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Research on the Integration and Sustainable Utilization of Digital Humanities Resources of Local Cultural Heritage in Southern China

,  und   
17. März 2025

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COVER HERUNTERLADEN

Introduction

Cultural heritage is the crystallization of the development and evolution of human society, and it is the human wealth with local characteristics formed in different countries due to the differences in their geographic location, resource endowment, social composition and so on, and then in the ideological concepts, customs, beliefs, arts, historical buildings and so on [1-4]. Ethnic areas in Southern China refer to the administrative areas at the prefecture, county and township level where ethnic minorities make up more than 50% of the household population, south of the Huaihe River and Qinling Mountains, not counting Tibet and Qinghai [5-6]. The local cultural heritage of southern China is the masterpiece of material and spiritual civilization formed by the Chinese nation nation over a long period of time, which carries the code of regional and national cultural life, and is a non-renewable valuable resource [7-9]. With the increasing trend of international globalization and domestic modernization, the rapid economic and social changes in the southern region, and because the protection and development of cultural heritage in ethnic areas is a complex and difficult systematic project, the integration of digital humanities resources of local cultural heritage has received more and more attention [10-13].

Integration of cultural heritage digital humanities resources is a new type of integration method emerging in the digital era, referring to the construction of digital means as a tool, and through the network sharing method of cultural resources inheritance and utilization of a class of repository, with openness, sharing and interactivity and other characteristics [14-17]. The integration and utilization of cultural heritage digital humanities resources is not only an important part of cultural construction in the digital era, but also an important support for scientific research and personnel training in the humanities, which is of great significance to the inheritance and development of local cultural heritage [18-21].

This paper constructs an integration platform focusing on local cultural heritage in southern China based on the framework of integrating digital humanities resources of cultural heritage. The platform utilizes digital humanities technology to digitally collect, restore and disseminate cultural heritage. Through the visualization of cultural digital information, the origin and dissemination history of cultural heritage in southern China is truly restored. The integration effect of the platform’s digital humanities resources and the analysis of sustainable utilization are evaluated by a fuzzy comprehensive judgment model.

Digital humanities display technologies for local cultural heritage

Digital display of cultural heritage is based on the theory of knowledge visualization, processing complex information into easy-to-understand pictures and visual forms, and then transforming them into dynamics and interactions, and effectively conveying them in the simplest way. The cultural heritage of different regions has different craft characteristics and cultural connotations, so for the digital display of cultural heritage, it is necessary to carry out reasonable information summarization and storage, and adopt appropriate and scientific digital technology to maximize the effect of cultural heritage display, such as traditional performances, which are mainly designed around the audio-visual, and traditional handicrafts, which can be used in the way of virtual vision, interactive experience, and so on. Figure 1 shows the process of digital display of cultural heritage.

Figure 1.

Digital display flowchart

Digital Acquisition
Application of high-precision digital camera technology

High-precision digital camera for cultural heritage is a commonly used means of collection and recording at present, which plays a vital role in the protection of cultural heritage. The first step of digital camera needs to determine the target cultural heritage, then obtain the optical image of the target cultural heritage, and then transform the optical signal into digital signal through photoelectric sensor, and finally form the digital image.

Application of three-dimensional scanning technology

A scanner is a device that converts information such as photographs, text pages, drawings, samples, etc. into digital signals by scanning them using optoelectronic technology and digital processing. Three-dimensional is a combination of a one-dimensional and a two-dimensional, compared to two-dimensional has a three-dimensional sense. Three-dimensional scanner combines a variety of high-tech, including optical technology, electrical technology and computer technology, can be a short period of time to quickly obtain the target object of the three-dimensional shape, pattern color, surface albedo and other information, and then use the computer system to carry out three-dimensional reconstruction calculations, so as to create a three-dimensional digital three-dimensional model of the same as the target object.

Database applications

Database is to organize, store and manage data in the form of data structure, and its basic structure contains three layers: physical data layer, conceptual data layer and user data layer. Cultural heritage database construction, first of all, need to digitize the collection of information related to various cultural heritage resources, and then the collected content as raw data for processing and classification storage, and then on the pre-collection of digital information to build the relevant bit strings, characters and words and in the database to form an effective link, so that people can enjoy digital searching, browsing, downloading, sharing and other services in the user data layer in the computer software system or the front-end display platform of the database. So that people can enjoy digital search, browsing, downloading, sharing and other services.

Digital restoration and reproduction
3D printing technology

The material used in 3D printer is adhesive material which is a real raw material, and the printed works are three-dimensional.3D printing technology has been applied more and more in cultural heritage, for those cultural heritage which has no integrity or has disappeared, it can be repaired and restored by 3D printing technology.

Application of virtual reality and augmented reality technology

Virtual reality technology [22-23] (VR), is a computer-generated interactive and dynamic three-dimensional effect of the complete virtual world, the participants only need to wear a virtual reality helmet display can be obtained “immersive” experience, at the same time, the participants can be able to get the sight, sound, smell and other sensory sensations, such as being in the presence of the real world.

Augmented reality technology (AR), is a human-computer interaction technology, it will be generated by computer technology, the real world does not exist in the virtual information through the corresponding auxiliary equipment superimposed on the same real environment, the real scene of the same picture or space, to realize the three-dimensional space to join the positioning of the virtual object, to achieve the effect of augmented reality, so that the user has a kind of hyper-realistic experience, and more embodies the concept of human-centeredness.

Digital presentation and dissemination

Heirloom preservation, as the oldest medium of cultural heritage communication, has an impact that is unrivaled by any other means.

Application of museum digitization

Museum digitization, on the one hand, to make up for the traditional museum exhibits can not be fully displayed or even if the display of visitors can only see part of the shortcomings of the museum into the digital technology can be a good solution to the problems that exist in the display. On the other hand, the traditional museums lack of interest, monotonous and dull atmosphere is difficult to please the tourists, tourists walk around type of visit mode can not make the cultural heritage to get a good dissemination. Digital technology of fun, interactivity and other characteristics are more likely to attract tourists, so that tourists can understand the cultural heritage more deeply.

Application of Artificial Intelligence Artificial Intelligence

As one of the branches of computer science and technology, it is a new technical science that researches and develops theories, methods, technologies and application systems used to simulate, extend and expand human intelligence. Artificial intelligence is the study of how to use computers to complete the work that only humans can implement in the past. As its theory and technology become more and more mature, the field and scope of application are expanding, and it also brings new opportunities to the protection of cultural heritage.

Construction of a framework for the integration of digital human resources for cultural heritage

In order to integrate heterogeneous metadata in the field of local cultural heritage in southern China, and reorganize and integrate the scattered and disordered metadata resources, this paper proposes a set of cultural heritage metadata integration framework. The integration framework of cultural heritage metadata includes as shown in Figure 2.

Figure 2.

Cultural heritage metadata integration framework

Data acquisition

Commonly used methods for accessing metadata include Application Programming Interfaces (APIs) and the Open Archive Metadata Harvesting Protocol (OAI-PHM), etc. An API consists of a set of defined methods that a user can use to communicate with a software system and return a response in a way that a computer can understand. Data users can access relevant data directly through the API without having to understand the details of the internal workings of the database or accessing the source code.OAI-PHM, on the other hand, is a set of six predicates or services used to lower the barrier mechanism for repository interoperability. A data provider exposes a repository of structured metadata through OAI-PMH, and then a data user issues an OAI-PMH service request to obtain that metadata.

Data integration

In the digital environment, traditional cultural heritage data can no longer meet the growing needs of the people, and the development of information technology has given different cultural institutions the freedom to create and preserve structured data in any domain. The integration of cultural heritage metadata includes the processing of metadata specification, completeness and association. The cultural heritage metadata integration framework constructed in this paper deals with the integration of metadata mainly including: the development of a unified metadata model, data mapping, and RDF representation of data. The unified metadata model is formulated by summarizing and analyzing the demand situation of different types of users for cultural heritage and understanding the characteristics of users’ demand for cultural heritage.

Data applications

The ultimate goal of cultural heritage resource integration is to provide users with resource data browsing and retrieval, including SPARQL query, full-text browsing, unified search and personalized services. Multi-source heterogeneous metadata can be integrated and processed through normalization and standardization, which can overall improve the quality of metadata in the cultural heritage domain, reveal the relationship between digital resources at a deeper level, and promote the discovery, management and utilization of resources.

In the context of digitization, there is an increasing demand for “one-stop” access to cultural heritage resources. By effectively integrating the digital resources of libraries, archives, museums and other cultural institutions, constructing a unified metadata model, and adopting effective technologies to organize, process and describe cultural heritage digital resources, we provide users with full-text searches, SPARQL query, classification query, online interaction and other personalized services to meet the demand for digital resources and long-term preservation, management and sharing of cultural heritage resources.

Building a platform for integrating digital humanities resources
Visual representation of cultural digital information

Information visualization is to transform data information and knowledge into a visual form, which is convenient for users to identify, recognize and understand the information. For the communication of cultural heritage digital information, visualization can be used to convey the information to users efficiently with the advantage of intuitive and vivid visual images, and to reshape the history of cultural heritage with the help of digital technology and tools. Based on the aforementioned, this paper collects digital information on cultural heritage resources in southern China according to the classification principle, and then carries out visual expression.

Visualization of 2D images
Picture processing

Collected picture data have different degrees of problems, such as photos broken, books paper yellowing, mold, etc., so the collection is completed, the need for picture processing and repair, will be damaged cultural relics as far as possible to restore, reproduce its original appearance. Using image processing technology to repair the pictures and scanned documents, using the software Adobe PhotoShop2020 to assist, complete the processing of picture data.

Mining Cultural Connotation

After the pictures were processed, this paper provides as much insight as possible into the local cultural heritage stories of the South through field research and talks with cultural heritage experts.

Visualization of 3D digital modeling
360-degree surround shooting

Through the preliminary research visits, this paper selects many cultural heritage museums and old sites in southern China for three-dimensional digital modeling, modeling method using point cloud modeling, and 360-degree surround shooting.

Solid modeling

Point cloud modeling refers to the three-dimensional modeling of pre-processed point cloud data through the modeling software. Import the photographed photos into the software, use the software Metashapepro to align the photos, establish a dense point cloud, obtain the point cloud data, and mesh optimization processing of the data, in the whole process, each step needs to be compared with the data, adjust, and delete redundant point cloud noise.

VR panoramic visualization processing

This paper analyzes the old sites of cultural heritage in many places in the south, most of the old sites are well preserved under the joint protection of the government and local villagers, but some of the old sites are in the residential area, and the production and life of the surrounding residents will inevitably have a certain impact on the old sites. Through VR panorama acquisition, VR panorama stitching, VR panorama processing and VR panorama display, the VR panorama visualization of the old sites of local cultural heritage in the south is presented.

Cultural digital information storage and display

Cultural heritage resources are mainly divided into five parts: non-heritage records, non-heritage old sites, non-heritage artifacts, non-heritage literature, and non-heritage documents, and different categories of cultural relics should be stored and displayed in different ways. Multi-angle, high-precision shooting can be carried out, using three-dimensional digital modeling visualization processing, and through the VR panoramic shooting, so that the static, cold historical relics really come alive, so that users in the interactive experience with the local cultural heritage to understand more clearly this period of history, to promote cultural self-confidence, so that the spirit of red will never die. Literary works, documents, these biased paper-based cultural relics, the display should be from the heritage itself, digging the essence of culture, to maintain the original state of the physical object, reduce the application of digital technology, to avoid the secondary destruction of cultural resources. For damaged cultural relics can be repaired through computer technology and input into the platform for long-term preservation and utilization.

Digital Humanities Resources Integration Platform Construction
Overall platform architecture

Figure 3 shows the information architecture of digital humanities resources integration platform. The information architecture of South China cultural heritage digital platform is mainly established on the basis of the completion of the visual expression and storage of cultural heritage information, and its main role is to meet the user’s information needs for cultural heritage on the one hand, and on the other hand, to achieve the permanent preservation of cultural resources and resource sharing through the digital platform.

Figure 3.

Platform information architecture

Platform interface structure

The interfaces of Southern China Cultural Heritage Digitization Platform are all in the form of frame structure, with the platform navigation on the top and the page contents on the bottom, which are overall unified and appropriately proportioned to facilitate users’ quick reading of information. For example, the home page is an upper-middle-lower frame structure, the upper part is the navigation bar and overall logo of the interface, the middle part is the six systems and wonderful topics, and the lower part is the platform service guide display, so that users can quickly locate the platform according to their personal needs and get the platform’s display information.

Platform visualization process

The visual flow of the interface design of Southern China Cultural Heritage Digital Platform is based on the user’s habit of use as the design guideline, using icons, colors, text and other elements to guide the user to browse according to the visual flow. The visual flow of the platform mainly utilizes the three types of visual flow: focus visual flow, guided visual flow and linear visual flow.

1) Focus visual flow is mainly used at the upper end of interfaces at all levels, highlighting the theme of the platform by focusing the viewers’ attention.

2) Orientation visual flow refers to giving certain guidance tips to the viewers, so that the users can react according to the tips.

3) Linear visual flow is most frequently used in the page design of the whole platform. Vertical visual flow gives people a clear and definite feeling, horizontal visual flow gives people a sense of stability and tranquility, and the visual flow of the whole platform is clear and easy to read.

Analysis of the cultural dissemination of the integrated platform of digital humanities resources
Assessment of the usability of the platform for integrating digital humanities resources

The usability test of the digital humanities resources integration platform for local cultural heritage in Southern China focuses on the functional part of the platform, which mainly includes five dimensions, namely, cultural communication and education, digital collection and display of cultural heritage, online interactive experience, personalized information recommendation, and virtual scenario construction, each of which is equipped with five statements describing the functionality of the platform in this paper. Fifty respondents were invited to participate in the platform usability questionnaire survey.

The questionnaire adopts a Likert scale, that is, the respondents are asked to agree or disagree with a series of statements or items set in this paper, usually categorized as “strongly disagree”, “disagree”, “neutral”, “agree”, “strongly agree”, and the average score of each dimension is recorded and counted. “The average score of each dimension is recorded and counted.

Figure 4 shows the results of the platform usability survey under the Likert scale. From the figure, we can conclude that the average recognition ratings of the platform’s cultural communication and education, digital collection and display of cultural heritage, online interactive experience, personalized information recommendation, and virtual scenario construction range from 4.08 to 4.61, all of which have reached the level of “recognition”.Among them, the user’s rating of the virtual scene construction is significantly higher than the other four dimensions, indicating that the platform in this paper is able to provide users with a highly realistic immersive experience, and that users can receive timely feedback from the background, which enhances the smoothness and interactivity of the virtual experience of their digital cultural heritage, and has a practicable effect.

Figure 4.

The Likert scale is the result of the platform usability survey

Effectiveness of Cultural Heritage Communication Based on Ripple Theory

Communication effect refers to the change of audience cognition and behavior caused by the information after it is accepted by the audience through certain communication channels. In this section, communication effects are divided into cognitive, emotional and behavioral effects according to the ripple theory. Accordingly, this study evaluates the communication effect of cultural heritage in southern China from the degree of communication goal realization, and sets evaluation indicators and corresponding questionnaire questions from three levels of cognitive effect, emotional effect and behavioral effect from five cultural heritage expression modes, i.e., digital collection, 3D printing, digital imaging, knowledge mapping, and virtual reality, which are recorded as expression modes 1-5 in order. The questionnaire was scored using a five-level Likert scale.

Figure 5 shows the results of the comparison of the communication goal realization of different means of expression. Comparing the communication goal realization scores of the five types of cultural heritage means of expression, it is found that the average communication goal realization of the five modes ranges from 4.11 to 4.54. The highest score is virtual reality, followed by 3D printing and digital acquisition, and finally knowledge mapping and digital imaging, and the communication goal realization degree of these two means of expression is significantly lower than that of the remaining three.

Figure 5.

Comparison results of the target implementation of different expressions

Fuzzy evaluation of the sustainable use of cultural heritage
Fuzzy Comprehensive Judgment Step

This paper uses fuzzy comprehensive judgment to analyze the integration effect as well as the sustainable use of digital humanities resources of local cultural heritage in southern China. The steps of the judgment [24-25] are as follows:

Determination of factor set

Factor set refers to the collection of factors affecting the value of the evaluation object, and the factor set is denoted by the letter U: U={ u1,u2,,un }

All these factors Ui in the factor set are ambiguous.

Determination of evaluation set

The evaluation set is the set of possible evaluations that the evaluator may make of the subject of the evaluation, and is denoted by the letter Ui: V={ v1,v2,,vm }

m is the number of ratings, generally categorized into 3 to 5 ratings.

The results of the integrated sustainable use evaluation were categorized into four levels with a rubric set V = {Excellent, Good, Moderate, Poor}.

Fuzzy judgment matrix determination

For the ith indicator, the affiliation to each rubric is a fuzzy subset on V, i.e., the set of one-factor evaluations for the ith factor is a fuzzy mapping from U to V: Ri={ r1,r12,,rim }

The evaluation set of n factors constitutes a total evaluation matrix R, i.e., each evaluated object determines a fuzzy relationship R from U to V, and the fuzzy comprehensive judgment matrix is: R=(rij)n×m=[ r11r12r1mr21r22r2mrn1rn2rnm ]

Where: rij denotes the degree of affiliation at which factor ui can be rated vj, i.e., the frequency distribution of the ith factor on the jth rubric, satisfying rij=1 .

Establishment of the set of judgment factor weights

Each factor ui has a different degree of influence on the evaluation object, and each factor should be given a corresponding weight, and the set of weights is called the set of factor weights, which is denoted by the letter A: A={ a1,a2,,an }

First-level fuzzy synthesis judgment

ai is the weight of the ith factor, since the weights of the factors are not equal, a fuzzy matrix operation is needed to uniquely determine a fuzzy transformation B from U to V, and B is the conclusion vector of the first level of the judging criterion: B=AR=(b1,b2,,bm)

bj reflects the affiliation of the jth judgment with the fuzzy set B.

Multi-level fuzzy comprehensive evaluation

The comprehensive sustainable utilization evaluation index system is a multi-level structure, which also requires multi-level fuzzy evaluation. The second-level comprehensive evaluation is to take the matrix composed of the conclusion vector of the first-level comprehensive evaluation as the single-factor evaluation matrix of the second-level comprehensive evaluation, and the single-factor evaluation matrix of the second-level comprehensive evaluation is shown in the following formula: RLevel2=[ BLevel11BLevel21BLeveln1 ]=[ A1RLevel11A2RLevel21AnRLeveln1 ]

Then the second level fuzzy comprehensive evaluation result is: BLevel2=ALevel2RLevel2=(bLevel12,bLevel22,,bLevelm2)

Evaluation result judgment

B is the condition description of the comprehensive condition of the evaluated object in grades, which cannot be directly used for the sorting evaluation or the evaluation of excellence among the evaluated objects, and usually adopts the principle of maximum affiliation to select the largest max(b1,b2,⋯,bm) in the final evaluation result B, and the corresponding grade is the final result of the fuzzy judgment.

Application of the hierarchical parameter evaluation methodology
Principle of Rank Parameter Judgment Method

In the practical application, it is found that according to the principle of maximum affiliation, only the largest in B is utilized, and all the information brought by the evaluation results is not fully utilized, and in the practical application, it is possible to stipulate the corresponding parameters for each grade as the rating standard. The fuzzy total evaluation result is B = A·R = (b1,b2,⋯,bm), and the parameter column vector of each grade is C = (c1,c2,⋯,cm)T, then the grade parameter judgment result is: Y=BC=(b1,b2,,bm)[ c1c2cm ]=j=1mbjcj=P(PR)

Comprehensive sustainable utilization evaluation level parameters

Based on previous experience and people’s habit of judging “excellent, good, medium and poor”, the rating interval of each level of comprehensive sustainable utilization evaluation is determined, and the rating interval is shown in Table 1, and the median of each rating interval is selected as the parameter of each level, and the level parameter is C = (95,85,70,30)T.

Scoring interval

Grade Excellence Good Medium Worse
Scoring interval [90,100] [80,90) [60,80) [0,60)
Analysis of integration effects and sustainable utilization based on fuzzy judgments
Analysis of the effect of integration of cultural heritage resources

This paper constructs an index system for assessing the effect of humanities resources integration based on local cultural heritage in southern China, including the coverage rate of digital humanities resources, the depth of cultural inheritance, the degree of participation, and the degree of satisfaction, which are noted as indicators 1-4 in turn.

The effectiveness of the integration of the traditional model and the platform based on this paper was carried out through a questionnaire survey, and throughout the activity, 100 questionnaires were distributed and 100 were recovered, with a recovery rate of 100%. The results of the survey showed that the investigators indicated that they were satisfied or very satisfied with the content of the activity, and the results of the survey were assigned and analyzed through the fuzzy judgment algorithm. Figure 6 demonstrates the results of the fuzzy judgment distribution of the resource integration effect.

Figure 6.

The resource integration effect is fuzzy evaluation distribution result

The data in the figure show that the integration effect under this paper’s platform is greatly improved compared with the traditional mode, with the coverage of digital humanities resources, the depth of cultural heritage, the degree of participation, and the degree of satisfaction increased by 12.75%, 12.48%, 23.10%, and 8.31%, respectively. It can be seen that this paper’s platform provides the greatest increase in participation for the investigators, indicating that the digital humanities technology makes the investigators’ interaction with cultural heritage increase, and improves the investigators’ experience feeling and interactivity.

Sustainable use of digital humanities resources

In order to verify whether the digital human resources integration platform for local cultural heritage in Southern China developed in this paper has sustainable utilization value, this section selects “cultural heritage integration plan”, “digital protection of cultural heritage”, “digital transmission of cultural heritage”, “public awareness and experience” and “feedback mechanism of the platform” as the sustainable utilization value. This section selects “cultural heritage integration program”, “cultural heritage digital preservation”, “cultural heritage digital inheritance”, “cultural heritage resilience assessment”, “public awareness and experience”, and “platform feedback mechanism” as the indicators for assessing the value of sustainable utilization. Each indicator includes five items. Twenty experts in related fields are invited to evaluate the items set in this paper, and then the fuzzy comprehensive judgment algorithm is used to classify the evaluation indicators, so as to study the sustainable utilization of this platform in the field of cultural heritage.

Figure 7 shows the results of the fuzzy composite scores of the six indicators. As can be seen from the figure, the fuzzy algorithm is calculated to get the score of each item between 86 and 96 points by the expert evaluation results. Specifically, “Cultural Heritage Integration Program”, “Cultural Heritage Digital Protection”, “Cultural Heritage Digital Inheritance”, “Cultural Heritage Resilience Assessment”, ‘Public Awareness and Experience’, and ‘Platform Feedback Mechanism’ have average scores of 91.01, 92.81, 91.86, 91.88, 93.64, 92.06, with a range of [90] to [90]. All scores are in the range of [90,100], and according to the evaluation parameter ranking table above, they are in the grade of “excellent”. Among them, “public awareness and experience” has the highest expert evaluation, which may be due to the fact that the public, as the main body of this platform, can contribute to the sustainable use of digital humanities resources through the understanding of the local culture of the South, interactive participation and other behaviors.

Figure 7.

The fuzzy comprehensive score of the six indexes

Conclusion

This study builds a framework for integrating digital humanities resources for cultural heritage, and on this basis, adopts a variety of digital humanities technologies, such as 3D scanning, virtual reality, etc., to develop a digital humanities resources integration platform applicable to local cultural heritage in southern China. The usability of this paper’s platform is evaluated through recognition research, and a number of indicators are established to assess the integration effect and sustainable utilization of the platform using fuzzy comprehensive judgment.

1) The average rating of this paper’s platform for cultural communication and education, digital collection and display of cultural heritage, online interactive experience, personalized information recommendation, and virtual scene construction is 4.322.

2) Digital collection, 3D printing, digital imaging, knowledge mapping, and virtual reality, the average communication goal fulfillment of the five methods is between 4.11 and 4.54.

3) The platform in this paper shows better integration effect of digital humanities resources than traditional methods.

4) The scores of “Cultural Heritage Integration Program”, “Digital Protection of Cultural Heritage”, “Digital Heritage Inheritance”, “Cultural Heritage Resilience Assessment”, “Public Awareness and Experience”, and “Platform Feedback Mechanism” are all between [90,100] and “Excellent”. The scores of “Cultural Heritage Integration Program”, “Cultural Heritage Digital Preservation”, “Cultural Heritage Digital Inheritance”, “Cultural Heritage Resilience Assessment”, “Public Awareness and Experience”, and “Platform Feedback Mechanism” are all in the range of [90,100], and the performance is “excellent”.

Acknowledgements

Major Humanities and Social Sciences Research and Development Program for Universities in Zhejiang Province: Research on the Rescue and Digital Protection of Endangered Local Knowledge of Jiangnan Tribute under the Background of Smart Prosperity (2023 QN136).

Sprache:
Englisch
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Fachgebiete der Zeitschrift:
Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere