Seawater temperatures rise due to global warming, which has an impact on marine life and their habitat [1]. For example, the lobsters in Maine have been gradually moving towards the cooler Arctic to maintain their habitat [2]. In Scotland, small fishing companies and small fishery vessels hold a huge investment in the fishing industry [3], and they usually rely on herrings and mackerels that are sensitive to water temperature [4]. Thus, like the lobster of Maine, these fish will migrate to areas with more suitable temperatures as sea temperatures rise. In the work presented here, the impact of this migration on the Scottish fishery is reported, and in particular on small fishing companies, and propose solutions to mitigate the impact on that fishery.

The sea surface temperature (SST) data supporting the mathematics model used here are from previously reported studies and datasets. The data are available at the Met Office Hadley Centre. (Met Office Hadley Centre observations datasets: Hadley Centre Sea Ice and Sea Surface Temperature data set [HadISST]). Since the area of the habitat for the fish covers an area of >10000 km^{2} [5], sharing the same order of magnitude with the area of 1° (longitude) × 1° (latitude), the centre of this lattice is used as a sampling point. The temperature change at the sampling point represents the water temperature change in the whole lattice. The time span is 1991–2019.

The distribution of landings data supporting the mathematics model used herein are from previously reported studies and datasets, which reflects where and how much mackerels and herrings can be caught in 2013. The resolution is 1° (longitude) × 0.5° (latitude). Compared to the distribution of landing in 2011, the distribution trend can be considered stable. The data are available (Fish and Shellfish Stocks: 2015 Edition,

The following details were used in our analyses:

Small fishing companies are defined as those that have limited or very limited financial resources to invest in new equipment/vessels, which engage in commercial fishing, and that they have only small fishing vessels without onboard refrigeration to harvest and deliver fresh fish to markets in Scottish fishing ports.

Scotland is in the Asia-Europe plate and is not in the plate boundary area. It has inactive volcanic activity, few earthquakes and usually low magnitudes, and few tsunamis [6]. Based on this fact, the assumption can be safely established, which there are no major disasters in the surrounding waters, and it will not have a direct impact on the fisheries.

It is generally believed that fish will seek to maintain a constant habitat. [7]. Although events such as genetic mutation or biological invasion may occur, these are low-probability events and thus their impact on the number of fish is uncertain and is not considered in our model.

Economic factors such as the financial crisis may have a huge impact on the financial situation of small companies [8], but these are cyclical [9]; since our model is based on long-term data, economic factors will not impact model's predictions.

Impact—relevant impacts are considered as general factors in the model.

Only concerned with the distribution of fish that can be caught (i.e. the habitat for fish extends beyond the range that is economical for small Scottish fishing companies, but for variable quantity control, these will not be considered). Therefore, in this study, fish positions are those where fish stocks can be caught (i.e. Figure 1). So, according to the 2015 official mackerel and herring fishing report [10], in 2013, the main populations gathered in the North Sea, and thus fishers also mainly captured mackerel from the northern part of the North Sea. Herring fish are distributed in two areas near Scotland: in the Atlantic, with a habitat in the northwest and north of Scotland, and in the North Sea, with a habitat in the central and northern North Sea.

If the temperature of their habitat in 2013 is known, the suitable temperature for their habitat can be inferred. Herring and mackerel generally move near the sea surface, but herring sometimes have a deeper home range [11]. Since the water temperature has the same changing pattern as a function of depth [12], SSTs are used to track the seawater temperature of the habitats of herring and mackerel. The movement of the habitat of the fish is extremely slow; changes are only noticeable over years. To simplify the calculation, the monthly average water temperature is used to represent the water temperature of the whole month, without compromising precision. Using published SSTs [13], the temperature distribution map for all of 2013 is plotted. From the data, temperatures in April–June can be considered to reflect the year average temperature (i.e. Figure 2), and, since this period is also the time for spawning and fishery for mackerel and herring [14], and the SSTs in April–June is the suitable temperature for these fishes. Combining the distribution of landing of mackerel and herring, the SSTs of the habitats of mackerel and herring are known, which range from 6.5°C to 10.5°C, and thus take 8.5°C as the suitable survival temperature for these two fish species.

Seawater temperatures are the most significant factors affecting the survival of fish [1], with the relationship between fish population and temperature satisfying a normal distribution function [15]. Fish populations are mainly distributed in waters with the most suitable temperature. Thus, the key to predicting the future habitats of herring and mackerel is predicting the trend in water temperature. In addition to the fact that global warming has caused sea temperatures to rise in general, multiple factors may affect seawater temperatures at a given location, such as ocean currents, the depth of the sea, tides, seasons, Sun-Earth distance and so on [16]. While it is difficult to understand precisely each factor's influence on water temperature, it is possible to summarise the patterns from years of records on seawater temperature since recorded temperatures are all quantities linked to nature's movements.

Considering the SST data from 1991 to 2019, the SST has risen, but in fluctuations, it complicates our effort to find a model to accurately describe the behaviour. Therefore, two fitting models are proposed, and they are compared to find the better one.

In this model, the fluctuation of temperatures is assumed to be like a radio signal. In a radio signal analysis, one typically introduces a sum of trigonometric functions to reflect the volatility of the signal [17]. The same concept is applied here. To reflect the overall trend of SST change concerning time, a linear term is introduced into the model, and to reflect the fluctuation of water temperature, a cosine squared term is introduced and the periodic nature of the trigonometric function is used to fit the fluctuations. The fitting result is:

Here,

Test: Comparing the predicted data and actual data for every sampling point, an average root mean squared error is arrived: _{1} = 1.026480.

As per the regularity of nature, the influencing factors of water temperature for each month are similar, and seasonal changes have the greatest impact on water temperature. Therefore, in this model, the temperature data for the same month in different years is fitted (i.e. 12 curves were fitted). From the SST data, the monthly temperature fluctuates year by year, and the fluctuation is still like a radio signal, so a linear combination of cosine squared and linear terms are still used here.

Fitting result:

Test: Comparing the predicted data and actual data for every sampling point, the average root mean squared error is arrived: _{2} = 0.363127.

In the past, it took approximately 20 years for the yearly average SSTs to increase by 1°C. By comparing the RMSEs of the two functions, _{2} _{1} is obvious, and the

In general, without refrigeration, the freshness of fish declines soon after they are caught (i.e. 1 day or less). Since, after landing, fish are typically delivered to customers, requiring 0–0.5 days, fishers who are not equipped with refrigeration must deliver their catch to port within 0.5 days of catching them so that their entire journey is restricted to 1 day. Therefore, it must be determined whether the mackerel or herring are located within a region that is practical for delivery for small vessels without refrigeration. Here, it is only considered whether fish can be caught, ignoring for the moment the economic problem. The design speed of fishing vessels is generally: v ≈ 10 knots (i.e. ≈ 18 km/h) (Bo, 2007), so that a fishing vessel can travel 216 km in 12 h. Thus 216 km is an upper limit, but in practice, they must return to port within the 12 h of the start of fishing to stay within the constraints outlined above so that their range is significantly less.

To minimise the errors in our predictions, a range of years instead of a certain year will be given. For this reason, the worst case, the best case, and the most likely case are considered, and then a range of years that the small vessel starts without catching fish is inferred from that three cases.

There are many fishing ports in Scotland. Different ports have different distances from fish habitats, which affects fishing production. As the habitat moves towards the northeast of Scotland, the port in the northeast corner of Scotland is set as the best case. The small fishing boats' ports that hunt for mackerel and herring are considered to be located in the east of Scotland, the port in the worst case is set to the southeast corner of Scotland; Peterhead is Scotland's largest fishing port [18], where lots of small companies are gathered, so Peterhead is set as the port for the most likely circumstance.

The rising sea temperature has caused herrings and mackerels to gradually migrate away from Scotland towards the coasts of Norway and Iceland where the temperature is lower. The faster the ocean temperature rises, the faster fish schools move away from Scotland, and the more difficult it is for fishing boats to catch fish near Scotland. Therefore, in terms of temperature change, where the temperature rises fast or slow, it is considered as the worst and best cases, respectively. The prediction in the migration route is based on the data for the past 29 years. The huge amount of data can minimise the error caused by occasionality. So, this is the most likely situation for temperature changes, but this situation may underestimate the impact of climate change since humans may emit more greenhouse gases in the future.

Here the best and worst cases are first considered. Regarding temperature, from the past data for a fixed reference point, the temperature increases faster in some time periods and slower in others. The worst-case prediction is that when the temperature-change rate in all future years is set to the most rapid temperature increment rate in the past years; and the best-case prediction is that when these changes are least rapid. To reduce the error when calculating the temperature increase rate of the past years in various time periods, the data contained in the time period cannot be too small, and the number of time periods cannot be too small. The appropriate time period selection scheme was determined by dividing these periods into different parts under the following three schemes:

5 years as a time period, and the data of each reference point over the past 29 years are divided into 1991–1995, 1996–2000, 2001–2005, 2006–2010, 2011–2015, 2016–2019.

7 years as a time period. The data of each reference point over the past 29 years are divided into four time periods: 1991–1997, 1998–2004, 2005–2011, and 2012–2019.

10 years as a time period. The data of each reference point over the past 29 years are divided into three time periods: 1991–2000, 2001–2010, and 2011–2019.

Trial process: Since predictions are made based on a monthly linear model, in this model, the temperature-year relation of the same month satisfies:

The a mount representing temperature increase in this model is

For the best case, the northeast corner of Scotland is taken as the centre and a 216 km straight line is drawn on the isotherm. Because the Earth is spherical, the distance between the two meridians is different at different latitudes. The actual distance between the two latitudes is 108 km, and the actual distance between the two longitudes is 108 km × cos

For small fishery companies, the most important factor is the economic benefit, and thus this will be the main factor in our assessment of the impact of global warming, which will determine when companies are no longer viable or whether companies need to change their operating strategy and how to change it. Various factors affect the economy of a commercial fishing company. The three main factors are: sales of fish

Use fees are mainly due to the fuel consumption of the fishing vessels [19], and the fuel consumption is related to the vessel type and fuel price. According to relevant data, the fuel consumption for the improved diesel engines of fishing boats is about 230 ml/kWh [20]. Small fishery company operates mostly small fishing boats whose lengths are <15 m [21]. To consider long-distance navigation, it is assumed that all fishing boats for this company are 12 metres long, with a speed of 10 knots and a maximum fish transport capacity of 10 t (large enough), a diesel engine power is 110 kW, carrying three people [22]. Diesel fuel prices often fluctuate and are affected by many factors; thus it is difficult to predict diesel fuel prices (or the prices of other commodities) [23]. The average price in recent years is used as a predictor of future fuel prices. In recent years, diesel fuel average price has been approximately 0.75 £/L [25]. It is assumed that over the long term, prices will follow the annual inflation rate. To sum up, for a vessel:

It is assumed that the fishers are all skilled workers over the age of 25. They are paid when they go out to the sea but otherwise are not paid. It is assumed that there are no vacations during the fishing season. The average daily wage of fishermen in 2015 was about 56 £, about 8 times the minimum daily wage of 6.7 £/ [5]. It is assumed that this relative relationship will not change in the future. According to the British minimum wage change table [5], the fitted curve shows that the minimum hourly wage satisfies the following functional relationship:

Here

For the fish sales model, the two quantities that affect sales are the price

The selling price of fish and the number of fish caught is considered separately.

In 2018, the price of herring was 0.38 £/kg, and the price of mackerel is 1.07 £/kg [25]. Due to the growing economy, the price of fish has increased year by year. In the long term, the increase in price for fish to reflect the overall UK Consumer Price Index (CPI) [26]. Because the CPI has not changed significantly in recent years, for calculation simplicity, the average value of these years is used as the proportion of the annual increase in fish price (+2.7%/year) in the forecast, that is:

From experience, a fishing boat generally catches 20–110 kg/h [27], which is not only a wide range but also inaccurate for science, and due to the temperature, the density of the fish will change, which will also affect the catch. To refine the fishing volume of fishing vessels, a model is built to estimate the fishing volume of fishing vessels.

Due to the different starting points for fishing vessels, the sailing distances to the same area vary. As an example, a relatively common port, for example, the Aberdeen port is chosen as the port of departure of the ship for calculation. From Marine Scotland Science Fish and Shellfish Stocks [10], the distribution of the mackerel and herring catch in 2013 can be known (i.e. Figure 1). Since the catch distribution, the school density and catches per hour are closely related, the change rate of the catch distribution at different positions is used to assess the change rate of fish density and catch per hour. From Figure 1, it is found that the distribution of the North Sea herring is generally decreasing on either side of the ocean centreline, while the distribution of the herring north of Scotland is approximately a fixed value, and the North Sea mackerel distribution is changing approximately along the North Sea to the northeast direction, first a constant, and then in increments. Based on these observations, the rules of the hourly capture volume is quantified (i.e. Figure 7) in different regions based on the following models:

Herring distribution model (i.e. Figure 7a). Point a: 58.62N, 4.98W; Point b: 62.15N, 5.11E; Point c: 59.88N, 1.05W; Point d: 52.48N, 5.09E. In Regions A and B, the hourly average catch decreases evenly from both sides of the line cd at Δm_{1}kg/(h*km), and the catch at Aberdeen port is m1 kg/h, at cd it is about (m_{1} + 200 * Δm_{1}) kg/h. In region C, the average value is used, so the hourly catch is (m_{1} + m_{1} + 200 * Δm_{1})/2 kg/h. Here, m_{1} is the weight of fish caught per hour. (20 ≤ m_{1} ≤ 110, 20 ≤ (m_{1} + 200 * Δm_{1}) ≤ 110).

Mackerel distribution model (i.e. Figure 7b). Point a: 58.62N, 4.98W; Point b: 62.15N, 5.11E; Point c: 57.16N, 1.71W; Point d: 59.51N, 5.36E; Point e: 54.62N, 1.09W; Point f: 58.05N, 8.00E. The hourly average catch in region C between the two parallel lines cd and ef is m_{2} kg/h. In Region B between cd and ab, the catch along the direction that is vertical to ab decreases at Δm_{2}kg/(h*km). In region A, the hourly average catch is about (m_{2} + 200 * Δm_{2}) kg/h. Here, m_{2} is the weight of fish caught per hour. (20 ≤ m_{2} ≤ 110, 20 ≤ (m_{2} + 200 * Δm_{2}) ≤ 110).

The number of fish populations has a normal distribution relationship with temperature [15], so the hourly volume and temperature also have a normal distribution function. The normal distribution function is fitted with two linear functions, which only consider the area of two standard deviations near the average density (i.e. according to the property of normal distribution function, since this area contains >95% of fish, there are no significant fish populations out of this area). From the calculation, the volume will decrease by 53 kg/h for each 1°C increase in temperature. Using the water temperature prediction model, the average growth rate of the North Atlantic water temperature (0.018°C/year) is calculated; that is, the decline in fishing is 0.9 kg per year. Taking 2013 as the base year and assuming that the vessel is not engaged in fishing during the voyage, and that the fishing vessel sails in a straight line after leaving the port, the catch going forward can be projected. The relationship between the hourly catch and the distance travelled by the vessel is:

For mackerel, the hourly volume is different in different places in Region B, as it is for herring in Region A. To determine the average hourly volume, the Aberdeen port is taken as the centre, and a line is drawn every ten degrees to calculate the volume for ships travelling along each line and the average taken as the first part in the equation. Then the earnings of a vessel are used to represent the earnings of the entire company (i.e. the small company consists of several vessels). Then,

According to the company's current operating strategy, the vessel can sail for a maximum of 1 day (i.e. _{1} and Δm_{2} cannot be found, and these may be different in different places since not only the SSTs but also fishery intensities affect them. In some locations, the temperatures only make a small difference in hourly capture volume, but the real landing volume has several time differences. Unless there are a large number of samples for different locations, it is difficult to determine accurate values for Δm_{1} and Δm_{2}. To see the tendency as the year changes, let Δm_{1n} = 0.35, Δm_{2n} = 0.3, and l = 100. Then the ranges of m_{1} and m_{2} are known, 20 ≤ m_{1} ≤ 40, 20 ≤ m_{2} ≤ 50. With these assumptions, it is found that small fishing vessels' earnings in these three areas will gradually decrease in the future, and that there will be a sharp decline to <0£ in the next 50 years (i.e. Figure 8).

Our research team, based on historical ocean temperature data collected by satellite and ocean buoys, conclude that, over time, the water temperature in the North Atlantic will continue to rise in the next 50 years, and that this will have a dramatic impact on the fishery in Scotland. Two major commercial fish species in Scotland, herring and mackerel, are suitable for seawater around 8.5°C; as the temperature rises in the next 50 years, these fish will move to cooler waters near Iceland and Norway. It will be more and more difficult for fishermen to catch these two fishes off Scotland, and this will cause small fishing company going bankrupt in the next 50 years. In the future, when the temperature of seawater increases and it is difficult to catch fish near the fishing ports, fishers who own ocean-going fishing vessels may be minimally impacted, but fishers operating near their home ports will find it uneconomical to continue.

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