The World Conference on Artificial Intelligence (AI) in Music (Summit on Music Intelligence [SOMI]: Music IntelLigence) was held in Beijing from 22 October to 24 October 2021. The conference was jointly organised by the Central Conservatory of Music and the China Association for Artificial Intelligence. International Nobel physicist Li Zhengdao wished this conference thus: ‘science and technology integration, the combination of science and technology, I wish the AI Music Conference a complete success!’ The development of human society and the development of science and technology will have a great impact on music. In the industrial age, the smelting technology invented the copper pipe and realised the symphony. The rise of electronic technology and computer applications has brought about the prosperity of intelligent music. Nowadays, with the rise of new information industry applications, such as fifth-generation wireless technology (5G), virtual reality (VR), augmented reality (AR), AI, cloud computing and big data, AI music is also rising [1].

In 2019, China Ping, an AI research institute, debuted the symphonic variations on ‘Me and My Motherland’ by AI at Shenzhen Concert Hall [2]. The work adopts the self-changing mode of ‘I and my Country,’ with other classical music elements added to the variations. The whole piece is divided into five sections, with Me and My Motherland as the theme, showing the grand picture of the development of new China. The music director of Shenzhen Philharmonic Orchestra, Lin Daye, highly praised the quality of its music and proposed that AI will be handed down in 5–10 years. In fact, AI music is not a new research direction, it has been developed over several years; especially in recent years, AI music has aroused great attention [3].

AI is generally defined as ‘machine-displayed intelligence,’ while AI music refers to music produced through operations based on systems such as computer neural networks (NNs). At present, AI technology is still in its infancy and far from real maturity. But some of its intelligence is already impressive, such as Google's AlphaGo, which beat the world's most famous Go player. The basic principle of AI and chess is basically the same; AI uses the genetic algorithm, NN, Markov chain, hybrid algorithm and other technologies (through the rules of the computer) and establishes a massive database and then applies deep learning and its rules, structure and other analyses [4].

From the traditional point of view, the advantage of machines is that they can help people to do repetitive mechanical work, rather than creative work. However, with the continuous development of AI technology, its application in music creation, production, analysis, education and other aspects is increasingly becoming extensive [5]. With the development of AI technology, the efficiency of music creation has not only been greatly improved, but it has also solved the previous work that was difficult to be effectively completed by humans. In the present reasonable method, rules and the corresponding algorithm model are used to create music. AI technology can solve the difficult problems in the traditional music industry, including ‘creation standards and evaluation of AI music’, ‘deep learning’, ‘the potential of AI virtual singers’, and the application of AI in various fields. Machine learning can be said to be an important branch of AI, and it has a profound impact on other aspects of AI [6]. Using AI technology to realise automatic singing bel canto is not new research; related research has been done for many years, but there have been technical limitations.

Kenneth Philles, director of the Canadian Institute of Telecommunications and Media Arts and professor of the Department of Music Artificial Intelligence and Information Technology at the Central Conservatory of Music, suggested that music is needed to solve the delay problem caused by cross-regional co-operation using the Internet [7]. The AI automatically handles the delay curve and timing settings at each node. Academician Guan Xiaohong discussed the mathematical characteristics of three kinds of musical melodies under the title of Quantitative Rules in Musical Melodies and constructed a mathematical model in order to find out the extent to which they change and then obtain their variance [8].

General Secretary Xi Jinping said, ‘Fine arts, art, science and technology complement and promote each other [9]. At present, music has become the forefront of the development of technology and art. With the continuous development of AI technology, from a single technology to the integrated technology, from a single intelligence to swarm intelligence, from data-driven to scenario-driven tasks, AI and cross-border integration of music art and the modern media, each note and every melody of music are likely to achieve the best effect in terms of hearing, sight and touch, apart from creating a sound–scene blend of artistic conception, letting the feast of hearing sublimate into a variety of sensory enjoyment, so that the immersion of music continues to convey the emotion contained in music. This paper focusses on the application of AI technology in bel canto, analyses the problems encountered at present and discusses how to use AI technology to better serve music.

Traditional AI thinks in the top–down manner; its essential characteristic is to simulate the human brain neuron. This method has two characteristics: first, calculation of the weight of the neighbouring neuron through the corresponding output function and its further processing; second, the weight value is used to determine the information transmission relationship between neurons, and the weight is constantly optimised and adjusted in this process [10]. At the same time, the NN also depends on a large amount of data during processing. Therefore, the NN shows non-linearity, distributed configuration, parallel structure, adaptability, self-organisation and other characteristics. Take people's music creation as an example: usually through the perception of music (appreciation), music imitation and writing, they finally achieve independent creation. The process of composition also includes the study of composition techniques, harmony theory and other aspects. Learners constantly improve their creative ideas in practice and under the guidance of teachers. This learning method can be simulated by using the structure of NN to a large extent, thus laying a foundation for the application of this technology [11].

The operation process of NN requires the architecture of input, output, weight and multi-level perception (Figure 1). NNs can be regarded as a ‘black box.’ As long as there are enough training sets, the desired value

Music is an art of time, and much of its message is based on time. On this basis, a variety of methods can be adopted to complete the processing of the timeline information, namely recurrent NN (RNN) [13, 14], which is an NN that can learn on the basis of existing and generated data. RNN is a time-shifted NN, which measures depth based on time. Circular networks generally have the same input layer and output layer. This is because the circular network expects the next entry to be the input of the next step, so as to generate the order; so RNN is a good implementation method [15].

Long short-term memory (LSTM) is a special RNN structure that belongs to feedback NN. LSTM is an NN formed to solve the problem of gradient disappearance or burst in an RNN cyclic network. RNN technology can process time dimension information at the same time, but if the data is stored for too long, it becomes very difficult to store the data, which becomes a big problem. Therefore, LSTM is a special hidden unit whose natural property is long-time storage. The main change to LSTM is the addition of three gates, namely the input gate, the output gate and the forget gate. In practice, LSTM has been proved to be superior to RNN [16]. It has been widely used in machine translation, conversation generation and compilation. LSTM can describe the logical thinking and cognitive activities of more complex people, so it is the most significant research field at present.

The autoencoder (AE) is shown in Figure 2. It uses an NN to convert an image or sound into a set of numbers. The goal is to make the image and sound searchable and then use that number to reconstruct the image and sound.

The VAE is an improvement of the AE. Its structure is similar to that of the AE, but it also includes an encoder and a decoder [17]. The hidden vector generated by the variational autocoding method must satisfy the standard normal distribution. The VAE mode was first used in The Google Music VAE mode, where the user can input two videos, which are then inserted by the model to produce a continuous transit.

Transformer is the first machine translation model introduced by Google Brain in 2017. The advent of this model has shaken the RNN in the field of deep learning. In many experiments, the transformer performed better than the RNN. Google also made a name for itself in 2018 by publishing an article on Music Transformer to solve the music generation problem [18]. The transformer model mechanism is shown in Figure 3.

This overall network structure is shown in Figure 4, including four parts: musical score encoder; duration predictor; length regulator and decoder.

It encodes the sequence of phonemes, note durations and pitches into a sequence of dense spatial vectors. Musical score = musical score; Phoneme ID = Phoneme to ID – encoded by phoneme embedding; Note duration = duration – encoded by duration embedding; Note pitch = pitch – encoded by pitch embedding; These three input vectors are then ‘stacked’ and thrown to multi-layer transformer encoder layers. As one can see, the position encoding information is also incorporated, followed by each FFT block [19, 20, 21]. The structure of the score encoder is shown in Figure 5.

The sheet music usually contains the lyrics, pitch and length of the note so that people can get hold of the sheet music and sing it. As shown in Figure 5, the first step is to convert the word form into phonetic phonemes (such as Chinese characters to pinyin), where each syllable (such as fang->f + ang, a vowel + consonant form, so that both f and ang exist as phonemes) is subdivided into several phonemes. Each pitch is converted to a pitch ID according to musical instrument digital interface (MIDI) standards [22, 23, 24, 25].

In addition, the length is converted to frame count (the number of phoneme frames) via music Tempo. Note pitch and Note duration are repeated to fit the length of each phoneme. Thus, it can be considered that the shape of the input score is

Type: N is the number of phonemes.

For example: WO ai ni Zhong Guo - wo ai n I zhong guo.

After three embedding layers respectively, the corresponding vectors of phoneme, duration and pitch will be added [26].

An FFT block consists of a multi-head self-attention layer, a two-layer 1D convolution layer (similar to the feed-forward linear layer) and the rectified linear unit (ReLU) activation function [27, 28]. There is no layer norm or residual connection in the paper as shown in Figure 6:

I - > Wu O O three phonemes; - converts to phoneme ID; And - > h e e; - > pitch, a quantified pitch number; You - > n I I three phonemes. - > beats, first converted to a specific time length (according to MIDI tempo) and then converted to 10 ms as a cut. For example: 1 s = 1000 ms - > 1000 ms/10 ms = 100.

According to the vector sequence obtained by the encoder, obtain phoneme duration, i.e. the duration of each phoneme (one phoneme, how long should be sung in the song) [29, 30]. What it yields is the duration of each phoneme (for example, a sequence of integers). This predictor includes several 1D convolutional networks, similar to those in FastSpeech. In addition to the duration of phonemes, the duration of syllables also plays an important role in learning the rhythmic patterns of ‘singing speech synthesis.’ So, in an attempt to learn better rhythm, we propose to add syllable-based level (pronunciation of individual characters: Wu o o = I, now it is one: wo, the control). A syllable can correspond to one or more notes. Therefore, the duration loss for a syllable (de-syllable level), loss of syllable duration (L-SD) is designed to reinforce the similarity between the ‘syllable duration for reference answer’ and ‘the sum of the predicted duration of all phonemes in that syllable as predicted by the model [31].’ These are as follows:

This is the loss of duration prediction. L-pd refers to the loss of phoneme duration and L-sd refers to the loss of syllable duration. W-pd and W-sd are their respective losses.

Its main work is to ‘extend’ the length of the ‘vector sequence obtained by the encoder’ according to the predicted tone length [32]. For example, if a phoneme lasts for 5 s (‘Ah... Ahh’), then the regulator expands it several times according to how many time slices correspond to 5 s (say, 20 ms time slices) (here 5000/20=250 times). The results for the encoding vector sequence after length extension are as shown in Figure 7.

The decoder, shown in Figure 8, is responsible for generating acoustic features from an expanded sequence of coding vectors [32, 33].

In this paper, the World Vocoder is used, which requires the decoder to be able to predict mel-generalised coefficient (MGC) and band aperiodicity (BAP), not mel spectrum. The definition of loss here is as follows:

The left side represents the loss in spectral parameters. On the right, L-M stands for loss of MGC; L-b indicates loss of BAP [34].

W-m and W-b are their respective weights. Compared with speech, singing has a more complex and sensitive F0 profile. For example, it has a wider range from 100 Hz to 3500 Hz. The dynamics of F0 movements, such as trills and overtones, help convey emotions more expressively [35].

Some prior research has shown that even a slight deviation from standard pitch can seriously damage the listening experience. On the other hand, it is difficult to cover all pitch ranges in sufficient cases using training data. This means that F0 prediction can be problematic if the pitch of the input note is not displayed or is rarely present in the training data. Data enhancement solves this problem by implementing pitch conversion on training data. But this is not economical and can lead to longer training sessions. Instead, we propose a residual connection between the input and output pitches (here, we use logF0, the logarithmic scale of F0) so that the decoder only needs to predict human bias based on the standard note pitch, which is more robust for rare or invisible data. Later experiments confirmed this [36, 37].

The prediction of F0, as usual, is accompanied by the voiced/unvoiced (V/UV) decision. Since the V/UV decision is binary, a logistic regression is used here. Thus, the loss function of the final decoder is as follows:

Here, L-f stands for loss of logF0; L-u stands for loss of V/UV decision and W-f and W-u are their respective weights.

The data included 1000 pieces of Chinese Mandarin bel canto music, with one girl singing, in a professional recording studio at 48 Hz and under 16-bit quantisation. Then, it underwent cuts for no more than 10 s. We ended up with 10,360 segments with 70 h of data. From this pool, 8756 fragments are used as training sets, and the remaining 1032 are used as validation sets and test sets. Acoustic features were extracted by World: 15 ms frame shift, 60-D MGC, 5-D BAP, 1-D logF0 and 1-D V/UV flag. The duration label (integer) of the phoneme is obtained by a hidden Markov model (HMM) forced alignment (probably something like HM-based speech synthesis system [H-triple-S or HTS]). In XiaoiceSing (Figure 1), six layers of FFT blocks are shared. The phoneme word list size is 72. Encoder output is a 384-D vector (one vector per phoneme); decoder output is 67-D acoustic signature. The loss of MGC, BAP and logF0 is calculated separately using L1 regularisation. The V/UV decision uses binary cross entropy loss, Adam optimiser NVIDIA P100 GPU, a batch size= 3230K iteration step convergence.

In this experiment, baseline and XiaoIceSing systems were compared to evaluate overall performance. We first conducted MOS test on the two systems. For each system, we prepared 30 audio samples, each completed in about 10 s. We asked 10 listeners to rate the MOS score of each sample based on articulation accuracy, tone quality and naturalness. The MOS score is the average of all samples to obtain the final score (see Table 1). The MOS score for pronunciation accuracy was 4.52, close to the recorded score of 4.89 and 1.28 higher than the baseline. The sound quality and naturalness also improved by 1.54 and 1.48, respectively, from the baseline. The standard deviation on the MOS was smaller than the baseline, indicating better performance stability across all test cases.

Mean opinion score test results

Pronununciation accuracy | 4.81±0.56 | 4.42±0.68 | 3.84±1.20 |

Sound quality | 4.64±0.50 | 3.80±0.74 | 2.56±0.85 |

Naturalness | 4.88±0.55 | 3.71±0.77 | 2.43±0.83 |

Some objective indicators were further calculated (Table 2). The quality of the synthesised song was measured by root mean square error of duration (Dur RMSE), duration correlation (Dur CORR), F0 RMSE, F0 CORR, mel cepstral distortion (MCD), band aperiodic distortion (BAPD) and voiced/unvoiced error rate (V/UV error). It shows that XiaoiceSing achieved lower RMSE and higher CORR in both duration and F0 than the baseline. Meanwhile, MCD, BAPD and V/UV errors were lower than baseline for XiaoiceSing. We can see that small ice stars have a greater ability to generate accurate phoneme duration, F0 and spectral features.

Objective evaluation results of different systems

DUR RMSE | 21.05 | 23.39 |

DUR CORR | 0.81 | 0.79 |

F0 RMSE(Hz) | 11.45 | 12.74 |

F0 CORR | 0.89 | 0.81 |

MCD (dB) | 4.42 | 6.89 |

BAPD (dB) | 24.12 | 27.39 |

V/UV error (%) | 2.86 | 5.27 |

BAPD, band band aperiodic distortion; Dur RMSE, root mean square error of duration; Dur CORR, duration correlation; F0 RMSE, xxx; F0 CORR, yyy; MCD, mel cepstral distortion; V/UV error, voiced/unvoiced error

Experimental results show that compared with the baseline system, it has a great advantage in terms of sound quality, pronunciation accuracy and naturalness. In particular, F0 perception performs very well due to the residual linkage between note pitch and predicted F0, and the improvement in duration prediction is significant due to the addition of a syllable duration constraint between the expected syllable duration and the predicted phoneme duration.

In this experiment, we compare XiaoiceSing's duration (duration) model with a separate LSTM-based duration (duration) model to evaluate the advantages of the proposed duration modelling. Similarly, another A/B test was conducted to assess the duration of rhythm preference, with 88.7% supporting XiaoiceSing and only 16.5% supporting the baseline. A single LSTM-based duration model is very unstable and predicts a very long duration for the last phoneme. Moreover, its cumulative error is much greater than that of XiaoiceSing. The results of the two A/B tests in the last two sections confirm the significant advantages of our proposed system in terms of duration and F0 prediction. The conclusion is consistent with the above objective evaluation.

‘The significance of scientific exploration lies in the pursuit of truth, the value of artistic creation lies in beauty, and the common pursuit of both lies in the development and enhancement of human creativity and appreciation. The rapid development of emerging technologies represented by AI has brought science and art closer together. To further promote communication between scientists and artists, thinking collusions and achievements, technology elements throughout the whole process produce works of art creation with the creative transformation of science and technology for art resources, innovative development, producing more perceptible, public art achievements of cognitive and cultural products so that the public can get more beautiful experience and knowledge harvest.’ In terms of AI technology itself, the biggest challenge is how to understand creative artistic thinking. At the moment, it is difficult for computers to programme understanding, and AI composing systems cannot replace human composers, but it does affect the production and composition process of music. The application of AI technology reduces the threshold of music education, greatly improves the efficiency of music education and solves the problem of music copyright to a certain extent. In the future, with the increase of relevant research at home and abroad and the attention of all sectors of society, more applications will emerge, thus spawning more suitable theories.

#### Mean opinion score test results

Pronununciation accuracy | 4.81±0.56 | 4.42±0.68 | 3.84±1.20 |

Sound quality | 4.64±0.50 | 3.80±0.74 | 2.56±0.85 |

Naturalness | 4.88±0.55 | 3.71±0.77 | 2.43±0.83 |

#### Objective evaluation results of different systems

DUR RMSE | 21.05 | 23.39 |

DUR CORR | 0.81 | 0.79 |

F0 RMSE(Hz) | 11.45 | 12.74 |

F0 CORR | 0.89 | 0.81 |

MCD (dB) | 4.42 | 6.89 |

BAPD (dB) | 24.12 | 27.39 |

V/UV error (%) | 2.86 | 5.27 |

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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 Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsResearch on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network