Roesser state space model is a common multi-dimensional system model based on practical engineering problems. It uses the input of the system and the previous state associated with it to control the current state. The nature of this local calculation not only greatly simplifies the mathematical expression of the multi-dimensional system, but also facilitates the analysis and research of the system. At present, the research based on Roesser model has made some progress [1]. These studies mainly focus on how to design algorithms to make the order of the implementation matrix of the system lower, such as EOA (elementary operation approach) transformation method and P-matrix method [2]. Using lower order implementation matrix to describe the system has strong practical application value, which can not only make the system respond more quickly, but also make the implementation and application of Roesser model in some energy limited systems possible. For example, in wireless sensor networks, the limited energy of sensor nodes is an important problem that puzzles its practical application. The energy consumption of sensor networks is mainly concentrated in the mutual communication between nodes, and its communication energy consumption is 2–4 times of the calculated energy consumption [3]. If each node can process the collected information and then spread it, the whole sensor network will have a longer network lifetime. With the introduction of dynamic system theory into the field of Applied Linguistics, language development can be regarded as a dynamic system, which opens a new perspective for the construction of demand analysis model of language courses. From the perspective of dynamic system theory, based on state space model, language development demand system can be regarded as a dynamic system composed of initial state, target state, system state variables and their dynamic relationship with time. With the rapid development of multimedia technology, multimedia sources can produce a large amount of data. Without data compression, the transmission and storage of multimedia information are difficult to be practical [4]. Multimedia coding and compression can quickly transmit multimedia sources, carry out more services in parallel and reduce storage costs. It is an important research direction in the field of multimedia communication. Multimedia coding is a field that covers many prerequisite courses. Only by mastering the relevant knowledge of random process, information theory and communication principle can we understand and practice the knowledge of multimedia coding [5]. Aiming at this research problem, Jothi S and others try to adopt new theories and new methods to solve the problems in multi-dimensional wireless sensor networks. However, the application of these new theories and methods is not mature, and there are still various deficiencies in the conclusions. Although multidimensional wireless sensor networks have important application prospects in reality, there is no representative application system of multidimensional wireless sensor networks at present, except that some simple regular structure wireless sensor networks are deployed to underwater sensor networks [6]. Swain C and others proposed a new EOA method. The EOA transformation method simplifies the implementation of Roesser state space model into linear transformation operation and specific supplementary operation on multi-dimensional characteristic polynomial matrix. This method is simple in concept and easy to calculate, and can analyze the influence of coefficient correlation on the implementation matrix [7]. Umamaheswari S and others found that each supplementary operation in EOA transformation method can only reduce one order. Although the supplement efficiency can be improved by some decomposition, in fact, only a few transfer functions are suitable for this decomposition method [8].

Based on the current research, according to the characteristics of space multimedia communication environment and communication equipment, this paper proposes a wireless English synchronous QoS control algorithm with low complexity and easy implementation. Using RTCPSRRTP timestamp and NTP absolute timestamp, the wireless English RTP timestamp is mapped to the same absolute reference clock (sender system time) respectively, and the wireless English synchronization detection decision rule is established according to the synchronization QoS performance requirements between wireless English media. At the receiving end, the wireless English stream is the main media stream and the video stream is the slave media stream. The synchronization detection and judgment is implemented in real time before the video frame is played. The synchronization between audio and video media is realized by corresponding synchronization control of wireless English playback. Simulation results show that the synchronization algorithm effectively improves the synchronization performance between audio and video media in space multimedia communication system and meets the QoS performance requirements of audio and video synchronization in space communication.

In 1990, Perona and Malik proposed a nonlinear anisotropic diffusion equation, namely the P-M model, in order to maintain image edge information. Definitions are as follows:

RTP / RTCP protocol is a network transmission protocol specially designed for real-time media transmission by the wireless English transmission working group of Internet Engineering Task Force (ETF). A synchronization control algorithm between wireless English media based on RTP / RTCP is proposed. The algorithm needs to process each RTCPSR (sender reports) message. The algorithm has high complexity and needs the support of network time protocol (NTP). In addition, the synchronization control is carried out by dropping frames or pausing decoding before wireless English decoding at the receiver, which not only ignores the delay jitter introduced by wireless English decoding, but also affects the normal decoding and reconstruction of video to a certain extent. According to the characteristics of space multimedia communication environment and communication equipment, this paper proposes a wireless English synchronous QoS control algorithm with low complexity and easy implementation [9].

Using RTCPSRRTP timestamp and NTP absolute timestamp, the wireless English RTP timestamp is mapped to the same absolute reference clock (sender system time) respectively, and the wireless English synchronization detection decision rule is established according to the synchronization QoS performance requirements between wireless English media. Wireless English synchronization control system model at the receiver. At the receiving end, the wireless English stream is the main media stream, and the video stream is the slave media stream. The synchronization detection and judgment are implemented in real time before the video frame is played. The synchronization between audio and video media is realized through the corresponding synchronization control of wireless English playback [10].

The RTP timestamp corresponds to the sampling time of the first data byte of the payload in the RTP packet. However, wireless English audio and video streams are transmitted in different RTP session streams, so the time stamps in RTP packets in different RTP session streams cannot be directly compared. The reason is that the initial value of the time stamp in the RTP packet is generated randomly, so even if the wireless English audio and video stream is sampled at the same time, the initial time stamp value of the RTP packet is different; The growth of RTP timestamp is monotonic and linear, but its growth rate is related to the media sampling rate. Generally, the sampling rate of wireless English audio and video media is different, so the timestamp growth rate of RTP packets in wireless English audio and video streams is also different. The increment of RTP timestamp in adjacent RTP packets is equal to the number of payload samples in RTP packets. In order to solve the above problems, the RTP timestamp in the wireless English audio and video stream is mapped to a common absolute reference time [11]. Using the relationship between RTP timestamp and NTP absolute timestamp carried in RTCPSR package and RTP timestamp in RTP package, the NTP absolute reference time corresponding to RTP timestamp in wireless English audio and video RTP package is calculated. The receiver can directly compare the calculation results and carry out corresponding synchronous QoS control.

The following formula can be obtained:

Where, R is the RTP timestamp clock frequency, that is, the media data sampling rate. Δ_{I}

_{I}

Substituting equations (2) and (3) into equation (1), we get:

In the communication process after a call connection is established, the type of wireless English audio and video encoder will not change, so the clock frequency of wireless English audio and video media timestamp will not change, that is, R can be considered as a constant value. The RTP timestamp and NTP timestamp carried by the 1st and i-th RTCPSR packets can be obtained:

The NTP absolute timestamp corresponding to the media package can be obtained from equations (4) and (5):

RFC3550 specification does not require that NTP absolute time in RTCP must be generated by NTP time server, and its specific implementation has exceeded the content of RTP protocol specification. The sender can directly generate the NTP absolute time through any reference clock. Because the implementation of NTP protocol is complex, the system clock of the sender can be used to generate the NTP absolute timestamp value in RTCPSR packet. Through equation (6), the RTP timestamp of audio and video packets is mapped to the same absolute reference clock, that is, the system time of the sender. Therefore, the algorithm in this paper does not need the support of the whole network synchronization clock or NTP protocol, and can directly use the system clock of the sender. It can be seen from equation (6) that the algorithm in this paper only needs to process the NTP absolute time in the first RTCPSR packet as the common clock reference of subsequent audio and video media packets [12].

Assuming that the _{V}_{V}

Case 1: _{−}, at this time, the wireless English audio and video are not synchronized, and the video lags behind the audio. Skip (discard) the video frame that arrives late and will not be played;

Case 2: _{−} ≤ _{+}, at this time, the wireless English audio and video is in the synchronization area. Play the video frame directly without synchronous control;

Case 3: _{+}, at this time, the wireless English audio and video are not synchronized, and the video is ahead of the audio. Delay the playback of the early video frame, delay skew (MS) time, and then conduct synchronous detection and judgment.

Among them, the time offset of wireless English audio and video is
_{−} = −80_{+} = +80

It can be seen from equation (6) that the wireless English audio and video synchronization algorithm proposed in this paper only needs to process one RTCPSR packet, while the traditional media synchronization algorithm based on RTP / RTCP needs to process multiple RTCPSR packets periodically (such as every 4 / 6 seconds) to continuously update the time stamps in the SR packets used in its algorithm, and its algorithm complexity is directly proportional to the number of SR packets processed. At the same time, this algorithm is easier to implement. Therefore, compared with the traditional media synchronization algorithm based on RTP / RTCP, this algorithm has lower algorithm complexity. In addition, the wireless English audio and video synchronization algorithm proposed in this paper also has the following characteristics:

Without the support of the whole network synchronization clock or NTP protocol, the system clock of the sender can be directly used. It is not affected by packet loss and can be applied to the environment with high packet loss rate of space communication. Media synchronization technology based on RTP / RTCP protocol is a relative timestamp synchronization technology based on time axis synchronization description model. Wireless English audio and video media objects are independently associated with a common time axis. The loss of any RTP packet will not affect the synchronization control of other media packets. If the first RTCPSR packet is lost, the next SR packet can be received as the first RTCPSR packet. Without feedback mechanism, it can be applied to the space communication network environment with long time delay [14].

System model is a mathematical model that reflects the causal relationship and transformation relationship between system variables. The commonly used mathematical models of discrete systems mainly include difference equation, transfer function model and state space model. Difference equation is a common mathematical model in one-dimensional system, but this model is not suitable for multi-dimensional system. The more complex the multidimensional system is, the higher the dimension of the system is. The higher the order of the difference equation (Discrete System) or differential equation (continuous time or space system) describing the system by the relationship between input and output is, the more difficult the system analysis is. Transfer function is the main mathematical model describing the system characteristics in classical control theory. It is suitable for the linear constant system of single input and single output (SISO). It can easily deal with the transient response analysis or frequency method analysis and design of this kind of system. However, this model is not suitable for multi input and multi output (MIMO) systems, time-varying systems and nonlinear systems. In addition, the transfer function is only an incomplete description of the system. It can only reflect the linear dynamic characteristics of the transfer between the input and output of the system, but can not reflect the dynamic change characteristics within the system, which greatly limits the application of the transfer function model in practice. The state space model is based on the analysis of the internal structure of the system, which is composed of the state equation describing the dynamic characteristics of the system and the output equation describing the transformation relationship between the system output variables and the state variables. It can reflect the changes of all independent variables in the multi-dimensional system, and then determine all internal motion states of the system [15]. Therefore, the state space model reflects all the information of the system dynamic behavior and is a complete description of the system behavior. The state space model has a wide range of applications. It is not only suitable for SISO linear constant systems, but also suitable for nonlinear systems, time-varying systems, MIMO systems and stochastic systems. For different systems, the mathematical expression is simple and unified. The more outstanding advantage is that the state space model adopts local calculation and uses the state variables inside the system to describe its dynamic characteristics. This property of local calculation not only greatly simplifies the mathematical expression of multi-dimensional system, but also facilitates the analysis and research of the system.

At present, the most representative state space models are Roesser model and Fornasini Marchesini model. Multidimensional Roesser state space model is based on the multidimensional system corresponding to the one-dimensional state space model of discrete-time system. It is a model established after the evolution of multidimensional system. The current input and the previous state of the system are associated with this control. Roesser state space model of one-dimensional discrete system is:

Where, u and y represent the input and output of the system respectively, and A, B, C and D are coefficient matrices. Formula and formula are the state equation describing the dynamic characteristics of the system and the output equation describing the transformation relationship between the system output variables and state variables. The two-dimensional Roesser state space model was first proposed by Roesser when he studied multi-dimensional linear filter networks in the 1970s. The Roesser state space model of single input and single output of two-dimensional linear discrete system is:

Where, ^{h}^{r1} and ^{v}^{r2} represent the state vectors in the horizontal and vertical directions respectively; ^{r×r}, ^{r×1}, ^{1×r}, ^{1×1}, _{1} + _{2}.

Extending the two-dimensional Roesser model in the horizontal and vertical directions to the multi-dimensional system, the Roesser state space model with multi-dimensional single input and single output is obtained as follows:

Where, _{k}_{1},…,_{n}^{rk}_{1},…,_{n}_{1},…,_{n}_{1},…,_{n}

The number of rows of local state _{1},…,_{n}_{k}_{1},…,_{n}_{k}

Where, _{1} _{r}_{1},…,_{n}_{rn}_{1},…,_{n}

Where _{1} _{n}_{r1},…,_{n}_{rn}_{1} _{r1} ⊕ ⋯ ⊕ _{n}_{rn}

For n-dimensional transfer function:

Or

If matrices A, B, C and d make the formula or formula valid, then a, B, C and D are the Roesser model implementation matrix of the given transfer function.

In the Roesser model with single input and single output, input _{1},…,_{n}_{1},…,_{n}

Wherein, _{1},…,_{n}^{q}_{1},…,_{n}^{p}_{k}_{1},…,_{n}^{rk}

Where _{1},…,_{n}_{1},…,_{n}

Where _{R}_{1},…,_{n}_{r}_{1},…,_{n}_{r}_{1},…,_{n}_{R}_{r}_{q}_{1},…,_{n}

The air link rate of the wireless transceiver is 512Kbps. In the experiment, the video is encoded based on H.264 and the audio is encoded based on G.729 Speech coding standard. The audio and video parameters in the experiment are shown in Table 1.

Audio and video parameters

Encoder | Bit rate | Frame rate | Format | |
---|---|---|---|---|

Audio | G 729A | 8kbps | 100fps | 8KHz 16-bit |

Video | H.264 | 50kbps | 15fps | CIF(352×288) |

The duration of each test is 5000 frames of video. The synchronization control algorithm between wireless English media based on RTP / RTCP and the synchronization algorithm proposed in this paper are used for audio and video synchronization. The RMSE results before and after audio and video synchronization are shown in Table 2, Figure 1 and Figure 2.

RMSE before and after synchronization

Before synchronization | 96.26 | 78.22 | 176 | 141.7 | 90 49 | 74.12 | 79.02 |

Inter media synchronization control algorithm | 40.19 | 37.06 | 40.01 | 39.05 | 41.09 | 37.64 | 39.09 |

Algorithm in this paper | 38.9 | 36.49 | 39.25 | 38.98 | 38.97 | 37.17 | 38.83 |

As shown in Table 2, compared with that before synchronization, the RMSE value after adopting the synchronization algorithm in this paper is reduced by 60.09% on average and 77.69% at the highest; Compared with the wireless English media synchronization control algorithm based on RTP / RTCP, the synchronization performance of this algorithm is better than the wireless English media synchronization control algorithm. The RMSE value is reduced by 2% on average and 5.2% at most. In addition, the synchronization control algorithm between wireless English media performs synchronization control by losing frames or pausing decoding before video decoding at the receiver, which affects the quality of wireless English video decoding and reconstruction.

This paper presents the analysis of wireless English multimedia communication based on spatial state model equation. The system model is a mathematical model that reflects the causal relationship and transformation relationship between system variables. The commonly used mathematical models of discrete systems mainly include difference equation, transfer function model and state space model. Difference equation is a common mathematical model in one-dimensional system, but this model is not suitable for multi-dimensional system. The more complex the multidimensional system is, the higher the dimension of the system is. The higher the order of the difference equation (Discrete System) or differential equation (continuous time or space system) describing the system by the relationship between input and output is, the more difficult the system analysis is. Space multimedia communication has the characteristics of high packet loss rate, long transmission time, large jitter and limited resources. In order to meet the QoS requirements of wireless English audio and video synchronization, a wireless English audio and video real-time synchronization algorithm based on RTP / RTCP protocol is proposed. The audio stream is the main media stream, and the wireless English audio and video synchronization is realized by controlling video playback. The algorithm does not need the whole network synchronous clock and feedback mechanism, has low algorithm complexity, and is suitable for spatial multimedia communication. Simulation results show that the synchronization algorithm effectively improves the synchronization performance between audio and video media in space multimedia communication system and meets the QoS performance requirements of audio and video synchronization in space communication. The research of this paper still has many places worthy of further study. Theoretically, we need to deeply analyze and compare the implementation methods of various multidimensional systems, so as to propose a new method to implement Roesser state space model. The application of Roesser in wireless sensor networks needs to be improved.

#### Audio and video parameters

Encoder | Bit rate | Frame rate | Format | |
---|---|---|---|---|

Audio | G 729A | 8kbps | 100fps | 8KHz 16-bit |

Video | H.264 | 50kbps | 15fps | CIF(352×288) |

#### RMSE before and after synchronization

Before synchronization | 96.26 | 78.22 | 176 | 141.7 | 90 49 | 74.12 | 79.02 |

Inter media synchronization control algorithm | 40.19 | 37.06 | 40.01 | 39.05 | 41.09 | 37.64 | 39.09 |

Algorithm in this paper | 38.9 | 36.49 | 39.25 | 38.98 | 38.97 | 37.17 | 38.83 |

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 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 Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules 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 Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators 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 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 Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things 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 Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform 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 Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project 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 An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation 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 Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation 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 Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption 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 driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country 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 Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method 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 Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation 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 Paris panxiensis , a new combination of Trilliaceae from Sichuan, ChinaImpact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method 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 Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence 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 VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec 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 study on the phenomenon of anaphoric correction in college students’ English conversation 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 Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups 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 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 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