Search

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.

With the in-depth development of data intelligence, the design of public environmental facilities has gone beyond mere aesthetics and practicality, and is moving towards a deeper integration with interaction design. This paper addresses this trend, discusses the strategies and principles of interaction design for public environmental facilities, and proposes an innovative single-facility siting problem model (MP) and multi-facility siting problem model (MWP). The article solves and analyzes the optimal siting problems in these models using the advanced new projection contraction algorithm (PC). To practically test the effectiveness of these designs, two sets of empirical experiments are conducted to explore them in depth. The results show that the optimized interaction design of the public facilities substantially increased the frequency of users, especially in the period from 15:00 to 15:10 on rest days, the number of users was as high as 43, of which the highest number of users was 46, mainly among the middle-aged and elderly people, especially the middle-aged group. In addition, this interaction design is excellent in satisfying people’s necessary, spontaneous, and social activities, with satisfaction levels of 0.78, 0.71, and 0.62, respectively. The interaction design strategy proposed in this paper effectively enhances the efficiency of the use of the public facilities and profoundly satisfies the users’ daily needs.

This paper proposes a new evaluation model for the current situation and challenges of further media communication of enterprise brands through diversified publicity. A comprehensive evaluation model based on AHP-EWM-TOPSIS is constructed by establishing an evaluation index system for the effect of new media operation and publicity, and preprocessing the indexes with the polar deviation method, combining the hierarchical analysis method and entropy value method for weight assignment. Through practical application to the evaluation of M Company’s publicity strategy, it is found that most employees evaluate the current strategy as average or poor, and the investment in new media operation cost is low. In addition, gender has no significant effect on the use of new media platforms, but the user web video usage rate has reached 90%. Therefore, it is recommended that enterprises adopt scientific and practical theoretical models such as the funnel propaganda model proposed in the paper to improve the efficiency of new media operation and brand communication effect, and promote the development of enterprises.

In the context of education informatization, this paper discusses how to deeply integrate advanced educational technology with traditional teaching. By constructing a blended teaching model with the goal of deep learning and using linear regression, decision tree and other algorithms to build a data analysis framework, this paper aims to assess the practical application effect of educational technology in universities. The empirical study explores the development of deep blending between educational technology and teaching by taking the Information Technology Course of University J as an example. The results showed that after the teaching, the posttest mean of profound learning ability of students in the mixed, online, and offline groups were 1.948, 0.182 and 0.065 higher than the pretest mean, respectively. z-values ranked in the top three were the perseverance of students in the mixed group (-12.642) and the ability to think creatively (-11.682) and critically (-9.875), which were higher than those of students in the online group and the offline group, the overall profound learning ability of students in the mixed group was effectively improved, which verified the effectiveness of the blended teaching model proposed in this paper.

This paper discusses the application of concrete in bridge and house reinforcement, especially for detecting tiny defects during construction. Taking the optical principle of shear device and the principle of scattering interferometry as the theoretical basis, the article proposes a nondestructive testing technique applicable to concrete construction in bridge engineering. This technique can effectively detect the tiny defects in the structure by combining the time phase shift interferometry. The research and analysis show that the digital shear scattering interferometric detection system proposed in this paper performs well in defect detection, and its calculated defect values are highly similar to the actual data with an error of less than 6%. The system can also present different responses in time according to the different lengths or depths of the defects. Further applications showed that the vibration resistance of the bridges was significantly improved after the concrete reinforcement construction using the defects detected by the system, and the self-oscillation cycles were reduced by 8.1% and 11.8%, respectively. Overall, the study provides an efficient technical method for detecting and treating defects in concrete reinforcement works.

In recent years, the rapid development of FinTech has attracted widespread attention globally. It not only brings unprecedented challenges to the financial industry, but also inspires significant reforms and innovations in banks’ internal operations. In this paper, based on the support of fintech, the Harris Hawk algorithm is used to optimize the GRU algorithm to construct an efficient digital operation system for banks. This system focuses on improving and enhancing the operation work of different business areas within the bank. After applying this system, the bank has combined fintech with risky operational work, resulting in an average capital adequacy ratio of 12.97, which is strong evidence of the bank’s high affordability in risk management. In addition, the banks’ efficiency of technological advancement grew at an average annual rate of 0.4%, which is the most significant change, showing a trend of growth in tandem with total factor productivity. The scale efficiency has an average annual growth rate of 0.5%, which further demonstrates the system’s significant effectiveness in enhancing banks’ operational efficiency. The system proposed in this paper can effectively promote the digitization process of bank operations and significantly improve banks’ operational efficiency and risk management capability.

The rapid development of cloud computing technology makes the English teaching corpus an excellent choice for innovative English teaching mode. This paper constructs a corpus of English teaching resources and English O2O teaching mode based on MOOC education platform, combines the probabilistic semantic analysis (PLSA) model with the potential semantic indexing to carry out microtext analysis of the English teaching corpus, and solves the PLSA model by using the expectation (EM) algorithm. For the English teaching corpus and English O2O teaching model constructed in this paper, a validation analysis was conducted in three aspects: micro text analysis, text lexical ability and teaching satisfaction. The results show that the PLSA model is able to obtain complete sentence expressions in the microtexture of the corpus when the weight coefficient of the lexical items is set to 0.3. The text vocabulary ability of students in English O2O teaching mode shows a significant difference level at 1% level, and the correlation coefficient of in-class to pre-class reaches 0.889. The English teaching corpus relying on MOOC platform and O2O teaching mode can effectively enhance students’ deep understanding of English sentences, improve students’ satisfaction with English teaching, and enhance students’ interest in learning English.

In the process of digitization in today's society, the organic combination of technological means and traditional arts, such as calligraphy culture, is a topic that China is facing. The topological data analysis method is used in this paper to conduct an in-depth study on the creation and aesthetic characteristics of contemporary calligraphy, taking into account the situation above. In this paper, the topological data analysis method is first utilized to calculate the position of the critical points in the vector field and draw the topological structure of the vector field. The Jacobi matrix is computed, and the numerical solutions of the eigenvalues and eigenvectors in the matrix are used to pinpoint critical points. The TDA algorithm allows for the visualization and modeling of aesthetic features in contemporary calligraphy creation using the data required for the acquired bulk body model. The aesthetic features of calligraphy creation are analyzed through simulation experiments in the end. The results of simulation experiments show that the TDA algorithm completes the convergence before 500 iterations under a 4-fold filter, the nodes are mainly concentrated in the range of [500, 1000], and the convergence speed is the fastest among the five algorithms. Testing the topological data analysis algorithm for the recognition performance of aesthetic features of calligraphy creation, the recognition rate of TDA is as high as 98.30%, which has a good recognition effect.

In this paper, the structural characteristics of the perceptron neural network and the calculation method of the hierarchical relationship of the MLP neural network model are first studied. Then the aspects of two-part settlement, generation-side settlement, and customer-side settlement in the electricity spot settlement mechanism are studied, and the importance of these mechanisms for the operation of the electricity market and risk identification is pointed out. Following that, the effectiveness of the risk identification model is assessed and analyzed. This paper examines market performance indicators, the impact of the dual-track mechanism, and the time characteristics of the price index to characterize risk. The results show that in Guangdong, for example, the price in the day-ahead market is much higher than the supply-demand equilibrium price most of the time, and the maximum difference can be as high as 0.662 yuan/(kW-h). For the entire month, the real-time market’s average price is RMB 0.546/(kW-h) and it is RMB 0.063/(kW-h) higher than the day-ahead market. The importance of this study lies in its role in managing and responding to risks for electricity market operators and participants.

This paper combines the LDA theme mining model with social network algorithms to construct an objective evaluation model for the imagery of cherry blossoms in Japanese literature and culture. To determine the number of topics, one needs to observe the change in perplexity degree for various numbers of topics. The degree of influence of surrounding nodes on this node is measured using in-degree and out-degree, and the degree of closeness between users in social networks is measured using the clustering coefficient. Based on the network data, we analyzed Japanese literary works related to cherry blossoms and readers’ comments on related literary review websites, followed by analyzing the rate of microblog retweets when a hot literary work was published to determine the theme density. In the beginning, Topic 1, which represents positivity, has the highest theme intensity of 0.2581, indicating that the imagery of cherry blossoms is skewed toward the positive in the minds of readers and netizens. Following the emergence of hot literature, the spread of Topic2, which is associated with negativity, reached its peak, with a density that reached as high as 2235721 times. At this time, the highest high-frequency words are death 5827 times, and poignant 5748 times, all of which are negative meanings, and the theme intensity of Topic 2 is 0.2992. The impression of people can be negatively impacted by cherry blossoms. By constructing a model for literary analysis of imagery, this paper serves as a reference and presents a new direction for textual research.