In the rapid development of modern science and technology, the human communication system has developed to 5G, and antenna in the related equipment research and technology application has also shown a positive role. With the increasing demand for antennas and their application scope, people have put forward more requirements on the beam shape of antennas. Therefore, it is very important to control the beam of multi-array antenna based on improved genetic algorithms in the new era. Therefore, on the basis of understanding the genetic algorithm and its application content, this paper studies the future development of related technologies based on the design content and test results of the broadband low-side lobe and high-gain microstrip display antenna developed in the new era.

#### Keywords

- genetic algorithm
- array
- the antenna
- beam
- low side lobe
- high gain
- microstrip
- display antenna
- design

#### MSC 2010

- 76M55

Assuming that the fitness of an individual _{i}

_{1} _{2} ..._{n}^{T} is marked by n and expressed by the symbol string formed by X_{i}_{1}_{2}..._{n} X_{1}_{2}..._{n}_{T}

In the construction and development of the new era, no matter what type of radio facilities, it is necessary to radiate or receive electromagnetic waves on the basis of the reasonable use of antennas. Thus, the antenna is not only an essential basic content of the development of related equipment but also the focus of research and development in the field of technology in the new era. In essence, antennas have two main functions in communication facilities: one is to refer to the energy conversion and the other is to specify the radiation or reception. Nowadays, with the expansion of antenna application scope, social development and technical innovation have raised the requirements for it, and some scene applications also have a new view on antenna patterns. In this context, in order to better respond to the antenna application requirements in various fields, the improved genetic algorithm can be combined with a deep exploration of the relevant technology methods and, thus, put forward a new control method [2–4].

First, _{4} = _{2} at the output end because of the short circuit between the inner conductor and the upper outer conductor, and the voltage formula between the two can be clearly expressed as _{a}_{4} + _{2} = 2_{1}.

Second, the voltage _{3} = 0 at the input port because there is a segment phenomenon between the outer conductors of the upper and lower parts, and so the formula _{i}_{1} + _{3} = _{1} can be obtained. At the same time, since _{3} does not pass through the inner conductor, _{i}_{1}.

Third, the input impedance formula of the coaxial mode is _{2} = _{2}/_{2} and _{c}

Fourth, in the two-wire die, the formulas 2_{4} = _{4} tan _{4} = 2_{4}/ _{d}_{d}

By (1) and (4), because _{i}_{1},_{i}_{1}, the calculation formula of the output port

In the case of _{in}_{c}_{o} = _{c}_{c}_{o}/4.

In this paper, we study a kind of antennas that have the characteristics of wide bandwidth, low-side lobe and high-gain microstrip antenna design on display form; its main characteristics are suspended stripline air as a power network, using the parasitic patch to improve the bandwidth of the antenna and then using Taylor weighted side lobe drop in order to meet the expected requirements of broadband and low-side lobe requirement. This kind of antenna has the advantages of low loss and high power in practical applications because the suspended air stripline is used as the power component network.

In this paper, the antenna design needs to ensure that the frequency is controlled between 14 GHz and 15.2 GHz, and the specific data are shown in Table 1.

Design indicators

Working bandwidth | Horizontal beam width | Pitch beam witch | Gain | Side lobe level |
---|---|---|---|---|

8% | <6.5° | <40° | >20.5 |
<-18dB |

Because the design of the display antenna requires a low paraboloidal surface, the best choice is the microstrip antenna, and because the power of this kind of antenna is too large, it needs to use the air suspended stripline structure for transmission. In this process, it helps the electromagnetic field to be concentrated in the air without considering the influence of the medium on its composition. At this time, the dielectric constant of the whole transmission line is very close to the dielectric constant of the air, which can be regarded as 1. At the same time, it is difficult to design the power division network and the antenna on the same floor, so it is necessary to choose a double-layer structure to make the power division network on the backboard. The advantage of this design is that it can control the influence of parasitic radiation on the microstrip line and promote the side lobe to descend faster. In addition, since the bandwidth of the lateral direct-fed rectangular microstrip patch antenna is relatively narrow, most of which is controlled at about 3%, it is difficult to meet the expected design requirements. Therefore, in order to expand the impedance bandwidth it has, a parasitic patch can be added to the radiation patch to form a resonance point adjacent to each other and to ensure that the final microstrip array antenna and its bandwidth meet the design requirements.

The Q value response generated by the antenna under the influence of radiation is approximately inversely proportional to the electrical thickness of the antenna itself, H/λ, and the impedance bandwidth of the patch antenna can be expanded by increasing the thickness of the antenna medium, which is one of the most common operation methods at present. However, with the increase of the value of H/λ , it is easy for the surface waves to appear on the surface of the patch. Therefore, in the research and design of this paper, on the basis of adjusting the equivalent circuit of the antenna, the method of the multi-tuning loop is used to improve the impedance bandwidth of the patch. In order to achieve this design requirement, according to the analysis of the current application form of technology, it is necessary to use a two-layer antenna structure, in which the upper part belongs to the metal patch, also known as the parasitic patch, and the lower part is called the radiation patch. The effective dielectric constant formed by the whole structure is different, so it is easy for the antenna to generate two resonant points near the frequency, so as to improve the overall bandwidth [5–7].

In this two-layer design, called symmetrical, the main lobe beam width of the patch antenna becomes too narrow due to the guiding effect of the upper conductor patch, thus increasing the gain actually contained. After the selected medium plate and antenna unit structure is defined, the model as shown in Figure 3 should be constructed with the electromagnetic simulation software, which provides an effective basis for subsequent simulation experiment analysis. After the design optimisation, the parasitic patch on the upper part and the radiation patch on the lower part of the antenna can be obtained, and the final result is far beyond the design target requirements.

In front of the array antenna design, must first clear unit which contains configuration, also as shown in the table above were analysed, and the content of the need to safeguard design display when horizontal polarisation antenna, and want to combine the pitch plane and the surface of the magnetic field of the antenna, some scene information such as the relationship between the size of the analysis and design, the number of units required. In this case, the estimation formulas of antenna beam width are, respectively, where Bwe represents the width of the electric field beam, BWh represents the width of the magnetic field beam, λ represents the wavelength and D represents the size of the antenna surface.

The main factor that affects the performance of the array antenna is the power component network contained in it. Therefore, in order to ensure that the power of the display antenna meets the requirements, the design is carried out in the way of air suspension stripline as outlined above, which requires the calculation of the dielectric constant and impedance values. The specific formulas are given below.

In the case of t/h < ≪ 1, the numerical formula for the dielectric constant and impedance of the air suspended stripline is as follows:

Calculation results of centimetre ratio

Unit | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Specific value | 0.38 | 0.48 | 0.52 | 0.65 | 0.78 | 0.96 |

Because the amplitude ratio of the port can be determined by optimisation calculation, the power value of one minute or two unequal power points at the upper level should be mastered in the calculation. The specific calculation formulas are

Among them, _{1}, _{2}, _{3} and _{4} in the formula, respectively, represent the normalised values of voltage amplitude at ports 1, 2, 3 and 4 and port 5; p2-1 and p2-2 represent the normalised values of power in the two output port regions of the power divider at the upper stage.

At the same time, because the voltage amplitude ratio of the left and right sides is the impedance ratio, in order to meet the design impedance requirements, it is necessary to use _{2} represents the impedance value of the right and _{0} represents the impedance value of the mainline; _{1} and _{2} are the amplitude of the work on the left and right sides.

After the completion of the above design work, the integrated research and simulation analysis should be carried out according to the power component network and unit combination obtained to ensure whether the values contained in it meet the requirements of side lobe and gain, etc. As shown in Figure 5, it is the structure diagram of the array antenna obtained in the research and design of this paper. The first layer is the parasitic patch; the second layer is the radiation patch and its medium layer; the following layer is the medium plate of the ground and power sub-network of the air cavity; and the last layer is the metal ground with air cavity.

After building the simulation model of the array antenna, it is necessary to ensure that the simulation values meet the requirements of the actual design objectives and then carry out processing tests on it. The final results are shown in Figure 6.

It can be seen from the above analysis that the straight line belongs to a VSWR of 2. It can be clear from the curve that the VSWR of this array of antennas is lower than 2 at 14 GHz–15.2 GHz, and it reaches the highest value at 14.903 GHz, namely 1.96, which is still lower than 2. It can be seen that the impedance bandwidth of the array antenna designed in this paper meets the practical design requirements, and the VSWR is less than 2 between 14 GHz and 15.2 GHz. When the designed array antenna is applied to the darkroom and the antenna far-field test method is used for operation, it must be guaranteed that it conforms to the

At the same time, according to the analysis shown in Table 3, at the final physical test result, compared with the design goal, the horizontal beam width of the existing array antenna at 14 GHz can reach up to 5.9°, which meets the design requirement of less than 6°. The maximum width of the pitching beam width can reach 38.1°, which meets the design requirement of less than 40°. The minimum gain value reaches 20.8 dB, which meets the design requirement of more than 20.5 dB. It can be seen that the beam control method of multi-array antenna based on the improved genetic algorithm is very effective.

Analysis of physical test results

Horizontal beam width | Pitch beam width | Gain (dB) | Side lobe level (dB) | |
---|---|---|---|---|

14 GHz | 5.9° | 38.1° | 20.8 | -18.4 |

14.6 GHz | 5.7° | 36.1° | 21.3 | -18.6 |

15.2 GHz | 5.4° | 34.6° | 22 | -18 |

Antenna array and its content such as the beam inform, nowadays, at home and abroad, the study of this aspect is still at the primary stage; there is a lot of work to do, especially under the background of a new era, in the face of all the various areas of innovation development that put forward new requirements and there must be new control method based on genetic algorithm research. On the one hand, the genetic algorithm and beam shaping program are combined effectively, and the electromagnetic simulation software is used to clarify the corresponding unit orientation diagram, and then the efficiency of beam shaping is improved in the simulation analysis. In this process, the improved genetic algorithm has more application value and can be optimised for different scenarios and conditions to ensure that the final applied beam shaping is more extensive. On the other hand, the design of a microstrip broadband array antenna based on the air suspended stripline introduced in this paper can not only meet the initial design requirements on the basis of controlling the side lobe amplitude but also use the improved genetic algorithm to calculate the related phase and amplitude. Under the background of the new era, it is believed that with the improvement of China’s scientific research technology, the application of optimisation algorithm is bound to obtain more array antenna design ideas and effectively control the beam shape. Then, on the basis of improving the application quality and efficiency of relevant scientific research facilities in China, the current communication mode in China can be further improved.

To sum up, although the current research in this field in China is still in the development stage, with the continuous accumulation of scientific research achievements in China and more study and reference of excellent research literature and materials at home and abroad, it is inevitable that more ideas for technology development can be obtained in practice and development. At the same time, in future development, it is necessary to strengthen the training of professional talents, pay attention to master the improved genetic algorithm and array antenna design requirements and then choose the appropriate technical solutions to build a more perfect control scheme so as to improve the level of communication network research and development in China. In addition, it is necessary to strengthen the attention of the public to the relevant scientific research activities, pay attention to actively participate in the relevant research and development work; only in this way, in the context of economic globalisation, it is possible to promote China to occupy an important position on the international stage.

#### Analysis of physical test results

Horizontal beam width | Pitch beam width | Gain (dB) | Side lobe level (dB) | |
---|---|---|---|---|

14 GHz | 5.9° | 38.1° | 20.8 | -18.4 |

14.6 GHz | 5.7° | 36.1° | 21.3 | -18.6 |

15.2 GHz | 5.4° | 34.6° | 22 | -18 |

#### Design indicators

Working bandwidth | Horizontal beam width | Pitch beam witch | Gain | Side lobe level |
---|---|---|---|---|

8% | <6.5° | <40° | >20.5 |
<-18dB |

#### Calculation results of centimetre ratio

Unit | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Specific value | 0.38 | 0.48 | 0.52 | 0.65 | 0.78 | 0.96 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Performance evaluation of college laboratories based on fusion of decision tree and BP neural network 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 Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 TOPSIS missile target selection method supported by the posterior probability of target recognition Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model The incentive contract of subject librarians in university library under the non-linear task importance Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot Visual error correction of continuous aerobics action images based on graph difference function Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Radioactive source search problem and optimisation model based on meta-heuristic algorithm Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity Data mining of Chain convenience stores location The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Parameter Id of Metal Hi-pressure State Equation Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control P-Matrix Reasoning and Information Intelligent Mining Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Application of regression function model based on panel data in bank resource allocation financial risk management Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Badminton players’ trajectory under numerical calculation method Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Study of a linear-physical-programming-based approach for web service selection under uncertain service quality 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 Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China The Law of Large Numbers in Children's Education Data structure simulation for the reform of the teaching process of university computer courses Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Good congruences on weakly U-abundant semigroups Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Mathematical simulation analysis of optimal detection of shot-putters’ best path Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Nonlinear Differential Equations in the Teaching Model of Educational Informatisation Fed-UserPro: A user profile construction method based on federated learning Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Computer Vision Communication Technology in Mathematical Modeling 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 in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption MCM of Student’s Physical Health Based on Mathematical Cone Attitude control for the rigid spacecraft with the improved extended state observer Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast 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 Informatisation of educational reform based on fractional differential equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm 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 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 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 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 System dynamics model of output of ball mill Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Design of Morlet wavelet neural network to solve the non-linear influenza disease system Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Motion about equilibrium points in the Jupiter-Europa system with oblateness Fractional Differential Equations in Electronic Information Models Badminton players’ trajectory under numerical calculation method BIM Engineering Management Oriented to Curve Equation Model Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model 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 The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model