The linear regression equation constructed according to the reading satisfaction of books can be used to express the uncertain linear relationship between Y and XI. The specific formula is as follows:

In the above formula, Y represents the dependent variable, namely, reader satisfaction, xi represents the evaluation factor affecting reader satisfaction, β is a regression coefficient, and ε refers to random error.

It is assumed that the satisfaction of library users will be affected by three indicators, the first is collection resources and equipment X1, the second is library service attitude X2, and the last is service and opening time x3. According to the accumulated data collected, the usual form of the assumed ternary linear regression equation is:

Then the least square estimation can be used to obtain:

Among them,

Calculate the available

It can be seen that the linear regression equation between y and X1, x2 and x3 is:

The variance analysis results are as follows:

The standardized regression coefficients obtained from the above research not only directly show the influence of various indicators on the overall satisfaction, but also grasp more basic information related to system design. For example, among the factors studied in constructing the equation model in this paper, collection resources and facilities are the most influential, followed by service and opening time, and finally the service attitude of library staff. Therefore, it is very important to select the collaborative filtering algorithm based on the results of linear regression equation analysis to build a personalized recommendation system for libraries, which is not only the basic platform of collection resources, but also an important facility for the implementation of various services.

On the one hand, content recommendation. This technology belongs to text processing content in essence, and its practical application and theoretical research are very mature. The most common application method is TF-IDF algorithm, which uses keywords to analyze wiJ of important level of text. The specific formula is as follows^{[1]}:

In the above formula, N represents the total number of texts, fij represents the number of occurrences of key word Ki in text DJ, and the actual text DJ can use vector DJ = (w1j, w2j... , WKJ), k refers to the number of keywords.

If Userprofile (C) = (w1c, w2c... , WKC) refers to the user's preference degree for various keywords. Then ric calculation formula of user C's preference score for text I is shown as follows:

The principle of content recommendation technology is very simple. It only needs to define the fixed content attributes of users and projects. Therefore, problems such as system cold start and data sparsity will not occur during operation. The accuracy of actual recommendations can be improved by assuming that users and project content can be represented visually with features.

Collaborative filtering, on the other hand. The principle of this technology can be divided into two types, one is memory algorithms, such as user-based or project-based collaborative filtering; The other is model algorithm, such as clustering algorithm, graph model algorithm and other content.

Firstly, user-based collaborative filtering needs to know user preference information first, and then calculate the similarity between active users and other users. Then select neighbors for active users according to similarity; Finally, the specific scores of active users for evaluation items are predicted by combining the historical preference information of similar neighbors, and the recommendation results are formed. The specific flow chart is as follows

Firstly, the similarity of users should be calculated. The most commonly used method is cosine similarity and Pearson correlation coefficient. The specific formula is as follows:

In the above formula, simuv represents the similarity between user U and user V, u and V represent the scoring vectors of two users, | u | and | v | represent the modules of two scoring vectors, rui and Rvi represent the scores of two users on item I.

The Pearson correlation coefficient can be calculated as follows:

In the above formula, R_{ui} and R_{vi} represent the score of user U and user V for item I, the average score of users, and Iuv represents the set of items jointly scored by two users.

Secondly, it is necessary to analyze and search for similar neighbors. The most common way is to use the K-nearest neighbor method, that is, to select K users with the largest similarity with the current active users as the actual similar neighbors. At the same time, after setting a certain threshold, the similarity between the user and the current active user can be judged. If the value exceeds the threshold, user V is regarded as a similar neighbor.

Finally, to study and generate recommendation results, the simplest way is to average the scores of neighboring users, and the specific formula is as follows^{[2]}:

In the above formula, N represents the similar nearest neighbors set of active users, and k represents the actual number of nearest neighbors in N. In order to obtain better recommendation effect, the method of weighted average can be used for calculation, one is to directly carry out weighted average of neighbor scores, the other is to calculate the increase of user scores first, and then carry out weighted average calculation, the specific formula is as follows:

Second, collaborative filtering algorithm based on item. According to the analysis of the operation flow chart shown in the figure below, there are two ways to calculate the similarity of items first, one is cosine vector, and the corresponding calculation formula is as follows:

The other refers to the correlation coefficient, and the actual calculation formula is:

Secondly, similar neighbors should be found, and the selection method is consistent with user-based collaborative filtering algorithm. Finally, the weighted average algorithm is also used to obtain the recommendation results, the specific formula is as follows:

Thirdly, model-based collaborative filtering needs to construct a recommendation model by machine learning or mathematical model in accordance with the user's scoring data, so as to recommend the content with the largest predicted value to users on the basis that there is no scoring item value in the predictive analysis.

According to the analysis of the personalized recommendation system proposed in the above research, it can be seen that in order to evaluate their recommendation effect in the book service system, the subordinate content should be selected for analysis:

First, it refers to the error standard. This calculation should start from two aspects. On the one hand, it refers to the average absolute error, which is one of the most common and simplest standards for system performance evaluation. The accuracy of the actual data is judged by comparing and analyzing the deviation between the predicted average value of the system and the actual score value. Example 6. For target user U, the score data of the actual test set is {Q1, Q2... , qn}, the data set of prediction score obtained by system calculation is {P1, P2... Pn}, then the corresponding mean absolute error can be calculated as follows^{[3]}:

On the other hand, it refers to the mean square error, which can intuitively show the discrete level of scoring data. The corresponding calculation formula is as follows:

In the above formula, n refers to the number of scores, QI refers to the actual score result of users, and PI refers to the predicted score result of users.

The second is the probability of hit ratio. This calculation should also start from two points, one is the accuracy rate, the specific formula is as follows:

In the above formula, T (u) represents the test data set, and R (u) represents the list of recommended items finally constituted by the system.

The second is the recall rate, the specific formula is as follows:

The last refers to the coverage rate, which is the proportion of the final recommended projects in the total number of projects, visually presenting the algorithm recommendation level. The specific formula is as follows:

In the above formula, U represents the user set, R (U) represents the combination of recommended items for a certain user in the user set, and I represents the set of all commodities.

Clustering is a process of dividing the data in the data set into different classes according to specified standards. It does not require any prior knowledge of classification information, but selects specific mathematical methods to automatically complete classification according to the rules. Suppose the data sample set is {X}, which contains N m-dimensional vectors, divided into k categories in total. If the center point of data class Cj is Y={y1, y2... Ym}, then the clustering criterion is that the sum of the distances between sample points in the class and the cluster center should be minimized. The actual calculation formula is as follows^{[4]}:

In the above formula, Y represents the center point of class Cj, x represents the vector of class Cj, and the distance d (x, y) between vector X and the center point of clustering can be calculated as follows:

In the above formula, m represents the dimension of the data, d (x, y) represents the Manhattan distance if q is equal to 1, and D (x, y) represents the Euclidean distance if q is equal to 2.To improve the traditional clustering algorithm, the clustering center should be selected first, that is, the final cluster number. It should be noted that quantity selection is subjective because it can be influenced by the user's experience. Therefore, in order to avoid affecting the final value, this paper proposes the idea of self-organizing clustering, that is, a membership threshold is specified to automatically finish the clustering process, and the actual number is determined according to the algorithm.

As the application content proposed by Gori, Pucci and others in their research, ItemRank algorithm will use the scoring mechanism of random walk to recommend. This algorithm is mainly divided into two parts, one is to constitute the association graph, the other is to carry out random walk in the association graph. When the association graph is generated, all products are regarded as nodes on the way of association, and there is a weight value WIJ between points. The actual size is the number of users scoring points, and the corresponding association matrix is^{[5]}:

The final correlation matrix can be obtained in the normalization process.

Assume that all user UJ's meet the following conditions:

So for M vectors, you can get it:

In the above formula, Ri represents the ith row in the scoring matrix R, and α represents the user defined constant term, which is generally 0.85. The improved content of ItemRank algorithm based on clustering is shown as follows:

The first step is to tag the user. In order to improve the computational efficiency of the application algorithm, the user rating vector can be analyzed by clustering. The improved clustering algorithm proposed in this paper only needs to propose predefined constants and does not need to specify the number of classes directly. At the same time, according to the scoring habits of different users, all scoring data can be normalized before clustering, so as to reduce data error. If the scoring vector of all user UI is [RI1, RI2... rim], then the normalized calculation formula is:

In the above formula, n and m represent the number of users and products in the system, and the user UI rating vector after normalization will be transformed into [xi1, XI2,... xim].

The second is matrix dimension reduction. For all products pj, its z-dimensional eigenvector xj is regarded as (xj1, xj2... , XJZ), z represents the number of clustering in the above operations, and the element numerical calculation formula of feature vector Xj is as follows:

Where the value range of δ DK is controlled as follows

The actual matrix T is:

Transform the original high-dimensional scoring matrix of order N ×m into low-dimensional scoring matrix, and the specific formula is as follows:

Again, it refers to composing the association graph. Among them, the weight calculation formula between nodes is as follows:

Among them,

In the above formula, if the weight value is too large, it is difficult to accurately recommend the product after partial clustering. Therefore, the actual upper limit can be set to 1. The corresponding association matrix is as follows:

Normalization is carried out according to Founder's recommendation, and the specific formula is:

In the above formula, the values of I and j are lower than q.

Finally, it refers to the recommendation, and the specific formula is as follows:

Based on the analysis of multiple linear regression equation constructed by the above research, and based on the collection of relevant book data resources, it is clear that three influencing factors, namely collection resources and facilities, service and opening time, and service attitude of library staff, have an impact on readers’ satisfaction. At this time, in order to meet the needs of readers and build an effective recommendation system by using the collaborative filtering algorithm studied above, it is necessary to pre-process the book information to remove worthless original records and save only the information useful for the recommendation process. The actual data cleaning code is shown in the Table 1 below:

Part of the code for data cleansing

SELECT User ID Book ID Day |

FROM Borrow_Update |

WHERE UserID In (SELECT Distinct(User ID) |

FROM Borrow_Update |

GROUP BY User ID |

HAVING Count(*)>=10) |

At the same time, the scoring information should be obtained according to the above equation model. Generally speaking, the longer a person borrows a book, the more he likes it. Therefore, the borrowing time of a user can be regarded as scoring information. If the user scores a book within 10 days and borrows a book for 90 days, the actual scoring formula is as follows:

In the above formula, Rui represents user U's score for book I, and TUi represents user U's borrowing time for book I. By calculating the average number of days for users to borrow books, the specific formula is as follows:

And put into the above scoring formula, a new scoring formula can be obtained^{[7,8]}:

At the same time, the user's reading time can further reduce the scoring error, as shown in the following formula:

In the above formula, TI represents the average number of days a book is borrowed.

In this paper, the selected data set is the book borrowing records of a university library in 2019 and 2020. After data cleaning and merging, 10,000 valid borrowing information are finally obtained. On the basis of sorting out and analyzing the multiple linear regression equation model proposed in this paper, the improved fuzzy recommendation algorithm (SCC) studied in this paper and the traditional ItemRank recommendation algorithm are compared and analyzed by designing experiments. The actual evaluation criteria are divided into three parts: MAE, precision and recall. The specific calculation formula is described above.

Users are divided into multiple subsets according to the number of users’ scores, and five users are selected from each interval to participate in the 50% discount cross-validation recommendation. The actual running results are shown in the following Table 2:

Analysis of experimental running results

Interval Indicators | MAE | Precision | Recall | |||
---|---|---|---|---|---|---|

ItemRank | SCC | ItemRank | SCC | ItemRank | SCC | |

25 | 0.9136 | 0.8759 | 25.6345 | 28.918 | 21.6987 | 36.8932 |

50 | 0.8695 | 0.8412 | 26.8482 | 32.7127 | 23.6854 | 35.2653 |

75 | 0.8373 | 0.8223 | 27.8232 | 37.0952 | 21.7249 | 32.0987 |

100 | 0.8223 | 0.8106 | 29.2438 | 39.1182 | 20.2262 | 31.9691 |

125 | 0.8191 | 0.8109 | 31.0859 | 42.9914 | 20.6581 | 32.0761 |

150 | 0.8113 | 0.8101 | 32.1153 | 43.2067 | 21.2249 | 33.1001 |

175 | 0.8104 | 0.8081 | 33.2696 | 45.2217 | 21.4403 | 31.9589 |

200 | 0.8095 | 0.8078 | 35.5989 | 46.2654 | 19.9823 | 31.1310 |

225 | 0.8093 | 0.8073 | 35.5621 | 48.1123 | 21.4682 | 33.1041 |

250 | 0.8088 | 0.8071 | 37.6690 | 48.1182 | 23.7641 | 33.6662 |

Combined with the above chart analysis, it is found that compared with the traditional ItemRank algorithm, the COMPUTATION performance of SCC algorithm studied in this paper has been effectively improved. From the calculation results of mean absolute error, the smaller the actual value is, the faster the prediction progress of the algorithm is and the stronger the application performance of the actual algorithm is. However, the broken lines formed by SCC algorithm in this paper are below the traditional ItemRank algorithm, in other words, the actual performance is superior. When the data is in the range of 25, the gap between them is more obvious, that is to say, when the data is too sparse, the improvement effect of SCC algorithm is more significant than that of traditional ItemRank algorithm. In the calculation of accuracy and recall rate, the higher the value of both, the stronger the application performance of the algorithm. The broken line of SCC algorithm is above the traditional ItemRank algorithm, which proves that the recommendation accuracy of the two algorithms will continue to improve with the increase of interval number, that is to say, the sparsity of data is getting lower and lower, and the number of scores proposed by users is increasing, and the accuracy of the two algorithms will also improve. In this paper, SCC algorithm conducts cluster analysis for collected data, and the actual calculation results are more clear. Therefore, the performance of SCC algorithm during calculation is superior to that of traditional ItemRank algorithm, and it is bound to provide interested books for users eventually[9,10].

To sum up, in the field of books, the construction of collaborative filtering personalized recommendation system based on recommendation algorithm is the main research topic at the present stage. Therefore, this paper selects ItemRank algorithm with clustering improvement as the core during the recommendation period, and the final practice results prove that it can not only effectively improve the comprehensive level of the application algorithm, but also can really recommend the books that users are interested in by complementing each other's advantages.

#### Analysis of experimental running results

Interval Indicators | MAE | Precision | Recall | |||
---|---|---|---|---|---|---|

ItemRank | SCC | ItemRank | SCC | ItemRank | SCC | |

25 | 0.9136 | 0.8759 | 25.6345 | 28.918 | 21.6987 | 36.8932 |

50 | 0.8695 | 0.8412 | 26.8482 | 32.7127 | 23.6854 | 35.2653 |

75 | 0.8373 | 0.8223 | 27.8232 | 37.0952 | 21.7249 | 32.0987 |

100 | 0.8223 | 0.8106 | 29.2438 | 39.1182 | 20.2262 | 31.9691 |

125 | 0.8191 | 0.8109 | 31.0859 | 42.9914 | 20.6581 | 32.0761 |

150 | 0.8113 | 0.8101 | 32.1153 | 43.2067 | 21.2249 | 33.1001 |

175 | 0.8104 | 0.8081 | 33.2696 | 45.2217 | 21.4403 | 31.9589 |

200 | 0.8095 | 0.8078 | 35.5989 | 46.2654 | 19.9823 | 31.1310 |

225 | 0.8093 | 0.8073 | 35.5621 | 48.1123 | 21.4682 | 33.1041 |

250 | 0.8088 | 0.8071 | 37.6690 | 48.1182 | 23.7641 | 33.6662 |

#### Part of the code for data cleansing

SELECT User ID Book ID Day |

FROM Borrow_Update |

WHERE UserID In (SELECT Distinct(User ID) |

FROM Borrow_Update |

GROUP BY User ID |

HAVING Count(*)>=10) |

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An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry 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