With the development of artificial intelligence technology, deep learning technology, such as the convolutional neural network (CNN), has attracted more and more attention from experts and engineering technicians and has been widely used [1,2,3,4,5]. For example, in the field of image analysis, relatively to fully connected neural networks, CNN has greatly improved the accuracy and efficiency of image analysis due to its few connection parameters, shared connection weight values, and local receptive fields, and has been widely recognised by experts and technicians in the field. However, if the structure of a CNN model is complex, the number of neurons contained and the weight parameters are too large, the sample set for training is too small, the number of training rounds is too large, etc., may make the model fall into overfitting during the training process [6, 7], which shows that during training, the data curve fits well and the correct rate is high, but when the trained model is used in the test data set, its correct rate is very low [8].

Aiming at the overfitting phenomenon in the process of model training, many scholars have proposed a series of solutions. For example, given the problems in early machine learning, Li et al. [9] discussed three solutions to overfitting problems based on the BP algorithm, namely early stopping method, adjustment method and automatic generation of hidden nodes. This is an earlier method of researching overfitting problems. The method of machine learning dropout in 2012 has already been proposed to solve the overfitting problems by Srivastava et al. [10] and Hinton [11]. Chen et al. [12] proposed an improved singular value decomposition (SVD) algorithm by studying the overfitting phenomenon in the scoring prediction problem. There are also related research reports in other documents [13,14,15]. For the overfitting problem of the CNN model based on deep learning, a series of solutions have been proposed [16, 17], including the data expansion method, regular method, integrated learning method, early stopping method, etc. However, affected by various factors, including knowledge level, technical application and research time, as well as the insufficient development of deep learning technology-related theories, these research results have their own advantages, but they all have certain limitations.

Based on the characteristics of CNN, the present research on the overfitting of the CNN model by the scholars was carried out. We discuss the method of the maximum value discarding of the pooling layer based on the mask, and by combining the weight decay technology, overfitting can be reduced. Through theoretical analysis and experimental comparison, it is proved that this method can avoid overfitting effectively in CNN model training and improve the ability to detect images.

In general, the CNN structure consists of three layers that are convolution, fully connected and pooling. A group of convolution operations and a group of pooling operations form a convolution-pooling operation. After a group of convolution-pooling operations is executed, the next group of convolution-pooling operations will continue to be executed to complete the sample feature extraction, and the final fully connected layer performs a one-dimensional operation on the obtained features to complete the feature classification. As CNN uses the local connection of neurons, with the sharing of local connection parameters, and the use of downsampling for pooling, it has fewer number of parameter of weight value, fewer features, and better object representation than the general neural network in the extraction process of sample features. Moreover, the characterisation ability has better generalisation.

Assume
^{l}^{l}^{l,k}^{l,k}^{l}^{+1,k} represents the output value obtained by adding the corresponding ^{l,k}^{l,k}^{l}^{l}

After the convolution operation, the next is a pooling layer, which samples the features of the convolution layer to reduce the dimensions and complexity of the network. The pooling operation is explained as follows:
^{l}^{+1,k}, the

Immediately after the pooled operation is completed, the full connection operation will be performed, and the weight parameters of the backpropagation are updated through the loss function calculation. The loss function is directly in contact with the CNN network training effect and model performance. Therefore, the loss function designing is very important. For an explanation, see ‘Weight Decay Calculation’ in the next section.

The previous section introduced the basic principles of CNN. This section is based on the above, a CNN model with maximum pooled dropout and weight decay is designed, to avoid overfitting in the process of model training as much as possible.

Maximum pooled is a common method in the CNN pooling layer. In this paper, the maximum pooled is introduced to reduce the occurrence of overfitting in the model training process. In addition, combined with the maximum pooled of dropout, it can also overcome the disadvantages of neurons with high activation value caused by average pooled, avoid the disadvantage of simple maximum pooled by ignoring the values of other pooling units and can effectively express the characteristics of pooling layer.

Before the maximum pooled dropout operation, first, we describe the mask processing method. The mask processing is to set the activation value of some neurons in the pooling region of the pooling layer to 0 with a certain probability and perform the maximum pooled dropout operation between the holding neurons. The following is a description of the design process.

Assuming ^{l}

In Figure 1, a 2*2 pooling kernel is adopted with a step of 2 for pooling. If only maximum pooled is adopted, the result is [[45], [57]]. If maximum pooled is carried out after using a mask, the result is [[42], [55]], because some pooling units are discarded.

The following is a method for designing the maximum pooled dropout and obtaining the maintenance probability (

From the above, the Bernoulli probability distribution

Analysing formula (6), it can be seen that when performing maximum pooled discarding in the pooling area, the

Assuming the number of feature maps is ^{2rs/t} (including a bias). After the maximum pooled dropout is introduced, under the relevant probability constraints, the pooling units are randomly suppressed, that is,

When training a big CNN, the above-mentioned maximum pooled dropout can better reduce the occurrence of overfitting. However, if the loss function value of the model changes drastically during the training process, it indicates that the weight value of related neurons is too large, so the absolute value of the derivative obtained by backpropagation is large, that is, the complexity of the model is large. The weight decay can reduce the complexity of the model by restricting the value of the neuron so it can’t be too big, thereby reducing the overfitting to a certain extent occurs.

Usually, we use the mean square deviation function as the loss function to detect overfitting of CNN, and is also used for linear regression. This function (named _{0}) is shown in Eq. (8), the parameter is: _{i}_{i}

To reduce the weight value of neurons in the network, we introduce a penalty term in the loss function shown in formula (8), then the loss function (_{w} ||^{2} and _{0}. 1/2 is a constant designed for the convenience of derivation. Taking the derivative of (9), we get:
_{i}_{i−1} +

Continue analysis of Eq. (11), when

Running parameters: The adaptive learning rate algorithm (AdaGrad) is applied in model training, which is an algorithm based on gradient optimisation. The initial the learning rate η = 0.1, and it can automatically adjust. The network weight

Experimental environment conditions: deep learning framework is TensorFlow, programming language is Python3.8.4, OS is Win10, Hardware includes Intel Core i7 CPU@3.00, RAM 8GB, NVIDIA GTX 3080Ti GPU.

Experimental data set: There are 2 data sets in this experiment, one is CVC-ClincDB [19], which belongs to a hospital in Barcelona, Spain. It is a collection of gastric polyp case images from 23 patients, including 31 sequences of 612 clear images, which are divided into 4 categories according to pathological types, namely normal images, polyp images 1, 2, and 3. The resolution of each image is 384*384, 3 channels (RGB), and some of the samples are shown in Figure 2 (left). Because the data set is small, it can be used to detect whether the method will be overfitting in the application of small data sets. Before the experiment, it was divided into a training set (500 images) and a test set (112 images), and the data were normalised to the interval [0, 1]. Another CIFAR-10 is a data set consisting of 60,000 colour images, which includes 10 categories. Some samples are shown in Figure 2 (right). Before the experiment, the data set is also divided into 50,000 images used for training and 10,000 images used to test. Each sample size is 32*32, 3 channels RGB image.

Comparative experiment: To compare experimental results, we selected the GPU parallel optimization-based immune CNN method proposed by Gong et al. [6] (ICNN), the improved neural networks of feature detector algorithm proposed by Hinton et al. [11] (INN_FD) and the random CNN pooling method proposed by Zeiler and Fergus [20] (SCP) for comparative experiments. Among them, the ICNN method has a low test accuracy in the data set (only 80.2%), but its performance is stable and has a solid theory basis. The INN_FD method proposed by Hinton is a discard algorithm combined with a fully connected layer, the method is mature in technology, simple and convenient to implement. The SCP method proposed in Ref. [20] uses a random selection of pooled mask values in the process of training the model, when applying the model to detect samples, the probability of pooling unit in the pooling area is used as the probability weighted mean value of the model, so this method is a better performance to reduce the overfitting of the training model. Therefore, it is feasible for us to choose the above three methods for comparative experiments.

Experimental evaluation indicators: one indicator is the change curve of the loss value and the accuracy, and the other indicator is the error rate generated when the 4 methods are used for data set detection. The actual effect of the method is verified by comparing the change of the curve and the error rate of the sample test with various methods.

For the convenience of description, the maximum pooled dropout and weight decay algorithm proposed in this paper is expressed as MD_WD. The CNN structure proposed by the MD_WD is 1*28*28->6C3->1P2->12C3->1P2->1000N->4N. The model consists of 2 groups of convolution-pooled layers and a fully connected layer. The input of the model is 28*28 single-channel image, and the output is 4 categories. The first group of convolution-pooled is 6C3->1P2, the second group of convolution-pooled is 12C3->1P2, where C means convolution, P means pooled, 6C3 means the number of convolution kernels is 6, and the size of each kernel is 3*3, 1P2 means step size is 1, the size of the pooled kernel is 2*2, 1000N represents the whole connecting layer with 1000 neurons The network structure of the other three comparison methods (ICNN/INN_FD/SCP) see relevant references, which is limited to space and will not be described in detail.

Figure 3 shows the change curve of the loss function value and the correct rate of the MD_WD method proposed during model training, where the maximum number of iterations epoch = 20,000. It can be seen from the left figure that with the increase in the number of iterations, the loss function value of both the training set and the verification set is decreasing. When the number of iterations reaches 10000, the change curve of the loss function value of the training set and the verification set tends to be stable. Similarly, it can be found from the right figure that with the increase of the number of iterations, the accuracy of the training set and the test set is also increasing. When the number of iterations reaches 10000, the curve changes tend to be stable, indicating that our method of MD_WD has not been overfitting in the experiment.

To further verify the performance of the proposed method, we use the above 4 methods to test the data set under different maintenance probabilities, and the error rates obtained are shown in Table 1. Because the ICNN method does not involve the change of maintenance probability, this method does not consider the impact of maintenance probability when the error rate test is carried out. Comparing the data from Table 1, firstly, looking from the horizontal, when the maintenance probability is 0.5, each method gets the lowest error rate except ICNN, but the error rate of the INN_FD varieties most sharply with the maintenance probability; Secondly, looking at the lowest error from 4 methods longitudinally, our MD_WD method has a minimum error, the value is only 1.63%, the SCP method has the smallest value of 2.08%, and the value of INN_FD is 6.23%, indicating that this method can be used on small data sets. It reduces overfitting very well and thus can achieve better detection results.

The error rate (%) under different maintenance probabilities in CVC-ClincDB.

ICNN | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 |

INN_FD | 7.27 | 6.85 | 6.50 | 6.23 | 6.20 | 6.31 | 6.38 | 6.40 | 6.51 |

SCP | 2.23 | 2.17 | 2.10 | 2.12 | 2.08 | 2.26 | 2.31 | 2.37 | 2.49 |

MD_WD | 2.21 | 2.15 | 2.03 | 1.95 | 1.63 | 1.88 | 2.19 | 2.26 | 2.27 |

The experiment in Section 4.2 is based on the test of a small data set, and the CIFA-10 is a large natural colour image data set with 3 channels. Comparing with the data set of CVC-ClincDB in Section 4.2, the difference in each category of this data set is larger. Therefore, the structure of CNN is explored: 3*32*32->16C5-> 2P2->64C3->2P2->2000N->10N, the meaning of each item in the network structure is the same as the previous experiment, and the experiments of the other three methods are the same as the experiments in Section 4.2. The training is carried out for 5000 iterations, and the change curve obtained by the method MD_WD is shown in Figure 4. By analysing the curve on the left of Figure 4, it can be found that with the increase of iteration rounds, the loss curve of the verification set continues to decline, and the curve changes tend to be stable after 4000 iterations. Although the loss value of the training set changes drastically during the iteration process, this value is also decreasing with the rounds of iterations increasing. The accuracy in the right figure gradually rises as the number of iteration rounds increases, and tends to level off around 4000 iterations. It shows that our MD_WD method can still effectively reduce the occurrence of overfitting when tested on large data sets. It shows that the method in this paper can still effectively reduce overfitting when applied to large data sets.

Same as the previous data set experiment, in this data set, we use the above 4 methods to test through the respective trained models under the constraints of different maintenance probability values

The error rate (%) under different maintenance probabilities in CIFAR-10.

ICNN | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 |

INN_FD | 8.87 | 7.95 | 7.76 | 7.10 | 6.15 | 7.21 | 7.38 | 8.12 | 8.69 |

SCP | 4.83 | 4.67 | 4.55 | 4.31 | 4.09 | 3.92 | 4.16 | 4.47 | 5.39 |

MD_WD | 3.21 | 3.08 | 2.97 | 2.93 | 2.81 | 2.88 | 3.08 | 3.16 | 3.35 |

The method of INN_FD has a minimum error rate of 6.15% when

One of the challenges encountered in deep neural networks is the generalisation of the network. The so-called generalisation is to make the model perform well on the test set and also on the training set. This paper proposed a maximum pooled and weight decay in the improved CNN structure and fuses them to reduce the occurrence of model overfitting during training, to improve the generalisation performance of the model. The characteristics of this paper include two aspects. One is to design a dropout method in pooling, that is, after the pooling layer is processed by the mask method, sort the unit values in the pooled area with a certain probability and then discard them according to the maximum value. The second is to introduce a penalty item to update the weight (weight decay) in the iterative update process of weights to reduce the complexity of the network, and analyse and derive it.

However, there are some shortcomings in the proposed method. One is that while performing maximum pooled dropout, when the convolution operation is completed and the semi-linear activation function (ReLU) is used for further processing, it may cause the value of the non-maximum output unit to be 0, thus causing the corresponding neuron to fail update (gradient is 0), that is, a dead neural unit. For another reason, the penalty term parameter

#### The error rate (%) under different maintenance probabilities in CVC-ClincDB.

ICNN | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 | 6.36 |

INN_FD | 7.27 | 6.85 | 6.50 | 6.23 | 6.20 | 6.31 | 6.38 | 6.40 | 6.51 |

SCP | 2.23 | 2.17 | 2.10 | 2.12 | 2.08 | 2.26 | 2.31 | 2.37 | 2.49 |

MD_WD | 2.21 | 2.15 | 2.03 | 1.95 | 1.63 | 1.88 | 2.19 | 2.26 | 2.27 |

#### The error rate (%) under different maintenance probabilities in CIFAR-10.

ICNN | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 | 7.44 |

INN_FD | 8.87 | 7.95 | 7.76 | 7.10 | 6.15 | 7.21 | 7.38 | 8.12 | 8.69 |

SCP | 4.83 | 4.67 | 4.55 | 4.31 | 4.09 | 3.92 | 4.16 | 4.47 | 5.39 |

MD_WD | 3.21 | 3.08 | 2.97 | 2.93 | 2.81 | 2.88 | 3.08 | 3.16 | 3.35 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Industrial transfer and regional economy coordination based on multiple regression model Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Research on sustainable design of sports centre based on algorithm verification Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology Research on innovative strategies of college students’ English teaching under the blessing of big data Institutional investor company social responsibility report and company performance Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups 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