The idea that reform drives innovation and entrepreneurship, and innovation and entrepreneurship drive development, has gradually become the main theme of the new era of Chinese society. As the ‘cradle’ of knowledge and technology innovation and the training and output of innovative talents, colleges and universities are the inevitable choices of the times to conform to the social trend and change to the development model of ‘entrepreneurial universities’. This article takes the reform of the development model of universities in Heilongjiang Province as the research object, and it qualitatively explores the status quo of the reform and development of universities in Heilongjiang Province to entrepreneurial universities, with the aid of the Loet Leydesdorff triple helix algorithm, based on the Web of Science database and national intellectual property ‘patent search and analysis’. The platform conducts data mining, conducts quantitative measurement research on the collaboration relationship between government, industry, university and research, and focuses on Heilongjiang Province for horizontal and vertical empirical analyses. The study proposes suggestions for improvement from the three dimensions of condensing the collaborative awareness of innovation subjects, reforming the development model of scientific research institutions, and improving the efficiency of the absorption and transformation of enterprise scientific and technological achievements. It has certain practical guidance for strengthening the mutual information coordination and structural stability of the government, industry, university and research under the collaborative innovation ecosystem.

#### Keywords

- collaborative innovation
- triple helix algorithm
- government-industry-university-research collaboration
- mutual information

In the era of knowledge economy, information changes rapidly, market competition tends to become deeper and more complicated, and the mutual penetration between knowledge and economy is becoming stronger. In 2018, the R&D investment intensity of Chinese scientific and technological achievements was 2.14%, which exceeds the average level of 1.97% of the 28 EU countries, which is close to the intensity level of R&D expenditures in developing countries. The national financial science and technology allocations reached 951.82 billion yuan, accounting for 4.30% of the national public financial expenditures. The Chinese government has continuously increased its investment in technological innovation, and the total amount of scientific and technological achievements of innovation represented by government, industry, university and research entities has increased significantly. The aggregation of innovative elements, integration of innovative resources and promotion of the formation of a collaborative innovation ecosystem of multiple entities have become the best way of China to adapt to the era of the knowledge economy [1]. From the perspective of collaborative innovation, building a coupled, symbiotic, stable and coexisting relationship between government, industry, university and research can not only accelerate the release of innovation and entrepreneurship, but also positively drive the efficiency of scientific and technological achievements. It is an inevitable development process to effectively improve regional innovation efficiency [2, 3].

From the perspective of input-output, it is impossible to measure the stability of the internal organisational structure of the collaborative innovation system and the smoothness of information flow. In order to measure the degree of coupling and synergy of collaborative innovation subjects and find the ‘power point’ that promotes cross-border organisational collaboration, Leydesdorff [4] proposed the triple helix (TH) algorithm. Based on the TH innovation theory and information entropy theory, the mutual information transfer value

With regard to the mutual information between innovation subjects as a relative frequency distribution, with the help of Shannon's information theory [7], the probability distribution of a certain information variable _{xy}

Using the Abramson formula and the Thiel decomposition algorithm, the information transfer amount

Based on Eq. (3), Abramson further expressed the three-dimensional (3D) mutual information transfer amount as follows [10]:

Scientometrics is a series of in-depth quantitative research on scientific and technological achievements, scientific journals, etc., to provide scientific and accurate analysis and evaluation for the operation mechanism, development trend, and application efficiency of knowledge and technology in regions and institutions. In the TH algorithm, the number of scientific papers co-authored and the patent cooperation applications is an important manifestation of the collaborative innovation among various organisations [12]. The data acquisition is more scientific and effective, so it is often used to characterise ‘government-industry-university-research’ innovation with the support of scientometrics and the data source for the quantitative measurement of the degree of coupling and collaboration between subjects [13]. It should be noted that the data acquisition process is based on the principle of fuzzy matching and the co-occurrence of institutional names. Therefore, in order to avoid weakening the authenticity of data in the statistical classification, universities, academies of sciences, research institutes and technology centres committed to knowledge creation and technological innovation will be regarded as research institutions (A). The ‘government-industry-university-research’ synergy relationship with government-industry-university-research organisations at the core can be characterised by the TH algorithm of the ‘research institutions-industry-government’ TH innovation entity measure [14].

The Web of Science database covers the world's most comprehensive high-quality paper information with country addresses, author names, affiliation, etc., and has a comprehensive record of grant funding. It is the preferred data for indicating the source of current research on the degree of collaboration across organisational boundaries. We obtain the data index of the database retrieval by changing the address field within a certain time range, as shown in Table 1.

Definition and acquisition of data variables of scientific papers

A_{x} |
Number of papers including information on scientific research institutions | Papers with ‘UNIV*’, ‘COLL*’, ‘ACAD*’, ‘NIH*’ in the address field |

I_{x} |
Number of papers including companies information | Papers with ‘GMBH*’, ‘CORP*’, ‘LTD*’, ‘AG*’, ‘INC*’ in the address field |

G_{x} |
Number of papers including government information | Papers with ‘NATL*’, ‘NACL*’, ‘NAZL*’, ‘GOVT*’, ‘MINIST*’, ‘ACAD*’, ‘CNRS*’ in the address field |

AI_{x} |
Number of papers including both scientific research institutions and companies information | The address field contains the number of papers representing both A_{x} and I_{x} contents |

G_{x}A |
Number of papers including information about scientific research institutions in the G_{X} dataset |
The number of papers containing A_{x} in the G_{x} subset |

GI_{x} |
Number of papers including both government and corporate information | The address field contains the number of papers representing G_{x} and I_{x} contents at the same time |

G_{x}AI |
Number of papers including information about companies in the G_{X} A dataset |
The number of papers containing I_{x} in the G_{x}A subset |

Based on the national intellectual property ‘patent search and analysis’ platform, we classified search ‘patent applicant’ information to characterise the data source of patent cooperation in the TH algorithm. Patent applicants are generally organisations with technological creativity, such as the company's R&D department, scientific research institutes and universities, so it is mainly based on a certain time frame, scientific research institutions (A_{y}), industrial institutions (I_{y}), scientific research–industrial institutions (AI_{y}) and three fields to retrieve statistical data.

Patents with the ‘university, college, research institute’ field in the applicant information belong to the A_{y} dataset; patents with the ‘company, group, factory’ field in the applicant information belong to the I_{y} dataset; and the applicant information includes the scientific research institution field. If it also contains the enterprise organisation field, the patent belongs to the cross-field cooperation AI_{y} dataset.

Using the bibliometric trend change mining 1.0 software to clean the data of the retrieved scientific papers and patent titles, the valid data variables are retained and the data indicators of the intermediate variables are automatically obtained. Then the TH is performed according to the calculation formula in Table 2 to obtain the algorithm variable conversion summary. The A, I, G, AI, AG, GI, AGI values are input into the specific program th.exe of the TH algorithm, and then the

Variable definition and calculation formula of collaborative innovation measure

A | The number of papers and patents exported only by scientific research institutions | A = A_{xy}-AI_{xy}-G_{x}A + G_{x}AI |

I | The number of papers and patents output only by the companies | I = I_{xy}-AI_{xy}-GI_{x} + G_{x}AI |

G | The number of papers and patents output only by government | G = G_{xy}-G_{xy}A-GI_{x} + G_{xy}AI |

AI | The number of papers and patents jointly published or applied only by scientific research institutions and enterprises | AI = AI_{xy}-G_{x}AI |

AG | The number of papers and patents jointly published or applied only by scientific research institutions and government | AG = G_{x}A-G_{x}AI |

GI | The number of papers and patent jointly published or applied only by government and enterprises | GI = GI_{x}-G_{x}AI |

AGI | The number of papers and patents output by government agencies, scientific research institutions and enterprises | AGI = G_{x}AI |

As a traditional industrial base, Heilongjiang Province, centring on the foundation and advantages of scientific and technological innovation, deeply connects with national plans and developments such as ‘Made in China 2025’ and ‘Science and Technology Innovation 2030-Major Projects’ and actively explores collaborative innovation mechanisms that serve the regional economy. It established an industry-university-research alliance mechanism to serve development strategies such as the ‘Harbin-Daqing-Qijiang Industrial Corridor’ and the ‘Russian Economic and Trade Strategy’. It also established innovation and entrepreneurship pilot zones, technology transformation centres and other organisations. It initiated the university students’ innovation and entrepreneurship in 2018. Based on the TH collaborative innovation ecosystem built in Heilongjiang Province, this paper uses the TH algorithm to conduct research on the degree of mutual information collaboration of the TH innovation subject ‘research institution-industry-government’ under the collaborative innovation system from both horizontal and vertical dimensions. It comprehensively measures and quantitatively analyses the output of scientific and technological achievements of research institutions-industry-government, and the coordination and stability of the collaborative innovation ecosystem, and optimises the overall system.

According to the ‘China Regional Innovation Capability Evaluation Report 2019’, from the comprehensive ranking of the innovation environment based on factors such as innovation infrastructure, entrepreneurship level, market environment and labour quality factors, Jilin and Liaoning Provinces, which rank close to Heilongjiang Province, were selected after conducting a horizontal comparative analysis of the degree of collaborative innovation coupling. We retrieved and extracted the panel data information of scientific papers and patent achievements in the three northeastern provinces in 2019. After data cleaning and classification transformation, the data of government, industry, university and research in each province are as summarised in Table 3.

Summary of scientific papers and patent achievements

Heilongjiang | 8362 | 4494 | 702 | 3166 | 2147 | 290 | 1180 |

Jilin | 8980 | 5203 | 100 | 4869 | 1523 | 189 | 1234 |

Liaoning | 10,351 | 8577 | 180 | 3858 | 2876 | 306 | 728 |

From the data of Heilongjiang, Jilin and Liaoning Provinces, the main strength in the output of papers and patents is scientific research institutions (A), accounting for 41.11%, 40.94% and 38.66% of the total output of papers and patents in each province in 2019. The total amount of knowledge and technology output of interaction and integration between scientific research institutions and the government or industrial enterprises is 5313, 6392 and 6734, respectively, which is much higher than the number of results of intercommunication and collaboration between the government and enterprises (GI). The backbone and promoter of collaborative innovation system development is universities and scientific research institutions (A) and industrial enterprises (I). (A) and (I) achieved remarkable results in the knowledge creation and innovation system, but the collaborative output (AI) of the two parties still has a lot of plastic development space compared with the interactive cooperation (AG) of the government and scientific research institutions. A number of studies have shown that the application of knowledge and technological achievements shared by universities and industrial enterprises has great scalability potential, and is a sharp edge in improving the efficiency of transformation of technological achievements and the development efficiency of regional collaborative innovation ecosystems. In the 2019 regional innovation capability rankings, among the three provinces, Liaoning Province, which has the highest total AI and AGI, was ranked 19th, and Jilin and Heilongjiang Provinces ranked 27th and 28th, respectively. Therefore, for Heilongjiang Province, expanding the path of industry-university-research cooperation can further enhance the competitiveness of regional collaborative innovation and inject new vitality into Longjiang's economic transformation and development.

The information transfer amount

Two-dimensional and three-dimensional T value in the three northeastern provinces

Heilongjiang | 49.82 | 11.73 | 0.25 | −309.21 |

Jilin | 51.24 | 9.27 | 0.55 | −345.13 |

Liaoning | 43.72 | 12.93 | 0.49 | −302.14 |

Based on 20-year time series data indicators, a 5-year time period is used to longitudinally explore the changing trends of the collaborative innovation system in Heilongjiang Province (Table 5). Since 2015, China has comprehensively deepened the reform of innovation and entrepreneurship education. Heilongjiang Province, which has 81 universities including Harbin Institute of Technology, 21 institutes directly under the central government, and 139 provincial scientific research institutes, has actively studied and responded to the call and implemented the national innovation-driven development strategy deployment. Variable indicators of A, AG, AI and GAI have increased significantly in the past 5 years, especially the independent output of universities and other research institutions and the results of interaction and collaboration with the government. Although the R&D and innovation of industrial enterprises only increased from 1 to 308, their joint output with universities and other institutes (AI) increased from 12 to 2904, a growth rate of 87.30% in the past 5 years, reflecting the new economic condition. The technological competition among industrial enterprises in Heilongjiang Province has consciously focused on cooperation and win–win cooperation with research institutions. Considering the high knowledge and technology output capabilities of universities and other scientific research institutions, there is still a lot of room for exploration in the interactive cooperation between research institutions and industrial enterprises and the joint output of research institutions and governments. The ability of industrial enterprises to absorb knowledge spillovers meets the needs of the industry competitive demand and can consolidate and extend its indisputable service regional economic development status.

Number of scientific papers and patents from 2000 to 2019

2000–2004 | 108 | 80 | 2 | 18 | 12 | 63 | 3 |

2005–2009 | 738 | 346 | 18 | 129 | 92 | 329 | 42 |

2010–2014 | 2533 | 1013 | 900 | 716 | 369 | 526 | 375 |

2015–2019 | 16,547 | 6308 | 1417 | 7514 | 2904 | 3690 | 2857 |

From the data in Table 5, we can further visually express the proportions of the four 2D and 3D variable indicators in the total output in each time dimension (Figure 1). Research institution-government cooperation (AG) and research institution-industry-government cooperation (GAI) output results have a significant increase in proportion of the collaborative innovation ecosystem, while the proportion of knowledge and technology achievements of research institutions and enterprise collaboration (AI) has been stable in various periods. The level of joint output and synergy matches with the development of the innovation ecosystem; however, compared with the collaborative development of research institutions and government, the interactive communication between the two is suppressed by barriers of the mechanism and system, and the potential for development capabilities has not been effectively stimulated. The cooperation between government and industrial enterprises (GI) dropped from 2.04% to 0.05%. However, with implementation of the action plans of Heilongjiang Province for cultivation of innovative enterprises and construction of science and technology parks, the results of cooperation between 2015 and 2019 showed a clear upward trend.

Compared with the period of 2000–2004, in the following 15 years, the interaction and collaboration between 2D innovation subjects has declined to a greater extent (Table 6), and the coupling and collaboration between industrial enterprises and research institutions have shown a serious weakening trend. The joint output of the authors increased significantly from the initial 12 to 2904, but the structural stability of the coupled system formed by the two and the efficiency of the knowledge and information flow is relatively low. Between 2000 and 2009, the amount of mutual information

Two-dimensional mutual information transfer volume in 2000–2019

2000–2004 | 48.95 | 64.26 | 100.41 |

2005–2009 | 26.01 | 23.83 | 80.98 |

2010–2014 | 18.06 | 25.42 | 40.52 |

2015–2019 | 9.54 | 37.02 | 32.18 |

As shown in Figure 2, from 2000 to 2014, the negative value of the amount of 3D mutual information transfer in Heilongjiang Province became smaller and smaller, indicating that the structural stability and overall effectiveness of the collaborative innovation system comprising research institutions-industrial enterprises-government has gradually increased and the overall effectiveness of the system has been effectively optimised. However, after 2015, with continuous advancement of the ‘Thirteenth Five-Year Science and Technology Innovation Plan of Heilongjiang Province’, the implementation of various activity plans such as the strategic alliance of industrial technology innovation and the scientific and technological innovation base, although the total output of scientific papers and patents is significant, the synergy of innovation entities represented by the amount of 3D mutual information transfer has not been consolidated and optimised overall, and the structural stability of the innovation system has weakened.

Through a comprehensive empirical analysis of the TH collaborative innovation system in Heilongjiang Province, we found that universities and other research institutions independently produced knowledge and technology achievements in different provinces. In addition, in different periods they are always far ahead, and knowledge and technology high-output institutions have become the promotion grounds of collaborative innovation ecology. The backbone of system development, the collaborative innovation system of coupling and symbiosis, needs to maintain a good hyper-cycle of information among subsystems such as universities, enterprises and governments [15]. The monopoly of research institutions will only increase the overall instability of the system. However, Heilongjiang Province has shown a weak degree of coordination in the interaction and cooperation between scientific research institutions and enterprises or government organisations. There are weak links in the process of knowledge and technology marketisation, especially the weak coupling of mutual information between scientific research institutions and enterprises. This will inevitably restrict the release of regional innovation competitiveness. For companies that can bring about huge social and economic impacts, the awareness and ability of innovation and creativity are still insufficient, and they are easily eliminated in the rapidly changing market economy. To this end, we propose the following suggestions.

Heilongjiang Province has shown a weakening trend in the amount of mutual information transfer that char-acterises the degree of super-circular synergy between the three-helix collaborative innovation subjects, which to a certain extent reflects every innovation. None of the subjects took the initiative to promote the coupling and symbiosis of the system. They were more compatible with some of the unique capabilities of the other two subjects, and the synergy across organisational boundaries was not better utilised [16]. The institutional reform has the characteristics of self-reinforcing, and a weak sense of coordination will solidify the functional positioning of the innovation subject and weaken the synergy of collaboration between innovation subjects.

To cultivate the collaborative cultural ideology of the innovation subject in the TH collaborative innovation ecosystem, the innovation subsystem must be guided by the common goal of ‘using collaborative innovation to guide the rapid development of the regional economy’; this sense of collaboration is based on a sound benefit distribution mechanism. Cross-organisation project cooperation should not only satisfy the academic value pursuit of scientific research institutions, but also meet the pursuit of corporate economic interests and the social interests of the government [17, 18].

Knowledge innovation and technology transformation are important sources of social development in the era of knowledge economy [19]. As the core body of knowledge production and output, universities and other research institutions, on the basis of cognitive ability and intellectual level, are teaching and researching to meet the needs of national and regional economic development. To realise the smooth and orderly interactive sharing of information and resources with the external environment, and to rationally promote transformation of the entrepreneurial model of knowledge and technology capitalisation has become an inevitable choice under the new normal era of the economy. At the level of knowledge creation, to do fine and detailed innovation and entrepreneurship education, we must break down the barriers between departments and disciplines, form an interdisciplinary research team, and fully create an atmosphere for the interactive sharing of resources and information among internal organisations. It is important to deeply establish mutual assistance and cooperation links between research institutions and enterprises and other collaborative innovation subsystems, promote the development of collaborative education and collaborative research, and maximise the output of human resources and technical resource information required by the TH innovation subsystem. At the level of knowledge application, universities and other scientific research organisations must consciously establish an ideological awareness of the dual rationality of economy and culture. On the basis of ensuring the output of high-quality technical results, it is important to pay attention to the commercialisation and capitalisation of knowledge and technology, and change the production of those technical results behind closed doors that result in low social value.

Perkmannm's research on the cooperation between universities and enterprises has shown that the interactive cooperation between industry, university and research would promote the emergence of technological achievements and improve the efficiency of technological achievements transformation in a recursive manner. In China, as the main body of technological innovation, enterprises have not fully realised their functional advantages as ‘transformers’ of technological achievements in the TH collaborative innovation system [20]. In 2018, the basic research funding of enterprises only accounted for 0.20% of the total R&D funding. Enterprises must pay attention to the construction of basic R&D platforms so that they can have a certain absorption capacity to undertake transformation of the overflow of scientific and technological achievements from universities and other research institutions. Regional basic industries should prioritise technological innovation, actively seek synergy and win–win cooperation with other innovation entities, build strategic alliances of industrial technology innovation and implement technical support from research institutions [21]. On one hand, they need to deepen the innovation-oriented transformation of basic industries to ensure that they can maintain their competitive advantage in the market and sustainable technological innovation vitality. On the other hand, they need to seize the new opportunities of technological innovation of prioritised industries to effectively enhance regional innovation competitiveness.

#### Definition and acquisition of data variables of scientific papers

A_{x} |
Number of papers including information on scientific research institutions | Papers with ‘UNIV*’, ‘COLL*’, ‘ACAD*’, ‘NIH*’ in the address field |

I_{x} |
Number of papers including companies information | Papers with ‘GMBH*’, ‘CORP*’, ‘LTD*’, ‘AG*’, ‘INC*’ in the address field |

G_{x} |
Number of papers including government information | Papers with ‘NATL*’, ‘NACL*’, ‘NAZL*’, ‘GOVT*’, ‘MINIST*’, ‘ACAD*’, ‘CNRS*’ in the address field |

AI_{x} |
Number of papers including both scientific research institutions and companies information | The address field contains the number of papers representing both A_{x} and I_{x} contents |

G_{x}A |
Number of papers including information about scientific research institutions in the G_{X} dataset |
The number of papers containing A_{x} in the G_{x} subset |

GI_{x} |
Number of papers including both government and corporate information | The address field contains the number of papers representing G_{x} and I_{x} contents at the same time |

G_{x}AI |
Number of papers including information about companies in the G_{X} A dataset |
The number of papers containing I_{x} in the G_{x}A subset |

#### Summary of scientific papers and patent achievements

Heilongjiang | 8362 | 4494 | 702 | 3166 | 2147 | 290 | 1180 |

Jilin | 8980 | 5203 | 100 | 4869 | 1523 | 189 | 1234 |

Liaoning | 10,351 | 8577 | 180 | 3858 | 2876 | 306 | 728 |

#### Variable definition and calculation formula of collaborative innovation measure

A | The number of papers and patents exported only by scientific research institutions | A = A_{xy}-AI_{xy}-G_{x}A + G_{x}AI |

I | The number of papers and patents output only by the companies | I = I_{xy}-AI_{xy}-GI_{x} + G_{x}AI |

G | The number of papers and patents output only by government | G = G_{xy}-G_{xy}A-GI_{x} + G_{xy}AI |

AI | The number of papers and patents jointly published or applied only by scientific research institutions and enterprises | AI = AI_{xy}-G_{x}AI |

AG | The number of papers and patents jointly published or applied only by scientific research institutions and government | AG = G_{x}A-G_{x}AI |

GI | The number of papers and patent jointly published or applied only by government and enterprises | GI = GI_{x}-G_{x}AI |

AGI | The number of papers and patents output by government agencies, scientific research institutions and enterprises | AGI = G_{x}AI |

#### Two-dimensional and three-dimensional T value in the three northeastern provinces

Heilongjiang | 49.82 | 11.73 | 0.25 | −309.21 |

Jilin | 51.24 | 9.27 | 0.55 | −345.13 |

Liaoning | 43.72 | 12.93 | 0.49 | −302.14 |

#### Number of scientific papers and patents from 2000 to 2019

2000–2004 | 108 | 80 | 2 | 18 | 12 | 63 | 3 |

2005–2009 | 738 | 346 | 18 | 129 | 92 | 329 | 42 |

2010–2014 | 2533 | 1013 | 900 | 716 | 369 | 526 | 375 |

2015–2019 | 16,547 | 6308 | 1417 | 7514 | 2904 | 3690 | 2857 |

#### Two-dimensional mutual information transfer volume in 2000–2019

2000–2004 | 48.95 | 64.26 | 100.41 |

2005–2009 | 26.01 | 23.83 | 80.98 |

2010–2014 | 18.06 | 25.42 | 40.52 |

2015–2019 | 9.54 | 37.02 | 32.18 |

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Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Motion about equilibrium points in the Jupiter-Europa system with oblateness Fractional Differential Equations in Electronic Information Models Badminton players’ trajectory under numerical calculation method BIM Engineering Management Oriented to Curve Equation Model Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model