Linguist Harris (R. Harris) first proposed the concept of metadiscourse in 1959 . Since then, this concept has gradually become a research hotspot in the field of English writing discourse after being critically inherited and developed by J. Williams and A. Crismore . As ‘discourse about discourse’, metadiscourse can not only organise discourse and propositional content, construct article framework, project self, and reveal the author's communicative intention but also communicate with readers and realise interactive functions . An academic paper is an article that presents the author's latest research findings and results after discussing an academic issue. It plays an important role in promoting academic exchanges and academic progress . Therefore, in terms of wording and sentences, the author should summarise his findings objectively, accurately and effectively so that the sentence is easy to be accepted by the reader so as to convince the reader. In view of this, authors need to rely on metadiscourse to organise language and maintain and strengthen their relationship with readers.
On the basis of previous theoretical research and metadiscourse classification, researchers began to exchange academic writing, especially empirical research on research papers. Foreign scholars have explored the application of metadiscourse in academic terminology from different perspectives. For example, a work  studied metadiscourse from the perspective of contrastive rhetoric. A previous study  explored how metadiscourse facilitates social interaction and knowledge exchange across disciplines and attempted to demonstrate the importance of metadiscourse by analysing the frequency and role of metadiscourse in 28 research papers from four disciplines. It is found that metadiscourse is a common feature of rhetorical writing in English majors, and there are also disciplinary differences in the use of metadiscourse. A previous work  used Hyland's metadiscourse interpersonal relationship model as the theoretical framework and comparatively studied the application of metadiscourse in English and Chinese academic texts from both quantitative and qualitative perspectives, and whether the application of metadiscourse in English and Chinese academic texts has a difference. Another work  studied using a corpus-based metadiscourse taxonomy. A comparative study of the cross-language variation of metadiscourse in the genre of Chinese and English academic book reviews have been carried out [5, 6, 7, 8].
However, the aforementioned individual words are largely lost. Therefore, this paper attempts to combine various traditional and latest sentence semantic representation methods, sentence distance calculation methods and clustering methods. Through a large number of comparative experiments, this paper finally proposes a recognition method combining the word movement distance (WMD) model and the R&L clustering algorithm model to cluster the verb variant word form recognition system. The best recognition performance is obtained on the problem of sentences with morphological forms of verbs.
The classification of metadiscourse mainly focuses on vocabulary, different texts are expanded according to different perspectives , the classification mode is more specific and the classification of modern metadiscourse is also developed more rationally. According to the theoretical basis of functional linguistics, it is divided into two categories: discourse metadiscourse and interpersonal metadiscourse. Among them, discourse metadiscourse is divided into discourse connectives, code annotations and power markers according to different levels of content. The functions of interpersonal metadiscourse are mainly reflected in rationality, modality markers, attitude markers and so on. Irrespective of the kind of classification, in practical application, it pays attention to interaction and focuses on attracting and guiding readers . Therefore, studying the application of metadiscourse in English papers is an important way to correctly understand the author's thoughts.
At the same time, by comparing the metadiscourse chunks used between disciplines, it is found that chunks in the papers of the two disciplines are significantly different in the dimensions of frequency and high-frequency chunks, formal structure and pragmatic function . The specific performance is as follows: (1) the total amount of metadiscourse words in engineering English academic papers is significantly larger than that in medical papers, and the high-frequency words are also different; (2) there is a formal structure of metadiscourse in medical papers and engineering papers. There are differences in distribution: the proportion of intermediary phrases in engineering papers is higher than that of noun phrases, while the proportion of noun phrases in medical libraries is higher; (3) the pragmatic function distributions of metadiscourse in medical and engineering papers are different. Hedges are used more frequently in medical papers than in engineering papers, while capabilities and possibilities, coercion and commands are used more frequently in engineering papers than in medical papers. At the same time, the frequency of metadiscourse, textual reference and topic development chunks used by engineering dissertation scholars is higher than that in medicine papers. These differences are closely related to the communicative purpose, writing tradition and information expression of the two topic papers .
Metadiscourse is an important textual mechanism for persuasive and informative discourse , and academic discourse is an example of such discourse, so the application of metadiscourse is particularly important. When the concept of metadiscourse was first proposed, it was mainly to explain the concept of language itself. The author uses metadiscourse to provide readers with directions for analysing the entire article . Over time, many scholars have further studied the concept of metadiscourse and expanded the scope of metadiscourse . These scholars believe that metadiscourse is a form of language in which the author influences the mind of the reader through the intervention of the text. Compared with other mature language samples, metadiscourse is not very mature under the framework of theoretical models, and the nature of its application in practical applications is also vague. In the past, when scholars studied information transfer  and emotion transfer in linguistics, they usually made a clear distinction between the two, focusing on the understanding of propositional meaning and the expression of self-thought. Other scholars engaged in communication; however, this way of thinking ignores the function of creating discourse. Thus, the emergence of the concept of the metadiscourse theory strongly responds to the language proposition. During the reading process, readers can directly receive the information conveyed by the author in the work. In the process of information transmission, in addition to the content of information transmission, it also includes readers' sense of belonging to the information , as well as the fit between the information and their own experience. The reader's expectations of the information and the reader's level of expertise determine the entire process. These factors fully reflect participants' interpretation of the information , various responses and interactions between authors and the information. Compared with other genres, academic papers reflect the individualism of the author more. Therefore, the use of metadiscourse is deeper than other styles. The metadiscourse theory shares a common core with English academic papers, namely, the exchange of information and ideas between authors and readers. Under this exchange, readers can choose their own positions and form alliances with those who hold corresponding positions. Metadiscourse itself has certain information and emotion, and it can not only involve people, places and activities in the real world but also promote the formation of social relations. Therefore, many experts and scholars regard metadiscourse as an important feature of written language theory, and it is widely used in the evaluation of various books, magazines and English works.
Patterns are the result of the predisposition and selectivity of words to syntactic forms . Traditional grammars describe speech structures in the form of subject–predicate, verb–object, or verb–complement. With the development of corpus linguistics, people have a deeper understanding of collocation. Hunston (2000), on the basis of corpus research such as Sinclair and Francis and other linguistic studies, combined with the com pilation work of Cobuild and the British dictionary database, expounded the description method system of lexical and syntactic features  and proposed the theory of formal grammar. The theory studies the definition of patterns, including concentrated parts of speech such as verbs, formal content words, adverbs and nouns. At the same time, the equation extraction principle and equation representation method of regularisation normalisation are proposed. Through the definition of form, the verb form is divided into the following three quantitative characteristics. The type extraction algorithm mentioned in this paper attempts to analyse these three characteristics.
First: Type typicality. A form is a common form of a verb. To quantify the typicality of a pattern, the proportion of that pattern among all patterns of equal length is used. In practical calculations, it is expressed as the ratio of the probability of a candidate type to the sum of the probabilities of all equal-length types in a data set, which is set to
In Eq. (1),
Second: Stickiness. Stickiness refers to the strong mutual selectivity and affinity between elements within a pattern. As the main feature of word collocation, stickiness is widely used in the research of word collocation extraction. It is used to measure  word collocations. Commonly used collocation measurement methods in existing research include the t-test, Z-test, logarithmic test, chi-square test and mutual information. Due to the similarity between the pattern feature and the word collocation feature, a similar method is also used to measure the stickiness of pattern elements. In the calculation of pattern extraction, mutual information is set as an optional measurement method. The following is the mutual information equation:
In Eq. (2),
Third: The difference in the use of forms between verbs. A verb type is compared with other verbs; do other verbs have the same type? Is there a difference in the frequency of use? For transitive verbs, there will be no difference in the form of
In Eq. (3),
The typicality of a verb form can be measured using the harmonic mean of Eqs (1) and (2):
Clustering is dividing a data set into several different clusters according to specific criteria  (such as distance criteria) so that the greater the similarity between data objects in the same class, the better, as well as the greater the difference between data objects in different classes. Currently, there are many kinds and numbers of clustering algorithms. Clustering algorithms commonly used in text clustering tasks include the k-means clustering algorithm and hierarchical clustering algorithm. This paper mainly introduces the partition-based R&L density peak clustering algorithm and selects the expectation-maximisation (EM) algorithm as a comparison. These two clustering algorithms are briefly described in the following text.
The clustering algorithm introduced in this article is a new clustering algorithm published in Its own density is very large, that is, the density of surrounding data points cannot be greater than it. It is far away from other cluster centres, that is, it is far away from other data points that are denser than itself.
Its own density is very large, that is, the density of surrounding data points cannot be greater than it.
It is far away from other cluster centres, that is, it is far away from other data points that are denser than itself.
After meeting the aforementioned requirements, the selection method of cluster centres is introduced in detail.
In Eq. (6),
To sum up, for each data point
The EM algorithm is a model-based clustering method. When implementing the EM algorithm, each category in the data is considered to conform to a multidimensional Gaussian distribution, which can be determined by the centre
According to the basic principle of the EM algorithm, each multidimensional Gaussian distribution has corresponding weight coefficients
EM first makes an initial estimate of the value of the parameter Take the data object Update the parameter values in the model according to Eqs (11)–(13):
Take the data object
Update the parameter values in the model according to Eqs (11)–(13):
The EM algorithm scans all objects in the data set to calculate the membership between each object and the corresponding class. This step is relatively computationally intensive and requires multiple iterations in order to maximise the log-likelihood
Through the previous analysis, it can be found that as long as the distribution function is selected correctly, the EM algorithm can identify data sets of any shape. Since the number of iterations is parameter-dependent and unpredictable, the algorithm has no obvious advantage in efficiency.
The method of analysing sentences using the mean of word vectors is widely accepted by most scholars because sentences usually have only a dozen words, so they can maintain relevant features even after averaging.
Since Bengio proposed neural probabilistic language models in 2003, word vectors have become a research hotspot. In 2008, Ronan Collobert and Jason Weston proposed a neural network language model called C&W. Different from Bengio's model, the model proposed by C&W is not a probabilistic semantic model but reads one N-gram, namely,
In the aforementioned equation,
The log-bilinear model is a probabilistic linear model proposed by Mnih and Hiton. It is trained by giving an N-gram model and predicting word vectors by concatenating the word vectors of the first N-1 words. The study by Mnih and Hinton in Nips in 2013 improves on the most time-consuming part of the aforementioned method, increasing the speed and ensuring the same effect. This model is called the ‘hierarchical log-bilinear’ model because it integrates the log-bilinear and hierarchical models, or simply the ‘HLBL’ model. A comparison of C&W and HLBL in terms of training corpus, dimensions and features is shown in Table 1.
Comparison of C&W and HLBL word vectors
|C&W||ENGLISH RCV1||150,000||Not case sensitive|
|HLBL||REUTERS RCV1||260,000||Case sensitive|
Since C&W and HLBL word vectors perform well in many NLP tasks, this article will represent text based on these two word vector addition methods as a comparative experiment for verb pattern clustering. This study builds a corpus based on these two word vectors and conducts experiments under different parameter combinations, that is, the word vectors of each word in the sentence are added and combined, and then divided by the sentence length to represent the sentence. This text representation can be represented as
The WMD model was proposed by Mattj et al. in 2015. At present, this method works best in the field of text similarity calculation. In this method, the n-dimensional vectors of all words are first obtained through the word2vec model, then the Euclidean distance between words is calculated and the word frequency of words in the article is calculated . The calculation problem of the distance between sentences can be transformed as follows: how to convert all the word units carried by sentence A into the corresponding word units of sentence B at the minimum cost so as to transform the problem into a transportation optimisation problem, which can be solved by a transportation optimisation algorithm. solve. Among them, the similarity of the word units corresponding to A and B before and after transportation is the standard to measure the processing cost. For example, if the sentence units are the same, moving the word ‘president’ in article A to the word ‘Clinton’ in article B will cost less than moving the word ‘president’ in article B to the word ‘Clare’.
The specific calculation method of WMD is as follows: with the cosine distance between words and word frequency as weights, under the weight constraints, find the optimal solution of WMD linear programming . Assuming that there are sentences A and B, the input is the word frequency of all words in file A, the word frequency of all words in file B and the distance value matrix of all single words in A to the corresponding words in B. Finally, get the distance between documents A and B, that is, the minimum weighted cumulative cost required to move all words from A to B. The calculation method is shown in Eqs (15)–(17):
In the aforementioned equations,
In order to cluster verb patterns in text using statistical machine learning methods, it is first necessary to formalise the text and then calculate text similarity. Finally, the text similarity value is used as input to implement verb pattern clustering. The expression of the text needs to fully express the semantics of the sentence. To fully express the semantic information of a sentence, not only the lexical information within the sentence but also the relationship information between words is needed. This work will study the formal representation of sentences from the lexical information and sentence structure information of sentences. At the same time, combined with the current popular sentence similarity research methods, different methods are used to cluster verb patterns. First, the data preprocessing  method is introduced, and then the influence of different text representation methods and clustering algorithms on the verb pattern clustering results is analysed using the WMD model.
Before performing semantic similarity-based verb pattern clustering on the corpus, the vector expression of the sentence needs to be obtained first and then the sentence vector expression is used as the input of the clustering algorithm to calculate the distance matrix of the entire text set.
In this paper, the evaluation criterion used in the verb pattern clustering task is the F1 value of combined precision and recall . The evaluation code is from the CPA evaluation task of SemEval 2015. The final evaluation score is obtained by averaging the F1 values of multiple target verbs. The F1 value calculation method and evaluation score calculation method of the verb pattern clustering task are shown in Eqs (18) and (19):
Among them, precision and recall are important criteria for algorithm evaluation. This paper adopts the B-cubed standard. It was originally used to refer to the evaluation of tasks and was later extended to evaluation metrics for cluster tasks. In this paper, all evaluation values are the average calculated based on the precision and recall rate of each category. The calculation of the precision rate and recall rate used in this paper takes sentence pairs as the count unit, that is, if there are
In the aforementioned equation,
Then, through the WMD model, with the text as the input, the distance value of the text is directly calculated – that is, based on the similarity of words, with the flow of word movement  as the weight, the distance value of the text is calculated according to Eq. (15), where the similarity of words is based on word2vec word vectors, calculated by cosine similarity, and the flow of word movement is calculated according to the constraints in Eq. (16).
The WMD model adopted in this study considers not only the word sense information and the semantic relationship between words but also the overall structural relationship of the sentence. Therefore, compared with other text representation models, the impact of the WMD model on the R&L algorithm will be significantly improved, which is beneficial to improve the accuracy of verb pattern clustering.
In verb pattern clustering, the most important work is to choose an appropriate text representation model and clustering method. Through comparative experiments, the WMD model is selected for text representation. At the same time, by comparing the experimental results of the multi-text representation models of the three clustering algorithms, it is found that the R&L algorithm is the most suitable algorithm for the verb pattern clustering task.
The R&L density peak clustering algorithm is a simple clustering algorithm. Its conception is novel , simple and vivid. It can identify clusters of various shapes whose parameters are easy to determine. When running the clustering algorithm, the cluster centre is based on the local density
The R&L algorithm only needs to determine one parameter
In order to verify the effectiveness of the clustering algorithm based on the WMD model, this study compares the C&W word vector addition and the HLBL word vector addition with the WMD model and downloads five English papers from related papers and journals as experimental data.
The title, abstract, outline, full text and other information of the paper are extracted from the full-text data, and another person selects the metadiscourse word blocks in the paper to build a word vector training corpus and selects the appropriate training model according to the amount of data and natural language processing tasks, optimisation algorithms and parameters. In this paper, the full text is divided into sentences, and textual features such as position, segmentation and contour of sentences are extracted. Taking each subsection as a unit, based on WMD and C&W word vector addition and HLBL word vector addition, the aforementioned word vector files are used to construct the semantic similarity between sentences, and the improved R&L algorithm is used to identify topic sentences. The obtained data are compared, and the results are shown in Table 2.
One round of recognition results
|HLBL word vector addition + R&L algorithm||22.34||21.24||20.54|
|C&W word vector addition + R&L algorithm||24.67||22.79||22.10|
|WMD model + R&L algorithm||29.70||28.03||28.63|
WMD, word movement distance
The experimental results in Table 2 show that although the results of this method are slightly better than those of other methods in the same text passage, the results of these three methods are not ideal. Using the analysis of the experimental data and results, the specific reasons are found as follows: In this paper, each subsection is used as the basic unit for identification, and the fixed proportion method is used for identification, assuming that the core topic sentences of the paper are evenly distributed in the text. In fact, the distribution of metadiscourses in the various parts of the paper is different. For example, the introduction, experimental results and conclusions reflect the main results of this paper. Its metadiscourse distribution is high, and its distribution is low in the introduction of related research and methods. The identification process of the same scale greatly affects the identification results.
Therefore, the selection method is improved, and the experimental process is the same as the aforementioned process. Five articles were randomly selected from the word vector training corpus, and the commonly recognised sentences were selected through multi-person collaborative annotation on the labelled data. At the same time, in the identification process, the identification ratio of the beginning and the end of the paper is twice that of other parts. The final experimental results are shown in Table 3.
Results of the second round of recognition
|HLBL word vector addition + R&L algorithm||25.89||37.42||29.54|
|C&W word vector addition + R&L algorithm||27.73||43.87||34.10|
|WMD model + R&L algorithm||30.06||50.89||37.63|
WMD, word movement distance
Through some adjustments to the experimental process, it can be seen that the accuracy rate of the WMD model + R&L algorithm reaches 30.06%, while the other two algorithms are still between 20% and 30%, indicating that the fusion algorithm in this paper has higher accuracy in identifying mutations; from the table, it can be observed that the recall rate of the algorithm in this paper is 50.89%, and that of the other two algorithms are 37.42% and 43.87%, respectively, which proves that the accuracy rate of the verbs recognised by the algorithm in this paper is high. The recognition effect obtained is higher than the F1 of the previous experiment, nearly 10%; the recognition effect based on the WMD model is about 3% higher than that of the other two recognition methods.
To sum up, the R&L algorithm based on the WMD model proposed in this paper has a better effect in identifying the variation of verb forms in English papers, reaching the average level of manual evaluation.
In recent years, metadiscourse in writing can enable authors to write with the relationship between the author and the reader in mind and to use metadiscourse to organise the entire text by combining reader-centred writing methods using language writing methods that revolve around the content of the text. Metadiscourse helps readers understand the author's intentions more accurately and deeply. Based on the R&L algorithm and the WMD model, this study designs an automatic extraction of verb pattern variation and classifies the syntactic components of patterns according to their semantic roles. From the aforementioned comparative experiments, we can find that although C&W word vector addition and HLBL word vector addition achieve complete coverage, the F1 data obtained through the experiment can reach about 10%, and the WMD model is effective in text distance calculation, which proves its effectiveness in the verb pattern clustering task. And in terms of sentence usability, although the recognition effect of this study still has much room for improvement, through careful analysis of the recognition results of this method, it is found that the sentences missed in the result set are generally valuable sentences, and the overall quality is better than that of other two methods. The verb pattern clustering method combining the WMD model and the R&L algorithm achieves good results in the verb pattern variation pattern clustering task, which is a great improvement compared to the known data set results.
Comparison of C&W and HLBL word vectors
|C&W||ENGLISH RCV1||150,000||Not case sensitive|
|HLBL||REUTERS RCV1||260,000||Case sensitive|
One round of recognition results
|HLBL word vector addition + R&L algorithm||22.34||21.24||20.54|
|C&W word vector addition + R&L algorithm||24.67||22.79||22.10|
|WMD model + R&L algorithm||29.70||28.03||28.63|
Results of the second round of recognition
|HLBL word vector addition + R&L algorithm||25.89||37.42||29.54|
|C&W word vector addition + R&L algorithm||27.73||43.87||34.10|
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differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification 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 Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory 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 Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network 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 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 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 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 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 of p-groups 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 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 Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area 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 Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network