In the 5000 year long history of the Chinese nation, ancient calligraphy and painting, as the essence of Chinese art and culture, has spread to this day. The art of Chinese calligraphy is the foundation of Chinese traditional culture. With the construction of changeable lines and the perfect unity of Qi, rhyme, spirit and interest, it occupies an important position in the history of world culture; Based on the art of Chinese calligraphy, the style of Chinese painting is abstract and subjective. Its content is not a simple mapping of real objects, but the charm of things expressed by the writer through condensation and sublimation. As a unique art form, ancient Chinese calligraphy and painting enjoys a high reputation in the cultural history of the world because of its deep-rooted and unique characteristics. Therefore, ancient Chinese calligraphy and painting has precious archaeological and cultural value. It plays a vital role and significance in the dissemination of history and culture and the study of history and culture. With the development of the Internet, more and more ink paintings appear on the Internet. How to easily retrieve and classify ink painting has become a hot spot of scientific research in recent years. Because Chinese painting is different from western art, its formation depends on brush, ink, water and color. The intensity change of ink can be expressed by the gray change of pen track. And Chinese painting usually represents the style of an artist by drawing the outline, texture and volume. It is mainly based on lines, while western painting emphasizes the vivid expression of objects with light. This makes Chinese and Western paintings have obvious differences in modeling methods. Therefore, some existing studies on Western painting can not be directly used for the analysis of ink painting. In addition, because ink painting does not use color or uses less color, most of them do not have rich color performance, so some existing color based feature extraction and classification algorithms are not suitable for the research of ink painting[1].

The traditional Chinese ancient calligraphy and painting takes rice paper, silk and silk as the basic materials. In the long-term preservation process, human factors or inevitable natural environment, such as humidity, high temperature, light and dust, will cause the ancient calligraphy and painting to be damaged and faded to varying degrees, which undoubtedly increases the difficulty and cost of management, collection and art dissemination. With the emergence of digital art with computer as the carrier, the digital management of ancient calligraphy and painting has attracted the attention of all sectors of society. The digitization of ancient Chinese calligraphy and painting and its storage, management and dissemination on the computer have brought great convenience to collectors and cultural workers. Especially for cultural workers, the use of computer technology for the simulation of ancient Chinese calligraphy and painting is a very ideal means of communication, so that it can be spread in emerging media, such as television, Internet and giant multimedia advertising. The digital application of calligraphy and painting can more easily spread Chinese traditional art and carry forward the quintessence of Chinese culture, which is conducive to the development of Oriental Art all over the world[2].

Firstly, in the pixel domain, an overall style feature extraction algorithm of ink painting based on histogram is proposed, and then the local area with the most representative stroke style is located based on Sobel edge detection method to obtain the local detail style information describing the stroke. In order to take into account the overall and local artistic style of ink painting, a diffusion fusion algorithm based on pseudo linear direction is proposed. The algorithm is regarded as a pointer to ensure that the final classification result tends to select the smallest artistic style features, so as to achieve the automatic classification of ink painting based on artistic style and eliminate the influence of content factors to the greatest extent[3].

Gidey HH and others believe that with the rapid development of material civilization and spiritual civilization, traditional Chinese painting, as a treasure of Chinese art, has received great attention. Because the paper scroll is not easy to preserve, the digitization of traditional Chinese painting is an irresistible trend, and the computerized management of traditional Chinese painting. Including indexing, retrieval, analysis and classification is becoming an important research topic in many research fields, such as image processing, multimedia, digital archiving and preservation[4]. AnsariA and others believe that traditional calligraphy and painting works are very rare and precious, and are vulnerable to natural factors such as light, temperature and humidity and some human factors. If they are not preserved properly, they will cause irreparable damage to calligraphy and painting and reduce their artistic value. The digitized calligraphy and painting can be saved permanently without losing any information[5]. LiB and others found that with the rapid development of China's economy and culture, intelligent analysis and processing of calligraphy and painting resources has increasingly become a social need. Digital calligraphy and painting library will also become the public information center and hub of the future society. Many existing books of traditional calligraphy and painting are rare and precious. Most of the works are distributed in museums all over the world[6]. XyA and others transform the fingerprint image with wavelet transform, and enhance the image by means of global texture filtering and local direction compensation on the sub image. This method is complex and time-consuming, which is not conducive to the requirements of real-time system[7]. WangZ and others used the pattern information to enhance the image. First estimated the direction of the fingerprint, and then enhanced the image according to the direction information. In order to prevent the influence of noise on the pattern estimation, this method needs to consider a large neighborhood and a large amount of calculation. Moreover, the above two methods can not effectively repair when there is a large fracture on the ridge[8].

After a lot of research and analysis, we found that most art historians distinguish the creators of ancient paintings mainly based on some typical strokes and ink technique characteristics reflected in the paintings when evaluating, analyzing, comparing and identifying the true and fake paintings. Artists often use a magnifying glass to see the details and local characteristics of a painting in order to identify the authenticity. And the overall characteristics of a painting can not accurately and completely interpret the artist's artistic style. Therefore, based on the description of the overall style of ink painting, this section studies the local area and stroke of ink painting in order to highlight the artist's grasp of the key local style.

Chinese painting is based on lines, which draw the outline, texture and volume. Therefore, the pen used in traditional Chinese painting mainly refers to the line, which is mainly represented by the slender pen path. The pen path is not only the basic element of ink painting, but also an important modeling means of ink painting. The brush track can reflect the skills of different painters, such as the direction, strength and speed of pen movement. Brushwork plays a decisive role in describing the artist's artistic style. Therefore, the primary task of extracting local features is to extract all brushwork in the whole painting, so as to locate the local area in the whole painting that can best reflect the artist's detailed brushwork information and brushwork features[9].

Edge detection technology can effectively capture the location of sharp changes in pixel gray value, so as to find line features, including image “edge” and “line”. “Edge” refers to the boundary between those regions with different local characteristics of the image, which is expressed as the discontinuity of the local image, such as the mutation of gray level, the mutation of texture structure and so on. The “line” can be considered as a pair of edges with small width and the same image characteristics in the middle area, that is, a pair of edges with small distance form a line. The edge detection of traditional Chinese painting can help to find the local feature areas with significant changes in the image attributes, so as to reflect the important events and changes of the attributes and the important structural attributes of the image. In this target local area, the gray histogram is taken to describe the detailed style information of the pen track: the following pen strength, the shape of the pen track, the distribution of the pen track and the hierarchical information between the pen tracks. In addition, two factors should be considered in local feature extraction: (1) detect the typical stroke information that can best reflect the painter's style; (2) locate the representative area that can best represent the painter's style on the whole image. Considering factor 1, this paper uses edge detection technology to extract all strokes in ink painting. For factor two, a window function is used to scan all areas of the whole image step by step to process all trace information. The proposed local feature extraction algorithm is as follows:

Let

Where ∇_{s} represents Sobel operator and

The next step is to segment the local region. There are many ways of region segmentation, such as quadtree method, ROI region of interest method, fixed size segmentation, etc. However, the fixed module segmentation method is adopted in this paper, which is simple and intuitive, and the experiment shows that the classification performance is very good. Inspired by image and video compression coding, the size of local area can generally be defined as 128×128, 64×64 or 32×32. In order to obtain enough detailed features without too much computation, this section defines a 64×64 pixel image block through experiments to locate the local area in an image that best reflects the characteristics of pen style:

Where 0 <

The most representative image block _{L}

Where

Therefore, _{L}_{L}

In essence, the design idea of local representative region location algorithm based on Sobel edge detection algorithm follows the following principles:

The result of edge detection contains the position information of all strokes;

Select _{L}_{L}

The implementation of this design has many advantages, which are listed as follows:

(1) The influence of the choice of threshold value on stroke extraction. Once we have calculated the derivative, the next step is to give a threshold to determine where the edge is.

The lower the threshold, the more edges can be detected, the more vulnerable the result is to the influence of image noise, and the easier it is to pick out irrelevant features from the image. In contrast, a high threshold will lose thin or short segments. A common method is threshold selection with hysteresis. This method uses different thresholds to find edges. The first is to use a threshold upper limit to find the starting point of the edge line. Once a starting point is found, we track the edge path point by point on the image. When it is greater than the lower limit of the threshold, we keep recording the edge position until the value is less than the lower limit. However, this method needs to find the appropriate threshold for each image of each artist, and requires human participation, which violates the principle of automatic classification and takes too much time[11].

(2) After region localization, the local features extract the histogram from the gray image, instead of simply considering the shape, color and other information of the edge after edge detection, so as to make the local features more comprehensive and effective.

The overall characteristics of the image can well describe the layout, pen and ink force distribution and other characteristics of the whole image from a macro perspective. On the other hand, the local characteristics of the image describe the detailed information of the pen track concentrated in a small neighborhood, and show the local characteristics of the image, such as the intensity, distribution, shape and contour of the pen track, which can reflect the detailed pen operation information and characteristics of the painter.

Moreover, according to the observation, when Chinese art historians identify whether art works are fakes or appreciate paintings, they often hang the paintings in the distance and observe the whole painting from the macro perspectives of overall momentum, white space layout, object and image distribution in the paintings. Then, put the painting in front of you and use a magnifying glass to carefully observe a certain stroke feature, or carefully experience the painter's treatment method and stroke characteristics in a local area of a certain detail. Finally, the comprehensive evaluation and appreciation results are given based on the two factors.

Information is a description of the uncertainty of the motion state or existence mode of things. Information entropy is a concept used to measure the amount of information in information theory. It describes the uncertainty of the source and the average amount of information of all targets in the source. Information quantity is the central concept of information theory. Taking entropy as the uncertainty of a random event or the measure of information quantity, it lays the scientific theoretical foundation of modern information theory and greatly promotes the development of information theory. Suppose

The direct value _{1},…, _{n}

Information entropy reflects the degree of uncertainty of information. In classical probability theory, it is expressed as the degree of uncertainty of random variables; In the theory of fuzzy mathematics, information entropy reflects the degree of fuzziness of things. The size of information line reflects our mastery of information. The more information we master, the smaller the information line. Therefore, it is very important to evaluate the information expected value of paintings.

The diffusion equation is a nonlinear partial differential equation, and the diffusion tensor needs to be updated in each iterative evolution. However, due to the existence of Gaussian convolution, the amount of calculation is very large. In order to reduce the amount of calculation, the pseudo linear directional diffusion equation is adopted in this paper. The main idea is that the diffusion tensor is updated only after a finite number of iterations, rather than every iteration. It is expressed as follows:

According to the above analysis, this paper proposes to use the following directional diffusion equation for image enhancement:

From the perspective of diffusion, the formula is actually a nonlinear diffusion along directions _{1} and _{2}. in this paper, it is called directional diffusion equation, because the value of

In this paper, the pseudo linear strategy is based on the diffusion equation, which mainly evolves along the grain direction, and this diffusion method will not cause the sharp change of the grain on the fingerprint image, so the diffusion tensor dependent on the grain direction will not mutate in a finite evolution. Therefore, the pseudo linear method can be adopted in the finite iterative evolution. It can basically keep the enhancement result consistent with the nonlinear diffusion result while improving the operation efficiency. The specific implementation of the formula is basically consistent with the formula, as long as the diffusion tensor is updated periodically. The selection of update cycle and the space-time step adopted are larger than the relevant space-time step ratio, so a shorter update cycle should be selected; on the contrary, a longer update cycle should be selected.

Chinese painting is a brilliant pearl in the world art world and an important part of China's traditional art and culture. As the essence of the country, the authenticity identification of Chinese painting has always been a difficult problem in the field of Chinese painting collection[13].

Authenticity identification refers to the use of a variety of methods to judge the works claimed to be authentic authors to see whether they are the same as authentic works. At present, there are three commonly used methods: first, expert empirical identification, mainly visual identification; Second, based on the authenticity identification of physics and chemistry, obtain some physical and chemical properties of the paper and other substances of the work through physical and chemical means to identify the author of the work; The third is computer-aided identification, which obtains a series of quantitative authenticity indicators and evidence through computer. The biggest disadvantage of the traditional identification method of authenticity of Chinese painting is that it contains too many subjective factors of identification experts, resulting in the lack of objective and quantifiable indicators, so that for the same calligraphy and painting works, different identification experts will have different identification opinions.

Because traditional Chinese paintings are composed of smooth regions, the algorithm in this paper is mainly based on the assumption of surface smoothing, that is, the depth values in regions with similar gray values of pixels are generally the same. Based on this assumption, a local area of the image can be regarded as a node to improve the original algorithm. There are many kinds of image segmentation algorithms. In this paper, ROI region extraction and feature ROI are used to convert the traditional direct calculation of the true and false state of each pixel into the calculation of the true and false state of each region. When messages are transmitted between regions, the algorithm speed is improved by removing the information with low support of true and false states. The algorithm mainly includes the following steps:

Select three types of objects in Qian Weicheng's landscape paintings and determine the samples (other paintings are classified according to the painting content);

ROI region extraction of sample image;

For each class of objects, the maximum likelihood estimation method is used to obtain the parameters of the interaction function and correlation function from a group of training samples, and then the function formula can be obtained;

For the sample area selected by each type of object, the interaction function and the compatibility matrix of adjacent areas are calculated.

Set the initial value of the message matrix in the eight directions in the sample image to 1; The experimental samples were selected from Li Keran's buffalo and his works in other periods, as well as the authentic works of Qian Weicheng's landscape paintings and the fake Eagle works copied by other painters. There were 20 true and false images of each type, 13 of which were true and 7 of which were false, all from the National Museum of China and the Institute of science, technology and art of China. Among them, from Qian Weicheng's landscape paintings, we selected Qiao tree trunks, Qiao rocks and 8 mountains and stones with vegetation as the experimental objects, and randomly intercepted 115 tree trunks with a size of 30×30 from each experimental object; 120 rock blocks of 60×60; There are 62 mountain rocks with vegetation of 60×60.

The object recognition results in the image are shown in Table 1, and Table 2 shows the comparison of algorithms in the literature[14].

Comparison of correct recognition rates of image blocks in landscape paintings

Block type | Number of test samples | Literature algorithm | In the algorithm |
---|---|---|---|

The trunk block | 114 | 83.00% | 89.00% |

Rock block | 120 | 89.00% | 89.00% |

Mountain stones with vegetation | 57 | 73.00% | 86.00% |

Comparison of the number of errors in the recognition and judgment of various objects in landscape paintings

Object type | Number of test samples | Literature algorithm | In the algorithm |
---|---|---|---|

Tree trunk | 15 | 1 | 1 |

Rock | 15 | 1 | 0 |

Mountains and rocks with vegetation | 8 | 2 | 0 |

For the original belief propagation algorithm, each pixel should be calculated when reasoning the state of the object block, and only the influence of four directions on the node should be considered in message transmission. After the image is divided into blocks, the algorithm considers the influence of eight directions on the region block, which improves the accuracy of image block and various object recognition. The two methods of image segmentation and eliminating non important information during message transmission both improve the running speed of the algorithm. From the analysis in Table 3, it can be seen that the running time of the improved algorithm is 46% of that of the original confidence propagation algorithm.

Algorithm time comparison (unit: seconds)

Block type | Number of pixels | Literature algorithm | Points the area block number | In the algorithm |
---|---|---|---|---|

The trunk block | 900 | 3.17294 | 36 | 1.58746 |

Rock block | 3600 | 6.91906 | 144 | 2.46921 |

Mountain stones with vegetation | 3600 | 7.25468 | 144 | 2.73526 |

Based on the analysis of the principle of pixel level confidence propagation algorithm, the original algorithm is improved by dividing traditional Chinese painting into blocks, considering the transmission information in eight directions around the area block, and eliminating non important information during message transmission. The experimental results show that the improved algorithm not only improves the recognition accuracy of image blocks and objects, but also reduces the running time of the algorithm. However, in the experiment, it is found that the improved confidence propagation algorithm has poor identification effect in traditional Chinese painting with rich texture information. In the next step, we will focus on how to improve the identification effect of the algorithm in this case.

This paper extracts ROI based on three low-order features of the image, including extracting the region with the fastest gray change of traditional Chinese painting based on color features; The corner of the image is extracted based on the shape feature, and the area around the corner is set as ROI area; Texture extraction based on texture features, and proposed the optimal weight algorithm to comprehensively extract the feature ROI of the image. For each different type of traditional Chinese painting works, there is an optimal weight corresponding to it.

At present, there are few studies on the use of image recognition technology to assist the authenticity identification of Chinese painting, and there are still many problems. Among them, because Chinese painting is reflected through strokes and ink, it is very difficult to extract fixed and unique features from this changeable description method. Therefore, the method in this paper is also difficult to completely extract the unique style of the author from a work. Therefore, the key research content in the next step is to consider how to extract the unique style features that can represent the author from the various forms of Chinese painting techniques, and the features are well invariant in the changing factors such as light and angle. In addition, the research in this paper mainly studies the painting content of Chinese painting. In the next step, we can study it from the two aspects of seal and title.

#### Algorithm time comparison (unit: seconds)

Block type | Number of pixels | Literature algorithm | Points the area block number | In the algorithm |
---|---|---|---|---|

The trunk block | 900 | 3.17294 | 36 | 1.58746 |

Rock block | 3600 | 6.91906 | 144 | 2.46921 |

Mountain stones with vegetation | 3600 | 7.25468 | 144 | 2.73526 |

#### Comparison of correct recognition rates of image blocks in landscape paintings

Block type | Number of test samples | Literature algorithm | In the algorithm |
---|---|---|---|

The trunk block | 114 | 83.00% | 89.00% |

Rock block | 120 | 89.00% | 89.00% |

Mountain stones with vegetation | 57 | 73.00% | 86.00% |

#### Comparison of the number of errors in the recognition and judgment of various objects in landscape paintings

Object type | Number of test samples | Literature algorithm | In the algorithm |
---|---|---|---|

Tree trunk | 15 | 1 | 1 |

Rock | 15 | 1 | 0 |

Mountains and rocks with vegetation | 8 | 2 | 0 |

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An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes 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 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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 Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on 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