Simply speaking, probability distribution function is mainly used to describe the basic law of random variable value distribution. For all real numbers x, the probability of the event [x Assuming

This formula is called the distribution function of the random variable X. Thus, the distribution function F (x) completely affects the probability of events, in other words, the distribution function F (x) comprehensively presents the statistical characteristics of random variables.

For example, for the probability distribution of discrete random variable, it can be assumed that _{1}, _{2},..., _{n}_{1}, _{2},..., _{n}

At the same time, probability Pi meets the following conditions:

Thus, the probability distribution function of discrete random variable X is:

In the analysis of the probability distribution of continuous random variables, it is assumed that the value interval of variable X is [a, B], the distribution function is a monotone increment function, differentiable under the condition of ===, and the actual derivative F (X) is continuous within the interval, then the probability that variable X falls within the interval [

In order to describe the law of probability distribution, the density function of probability distribution should be used to define it, as shown below:

At this point, the probability distribution function can be transformed into the probability integral form, as shown below:

Given the probability distribution density function of a continuous random variable X, the specific probability of variable X in a certain interval (x1, X2) can be calculated, and the specific formula is as follows:

Then the corresponding distribution density function is:

Using the bucket ranking algorithm in probability distribution, this paper analyzes the survey data of college students' English learning motivation, mainly discusses how to evenly distribute the ranking records among all buckets, which is also the key factor to improve the ranking technology. From the point of view of the current statistical data application, it mainly obeys a certain probability distribution in a certain interval. For this kind of data sorting, the hash function can be constructed according to the density function of probability distribution, and then the N records to be arranged are evenly distributed to N buckets according to the size of key code value, so as to ensure that the running time of bucket sorting can reach O (n) under all conditions.[1]

Computer internal sorting algorithm is mainly divided into two kinds, one kind is refers to the comparison of sorting algorithm, research scholars at home and abroad the analysis is improved, not only increase the application rate, also have more data distribution, originally is the best features of Ω time consumption, and improved characteristics can be O (n). The other is the use of numbers and address computing as the core of the sorting algorithm. The critical code finite type is 1,... In the case of m, the calculation time complexity of the algorithm is O (m+n).[2.3]

Reordering the records in all buckets using other sorting techniques. The purpose is to allocate fewer records to each bucket with a less expensive bucket processing technique, and to complete the record sorting of all buckets according to a faster end sorting. Therefore, how to evenly distribute the waiting sort records to all buckets is the core content of the promotion bucket sorting technology.

Since the investigation of college students' English learning motivation involves a lot of data information, the sorting algorithm following a certain probability distribution is used to construct a hash function, so as to evenly distribute the multiple records waiting for sorting into buckets, so as to improve the efficiency and quality of data research.

In all intervals, assuming that there are n records of key code A [I]. Key obeying a certain probability distribution, the density function of probability distribution can be used to evenly distribute all records to the bucket.

It is proved that if the density function of probability distribution on interval [c, d] in key code A [I].key is φ (x), then the interval [C, d] should be divided into n intercells by using special points, so as to ensure that the area of curvilinear trapezoid formed by X-axis and curve is consistent on intercell [ck, ck+1]. At this point, the area calculation formula of all intervals is as follows:

According to the analysis of probability theory, it is found that the corresponding probability of the same area between the segments is also similar. If each interval corresponds to a bucket and all data in array A [n] has the same probability of falling into the bucket, data records can be evenly distributed into the bucket.

Note that since c=c0, c1..., cn=d is not necessarily the equipartition point, so the actual position cannot be determined. From the point of view of practical application, it is not necessary to specify the location of the point, as long as the correct calculation can master the key code area of the waiting sorting record.

Assume that S (a[I].key) represents the serial number of the bucket where A [I] resides. The actual calculation formula is as follows:

In the above formula, [] stands for integer, which is consistent with the following studies. This formula stands for the hash function.

If

Assuming

Because the condition

It can also be made clear:

In other words,

A key with a small serial number must be small. If records are sorted according to the size of the serial number, the actual key has orderliness.

From the perspective of uniform distribution, assuming that the compliance condition of waiting sort key a[n]. Key on interval [C, d] is uniform distribution, the actual density function is shown as follows:

Combining the above formula to calculate the number of bucket where a[n]. Key resides, the following formula can be obtained:

From the perspective of normal distribution, the actual density function formula is as follows:

In the above formula, m represents the mean and Z represents the mean square deviation.

At the same time, although the original function of the integral of the normal distribution function φ (x) exists, it cannot be expressed by the elementary function, so a function should be constructed in the interval [C, d] to approximate the function φ (x). It should be noted that the curve of sinx function on interval

Thus, it can be obtained:

And meet the following conditions:

Assuming

After transformation, the function still has the mean and mean square deviation of the original normal distribution density function. The calculation result of the mean is as follows:

The calculation results of mean square error Z are as follows:

After the coordinate transformation, the interval can be effectively extended according to the symmetry of function φ (x), but there is no distributed key code inside. When calculating the serial number, the integral interval still stays in the original [C, D] interval. At this point, the serial number calculation formula is as follows[4.5]:

Assumptions:

Then we can get:

During data sort, it is clear that the array to be read into is a[n], and the corresponding type is:

Meanwhile, the data type of pointer array q[n] is:

The description of the sorting algorithm is as follows:

In view of the current situation of college students' English learning, this paper conducts a questionnaire survey on students' learning motivation based on probability distribution. Practical problems involve the following points: First, to understand the self-state of college students' English learning motivation; Secondly, the self-systematic characteristics of English learning motivation of students of different ages, majors, genders and levels should be clarified. Finally, the impact of the differences on English language teaching should be deeply explored.

In this paper, the probability distribution method is used to collect relevant data and information, and quantitative and qualitative methods are combined for in-depth discussion. The actual research tool is the self-questionnaire of motivation proposed by Taguchi, Magid, Papi et al., and the questionnaire of college students' English learning motivation proposed by Liu Fengge et al. In the design of the questionnaire, two aspects are mainly concerned: on the one hand, the background investigation of students; on the other hand, combined with the second language motivational self system theory, the four aspects of learning motivation intensity, ideal self, should self and learning experience of students are systematically investigated. After completing the initial questionnaire, the Likert rating scale was used to set the option score, and the one-to-one semi-structured interview was proposed in combination with qualitative analysis.[6.7]

In this study, a certain university was taken as the data source, and questionnaires were sent to college students through QQ group or wechat group. After 400 questionnaires were collected, invalid questionnaires that did not meet the requirements due to disciplines, age and other factors were removed, and 369 valid samples were finally obtained. Statistical software S P S S 17.0 was used to analyze the probability distribution and validate the validity of the data, and descriptive statistical analysis was conducted on the participants' second language learning motivation self-system, which involved correlation, one-way variance, robustness and other test methods.

Combined with the results of the self-questionnaire on college students' second language motivation as shown in Table 1 below, it is found that the mean values of emotion and behavior in motivation intensity are both over the median of 3.5, which proves that college students' English learning motivation is positive, but the actual level is not high. The overall average value of ideal self and learning experience is more than 3.5, which proves that these two factors are dominant influencing factors, which often appear in students' English learning and are the main contents of learning motivation. The overall mean value of the should self is the median, so it is a non-dominant factor, but it contains components, whether defensive motivation or family influence factors are dominant factors. According to these four description result, the study found the ideal self has the highest average value, so the second language ego ideal for college students of English learning effect is the largest, the second is the learning experience, this and other scientific research scholar's research results both at home and abroad, thus proves that motivation system yourself in English learning motivation research in our country has a certain application advantages.

Descriptive statistical results of the motivational self-questionnaire

The number of | The mean | The standard deviation | ||
---|---|---|---|---|

The intensity of motivation | The emotion motive | 369 | 3.85 | 1.55 |

Motivation behavior | 369 | 3.89 | 1.35 | |

Ideal self | International vision | 369 | 5.26 | 1.35 |

Facilitative tool motivation | 369 | 5.63 | 1.26 | |

Integrative instrumental motivation | 369 | 5.21 | 1.58 | |

Should be self | Family influence | 369 | 5.12 | 1.38 |

Defensive motivation | 369 | 3.55 | 1.53 | |

Contextual motivation | 369 | 2.83 | 1.58 | |

Learning experience | Learn confidence | 369 | 5.39 | 1.28 |

Learning anxiety | 369 | 3.36 | 1.58 |

This paper uses one-way anOVA to compare and discuss the differences in English learning motivation among college students of different grades. The actual results are shown in Table 2 below:

Results of self-variance test of motivation of college students of all grade

A freshman | A sophomore | Junior year | Senior year | The F value | Df2 | Sig value | |
---|---|---|---|---|---|---|---|

The emotion motive | 4.03 | 3.42 | 3.84 | 3.58 | 3.132 | 0.025 | |

Motivation behavior | 4.04 | 3.08 | 4.07 | 3.40 | 174.213 | 0.011 | |

International vision | 4.28 | 4.14 | 4.24 | 4.70 | 1.875 | 0.133 | |

Facilitative tool motivation | 4.42 | 4.55 | 4.48 | 4.90 | 0.949 | 0.417 | |

Integrative instrumental motivation | 4.34 | 4.07 | 4.09 | 4.44 | 1.504 | 0.188 | |

Family influence | 4.19 | 4.08 | 4.20 | 3.89 | 0.330 | 0.803 | |

Defensive motivation | 3.35 | 3.54 | 3.59 | 3.41 | 0.947 | 0.418 | |

Contextual motivation | 2.54 | 2.82 | 3.27 | 2.90 | 1.927 | 0.124 | |

Learn confidence | 4.48 | 4.29 | 4.43 | 4.35 | 0.757 | 0.413 | |

Learning anxiety | 3.08 | 3.49 | 3.27 | 3.83 | 3.332 | 0.020 |

Note :(df2) is the result of robustness test when homogeneity of variance is not satisfied

According to the analysis results in the table above, there are significant differences in learning anxiety, motivated behavior and emotional motivation, while there are no significant differences in other parts. From the average value, the order of emotional motivation is freshman, junior, senior and sophomore; The ranking results of behavioral motivation were junior, freshman, senior and sophomore. The ranking results of learning anxiety were senior year, sophomore year, junior year and freshman year. In practice, some researchers found that the higher the grade of college students, the stronger the motivation of English learning, which is quite different from the research results in this paper. The reason for this phenomenon is that there is a discrepancy between the actual questionnaire and the subjects of the study. According to the analysis of relevant numerical changes, it is found that the students with the strongest emotional learning motivation are the students with the strongest behavioral motivation. Through one-to-one interviews with students, it is found that students have higher interest in learning and higher actual expectations. However, due to the lack of professional and systematic guidance and management, students do not have a strong sense of independent control, so they cannot achieve good learning results. Sophomores' behavioral motivation and emotional motivation are all at the lowest level, because their professional courses are getting more and more difficult, their knowledge is too boring, and their interest in English learning is getting lower and lower. At this stage, students are in a downturn. Most of the junior college students are facing the postgraduate entrance examination or examination, the actual learning motivation is stronger; However, as senior students have basically completed their undergraduate learning tasks, their actual motivation to learn English begins to decline slowly.[9.10]

The T test of independent samples was used to judge the differences between boys and girls in the motivational self system, and the specific results are shown in Table 2 below:

Sample test results of male and female students in the motivational self system

The mean | T value | |||
---|---|---|---|---|

female | male | |||

The intensity of motivation | The emotion motive | 4.14 | 3.34 | 0.004 |

Motivation behavior | 3.83 | 3.49 | 0.337 | |

Ideal self | International vision | 4.39 | 4.01 | 0.009 |

Facilitative tool motivation | 3.83 | 4.24 | 0.000 | |

Integrative instrumental motivation | 4.44 | 3.74 | 0.000 | |

Should be self | Family influence | 4.17 | 4.02 | 0.291 |

Defensive motivation | 3.44 | 3.72 | 0.094 | |

Contextual motivation | 2.47 | 3.12 | 0.004 | |

Learning experience | Learn confidence | 4.44 | 4.07 | 0.001 |

Learning anxiety | 3.34 | 3.37 | 0.948 |

According to the research results in the table above, the emotional motivation value of both male and female students is 0.005, which proves that there is a significant difference in their motivation during English learning. On average, girls are higher than boys. However, the constitutions of motivation behavior are all over 0.05, which proves that girls' interest in learning is higher than boys', but there is no significant difference in learning behavior. It can be seen that gender differences in self are not obvious, but the actual mean value proves that male students have stronger defensive motivation than female students and are highly susceptible to the influence of the surrounding environment.

According to the results of self-variance test of motivation shown in Table 3 below, there are significant differences in students' motivation under different academic backgrounds. Among them, science students have higher learning emotional motivation and motivated behavior, and art students have the lowest learning motivation.

Results of motivational self-examination for each discipline backgroun

Academic background and motivation | Families | In science and engineering | The arts | The F value | Df2 | Sig value | |
---|---|---|---|---|---|---|---|

The intensity of motivation | The emotion motive | 3.73 | 3.92 | 3.34 | 3.384 | 0.035 | |

Motivation behavior | 3.82 | 3.91 | 3.38 | 193.014 | 0.048 | ||

Ideal self | International vision | 4.17 | 4.42 | 4.09 | 1.839 | 0.160 | |

Facilitative tool motivation | 4.54 | 4.76 | 4.52 | 1.435 | 0.299 | ||

Integrative instrumental motivation | 4.27 | 4.10 | 4.34 | 0.778 | 0.460 | ||

Should be self | Family influence | 4.17 | 4.16 | 3.88 | 1.043 | 0.354 | |

Defensive motivation | 3.37 | 3.68 | 3.63 | 1.749 | 0.175 | ||

Contextual motivation | 2.55 | 2.98 | 3.17 | 192.006 | 0.009 | ||

Learning experience | Learn confidence | 4.40 | 4.44 | 4.23 | 0.583 | 0.559 | |

Learning anxiety | 3.23 | 3.34 | 3.79 | 3.136 | 0.045 |

Note :(df2) is the result of robustness test when homogeneity of variance is not satisfied

According to the self-examination results of motivation of students at different levels as shown in Table 4 below, primary means below LEVEL 4, intermediate means between level 4 and level 6, and senior means above level 6.

Results of self-examination of motivation of students of different levels

English proficiency and motivation | primary | The intermediate | senior | The F value | Df2 | Sig value | |
---|---|---|---|---|---|---|---|

The intensity of motivation | The emotion motive | 3.59 | 4.29 | 4.71 | 10.924 | 0.000 | |

Motivation behavior | 3.66 | 4.16 | 4.67 | 8.847 | 0.000 | ||

Ideal self | International vision | 4.17 | 4.56 | 4.83 | 3.958 | 0.000 | |

Facilitative tool motivation | 4.53 | 4.87 | 5.38 | 90.636 | 0.000 | ||

Integrative instrumental motivation | 4.14 | 4.47 | 4.67 | 2.162 | 0.117 | ||

Should be self | Family influence | 4.08 | 4.14 | 4.54 | 1.253 | 0.287 | |

Defensive motivation | 3.55 | 3.68 | 3.13 | 1.083 | 0.340 | ||

Contextual motivation | 2.74 | 3.33 | 2.92 | 3.130 | 0.045 | ||

Learning experience | Learn confidence | 4.34 | 4.43 | 5.00 | 3.080 | 0.047 | |

Learning anxiety | 3.39 | 3.49 | 2.79 | 2.004 | 0.136 |

Note :(df2) is the result of robustness test when homogeneity of variance is not satisfied

Combined with the numerical analysis in the table above, it is found that students at different English learning levels have significant differences in experience, ideal self and motivation intensity. For example, in motivation intensity, the higher the English learning level of college students, the higher the behavioral motivation and emotional motivation; In terms of ideal second language self, the higher the English learning level of college students, both the stimulative tool and the international perspective motivation are constantly enhanced; During the application of SECOND language self, although there are obvious differences due to the influence of surrounding environmental factors, the actual average value is not a significant result, which proves that there is no significant difference in second language self. This research result is consistent with the content proposed by current scientific research scholars. In addition, students at different learning levels also have different self-confidence. The stronger the actual ability, the higher the self-learning consciousness, which is consistent with the conventional phenomenon.[11.12]

To sum up, combined with probability distribution for the current college students' English learning motivation system investigation, not only can clearly recognize the students learning situation, can also according to the study demand effective intervention countermeasures, and actively to strengthen students' self-confidence, prompt them to eliminate bad feelings at the same time, to raise their level of English learning. Therefore, on the basis of integrating the relevant topics and research results of domestic and foreign scholars, colleges and universities should put forward effective educational guidance schemes aiming at the current situation of college English teaching and learning, so as to optimize students' English experience on the basis of strengthening their learning motivation.

#### Results of self-examination of motivation of students of different levels

English proficiency and motivation | primary | The intermediate | senior | The F value | Df2 | Sig value | |
---|---|---|---|---|---|---|---|

The intensity of motivation | The emotion motive | 3.59 | 4.29 | 4.71 | 10.924 | 0.000 | |

Motivation behavior | 3.66 | 4.16 | 4.67 | 8.847 | 0.000 | ||

Ideal self | International vision | 4.17 | 4.56 | 4.83 | 3.958 | 0.000 | |

Facilitative tool motivation | 4.53 | 4.87 | 5.38 | 90.636 | 0.000 | ||

Integrative instrumental motivation | 4.14 | 4.47 | 4.67 | 2.162 | 0.117 | ||

Should be self | Family influence | 4.08 | 4.14 | 4.54 | 1.253 | 0.287 | |

Defensive motivation | 3.55 | 3.68 | 3.13 | 1.083 | 0.340 | ||

Contextual motivation | 2.74 | 3.33 | 2.92 | 3.130 | 0.045 | ||

Learning experience | Learn confidence | 4.34 | 4.43 | 5.00 | 3.080 | 0.047 | |

Learning anxiety | 3.39 | 3.49 | 2.79 | 2.004 | 0.136 |

#### Results of motivational self-examination for each discipline backgroun

Academic background and motivation | Families | In science and engineering | The arts | The F value | Df2 | Sig value | |
---|---|---|---|---|---|---|---|

The intensity of motivation | The emotion motive | 3.73 | 3.92 | 3.34 | 3.384 | 0.035 | |

Motivation behavior | 3.82 | 3.91 | 3.38 | 193.014 | 0.048 | ||

Ideal self | International vision | 4.17 | 4.42 | 4.09 | 1.839 | 0.160 | |

Facilitative tool motivation | 4.54 | 4.76 | 4.52 | 1.435 | 0.299 | ||

Integrative instrumental motivation | 4.27 | 4.10 | 4.34 | 0.778 | 0.460 | ||

Should be self | Family influence | 4.17 | 4.16 | 3.88 | 1.043 | 0.354 | |

Defensive motivation | 3.37 | 3.68 | 3.63 | 1.749 | 0.175 | ||

Contextual motivation | 2.55 | 2.98 | 3.17 | 192.006 | 0.009 | ||

Learning experience | Learn confidence | 4.40 | 4.44 | 4.23 | 0.583 | 0.559 | |

Learning anxiety | 3.23 | 3.34 | 3.79 | 3.136 | 0.045 |

#### Results of self-variance test of motivation of college students of all grade

A freshman | A sophomore | Junior year | Senior year | The F value | Df2 | Sig value | |
---|---|---|---|---|---|---|---|

The emotion motive | 4.03 | 3.42 | 3.84 | 3.58 | 3.132 | 0.025 | |

Motivation behavior | 4.04 | 3.08 | 4.07 | 3.40 | 174.213 | 0.011 | |

International vision | 4.28 | 4.14 | 4.24 | 4.70 | 1.875 | 0.133 | |

Facilitative tool motivation | 4.42 | 4.55 | 4.48 | 4.90 | 0.949 | 0.417 | |

Integrative instrumental motivation | 4.34 | 4.07 | 4.09 | 4.44 | 1.504 | 0.188 | |

Family influence | 4.19 | 4.08 | 4.20 | 3.89 | 0.330 | 0.803 | |

Defensive motivation | 3.35 | 3.54 | 3.59 | 3.41 | 0.947 | 0.418 | |

Contextual motivation | 2.54 | 2.82 | 3.27 | 2.90 | 1.927 | 0.124 | |

Learn confidence | 4.48 | 4.29 | 4.43 | 4.35 | 0.757 | 0.413 | |

Learning anxiety | 3.08 | 3.49 | 3.27 | 3.83 | 3.332 | 0.020 |

#### Sample test results of male and female students in the motivational self system

The mean | T value | |||
---|---|---|---|---|

female | male | |||

The intensity of motivation | The emotion motive | 4.14 | 3.34 | 0.004 |

Motivation behavior | 3.83 | 3.49 | 0.337 | |

Ideal self | International vision | 4.39 | 4.01 | 0.009 |

Facilitative tool motivation | 3.83 | 4.24 | 0.000 | |

Integrative instrumental motivation | 4.44 | 3.74 | 0.000 | |

Should be self | Family influence | 4.17 | 4.02 | 0.291 |

Defensive motivation | 3.44 | 3.72 | 0.094 | |

Contextual motivation | 2.47 | 3.12 | 0.004 | |

Learning experience | Learn confidence | 4.44 | 4.07 | 0.001 |

Learning anxiety | 3.34 | 3.37 | 0.948 |

#### Descriptive statistical results of the motivational self-questionnaire

The number of | The mean | The standard deviation | ||
---|---|---|---|---|

The intensity of motivation | The emotion motive | 369 | 3.85 | 1.55 |

Motivation behavior | 369 | 3.89 | 1.35 | |

Ideal self | International vision | 369 | 5.26 | 1.35 |

Facilitative tool motivation | 369 | 5.63 | 1.26 | |

Integrative instrumental motivation | 369 | 5.21 | 1.58 | |

Should be self | Family influence | 369 | 5.12 | 1.38 |

Defensive motivation | 369 | 3.55 | 1.53 | |

Contextual motivation | 369 | 2.83 | 1.58 | |

Learning experience | Learn confidence | 369 | 5.39 | 1.28 |

Learning anxiety | 369 | 3.36 | 1.58 |

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Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation 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 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 Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling 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 Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations 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 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 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 Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand 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 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Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection 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 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 Research on non-linear visual matching model under inherent constraints of images 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 A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes 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 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 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 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 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 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 Research on threat assessment problems of island air defence system based on the leader-follower model 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 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 Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm 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 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 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