequently be updated by such operations as speech-to-text conversion, word segmentation, core word extraction and calculation of word correlation. With the help of speech recognition tools, crawlers and abundant network resources, the source of the corpus shows an unprecedented affluence. With NLTK, Gensim and other natural language processing packages, it is easy to remove stop words, extract core words and train word vector function by calculating TF-IDF [22]. Through the co-occurrence word matrix and the trained word vector, co-occurrence words and similar words can be mined to prepare for the subsequent recommendation words. At the same time, administrators can review the corpus materials uploaded by users, continuously extract the latest materials and update the existing corpus.

The test module in commonly-used vocabulary learning systems is particularly poor [23]. Many software retain the function of vocabulary testing, but they are additional functions in systematic design. Except for the data of vocabulary range and ranking, which does not achieve the effect of supporting and assisting users to improve the efficiency of memorising words. In addition, besides pre-test and summative test, the role of formative assessment in the learning process cannot be ignored. An online vocabulary learning system can’t represent all the input sources of English resources for users in a certain period of time, and users’ vocabulary size should be a dynamic value. Especially with the coming of examination and grading, a user's vocabulary can be improved dramatically in a relatively short time. Therefore, as shown in Figure 6, users can choose to retake the test at any time when they feel that their vocabulary has greatly improved, or that the last test did not accurately reflect their true level. Afterwards, the system constantly updates the recommended vocabulary list according to the test results of users, so as to ensure the efficiency of memorising words.

At present, the open corpus data set is very rich, for example, Wikipedia has opened the download channel of its multilingual webpage data. Take news corpus as an example; there is a plethora of available data sets, including: English News Data of Reuters Corpora [24] (Reuters English news text and corresponding data of news category), data set of New York Times (registered developer account application api, which can be traced back to 1851, any searchable and indexable article), data set of 20Newsgroups [25] (about 20,000 newsgroup documents are collected, which are evenly divided into newsgroup collections of 20 different topics), etc. The experimental data set used in this paper is 3,000 news reports from the figure-eight website [26, 27].

In the process of processing the original corpus, there are many meaningless symbols and function words, and thus it is necessary to remove stop words, extract stem, restore word form and carry out other operations. Firstly, the Word_tokenize () function in NLTK package is used to segment the text data, and the information is processed into the smallest unit that the computer can handle. Similarly, NLTK package is adopted to remove function words (conjunctions, prepositions, articles, etc.) and punctuation marks from the corpus. First, by defining an empty list and traversing the segmented text list, the empty list is appended if the word does not exist in the deactivated word list. Secondly, Porter's stem extraction tool is used to extract the same stem from different inflections of English words. Finally, the WordNetLemmatizer function is used to restore the morphology. Thus, it is enough simply to understand the data structure of the incoming function. When these steps are implemented in Python language, importing packages and calling functions can be easily implemented. The example code is as follows:

fromnltk.corpusimportstopwords

fromnltk.stem.porterimportPorterStemmer

fromnltk.stemimportWordNetLemmatizer

Text=paragraph.lower()# Enter the paragraph text paragraph and convert it into lowercase characters.

Text _ list = nltk.word _ tokenize (text) # participle

english_punctuations=[’,’,’.’,’:’,’;’,’?’,’(’,’)’,’[’,’]’,’&’,’!’,’*’,’@’,’#’,’$’,’%’]

text_list=[wordforwordintext_listifwordnotinenglish_punctuations]

# Remove punctuation marks

Stop _ list = set (stop words.words (“English”)) # Take out all English stop words.

stopped_token=[wordforwordintext_listifwordnotinstopword_list]

Stemmed _ token = [porter stemmer (). stem (I)foriinstall_token] # stem extraction

lemmatized_token=[WordNetLemmatizer().lemmatize(i)foriinstemmed_token]

In order to solve the “cold-start” of the system, the method of mining co-occurrence words and similar words of words is also adopted to realise mixed recommendation of words. The experimental corpus is trained by word2vec model of Gensim toolkit in python [28, 29], where the trained model is used to output similar words. It is very convenient to train word vectors in Gensim. We save the trained model and load it, and then call the most_similar () method to get similar words.

Taking the professional category as the boundary, the system pre-processes the corpus materials uploaded by administrators and users, and the number of core words obtained is limited (assuming that there are N words). By creating a co-occurrence word matrix, the common frequency of all words can be obtained. The higher the frequency, the greater the correlation between words, and it is classified as a list of preferred words, thus realising mixed recommendation. The specific implementation logic is shown in Table 1. The N*N matrix is constructed with all N core words as the number of rows and columns. The data on the diagonal line are uniformly defined as 0, and the data on both sides of the diagonal line are symmetrically distributed. The number in

Principle of co-occurrence word matrix

Order | 1 | 2 | 3 | 4 | ……… | N | |
---|---|---|---|---|---|---|---|

Order | Trump | Corruption | Scandal | Governor | Senate | ||

1 | Trump | 0 | 5 | 4 | 0 | 0 | 5 |

2 | Corruption | 5 | 0 | 1 | 2 | 0 | 3 |

3 | Scandal | 4 | 1 | 0 | 5 | 0 | 2 |

4 | Governor | 0 | 2 | 5 | 0 | 0 | 8 |

…… | 0 | 0 | 0 | 0 | 0 | 0 | |

N | Senate | 5 | 3 | 2 | 8 | 0 | 0 |

Owing to the large number of words, it is an important step to filter out unimportant words in the text and then calculate their total number. The text feature extraction algorithm TF-IDF is used to extract feature word vectors. The purpose of this algorithm can be understood as calculation of the importance of a word in a document [30, 31]. For the word

Vector = tfidfvectolizer (stop _ words = stopwords _ 1ist) # Call the tfidfvectolizer method to convert the input corpus into a word vector.

tf idf=vectorfittransform(corpus)

Word _ list = vector.get _ feature _ names0 # Get all the words of the word bag model.

weight_list=tfidf.toarray()

for i in range(len(weight list))

Print(len(weight_list)) # Number of all words

Print (“-the first”, i+1, “tf-idf weight of paragraph text”)

for j in range(len(word_list)):

If weight list[i][j]>0.01: # Only words with values greater than 001 are reserved.

print(word_list[j],weight_list[i][j])

else:

j+−1

To build a word network, first, a common empty matrix needs to be built; we fill the first row and the first column of the matrix with feature words, and then calculate the common comments of feature words in each corpus. The main calculation of this segment code focuses on calculating the contribution times of feature words, which requires constant recursive operation. In order to improve the operation efficiency, the location of each feature word is stored in a dictionary {’feature words ’:[1,3,5,29,45,89]}. Then, we take out the corresponding position list of two feature words that need to be compared from the dictionary, turn the list into a set and use the method of intersection between two sets to ascertain the co-occurrence frequency of the two feature words. The final implementation algorithm is as follows:

defcount_matrix(matrix,formated_data):

Calculate the number of times each keyword appears.

# Construct a dictionary where keywords appear. keyword_location

keywordlistmatrix=[o][1:]

forwordinkeywordlist:

keyword_location[word]=[]

i=1

foreach_lineinformated_data:

eachline=str(each_line)

#pring(eachline)

ifwordineachline:

print(word)

keyword_location[word].append(i)

i=i+1

print(’Construct a dictionary of keyword occurrence locations’)

print(keywordlocation)

#Traverse the line, skip elements with subscript 0

forcolinrange(1,len(matrix)):

counter=0

ifcol>=raw:

ifraw=col:

matrix[raw][col]=counter

else:

counter=len(set(keyword_location[matrix[raw][0]])&set(keyword_location[matrix[0][col]]))matrix[raw] [col]counter

else:

matrix[raw][col]=matrix[col][raw]

print(’Finish!)

return matrix

As the selected corpus is sourced from news articles, the experimental design utilised the services of 20 undergraduate students majoring in journalism in S University who had studied with traditional memorisation software for more than 3 months to test the function of similar vocabulary recommendation. They were asked to learn the randomly recommended vocabulary, which contains 30 words. Then, according to their condition of marking new words, intelligent recommendation was used to mine the co-occurrence words and similar words of new words, and a word list of 30 words is formed again. After learning two lists, the users evaluated the word qualities of the different lists, and verified whether the words intelligently recommended by the system increased the proportion of recommended new words in practical application.

According to their feedback, there is no significant difference in the probability of recommended new words between the intelligent recommended word list and the randomly composed word list. However, the users are generally satisfied with the intelligent recommended word list, and can clearly distinguish the randomly composed word list from the intelligent recommended word list. After further interviews, it was ascertained that users were of the opinion that the correlation between words was strong in the intelligent recommended word list, which can remind them of the specific usage scenarios of similar words, help them associate memories and finally enhance their initiative and participation in English vocabulary learning.

From the perspective of artificial intelligence, in this paper, an intelligent recommendation model for memorising and learning English vocabulary based on crowd sensing is implemented. By taking adaptive learning as the main idea, an intelligent recommendation system that meets users’ needs is built, where the personalised intelligent recommendation function of machine learning algorithms, such as clustering algorithm, word vector training and collaborative filtering recommendation, is realised. The data set of public news is selected as experimental corpus that the functions of corpus processing, core word extraction, co-occurrence words and similar words mining are realised. The results of the deployment of a small-scale experimental test indicated that users were generally satisfied with the intelligent recommendation system for English vocabulary learning, and their initiative and participation were significantly improved.

#### Principle of co-occurrence word matrix

Order | 1 | 2 | 3 | 4 | ……… | N | |
---|---|---|---|---|---|---|---|

Order | Trump | Corruption | Scandal | Governor | Senate | ||

1 | Trump | 0 | 5 | 4 | 0 | 0 | 5 |

2 | Corruption | 5 | 0 | 1 | 2 | 0 | 3 |

3 | Scandal | 4 | 1 | 0 | 5 | 0 | 2 |

4 | Governor | 0 | 2 | 5 | 0 | 0 | 8 |

…… | 0 | 0 | 0 | 0 | 0 | 0 | |

N | Senate | 5 | 3 | 2 | 8 | 0 | 0 |

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