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In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class B . As application, we obtain the Pitt’s inequality for power weights.

The classroom teaching mode combining the flipped classroom and the paired classroom can better emphasize the exchange of information between teaching and learning, learning and learning, and then solve the problems of students’ explanation, demonstration, and practice ability. This paper explores the English teaching process in public security colleges under the guidance of the new teaching mode on the basis of the flipped classroom and analyzes the applicability and feasibility of the flipped classroom to English teaching in public security colleges. In order to explore whether the English teaching mode of public security colleges under the flipped classroom can improve students’ English performance, this paper constructs an English teaching quality evaluation model for public security colleges under the flipped classroom by improving the BP neural network. Through the teaching experiment to explore the changes in students’ English performance, the English performance of the experimental class fluctuated greatly, with an average score rising from 60.563 to 77.582, which is an improvement of 28.1%. It shows that the effectiveness of English teaching is better in the flipped classroom teaching mode.

Hypertension (HTN) affects nearly 75 million in the United States, and percentages increase with low socioeconomic status (SES) due to poor access to, and quality of, care, and poor self-care behaviors. Federally Qualified Health Centers (FQHCs) employ evidence-based strategies, such as telehealth interventions, to improve blood pressure (BP) control in under-resourced communities, yet a southeastern FQHC could achieve a BP control rate of only 27.6%, well below the Health People 2020 goal of 61.2%. This pilot project used a pre/post, matched-cohort design to evaluate the effect of a telehealth intervention on BP control and self-care behaviors. Secondary outcomes included self-efficacy and perceived stress. Frequency and percentage, Wilcoxon signed-rank, and McNemar tests were used for statistical analysis of results from a convenience sample of 27 participants. Baseline HTN management guidance that incorporated home blood pressure monitoring (HBPM) was reinforced through telephone counseling every two weeks. Although BP control was not achieved, average scores for systolic and diastolic blood pressures decreased significantly: 13 mm Hg (p = 0.0136) and 5 mm Hg (p = 0.0095), respectively. Statistically significant differences were also seen in select self-care behaviors. Greater BP reduction aligned with higher self-efficacy scores and call engagement. Overall, telephone counseling and HBPM were feasible and effective in reducing BP and increasing self-care behaviors. The inability to control BP may be attributable to under-recognition of stress, lack of medication adherence/reconciliation, and underutilization of guideline-based prescribing recommendations. Findings elucidate the potential effectiveness of a sustainable telehealth intervention to improve BP in low-SES populations.

The Chlorophyll-a (Chl-a) concentration is an important indicator of water environmental conditions; thus, the simultaneous monitoring of large-area water bodies can be realized through the remote sensing-based retrieval of the Chl-a concentrations. The back propagation (BP) neural network learning method has been widely used for the remote sensing retrieval of water quality in first and second-class water bodies. However, many Chl-a concentration measurements must be used as learning samples with this method, which is constrained by the number of samples, due to the limited time and resources available for simultaneous measurements. In this paper, we conduct correlation analysis between the Chl-a concentration data measured at Dianshan Lake in 2020 and 2021 and synchronized Landat-8 data. Through analysis and study of the radiative transfer model and the retrieval method, a BP neural network retrieval model based on multi-phase Chl-a concentration data is proposed, which allows for the realization of remote sensing-based Chl-a monitoring in third-class water bodies. An analysis of spatiotemporal distribution characteristics was performed, and the method was compared with other constructed models. The research results indicate that the retrieval performance of the proposed BP neural network model is better than that of models constructed using multiple regression analysis and curve estimation analysis approaches, with a coefficient of determination of 0.86 and an average relative error of 19.48%. The spatial and temporal Chl-a distribution over Dianshan Lake was uneven, with high concentrations close to human production and low concentrations in the open areas of the lake. During the period from 2020 to 2021, the Chl-a concentration showed a significant upward trend. These research findings provide reference for monitoring the water environment in Dianshan Lake.

Artificial neural network is also referred to as neural network or connection model, it’s a model animal neural network, the mathematical model of distributed and information processing algorithm. Because of its good abstract classification, Has been used in all aspects of life. And in recent years, the traditional English teaching mode in colleges and universities has been gradually replaced by CAI new teaching methods, much progress has been made, Increasing resources to open schools and curricula, effectively promote the sharing of quality teaching resources, it promotes the improvement of students’ English listening, speaking, reading, writing and translation. But the general problems of English CAI teaching have gradually emerged, for example, curriculum design does not pay enough attention to individual differences, online teaching lacks interaction between teachers and students, lack of effective supervision and assessment of learning results. At present, the student-centered teaching concept based on the class-flipping classroom and the “online and offline” mixed teaching model is becoming popular, which has had a great impact on the traditional foreign language teaching model. Designing English intelligent computer-assisted teaching (intelligent computer-assisted teaching) can intelligently meet the individual needs of students according to the learning effect, realize the interaction between teachers and students through human-computer interaction, and facilitate the management and evaluation of the teaching process by managers. This is referred to as ICAI. It is an urgent problem in English teaching, especially in the teaching of college English public courses. This paper designs an English ICAI language curriculum system based on BP neural network algorithm and SSH architecture.

The economic development of various regions is influenced by high-quality population mobility. The research object of this article is the employment mobility data of “Double First-Class” university graduates from 2014 to 2019; the subsequent analysis is based on these data. First, this paper summarizes the current state of university graduates’ employment mobility. Second, this paper employs the fixed-effect model and PCA method to conclude that economic factors are the primary factors influencing university graduates’ employment mobility. Finally, based on the nonlinear, small sample, and high-dimensional characteristics of university graduates’ employment mobility data, this paper employs the random forest and BP neural network methods to build a prediction model for university graduates’ employment retention rate. The results show that the BP neural network model outperforms the random forest model in terms of prediction accuracy. The BP neural network model can accurately predict the employment retention rate of “Double First-Class” university graduates, which can guide the reasonable mobility of university graduates and provide a reference for government universities and individuals to make decisions.

To improve the accuracy of deformation perception and shape reconstruction of flexible thin-walled structures, this paper proposes a method based on the combination of FOSS (fiber optic sensor system) and machine learning. In this method, the sample collection of strain measurement and deformation change at each measuring point of the flexible thin-walled structure was completed by ANSYS finite element analysis. The outliers were removed by the OCSVM (one-class support vector machine) model, and the unique mapping relationship between the strain value and the deformation variables (three directions of x-, y-, and z-axis) at each point was completed by a neural-network model. The test results show that the maximum error of the measuring point in the direction of the three coordinate axes: the x-axis is 2.01%, the y-axis is 29.49%, and the z-axis is 15.52%. The error of the coordinates in the y and z directions was large, and the deformation variables were small, the reconstructed shape had good consistency with the deformation state of the specimen under the existing test environment. This method provides a new idea with high accuracy for real-time monitoring and shape reconstruction of flexible thin-walled structures such as wings, helicopter blades, and solar panels.

To address the subjectivity and uncertainty in traditional music teaching quality evaluation methods, a method based on the PSO-BP neural network model is proposed. This method selects evaluation indicators from multiple dimensions such as teaching ability, learning effectiveness, teaching resources, teaching interaction, and music emotion. By optimizing the initial connection weights and thresholds of the BP neural network through PSO algorithm, an objective, accurate, and efficient music teaching quality evaluation system is constructed. Compared to traditional methods, it not only significantly enhances objectivity and accuracy but also further refines the evaluation criteria by introducing multi-level evaluation dimensions such as technicality, motivation, teaching, interactivity, artistry, and standardization. The case analysis shows that this method performs well in practical applications, and the evaluation results are closer to reality, providing strong support for the improvement of music teaching quality.

Through scientific and effective evaluation of dance classroom teaching quality, teachers can objectively and accurately evaluate teaching methods, attitudes and effects, and lay a cognitive foundation for the improvement of dance teaching quality. The purpose of this article is to evaluate the teaching quality of dance multimedia in vocational colleges based on artificial intelligence technology. The application of BP neural network in teaching evaluation and the algorithm of BP neural network teaching quality evaluation model are studied, and the construction of dance classroom teaching quality evaluation system is discussed. First, the same teacher uses the same teaching materials and uses different teaching methods to teach the students in the two classes respectively, and secondly, an interest survey on dance classes. The experimental results show that multimedia teaching has brought great convenience to teachers in preparing lessons and improved their professional level. In addition, the use of courseware to demonstrate actions in teaching avoids the negative impact on student presentations due to differences in teacher age, technology, and personal understanding. Compared with the control class, the experimental class increased the density of free practice by 10.93%, and the heart rate increased by 8 times / min.

Wireless communication technology is playing an increasingly important role in society. In view of the current situation of physical education teaching in colleges, the construction of a sports network teaching platform is conducive to students' autonomous, collaborative and exploratory sports knowledge and skills. This paper presents a method of evaluating the quality of physical education teaching in Colleges based on a wireless communication system. This method is based on a wireless communication system and is used for information exchange between students and teachers in physical education. After collecting the information, the evaluation of college physical education teaching quality is realized on Matlab based on analytic hierarchy process and BP network. The results show that this method successfully solves the problems of incompleteness and subjectivity when experts determine the weight of college physical education teaching indicators in the past, and realizes the prediction and warning function of college physical education teaching based on wireless communication systems.