When athletes carry out special physical training, they should first make a scientific diagnosis of their own special physical level, then understand the level of their own special physical level, and distinguish their own advantages and disadvantages. If we only rely on the self perception of athletes and the experience perception of coaches to judge, it is easy to form a certain deviation from the actual situation, which makes it difficult for athletes to clearly understand their own advantages and disadvantages, so as to induce athletes to practice in the wrong direction, which not only wastes precious training time, but also may lead to the stagnation of their own special physical fitness level and technical level [1]. The formation of special physical fitness evaluation index system has objectivity and authenticity. The special physical fitness evaluation standards involved can objectively and effectively diagnose the unilateral and overall reality of athletes' special physical fitness level, and help coaches carry out targeted special physical fitness training activities. At the same time, it can also make athletes clearly aware of what aspects of training they should strengthen, and avoid training deviation caused by subjective judgment, which ensures the scientific rationality of diagnosis. By consulting the relevant literature in China, we know that many traditional sports in China have formed a relatively complete set of scientific research system for athletes' special physical fitness evaluation. These studies have laid a solid theoretical foundation for the improvement of athletes' special physical fitness level and their technical and tactical level. Chen Z and others believe that for tennis events, at present, there are relatively few scholars involved in the research on the special physical fitness evaluation index system of high-level tennis players in Colleges and universities. Therefore, in order to improve the current situation, it is necessary to study the construction of the special physical fitness evaluation index system of high-level tennis players in Colleges and universities [2]. After consulting relevant literature and actual visit and investigation, it is found that a university is affected by the climate, coupled with relatively backward economic development, lack of venues, weak tennis teachers, unreasonable curriculum and coaches' neglect of athletes' “special physical fitness” training. It not only makes the development level of tennis form a certain gap with colleges and universities in economically developed areas, but also affects some high-level tennis players. After entering the school, their professional and technical level has not been greatly improved, and their special physical fitness level has decreased slightly, which restricts the improvement of their tennis competitive level to a certain extent. Therefore, by constructing the special physical fitness evaluation index system of high-level tennis players in an ordinary university, in order to provide a theoretical basis for their special physical fitness training and effectively promote the improvement of their special physical fitness level. Aswal D and others found that at present, there is a relative lack of systematic research on the evaluation index system of special physical fitness of tennis players by Chinese scholars, especially the relevant research based on the level of high-level tennis players in an ordinary university. Therefore, this study attempts to build a scientific and reasonable special physical fitness evaluation index system for high-level tennis players in Colleges and Universities Affiliated to Heilongjiang Province through in-depth understanding of the characteristics of tennis events, in order to provide a theoretical basis for effectively improving the scientific physical fitness training of athletes [3]. Through the research on the construction of special physical fitness evaluation index system for high-level tennis players in an ordinary university, it can promote the improvement of relevant research to a certain extent, enrich relevant databases, and provide a certain scientific basis for the selection, special physical fitness training and evaluation of high-level tennis players in other universities. At the same time, it can also provide theoretical reference for other researchers to study the special physical fitness evaluation index system of athletes in the same group. By constructing the special physical fitness evaluation index system of high-level tennis players in an ordinary university, firstly, according to the evaluation index model, it is convenient for coaches to select special materials and carry out special physical fitness training activities. Secondly, the evaluation index weight model constructed by Zhang R and others is convenient for athletes to grasp the importance of special physical fitness evaluation indexes at all levels and focus on it in training [4]. Moreover, the use of the constructed single index and comprehensive evaluation criteria is convenient for athletes to scientifically and objectively diagnose their own special physical fitness training level, make qualitative and quantitative evaluation of their own special physical fitness level, and explore their own advantages and disadvantages. At the same time, it is also convenient for coaches to monitor athletes in different training stages in real time in special physical training activities, formulate targeted training plans, and promote the improvement of athletes' own special physical fitness level and the quality of sports team construction.

Taking some college tennis players in a university as the research object. 28 male athletes and 12 female athletes were selected. As shown in Table 1.

Height and weight of athletes

Name | Height (CM) | Weight (kg) | Name | Height (CM) | Weight (kg) |
---|---|---|---|---|---|

1 | 176 | 68 | 21 | 176 | 68 |

2 | 186 | 91 | 22 | 178 | 66 |

3 | 184 | 75 | 23 | 168 | 60 |

4 | 180 | 75 | 24 | 174 | 68 |

5 | 178 | 80 | 25 | 166 | 53 |

6 | 164 | 69 | 26 | 178 | 73 |

7 | 160 | 68 | 27 | 180 | 76 |

8 | 178 | 70 | 28 | 168 | 53 |

9 | 170 | 60 | 29 | 178 | 75 |

10 | 175 | 70 | 30 | 169 | 59 |

11 | 168 | 60 | 31 | 180 | 78 |

12 | 172 | 62 | 32 | 176 | 68 |

13 | 170 | 61 | 33 | 184 | 78 |

14 | 177 | 72 | 34 | 195 | 80 |

15 | 183 | 80 | 35 | 188 | 82 |

16 | 170 | 72 | 36 | 174 | 70 |

17 | 179 | 75 | 37 | 185 | 75 |

18 | 166 | 62 | 38 | 183 | 78 |

19 | 165 | 59 | 39 | 168 | 65 |

20 | 173 | 68 | 40 | 174 | 60 |

Through computer and manual access to a large number of literature on physical fitness, special physical fitness, competition load, tennis physical fitness and tennis competition load characteristics. Through the electronic reading room of Suzhou University Library, I consulted relevant papers and professional works such as sports training, structural characteristics and basic training methods of athletes' competitive ability, physical and psychological training manual of tennis players, sports physiology and rapid strength of sports nutrition [5]. More than 130 papers on the research of ball physical fitness and competition load characteristics in recent years were consulted in the literature libraries such as China HowNet, Chongqing VIP and Wanfang Data Resource System. Combined with the research of other related sports in special physical fitness and competition load, the special physical fitness and competition load characteristics of College Tennis players in a province were systematically analyzed and studied.

Recording instrument: Canon DC40.

Number of recording fields: 20 in total.

Data analysis: analyze the recorded video through Simi scout software to obtain relevant data, and then evaluate the special physical fitness and competition load of college tennis players in a province according to the data.

Test index

Morphological indicators: height, weight, lower limb length, arm length.

Physiological and biochemical indexes: heart rate, blood lactic acid.

Main testing instruments and methods

Height and weight machine: mainly used to test height and weight.

Tape measure: mainly used to test the length of lower limbs and arms.

Physiological and biochemical indexes

Heart rate: measure the athlete's quiet heart rate before the competition and record it; Measure the heart rate of maximum intensity and record it; Measure and record the heart rate 20 s after the highest intensity; The heart rate 90 s after high intensity was recorded; Measure and record the heart rate immediately after the game; Measure and record the heart rate 5 minutes after the competition; Measure and record the heart rate 10 minutes after the competition; Measure the morning pulse of the next day and record it.

Blood lactic acid test: reagent configuration and storage: Take - package of YSI supporting concentrated buffer, pour it into the mixing bottle and dissolve it with 500ml distilled water. Hemolytic agent and 5mmol / L standard solution are provided for matching. Test steps: add 40 μ l hemolytic agent into each lactate tube. Take ear blood with a 20 μ l capillary tube, add it into a lactic acid tube and shake it evenly [6].

Carry out calibration and other test operations according to the instrument instructions. In order to ensure the reliability of the test, calibrate every 5 samples. Through the experiment, a series of indexes about tennis special physical fitness and competition load are obtained. Through questionnaires, expert interviews and other specific methods, combined with the processing of relevant data, this paper determines the evaluation indexes or parameters of special physical fitness and competition load of college tennis players in a university. Under the careful guidance and help of the tutor, the opinions of experts and scholars were widely solicited. In order to ensure the objectivity, authenticity and effectiveness of the questionnaire, the expert evaluation method is used to test the content validity and structural validity of the questionnaire. After the first draft of the questionnaire is completed, the opinions of the tutor are consulted and revised repeatedly, and then the opinions of experts are consulted to form a more reasonable questionnaire. Finally, 10 experts were invited to test the validity of the two questionnaires. 90% of the experts thought that the content and structure design of the questionnaire were very reasonable and 10% thought it was more reasonable (see Table 2), indicating that the questionnaire has high validity.

Evaluation results of questionnaire validity

Validity | Very reasonable | More reasonable | Commonly | Unreasonable | Very unreasonable |
---|---|---|---|---|---|

Number of people | 9 | 1 | 0 | 0 | 0 |

Percentage (%) | 90 | 10 | 0 | 0 | 0 |

Sort out and summarize the contents of the video and the contents obtained from the questionnaire survey, then make statistical analysis and classification of the relevant data (SPSS13.0), and make charts or tables, and finally make statistical analysis of the characteristics of athletes' special physical fitness and competition load and their evaluation indicators or parameters.

Combined with the relevant research results, we define the physical fitness as follows: the physical fitness of athletes refers to the sum of the physical exercise ability possessed by athletes themselves and acquired through exercise. It is composed of physical fitness, physical function and body shape comprehensively applied in training and competition. Through the analysis, definition and summary of relevant concepts and theoretical knowledge, as well as the analysis and summary of the concept of special physical fitness by relevant experts, the special physical fitness of athletes is defined as: the subjective ability of athletes to participate in training and competition acquired by the day after tomorrow under the constraints of sports characteristics and competition needs. It is the athlete's body shape, organ function, sports quality and the ability of special training and competition after interacting with the technical, tactical and psychological level. From a systematic point of view, athletes' physical fitness is a complete system composed of multi factors and multi-level structure. Hierarchy is a basic feature of the system. The hierarchy of the system is because there are various differences in the elements of the system, including the differences in the combination mode. Therefore, the elements (or groups of elements) of the system are hierarchical and procedural in terms of status, function, structure and function, showing different system levels or hierarchical differences in the system with qualitative differences [7]. The overall control of this system is the core of the training work. However, in order to achieve the scientific and accurate control of such a developing and changing dynamic whole, it is inseparable from the in-depth investigation and analysis of the constituent elements of the system itself, the embodiment of the internal structure and function of the system. Without in-depth and detailed analysis, it is difficult to form a thorough understanding of the essential law of the physical training system. Therefore, using the system structure theory to scientifically analyze and evaluate the level of athletes' physical structure has important theoretical value. From the perspective of internal system structure, structure reflects the internal relationship of the system, and function is the beneficial effect of things or methods. Research shows that the morphological structure of human organs, tissues and cells is the material basis of its function. Certain morphological structure has certain functions, that is, structure determines function, and specific morphological structure realizes specific functional activities. On the contrary, the functional state can also have a corresponding impact on the morphological structure. The two are interdependent and restrict each other. Sports quality refers to the various abilities of athletes in sports. It usually includes strength, speed, endurance and flexibility. In fact, sports qualities such as strength, speed, endurance and flexibility are the comprehensive performance of human body morphological structure, physiological function and metabolic status. They are the overall sports ability of athletes. At the same time, the development of sports quality has a certain impact on Athletes' morphological structure and physiological function. Among the three constituent factors, sports quality is the external performance of physical fitness. We regard the physical system structure of athletes and the physical structure of each subsystem as a system, whose form, function and sports quality are in a specific position and contribute their own functions. Each ability has its own specific constituent elements, and each element is determined by a specific form, content or function, thus forming the hierarchy of athletes' physical structure. From the general structure, it is a complex system composed of multi-level vertical system and multi system parallel horizontal system. In terms of its primary subsystem, it includes three subsystems: body shape, physiological function and sports quality. They constitute three interrelated subsystems that are relatively independent and interrelated. Each subsystem is divided into several levels of subsystems, thus forming the network system of athletes' physical fitness [8].

The square root method is used to calculate the weight of relevant indicators of special physical fitness of tennis players in Colleges and Universities Affiliated to Heilongjiang Province. The specific operation steps are as follows:

Calculate the product of each row element of the judgment matrix B, that is _{i}

Calculate the value of the product _{t}

In this paper, the order of fractions is an adaptive process related to local variance:

Normalize the vector

The main reason why the constructed judgment matrix is unreasonable is that experts and coaches judge the importance of indicators differently. Therefore, in order to avoid the self contradiction of importance between indicators at the same level, it is necessary to test the consistency of the final judgment matrix. According to AHP theory, when the consistency ratio CR < 0.1, it is considered that the constructed judgment matrix is relatively reasonable and ensures the relative accuracy of index weights at all levels. The specific operation steps of consistency test are as follows:

Calculate the maximum eigenvalue of the matrix, see equation (4);

Calculate the value of the consistency index CI of the matrix, as shown in equation (5).

Through the first round of expert questionnaire, the indicators with an expert consent rate of more than 70% are selected as the primary indicators. However, since the more index test items, the greater the amount of information, it is necessary to screen the indicators in the first round again, so that the established index system is more direct and the evaluation is easier to operate. The second expert questionnaire is used to screen the indicators again, and the expert survey method and expert experience are used to screen the indicators to further modify the primary indicators, but the premise of this method is that the researchers must have high consistency. Principal component analysis is a multivariate statistical analysis method that transforms multiple measured variables into a few irrelevant comprehensive indicators. Its advantage is that the principal component score obtained by principal component analysis is far less than the number of original variables, but the information loss is very small. The extracted principal components and the naming results of principal components according to the load after rotation are shown in Tables 3 and 4. KMO values are above 7.0, indicating that various indicators are suitable for principal component analysis, and the cumulative contribution rate is more than 75%, indicating that the analysis effect is good. According to principal component analysis (PCA, also known as principal component analysis, aims to use the idea of dimension reduction to transform multiple indicators into a few comprehensive indicators. In empirical research, in order to comprehensively and systematically analyze problems, we must consider many influencing factors. These factors are generally referred to as indicators and variables in multivariate statistical analysis [9]. Because each variable reflects some information of the research problem to varying degrees, and there is a certain correlation between the indicators, the information reflected by the obtained statistical data overlaps to a certain extent. When using statistical methods to study multivariable problems, too many variables will increase the amount of calculation and increase the complexity of the analysis. People hope that in the process of quantitative analysis, less variables are involved and more information is obtained. Finally, a special physical fitness index system of a college tennis player is obtained [10].

Principal component analysis results of body shape indicators

Gender | Serial number | Contribution rate (%) | Principal component naming | Representative indicators |
---|---|---|---|---|

Male | 1 | 23.378 | Body length factor | Height |

2 | 26.776 | Body composition factor | Ketole index | |

3 | 20.013 | Longitudinal scale factor of body structure | Lower limb length / height | |

4 | 17.885 | Lateral scale factor of body structure | Arm span / height | |

Total | 83.072 | KMO value = 0.712 | ||

Female | 1 | 23.678 | Body length factor | Height |

2 | 26.776 | Body composition factor | Ketole index | |

3 | 21.013 | Longitudinal scale factor of body structure | Lower limb length / height | |

4 | 16.784 | Lateral scale factor of body structure | Arm span / height | |

Total | 80.965 | KMO value = 0.738 |

Principal component analysis results of physiological function indexes

Gender | Serial number | Contribution rate (%) | Principal component naming | Representative indicators |
---|---|---|---|---|

Male | 1 | 28.798 | Body function factor | Vital capacity |

2 | 30.225 | Motor function factor | Heart rate immediately after exercise | |

3 | 33.895 | Motor function factor | Blood lactic acid | |

Total | 91.888 | KMO value = 0.905 | ||

Female | 1 | 26.255 | Body function factor | Vital capacity |

2 | 27.775 | Motor function factor | Heart rate immediately after exercise | |

3 | 27.846 | Motor function factor | Blood lactic acid | |

Total | 87.883 | KMO value = 0.809 |

In the screening process, RSR (rank sum ratio) - a comprehensive evaluation method of nonparametric statistics is adopted. When this method is applied, it can quickly reflect the status and role of indicators in the evaluation without any exchange. RSR=ZR(mXn), where ZR represents the rank sum value of body shape, sports function and special quality indicators of college tennis players in Jiangsu Province, m is the number of indicators and n is the number of experts. Compare the value of each RSR with the value of each RSR to obtain the weight [11].

In order to intuitively and scientifically judge the level and level of special physical fitness and comprehensive physical fitness of college tennis players in a province, it is necessary to establish the grade evaluation standard of tennis special students' physical fitness and comprehensive physical fitness. According to the measurement and evaluation theory, the grade evaluation usually adopts the five grade evaluation method (i.e. upper, middle, upper, middle, lower and lower) [12]. The fifth grade evaluation can adopt both dispersion method and percentile method. Compared with the dispersion method, the percentile method not only has the advantages of the dispersion method, but also uses the median as the reference value and other percentiles as the discrete distance to divide the evaluation grade, instead of taking the average as the reference value and the standard deviation as the discrete distance. It is applicable to all kinds of data with normal distribution or non normal distribution, and also reduces the link that the normal test must be carried out on relevant data because the distribution characteristics of data are not clear before formulating the evaluation standard [13]. Especially for non normal distribution data, it can be evaluated more accurately. Therefore, percentile method is more and more used at home and abroad in recent years. Therefore, in order to objectively reflect the level and level differences between the first-class physical fitness index and comprehensive physical fitness of athletes, this study uses the percentile method to establish the first-class special physical fitness index and comprehensive physical fitness grade evaluation standard of college tennis players in a province, and obtains the grade position of the first-class index and comprehensive physical fitness of college tennis players in a province according to the grade standard.

Through the above evaluation results, we can find the basic situation of college tennis players' special physical fitness in a province, so that teachers can have a certain understanding of students' special physical fitness, and reasonably plan the teaching and training process, so as to provide a basis for the overall improvement of students' competitive ability. The indexes of special physical fitness of college tennis players in a province are selected, the weight of each index is established by analytic hierarchy process, and the evaluation standard of physical fitness of college tennis players is determined by percentile method. The evaluation index system is established by organically combining single evaluation and grade evaluation, which provides a basis for athletes to further check and diagnose the actual state of competitive ability [14].

Exercise load includes two aspects: exercise volume and exercise intensity. Load is the amount of stimulation to the body and an important aspect of exercise load. The body reaction caused by it is relatively stable. It also subsides slowly after relieving the load. Therefore, the measurement of competition load can be carried out by measuring the load. The measurement of load usually includes the time of practice, the number of times (groups), the total distance of practice, the total weight and so on. Exercise intensity refers to the degree of physiological stimulation of physical exercise on human body, which is commonly expressed by physiological indicators. Such as measuring the amount of exercise in school physical education by heart rate, the transformation of blood lactic acid, etc. Speed quality - the speed of the baseline movement, explosive force - the serving speed, endurance quality - the displacement and strength quality of the whole game - the forehand hitting speed.

Test tool: polar meter collects heart rate on site. It includes 10 team heart rate transmission belts and elastic belts, a rechargeable data transmitter, a computer data line, and Polar precision Performance training and analysis software.

Test method: the sampling frequency is 12 times / min until the end of the test. After the test, input the stored heart rate data into the computer through the data transmitter, number and classify the stored data, and conduct statistical analysis with Polar Precision Performance training and analysis software. According to the human body's response to exercise load, it is divided into four intensity levels based on the heart rate, that is, it is high intensity when the heart rate is more than 157 times every 60s; 156 ~ 139 times are medium strength; 138 ~ 120 times is low strength; The following 120 times are general activities. Test results and analysis: see Table 5.

Changes of heart rate of college tennis players in Jiangsu Province before and after competition

N=40 | HR(bpm) |
---|---|

Before the game | 67.28±3.98 |

Immediately after high intensity | 146.67±5.69ΔΔ |

20s after high strength | 111.25±6.40 ΔΔ▲▲ |

90s after high strength | 86.75±5.4ΔΔ▲▲ |

Immediately after the game | 112.17±6.47ΔΔ |

90s after the game | 83.17±4.73ΔΔ★★ |

5 minutes after the game | 77.77±3.68ΔΔ★★ |

10min after the game | 71.25±4.08ΔΔ★★ |

The next morning | 64.45±4.57 |

In sports center, the change of rate can reflect energy metabolism, body function level, training load intensity and body function recovery. When athletes participate in sports and muscle activities, the increase of HR is related to exercise intensity, and the range of increase is also related to physical fitness level, duration and training level. When the variation range of heart rate is between 110–180 beats / zone, there is a significant linear relationship between heart rate and exercise intensity, oxygen uptake and energy metabolism. The latest view is that heart rate can reflect the comprehensive physiological stress level of the body. When the human body is in intense exercise, the body will produce a series of psychological stress reactions, which will play a positive role in the functional regulation and energy supply of human movement.

In the above experiment, the changes of the average heart rate of college tennis players in a province before, during and after the tennis game are described. The heart rate of the players before the game is within a normal range, which is significantly higher than the pre game value compared with the heart rate immediately after the game (P < 0.01). In the high-intensity round, the center rate has a more obvious change, which has a great relationship with the fast running, hitting and tense competition mood of the tested athletes. The heart rate of the athletes drops correspondingly in the 20s and 90s after the high-intensity. After the competition, after the athletes get the corresponding rest, the heart rate gradually recovers, and the heart rate of the test exercise will return to normal the next morning. We can see that in the college tennis competition in Jiangsu Province, the heart rate of athletes changes. With the change of competition load, the heart rate of athletes is also changing. During the interval of the competition, the load stops, and the heart rate of athletes falls back until it returns to normal. It can be seen that although the load intensity of College Students' tennis teaching competition is small, the change of heart rate can sensitively reflect the size of competition load.

The immediate heart rate of college students after tennis teaching competition was 112.17 + 6.47 BPM, which was significantly lower than that before the competition (P < 0.01), but the change range was small; The maximum heart rate after the high-intensity round in the game is 146bpm. The heart rate recovers obviously during the interval, and can fully recover to the pre game state the next morning. The change characteristics are obvious in the process of College Students' tennis competition, which can reflect the change of their competition load intensity, and can be used as an effective physiological index for college students' tennis load intensity monitoring. Therefore, we can see that the load intensity of College Students' tennis competition in a province is not large. During human exercise, blood lactic acid also increases gradually with the increase of exercise intensity. During light load exercise, the blood lactic acid value is not very high. With the gradual increase of intensity, when the load intensity exceeds a certain level, the blood lactic acid will rise sharply (about 80% ~ 90% of the maximum intensity). The average blood lactic acid level of the tested athletes before the competition is 1.58 + 0.41 mmol / L for men and 1.56 + 0.34 mmol / L for women. In quiet time, lactic acid is mainly produced by tissues with more energy consumption, such as nerve, retina, red blood cells and so on. Under normal conditions, the production and clearance of lactic acid are in dynamic balance. The blood lactic acid concentration is 1–2 mmol / L. there is no difference in the quiet value of exercise blood lactic acid between normal people and normal people. The special foundation of tennis is mainly reflected in speed strength and speed endurance. The fast attack and defense, fierce confrontation and multi shot back and forth in the competition require athletes to have high back and forth fast running ability of the bottom line. Athletes should have a certain level of lactic acid supply after the competition. Therefore, they should have a certain proportion of lactic acid supply system to participate in the competition. The level of blood lactic acid value after exercise reflects the athletes' exercise ability and ability to tolerate lactic acid. From the above experimental results, it can be seen that from the experimental results

It is calculated that the blood lactic acid level of athletes from the beginning of the competition to the end of the competition is 4.77 + 1.62 mmol / L for men and 4.11 + 2.13 mmol / L for women, which is 2–3 times that of quiet. The change of blood lactic acid is related to the energy system used during exercise, and also reflects the metabolic rate of muscle fibers. During the exercise of increasing intensity, the continuous increase of blood lactic acid shows that there is little change in blood lactic acid in the fierce tennis game. This may be because the intermittent rest time of tennis game is long, and the lactic acid is continuously generated and eliminated at the same time. Therefore, the accumulation of blood lactic acid is not much after the end of the whole game. This further shows that tennis is basically an anaerobic and lactic acid free sport. It can be seen that the load intensity of College Students' tennis competition in a province is not large.

Through the comparative analysis of college male tennis players in a province, it is found that their speed utilization rate is low, their service technology level and application ability are poor, and their mastery and understanding of service technology is not very stable. Although the speed utilization rate and one shot success rate of individual athletes are close to or even higher than those of high-level athletes, the average absolute speed and scoring rate are significantly lower than those of high-level athletes. Similarly, the comparative analysis of female tennis players of college students in Jiangsu Province shows that their speed utilization rate is also low, even lower than that of male players, and their service technology level and application ability are poor, and their mastery and understanding of service technology are also unstable. Through the comparison of service speed, we can know the intensity of athletes' competition in the process of competition, which reflects the small load of College Students' tennis competition in Jiangsu Province. Therefore, the training of tennis players in a province should not only take into account the service technology and the absolute speed of service, but also consider the tactical training of service, teach students according to their aptitude and strengthen training for weak links.

#### Height and weight of athletes

Name | Height (CM) | Weight (kg) | Name | Height (CM) | Weight (kg) |
---|---|---|---|---|---|

1 | 176 | 68 | 21 | 176 | 68 |

2 | 186 | 91 | 22 | 178 | 66 |

3 | 184 | 75 | 23 | 168 | 60 |

4 | 180 | 75 | 24 | 174 | 68 |

5 | 178 | 80 | 25 | 166 | 53 |

6 | 164 | 69 | 26 | 178 | 73 |

7 | 160 | 68 | 27 | 180 | 76 |

8 | 178 | 70 | 28 | 168 | 53 |

9 | 170 | 60 | 29 | 178 | 75 |

10 | 175 | 70 | 30 | 169 | 59 |

11 | 168 | 60 | 31 | 180 | 78 |

12 | 172 | 62 | 32 | 176 | 68 |

13 | 170 | 61 | 33 | 184 | 78 |

14 | 177 | 72 | 34 | 195 | 80 |

15 | 183 | 80 | 35 | 188 | 82 |

16 | 170 | 72 | 36 | 174 | 70 |

17 | 179 | 75 | 37 | 185 | 75 |

18 | 166 | 62 | 38 | 183 | 78 |

19 | 165 | 59 | 39 | 168 | 65 |

20 | 173 | 68 | 40 | 174 | 60 |

#### Changes of heart rate of college tennis players in Jiangsu Province before and after competition

N=40 | HR(bpm) |
---|---|

Before the game | 67.28±3.98 |

Immediately after high intensity | 146.67±5.69ΔΔ |

20s after high strength | 111.25±6.40 ΔΔ▲▲ |

90s after high strength | 86.75±5.4ΔΔ▲▲ |

Immediately after the game | 112.17±6.47ΔΔ |

90s after the game | 83.17±4.73ΔΔ★★ |

5 minutes after the game | 77.77±3.68ΔΔ★★ |

10min after the game | 71.25±4.08ΔΔ★★ |

The next morning | 64.45±4.57 |

#### Principal component analysis results of body shape indicators

Gender | Serial number | Contribution rate (%) | Principal component naming | Representative indicators |
---|---|---|---|---|

Male | 1 | 23.378 | Body length factor | Height |

2 | 26.776 | Body composition factor | Ketole index | |

3 | 20.013 | Longitudinal scale factor of body structure | Lower limb length / height | |

4 | 17.885 | Lateral scale factor of body structure | Arm span / height | |

Total | 83.072 | KMO value = 0.712 | ||

Female | 1 | 23.678 | Body length factor | Height |

2 | 26.776 | Body composition factor | Ketole index | |

3 | 21.013 | Longitudinal scale factor of body structure | Lower limb length / height | |

4 | 16.784 | Lateral scale factor of body structure | Arm span / height | |

Total | 80.965 | KMO value = 0.738 |

#### Principal component analysis results of physiological function indexes

Gender | Serial number | Contribution rate (%) | Principal component naming | Representative indicators |
---|---|---|---|---|

Male | 1 | 28.798 | Body function factor | Vital capacity |

2 | 30.225 | Motor function factor | Heart rate immediately after exercise | |

3 | 33.895 | Motor function factor | Blood lactic acid | |

Total | 91.888 | KMO value = 0.905 | ||

Female | 1 | 26.255 | Body function factor | Vital capacity |

2 | 27.775 | Motor function factor | Heart rate immediately after exercise | |

3 | 27.846 | Motor function factor | Blood lactic acid | |

Total | 87.883 | KMO value = 0.809 |

#### Evaluation results of questionnaire validity

Validity | Very reasonable | More reasonable | Commonly | Unreasonable | Very unreasonable |
---|---|---|---|---|---|

Number of people | 9 | 1 | 0 | 0 | 0 |

Percentage (%) | 90 | 10 | 0 | 0 | 0 |

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Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Paris panxiensis , a new combination of Trilliaceae from Sichuan, ChinaImpact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors 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