Carbohydrate metabolism can provide energy for human exercise. However, different exercise intensities will consume different amounts of energy. For this reason, the paper uses a fractional linear regression equation to study the characteristics of carbohydrate metabolism and energy consumption of other groups of human beings with the same oxygen consumption during exercise. In addition, the thesis measures energy consumption during exercise and body recovery by analyzing gas metabolism methods. As a result, we found that the sugar, fat metabolism, and energy consumption of heavier volunteers under the same exercise intensity were lower than those of regular weight volunteers. Thus, the fractional linear regression method can help us analyze the relationship between glucose metabolism and exercise energy.
Keywords
- Fractional linear regression equation
- continuous exercise
- intermittent exercise
- energy expenditure
- glucose metabolism
MSC 2010
- 62J05
Obesity has become a global social problem. Cardiovascular and cerebrovascular diseases and diabetes-related to obesity endanger human health. Prolonged aerobic exercise can reduce the risk of metabolic diseases, improve cardiorespiratory function and maintain weight. How to achieve rapid weight loss and health promotion by changing the intensity and method of exercise needs further research [1]. At present, some scholars have proposed that high-intensity interval exercise training (HIIT) can increase a person's maximum oxygen uptake level and improve body fat distribution. The weight loss effect is significantly better than continuous exercise. To explore the characteristics of substrate metabolism and energy consumption of two different exercise methods under the same average oxygen consumption of different weights. In this study, two exercise methods, including 50% VO_{2}max, 75% VO_{2}max, and 100% VO_{2}max, were used for obese and normal-weight people: continuous running and intermittent running. We compare and analyze the characteristics of its substrate metabolism and energy consumption to obtain the relationship between the optimal amount of exercise based on energy metabolism and the body's energy consumption and substrate metabolism characteristics during exercise [2]. Thus, we provide a scientific basis for formulating obese weight exercise and weight loss programs and guide the public to perform correct fitness and weight loss.
Basic situation of research subjects.
Group | Age | Height (m) | Weight (kg) | BMI (kg/m^{2}) | VO_{2}max (ml/min/kg) |
---|---|---|---|---|---|
Normal body reorganization | 17.25±0.7 | 1.75±0.05 | 69.63±7.19 | 22.64±1.65 | 42.11±4.48 |
Obese body restructuring | 17.27±0.6 | 1.76±0.04 | 106.8±10.34 | 32.0±2.51 | 32.63±4.78 |
We use random sampling to select 16 students from a particular university (voluntarily participate in this experiment). Among them, 8 were young men of average weight, and 8 were obese young men [3]. The inclusion criteria are as follows: 1) The consequence has been stable in the past three months. According to the Chinese adult BMI standard: average body weight BMI 18.5–23.9, obesity BMI ≥ 28. 2) No history of motion sickness and no organic disease. Through incremental exercise load test and physical examination, and eliminate risk factors such as cardiovascular dysfunction. 3) I have not taken hormone drugs recently. 4) No bad habits such as smoking and drinking.
All subjects performed 4 experiments. First, we obtain the respective maximum oxygen uptake based on the incremental load results. Second, we determine the treadmill speed of 50% VO_{2}max, 75% VO_{2}max, and 100% VO_{2}max exercise intensity. Third, three exercise tests were carried out after 5 minutes of preparation for the experiment: (1) Volunteers continued to run for 30 minutes and recover for 30 minutes at an exercise intensity of 50% VO_{2}max. (2) Volunteers run at 75% VO_{2}max exercise intensity for 4 minutes and intermittently recover for 2 minutes as a group of intermittent exercises, perform 5 consecutive groups, and recover for 30 minutes after 5 groups exercises. (3) Volunteers run for 3 minutes at an exercise intensity of 100% VO_{2}max and intermittently recover for 3 minutes as a group of intermittent exercises. Finally, the volunteers recovered for 30 minutes after performing 5 consecutive exercises [4]. Throughout the experiment, the MAX-II test system was used to measure the body's gas metabolism indicators.
This experiment uses complete rest during the intermittent period. We performed the statistics in the above table to prove that the body function did not return to a normal state after taking complete rest. Table 2 shows that after 75% VO_{2}max and 100% VO_{2}max are intermittent for 2 min and 3 min, the final heart rate (HR) is still 135 beats/min. This shows that the subjects have not fully recovered before the next exercise and ensure the primary conditions for intermittent exercise.
Intermittent recovery of terminal heart rate during intermittent exercise.
Group | strength | Recovery interval | HR | RQ |
---|---|---|---|---|
Obesity group | 75% VO_{2}max | 2min | 140.94±10.73 | 0.96±0.09 |
100% VO_{2}max | 3min | 148.61±20.74 | 1.10±0.11 | |
Normal body reorganization | 75% VO_{2}max | 2min | 134.21±13.11 | 0.98±0.07 |
100% VO_{2}max | 3min | 148.74±7.27 | 1.12±0.03 |
During the maximal oxygen uptake test, the subjects were allowed to perform an incremental load experiment on the treadmill until exhaustion. The movement is completed within 12 minutes. We use an Italian COSMEDT150 sports treadmill. The subjects used 7km/h as the initial speed, and the movement frequency was increased by 1km/2min, and the horizontal slope remained unchanged.
Discrimination criteria: HR≥180 times/min. Respiratory quotient ≥ 1.10. As the load increases, oxygen consumption remains in a straight line and enters a plateau [5]. The subject was unable to exercise continuously after being motivated. The experiment meets 3 or more of them can be considered to reach VO_{2}max.
The current international calculation formula is as follows:
Sugar Oxidation (
Fat Oxidation (
Total energy output (
We collect data through a gas analyzer and create a data table. We use Excle2010 and SPSS20.0 statistical software for data processing. The paper uses ±s to describe the statistical indicators, uses two-way analysis of variance and independent sample T-test to analyze the data and draw conclusions [6]. The difference was statistically significant when P<0.05.
During the development of the fractional calculus theory, many definitions of fractional calculus of middle function appeared, such as the definition of Grünwald-Letnikov fractional calculus, the definition of Riemann-Liouville fractional calculus, and the definition of Caputo. This section will introduce the fractional Caputo to define the differential operator and introduce the equivalent transformation relations and related functions used in this article:
Definition of Caputo fractional differential
Integral transformation of Caputo fractional calculus
Laplace transform of the fractional differential of the function Caputo:
Mittag-Leffler function
The Mittag-Leffler function with two parameters in the paper is defined as follows:
The Laplace transformation of the Mittag-Leffler process used in this article is:
Time fractional lossy transmission line equation analysis. Take the Laplace to transform defined by the Caputo fractional order of time t on both sides of equation (5), then:
Organize to get:
Assuming
The paper uses the Adomian decomposition method to decompose
We can use MATLAB software to get:
Finally, the inverse Laplace transformation of the Mittag-Leffler function can be used to obtain the voltage response:
Table 3 shows that the sugar oxidation amount, sugar oxidation energy supply ratio, fat oxidation amount, and oxidation energy supply ratio per kilogram bodyweight of the obese group are lower than average body weight under the same exercise intensity.
Comparison of substrate metabolism and energy consumption during exercise period (30min) between obesity group and normal body recombination.
Group | Obesity group | |||
---|---|---|---|---|
Exercise mode | 50% VO_{2}max continuous exercise | 75% VO_{2}max intermittent exercise | 100% VO_{2}max intermittent exercise | |
Sugar oxidation | 10.96±1.49 | 17.96±2.06 | 25.91±4.48 | 25.91±4.48 |
Fat oxidation | 4.37±0.31 | 4.35±1.25 | 2.33±0.96 | 2.33±0.96 |
Total energy consumption | 84.27±6.88 | 111.00±11.70 | 124.59±10.42 | 124.59±10.42 |
Fat oxidation for energy | 50.27±3.53 | 37.59±4.37 | 27.57±3.08 | 27.57±3.08 |
Sugar Oxidation Energy Supply Ratio | 46.75±3.48 | 59.68±4.49 | 68.01±5.06 | 68.01±5.06 |
Group | Normal body reorganization | |||
---|---|---|---|---|
Exercise mode | 50% VO_{2}max continuous exercise | 75% VO_{2} max intermittent exercise | 100% VO_{2} max intermittent exercise | |
Sugar oxidation | (mg/min/kg) | 13.32±1.80 | 22.52±3.11 | 40.17±4.84 |
Fat oxidation | (mg/min/kg) | 6.29±1.44 | 5.70±0.20 | 2.47±0.03 |
Total energy consumption | (cal/min/kg) | 109.87±10.80 | 141.34±12.56 | 182.96±13.29 |
Fat oxidation for energy | Proportion (Fat%) | 54.19±6.29 | 38.24±4.62 | 25.23±3.07 |
Sugar Oxidation Energy Supply Ratio | Example (CHO%) | 42.66±4.34 | 58.73±6.68 | 72.25±8.03 |
Exercise intensity and body weight are two factors that affect substrate metabolism and energy consumption [7]. Table 4 shows that the main effects of exercise intensity on substrate metabolism and energy consumption reached a significant level during exercise through the two-factor analysis of variance. Still, the main results of bodyweight-only on sugar and total energy consumption reached a considerable level. Therefore, there is only interaction between strength and body weight in the amount of sugar oxidation.
Two-factor analysis of variance results of the influence of exercise intensity and body weight on substrate metabolism and energy expenditure.
Sugar oxidation | Fat oxidation | Total energy consumption | Fat% | CHO% | |
---|---|---|---|---|---|
Exercise intensity | F=30.86 | F=10.60 | F=41.28 | F=16.329 | F=17.219 |
P=0.000 | P=0.000 | P=0.000 | P=0.000 | P=0.000 | |
body weight | F=13.070 | F=3.981 | F=55.88 | F=0.045 | F=0.006 |
P=0.001 | P=0.052 | P=0.000 | P=0.832 | P=0.094 | |
Strength*weight | F=3.98 | F=0.83 | F=4.34 | F=0.26 | F=0.45 |
P=0.026 | P=0.44 | P=0.19 | P=0.773 | P=0.637 |
Table 5 shows that under the same exercise intensity, the obesity group only had higher sugar oxidation per kilogram body weight and oxidation energy supply ratio than average body weight. And the total energy consumption, fat oxidation amount, and oxidation energy supply ratio per kilogram weight were lower than the medium bodyweight group.
Comparison of substrate metabolism and energy consumption during the recovery period (30min) between the obese group and the average body with different exercise methods.
Group | Obesity group | |||
---|---|---|---|---|
Exercise mode | 50% VO_{2}max | 75%VO_{2}max | 100%VO_{2}max | |
Sugar oxidation | mg/min/kg | 3.72±0.90 | 3.08±0.31 | 2.24±0.33 |
Fat oxidation | mg/min/kg | 1.21±0.53 | 1.30±0.71 | 2.15±0.97 |
Total energy consumption | cal/min/kg | 25.8±3.12 | 24.03±2.62 | 28.28±3.23 |
Fat oxidation energy supply ratio | Fat% | 44.29±5.51 | 50.82±3.20 | 64.42±4.98 |
Sugar oxidation energy supply ratio | CHO% | 44.79±5.87 | 37.53±3.88 | 26.43±3.35 |
Group | Normal body reorganization | |||
---|---|---|---|---|
Exercise mode | 50%VO_{2}max | 75%VO_{2}max | 100%VO_{2}max | |
Sugar oxidation | mg/min/kg | 3.37±0.08 | 3.49±0.64 | 1.05±0.05 |
Fat oxidation | mg/min/kg | 1.77±0.82 | 1.63±0.85 | 3.2±0.28** |
Total energy consumption | cal/min/kg | 29.4±3.95 | 28.59±4.41 | 32.99±3.57* |
Fat oxidation energy supply ratio | Fat% | 52.47±4.19 | 51.87±3.34 | 72.46±5.46 |
Sugar oxidation energy supply ratio | CHO% | 32.56±3.84 | 34.53±4.29 | 16.58±2.98* |
The results of the two-way analysis of variance are shown in Table 6. In the recovery period after exercise, the main effects of exercise intensity on substrate metabolism and energy consumption reached a significant level (P<0.05). In addition, the main products of body weight on fat oxidation, total energy consumption. And sugar oxidation energy supply ratio reached significant levels (P<0.05), but there was no significant effect on sugar oxidation and fat oxidation energy supply ratio [8]. Thus, there is no interaction between exercise intensity and body weight on substrate metabolism and energy consumption during the recovery period.
Two-factor analysis of variance results of the effects of exercise intensity and body weight on substrate metabolism and energy expenditure during the recovery period after exercise.
Group | Sugar oxidation | Fat oxidation | Total energy consumption | Fat% | CHO% |
---|---|---|---|---|---|
Exercise intensity | F=9.62 | F=20.96 | F=4.162 | F=0.624 | F=8.359 |
P=0.000 | P=0.000 | P=0.022 | P=0.000 | P=0.01 | |
body weight | F=0.982 | F=13.77 | F=11.66 | F=2.254 | F=5.13 |
P=0.327 | P=0.001 | P=0.001 | P=0.14 | P=0.028 | |
Strength*weight | F=1.476 | F=1.552 | F=0.74 | F=0.365 | F=0.552 |
P=0.24 | P=0.224 | P=0.929 | P=0.696 | P=0.58 |
Continuous exercise and intermittent exercise on substrate metabolism and energy consumption are all related to exercise intensity. With the increase of exercise intensity, the amount of sugar oxidation and the ratio of oxidative energy supply, and the total energy consumption gradually increase, the amount of fat oxidation and the percentage of oxidation energy supply decrease progressively [9]. These changes are related to output power. Thus, with the increase of exercise intensity, the body puts forward higher requirements for the energy supply rate.
In the primary effect analysis, it was found that body weight has a significant effect on sugar and total energy consumption but has no significant impact on the ratio of fat and substrate metabolism. The reason may be that different body fat levels, and body weight has a particular effect on exercise capacity. Among them, it has the most significant impact on lean body weight. The slender body mass is highly correlated with the aerobic and anaerobic capacity of the human body, and the lean body mass varies greatly between body weights [10]. Therefore, there is a significant difference between body weights when sugars are needed for rapid oxidation for energy. In addition, it may be because the absolute exercise intensity of normal-weight people is greater than that of obese people.
Exercise weight loss mainly considers total energy expenditure. Therefore, for fat loss, the total energy consumption during exercise and recovery period is more important than the effect of energy consumption during exercise alone. This is also why some scholars have strongly advocated high-intensity interval training (HIIT) in recent years [11]. This study found that exercise intensity significantly impacts substrate metabolism and energy consumption during the recovery period after exercise. With the increase of exercise intensity, the amount of sugar oxidation and the ratio of energy supply for sugar metabolism gradually decrease after training, the amount of oxidation of fat, the proportion of energy supply for fat metabolism, and the total energy consumption increase progressively. This is mainly because endocrine hormones, body temperature, pulmonary ventilation, etc., remain at high levels after intensive exercise. Therefore, oxygen reserves need to be restored as soon as possible. The ATP-CP system needs to be quickly replenished, and lactic acid needs to be cleared as soon as possible. Currently, the primary energy supply mode has been changed from anaerobic energy supply to aerobic energy supply, and glycogen in the body has almost been exhausted during exercise. Therefore, the primary substance for aerobic energy is changed from sugar to fat. As a result, the free fatty acid level in the blood increased significantly after the training. Studies have proved that the energy supply ratio of fat after exercise is closely related to exercise intensity and exercise time. Exercise intensity affects the amount of excess oxygen consumption after exercise, and exercise time will prolong excessive oxygen consumption after exercise. In theory, high-intensity training to reduce fat is mainly in the excess oxygen consumption after exercise. The greater the exercise intensity, the higher the excess oxygen consumption after exercise.
There was no significant difference in comparing substrate metabolism and energy consumption during the recovery period between 50% VO_{2}max and 75% VO_{2}max. It shows that when the intensity exceeds 50% VO_{2}max, excessive oxygen consumption and substrate metabolism changes are not apparent after exercise. Or at this time, the excessive oxygen consumption after exercise temporarily enters the plateau period. Exercise intensity as an independent factor can affect substrate metabolism and energy consumption after practice remains to be studied [12]. There is a significant difference in the ratio of substrate metabolism energy supply between interval and continuous exercise. The reasons may be as follows: during high-intensity intermittent exercise, the pituitary-adrenal axis reacts more intensely, which leads to increased hormone secretion and improves fat oxidation energy supply ratio. It is also possible that intermittent exercise consists of the exercise period and the recovery period. The two periods continue to intersect, increasing the number of substrate mobilizations, producing numerous metabolites, increasing the amount of fat and the ratio of the oxidative energy supply after exercise.
Exercise intensity as the main effect significantly impacts the amount of sugar oxidation and total energy consumption. During the whole exercise process, with the increase of exercise intensity, the oxidation amount of sugar, the ratio of oxidation energy supply, and the total energy consumption gradually increase. In contrast, the oxidation amount of fat and the percentage of oxidation energy supply decrease progressives; there are significant differences in substrate metabolism and energy consumption characteristics during and after exercise. Still, the trends of the two are exactly opposite. This is because the body's regulation realizes the sugar oxidation energy supply ratio and the fat oxidation energy supply ratio.
The whole process of comprehensive exercise and recovery period found that moderate-intensity continuous training is better than an intermittent exercise in terms of the fat burning effect. The amount of fat oxidation and the ratio of oxidative energy supply in the constant movement are higher than that in intermittent exercise. Although the total energy consumption of intermittent exercise is higher than that of continuous practice, the energy is mainly provided by the burning of sugar. Keeping the hormone content at a high level after exercise also increases excessive oxygen consumption after exercise. Due to the short rest time during the recovery period after training in this study, the gas of excessive oxygen consumption after training was not fully collected, which resulted in the relative value of substrate metabolism, and the energy consumption is significantly lower than in other studies.
Under the exact condition of average oxygen consumption, the fat metabolism level of continuous exercise during exercise is higher than that of erratic movement. The story of glucose metabolism and the total energy consumption is lower than that of sporadic activity. During the recovery period, the fat metabolism level and total energy consumption of continuous exercise are lower than erratic movement. The glucose metabolism level is higher than that of sporadic activity. Under the same exercise intensity, the sugar, fat metabolism, and energy consumption per kilogram of body weight in the obese group were lower than average body weight.
Two-factor analysis of variance results of the influence of exercise intensity and body weight on substrate metabolism and energy expenditure.
Sugar oxidation | Fat oxidation | Total energy consumption | Fat% | CHO% | |
---|---|---|---|---|---|
Exercise intensity | F=30.86 | F=10.60 | F=41.28 | F=16.329 | F=17.219 |
P=0.000 | P=0.000 | P=0.000 | P=0.000 | P=0.000 | |
body weight | F=13.070 | F=3.981 | F=55.88 | F=0.045 | F=0.006 |
P=0.001 | P=0.052 | P=0.000 | P=0.832 | P=0.094 | |
Strength*weight | F=3.98 | F=0.83 | F=4.34 | F=0.26 | F=0.45 |
P=0.026 | P=0.44 | P=0.19 | P=0.773 | P=0.637 |
Intermittent recovery of terminal heart rate during intermittent exercise.
Group | strength | Recovery interval | HR | RQ |
---|---|---|---|---|
Obesity group | 75% VO_{2}max | 2min | 140.94±10.73 | 0.96±0.09 |
100% VO_{2}max | 3min | 148.61±20.74 | 1.10±0.11 | |
Normal body reorganization | 75% VO_{2}max | 2min | 134.21±13.11 | 0.98±0.07 |
100% VO_{2}max | 3min | 148.74±7.27 | 1.12±0.03 |
Comparison of substrate metabolism and energy consumption during the recovery period (30min) between the obese group and the average body with different exercise methods.
Group | Obesity group | |||
---|---|---|---|---|
Exercise mode | 50% VO_{2}max | 75%VO_{2}max | 100%VO_{2}max | |
Sugar oxidation | mg/min/kg | 3.72±0.90 | 3.08±0.31 | 2.24±0.33 |
Fat oxidation | mg/min/kg | 1.21±0.53 | 1.30±0.71 | 2.15±0.97 |
Total energy consumption | cal/min/kg | 25.8±3.12 | 24.03±2.62 | 28.28±3.23 |
Fat oxidation energy supply ratio | Fat% | 44.29±5.51 | 50.82±3.20 | 64.42±4.98 |
Sugar oxidation energy supply ratio | CHO% | 44.79±5.87 | 37.53±3.88 | 26.43±3.35 |
Two-factor analysis of variance results of the effects of exercise intensity and body weight on substrate metabolism and energy expenditure during the recovery period after exercise.
Group | Sugar oxidation | Fat oxidation | Total energy consumption | Fat% | CHO% |
---|---|---|---|---|---|
Exercise intensity | F=9.62 | F=20.96 | F=4.162 | F=0.624 | F=8.359 |
P=0.000 | P=0.000 | P=0.022 | P=0.000 | P=0.01 | |
body weight | F=0.982 | F=13.77 | F=11.66 | F=2.254 | F=5.13 |
P=0.327 | P=0.001 | P=0.001 | P=0.14 | P=0.028 | |
Strength*weight | F=1.476 | F=1.552 | F=0.74 | F=0.365 | F=0.552 |
P=0.24 | P=0.224 | P=0.929 | P=0.696 | P=0.58 |
Basic situation of research subjects.
Group | Age | Height (m) | Weight (kg) | BMI (kg/m^{2}) | VO_{2}max (ml/min/kg) |
---|---|---|---|---|---|
Normal body reorganization | 17.25±0.7 | 1.75±0.05 | 69.63±7.19 | 22.64±1.65 | 42.11±4.48 |
Obese body restructuring | 17.27±0.6 | 1.76±0.04 | 106.8±10.34 | 32.0±2.51 | 32.63±4.78 |
Comparison of substrate metabolism and energy consumption during exercise period (30min) between obesity group and normal body recombination.
Group | Obesity group | |||
---|---|---|---|---|
Exercise mode | 50% VO_{2}max continuous exercise | 75% VO_{2}max intermittent exercise | 100% VO_{2}max intermittent exercise | |
Sugar oxidation | 10.96±1.49 | 17.96±2.06 | 25.91±4.48 | 25.91±4.48 |
Fat oxidation | 4.37±0.31 | 4.35±1.25 | 2.33±0.96 | 2.33±0.96 |
Total energy consumption | 84.27±6.88 | 111.00±11.70 | 124.59±10.42 | 124.59±10.42 |
Fat oxidation for energy | 50.27±3.53 | 37.59±4.37 | 27.57±3.08 | 27.57±3.08 |
Sugar Oxidation Energy Supply Ratio | 46.75±3.48 | 59.68±4.49 | 68.01±5.06 | 68.01±5.06 |
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of Screening English Teaching Courses Based on Fractional Differential Equations 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 ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer 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 The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities A generative design method of building layout generated by path 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 The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Nonlinear Differential Equations in Preventing Financial Risks 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 Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis 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 Limit cycles of a generalised Mathieu differential system 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 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 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 Enterprise Financial Risk Early Warning System Based on Structural Equation Model Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Image denoising model based on improved fractional calculus mathematical equation The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Evaluation and Verification of Patent Value Based on Combination Forecasting Model Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations 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 Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Good congruences on weakly U-abundant semigroups 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 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 Fed-UserPro: A user profile construction method based on federated learning 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 Computer Vision Communication Technology in Mathematical Modeling 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 in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics MCM of Student’s Physical Health Based on Mathematical Cone 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 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 Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis 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 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 Human gait modelling and tracking based on motion functionalisation 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 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 Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model 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 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 The trend and influence of media information Propagation based on nonlinear Differential equation Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H_{2}-N_{2} atmosphere Algorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model