Search

We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma's martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann's continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups. [ABSTRACT FROM AUTHOR]

Examining Li traditional sports culture’s inheritance and innovation status from the non-heritage perspective can guide its further inheritance and development. This paper measures the level of inheritance and innovation of traditional sports in the Li ethnic group using a multi-dimensional analysis perspective. A consumption-based inheritance mechanism is proposed to assess the impact of traditional culture inheritance from the consumption perspective. The measurement indexes are standardized, and weights are assigned objectively to them to obtain the development index of the sports and culture industry of the Li ethnic group through the use of the entropy weight method. Synthesizing the characteristics of the sports and culture industries, a quantitative assessment model of the consumptive inheritance effect is constructed, and the DEA benefit index of the Li sports industry is measured simultaneously. Based on the three dimensions of emotional value, innovative development of the cultural sector, and cultural protection and inheritance effect, a quantitative assessment of Li sports culture’s inheritance and innovation effect is conducted. Through the model, the development value of Li sports resources was calculated to be 75.51 points, which has achieved good results while preserving cultural heritage. In the comprehensive effect of Li traditional sports culture protection, the scores of cultural and social benefits are 8.89 and 8.48, respectively, at a reasonable level. Still, the economic benefit is only 4.28, the lowest among the three dimensions. The study acknowledges the problems that persist in the inheritance of Li sports culture and recommends an efficient path for development.

In the context of the rapid development of modernization and urbanization, the inheritance and research of music and musical instruments by ethnic minorities are facing great challenges. It is, therefore, of enormous significance to uncover the performance characteristics of ethnic minority musical instruments. This paper focuses on four categories of Yao musical instruments, namely reed instruments, air-pipe instruments, wind instruments, and percussion instruments. We mine the performance features of Yao musical instruments using MFCC feature extraction, perceptual linear prediction parameter extraction, and other methods. The performance of this paper’s algorithm is explored by comparing the detection and recognition accuracy of its algorithm with SVM on four types of musical instruments. The performance characteristics of Yao musical instruments are explored by analyzing the timbre characteristics, auditory characteristics, and beat statistics of the four instruments. This paper’s algorithm significantly outperforms the SVM algorithm in the recognition correct rate of four different types of musical instruments, with differences of 2.1905%, 7.1574%, 5.3758%, and 3.6962%, respectively. The extracted performance features of Yao music instruments reveal that reed instruments and air-pipe instruments have a superior timbral effect than wind instruments and percussion instruments. The sound of pneumatic instruments and wind instruments is the best when it comes to audibility, and the beats of reed instruments and wind instruments are the best among the four instruments.

The problem of population aging is intensifying worldwide. The proportion of the elderly population is gradually increasing, and the wisdom of elderly care will become a social development trend. This paper explores the status quo and problems of community home care services in the Internet+ era through a questionnaire survey on the supply of intelligent community care services. Based on this basis, a smart community home care system is developed based on Internet of Things (IoT) technology. Embedded control modules such as sensors and buzzer alarms are used to collect information about the posture and vital signs of older adults and to issue an alarm when they fall. Zigbee technology is used to design the communication module of the system so that communication messages can be sent in case of emergency help to older adults. The Mahony fusion-based fall detection algorithm is utilized to determine the falls of older adults and combined with a beeping alarm to ensure real-time monitoring of the personal safety of older people. An empirical study was designed to analyze the satisfaction and perceived importance of the home care system for elderly users, and the results show that the average value of the satisfaction and perceived importance scores of the elderly users participating in the study is above 3.9, and the standard deviation is small. This paper’s smart community home care information system’s feasibility and effectiveness have been fully proven by the result.

This paper proposes a method for data acquisition of yoga movements and analyzes it using the Fourier transform. It aims to help residents choose a more scientific and effective exercise method to relieve physical fatigue, reduce body stiffness, and improve body flexibility. Initially, we transform the yoga movements into RGB and optical flow, feeding them into the STF-ResNet network to extract the temporal and spatial features of the movement data. Next, we combine the spatial and temporal flow features with residuals to compensate for the loss of high-level feature information. Finally, we add the convolutional block attention module to further filter the yoga movement features from both channel and spatial dimensions. Next, we introduce the Fourier transform to parse the gathered yoga movement features. We conducted experiments both with and without yoga movements interfering with body soft rhythms to investigate their effects. The experimental group improved the test scores of the forward and backward splitting test and the backward bending body bridge building test, with the mean value of standing forward bending being 5.11 higher after the experiment than before. It shows that yoga intervenes in the flexibility of the human body through auxiliary training, and yoga postures can have a significant beneficial effect on body flexibility.

In this paper, we use VR equipment to collect relevant facial expression images and normalize the angle, scale, and gray scale of the collected images. The direction quantization of image features is realized by 3D gradient computation, and then the histogram of the direction gradient of each video sub-block is cascaded into the final HOG3D descriptor so as to complete the extraction of dynamic expression features. In view of the multi-dimensional problem of the features, it is proposed to use a principal component analysis algorithm to reduce their dimensionality and use a multi-layer perceptron and deep confidence network to jointly construct the facial expression tracking recognition model. The datasets are used to analyze real-time facial expression tracking in virtual reality. The results present that the verification correctness of both datasets A and B reaches the maximum at the 120th iteration. In contrast, the loss value reaches the equilibrium state quickly at the 40th iteration. The dynamic occlusion expression recognition rate of the deep confidence network on dataset A (66.52%) is higher than that of the CNN (62.74%), which fully demonstrates that the method of this paper is able to effectively improve the performance of real-time facial expression tracking performance in virtual reality. This study can help computers further understand human emotions through facial expressions, which is of great significance to the development of the human-computer interaction field.

The study of the overburden rock transportation law of different mining thicknesses can provide a theoretical basis for the actual site of the mine and ensure the safety of coal mining. On the basis of analyzing the deformation characteristics of the overburden rock, the article studies the relevant factors affecting the mobile deformation of the overburden rock and gives the nonlinear mechanical, mathematical model of the overburden rock movement in the quarry, i.e., the yield failure criterion, the GHB flow law, and plasticity increment theory. Based on the nonlinear mechanics theory, the generalized Kelvin model was established, and its constitutive equations were transformed by the Laplace transformation method, and the viscoelastic finite element numerical simulation model was constructed by combining with MIDAS GTS NX software. When the mining depth is 150 meters, and the thickness of the mining is 9 meters, the maximum tensile stress of the quarry overburden is 274.28MPa, which will damage the movement and deformation of the overburden. When the mining thickness increases from 3 meters to 9 meters, the maximum value of settlement and horizontal displacement of the overburden is 0.038 meters. There is a significant positive correlation between the mining thickness and the movement and deformation of the overburden, i.e., the greater the mining thickness, the more serious the movement and deformation of the overburden. In order to ensure the safety of mining work, it is essential to establish a reasonable mining thickness in the actual operation.

The rapid development of urbanization brings a lot of problems, and the protection of the heritage of historical and cultural districts needs to formulate the protection strategy according to the local environmental adaptation and continuously improve and amend it. In this paper, a model is developed for the environmental adaptation mechanism of the heritage of historical and cultural districts, and the spatial structure of the heritage of historical and cultural districts is calculated using spatial statistical methods. Subsequently, an environmental calculation simulation model is proposed based on ENVI-met software, which combines the spatial structure to simulate and analyze the environment of the Shengjin Tower Historical and Cultural District Heritage in Nanchang City, and analyze its environmental adaptability. The test results show that the environmental simulation model proposed in this paper can accurately simulate the environmental change values of the heritage of the historical and cultural district according to the values of external environmental factors. The results of the analysis of the Shengjin Tower Historical and Cultural District Heritage show that the plots in the districts have an average thermal environment adaptation degree of 1.02, and the average air environment adaptation degree is 1.08. Meanwhile, West Street shows higher performance in air environment adaptation degree, with an average of 1.10. The adaptive degree of the plots in the downwind direction is poor, and they are easily affected by the external environment. This paper lays the foundation for other studies on the environmental adaptation of heritage in historical and cultural districts, and the conservation strategies proposed in terms of symbiosis, wholeness, and dynamic sustainability provide references for the conservation and inheritance of heritage in historical and cultural districts.

Photocatalytic technology is known as a green technology in solving energy problems and pollution problems, which can generate clean energy and degrade pollutants. In order to study the degradation performance of carbon nitride and its composites on air pollutants and water pollutants, this paper constructs TiO2/g-C3N4 composite photocatalysts by compositing graphite-like phase carbon nitride (g-C3N4) with titanium dioxide (TiO2) using titanium tetrachloride and melamine as raw materials in a water bath method. The physicochemical properties of the prepared complexes were analytically characterized by X-ray diffraction, UV-Vis diffuse reflectance, and X-ray photoelectron spectroscopy, and their degradation activities were examined and compared. The results of all the tests showed that the prepared 5 wt% TiO2/g-C3N4 nanocomposites performed better compared to other mass percentages of nanomaterials. The degradation of pollutants also resulted in better photocatalytic performance of the 5 wt% nanomaterials, with catalytic efficiencies of 54.2% and 99.5% for NO and methylene blue, respectively, at 30 min, and the good photocatalytic activity remained after five cycles.

Due to the advantages of millimeter-wave radar, such as its relatively simple structure, small size, high sensitivity, etc., it is used to obtain the human pulse signal and blood flow signal. Using the methods of mean cancellation, phase differencing, and smoothing, static clutter removal and heartbeat signal enhancement can be achieved, which can effectively eliminate interference information. Based on the collected information, the three-dimensional Navier-Stokes equations and boundary conditions are determined, and the theoretical knowledge related to fluid mechanics and bioengineering is used to construct the model of the multidimensional blood monitoring system, and the nonlinear signal analysis method is used to analyze the application of the constructed model. Based on the data, there is only a 0.1% difference between the waveform of the blood vessel diameter measured by the multidimensional blood monitoring system and that of the blood vessel diameter tested by commercial ultrasound equipment. The waveform trend is also consistent. In addition, the blood flow velocity at point 5 was much greater than that at point 2, when the vessel stenosis exceeded 50%. This study can accurately and efficiently monitor blood flow velocity for single and multiple individuals, which is critical for the healthcare field's development and innovation.

The role of cultural cognition on English proficiency has received extensive attention in the academic community, and this article analyzes the role of cultural cognitive ability on English proficiency by taking advantage of the advantages of factor analysis in revealing the underlying structure and data interpretation and understanding. The article firstly argues the importance of cultural cognitive ability on English proficiency and then elaborates on the mathematical model of factor analysis from the aspects of raw data and correlation matrix, factor analysis, and factor loading. Factor analysis is used to calculate the correlation matrix and extract four common factors according to the rule of eigenvalue greater than 1. The distribution of factors was adjusted by factor rotation, and the common factors that could explain 71.686% of the test data were named “English Expression Ability”, “English Comprehension Ability”, “Cultural Receptivity Ability,” and “Cultural Communication Ability”, and then classified as “Cultural Cognitive Ability” and “English Ability”. It is found that the loading coefficients of English expression, comprehension, and cultural acceptance and communication ability on English proficiency and cultural cognitive ability are 0.642, 0.591, 0.547, 0.392, 0.438, 0.511, 0.421, and 0.604, respectively, which indicates that cultural cognitive ability has a facilitating effect on the students’ English expression and comprehension, and therefore should be cultivated at the while focusing on the cultivation of cultural cognitive ability.

This paper integrates the historical information related to the four rural study halls at the historical material level to understand and deeply explore their value characteristics. Based on this, we sort out the influencing factors of the conservation effect of the rural study halls, sort out the influencing factors of the conservation effect of the rural study halls through principal component analysis and the CHAID model and explain the various factors affecting the conservation effect and their interrelationships through statistical analysis. According to the empirical results, the revitalization strategy is introduced to provide suggestions for the development of rural bookstores. The historical value of the village academy is the most important value element in the comprehensive value comparison, with a high rating of over 1.2 points, followed by the cultural value. The factors affecting the protection effect are sorted out. The final model reflects the problem in which the survival environment dimension is negatively affected overall (-0.004). The cultural places related to the rural academy should be repaired and built in addition, on the basis of which various activities are guaranteed to be carried out on a regular basis. In terms of government support (0.351) and inheritor protection (0.173), the current initiatives have certain positive effects.

The innovative design of teaching methods of Civics classes in colleges and universities is an effective measure to help the teaching of Civics classes in colleges and universities. In this paper, the significance of innovative Civics teaching methods is addressed, and a novel path for teaching Civics courses in colleges and universities is proposed. Through feature selection, the K-Means clustering algorithm is optimized, and after optimal selection of the initial clustering center, balanced discriminant function, and combing of the optimization process, the model is applied to the actual innovation of Civics and Political Science teaching, quantitatively assessing the behavioral characteristics of the students and constructing the prediction model to achieve dynamic monitoring of students’ performance. The empirical teaching analysis method is aimed at quantitatively assessing the path proposed in this paper. The clustering results show that consistent with the preset, the model divides students’ learning behavioral characteristics into four categories with clear boundaries and good clustering effect, and most of the student’s grades are concentrated around 60-80 points, according to which the teachers can adjust their teaching strategies in time to improve the teaching effect. Through the control experiment, we know that for the students who have gone through the innovative Civics teaching mode, the mean value of Civics achievement is 71.594, which is 19.329 points higher than the students who have studied in traditional Civics teaching, which is confirmed by the P-value in the t-test of independence which is less than 0.05. It indicates that the innovative teaching method for civics has a significant effect on improving students’ civics achievement.

The electricity ticket system is an important basis for staff to carry out maintenance plan designation and execution. With the gradual progress of the work of the grid grassroots staff to reduce the burden, the need to simplify the process of electricity ticket invoicing and improve the efficiency of electricity ticket invoicing is increasing. This study first optimizes the scheduling and data capture problem of electricity based on queuing theory. Then, it constructs a recognition model for electric ticket data based on deep learning and combines the CTPN text detection algorithm with the DesNets text recognition algorithm to establish the CDNets algorithm model for recognition optimization. An automated generation model of the blackout ticket was created using the LSTM network. Taking into account the power company’s needs, combined with Intranet intranet software development concepts and Net software technology development and design of the ticket automation system. The AP of this paper’s blackout ticket recognition model under the mixed date of the ticket has a disadvantage of 0.7% compared with YOLOv4, but the reasoning speed is relatively improved by 2 times, and the overall algorithm is more cost-effective. The highest accuracy, F-value, and AP of this paper’s model for stamp data are 95.3%, 97.6%, and 99.2%, respectively. And in the login test and invoicing test, the system in this paper is faster than the traditional system by 298.4ms and 136.7ms, respectively. The electric ticket automation system in this paper is able to improve the automatic generation of electric tickets and the efficiency of electric ticket invoicing, and to enhance the level of lean management at the grassroots level of the grid, with wide adaptability.

With the rapid development of networks and information technology, the form of mass communication is changing day by day, and the efficient and convenient communication of information also brings challenges to the dissemination of traditional culture. This paper proposes a deep recommendation algorithm based on user-adaptive networks after examining the functional advantages of adaptive network platforms and optimizing the drawbacks of current network platform recommendations. It contains two parts: the main network and the strategy network, which combine the null convolutional neural network and the residual network, which is capable of better modeling the user’s historical behavior sequence. On this basis, the algorithm is combined with the development of the traditional culture dissemination-oriented network platform system, constructed by the user layer, testing layer, learning layer, support layer, and management layer composed of a traditional culture adaptive network platform. Then, the performance of the system is tested. The adaptive network platform system of this paper has the lowest number of nodes with latency distribution of [1, 3.1] ms and [4, 10] ms. The lowest load reaches 0.05, and the proportion of users with a continuity index less than 0.9 is only about 36%. Meanwhile, the average playback volume of the platform video is 6,275,800, and the average number of likes reaches 207,906, which is much higher than the average value of 8800 of the number of points stepped on, indicating that the system in this paper is optimal in all aspects of the performance and that the dissemination of traditional culture is excellent. This study presents an effective communication method for traditional culture that is widely applicable and makes a significant contribution to the promotion of traditional culture.

Miao batik’s unique cultural connotation suggests that it has important inheritance significance as a part of Chinese traditional culture. Combined with the discussion on the protection and inheritance of Miao batik, this paper proposes to utilize the entropy value method and the hierarchical analysis method to analyze and screen the influencing factors of the inheritance and development of Miao batik in college education and to calculate the weight coefficients of the four levels of human resources, material resources, financial resources, and intelligence. By using the greyscale correlation analysis method, the correlation between each influential factor and the development of the educational inheritance of Miao batik in colleges and universities can be calculated, and the degree of importance can be ranked. Based on the development of traditional culture courses in colleges and universities, the teaching path of Miao batik technique courses in colleges and universities is proposed, assisted by information technology. According to the ranking of the degree of relevance, the indicator “curriculum construction (0.9364)” has the greatest relevance to the development of the educational inheritance of Hmong batik culture in colleges and universities, and the relevance of “club construction (0.6008)” to the development of the educational inheritance of Hmong batik culture in colleges and universities is the smallest. Minimum. Colleges and universities can adjust the curriculum structure of Miao batik to improve the extension and development of traditional Chinese culture represented by Miao batik in colleges and universities.

The construction of smart stadiums is an important direction for the development of the sports industry. This paper builds a digital empowerment analysis framework for stadiums from the main body of stadium intelligent construction and designs and builds a smart stadium management information system platform. Examine the advantages of VR technology in sports training, process motion capture data, and propose motion recognition technology based on skeletal data. Use the satisfaction index to measure the effectiveness of intelligent transformation applications in sports stadiums that utilize VR technology. We analyze the whole life cycle cost of sports building projects, calculate the revenue and operation cost of intelligent construction of stadiums from the perspective of the composition of sports building projects, and predict the return on investment of intelligent construction of stadiums by combining the investment ratio of different partners. In the dimension of “intelligent service”, the satisfaction score of the training service (VR technology sports training service) is 3.689 with a standard deviation of 0.825, and the return on investment is 17.59% during the 14-year construction and operation period of the project when the share ratio of the partner is 60%.

Carrying out mental health education is an important way to carry out college students’ mental health education work, and it is also an important way to popularize mental health knowledge and improve college students’ psychological literacy. Combined with the IMB model, the article proposes an effective way of mental health education for college students, and out of the need to objectively analyze the psychological well-being of students, it designs and implements a psychological knowledge map model and finally constructs an SVM prediction model based on the knowledge map. The main conclusions drawn from the experiments using the model proposed in this paper are: a portion of the students have a potential risk of suicide, with 33.32% of the lower and above, 18.65% of the medium and above, and 5.86% of the higher and above, and more than half of the first-year college students have different degrees of depression. In the test of the difference between experimental and control classes on the posttest, p=0.021

Geoparks are both the concentration of valuable geological remains and an important carrier of tourism activities. Relying on a geographic information system (GIS), this project takes the landscape change of a geopark from 2005 to 2020 as an example, and after processing the remote sensing images, quantitative analysis is carried out by using the landscape pattern index method, which reveals the landscape change characteristics of the sample geopark. The data related to natural and human factors was collected, and the driving factors of landscape changes in geoparks were analyzed by combining probes. The main landscape types of the sample geoparks are cropland, woodland, and rocky desertification land, and the study period presents landscape changes of decreasing cropland area (22.96%), fluctuating woodland area, and increasing desertification area (37.40%), and the development of the park landscape changes presents irregularity and complexity. The main drivers of landscape change in geoparks are geological conditions, topography and geomorphology, vegetation, economic development capacity, and ecological environment quality (q value = 0.438~0.521), of which economic development capacity and ecological environment quality play a dominant role in the interaction of factors (0.86).

The rapid development of information technology and mobile Internet technology has brought about innovations in the field of education. The application of financial statement automation analysis methods in the teaching of accounting majors in higher vocational colleges and universities is conducive to improving the quality of the training of accounting talents in higher vocational colleges and universities so as to accelerate the construction of the modern accounting industry college. This study proposes the application of relevant deep learning techniques in the process of automated analysis of financial statements in terms of recognition and analysis, such as text detection based on CTPN and text recognition technology based on CRNN-Attention, which makes the processing of financial statements more automated and intelligent. It is also proposed to utilize the K-means algorithm to perform cluster analysis on the model output to extract the financial status of the company. To evaluate the model’s performance, several financial statement images of 12 companies are sampled for example analysis. The experimental data shows that the model has a high percentage of image skew correction, e.g., the ratio of image skew correction for the income statement and cash flow statement is 100%. The recognition speed of the model is also faster, with the consumption time of the profit and loss statement recognition task being around 0.3 seconds in 20 tests. In the financial statement analysis session, each of the three clusters of companies under the K-means algorithm clustering has its characteristics, with the first cluster of companies having a stronger quality of earnings, the third cluster of companies having outstanding profitability, and the second cluster of companies having average indicator data.

The quality of classroom interaction has received more and more attention as an important part of the teaching quality of English-specialized courses in colleges and universities. After completing the decision tree-based English classroom interaction analysis model based on the ID3 algorithm, this paper quantitatively analyzes the English classroom interaction rules and then designs the English classroom interaction enhancement strategies containing the three directions of teacher-teacher, teacher-student, and student-student on the basis of the derived rules and conducts a one-academic-year teaching experiment for English majors in a university in Guangzhou. It was found that the experimental class and the control class had the largest gap in two indicators: classroom discussion sessions (19.38% and 2.61%) and student manipulation techniques (9.07% and 0.41%). In the two classes at the beginning of the semester, the quality level scores of classroom interactions in both classes were below 30. In contrast, in the last two classes of the school year, the experimental class remained stable above 70 points until the end of classroom instruction. The control class remained below 30 points. After the beginning of the teaching experiment, the probability of students’ active speaking, group collaboration, or discussion in the experimental class increased rapidly. The probability of students’ active speaking stabilized at about 0.8 by the end of the 16th week. In contrast, the probability points of the control class were distributed more discretely in the course of the experiment, and the probability was basically below 0.4. In the experimental class, the English classroom interaction enhancement strategy proposed in this paper has yielded better results.

[Objective/Significance] This article explores the theme of elderly care and its emotional trend, providing a scientific basis for formulating and optimizing elderly care policies, thereby improving the quality of elderly care services and promoting the harmonious and stable development of society. [Method/Process] This study uses the message data related to pension issues in the “leadership message board” platform of People’s Daily Online as the research object, the LDA model to extract relevant topics, and the BERT-BiLSTM model to analyze the emotional trend changes of each subject. [Result/Conclusion] The research results show that the theme of pension covers 16 sub-subjects, such as “environmental noise problem of pension,” “pension community construction planning,” and “retirement pension policy treatment.” The classification accuracy of the BERT-BiLSTM model is 0.89, and the F1 value is 0.86, which shows its superiority in sentiment evolution analysis. The expression of negative emotions in pension theme messages is generally higher than that of neutral and positive feelings, and the elderly group’s emotional attitude shows significant differences under different themes of raising older people.

Network ideological and political education is a great extension of school education, but the complex and confusing network information is also easy to give students bad emotional guidance. In this paper, microblogging data and topic clustering technology are used to obtain the emotional text data of network ideological and political education, based on the LDA model for topic feature extraction, to remove the data that has a lower degree of relevance to ideological and political education emotion in the data. Then, combined with the Jieba segmentation tool, based on the TF-IDF algorithm, for keyword extraction of the data that has been segmented. The text semantic features extracted based on the Word2Vec word vector model are used as the input information of this model, and the unique memory unit and gating structure of LSTM are utilized to solve the problem of storing memory of a priori knowledge and the problem of gradient dissipation caused by too long time threshold in long text classification. The Word2Vec-LSTM text sentiment classification model is developed and trained using Python and related machine learning libraries, and comparative experiments are carried out to validate the algorithm’s effectiveness and feasibility. The performance of Word2Vec-LSTM sentiment analysis on the dataset is higher than Word2Vec and LSTM algorithms. In addition, the value of sentiment perplexity is the smallest when the number of topics is set to be about 8, and its value is 0.542, and the positive sentiment density reaches the maximum value (0.648) as the sentiment score grows to 0.48. This paper explores the application of emotion analysis results in network ideological and political education to further improve the construction of a network ideological and political education system.

Setting reasonable drug prices is the fundamental goal of drug price elasticity analysis, and the game theory method can play a role in drug pricing by analyzing the behaviors of multiple game subjects to give a plan that meets the best interests of all parties. The optimal pricing strategies under different threshold conditions are summarized by establishing four model assumptions and solving them based on the basic model of game theory and the bidding process. Accordingly, the drug pricing of Pharmaceutical Company F was analyzed, and it was found that its optimal pricing was 21.3yuan, at which time the profit was 132.74% higher than the original pricing profit. After applying this pricing, it was found that the implementation of the new pricing increased the mean score of the company’s profitability by 0.16738 to 0.19504 as compared to before the optimized drug pricing strategy, indicating that the pricing strategy improved by the game theory model is able to provide the company’s level of profitability and is feasible.

Adolescent physical and mental development is a perspective that the humanistic sociology of sports focuses on in the field of youth sports. This paper investigates how the use of AI technology in sports will affect the physical and mental development of youth. In order to overcome the shortcomings of small samples, high dimensionality, and high noise in youth physical and mental development data, this paper adopts dimensionality reduction methods such as principal component analysis and linear discriminant analysis to reduce the dimensionality of high-dimensional data. Using the processed data, the physical and mental development data of youth were successfully classified into four categories: social interaction, training intensity, psychological state, and cultural influence. The study on the correlation between the AI model and youth physical and mental development takes soccer as an example and adopts the method of pre and post-tests of actual experiments to select students from a high school to conduct the test of physical and psychological indexes before and after the experiments. Physical and psychological index tests before and after the experiment were significantly better for students in the experimental group using AI technology compared to those in the control group not using AI technology.

Improving the accuracy and stability of players’ stroke speed and stroke landing point and maximizing the energy conversion have become important tasks in table tennis skill practice. This paper analyzes the forces during ball collision and the energy conversion law of its motion state and proposes to measure and identify the key mechanical parameters of table tennis motion from the aspects of batting speed, rotation, and batting angle. The 3D coordinates of the ball are reconstructed, and the parameters are measured in the translational and rotational states of the ball, respectively. The UKF state estimator is used to construct the system process equations of the table tennis ball motion model, and the mathematical expressions are further derived to obtain the kinematic-based post-collision trajectory prediction model of the table tennis ball. The accuracy of the model in predicting the trajectory of the table tennis ball movement is evaluated by the distribution of the error points of the collision points of the table tennis ball, and it is known through experiments that the range of the error of the collision point prediction of the table tennis ball by the method used in this paper is in the range of (x±0.05, y±0.05) m, which is smaller than that estimated by the traditional table tennis ball physical model, and the model’s prediction accuracy is good. After analyzing the motion trajectories with different angular velocities, drag coefficients, initial velocities, and exit angles, the optimal hitting speed of a curved circle ball is obtained as V=15m/s.

The lack of an effective evaluation system for the process and effect of interactive teaching of English in colleges and universities has resulted in a disconnect between the status quo of English teaching in many colleges and universities and the effect of teaching, so it is of great significance to know how to put forward a quantitative analytical model to promote the effect of interactive teaching of English in colleges and universities. The article takes University A as the research object, constructs the evaluation index system of the interactive teaching effect of English in colleges and universities, and adopts the fuzzy hierarchical analysis method to evaluate the interactive teaching effect of English in colleges and universities. Finally, the qualitative comparative analysis method is used to further explore the specific factors that affect the interactive teaching effect of English in colleges and universities. The total affiliation vector B=(0.06,0.07,0.04,0.02), combined with the teaching quality evaluation grade classification standard, determines that the English classroom interactive teaching effect grade is good. The conditional grouping patterns of high-level problem solving can be derived into four groups, namely, gender-balanced type fueled by collaborative relationships, gender-balanced type fueled by teaching interventions, heterogeneous type within the group dominated by teaching interventions, and close relationship type dominated by teaching interventions.

In the contemporary era of increasing population aging, improving the service quality of senior care institutions and optimizing the regulatory behavior of multiple subjects has become a hot topic in society nowadays. Based on the welfare plurality theory and Li Yapunov theory, this paper analyzes the behavior of the government, senior care institutions, and the elderly in the regulation of senior care institutions, establishes a game model for the regulation of senior care institutions, and analyzes the mutual influence of the behavior of the multiple subjects in the regulation of senior care institutions by using the evolutionary game method. The results show that the service quality of senior care institutions is affected by many aspects, and with time, the rate at which senior care institutions, the government and the elderly converge to the equilibrium strategy becomes smaller and smaller, and the system will eventually reach a stable state at (1,1,1) (i.e., active government supervision, self-regulation of senior care institutions, and supervision of the elderly), and the government has a certain role in leading the optimization of senior care institutions’ supervision behaviors. This study has practical value for improving the quality of services offered by senior care institutions, meeting the senior care needs of elderly individuals, and enhancing collaborative governance among multiple stakeholders.

In the process of applying traditional teaching forms, problems such as low participation in classroom activities and poor independent learning are gradually highlighted. This paper first designs the task-based cooperative language acquisition model then constructs the supervision and management system for cooperative learning, and finally establishes the evaluation mechanism for task-based cooperative learning. This paper uses the questionnaire survey method, Pearson correlation coefficient method, principal component analysis method, and multiple regression analysis methods as data analysis methods. By establishing a mathematical model, the parameters to be estimated are listed, and then these data are fitted, and finally, a statistical analysis is performed. Through the questionnaire survey method, this paper verified that the method had a positive effect on students’ Japanese learning; 46.2% of students enjoyed learning Japanese, and 92.3% participated in group discussions. The effectiveness of Japanese language teaching was assessed by extracting three main factors through principal component analysis, which were summarised as pre-study performance, classroom performance, and individual thinking performance. Under the language acquisition model, teachers can improve students’ learning effectiveness by monitoring and encouraging their performance on these three indicators.

As an important part of overseas Chinese literature, Southeast Asian Chinese literature has entered the research field of mainland scholars since the 1980s with the deepening of economic, trade, and cultural exchanges between mainland China and Southeast Asian countries. In this paper, we use the linguistic characteristics of Southeast Asian Chinese literature as the research landing point, establish the mathematical model of regression analysis, and transform the coordinate system to simplify the derivation formula. The slope is used to determine the macro change direction of the regression curve, and the slope formula is further derived to get the expression for judging the micro change trend of the curve, which completes the construction of the mathematical model of language pattern and cultural identity law. Based on the knowledge graph visualization and analysis tool CiteSpase, the data of language patterns and cultural identity samples were processed and analyzed in terms of the number of publications, author groups, research institutions, and publishing journals. 2016 was the year with the highest number of publications, and the number of publications in this year was 55. “Malay-Chinese literature” ranked first among the high-frequency keywords, with a word frequency and centrality of 173 and 0.82, respectively. The correlation coefficient between Southeast Asian Chinese’s attitude towards Chinese language and Chinese cultural identity (Spearman’s rho=865, p

This paper proposes a values sentiment analysis model based on RoBERTa-BiLSTM-Attention based on the mechanism and path of values process evaluation under sentiment analysis. After extracting and presenting the values and sentiment features data, we build the values dataset of college students, finish the training of the model, and obtain the classification results of values and sentiment. The college students’ value identity model is established to analyze the value shaping of education at the national, social, and individual levels. The correlation coefficients of the influencing factors of college students’ values were analyzed, and the correlation coefficients of the influencing factors were less than 0.75, and the p-value was less than 0.01. The hypotheses were put forward, and the standardized regression coefficient of the “social role model” was 0.2658, which was significantly higher than that of the other indicators, and the standardized regression coefficient of “emotional satisfaction” was 0.2658. The regression coefficient of “emotional satisfaction” is 0.1987, second only to cognitive identity. In view of the existence of the problem of values, the proposed political education intervention guidance strategy, after the political education intervention, 71.3625% of the students think that the values of guidance have a great help, but there are still some shortcomings, compared with this paper puts forward the optimization of the values of guidance recommendations.

E-commerce platforms are becoming increasingly competitive, and how to attract and retain users has become a problem that operators need to solve. The study improves the K-means clustering algorithm by introducing the concepts of mean sample distance and SSE and using the median to construct profile coefficients. Based on this, the user labels of cross-border e-commerce companies are selected, and clustering segmentation is performed after collecting the user data of Company T on cross-border e-commerce platforms to reveal the basic characteristics, purchasing preferences, and behavioral habits of different e-commerce users. A cross-border e-commerce marketing strategy based on customer segmentation has been formulated, and its effectiveness has been verified. Through clustering analysis, users are successfully classified into three types: high-value (4.01%), dynamic (7.35%), and growth (88.64%). After implementing the marketplace strategy, the sample companies gained significant growth in user growth, referral effect, and merchandise sales, as reflected in the number of first-buy users (63.46%), effective users (21.45%), ad click rate (18%~22%) and sales volume (166.43%). This study can help cross-border e-commerce enterprises better understand user needs and behavioral patterns and formulate more accurate marketing strategies to enhance their competitiveness and market share.

Cognitive diagnostic theory can provide a comprehensive and detailed objective evaluation of individual macro learning ability, thus providing an effective reference for targeted teaching and learning. In this paper, a fuzzy cognitive diagnostic model is used to evaluate the degree of mastery of a college student on the physical education course, calculate the probability of mastery of each attribute, and statistically analyze the degree of mastery of the attributes of the individual as well as the class as a whole. Then, a learning effect evaluation standard is constructed to evaluate the learning effects of the physical education course for all students. The empirical results show that the mean value of the evaluation of the students’ cognition of physical education in School X is 0.6587, and the average probability of mastery of physical education emotion is 0.6021, both of which have reached the degree of good mastery. The average probability of mastering sports operations was 0.5909, which indicates that university students have an average level of mastery in all sports skills through the physical education program. The outcome is in line with the current situation, which can serve as a reference for teachers to make targeted teaching decisions. The study has both theoretical value and practical significance in promoting the development of wisdom education.

The consciousness and behavior of students in the Ideological and Political Education curriculum generate massive amounts of data information, how to allow educators to quickly obtain information from the massive amount of text data is very important to improve the energy efficiency of classroom education. SVM technology is employed in this paper for data mining and text classification. Firstly, using the web crawler method, the text of messages related to the Ideological and Political Science course posted by students on social networks is collected. The short text was preprocessed before performing sentiment analysis, which mainly included interaction information filtering, word segmentation, and lexical labeling. Then, the SVM model suitable for students’ ideology analysis is constructed, using the Gauss radial basis kernel function to accurately depict the distribution structure of the data, and the L1-SVM model with more stable computational performance is also proposed. The extension method of the classification algorithm in the real number domain is summarized at the end. This algorithm’s accuracy is 78%, and its F1 value is 80%, which is higher than the other three algorithms. DAG-SVM and recall are both optimized to a lesser extent. Overall, the classification efficiency of the algorithm in this paper has been improved. The positive effect of this paper’s algorithm on improving the effectiveness of Ideological and Political Education can be seen in the significant increase in the learning interest of the experimental class.

By the Galvin–Mycielski–Solovay theorem, a subset X of the line has Borel's strong measure zero if and only if $M+X\neq \mathbb {R}$ for each meager set M. A set $X\subseteq \mathbb {R}$ is meager-additive if $M+X$ is meager for each meager set M. Recently a theorem on meager-additive sets that perfectly parallels the Galvin–Mycielski–Solovay theorem was proven: A set $X\subseteq \mathbb {R}$ is meager-additive if and only if it has sharp measure zero, a notion akin to strong measure zero. We investigate the validity of this result in Polish groups. We prove, e.g., that a set in a locally compact Polish group admitting an invariant metric is meager-additive if and only if it has sharp measure zero. We derive some consequences and calculate some cardinal invariants. [ABSTRACT FROM AUTHOR]

For a real-valued sequence u let τ u (R) = { x ∈ R : u n x → 0 mod Z } . In Barbieri et al. (Topol Appl 221:534–555, 2017) there were given conditions which imply that τ u (R) ⊈ τ v (R) . Here we positively answer a question posed in Barbieri et al. (2017) and then in Di Santo et al. (Ric Mat 67:625–655, 2018) showing that these conditions imply that even (τ u (R) : τ u (R) ∩ τ v (R)) > ℵ 0 . Hereby the group c u (R) : = { x ∈ R : (u n x) n ∈ N converges mod Z in R } plays an important role. We also present some basic properties of c u (R) , the relationship between c u (R) and τ u (R) and the connection between these groups and certain totally bounded group topologies on Z and R . [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new concept of convexity which is generated by a family of endomorphisms of an Abelian group. In Abelian groups, equipped with a translation invariant metric, we define the boundedness, the norm, the modulus of injectivity and the spectral radius of endomorphisms. Beyond the investigation of their properties, our first main goal is an extension of the celebrated Rådström cancellation theorem. Another result generalizes the Neumann invertibility theorem. Next we define the convexity of sets with respect to a family of endomorphisms, and we describe the set-theoretical and algebraic structure of the class of such sets. Given a subset, we also consider the family of endomorphisms that make this subset convex, and we establish the basic properties of this family. Our first main result establishes conditions which imply midpoint convexity. The next main result, using our extension of the Rådström cancellation theorem, presents further structural properties of the family of endomorphisms that make a subset convex. [ABSTRACT FROM AUTHOR]

A subgroup H of the circle group T is said to be characterized by a sequence u=(un)n∈N of integers if H={x∈T:unx→0}. The characterized subgroups of T are known also under the name topologically u-torsion subgroups. This survey paper is dedicated to the characterized subgroups of T: we recall their main properties and collect most of the basic results from the wide bibliography, following, when possible, the historical line, and trying to show the deep roots of this topic in several areas of Mathematics. Due to this universality of the topic, many notions and results were found independently by various authors working unaware of each other, so our effort is also directed towards giving credit to all of them to the best of our knowledge. We provide also some background on the notions of characterized subgroup and topologically u-torsion subgroup in the general case of topological abelian groups, where they differ very substantially. [ABSTRACT FROM AUTHOR]

We show that the Lindelöf property of a topological group is not inherited by its square, thus solving an old problem from [2] . Our construction introduces a new method to this area of mathematics and is of independent interest as it may have some further applications. Our method builds on ideas of [11] and techniques from [20] and give us also an optimal result about the partition properties on ω 1 . [ABSTRACT FROM AUTHOR]

A subset A of the circle group T is a Dirichlet set if there exists an increasing sequence u = ( u n ) n ∈ N 0 in N such that ‖ u n x ‖ → 0 uniformly on A . In particular, A is contained in the subgroup t u ( T ) : = { x ∈ T : ‖ u n x ‖ → 0 } , which is the subgroup of T characterized by u . Using strictly increasing sequences u in N such that u n divides u n + 1 for every n ∈ N , we find in T a family of closed perfect D -sets that are also Cantor-like sets. Moreover, we write T as the sum of two closed perfect D -sets. As a consequence, we solve an open problem by showing that T can be written as the sum of two of its proper characterized subgroups, i.e., T is factorizable. Finally, we describe all countable subgroups of T that are factorizable and we find a class of uncountable characterized subgroups of T that are factorizable. [ABSTRACT FROM AUTHOR]

A subgroup H of R is characterized if H = τ u ( R ) : = { x ∈ R : u n x → 0 mod Z } for some sequence u in R . Given two sequences u and v in R , we find conditions under which τ u ( R ) is contained or not in τ v ( R ) . As a by-product of our main theorems, we find a known result by Eliaš on inclusions of characterized subgroups of T , motivated by problems in harmonic analysis. [ABSTRACT FROM AUTHOR]

The notion of partial groups and their basic properties have been given in [1,2] . In this paper, we introduce the concept of topological partial groups and discuss some of their basic properties. So, the category of topological partial groups Tpg, as objects, and the homomorphisms of topological partial groups, as arrows, have some deficiencies. To get over these deficiencies, we introduced the category of locally compact partial groups denoted by Lcpg. Finally, we introduced the category of strong semilattices of topological groups denoted by Sstg. [ABSTRACT FROM AUTHOR]

For a Hausdorff Abelian topological group X , we denote by F 0 ( X ) the group of all X -valued null sequences endowed with the uniform topology. We prove that if X is an ( E )-space (respectively, a strictly angelic space or a Š-space), then so is F 0 ( X ) . We essentially simplify and clarify the theory of properties respected by the Bohr functor on Abelian topological groups, denoted below by X ↦ X + . We prove that for a complete maximally almost periodic group X , the group X shares with X + the same functionally bounded sets iff it shares the same compact sets and X + is a μ -space. We show that for a locally compact Abelian (LCA) group X the following are equivalent: 1) X is totally disconnected, 2) F 0 ( X ) is a Schwartz group, 3) F 0 ( X ) respects compactness, 4) F 0 ( X ) has the Schur property. So, if a LCA group X is not totally disconnected, the group F 0 ( X ) is a reflexive non-Schwartz group which does not have the Schur property. We prove also that for every compact connected metrizable Abelian group X the group F 0 ( X ) is monothetic and every real-valued uniformly continuous function on F 0 ( X ) is bounded. [ABSTRACT FROM AUTHOR]

We consider the Hyers-Ulam stability of a functional equation for continuous functions on a space on which a topological group acts, analogously to the additive functional equation on a group. We show, among other things, that our generalized additive equation, for continuous functions on a homogeneous space of a strongly amenable topological group, is stable provided that the canonical projection from that group to its homogeneous space is a fiber bundle. [ABSTRACT FROM AUTHOR]