In recent years, the new generation technology in the 21st century represented by mobile Internet, Internet of things and AI is bringing another information revolution that has a deep impact on people's intelligent life [1]. In terms of urban infrastructure, urban operation and maintenance, intelligent transportation and other aspects, information technology is deeply combined with it, showing a new form in a different way. Among them, the construction of smart water platform is also one of the important components of Smart City mountain construction. In recent years, it has also been highly valued by the state, and its development strategy has also been put on the agenda. The government is also actively promoting the development of smart water, increasing R & D investment and accelerating the construction of water informatization through cooperation with enterprises. The “wisdom” of smart water is reflected in three aspects. From the perception level, the system collects information about water through wireless networks, such as online monitoring equipment for pressure, flow and water quality, and senses the real-time operation status of the whole urban water supply and drainage pipe network system; From the presentation layer, friendly visual interface and organic integration of all water supply and drainage facilities in water affairs for dynamic image display to form a dynamic and intelligent “urban water Internet of things” platform, as shown in Figure 1; In terms of big data, the system timely and effectively analyzes and processes a large amount of water affairs information, and models it in combination with the corresponding mathematical model, so as to provide decision-making help for the better allocation of resources in the city, save energy, reduce the output of redundant labor force, increase the use efficiency of human and material resources, and contribute to urban green environmental protection [2]. Alibaba's main project in recent years is the brain of smart city, realizing the intelligent management of the city, increasing the efficiency of various services in the city and better coordinating various work. Smart water is also a part of it. Smart water system is mainly divided into four parts: SCADA system, GIS geographic information system, revenue system, water quality management, water sample detection and other production management systems. SCADA is referred to as data acquisition and monitoring control system for short. The data acquisition system, which is mainly based on computer technology and integrates communication technology and control technology, can control the instructions issued by the monitoring equipment on the production site and monitor the on-site environment. The administrator can customize the alarm rules, realize the different step alarm mechanism and enhance the monitoring efficiency. The concept of SCADA was formed in the 1960s and took shape in the 1970s. After the 1980s, the rapid development of microcomputer technology also promoted the realization of SCADA system. In fact, the real rapid realization of SCADA system was at the end of the 20th century. With the rapid development of Internet, the demand of enterprises for management automation and monitoring automation promoted the rapid development of SCADA system [3].

He R and others make reasonable planning in advance, promote the implementation by sections, formulate the work objectives in the leakage control stage, explore the optimal management measures and gradually implement them in combination with technical means according to the scale of water supply pipe network and water supply facilities, the asset status and leakage of pipe network and ancillary facilities [4]. Literature shows that Britain is one of the countries with early urban modernization. The construction of centralized water supply facilities has a history of 200 years. In the 1980s, the leakage of water supply system was also very serious. Therefore, they strengthened the frequency and density of leak detection, promoted the renewal and transformation of pipe network, and carried out DMA zoning construction. After 20 years of efforts, the leakage rate of centralized water supply network has been reduced from 29.5% to 18.7%. Yiran L and others found that in the early 1980s, in the practice of pipe network management, in order to monitor the pipe network leakage for a long time, find the macro distribution of pipe network leakage, balance the service pressure of pipe network, and then reduce the leakage rate, the British water management organization put forward the concept of district metered areas (DMA) management [5]. Ulusoy A J and others believe that DMA refers to the construction of an independent area in which the inlet and outlet flow can be recorded in a certain area of the water supply and distribution system by closing some valves and installing flow meters at the inlet and outlet of the independent area [6]. Northwest water has established 3000 DMA management areas in its water supply network; London's water supply network is divided into 16 districts. With the help of DMA, British water company has comprehensively evaluated the water leakage of the pipe network by checking the basic data, leakage level test, “zero pressure” test and other steps. When it is determined that there is water leakage in a water supply area, the location of the water leakage point shall be further determined through appropriate technical means. Although there are many methods to determine the water leakage point of the pipe network, including passive leak detection method, listening leak detection method, regional meter installation method, regional leak detection method, leak detection compound method and pressure adjustment method, none of them is omnipotent, but it is more effective to combine multiple methods to give full play to their respective advantages. The establishment of DMA leak detection area can adopt different modes for different pipe network forms, i.e. tree water supply network and ring water supply network. Due to many factors such as urban planning and water supply planning, the construction of DMA needs to be carried out with the practice of pipe network zoning management and with the means of pipe network modeling. There are many factors affecting DMA leakage rate, such as the accuracy of meter reading, pipeline decompression and flushing, water for pipe network maintenance and emergency repair, etc. Therefore, Xu J and others can effectively carry out regional leakage control with the help of DMA, which requires the organic cooperation of all departments of the water supply enterprise. If a DMA area has reached the leakage control target after evaluation, it can start to prepare the leakage control report of the area, analyze the investment benefit ratio of leakage control, analyze the problems found in the leakage control process, put forward improvement methods, and guide the main direction of leakage control in the future [7]. Developed countries attach great importance to the research and development of pipe network leakage detection equipment. The leak detector developed by the United States, Britain, France, Germany and Japan has been continuously updated with the development of science and technology. Digital leak detector, multi probe correlation instrument and regional leak monitor have been launched one after another, which greatly improves the reliability and accuracy of leak detection.

For most water supply enterprises, the level of non profitable water volume (NRW) is a very important performance indicator”. However, due to institutional and political pressure and lack of knowledge to strictly determine the level of NRW, many water supply enterprises tend to underestimate NRW. Senior managers are eager to see the report of low-level NRW. However, these reports are either based on deliberately provided wrong information or lack of accurate information, which can not help water supply enterprises reduce costs or improve benefits. On the contrary, it will cover up the truth of the problem and affect the operation efficiency of water supply enterprises. Only by quantifying NRW and its constituent elements, calculating reasonable performance indicators, and changing the leakage water to monetary value, can water supply enterprises accurately understand the situation of NRW and take necessary measures. The establishment process of water balance table can help the managers of water supply enterprises understand the size, source and cost of NRW. The International Water Association (IWA) has formulated the elements and technical terms of a standard international water balance (as shown in Table 1) [8].

Water balance recommended by IWA

water system | legal water | Legal water bill | Pay metered water | income from buying water |

Water usage is not a measure of cost | ||||

Legal water is free | Free water test | no income to irrigate | ||

water outflow | Apparent leakage | Free and unlimited water illegal use of water |
||

real leak | cover up |

The total amount of water flowing into the water supply network from the water plant (referred to as “system supply water”) minus the total amount of charged legal industrial and residential water (referred to as “charged legal water”), i.e. non revenue water (NRW), see formula (1).

The assumptions of this equation are as follows:

The system water supply has corrected some known errors;

The charging and metering water consumption recorded by the user's meter reading shall be consistent with the statistical time of the water supplied by the system.

The managers of water supply enterprises should calculate each constituent element according to the water balance table, so as to find out the cause of leakage. This will determine the priority of policy changes and business methods and their implementation plans.

At present, some water departments in China have also begun to try to carry out water balance test, which usually adopts the “table filling” method, that is, fill the corresponding water volume data item by item in the “water balance table”, and calculate the “leakage water volume” and “non revenue water volume” by recursive decline. This case uses wb-easycalcv300 (free software) synchronously recommended by the International Water Association. Z water division was founded in 1953. There are 7 main water supply plants, including 5 surface water plants, which mainly use the water source of South-to-North Water Transfer, the water source of the Yellow River is standby, and 2 groundwater plants use the Yellow River to measure seepage. The daily water supply capacity is 1.77 million m^{3} / D, the water supply population is 4.5 million, the water supply area is 600 square kilometers, the pipe network above dn75 is 3600 kilometers long, and the registered users are 1.3 million. The statistical cycle of water balance in this case is 181 days in half a year (January 1, 2014 – June 30, 2014). The water balance analysis process is shown in Figure 1 [9].

Step 1: First determine the water supply volume of the water supply system ① The system has 4 water supply systems, 1 pressure make-up water system and 19 pressure make-up wells, all of which have suitable water meters and have been regularly checked;

Step 2: The second step is to count the medicinal water consumption in the calculation cycle ②, including 9 categories such as industrial, living, and wholesale;

Step 3: The third step calculates the unmeasured cost water consumption during the calculation period ③, including prepaid water, construction water, compensation conversion water, etc. The sum of ③ and ② is the water intake of the system;

Step 4: The fourth step is to calculate the measured water consumption free of charge in the calculation cycle ④, such as the water consumption reduced by the policy, the free water consumption agreed in the agreement, etc;

Step 5: The fifth step is to estimate the unpaid and unmeasured water consumption⑤, such as the free water consumption of the contract village, the emptying and filling water consumption of the pipe network construction, the dead end drainage of the pipe network, the temporary water supply of the water supply section, and the household meter conversion. Temporary water supply, long flow of various online instruments in the pipeline network, etc. The sum of ⑤ and ④ is the unpaid legal water consumption;

Step 6: The sixth step is to estimate the apparent leakage ⑥, through a reasonable and feasible sampling detection method, evaluate the illegal water consumption and measurement error, and estimate the apparent leakage. According to the water balance sheet, apparent leakage can be divided into two categories: “illegal water use” and “water loss caused by user measurement errors and data processing errors” are water losses caused by corporate negligence, especially, illegal water pollution in the form of complex of. This article illustrates a methodology for estimating water use in this area using the example of a thorough investigation of water stolen from fire hydrants in violation of sprinkling, sweeping, and dust suppression regulations. The water volume of the sanitary and clean registered water meter is part of the “charged metered water consumption metering”, and its water consumption trend is regularly monitored. Differences can be determined by comparison with the frequency of operation of road cleaning vehicles and municipal administrations; for “water loss due to measurement error,” a sample test can be done by changing water consumption before and after a centralized community replacement of water meters. Similar experimental studies have been carried out by many water conservancy departments in China;

Step 7: Step 7: Calculate the actual leakage ⑦ and calculate or estimate the actual leakage by reasonably feasible methods (night flow analysis, pipeline rupture frequency, flow rate, duration, hydraulic model, etc.). For areas that can be independently measured, the leakage can be pre-analyzed by night current analysis technology and extended to all areas covered by the pipe network; the water loss caused by pipeline rupture can be based on the pipeline rupture repair time recorded by the pipe network management department, crack area and nearby pipe network pressure calculation; according to the leak detection quantity and leak detection period in the statistical period provided by the leak detection department to calculate the hidden leakage amount. For background leakage, the IWA calculation formula for background leakage must be followed;

Step 8: Perform multiple balance checks using data from previous periods.[10].

The city's non-revenue water ratio (production-sales difference rate) is 16%, and the leakage rate is 13.80%. According to the above analysis, first of all, the important factors affecting the non-revenue water ratio (production and sales difference rate) of the water supply system in Z city are 5, 1. Background leakage 2. Various fire hydrants steal water; 3. Light leakage 4. Illegal water use in urban villages; 5. Water loss caused by various measurement errors and data processing errors. Enterprise managers can accurately evaluate the economic benefits of corresponding technical solutions, and decide on investment and management ranking.

In the process of balance analysis, deception in the management stage can be found through reverse guidance. For example, during the calculation period, if it is converted into 36,902 households in Z city for household meter renovation (managed by the household meter renovation department) and 41525 households for new households (managed by the customer service department), the total construction cleaning water volume of the two projects is 7933m' (Operating expenses department management), 0.10m^{3}/household, it can be seen that there is a management loophole in the calculation of construction cleaning water volume. Many components that affect the non-revenue quantity cannot be measured, and different departments of the enterprise need to use certain methods to estimate. Among them, the data reporting department deliberately modified the estimation results based on its own performance interests, resulting in a serious imbalance in the analysis process. Therefore, various statistical methods for estimating water volume must be objective. Perform sample testing or method validation. The water balance table recommended by the International Water Association (IWA) is a horizontal, macro, and system-wide leakage component analysis unit. For water supply enterprises that have achieved classified measurement, they can inherit deeper and different measurement classifications.

Therefore, all kinds of statistical methods for estimating water volume must be objective and verified by sample test or method.

The water balance table recommended by the International Water Association (IWA) is a horizontal, macro and system wide analysis method of water leakage components. For water supply enterprises that have achieved zoning measurement, we can continue to carry out longitudinal water balance analysis for different metering zones. The purpose of constructing the performance evaluation system of water supply industry is to promote the benign objectives of water supply enterprises, such as safe water supply, high-quality service, cost transparency and efficiency improvement, through the vertical comparison of their own business performance and the horizontal comparison of business performance between industries. In view of the relevant performance evaluation indexes of water supply system leakage management, the national industry standard “urban water supply leakage control and evaluation standard” (cjj92-2002) puts forward the basic countermeasures and evaluation standards for strengthening leakage control in China, and determines the benchmark evaluation standards for leakage control, such as “leakage rate” and “unmeasured water rate”. With the improvement of the leakage management level of urban water supply system in the domestic water supply industry, the limitations of indicators such as “leakage rate” and “unmeasured water rate” expressed in percentage in practical application have gradually been exposed, and domestic peers have gradually realized the rationality of the water balance calculation method and water supply service performance indicators recommended by the International Water Association (IWA).

Firstly, HPSO algorithm generates a random particle swarm (random solution). Each particle flies (optimizes) in its multi-dimensional solution space, and the flight speed is dynamically adjusted according to its own and other particle flight conditions and experience. There are N particles in d-dimensional space, and the best position in history is _{best}

The position and velocity vectors of offspring particles are shown in formula (2) (3):

Before data modeling, we must first clarify the purpose of modeling and the effect to be achieved [11]. Data modeling is a series of operation sets that do some customization, logicalization, model matching and other work on the data template. The final result of modeling still serves people. How to enable users to clearly get the knowledge they need from the data model is a necessary function of the model.

There are two points to summarize the modeling requirements of this system:

The purpose of the behavior analysis model is to realize the front-end intelligence, so that the terminal has the ability of self prediction. In case of abnormality, it can wake up from the deep sleep and notify the user. This is mainly based on the practical application scenario of smart water in pipe network monitoring. In pipe network monitoring, the equipment is generally set to sample once in 20 minutes and send it once in four hours. They don't need intensive data collection. The period of manual meter reading is one month. In order to prolong the service life of the equipment to a greater extent, the equipment is in a dormant state before the scheduled sampling, so as to save energy to the greatest extent. However, in the actual modeling and analysis, we should consider the dimension of time. The 20 minute sampling period can only represent the data at a certain time. Therefore, in the process of practical application, we adopt the random discrete sampling distribution algorithm for the equipment to ensure the dispersion of the sampling data, so as to predict the behavior more accurately in the data modeling. However, the device will still keep sampling at the sampling point required by the user. In this way, business requirements and modeling are correct. At the end of the model analysis, the server model middleware issues the simplification strategy and converts it into the instructions that can be recognized by the terminal, which is pushed to the terminal, so that the terminal has some decision-making ability, and sends an alarm in time when the terminal behavior deviates beyond the tolerance range. This will provide timely and important information on leakage detection, control and repair [12].

The main purpose of the model is to dynamically adjust the supply according to the actual demand of the water area. First, it can improve user satisfaction and second, it can save energy. For example, at 6 o'clock every day, in a certain area, there is a community with huge water consumption, and the pressure will drop to the normal. In another place, there is less water, and the corresponding pressurizing device should also operate in real time [13]. In view of this situation, we can give auxiliary suggestions according to the pipe network model. It is suggested to add pressurizing devices at the inlet of the community and appropriately reduce the configuration of pressurizing devices at another place. Save resources. The water department can even analyze according to this model, optimize the layout of pipe network and increase the output ratio. However, the model needs to be based on the DMA partition principle.

According to the two requirements, we conduct data statistical analysis on the pressure and flow data. In terms of two types of data statistics, we mainly take the day as the cycle, scatter all sampling data to some time of the day, and form multiple data combinations in divided units. The types of statistical data mainly include: original data, derivative of data relative to time, cumulative value and transient [14]. For the statistical data, we should first remove the noise according to certain rules, and take it out. We will do the positive distribution operation on the data at all times to obtain a more reasonable range. We will dynamically adjust this parameter according to the tolerance range of users. Then take the result of positive Pacific distribution at all times as the a priori probability statistics of Bayesian decision theory, and calculate the a posteriori probability of the next time with time as the reference. However, there are two kinds of algorithms at the moment: one is that all data get a behavior prediction in a day cycle, and the other is multi-dimensional and multi-directional statistics. The second is mainly considering that the water consumption on Monday and Saturday is different, the water consumption on Monday in March and Monday in September may be different, or there may be a factory in this area that needs a lot of water for production on specific days of each month. In view of these different situations, in the subsequent data modeling, we should consider customized selection, distributed statistics and modeling to better meet the practical application scenarios.

After obtaining a reasonable interval distribution, after the user specifies the deviation tolerance of the data, we get the interval range required by the user according to the distribution equation, then screen the data according to the interval range, then predict the trend of the data in the interval, use polynomial to fit the horizontal data behavior of the interval distribution, and display the data analysis results through c# data analysis host computer. In the process of fitting, we divide the data into cumulative quantity and periodic quantity. Later, we will find that the derivative of cumulative quantity is also periodic quantity. In the analysis of the cumulative quantity, after the data distribution operation, the weighted curve is obtained, and then the weighted curve is fitted by the least square method, and the fitting degree value R2 is obtained. In the process of fitting, it is easy to find that the more the order is, the better the fitting degree is, that is, the closer the R2 value is to 1. However, due to the calculation ability, the fitting order cannot be too large. No matter how good the fitting degree is, there will be a certain dispersion between the behavior equation and the actual scatter distribution, because this method is the prediction of the variation, that is, the derivative, and the dispersion within a certain range is allowed. In the actual use of the model, it is also allowed to exist in a certain range of dispersion, which is also the user tolerance range, but how to reflect it offline in the process of model use. This paper designs two schemes, one is using differential mode analysis, the other is using envelope analysis. Behavior model analysis is mainly used in intelligent early warning, which can predict and compare the behavior of the current station in the future to decide whether to give an alarm. This intelligent early warning is mainly caused by pipe explosion in the pipe network, resulting in sudden increase of flow and decrease of pressure. This method can accurately locate the parameters such as pipe explosion section, leakage speed, leakage pipe pressure loss and so on. It is convenient for maintenance personnel to arrive at the site quickly and accurately and reduce the loss. On the other hand, there is abnormal water use. A feedback from the customer is that when the secondary water supplier takes water from the primary water supplier, the measurement is damaged intermittently due to human reasons, so as to reduce the actual statistical flow. This is unacceptable for the primary water supplier. It is precisely because the traditional measurement method can not find this anomaly, which contributes to this bad atmosphere. The secondary water supplier uses intermittent operation, and the primary water supplier is also difficult to find [15]. Using this model analysis, if the secondary water supplier carries out illegal operation at any time, it will trigger the equipment early warning and return to normal. During this period, the primary water supplier can find the abnormality in time and specify that the data in the corresponding time period is illegal data and will not participate in the decision-making. Other data will be used as the source of model data. Timely communication can not only reduce losses, but also reduce this bad atmosphere. The production model mainly analyzes the regional water consumption and pressure of DMA partition, and gives the analysis model. The analysis model will visually display the water supply parameters of each region in combination with GIS pipe network system. The model can point out the water supply suggestions, resource ratio and pipe network optimization suggestions in different periods of time. The water department can conduct secondary transformation evaluation, resource distribution evaluation, zoning optimization and so on according to the analysis model to assist decision-making. This is also the main embodiment of the “wisdom” of the future intelligent water supply system.

The leakage control of urban water supply network is a long-term and arduous task. This paper deeply and systematically studies and analyzes the current situation of non profitable water volume (NRW) of water supply network, and puts forward and gradually implements the non profitable water volume control strategy based on the scientific system of International Water Association (IWA). On this basis, actively explore economic and effective management means to make the leakage level of water supply enterprises adapt to and meet relevant national and industrial standards. This paper systematically studies and discusses the key technical problems of non-profit water volume control commonly existing in the water supply industry, introduces advanced non-profit water volume control technologies and methods, and studies the non-profit water volume management system, main countermeasures and technical scheme of water supply network. The leakage control of water supply network is studied and discussed as a complete system engineering from basic water quantity analysis to management means, from target determination to technical measure selection. Taking the water supply network of KT City, LZ city and Z City as the main objects of analysis and research and the application of specific engineering measures, this paper puts forward a set of relatively complete and flexible pipe network leakage control countermeasures, implements the theoretical research into practice, not only expands and enriches the research content, but also verifies the theoretical research to a certain extent, and determines its feasibility.

#### Water balance recommended by IWA

water system | legal water | Legal water bill | Pay metered water | income from buying water |

Water usage is not a measure of cost | ||||

Legal water is free | Free water test | no income to irrigate | ||

water outflow | Apparent leakage | Free and unlimited water illegal use of water |
||

real leak | cover up |

_{2}-EOR project based on machine learning methods and greedy algorithm[J]. Energy Reports, 2021, 7(342):3664–3677._{2}-EOR project based on machine learning methods and greedy algorithm

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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