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In this paper, we firstly explore the existence of solutions to the following linear Schrödinger Kirchhoff Poisson equation with critical exponential growth on the full space □3 by using the discontinuous finite element (DG) as well as the principle of centralized compactness: {−(a+b∫□3|∇u|2)Δu+V(x)u+φu-12uΔ(u2)=K(x)up−2u,x∈□3−Δφ=u2,x∈□3\left\{ {\matrix{{ - \left( {a + b\int_{{\square^3}} {{{\left| {\nabla u} \right|}^2}} } \right)\Delta u + V\left( x \right)u + \phi u - {1 \over 2}u\Delta \left( {{u^2}} \right) = K\left( x \right){u^{p - 2}}u,} & {x \in {\square^3}} \cr { - \Delta \phi = {u^2},} & {x \in {\square^3}} \cr } } \right., x ∈. Secondly, we make reasonable assumptions on the V, K , f functions of the equation, and use the principle of variational division to firstly obtain the corresponding energy generalization of this equation, and then we prove the corresponding generalizations of the equation satisfy the (C)c conditions. Finally, the existence of the solution of the equation is obtained by numerical simulation and then by using the Yamaji Lemma. The results show that the error of the finite element solution of the linear Schrödinger Kirchhoff Poisson equation in the spatial direction P1 reaches the optimal estimation under the L2 -parameter in an intermittent finite element numerical simulation environment, i.e., it is proved that there exist at least 1 and 3 positive solutions to the problem. The paper achieves rich research results which are informative for the solution of this class of linear differential equations.

As the living standard of the people in China has changed drastically, the aesthetic quality of daily life has been increasing day by day, and people’s desire for a better life is also increasing. This paper proposes a color harmony model based on hue statistical features, using maximum likelihood estimation to extract the main hue region and extract related features from the corresponding region. Based on the inconsistencies in feature dimensions, a model is created to evaluate color harmony using Gaussian mixture training and is employed for image aesthetics evaluation. Finally, regression is employed to analyze the factors that influence life aesthetics evaluation, and the model is tested and analyzed using linear diagnosis and residual analysis. The results show that the influence index affecting the evaluation of daily life aesthetics is judgment beauty, and its influence coefficient is 4.4323. The product of image entropy and image gradient is used as the connotation of judging the aesthetics of daily human life, which is consistent with the evaluation of human aesthetic judgment. The theoretical connotations of life aesthetics are clarified and enhanced in this paper, and it develops its thinking to construct the reality of the good life.

This paper explores new approaches to the application and creation of digital media in the context of the rapid development of artificial intelligence technology, with a particular focus on virtual reality interaction. The study utilizes the spatial distance of the enclosing spheres in the hybrid hierarchical enclosing box and the characteristic of non-intersection between the enclosing boxes for collision detection, and the collision information returned by the rays is analyzed in depth. Meanwhile, the intersection test method is used to improve the efficiency of collision detection. And a subjective evaluation of 10 users’ experience in virtual reality art interaction was conducted. The results showed that the system was highly rated in accuracy (average score of 8.39), but rated lower in simplicity (average score of 4.28). There was a positive relationship between the user’s eye gaze duration and the number of interruptions and misoperations in art interactions. At an eye gaze duration of 0.2 seconds, half of the users did not experience interaction interruptions; when the gaze duration increased to 1.2 seconds, all users had no interruptions. This paper provides a practical reference case for using AI technology in digital media applications and creation, especially in enhancing the accuracy and efficiency of virtual reality interactions.

The teaching of vocal singing in colleges and universities needs to create a teaching environment that is both interesting and knowledgeable for students, and continuously improve their aesthetic ability and comprehensive quality. Based on the ARCS model, this paper designs the structure of the SPOC teaching platform and establishes the teaching mode of vocal singing flipped classroom based on the original folk songs in the cultural tourism industry as the main source of teaching resources. A multiple linear regression model is chosen to analyze the influencing factors of the teaching quality of vocal singing flipped classrooms, and the least squares estimation of the regression model is used to decompose the singular value. For the vocal singing flipped classroom teaching model established in this paper, a multiple linear regression model was established by choosing teaching content, teaching environment, and teaching method as explanatory variables, and the validity was verified in terms of benchmark regression and teaching practice. The results show that teaching content, teaching environment, and teaching method are all significant at a 1% level on the teaching quality of vocal singing flipped classroom, and the fitting value of the three is 0.7856, and the singing emotion expression scores of the students in the group with serious singing problems before and after the teaching experiment have been improved by 6.11 points as a whole. Enhancing students’ aesthetic abilities and emotional expression can be achieved through teaching vocal singing based on aesthetic elements.

In this paper, the cited papers and cited patents of world-class agriculture-related universities are taken as the research objects, and the preprocessing process of the research hotspot text of agriculture-related universities is accomplished by combining the participle processing method and the TF-IDF method. To make up for the shortcomings of the semantic level of the LDA model, BERTopic is utilized to obtain the document-topic distribution probability and the topic-topic word distribution probability, and the topic hotness of different topics is calculated. Then the Glove method is used to extract the word vector features of the topic words, normalize them, calculate the word vectors by taking the distribution probability values as the weighted weights, solve the topic vectors, and then calculate the similarity of the hot topics in different time windows by the cosine similarity to explore the hot topics and the evolution of the world’s first-class agriculture-related colleges and universities research.

By combining mining algorithms, this paper provides a new method for quantifying the characteristics of literary language, thereby reducing the subjectivity of the value and language discussion of ancient literature in Chinese. Firstly, the TF-IDF algorithm is improved, the methods of inter-class dispersion and intra-class dispersion are adopted, and the optimal number of topics K of the LDA topic model is determined by using the confusion degree, and the quantitative model of the value and language characteristics of ancient literary texts is constructed. Furthermore, the concept of maximum word-to-frequency ratio is introduced. It is integrated into the traditional information gain method, and an old academic text recognition algorithm based on XGBoost model is constructed. The model’s results were applied to the network corpus mining and analysis, and the results showed that the word “cherishing spring” ranked first with a frequency of 7085 occurrences, followed by “hurt autumn” with 4598 occurrences. Among the eight themes, “natural imagery” (Topic 3) accounted for the highest proportion, reaching 23.68%, followed by “landscape and pastoral” (Topic 7) and “euphemistic words” (Topic2), accounting for 16.29% and 14.54%, respectively. The method of this paper not only provides a new perspective and tool for the quantitative analysis of the linguistic characteristics of literary works, but also points out a new research direction for the in-depth discussion of textual value and linguistic characteristics in the future.

In recent years, higher education management has been improving, but the coordinated development of the overall educational management and student management system of colleges and universities still needs to be further improved and enhanced. This paper uses data envelopment analysis and data fusion technology to establish DEA fusion algorithm and DEA-Malmquist index method to evaluate and analyze students’ learning efficiency in colleges and universities. The results indicated that the average degree of perfection of online teaching management in higher education is low, 86.2%. Students’ overall satisfaction with this is also expected at 56.2%. There is a need to strengthen management and improve classroom interactivity and innovation, to enhance the quality and attractiveness of courses, and to avoid excessive fragmentation. In addition to the existing problems, the results achieved include more accessible access to learning resources, with a percentage of 88.6%. The algorithm of this paper is used to study the efficiency of higher education and student learning, and to provide a more comprehensive and objective approach to the development of the quality of higher education and student management for the later development of higher education.

With the development of the times, the cultivation of literary appreciation ability in the education system of colleges and universities has been gradually emphasized. This paper constructs a multimodal semantic analysis model based on text feature extraction, image feature extraction and audio feature extraction, and after fusing multiple modalities, combines them with sentiment semantic Analysis, optimizes them through the self-attention mechanism module, and finally constructs a sentiment semantic analysis model based on multimodal feature fusion. Through the performance analysis of the multimodal feature emotion semantic model, the algorithm model accuracy of this paper is as high as 89%, and the recognition accuracy of emotion is stable at about 80~85%. The multimodal sentiment semantic model proposed in this paper has an accuracy rate higher than 80% on literature appreciation related datasets. In the empirical evidence of literature appreciation, the average recognition accuracy rate of emotions expressed in literature is 62.80%. The study provides an achievable path for the multimodal semantic Analysis of contemporary literature appreciation integrated into college teaching, which is of practical significance for developing literature appreciation teaching in colleges and universities.

In the current aviation industry’s demand for excellent service personnel surge, this paper emphasizes the importance of physical training for college aviation service personnel to improve the image of individuals and companies. To this end, this study is oriented to the employment needs of aviation enterprises, creates the “9C cooperation” physical training and nurturing model, and establishes a detailed set of physical training quality evaluation index system. Taking University S as a case study, the data were collected through questionnaires, and factor analysis was applied to comprehensively assess the quality of training and nurturing of aviation service talents. Combined with the IPA analysis model, this paper further explores the correlation between corporate satisfaction and importance and the physical training system. The study results showed that the total variance contribution of the four main factors to the quality of physical training and nurturing was as high as 91.33%, while the overall score of the quality of training and nurturing was 3.153. The importance and satisfaction of enterprises to the quality of form training are distributed in a high range, showing that the training system needs to be further improved. Therefore, colleges and universities need to refine the teaching objectives and contents to ensure that the quality of physical training for aviation service talents can meet the actual needs of aviation enterprises and promote the industry’s overall development.

With the development of the information age, international teaching cooperation and exchanges have become increasingly frequent, and educational sovereignty and cultural security in higher education international exchanges have gradually become the focus of attention. This paper constructs a multiple regression model of educational sovereignty related to international exchanges, and designs a cultural security risk assessment model in international exchanges by combining fault tree and Bayesian network to prevent cultural invasion. Empirical Analysis is carried out on this basis to explore the factors and preventive measures affecting educational sovereignty and cultural security in higher education international exchanges. In the regression results, the standard regression coefficient of national comprehensive strength is the highest at 0.272, in which the significance of intellectual property rights, educational legislation, educational administration, state authority and national total strength are all less than 0.001. The accuracy rate is more than 90% for identifying cultural security risks. In the research of this paper, the cultural security risk problems can be effectively identified, and the cultural security problems in the international exchange of university education can be improved with practical guarantee.